Subgroups — C₂×C₆₇×#3521 #30742031

Order 17152.

7314 conjugacy classes of subgroups.

The subgroup lattice has 1292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3521	C₂	1	32	yes	maximal, direct product factor
2	C₂×#556×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#556×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#554×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#553×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#553×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂×#552×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#552×C₆₇	C₂	1	2	yes	maximal, complemented
9	C₂×#551×C₆₇	C₂	1	2	yes	maximal, complemented
10	C₂×#551×C₆₇	C₂	1	2	yes	maximal, complemented
11	C₂×#547×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#546×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#546×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#542×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#541×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#539×C₆₇	C₂	1	2	yes	maximal, complemented
17	C₂×#538×C₆₇	C₂	1	2	yes	maximal, complemented
18	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#529×C₆₇	C₂	1	2	yes	maximal, complemented
20	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂²×#126×C₆₇	C₂	1	2	yes	maximal, complemented
22	C₂×#520×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#518×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
26	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
27	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
28	#556×C₆₇	C₂²	1	16	yes	complemented
29	#556×C₆₇	C₂²	1	16	yes	complemented
30	#554×C₆₇	C₂²	1	16	yes	complemented
31	#553×C₆₇	C₂²	1	16	yes	complemented
32	#553×C₆₇	C₂²	1	32	yes	complemented
33	#552×C₆₇	C₂²	1	16	yes	complemented
34	#552×C₆₇	C₂²	1	32	yes	complemented
35	#551×C₆₇	C₂²	1	32	yes	complemented
36	#551×C₆₇	C₂²	1	32	yes	complemented
37	#547×C₆₇	C₂²	1	16	yes	complemented
38	#546×C₆₇	C₂²	1	16	yes	complemented
39	#546×C₆₇	C₂²	1	16	yes	complemented
40	#542×C₆₇	C₂²	1	16	yes	complemented
41	#541×C₆₇	C₂²	1	16	yes	complemented
42	#539×C₆₇	C₂²	1	32	yes	complemented
43	#538×C₆₇	C₂²	1	32	yes	complemented
44	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#529×C₆₇	C₂²	1	16	yes	complemented
47	#529×C₆₇	C₂²	1	32	yes	complemented
48	#529×C₆₇	C₂²	1	16	yes	complemented
49	C₂×#126×C₆₇	C₂²	1	1	yes	characteristic
50	C₂×#126×C₆₇	C₂²	1	2	yes	—
51	C₂×#126×C₆₇	C₂²	1	2	yes	—
52	C₂×#126×C₆₇	C₂²	1	2	yes	—
53	C₂×#126×C₆₇	C₂²	1	2	yes	—
54	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
55	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
56	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
57	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
58	C₂×#126×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
60	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
61	C₂×#126×C₆₇	C₂²	1	32	yes	complemented
62	C₂×#125×C₆₇	C₂²	1	2	yes	complemented
63	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	C₂×#125×C₆₇	C₂²	1	2	yes	complemented
66	C₂×#125×C₆₇	C₂²	1	2	yes	complemented
67	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
69	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
70	C₂×#124×C₆₇	C₂²	1	2	yes	—
71	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
72	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
73	C₂×#123×C₆₇	C₂²	1	2	yes	—
74	C₂×#123×C₆₇	C₂²	1	1	yes	characteristic
75	C₂×#123×C₆₇	C₂²	1	2	yes	—
76	C₂×#123×C₆₇	C₂²	1	2	yes	—
77	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
78	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
79	C₂×#123×C₆₇	C₂²	1	1	yes	characteristic, complemented
80	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
81	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
82	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
83	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
84	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
85	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
86	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
87	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
88	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
89	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
90	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
91	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
93	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
94	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
95	C₂×#121×C₆₇	C₂²	1	2	yes	—
96	C₂×#121×C₆₇	C₂²	1	2	yes	—
97	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
98	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
99	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
100	C₂×#120×C₆₇	C₂²	1	2	yes	—
101	C₂×#120×C₆₇	C₂²	1	2	yes	—
102	#520×C₆₇	C₂²	1	16	yes	complemented
103	#518×C₆₇	C₂²	1	16	yes	complemented
104	C₄×#41×C₆₇	C₂²	1	16	yes	complemented
105	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
109	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
110	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
111	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
112	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
113	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
114	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
115	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
116	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
117	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
118	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
119	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
120	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
121	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
122	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
123	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
124	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
125	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
126	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
127	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
128	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
129	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
130	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
131	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
132	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
133	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
134	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
135	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
136	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
137	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
138	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
139	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
140	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
141	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
142	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
143	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
144	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
145	C₂²×C₄²×C₆₇	C₂²	1	2	yes	complemented
146	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
147	C₂⁵×C₆₇	C₂³	1	2	yes	—
148	C₂×#41×C₆₇	—	2	8	no	—
149	C₂×#41×C₆₇	—	2	8	no	—
150	C₂×#41×C₆₇	C₂³	1	8	yes	—
151	C₂×#41×C₆₇	C₂³	1	8	yes	—
152	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
153	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
154	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
155	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
156	C₂²×D₄×C₆₇	—	2	8	no	—
157	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
158	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
159	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
160	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
161	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
162	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
163	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
164	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
165	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
166	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
167	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
168	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
169	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
170	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
171	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
172	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
173	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
174	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
175	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
177	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
178	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
179	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
180	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
181	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
182	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
183	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
184	#126×C₆₇	C₂³	1	8	yes	—
185	#126×C₆₇	C₂³	1	16	yes	—
186	#126×C₆₇	C₂³	1	16	yes	—
187	#126×C₆₇	C₂³	1	16	yes	—
188	#126×C₆₇	C₂³	1	16	yes	—
189	#126×C₆₇	C₂³	1	16	yes	complemented
190	#126×C₆₇	C₂³	1	16	yes	complemented
191	#126×C₆₇	C₂³	1	16	yes	complemented
192	#126×C₆₇	C₂³	1	16	yes	complemented
193	#126×C₆₇	C₂³	1	8	yes	complemented
194	#126×C₆₇	C₂³	1	16	yes	complemented
195	#126×C₆₇	C₂³	1	16	yes	complemented
196	#125×C₆₇	C₂³	1	16	yes	complemented
197	#125×C₆₇	C₂³	1	8	yes	complemented
198	#125×C₆₇	C₂³	1	8	yes	complemented
199	#125×C₆₇	C₂³	1	16	yes	complemented
200	#125×C₆₇	C₂³	1	16	yes	complemented
201	#125×C₆₇	C₂³	1	8	yes	complemented
202	#124×C₆₇	C₂³	1	8	yes	—
203	#124×C₆₇	C₂³	1	8	yes	—
204	#124×C₆₇	C₂³	1	16	yes	—
205	#124×C₆₇	C₂³	1	8	yes	—
206	#124×C₆₇	C₂³	1	16	yes	complemented
207	#123×C₆₇	C₂³	1	16	yes	—
208	#123×C₆₇	C₂³	1	8	yes	—
209	#123×C₆₇	C₂³	1	16	yes	—
210	#123×C₆₇	C₂³	1	16	yes	—
211	#123×C₆₇	C₂³	1	16	yes	complemented
212	#123×C₆₇	C₂³	1	16	yes	complemented
213	#123×C₆₇	C₂³	1	8	yes	complemented
214	#123×C₆₇	C₂³	1	16	yes	complemented
215	#123×C₆₇	C₂³	1	16	yes	complemented
216	#123×C₆₇	C₂³	1	16	yes	complemented
217	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
218	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
219	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
220	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
221	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
222	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
223	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
224	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
225	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
226	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
227	#121×C₆₇	C₂³	1	8	yes	—
228	#121×C₆₇	C₂³	1	8	yes	—
229	#121×C₆₇	C₂³	1	16	yes	—
230	#121×C₆₇	C₂³	1	16	yes	—
231	#121×C₆₇	C₂³	1	8	yes	—
232	#121×C₆₇	C₂³	1	16	yes	complemented
233	#121×C₆₇	C₂³	1	16	yes	complemented
234	#120×C₆₇	C₂³	1	16	yes	—
235	#120×C₆₇	C₂³	1	16	yes	—
236	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
237	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
238	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
239	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
240	C₄×Q₈×C₆₇	C₂³	1	16	yes	complemented
241	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
242	C₄×D₄×C₆₇	C₂³	1	8	yes	—
243	C₄×D₄×C₆₇	C₂³	1	8	yes	—
244	C₄×D₄×C₆₇	C₂³	1	16	yes	—
245	C₄×D₄×C₆₇	C₂³	1	8	yes	—
246	C₄×D₄×C₆₇	C₂³	1	8	yes	—
247	C₄×D₄×C₆₇	C₂³	1	16	yes	—
248	C₄×D₄×C₆₇	C₂³	1	8	yes	—
249	C₄×D₄×C₆₇	C₂³	1	8	yes	—
250	C₄×D₄×C₆₇	C₂³	1	8	yes	—
251	C₄×D₄×C₆₇	C₂³	1	8	yes	—
252	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
253	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
254	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
255	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
256	C₄×D₄×C₆₇	C₂³	1	8	yes	complemented
257	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
258	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
259	#117×C₆₇	C₂³	1	8	yes	—
260	#117×C₆₇	C₂³	1	8	yes	—
261	#117×C₆₇	C₂³	1	16	yes	complemented
262	#117×C₆₇	C₂³	1	8	yes	complemented
263	#117×C₆₇	C₂³	1	8	yes	complemented
264	#117×C₆₇	C₂³	1	16	yes	complemented
265	#117×C₆₇	C₂³	1	16	yes	complemented
266	#117×C₆₇	C₂³	1	16	yes	complemented
267	#117×C₆₇	C₂³	1	16	yes	complemented
268	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
270	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
274	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
275	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
276	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
277	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
278	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
279	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
280	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
281	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
282	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
283	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
284	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
285	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
286	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
287	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
288	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
289	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
290	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
291	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
292	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
293	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
295	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
296	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
297	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
298	C₂×C₄⋊C₄×C₆₇	C₂³	1	16	yes	complemented
299	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	complemented
300	C₂×C₄⋊C₄×C₆₇	C₂³	1	16	yes	complemented
301	C₂×C₄⋊C₄×C₆₇	C₂³	1	16	yes	complemented
302	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
303	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
304	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
305	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
306	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
307	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
308	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
309	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
310	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
311	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
312	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
313	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	—
314	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	—
315	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
316	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
317	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
318	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
319	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	—
320	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	—
321	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
322	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
323	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
324	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
325	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
326	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
327	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
328	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
329	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
330	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
331	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
332	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
333	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
334	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
335	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
336	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
337	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
338	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
339	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
340	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
341	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
342	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
343	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
344	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
345	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
346	C₂×C₄²×C₆₇	C₂³	1	16	yes	complemented
347	C₂×C₄²×C₆₇	C₂³	1	8	yes	complemented
348	C₂⁴×C₆₇	—	2	8	no	—
349	C₂⁴×C₆₇	—	4	4	no	—
350	C₂⁴×C₆₇	—	4	4	no	—
351	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
352	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
353	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
354	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
355	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
356	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
357	#41×C₆₇	—	2	32	no	—
358	#41×C₆₇	—	2	32	no	—
359	C₂×Q₈×C₆₇	—	2	4	no	—
360	C₂×Q₈×C₆₇	—	2	4	no	—
361	C₂×Q₈×C₆₇	—	4	2	no	—
362	C₂×Q₈×C₆₇	—	4	4	no	—
363	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
364	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
365	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
366	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
367	C₂×D₄×C₆₇	—	2	8	no	—
368	C₂×D₄×C₆₇	—	2	8	no	—
369	C₂×D₄×C₆₇	—	2	8	no	—
370	C₂×D₄×C₆₇	—	2	32	no	—
371	C₂×D₄×C₆₇	—	2	4	no	—
372	C₂×D₄×C₆₇	—	4	4	no	—
373	C₂×D₄×C₆₇	—	4	2	no	—
374	C₂×D₄×C₆₇	—	4	2	no	—
375	C₂×D₄×C₆₇	—	4	4	no	—
376	C₂×D₄×C₆₇	—	4	2	no	—
377	C₂×D₄×C₆₇	#41	1	8	yes	—
378	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
379	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
380	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
381	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
382	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
383	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
384	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
385	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
386	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
387	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
388	C₂²×C₄×C₆₇	—	2	8	no	—
389	C₂²×C₄×C₆₇	—	2	8	no	—
390	C₂²×C₄×C₆₇	—	2	4	no	—
391	C₂²×C₄×C₆₇	—	2	4	no	—
392	C₂²×C₄×C₆₇	—	2	4	no	—
393	C₂²×C₄×C₆₇	—	4	4	no	—
394	C₂²×C₄×C₆₇	—	4	2	no	—
395	C₂²×C₄×C₆₇	—	4	4	no	—
396	C₂²×C₄×C₆₇	—	4	4	no	—
397	C₂²×C₄×C₆₇	—	4	4	no	—
398	C₂²×C₄×C₆₇	—	4	4	no	—
399	C₂²×C₄×C₆₇	—	4	2	no	—
400	C₂²×C₄×C₆₇	—	4	4	no	—
401	C₂²×C₄×C₆₇	—	4	4	no	—
402	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
403	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
404	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
405	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
406	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
407	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
412	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
413	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
414	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
415	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
417	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
418	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
419	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
420	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
421	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
423	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
424	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
425	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
426	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
427	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
428	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
429	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
430	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
431	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
432	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
433	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
434	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
435	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
436	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
437	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
438	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
439	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
440	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
441	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
442	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
443	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
444	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
445	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
446	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
447	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
448	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
449	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
450	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
451	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
452	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
453	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
454	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
455	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
456	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
457	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
458	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
459	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
460	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
461	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
462	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
463	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
464	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
465	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
466	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
467	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
468	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
469	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
470	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
471	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
472	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
473	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
474	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
475	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
476	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
477	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
478	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
479	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
480	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
481	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
482	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
483	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
484	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
485	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
486	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
487	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
488	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
489	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
490	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
491	C₂²⋊C₄×C₆₇	C₂⁴	1	4	yes	—
492	C₄²×C₆₇	C₂⁴	1	4	yes	—
493	C₄²×C₆₇	C₂⁴	1	4	yes	—
494	C₄²×C₆₇	C₂⁴	1	4	yes	—
495	C₄²×C₆₇	C₂⁴	1	8	yes	—
496	C₄²×C₆₇	C₂⁴	1	8	yes	—
497	C₄²×C₆₇	C₂⁴	1	4	yes	—
498	C₄²×C₆₇	C₂⁴	1	8	yes	—
499	C₄²×C₆₇	C₂⁴	1	8	yes	—
500	C₄²×C₆₇	C₂⁴	1	4	yes	—
501	C₄²×C₆₇	C₂⁴	1	8	yes	—
502	C₄²×C₆₇	C₂⁴	1	8	yes	—
503	C₄²×C₆₇	C₂⁴	1	4	yes	—
504	C₂³×C₆₇	—	2	4	no	—
505	C₂³×C₆₇	—	2	4	no	—
506	C₂³×C₆₇	—	2	2	no	—
507	C₂³×C₆₇	—	2	2	no	—
508	C₂³×C₆₇	—	2	2	no	—
509	C₂³×C₆₇	—	2	4	no	—
510	C₂³×C₆₇	—	2	2	no	—
511	C₂³×C₆₇	—	2	2	no	—
512	C₂³×C₆₇	—	2	2	no	—
513	C₂³×C₆₇	—	2	4	no	—
514	C₂³×C₆₇	—	2	4	no	—
515	C₂³×C₆₇	—	2	2	no	—
516	C₂³×C₆₇	—	2	2	no	—
517	C₂³×C₆₇	—	2	2	no	—
518	C₂³×C₆₇	—	2	16	no	—
519	C₂³×C₆₇	—	4	8	no	—
520	C₂³×C₆₇	—	4	8	no	—
521	C₂³×C₆₇	—	8	16	no	—
522	C₂³×C₆₇	C₂×#41	1	8	yes	—
523	C₂³×C₆₇	C₂⁵	1	2	yes	—
524	C₂³×C₆₇	C₂⁵	1	4	yes	—
525	C₂³×C₆₇	C₂⁵	1	2	yes	—
526	C₂³×C₆₇	C₂⁵	1	2	yes	—
527	C₂³×C₆₇	C₂⁵	1	4	yes	—
528	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
529	Q₈×C₆₇	—	2	8	no	—
530	Q₈×C₆₇	—	2	8	no	—
531	Q₈×C₆₇	—	4	4	no	—
532	Q₈×C₆₇	—	4	8	no	—
533	D₄×C₆₇	—	2	16	no	—
534	D₄×C₆₇	—	2	16	no	—
535	D₄×C₆₇	—	2	16	no	—
536	D₄×C₆₇	—	2	8	no	—
537	D₄×C₆₇	—	4	8	no	—
538	D₄×C₆₇	—	4	4	no	—
539	D₄×C₆₇	—	4	4	no	—
540	D₄×C₆₇	—	4	8	no	—
541	D₄×C₆₇	—	4	4	no	—
542	D₄×C₆₇	C₂×#41	1	16	yes	—
543	C₂×C₄×C₆₇	—	2	2	no	—
544	C₂×C₄×C₆₇	—	2	2	no	—
545	C₂×C₄×C₆₇	—	2	2	no	—
546	C₂×C₄×C₆₇	—	2	4	no	—
547	C₂×C₄×C₆₇	—	2	4	no	—
548	C₂×C₄×C₆₇	—	2	16	no	—
549	C₂×C₄×C₆₇	—	2	16	no	—
550	C₂×C₄×C₆₇	—	2	2	no	—
551	C₂×C₄×C₆₇	—	2	4	no	—
552	C₂×C₄×C₆₇	—	2	2	no	—
553	C₂×C₄×C₆₇	—	2	2	no	—
554	C₂×C₄×C₆₇	—	2	4	no	—
555	C₂×C₄×C₆₇	—	2	2	no	—
556	C₂×C₄×C₆₇	—	2	2	no	—
557	C₂×C₄×C₆₇	—	2	2	no	—
558	C₂×C₄×C₆₇	—	2	4	no	—
559	C₂×C₄×C₆₇	—	2	2	no	—
560	C₂×C₄×C₆₇	—	2	4	no	—
561	C₂×C₄×C₆₇	—	2	2	no	—
562	C₂×C₄×C₆₇	—	2	8	no	—
563	C₂×C₄×C₆₇	—	2	8	no	—
564	C₂×C₄×C₆₇	—	2	8	no	—
565	C₂×C₄×C₆₇	—	4	8	no	—
566	C₂×C₄×C₆₇	—	4	4	no	—
567	C₂×C₄×C₆₇	—	4	8	no	—
568	C₂×C₄×C₆₇	—	4	8	no	—
569	C₂×C₄×C₆₇	—	4	8	no	—
570	C₂×C₄×C₆₇	—	4	8	no	—
571	C₂×C₄×C₆₇	—	4	4	no	—
572	C₂×C₄×C₆₇	—	4	8	no	—
573	C₂×C₄×C₆₇	—	4	8	no	—
574	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
575	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
576	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
577	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
578	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
579	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
580	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
581	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
582	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
583	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
584	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
585	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
586	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
587	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
588	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
589	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
590	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
591	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
592	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
593	C₂²×C₆₇	—	2	4	no	—
594	C₂²×C₆₇	—	2	4	no	—
595	C₂²×C₆₇	—	2	16	no	—
596	C₂²×C₆₇	—	2	2	no	—
597	C₂²×C₆₇	—	2	2	no	—
598	C₂²×C₆₇	—	2	2	no	—
599	C₂²×C₆₇	—	2	4	no	—
600	C₂²×C₆₇	—	2	2	no	—
601	C₂²×C₆₇	—	2	2	no	—
602	C₂²×C₆₇	—	2	2	no	—
603	C₂²×C₆₇	—	2	4	no	—
604	C₂²×C₆₇	—	2	4	no	—
605	C₂²×C₆₇	—	2	2	no	—
606	C₂²×C₆₇	—	2	2	no	—
607	C₂²×C₆₇	—	2	2	no	—
608	C₂²×C₆₇	—	4	4	no	—
609	C₂²×C₆₇	—	4	4	no	—
610	C₂²×C₆₇	—	4	8	no	—
611	C₂²×C₆₇	—	4	4	no	—
612	C₂²×C₆₇	—	8	16	no	—
613	C₂²×C₆₇	C₂²×#41	1	8	yes	—
614	C₂²×C₆₇	C₂²×#41	1	2	yes	—
615	C₂²×C₆₇	#585	1	2	yes	—
616	C₂²×C₆₇	#585	1	2	yes	—
617	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
618	C₄×C₆₇	—	2	2	no	—
619	C₄×C₆₇	—	2	2	no	—
620	C₄×C₆₇	—	2	2	no	—
621	C₄×C₆₇	—	2	4	no	—
622	C₄×C₆₇	—	2	4	no	—
623	C₄×C₆₇	—	2	2	no	—
624	C₄×C₆₇	—	2	4	no	—
625	C₄×C₆₇	—	2	2	no	—
626	C₄×C₆₇	—	2	2	no	—
627	C₄×C₆₇	—	2	4	no	—
628	C₄×C₆₇	—	2	2	no	—
629	C₄×C₆₇	—	2	2	no	—
630	C₄×C₆₇	—	2	2	no	—
631	C₄×C₆₇	—	2	4	no	—
632	C₄×C₆₇	—	2	2	no	—
633	C₄×C₆₇	—	2	4	no	—
634	C₄×C₆₇	—	2	2	no	—
635	C₄×C₆₇	C₂²×#41	1	4	yes	—
636	C₂×#3521	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
637	C₂×C₆₇	—	2	8	no	—
638	C₂×C₆₇	—	4	2	no	—
639	C₂×C₆₇	—	4	2	no	—
640	C₂×C₆₇	—	4	4	no	—
641	C₂×C₆₇	—	4	2	no	—
642	C₂×C₆₇	#3521	1	4	yes	direct product factor
643	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
644	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
645	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
646	#3521	C₂×C₆₇	1	32	yes	direct product factor
647	C₂×#556	C₂×C₆₇	1	1	yes	characteristic, complemented
648	C₂×#556	C₂×C₆₇	1	1	yes	characteristic, complemented
649	C₂×#554	C₂×C₆₇	1	1	yes	characteristic, complemented
650	C₂×#553	C₂×C₆₇	1	1	yes	characteristic, complemented
651	C₂×#553	C₂×C₆₇	1	2	yes	complemented
652	C₂×#552	C₂×C₆₇	1	1	yes	characteristic, complemented
653	C₂×#552	C₂×C₆₇	1	2	yes	complemented
654	C₂×#551	C₂×C₆₇	1	2	yes	complemented
655	C₂×#551	C₂×C₆₇	1	2	yes	complemented
656	C₂×#547	C₂×C₆₇	1	1	yes	characteristic, complemented
657	C₂×#546	C₂×C₆₇	1	1	yes	characteristic, complemented
658	C₂×#546	C₂×C₆₇	1	1	yes	characteristic, complemented
659	C₂×#542	C₂×C₆₇	1	1	yes	characteristic, complemented
660	C₂×#541	C₂×C₆₇	1	1	yes	characteristic, complemented
661	C₂×#539	C₂×C₆₇	1	2	yes	complemented
662	C₂×#538	C₂×C₆₇	1	2	yes	complemented
663	C₂×#529	C₂×C₆₇	1	1	yes	characteristic, complemented
664	C₂×#529	C₂×C₆₇	1	2	yes	complemented
665	C₂×#529	C₂×C₆₇	1	1	yes	characteristic, complemented
666	C₂²×#126	C₂×C₆₇	1	2	yes	complemented
667	C₂×#520	C₂×C₆₇	1	1	yes	characteristic, complemented
668	C₂×#518	C₂×C₆₇	1	1	yes	characteristic, complemented
669	C₂×C₄×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
670	C₆₇	C₂×#3521	1	1	yes	characteristic, direct product factor, Sylow
671	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
672	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
673	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
674	#556	C₂²×C₆₇	1	16	yes	complemented
675	#556	C₂²×C₆₇	1	16	yes	complemented
676	#554	C₂²×C₆₇	1	16	yes	complemented
677	#553	C₂²×C₆₇	1	16	yes	complemented
678	#553	C₂²×C₆₇	1	32	yes	complemented
679	#552	C₂²×C₆₇	1	16	yes	complemented
680	#552	C₂²×C₆₇	1	32	yes	complemented
681	#551	C₂²×C₆₇	1	32	yes	complemented
682	#551	C₂²×C₆₇	1	32	yes	complemented
683	#547	C₂²×C₆₇	1	16	yes	complemented
684	#546	C₂²×C₆₇	1	16	yes	complemented
685	#546	C₂²×C₆₇	1	16	yes	complemented
686	#542	C₂²×C₆₇	1	16	yes	complemented
687	#541	C₂²×C₆₇	1	16	yes	complemented
688	#539	C₂²×C₆₇	1	32	yes	complemented
689	#538	C₂²×C₆₇	1	32	yes	complemented
690	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
691	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
692	#529	C₂²×C₆₇	1	16	yes	complemented
693	#529	C₂²×C₆₇	1	32	yes	complemented
694	#529	C₂²×C₆₇	1	16	yes	complemented
695	C₂×#126	C₂²×C₆₇	1	1	yes	characteristic
696	C₂×#126	C₂²×C₆₇	1	2	yes	—
697	C₂×#126	C₂²×C₆₇	1	2	yes	—
698	C₂×#126	C₂²×C₆₇	1	2	yes	—
699	C₂×#126	C₂²×C₆₇	1	2	yes	—
700	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
701	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
702	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
703	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
704	C₂×#126	C₂²×C₆₇	1	1	yes	characteristic, complemented
705	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
706	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
707	C₂×#126	C₂²×C₆₇	1	32	yes	complemented
708	C₂×#125	C₂²×C₆₇	1	2	yes	complemented
709	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
710	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
711	C₂×#125	C₂²×C₆₇	1	2	yes	complemented
712	C₂×#125	C₂²×C₆₇	1	2	yes	complemented
713	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
714	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
715	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
716	C₂×#124	C₂²×C₆₇	1	2	yes	—
717	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
718	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
719	C₂×#123	C₂²×C₆₇	1	2	yes	—
720	C₂×#123	C₂²×C₆₇	1	1	yes	characteristic
721	C₂×#123	C₂²×C₆₇	1	2	yes	—
722	C₂×#123	C₂²×C₆₇	1	2	yes	—
723	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
724	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
725	C₂×#123	C₂²×C₆₇	1	1	yes	characteristic, complemented
726	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
727	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
728	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
729	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
730	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
731	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
732	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
733	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
734	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
735	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
736	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
737	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
738	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
739	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
740	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
741	C₂×#121	C₂²×C₆₇	1	2	yes	—
742	C₂×#121	C₂²×C₆₇	1	2	yes	—
743	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
744	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
745	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
746	C₂×#120	C₂²×C₆₇	1	2	yes	—
747	C₂×#120	C₂²×C₆₇	1	2	yes	—
748	#520	C₂²×C₆₇	1	16	yes	complemented
749	#518	C₂²×C₆₇	1	16	yes	complemented
750	C₄×#41	C₂²×C₆₇	1	16	yes	complemented
751	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
752	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
753	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
754	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
755	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
756	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
757	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
758	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
759	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
760	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
761	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
762	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
763	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
764	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
765	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
766	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
767	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
768	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
769	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
770	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
771	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
772	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
773	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
774	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
775	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
776	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
777	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
778	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
779	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
780	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
781	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
782	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
783	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
784	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
785	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
786	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
787	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
788	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
789	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
790	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
791	C₂²×C₄²	C₂²×C₆₇	1	2	yes	complemented
792	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
793	C₂⁵	C₂³×C₆₇	1	2	yes	—
794	C₂×#41	—	2	8	no	—
795	C₂×#41	—	2	8	no	—
796	C₂×#41	C₂³×C₆₇	1	8	yes	—
797	C₂×#41	C₂³×C₆₇	1	8	yes	—
798	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
799	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
800	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
801	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
802	C₂²×D₄	—	2	8	no	—
803	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
804	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
805	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
806	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
807	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
808	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
809	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
810	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
811	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
812	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
813	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
814	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
815	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
816	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
817	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
818	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
819	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
820	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
821	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
822	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
823	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
824	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
825	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
826	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
827	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
828	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
829	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
830	#126	C₂³×C₆₇	1	8	yes	—
831	#126	C₂³×C₆₇	1	16	yes	—
832	#126	C₂³×C₆₇	1	16	yes	—
833	#126	C₂³×C₆₇	1	16	yes	—
834	#126	C₂³×C₆₇	1	16	yes	—
835	#126	C₂³×C₆₇	1	16	yes	complemented
836	#126	C₂³×C₆₇	1	16	yes	complemented
837	#126	C₂³×C₆₇	1	16	yes	complemented
838	#126	C₂³×C₆₇	1	16	yes	complemented
839	#126	C₂³×C₆₇	1	8	yes	complemented
840	#126	C₂³×C₆₇	1	16	yes	complemented
841	#126	C₂³×C₆₇	1	16	yes	complemented
842	#125	C₂³×C₆₇	1	16	yes	complemented
843	#125	C₂³×C₆₇	1	8	yes	complemented
844	#125	C₂³×C₆₇	1	8	yes	complemented
845	#125	C₂³×C₆₇	1	16	yes	complemented
846	#125	C₂³×C₆₇	1	16	yes	complemented
847	#125	C₂³×C₆₇	1	8	yes	complemented
848	#124	C₂³×C₆₇	1	8	yes	—
849	#124	C₂³×C₆₇	1	8	yes	—
850	#124	C₂³×C₆₇	1	16	yes	—
851	#124	C₂³×C₆₇	1	8	yes	—
852	#124	C₂³×C₆₇	1	16	yes	complemented
853	#123	C₂³×C₆₇	1	16	yes	—
854	#123	C₂³×C₆₇	1	8	yes	—
855	#123	C₂³×C₆₇	1	16	yes	—
856	#123	C₂³×C₆₇	1	16	yes	—
857	#123	C₂³×C₆₇	1	16	yes	complemented
858	#123	C₂³×C₆₇	1	16	yes	complemented
859	#123	C₂³×C₆₇	1	8	yes	complemented
860	#123	C₂³×C₆₇	1	16	yes	complemented
861	#123	C₂³×C₆₇	1	16	yes	complemented
862	#123	C₂³×C₆₇	1	16	yes	complemented
863	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
864	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
865	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
866	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
867	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
868	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
869	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
870	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
871	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
872	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
873	#121	C₂³×C₆₇	1	8	yes	—
874	#121	C₂³×C₆₇	1	8	yes	—
875	#121	C₂³×C₆₇	1	16	yes	—
876	#121	C₂³×C₆₇	1	16	yes	—
877	#121	C₂³×C₆₇	1	8	yes	—
878	#121	C₂³×C₆₇	1	16	yes	complemented
879	#121	C₂³×C₆₇	1	16	yes	complemented
880	#120	C₂³×C₆₇	1	16	yes	—
881	#120	C₂³×C₆₇	1	16	yes	—
882	C₄×Q₈	C₂³×C₆₇	1	8	yes	complemented
883	C₄×Q₈	C₂³×C₆₇	1	8	yes	complemented
884	C₄×Q₈	C₂³×C₆₇	1	8	yes	complemented
885	C₄×Q₈	C₂³×C₆₇	1	8	yes	complemented
886	C₄×Q₈	C₂³×C₆₇	1	16	yes	complemented
887	C₄×Q₈	C₂³×C₆₇	1	8	yes	complemented
888	C₄×D₄	C₂³×C₆₇	1	8	yes	—
889	C₄×D₄	C₂³×C₆₇	1	8	yes	—
890	C₄×D₄	C₂³×C₆₇	1	16	yes	—
891	C₄×D₄	C₂³×C₆₇	1	8	yes	—
892	C₄×D₄	C₂³×C₆₇	1	8	yes	—
893	C₄×D₄	C₂³×C₆₇	1	16	yes	—
894	C₄×D₄	C₂³×C₆₇	1	8	yes	—
895	C₄×D₄	C₂³×C₆₇	1	8	yes	—
896	C₄×D₄	C₂³×C₆₇	1	8	yes	—
897	C₄×D₄	C₂³×C₆₇	1	8	yes	—
898	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
899	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
900	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
901	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
902	C₄×D₄	C₂³×C₆₇	1	8	yes	complemented
903	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
904	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
905	#117	C₂³×C₆₇	1	8	yes	—
906	#117	C₂³×C₆₇	1	8	yes	—
907	#117	C₂³×C₆₇	1	16	yes	complemented
908	#117	C₂³×C₆₇	1	8	yes	complemented
909	#117	C₂³×C₆₇	1	8	yes	complemented
910	#117	C₂³×C₆₇	1	16	yes	complemented
911	#117	C₂³×C₆₇	1	16	yes	complemented
912	#117	C₂³×C₆₇	1	16	yes	complemented
913	#117	C₂³×C₆₇	1	16	yes	complemented
914	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
915	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
916	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
917	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
918	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
919	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
920	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
921	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
922	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
923	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
924	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
925	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
926	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
927	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
928	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
929	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
930	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
931	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
932	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
933	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
934	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
935	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
936	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
937	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
938	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
939	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
940	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
941	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
942	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
943	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
944	C₂×C₄⋊C₄	C₂³×C₆₇	1	16	yes	complemented
945	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	complemented
946	C₂×C₄⋊C₄	C₂³×C₆₇	1	16	yes	complemented
947	C₂×C₄⋊C₄	C₂³×C₆₇	1	16	yes	complemented
948	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
949	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
950	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
951	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
952	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
953	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
954	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
955	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
956	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
957	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
958	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
959	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	—
960	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	—
961	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
962	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
963	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
964	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
965	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	—
966	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	—
967	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
968	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
969	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
970	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
971	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
972	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
973	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
974	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
975	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
976	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
977	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
978	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
979	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
980	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
981	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
982	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
983	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
984	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
985	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
986	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
987	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
988	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
989	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
990	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
991	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
992	C₂×C₄²	C₂³×C₆₇	1	16	yes	complemented
993	C₂×C₄²	C₂³×C₆₇	1	8	yes	complemented
994	C₂⁴	—	2	8	no	—
995	C₂⁴	—	4	4	no	—
996	C₂⁴	—	4	4	no	—
997	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
998	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
999	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
1000	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
1001	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
1002	C₂⁴	C₂⁴×C₆₇	1	8	yes	—
1003	#41	—	2	32	no	—
1004	#41	—	2	32	no	—
1005	C₂×Q₈	—	2	4	no	—
1006	C₂×Q₈	—	2	4	no	—
1007	C₂×Q₈	—	4	2	no	—
1008	C₂×Q₈	—	4	4	no	—
1009	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
1010	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
1011	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
1012	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
1013	C₂×D₄	—	2	8	no	—
1014	C₂×D₄	—	2	8	no	—
1015	C₂×D₄	—	2	8	no	—
1016	C₂×D₄	—	2	32	no	—
1017	C₂×D₄	—	2	4	no	—
1018	C₂×D₄	—	4	4	no	—
1019	C₂×D₄	—	4	2	no	—
1020	C₂×D₄	—	4	2	no	—
1021	C₂×D₄	—	4	4	no	—
1022	C₂×D₄	—	4	2	no	—
1023	C₂×D₄	#41×C₆₇	1	8	yes	—
1024	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
1025	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
1026	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
1027	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
1028	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
1029	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
1030	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
1031	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
1032	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
1033	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
1034	C₂²×C₄	—	2	8	no	—
1035	C₂²×C₄	—	2	8	no	—
1036	C₂²×C₄	—	2	4	no	—
1037	C₂²×C₄	—	2	4	no	—
1038	C₂²×C₄	—	2	4	no	—
1039	C₂²×C₄	—	4	4	no	—
1040	C₂²×C₄	—	4	2	no	—
1041	C₂²×C₄	—	4	4	no	—
1042	C₂²×C₄	—	4	4	no	—
1043	C₂²×C₄	—	4	4	no	—
1044	C₂²×C₄	—	4	4	no	—
1045	C₂²×C₄	—	4	2	no	—
1046	C₂²×C₄	—	4	4	no	—
1047	C₂²×C₄	—	4	4	no	—
1048	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1049	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1050	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1051	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1052	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1053	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1054	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1055	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1056	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1057	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1058	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1059	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1060	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1061	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1062	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1063	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1064	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1065	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1066	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1067	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1068	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1069	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1070	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1071	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1072	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1073	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
1074	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1075	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1076	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1077	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1078	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
1079	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1080	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1081	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1082	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1083	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1084	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1085	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1086	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1087	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1088	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1089	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1090	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1091	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1092	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1093	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1094	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1095	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1096	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1097	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1098	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1099	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1100	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1101	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1102	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1103	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1104	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1105	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1106	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1107	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1108	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1109	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1110	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1111	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1112	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1113	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1114	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1115	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1116	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1117	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1118	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1119	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1120	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1121	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1122	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1123	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1124	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1125	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1126	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1127	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1128	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1129	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1130	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1131	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1132	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1133	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1134	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1135	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1136	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
1137	C₂²⋊C₄	C₂⁴×C₆₇	1	4	yes	—
1138	C₄²	C₂⁴×C₆₇	1	4	yes	—
1139	C₄²	C₂⁴×C₆₇	1	4	yes	—
1140	C₄²	C₂⁴×C₆₇	1	4	yes	—
1141	C₄²	C₂⁴×C₆₇	1	8	yes	—
1142	C₄²	C₂⁴×C₆₇	1	8	yes	—
1143	C₄²	C₂⁴×C₆₇	1	4	yes	—
1144	C₄²	C₂⁴×C₆₇	1	8	yes	—
1145	C₄²	C₂⁴×C₆₇	1	8	yes	—
1146	C₄²	C₂⁴×C₆₇	1	4	yes	—
1147	C₄²	C₂⁴×C₆₇	1	8	yes	—
1148	C₄²	C₂⁴×C₆₇	1	8	yes	—
1149	C₄²	C₂⁴×C₆₇	1	4	yes	—
1150	C₂³	—	2	4	no	—
1151	C₂³	—	2	4	no	—
1152	C₂³	—	2	2	no	—
1153	C₂³	—	2	2	no	—
1154	C₂³	—	2	2	no	—
1155	C₂³	—	2	4	no	—
1156	C₂³	—	2	2	no	—
1157	C₂³	—	2	2	no	—
1158	C₂³	—	2	2	no	—
1159	C₂³	—	2	4	no	—
1160	C₂³	—	2	4	no	—
1161	C₂³	—	2	2	no	—
1162	C₂³	—	2	2	no	—
1163	C₂³	—	2	2	no	—
1164	C₂³	—	2	16	no	—
1165	C₂³	—	4	8	no	—
1166	C₂³	—	4	8	no	—
1167	C₂³	—	8	16	no	—
1168	C₂³	C₂×#41×C₆₇	1	8	yes	—
1169	C₂³	C₂⁵×C₆₇	1	2	yes	—
1170	C₂³	C₂⁵×C₆₇	1	4	yes	—
1171	C₂³	C₂⁵×C₆₇	1	2	yes	—
1172	C₂³	C₂⁵×C₆₇	1	2	yes	—
1173	C₂³	C₂⁵×C₆₇	1	4	yes	—
1174	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
1175	Q₈	—	2	8	no	—
1176	Q₈	—	2	8	no	—
1177	Q₈	—	4	4	no	—
1178	Q₈	—	4	8	no	—
1179	D₄	—	2	16	no	—
1180	D₄	—	2	16	no	—
1181	D₄	—	2	16	no	—
1182	D₄	—	2	8	no	—
1183	D₄	—	4	8	no	—
1184	D₄	—	4	4	no	—
1185	D₄	—	4	4	no	—
1186	D₄	—	4	8	no	—
1187	D₄	—	4	4	no	—
1188	D₄	C₂×#41×C₆₇	1	16	yes	—
1189	C₂×C₄	—	2	2	no	—
1190	C₂×C₄	—	2	2	no	—
1191	C₂×C₄	—	2	2	no	—
1192	C₂×C₄	—	2	4	no	—
1193	C₂×C₄	—	2	4	no	—
1194	C₂×C₄	—	2	16	no	—
1195	C₂×C₄	—	2	16	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	4	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	2	no	—
1200	C₂×C₄	—	2	4	no	—
1201	C₂×C₄	—	2	2	no	—
1202	C₂×C₄	—	2	2	no	—
1203	C₂×C₄	—	2	2	no	—
1204	C₂×C₄	—	2	4	no	—
1205	C₂×C₄	—	2	2	no	—
1206	C₂×C₄	—	2	4	no	—
1207	C₂×C₄	—	2	2	no	—
1208	C₂×C₄	—	2	8	no	—
1209	C₂×C₄	—	2	8	no	—
1210	C₂×C₄	—	2	8	no	—
1211	C₂×C₄	—	4	8	no	—
1212	C₂×C₄	—	4	4	no	—
1213	C₂×C₄	—	4	8	no	—
1214	C₂×C₄	—	4	8	no	—
1215	C₂×C₄	—	4	8	no	—
1216	C₂×C₄	—	4	8	no	—
1217	C₂×C₄	—	4	4	no	—
1218	C₂×C₄	—	4	8	no	—
1219	C₂×C₄	—	4	8	no	—
1220	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
1221	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1222	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1223	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1224	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1225	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1226	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1227	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1228	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1229	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1230	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1231	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1232	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1233	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1234	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1235	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1236	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1237	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1238	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1239	C₂²	—	2	16	no	—
1240	C₂²	—	2	4	no	—
1241	C₂²	—	2	4	no	—
1242	C₂²	—	2	2	no	—
1243	C₂²	—	2	2	no	—
1244	C₂²	—	2	2	no	—
1245	C₂²	—	2	4	no	—
1246	C₂²	—	2	2	no	—
1247	C₂²	—	2	2	no	—
1248	C₂²	—	2	2	no	—
1249	C₂²	—	2	4	no	—
1250	C₂²	—	2	4	no	—
1251	C₂²	—	2	2	no	—
1252	C₂²	—	2	2	no	—
1253	C₂²	—	2	2	no	—
1254	C₂²	—	4	4	no	—
1255	C₂²	—	4	8	no	—
1256	C₂²	—	4	4	no	—
1257	C₂²	—	4	4	no	—
1258	C₂²	—	8	16	no	—
1259	C₂²	C₂²×#41×C₆₇	1	8	yes	—
1260	C₂²	C₂²×#41×C₆₇	1	2	yes	—
1261	C₂²	#585×C₆₇	1	2	yes	—
1262	C₂²	#585×C₆₇	1	2	yes	—
1263	C₂²	C₂⁶×C₆₇	1	1	yes	characteristic
1264	C₄	—	2	2	no	—
1265	C₄	—	2	2	no	—
1266	C₄	—	2	2	no	—
1267	C₄	—	2	4	no	—
1268	C₄	—	2	4	no	—
1269	C₄	—	2	2	no	—
1270	C₄	—	2	4	no	—
1271	C₄	—	2	2	no	—
1272	C₄	—	2	2	no	—
1273	C₄	—	2	4	no	—
1274	C₄	—	2	2	no	—
1275	C₄	—	2	2	no	—
1276	C₄	—	2	2	no	—
1277	C₄	—	2	4	no	—
1278	C₄	—	2	2	no	—
1279	C₄	—	2	4	no	—
1280	C₄	—	2	2	no	—
1281	C₄	C₂²×#41×C₆₇	1	4	yes	—
1282	C₂	—	2	8	no	—
1283	C₂	—	4	2	no	—
1284	C₂	—	4	4	no	—
1285	C₂	—	4	2	no	—
1286	C₂	—	4	2	no	—
1287	C₂	C₆₇×#3521	1	4	yes	direct product factor
1288	C₂	C₂³×#41×C₆₇	1	1	yes	characteristic
1289	C₂	C₂×#585×C₆₇	1	1	yes	characteristic
1290	C₂	C₂×#585×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₆₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₆₇×#3521	C₂	direct (N × H)
2. C₂×#556×C₆₇	C₂	semidirect
3. C₂×#556×C₆₇	C₂	semidirect
4. C₂×#554×C₆₇	C₂	semidirect
5. C₂×#553×C₆₇	C₂	semidirect
6. C₂×#553×C₆₇	C₂	semidirect
7. C₂×#552×C₆₇	C₂	semidirect
8. C₂×#552×C₆₇	C₂	semidirect
9. C₂×#551×C₆₇	C₂	semidirect
10. C₂×#551×C₆₇	C₂	semidirect
11. C₂×#547×C₆₇	C₂	semidirect
12. C₂×#546×C₆₇	C₂	semidirect
13. C₂×#546×C₆₇	C₂	semidirect
14. C₂×#542×C₆₇	C₂	semidirect
15. C₂×#541×C₆₇	C₂	semidirect
16. C₂×#539×C₆₇	C₂	semidirect
17. C₂×#538×C₆₇	C₂	semidirect
18. C₂×#529×C₆₇	C₂	semidirect
19. C₂×#529×C₆₇	C₂	semidirect
20. C₂×#529×C₆₇	C₂	semidirect
21. C₂²×#126×C₆₇	C₂	semidirect
22. C₂×#520×C₆₇	C₂	semidirect
23. C₂×#518×C₆₇	C₂	semidirect
24. C₂×C₄×#41×C₆₇	C₂	semidirect
28. #556×C₆₇	C₂²	semidirect
29. #556×C₆₇	C₂²	semidirect
30. #554×C₆₇	C₂²	semidirect
31. #553×C₆₇	C₂²	semidirect
32. #553×C₆₇	C₂²	semidirect
33. #552×C₆₇	C₂²	semidirect
34. #552×C₆₇	C₂²	semidirect
35. #551×C₆₇	C₂²	semidirect
36. #551×C₆₇	C₂²	semidirect
37. #547×C₆₇	C₂²	semidirect
38. #546×C₆₇	C₂²	semidirect
39. #546×C₆₇	C₂²	semidirect
40. #542×C₆₇	C₂²	semidirect
41. #541×C₆₇	C₂²	semidirect
42. #539×C₆₇	C₂²	semidirect
43. #538×C₆₇	C₂²	semidirect
44. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
45. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
46. #529×C₆₇	C₂²	semidirect
47. #529×C₆₇	C₂²	semidirect
48. #529×C₆₇	C₂²	semidirect
54. C₂×#126×C₆₇	C₂²	semidirect
55. C₂×#126×C₆₇	C₂²	semidirect
56. C₂×#126×C₆₇	C₂²	semidirect
57. C₂×#126×C₆₇	C₂²	semidirect
58. C₂×#126×C₆₇	C₂²	semidirect
59. C₂×#126×C₆₇	C₂²	semidirect
60. C₂×#126×C₆₇	C₂²	semidirect
61. C₂×#126×C₆₇	C₂²	semidirect
62. C₂×#125×C₆₇	C₂²	semidirect
63. C₂×#125×C₆₇	C₂²	semidirect
64. C₂×#125×C₆₇	C₂²	semidirect
65. C₂×#125×C₆₇	C₂²	semidirect
66. C₂×#125×C₆₇	C₂²	semidirect
67. C₂×#125×C₆₇	C₂²	semidirect
72. C₂×#124×C₆₇	C₂²	semidirect
77. C₂×#123×C₆₇	C₂²	semidirect
78. C₂×#123×C₆₇	C₂²	semidirect
79. C₂×#123×C₆₇	C₂²	semidirect
80. C₂×#123×C₆₇	C₂²	semidirect
81. C₂×#123×C₆₇	C₂²	semidirect
82. C₂×#123×C₆₇	C₂²	semidirect
85. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
86. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
87. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
88. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
89. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
90. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
91. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
92. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
98. C₂×#121×C₆₇	C₂²	semidirect
99. C₂×#121×C₆₇	C₂²	semidirect
102. #520×C₆₇	C₂²	semidirect
103. #518×C₆₇	C₂²	semidirect
104. C₄×#41×C₆₇	C₂²	semidirect
105. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
106. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
107. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
108. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
109. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
110. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
121. C₂×C₄×D₄×C₆₇	C₂²	semidirect
122. C₂×C₄×D₄×C₆₇	C₂²	semidirect
123. C₂×C₄×D₄×C₆₇	C₂²	semidirect
124. C₂×C₄×D₄×C₆₇	C₂²	semidirect
125. C₂×C₄×D₄×C₆₇	C₂²	semidirect
126. C₂×C₄×D₄×C₆₇	C₂²	semidirect
127. C₂×C₄×D₄×C₆₇	C₂²	semidirect
130. C₂×#117×C₆₇	C₂²	semidirect
131. C₂×#117×C₆₇	C₂²	semidirect
132. C₂×#117×C₆₇	C₂²	semidirect
133. C₂×#117×C₆₇	C₂²	semidirect
134. C₂×#117×C₆₇	C₂²	semidirect
135. C₂×#117×C₆₇	C₂²	semidirect
136. C₂×#117×C₆₇	C₂²	semidirect
137. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
138. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
139. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
140. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
145. C₂²×C₄²×C₆₇	C₂²	semidirect
146. C₂²×C₄²×C₆₇	C₂²	semidirect
182. C₄⋊Q₈×C₆₇	C₂³	semidirect
183. C₄⋊Q₈×C₆₇	C₂³	semidirect
189. #126×C₆₇	C₂³	semidirect
190. #126×C₆₇	C₂³	semidirect
191. #126×C₆₇	C₂³	semidirect
192. #126×C₆₇	C₂³	semidirect
193. #126×C₆₇	C₂³	semidirect
194. #126×C₆₇	C₂³	semidirect
195. #126×C₆₇	C₂³	semidirect
196. #125×C₆₇	C₂³	semidirect
197. #125×C₆₇	C₂³	semidirect
198. #125×C₆₇	C₂³	semidirect
199. #125×C₆₇	C₂³	semidirect
200. #125×C₆₇	C₂³	semidirect
201. #125×C₆₇	C₂³	semidirect
206. #124×C₆₇	C₂³	semidirect
211. #123×C₆₇	C₂³	semidirect
212. #123×C₆₇	C₂³	semidirect
213. #123×C₆₇	C₂³	semidirect
214. #123×C₆₇	C₂³	semidirect
215. #123×C₆₇	C₂³	semidirect
216. #123×C₆₇	C₂³	semidirect
219. C₂²⋊Q₈×C₆₇	C₂³	semidirect
220. C₂²⋊Q₈×C₆₇	C₂³	semidirect
221. C₂²⋊Q₈×C₆₇	C₂³	semidirect
222. C₂²⋊Q₈×C₆₇	C₂³	semidirect
223. C₂²⋊Q₈×C₆₇	C₂³	semidirect
224. C₂²⋊Q₈×C₆₇	C₂³	semidirect
225. C₂²⋊Q₈×C₆₇	C₂³	semidirect
226. C₂²⋊Q₈×C₆₇	C₂³	semidirect
232. #121×C₆₇	C₂³	semidirect
233. #121×C₆₇	C₂³	semidirect
236. C₄×Q₈×C₆₇	C₂³	semidirect
237. C₄×Q₈×C₆₇	C₂³	semidirect
238. C₄×Q₈×C₆₇	C₂³	semidirect
239. C₄×Q₈×C₆₇	C₂³	semidirect
240. C₄×Q₈×C₆₇	C₂³	semidirect
241. C₄×Q₈×C₆₇	C₂³	semidirect
252. C₄×D₄×C₆₇	C₂³	semidirect
253. C₄×D₄×C₆₇	C₂³	semidirect
254. C₄×D₄×C₆₇	C₂³	semidirect
255. C₄×D₄×C₆₇	C₂³	semidirect
256. C₄×D₄×C₆₇	C₂³	semidirect
257. C₄×D₄×C₆₇	C₂³	semidirect
258. C₄×D₄×C₆₇	C₂³	semidirect
261. #117×C₆₇	C₂³	semidirect
262. #117×C₆₇	C₂³	semidirect
263. #117×C₆₇	C₂³	semidirect
264. #117×C₆₇	C₂³	semidirect
265. #117×C₆₇	C₂³	semidirect
266. #117×C₆₇	C₂³	semidirect
267. #117×C₆₇	C₂³	semidirect
298. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
299. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
300. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
301. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
346. C₂×C₄²×C₆₇	C₂³	semidirect
347. C₂×C₄²×C₆₇	C₂³	semidirect
636. C₂×#3521	C₆₇	direct (N × H)
642. C₂×C₆₇	#3521	direct (N × H)
646. #3521	C₂×C₆₇	direct (N × H)
647. C₂×#556	C₂×C₆₇	semidirect
648. C₂×#556	C₂×C₆₇	semidirect
649. C₂×#554	C₂×C₆₇	semidirect
650. C₂×#553	C₂×C₆₇	semidirect
651. C₂×#553	C₂×C₆₇	semidirect
652. C₂×#552	C₂×C₆₇	semidirect
653. C₂×#552	C₂×C₆₇	semidirect
654. C₂×#551	C₂×C₆₇	semidirect
655. C₂×#551	C₂×C₆₇	semidirect
656. C₂×#547	C₂×C₆₇	semidirect
657. C₂×#546	C₂×C₆₇	semidirect
658. C₂×#546	C₂×C₆₇	semidirect
659. C₂×#542	C₂×C₆₇	semidirect
660. C₂×#541	C₂×C₆₇	semidirect
661. C₂×#539	C₂×C₆₇	semidirect
662. C₂×#538	C₂×C₆₇	semidirect
663. C₂×#529	C₂×C₆₇	semidirect
664. C₂×#529	C₂×C₆₇	semidirect
665. C₂×#529	C₂×C₆₇	semidirect
666. C₂²×#126	C₂×C₆₇	semidirect
667. C₂×#520	C₂×C₆₇	semidirect
668. C₂×#518	C₂×C₆₇	semidirect
669. C₂×C₄×#41	C₂×C₆₇	semidirect
670. C₆₇	C₂×#3521	direct (N × H)
674. #556	C₂²×C₆₇	semidirect
675. #556	C₂²×C₆₇	semidirect
676. #554	C₂²×C₆₇	semidirect
677. #553	C₂²×C₆₇	semidirect
678. #553	C₂²×C₆₇	semidirect
679. #552	C₂²×C₆₇	semidirect
680. #552	C₂²×C₆₇	semidirect
681. #551	C₂²×C₆₇	semidirect
682. #551	C₂²×C₆₇	semidirect
683. #547	C₂²×C₆₇	semidirect
684. #546	C₂²×C₆₇	semidirect
685. #546	C₂²×C₆₇	semidirect
686. #542	C₂²×C₆₇	semidirect
687. #541	C₂²×C₆₇	semidirect
688. #539	C₂²×C₆₇	semidirect
689. #538	C₂²×C₆₇	semidirect
690. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
691. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
692. #529	C₂²×C₆₇	semidirect
693. #529	C₂²×C₆₇	semidirect
694. #529	C₂²×C₆₇	semidirect
700. C₂×#126	C₂²×C₆₇	semidirect
701. C₂×#126	C₂²×C₆₇	semidirect
702. C₂×#126	C₂²×C₆₇	semidirect
703. C₂×#126	C₂²×C₆₇	semidirect
704. C₂×#126	C₂²×C₆₇	semidirect
705. C₂×#126	C₂²×C₆₇	semidirect
706. C₂×#126	C₂²×C₆₇	semidirect
707. C₂×#126	C₂²×C₆₇	semidirect
708. C₂×#125	C₂²×C₆₇	semidirect
709. C₂×#125	C₂²×C₆₇	semidirect
710. C₂×#125	C₂²×C₆₇	semidirect
711. C₂×#125	C₂²×C₆₇	semidirect
712. C₂×#125	C₂²×C₆₇	semidirect
713. C₂×#125	C₂²×C₆₇	semidirect
718. C₂×#124	C₂²×C₆₇	semidirect
723. C₂×#123	C₂²×C₆₇	semidirect
724. C₂×#123	C₂²×C₆₇	semidirect
725. C₂×#123	C₂²×C₆₇	semidirect
726. C₂×#123	C₂²×C₆₇	semidirect
727. C₂×#123	C₂²×C₆₇	semidirect
728. C₂×#123	C₂²×C₆₇	semidirect
731. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
732. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
733. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
734. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
735. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
736. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
737. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
738. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
744. C₂×#121	C₂²×C₆₇	semidirect
745. C₂×#121	C₂²×C₆₇	semidirect
748. #520	C₂²×C₆₇	semidirect
749. #518	C₂²×C₆₇	semidirect
750. C₄×#41	C₂²×C₆₇	semidirect
751. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
752. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
753. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
754. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
755. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
756. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
767. C₂×C₄×D₄	C₂²×C₆₇	semidirect
768. C₂×C₄×D₄	C₂²×C₆₇	semidirect
769. C₂×C₄×D₄	C₂²×C₆₇	semidirect
770. C₂×C₄×D₄	C₂²×C₆₇	semidirect
771. C₂×C₄×D₄	C₂²×C₆₇	semidirect
772. C₂×C₄×D₄	C₂²×C₆₇	semidirect
773. C₂×C₄×D₄	C₂²×C₆₇	semidirect
776. C₂×#117	C₂²×C₆₇	semidirect
777. C₂×#117	C₂²×C₆₇	semidirect
778. C₂×#117	C₂²×C₆₇	semidirect
779. C₂×#117	C₂²×C₆₇	semidirect
780. C₂×#117	C₂²×C₆₇	semidirect
781. C₂×#117	C₂²×C₆₇	semidirect
782. C₂×#117	C₂²×C₆₇	semidirect
783. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
784. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
785. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
786. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
791. C₂²×C₄²	C₂²×C₆₇	semidirect
792. C₂²×C₄²	C₂²×C₆₇	semidirect
828. C₄⋊Q₈	C₂³×C₆₇	semidirect
829. C₄⋊Q₈	C₂³×C₆₇	semidirect
835. #126	C₂³×C₆₇	semidirect
836. #126	C₂³×C₆₇	semidirect
837. #126	C₂³×C₆₇	semidirect
838. #126	C₂³×C₆₇	semidirect
839. #126	C₂³×C₆₇	semidirect
840. #126	C₂³×C₆₇	semidirect
841. #126	C₂³×C₆₇	semidirect
842. #125	C₂³×C₆₇	semidirect
843. #125	C₂³×C₆₇	semidirect
844. #125	C₂³×C₆₇	semidirect
845. #125	C₂³×C₆₇	semidirect
846. #125	C₂³×C₆₇	semidirect
847. #125	C₂³×C₆₇	semidirect
852. #124	C₂³×C₆₇	semidirect
857. #123	C₂³×C₆₇	semidirect
858. #123	C₂³×C₆₇	semidirect
859. #123	C₂³×C₆₇	semidirect
860. #123	C₂³×C₆₇	semidirect
861. #123	C₂³×C₆₇	semidirect
862. #123	C₂³×C₆₇	semidirect
865. C₂²⋊Q₈	C₂³×C₆₇	semidirect
866. C₂²⋊Q₈	C₂³×C₆₇	semidirect
867. C₂²⋊Q₈	C₂³×C₆₇	semidirect
868. C₂²⋊Q₈	C₂³×C₆₇	semidirect
869. C₂²⋊Q₈	C₂³×C₆₇	semidirect
870. C₂²⋊Q₈	C₂³×C₆₇	semidirect
871. C₂²⋊Q₈	C₂³×C₆₇	semidirect
872. C₂²⋊Q₈	C₂³×C₆₇	semidirect
878. #121	C₂³×C₆₇	semidirect
879. #121	C₂³×C₆₇	semidirect
882. C₄×Q₈	C₂³×C₆₇	semidirect
883. C₄×Q₈	C₂³×C₆₇	semidirect
884. C₄×Q₈	C₂³×C₆₇	semidirect
885. C₄×Q₈	C₂³×C₆₇	semidirect
886. C₄×Q₈	C₂³×C₆₇	semidirect
887. C₄×Q₈	C₂³×C₆₇	semidirect
898. C₄×D₄	C₂³×C₆₇	semidirect
899. C₄×D₄	C₂³×C₆₇	semidirect
900. C₄×D₄	C₂³×C₆₇	semidirect
901. C₄×D₄	C₂³×C₆₇	semidirect
902. C₄×D₄	C₂³×C₆₇	semidirect
903. C₄×D₄	C₂³×C₆₇	semidirect
904. C₄×D₄	C₂³×C₆₇	semidirect
907. #117	C₂³×C₆₇	semidirect
908. #117	C₂³×C₆₇	semidirect
909. #117	C₂³×C₆₇	semidirect
910. #117	C₂³×C₆₇	semidirect
911. #117	C₂³×C₆₇	semidirect
912. #117	C₂³×C₆₇	semidirect
913. #117	C₂³×C₆₇	semidirect
944. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
945. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
946. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
947. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
992. C₂×C₄²	C₂³×C₆₇	semidirect
993. C₂×C₄²	C₂³×C₆₇	semidirect
1287. C₂	C₆₇×#3521	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₆₇×#3521	2
C₂×#556×C₆₇	2
C₂×#554×C₆₇	2
C₂×#553×C₆₇	2
C₂×#552×C₆₇	2
C₂×#551×C₆₇	2
C₂×#547×C₆₇	2
C₂×#546×C₆₇	2
C₂×#542×C₆₇	2
C₂×#541×C₆₇	2
C₂×#539×C₆₇	2
C₂×#538×C₆₇	2
C₂×#529×C₆₇	2
C₂²×#126×C₆₇	2
C₂×#520×C₆₇	2
C₂×#518×C₆₇	2
C₂×C₄×#41×C₆₇	2
C₂×#3521	67

Subgroups — C2×C67×#3521 #30742031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3521 #30742031