Subgroups — C₂×C₆₇×#3514 #30742029

Order 17152.

8006 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3514	C₂	1	32	yes	maximal, direct product factor
2	C₂×#559×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#556×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#555×C₆₇	C₂	1	2	yes	maximal, complemented
5	C₂×#551×C₆₇	C₂	1	4	yes	maximal, complemented
6	C₂×D₄×Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#548×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₂×#546×C₆₇	C₂	1	2	yes	maximal, complemented
9	C₂×#546×C₆₇	C₂	1	2	yes	maximal, complemented
10	C₂×D₄²×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#542×C₆₇	C₂	1	2	yes	maximal, complemented
12	C₂×#538×C₆₇	C₂	1	4	yes	maximal, complemented
13	C₂×#532×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#529×C₆₇	C₂	1	2	yes	maximal, complemented
16	C₂²×#124×C₆₇	C₂	1	2	yes	maximal, complemented
17	C₂×#518×C₆₇	C₂	1	2	yes	maximal, complemented
18	C₂×C₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
21	C₂³×Q₈×C₆₇	C₂²	1	2	yes	complemented
22	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
23	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
24	#559×C₆₇	C₂²	1	16	yes	complemented
25	#556×C₆₇	C₂²	1	16	yes	complemented
26	#555×C₆₇	C₂²	1	32	yes	complemented
27	#551×C₆₇	C₂²	1	64	yes	complemented
28	D₄×Q₈×C₆₇	C₂²	1	16	yes	complemented
29	#548×C₆₇	C₂²	1	32	yes	complemented
30	#546×C₆₇	C₂²	1	32	yes	complemented
31	#546×C₆₇	C₂²	1	32	yes	complemented
32	D₄²×C₆₇	C₂²	1	16	yes	complemented
33	#542×C₆₇	C₂²	1	32	yes	complemented
34	#538×C₆₇	C₂²	1	64	yes	complemented
35	#532×C₆₇	C₂²	1	16	yes	complemented
36	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
38	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
39	#529×C₆₇	C₂²	1	16	yes	complemented
40	#529×C₆₇	C₂²	1	32	yes	complemented
41	C₂×#126×C₆₇	C₂²	1	4	yes	complemented
42	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
43	C₂×#126×C₆₇	C₂²	1	4	yes	complemented
44	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×#124×C₆₇	C₂²	1	2	yes	—
47	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
48	C₂×#124×C₆₇	C₂²	1	4	yes	complemented
49	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
50	C₂×#124×C₆₇	C₂²	1	4	yes	complemented
51	C₂×#124×C₆₇	C₂²	1	4	yes	complemented
52	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
53	C₂×#124×C₆₇	C₂²	1	32	yes	complemented
54	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
55	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
56	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
57	C₂×#123×C₆₇	C₂²	1	4	yes	complemented
58	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
59	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
61	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
62	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	complemented
63	C₂×#121×C₆₇	C₂²	1	2	yes	—
64	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
65	C₂×#121×C₆₇	C₂²	1	2	yes	—
66	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
67	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
68	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
69	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
70	C₂×#120×C₆₇	C₂²	1	4	yes	—
71	C₂×#120×C₆₇	C₂²	1	4	yes	complemented
72	#518×C₆₇	C₂²	1	32	yes	complemented
73	C₄×#41×C₆₇	C₂²	1	16	yes	complemented
74	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
75	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
76	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
77	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
79	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
80	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
81	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
82	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
83	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
84	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
85	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
86	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
87	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
88	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
89	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
90	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
91	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
92	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
93	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
94	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
95	C₂×#117×C₆₇	C₂²	1	4	yes	complemented
96	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
97	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
98	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	complemented
99	C₂²×C₄²×C₆₇	C₂²	1	2	yes	complemented
100	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	C₂⁵×C₆₇	C₂³	1	4	yes	—
102	C₂×#41×C₆₇	—	2	8	no	—
103	C₂×#41×C₆₇	—	4	8	no	—
104	C₂×#41×C₆₇	C₂³	1	8	yes	—
105	C₂×#41×C₆₇	C₂³	1	16	yes	complemented
106	C₂²×Q₈×C₆₇	—	4	8	no	—
107	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
110	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
111	C₂²×Q₈×C₆₇	C₂³	1	16	yes	complemented
112	C₂²×D₄×C₆₇	—	2	16	no	—
113	C₂²×D₄×C₆₇	—	4	8	no	—
114	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
116	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
117	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
118	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
119	C₂²×D₄×C₆₇	C₂³	1	16	yes	—
120	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
121	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
122	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
123	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
124	C₂²×D₄×C₆₇	C₂³	1	16	yes	—
125	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
127	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
129	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
131	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
132	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
134	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
135	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
136	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
137	C₄⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
138	#127×C₆₇	C₂³	1	8	yes	—
139	#126×C₆₇	C₂³	1	32	yes	complemented
140	#126×C₆₇	C₂³	1	16	yes	complemented
141	#126×C₆₇	C₂³	1	32	yes	complemented
142	#125×C₆₇	C₂³	1	8	yes	complemented
143	#124×C₆₇	C₂³	1	8	yes	—
144	#124×C₆₇	C₂³	1	16	yes	—
145	#124×C₆₇	C₂³	1	16	yes	complemented
146	#124×C₆₇	C₂³	1	32	yes	complemented
147	#124×C₆₇	C₂³	1	16	yes	complemented
148	#124×C₆₇	C₂³	1	32	yes	complemented
149	#124×C₆₇	C₂³	1	32	yes	complemented
150	#124×C₆₇	C₂³	1	16	yes	complemented
151	#123×C₆₇	C₂³	1	16	yes	complemented
152	#123×C₆₇	C₂³	1	32	yes	complemented
153	#123×C₆₇	C₂³	1	32	yes	complemented
154	#123×C₆₇	C₂³	1	32	yes	complemented
155	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
156	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
157	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	complemented
158	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	complemented
159	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	complemented
160	#121×C₆₇	C₂³	1	16	yes	—
161	#121×C₆₇	C₂³	1	8	yes	—
162	#121×C₆₇	C₂³	1	16	yes	—
163	#121×C₆₇	C₂³	1	16	yes	complemented
164	#121×C₆₇	C₂³	1	16	yes	complemented
165	#121×C₆₇	C₂³	1	32	yes	complemented
166	#121×C₆₇	C₂³	1	32	yes	complemented
167	#120×C₆₇	C₂³	1	32	yes	—
168	#120×C₆₇	C₂³	1	32	yes	complemented
169	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
170	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
171	C₄×Q₈×C₆₇	C₂³	1	16	yes	complemented
172	C₄×Q₈×C₆₇	C₂³	1	8	yes	complemented
173	C₄×D₄×C₆₇	C₂³	1	8	yes	—
174	C₄×D₄×C₆₇	C₂³	1	8	yes	—
175	C₄×D₄×C₆₇	C₂³	1	16	yes	—
176	C₄×D₄×C₆₇	C₂³	1	8	yes	—
177	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
178	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
179	C₄×D₄×C₆₇	C₂³	1	32	yes	complemented
180	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
181	C₄×D₄×C₆₇	C₂³	1	32	yes	complemented
182	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
183	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
184	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
185	C₄×D₄×C₆₇	C₂³	1	16	yes	complemented
186	#117×C₆₇	C₂³	1	16	yes	complemented
187	#117×C₆₇	C₂³	1	8	yes	complemented
188	#117×C₆₇	C₂³	1	16	yes	complemented
189	#117×C₆₇	C₂³	1	16	yes	complemented
190	#117×C₆₇	C₂³	1	32	yes	complemented
191	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
198	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
200	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
203	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
204	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
208	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
211	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
212	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
213	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
214	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
215	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
216	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
217	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
219	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
221	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
222	C₂×C₂²⋊C₄×C₆₇	C₂³	1	32	yes	complemented
223	C₂×C₂²⋊C₄×C₆₇	C₂³	1	32	yes	complemented
224	C₂×C₂²⋊C₄×C₆₇	C₂³	1	32	yes	complemented
225	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
227	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
231	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
232	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
233	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
234	C₂×C₄²×C₆₇	C₂³	1	16	yes	complemented
235	C₂×C₄²×C₆₇	C₂³	1	8	yes	complemented
236	C₂⁴×C₆₇	—	2	16	no	—
237	C₂⁴×C₆₇	—	4	8	no	—
238	C₂⁴×C₆₇	—	4	8	no	—
239	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
240	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
241	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
242	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
243	C₂⁴×C₆₇	C₂⁴	1	16	yes	—
244	#41×C₆₇	—	2	32	no	—
245	#41×C₆₇	—	4	32	no	—
246	C₂×Q₈×C₆₇	—	2	4	no	—
247	C₂×Q₈×C₆₇	—	2	4	no	—
248	C₂×Q₈×C₆₇	—	2	8	no	—
249	C₂×Q₈×C₆₇	—	4	8	no	—
250	C₂×Q₈×C₆₇	—	4	32	no	—
251	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
252	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
253	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
254	C₂×Q₈×C₆₇	C₂⁴	1	16	yes	—
255	C₂×D₄×C₆₇	—	2	16	no	—
256	C₂×D₄×C₆₇	—	2	8	no	—
257	C₂×D₄×C₆₇	—	2	64	no	—
258	C₂×D₄×C₆₇	—	2	8	no	—
259	C₂×D₄×C₆₇	—	2	4	no	—
260	C₂×D₄×C₆₇	—	2	8	no	—
261	C₂×D₄×C₆₇	—	4	32	no	—
262	C₂×D₄×C₆₇	—	4	8	no	—
263	C₂×D₄×C₆₇	—	4	4	no	—
264	C₂×D₄×C₆₇	—	4	4	no	—
265	C₂×D₄×C₆₇	—	4	8	no	—
266	C₂×D₄×C₆₇	#41	1	8	yes	complemented
267	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
268	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
269	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
270	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
271	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
272	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
273	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
274	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
275	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
276	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
277	C₂²×C₄×C₆₇	—	2	8	no	—
278	C₂²×C₄×C₆₇	—	2	8	no	—
279	C₂²×C₄×C₆₇	—	2	4	no	—
280	C₂²×C₄×C₆₇	—	2	8	no	—
281	C₂²×C₄×C₆₇	—	2	4	no	—
282	C₂²×C₄×C₆₇	—	4	4	no	—
283	C₂²×C₄×C₆₇	—	4	8	no	—
284	C₂²×C₄×C₆₇	—	4	2	no	—
285	C₂²×C₄×C₆₇	—	4	8	no	—
286	C₂²×C₄×C₆₇	—	4	8	no	—
287	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
288	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
289	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
290	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
291	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
292	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
303	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
304	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
305	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
306	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
307	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
308	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
311	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
312	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
313	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
314	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
315	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
316	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
317	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
318	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
319	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
320	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
321	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
322	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
323	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
324	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
325	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
326	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
327	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
328	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
329	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
330	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
331	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
332	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
333	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
334	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
335	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
336	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
337	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
338	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
339	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
340	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
341	C₄²×C₆₇	C₂⁴	1	4	yes	—
342	C₄²×C₆₇	C₂⁴	1	8	yes	—
343	C₄²×C₆₇	C₂⁴	1	4	yes	—
344	C₄²×C₆₇	C₂⁴	1	4	yes	—
345	C₄²×C₆₇	C₂⁴	1	4	yes	—
346	C₄²×C₆₇	C₂⁴	1	8	yes	—
347	C₄²×C₆₇	C₂⁴	1	8	yes	—
348	C₄²×C₆₇	C₂⁴	1	16	yes	—
349	C₄²×C₆₇	C₂⁴	1	8	yes	—
350	C₂³×C₆₇	—	2	4	no	—
351	C₂³×C₆₇	—	2	4	no	—
352	C₂³×C₆₇	—	2	2	no	—
353	C₂³×C₆₇	—	2	4	no	—
354	C₂³×C₆₇	—	2	8	no	—
355	C₂³×C₆₇	—	2	2	no	—
356	C₂³×C₆₇	—	2	8	no	—
357	C₂³×C₆₇	—	2	4	no	—
358	C₂³×C₆₇	—	2	2	no	—
359	C₂³×C₆₇	—	2	8	no	—
360	C₂³×C₆₇	—	2	4	no	—
361	C₂³×C₆₇	—	2	32	no	—
362	C₂³×C₆₇	—	4	16	no	—
363	C₂³×C₆₇	—	4	16	no	—
364	C₂³×C₆₇	—	8	32	no	—
365	C₂³×C₆₇	C₂×#41	1	8	yes	—
366	C₂³×C₆₇	C₂⁵	1	4	yes	—
367	C₂³×C₆₇	C₂⁵	1	8	yes	—
368	C₂³×C₆₇	C₂⁵	1	2	yes	—
369	C₂³×C₆₇	C₂⁵	1	4	yes	—
370	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
371	Q₈×C₆₇	—	2	8	no	—
372	Q₈×C₆₇	—	2	8	no	—
373	Q₈×C₆₇	—	2	16	no	—
374	Q₈×C₆₇	—	4	16	no	—
375	D₄×C₆₇	—	2	32	no	—
376	D₄×C₆₇	—	2	16	no	—
377	D₄×C₆₇	—	2	16	no	—
378	D₄×C₆₇	—	2	8	no	—
379	D₄×C₆₇	—	2	16	no	—
380	D₄×C₆₇	—	4	16	no	—
381	D₄×C₆₇	—	4	8	no	—
382	D₄×C₆₇	—	4	8	no	—
383	D₄×C₆₇	—	4	16	no	—
384	D₄×C₆₇	C₂×#41	1	16	yes	complemented
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	2	4	no	—
387	C₂×C₄×C₆₇	—	2	4	no	—
388	C₂×C₄×C₆₇	—	2	16	no	—
389	C₂×C₄×C₆₇	—	2	2	no	—
390	C₂×C₄×C₆₇	—	2	4	no	—
391	C₂×C₄×C₆₇	—	2	8	no	—
392	C₂×C₄×C₆₇	—	2	4	no	—
393	C₂×C₄×C₆₇	—	2	2	no	—
394	C₂×C₄×C₆₇	—	2	4	no	—
395	C₂×C₄×C₆₇	—	2	4	no	—
396	C₂×C₄×C₆₇	—	2	2	no	—
397	C₂×C₄×C₆₇	—	2	16	no	—
398	C₂×C₄×C₆₇	—	2	8	no	—
399	C₂×C₄×C₆₇	—	2	16	no	—
400	C₂×C₄×C₆₇	—	2	8	no	—
401	C₂×C₄×C₆₇	—	4	8	no	—
402	C₂×C₄×C₆₇	—	4	16	no	—
403	C₂×C₄×C₆₇	—	4	4	no	—
404	C₂×C₄×C₆₇	—	4	16	no	—
405	C₂×C₄×C₆₇	—	4	16	no	—
406	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
407	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
408	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
409	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
410	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
411	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
412	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
413	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
414	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
415	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
416	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
417	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
418	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
419	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
420	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
421	C₂²×C₆₇	—	2	4	no	—
422	C₂²×C₆₇	—	2	4	no	—
423	C₂²×C₆₇	—	2	16	no	—
424	C₂²×C₆₇	—	2	2	no	—
425	C₂²×C₆₇	—	2	4	no	—
426	C₂²×C₆₇	—	2	8	no	—
427	C₂²×C₆₇	—	2	2	no	—
428	C₂²×C₆₇	—	2	8	no	—
429	C₂²×C₆₇	—	2	4	no	—
430	C₂²×C₆₇	—	2	2	no	—
431	C₂²×C₆₇	—	2	8	no	—
432	C₂²×C₆₇	—	2	4	no	—
433	C₂²×C₆₇	—	4	4	no	—
434	C₂²×C₆₇	—	4	16	no	—
435	C₂²×C₆₇	—	4	8	no	—
436	C₂²×C₆₇	—	8	32	no	—
437	C₂²×C₆₇	C₂²×#41	1	8	yes	—
438	C₂²×C₆₇	C₂²×#41	1	2	yes	—
439	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
440	C₂²×C₆₇	#585	1	2	yes	—
441	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
442	C₄×C₆₇	—	2	2	no	—
443	C₄×C₆₇	—	2	4	no	—
444	C₄×C₆₇	—	2	4	no	—
445	C₄×C₆₇	—	2	2	no	—
446	C₄×C₆₇	—	2	4	no	—
447	C₄×C₆₇	—	2	8	no	—
448	C₄×C₆₇	—	2	4	no	—
449	C₄×C₆₇	—	2	2	no	—
450	C₄×C₆₇	—	2	4	no	—
451	C₄×C₆₇	—	2	4	no	—
452	C₄×C₆₇	—	2	2	no	—
453	C₄×C₆₇	C₂²×#41	1	4	yes	—
454	C₄×C₆₇	C₂×H(5,𝔽₂)	1	4	yes	—
455	C₂×#3514	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
456	C₂×C₆₇	—	2	8	no	—
457	C₂×C₆₇	—	4	2	no	—
458	C₂×C₆₇	—	4	8	no	—
459	C₂×C₆₇	—	4	4	no	—
460	C₂×C₆₇	#3514	1	4	yes	direct product factor
461	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
462	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
463	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
464	#3514	C₂×C₆₇	1	32	yes	direct product factor
465	C₂×#559	C₂×C₆₇	1	1	yes	characteristic, complemented
466	C₂×#556	C₂×C₆₇	1	1	yes	characteristic, complemented
467	C₂×#555	C₂×C₆₇	1	2	yes	complemented
468	C₂×#551	C₂×C₆₇	1	4	yes	complemented
469	C₂×D₄×Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
470	C₂×#548	C₂×C₆₇	1	2	yes	complemented
471	C₂×#546	C₂×C₆₇	1	2	yes	complemented
472	C₂×#546	C₂×C₆₇	1	2	yes	complemented
473	C₂×D₄²	C₂×C₆₇	1	1	yes	characteristic, complemented
474	C₂×#542	C₂×C₆₇	1	2	yes	complemented
475	C₂×#538	C₂×C₆₇	1	4	yes	complemented
476	C₂×#532	C₂×C₆₇	1	1	yes	characteristic, complemented
477	C₂×#529	C₂×C₆₇	1	1	yes	characteristic, complemented
478	C₂×#529	C₂×C₆₇	1	2	yes	complemented
479	C₂²×#124	C₂×C₆₇	1	2	yes	complemented
480	C₂×#518	C₂×C₆₇	1	2	yes	complemented
481	C₂×C₄×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
482	C₆₇	C₂×#3514	1	1	yes	characteristic, direct product factor, Sylow
483	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
484	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
485	C₂³×Q₈	C₂²×C₆₇	1	2	yes	complemented
486	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
487	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
488	#559	C₂²×C₆₇	1	16	yes	complemented
489	#556	C₂²×C₆₇	1	16	yes	complemented
490	#555	C₂²×C₆₇	1	32	yes	complemented
491	#551	C₂²×C₆₇	1	64	yes	complemented
492	D₄×Q₈	C₂²×C₆₇	1	16	yes	complemented
493	#548	C₂²×C₆₇	1	32	yes	complemented
494	#546	C₂²×C₆₇	1	32	yes	complemented
495	#546	C₂²×C₆₇	1	32	yes	complemented
496	D₄²	C₂²×C₆₇	1	16	yes	complemented
497	#542	C₂²×C₆₇	1	32	yes	complemented
498	#538	C₂²×C₆₇	1	64	yes	complemented
499	#532	C₂²×C₆₇	1	16	yes	complemented
500	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
501	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
502	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
503	#529	C₂²×C₆₇	1	16	yes	complemented
504	#529	C₂²×C₆₇	1	32	yes	complemented
505	C₂×#126	C₂²×C₆₇	1	4	yes	complemented
506	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
507	C₂×#126	C₂²×C₆₇	1	4	yes	complemented
508	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
509	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
510	C₂×#124	C₂²×C₆₇	1	2	yes	—
511	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
512	C₂×#124	C₂²×C₆₇	1	4	yes	complemented
513	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
514	C₂×#124	C₂²×C₆₇	1	4	yes	complemented
515	C₂×#124	C₂²×C₆₇	1	4	yes	complemented
516	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
517	C₂×#124	C₂²×C₆₇	1	32	yes	complemented
518	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
519	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
520	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
521	C₂×#123	C₂²×C₆₇	1	4	yes	complemented
522	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
523	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
524	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
525	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
526	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	complemented
527	C₂×#121	C₂²×C₆₇	1	2	yes	—
528	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
529	C₂×#121	C₂²×C₆₇	1	2	yes	—
530	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
531	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
532	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
533	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
534	C₂×#120	C₂²×C₆₇	1	4	yes	—
535	C₂×#120	C₂²×C₆₇	1	4	yes	complemented
536	#518	C₂²×C₆₇	1	32	yes	complemented
537	C₄×#41	C₂²×C₆₇	1	16	yes	complemented
538	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
539	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
540	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	complemented
541	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
542	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
543	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
544	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
545	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
546	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
547	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
548	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
549	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
550	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
551	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
552	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
553	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
554	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
555	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
556	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
557	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
558	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
559	C₂×#117	C₂²×C₆₇	1	4	yes	complemented
560	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
561	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
562	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	complemented
563	C₂²×C₄²	C₂²×C₆₇	1	2	yes	complemented
564	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
565	C₂⁵	C₂³×C₆₇	1	4	yes	—
566	C₂×#41	—	2	8	no	—
567	C₂×#41	—	4	8	no	—
568	C₂×#41	C₂³×C₆₇	1	8	yes	—
569	C₂×#41	C₂³×C₆₇	1	16	yes	complemented
570	C₂²×Q₈	—	4	8	no	—
571	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
572	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
573	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
574	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
575	C₂²×Q₈	C₂³×C₆₇	1	16	yes	complemented
576	C₂²×D₄	—	2	16	no	—
577	C₂²×D₄	—	4	8	no	—
578	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
579	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
580	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
581	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
582	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
583	C₂²×D₄	C₂³×C₆₇	1	16	yes	—
584	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
585	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
586	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
587	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
588	C₂²×D₄	C₂³×C₆₇	1	16	yes	—
589	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
590	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
591	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
592	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
593	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
594	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
595	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
596	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
597	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
598	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
599	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
600	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
601	C₄⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
602	#127	C₂³×C₆₇	1	8	yes	—
603	#126	C₂³×C₆₇	1	32	yes	complemented
604	#126	C₂³×C₆₇	1	16	yes	complemented
605	#126	C₂³×C₆₇	1	32	yes	complemented
606	#125	C₂³×C₆₇	1	8	yes	complemented
607	#124	C₂³×C₆₇	1	8	yes	—
608	#124	C₂³×C₆₇	1	16	yes	—
609	#124	C₂³×C₆₇	1	16	yes	complemented
610	#124	C₂³×C₆₇	1	32	yes	complemented
611	#124	C₂³×C₆₇	1	16	yes	complemented
612	#124	C₂³×C₆₇	1	32	yes	complemented
613	#124	C₂³×C₆₇	1	32	yes	complemented
614	#124	C₂³×C₆₇	1	16	yes	complemented
615	#123	C₂³×C₆₇	1	16	yes	complemented
616	#123	C₂³×C₆₇	1	32	yes	complemented
617	#123	C₂³×C₆₇	1	32	yes	complemented
618	#123	C₂³×C₆₇	1	32	yes	complemented
619	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
620	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
621	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	complemented
622	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	complemented
623	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	complemented
624	#121	C₂³×C₆₇	1	16	yes	—
625	#121	C₂³×C₆₇	1	8	yes	—
626	#121	C₂³×C₆₇	1	16	yes	—
627	#121	C₂³×C₆₇	1	16	yes	complemented
628	#121	C₂³×C₆₇	1	16	yes	complemented
629	#121	C₂³×C₆₇	1	32	yes	complemented
630	#121	C₂³×C₆₇	1	32	yes	complemented
631	#120	C₂³×C₆₇	1	32	yes	—
632	#120	C₂³×C₆₇	1	32	yes	complemented
633	C₄×Q₈	C₂³×C₆₇	1	8	yes	complemented
634	C₄×Q₈	C₂³×C₆₇	1	8	yes	complemented
635	C₄×Q₈	C₂³×C₆₇	1	16	yes	complemented
636	C₄×Q₈	C₂³×C₆₇	1	8	yes	complemented
637	C₄×D₄	C₂³×C₆₇	1	8	yes	—
638	C₄×D₄	C₂³×C₆₇	1	8	yes	—
639	C₄×D₄	C₂³×C₆₇	1	16	yes	—
640	C₄×D₄	C₂³×C₆₇	1	8	yes	—
641	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
642	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
643	C₄×D₄	C₂³×C₆₇	1	32	yes	complemented
644	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
645	C₄×D₄	C₂³×C₆₇	1	32	yes	complemented
646	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
647	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
648	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
649	C₄×D₄	C₂³×C₆₇	1	16	yes	complemented
650	#117	C₂³×C₆₇	1	16	yes	complemented
651	#117	C₂³×C₆₇	1	8	yes	complemented
652	#117	C₂³×C₆₇	1	16	yes	complemented
653	#117	C₂³×C₆₇	1	16	yes	complemented
654	#117	C₂³×C₆₇	1	32	yes	complemented
655	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
656	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
664	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
668	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
672	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
673	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₆₇	1	32	yes	complemented
687	C₂×C₂²⋊C₄	C₂³×C₆₇	1	32	yes	complemented
688	C₂×C₂²⋊C₄	C₂³×C₆₇	1	32	yes	complemented
689	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
690	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
691	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
692	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
693	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
694	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
695	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
696	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
697	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₆₇	1	16	yes	complemented
699	C₂×C₄²	C₂³×C₆₇	1	8	yes	complemented
700	C₂⁴	—	2	16	no	—
701	C₂⁴	—	4	8	no	—
702	C₂⁴	—	4	8	no	—
703	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
704	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
705	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
706	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
707	C₂⁴	C₂⁴×C₆₇	1	16	yes	—
708	#41	—	2	32	no	—
709	#41	—	4	32	no	—
710	C₂×Q₈	—	2	4	no	—
711	C₂×Q₈	—	2	4	no	—
712	C₂×Q₈	—	2	8	no	—
713	C₂×Q₈	—	4	8	no	—
714	C₂×Q₈	—	4	32	no	—
715	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
716	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
717	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
718	C₂×Q₈	C₂⁴×C₆₇	1	16	yes	—
719	C₂×D₄	—	2	16	no	—
720	C₂×D₄	—	2	8	no	—
721	C₂×D₄	—	2	64	no	—
722	C₂×D₄	—	2	8	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	2	8	no	—
725	C₂×D₄	—	4	32	no	—
726	C₂×D₄	—	4	8	no	—
727	C₂×D₄	—	4	8	no	—
728	C₂×D₄	—	4	4	no	—
729	C₂×D₄	—	4	4	no	—
730	C₂×D₄	#41×C₆₇	1	8	yes	complemented
731	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
732	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
733	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
734	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
735	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
736	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
737	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
738	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
739	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
740	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
741	C₂²×C₄	—	2	8	no	—
742	C₂²×C₄	—	2	8	no	—
743	C₂²×C₄	—	2	4	no	—
744	C₂²×C₄	—	2	8	no	—
745	C₂²×C₄	—	2	4	no	—
746	C₂²×C₄	—	4	8	no	—
747	C₂²×C₄	—	4	8	no	—
748	C₂²×C₄	—	4	4	no	—
749	C₂²×C₄	—	4	8	no	—
750	C₂²×C₄	—	4	2	no	—
751	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
755	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
762	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
763	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
764	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
765	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
766	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
767	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
768	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
769	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
770	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
771	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
772	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
774	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
775	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
776	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
777	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
778	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
779	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
780	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
781	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
782	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
783	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
784	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
785	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
786	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
787	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
788	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
789	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
790	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
791	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
792	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
793	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
794	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
795	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
796	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
797	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
798	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
799	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
800	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
801	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
802	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
803	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
804	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
805	C₄²	C₂⁴×C₆₇	1	4	yes	—
806	C₄²	C₂⁴×C₆₇	1	8	yes	—
807	C₄²	C₂⁴×C₆₇	1	4	yes	—
808	C₄²	C₂⁴×C₆₇	1	4	yes	—
809	C₄²	C₂⁴×C₆₇	1	4	yes	—
810	C₄²	C₂⁴×C₆₇	1	8	yes	—
811	C₄²	C₂⁴×C₆₇	1	8	yes	—
812	C₄²	C₂⁴×C₆₇	1	16	yes	—
813	C₄²	C₂⁴×C₆₇	1	8	yes	—
814	C₂³	—	2	4	no	—
815	C₂³	—	2	4	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	4	no	—
818	C₂³	—	2	8	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	8	no	—
821	C₂³	—	2	4	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	8	no	—
824	C₂³	—	2	4	no	—
825	C₂³	—	2	32	no	—
826	C₂³	—	4	16	no	—
827	C₂³	—	4	16	no	—
828	C₂³	—	8	32	no	—
829	C₂³	C₂×#41×C₆₇	1	8	yes	—
830	C₂³	C₂⁵×C₆₇	1	4	yes	—
831	C₂³	C₂⁵×C₆₇	1	8	yes	—
832	C₂³	C₂⁵×C₆₇	1	2	yes	—
833	C₂³	C₂⁵×C₆₇	1	4	yes	—
834	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
835	Q₈	—	2	8	no	—
836	Q₈	—	2	8	no	—
837	Q₈	—	2	16	no	—
838	Q₈	—	4	16	no	—
839	D₄	—	2	32	no	—
840	D₄	—	2	16	no	—
841	D₄	—	2	16	no	—
842	D₄	—	2	8	no	—
843	D₄	—	2	16	no	—
844	D₄	—	4	16	no	—
845	D₄	—	4	16	no	—
846	D₄	—	4	8	no	—
847	D₄	—	4	8	no	—
848	D₄	C₂×#41×C₆₇	1	16	yes	complemented
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	4	no	—
851	C₂×C₄	—	2	4	no	—
852	C₂×C₄	—	2	16	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	4	no	—
855	C₂×C₄	—	2	8	no	—
856	C₂×C₄	—	2	4	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	4	no	—
859	C₂×C₄	—	2	4	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	16	no	—
862	C₂×C₄	—	2	8	no	—
863	C₂×C₄	—	2	16	no	—
864	C₂×C₄	—	2	8	no	—
865	C₂×C₄	—	4	16	no	—
866	C₂×C₄	—	4	16	no	—
867	C₂×C₄	—	4	8	no	—
868	C₂×C₄	—	4	16	no	—
869	C₂×C₄	—	4	4	no	—
870	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
871	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
872	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
873	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
874	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
875	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
876	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
877	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
878	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
879	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
880	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
881	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
882	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
883	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
884	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
885	C₂²	—	2	4	no	—
886	C₂²	—	2	4	no	—
887	C₂²	—	2	16	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	2	4	no	—
890	C₂²	—	2	8	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	2	8	no	—
893	C₂²	—	2	4	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	8	no	—
896	C₂²	—	2	4	no	—
897	C₂²	—	4	8	no	—
898	C₂²	—	4	16	no	—
899	C₂²	—	4	4	no	—
900	C₂²	—	8	32	no	—
901	C₂²	C₂²×#41×C₆₇	1	8	yes	—
902	C₂²	C₂²×#41×C₆₇	1	2	yes	—
903	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
904	C₂²	#585×C₆₇	1	2	yes	—
905	C₂²	C₂⁶×C₆₇	1	1	yes	characteristic
906	C₄	—	2	2	no	—
907	C₄	—	2	4	no	—
908	C₄	—	2	4	no	—
909	C₄	—	2	2	no	—
910	C₄	—	2	4	no	—
911	C₄	—	2	8	no	—
912	C₄	—	2	4	no	—
913	C₄	—	2	2	no	—
914	C₄	—	2	4	no	—
915	C₄	—	2	4	no	—
916	C₄	—	2	2	no	—
917	C₄	C₂²×#41×C₆₇	1	4	yes	—
918	C₄	C₂×H(5,𝔽₂)×C₆₇	1	4	yes	—
919	C₂	—	2	8	no	—
920	C₂	—	4	4	no	—
921	C₂	—	4	8	no	—
922	C₂	—	4	2	no	—
923	C₂	C₆₇×#3514	1	4	yes	direct product factor
924	C₂	C₂³×#41×C₆₇	1	1	yes	characteristic
925	C₂	C₂²×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
926	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×#3514	C₂	direct (N × H)
2. C₂×#559×C₆₇	C₂	semidirect
3. C₂×#556×C₆₇	C₂	semidirect
4. C₂×#555×C₆₇	C₂	semidirect
5. C₂×#551×C₆₇	C₂	semidirect
6. C₂×D₄×Q₈×C₆₇	C₂	semidirect
7. C₂×#548×C₆₇	C₂	semidirect
8. C₂×#546×C₆₇	C₂	semidirect
9. C₂×#546×C₆₇	C₂	semidirect
10. C₂×D₄²×C₆₇	C₂	semidirect
11. C₂×#542×C₆₇	C₂	semidirect
12. C₂×#538×C₆₇	C₂	semidirect
13. C₂×#532×C₆₇	C₂	semidirect
14. C₂×#529×C₆₇	C₂	semidirect
15. C₂×#529×C₆₇	C₂	semidirect
16. C₂²×#124×C₆₇	C₂	semidirect
17. C₂×#518×C₆₇	C₂	semidirect
18. C₂×C₄×#41×C₆₇	C₂	semidirect
20. C₂²×#41×C₆₇	C₂²	semidirect
21. C₂³×Q₈×C₆₇	C₂²	semidirect
24. #559×C₆₇	C₂²	semidirect
25. #556×C₆₇	C₂²	semidirect
26. #555×C₆₇	C₂²	semidirect
27. #551×C₆₇	C₂²	semidirect
28. D₄×Q₈×C₆₇	C₂²	semidirect
29. #548×C₆₇	C₂²	semidirect
30. #546×C₆₇	C₂²	semidirect
31. #546×C₆₇	C₂²	semidirect
32. D₄²×C₆₇	C₂²	semidirect
33. #542×C₆₇	C₂²	semidirect
34. #538×C₆₇	C₂²	semidirect
35. #532×C₆₇	C₂²	semidirect
36. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
37. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
39. #529×C₆₇	C₂²	semidirect
40. #529×C₆₇	C₂²	semidirect
41. C₂×#126×C₆₇	C₂²	semidirect
42. C₂×#126×C₆₇	C₂²	semidirect
43. C₂×#126×C₆₇	C₂²	semidirect
44. C₂×#125×C₆₇	C₂²	semidirect
47. C₂×#124×C₆₇	C₂²	semidirect
48. C₂×#124×C₆₇	C₂²	semidirect
49. C₂×#124×C₆₇	C₂²	semidirect
50. C₂×#124×C₆₇	C₂²	semidirect
51. C₂×#124×C₆₇	C₂²	semidirect
52. C₂×#124×C₆₇	C₂²	semidirect
53. C₂×#124×C₆₇	C₂²	semidirect
54. C₂×#123×C₆₇	C₂²	semidirect
55. C₂×#123×C₆₇	C₂²	semidirect
56. C₂×#123×C₆₇	C₂²	semidirect
57. C₂×#123×C₆₇	C₂²	semidirect
58. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
59. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
60. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
61. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
62. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
66. C₂×#121×C₆₇	C₂²	semidirect
67. C₂×#121×C₆₇	C₂²	semidirect
68. C₂×#121×C₆₇	C₂²	semidirect
69. C₂×#121×C₆₇	C₂²	semidirect
71. C₂×#120×C₆₇	C₂²	semidirect
72. #518×C₆₇	C₂²	semidirect
73. C₄×#41×C₆₇	C₂²	semidirect
74. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
75. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
76. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
77. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
82. C₂×C₄×D₄×C₆₇	C₂²	semidirect
83. C₂×C₄×D₄×C₆₇	C₂²	semidirect
84. C₂×C₄×D₄×C₆₇	C₂²	semidirect
85. C₂×C₄×D₄×C₆₇	C₂²	semidirect
86. C₂×C₄×D₄×C₆₇	C₂²	semidirect
87. C₂×C₄×D₄×C₆₇	C₂²	semidirect
88. C₂×C₄×D₄×C₆₇	C₂²	semidirect
89. C₂×C₄×D₄×C₆₇	C₂²	semidirect
90. C₂×C₄×D₄×C₆₇	C₂²	semidirect
91. C₂×#117×C₆₇	C₂²	semidirect
92. C₂×#117×C₆₇	C₂²	semidirect
93. C₂×#117×C₆₇	C₂²	semidirect
94. C₂×#117×C₆₇	C₂²	semidirect
95. C₂×#117×C₆₇	C₂²	semidirect
96. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
97. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
98. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
99. C₂²×C₄²×C₆₇	C₂²	semidirect
100. C₂²×C₄²×C₆₇	C₂²	semidirect
105. C₂×#41×C₆₇	C₂³	semidirect
111. C₂²×Q₈×C₆₇	C₂³	semidirect
136. C₄⋊Q₈×C₆₇	C₂³	semidirect
137. C₄⋊Q₈×C₆₇	C₂³	semidirect
139. #126×C₆₇	C₂³	semidirect
140. #126×C₆₇	C₂³	semidirect
141. #126×C₆₇	C₂³	semidirect
142. #125×C₆₇	C₂³	semidirect
145. #124×C₆₇	C₂³	semidirect
146. #124×C₆₇	C₂³	semidirect
147. #124×C₆₇	C₂³	semidirect
148. #124×C₆₇	C₂³	semidirect
149. #124×C₆₇	C₂³	semidirect
150. #124×C₆₇	C₂³	semidirect
151. #123×C₆₇	C₂³	semidirect
152. #123×C₆₇	C₂³	semidirect
153. #123×C₆₇	C₂³	semidirect
154. #123×C₆₇	C₂³	semidirect
155. C₂²⋊Q₈×C₆₇	C₂³	semidirect
156. C₂²⋊Q₈×C₆₇	C₂³	semidirect
157. C₂²⋊Q₈×C₆₇	C₂³	semidirect
158. C₂²⋊Q₈×C₆₇	C₂³	semidirect
159. C₂²⋊Q₈×C₆₇	C₂³	semidirect
163. #121×C₆₇	C₂³	semidirect
164. #121×C₆₇	C₂³	semidirect
165. #121×C₆₇	C₂³	semidirect
166. #121×C₆₇	C₂³	semidirect
168. #120×C₆₇	C₂³	semidirect
169. C₄×Q₈×C₆₇	C₂³	semidirect
170. C₄×Q₈×C₆₇	C₂³	semidirect
171. C₄×Q₈×C₆₇	C₂³	semidirect
172. C₄×Q₈×C₆₇	C₂³	semidirect
177. C₄×D₄×C₆₇	C₂³	semidirect
178. C₄×D₄×C₆₇	C₂³	semidirect
179. C₄×D₄×C₆₇	C₂³	semidirect
180. C₄×D₄×C₆₇	C₂³	semidirect
181. C₄×D₄×C₆₇	C₂³	semidirect
182. C₄×D₄×C₆₇	C₂³	semidirect
183. C₄×D₄×C₆₇	C₂³	semidirect
184. C₄×D₄×C₆₇	C₂³	semidirect
185. C₄×D₄×C₆₇	C₂³	semidirect
186. #117×C₆₇	C₂³	semidirect
187. #117×C₆₇	C₂³	semidirect
188. #117×C₆₇	C₂³	semidirect
189. #117×C₆₇	C₂³	semidirect
190. #117×C₆₇	C₂³	semidirect
222. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
223. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
224. C₂×C₂²⋊C₄×C₆₇	C₂³	semidirect
234. C₂×C₄²×C₆₇	C₂³	semidirect
235. C₂×C₄²×C₆₇	C₂³	semidirect
266. C₂×D₄×C₆₇	#41	semidirect
384. D₄×C₆₇	C₂×#41	semidirect
455. C₂×#3514	C₆₇	direct (N × H)
460. C₂×C₆₇	#3514	direct (N × H)
464. #3514	C₂×C₆₇	direct (N × H)
465. C₂×#559	C₂×C₆₇	semidirect
466. C₂×#556	C₂×C₆₇	semidirect
467. C₂×#555	C₂×C₆₇	semidirect
468. C₂×#551	C₂×C₆₇	semidirect
469. C₂×D₄×Q₈	C₂×C₆₇	semidirect
470. C₂×#548	C₂×C₆₇	semidirect
471. C₂×#546	C₂×C₆₇	semidirect
472. C₂×#546	C₂×C₆₇	semidirect
473. C₂×D₄²	C₂×C₆₇	semidirect
474. C₂×#542	C₂×C₆₇	semidirect
475. C₂×#538	C₂×C₆₇	semidirect
476. C₂×#532	C₂×C₆₇	semidirect
477. C₂×#529	C₂×C₆₇	semidirect
478. C₂×#529	C₂×C₆₇	semidirect
479. C₂²×#124	C₂×C₆₇	semidirect
480. C₂×#518	C₂×C₆₇	semidirect
481. C₂×C₄×#41	C₂×C₆₇	semidirect
482. C₆₇	C₂×#3514	direct (N × H)
484. C₂²×#41	C₂²×C₆₇	semidirect
485. C₂³×Q₈	C₂²×C₆₇	semidirect
488. #559	C₂²×C₆₇	semidirect
489. #556	C₂²×C₆₇	semidirect
490. #555	C₂²×C₆₇	semidirect
491. #551	C₂²×C₆₇	semidirect
492. D₄×Q₈	C₂²×C₆₇	semidirect
493. #548	C₂²×C₆₇	semidirect
494. #546	C₂²×C₆₇	semidirect
495. #546	C₂²×C₆₇	semidirect
496. D₄²	C₂²×C₆₇	semidirect
497. #542	C₂²×C₆₇	semidirect
498. #538	C₂²×C₆₇	semidirect
499. #532	C₂²×C₆₇	semidirect
500. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
501. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
503. #529	C₂²×C₆₇	semidirect
504. #529	C₂²×C₆₇	semidirect
505. C₂×#126	C₂²×C₆₇	semidirect
506. C₂×#126	C₂²×C₆₇	semidirect
507. C₂×#126	C₂²×C₆₇	semidirect
508. C₂×#125	C₂²×C₆₇	semidirect
511. C₂×#124	C₂²×C₆₇	semidirect
512. C₂×#124	C₂²×C₆₇	semidirect
513. C₂×#124	C₂²×C₆₇	semidirect
514. C₂×#124	C₂²×C₆₇	semidirect
515. C₂×#124	C₂²×C₆₇	semidirect
516. C₂×#124	C₂²×C₆₇	semidirect
517. C₂×#124	C₂²×C₆₇	semidirect
518. C₂×#123	C₂²×C₆₇	semidirect
519. C₂×#123	C₂²×C₆₇	semidirect
520. C₂×#123	C₂²×C₆₇	semidirect
521. C₂×#123	C₂²×C₆₇	semidirect
522. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
523. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
524. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
525. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
526. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
530. C₂×#121	C₂²×C₆₇	semidirect
531. C₂×#121	C₂²×C₆₇	semidirect
532. C₂×#121	C₂²×C₆₇	semidirect
533. C₂×#121	C₂²×C₆₇	semidirect
535. C₂×#120	C₂²×C₆₇	semidirect
536. #518	C₂²×C₆₇	semidirect
537. C₄×#41	C₂²×C₆₇	semidirect
538. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
539. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
540. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
541. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
546. C₂×C₄×D₄	C₂²×C₆₇	semidirect
547. C₂×C₄×D₄	C₂²×C₆₇	semidirect
548. C₂×C₄×D₄	C₂²×C₆₇	semidirect
549. C₂×C₄×D₄	C₂²×C₆₇	semidirect
550. C₂×C₄×D₄	C₂²×C₆₇	semidirect
551. C₂×C₄×D₄	C₂²×C₆₇	semidirect
552. C₂×C₄×D₄	C₂²×C₆₇	semidirect
553. C₂×C₄×D₄	C₂²×C₆₇	semidirect
554. C₂×C₄×D₄	C₂²×C₆₇	semidirect
555. C₂×#117	C₂²×C₆₇	semidirect
556. C₂×#117	C₂²×C₆₇	semidirect
557. C₂×#117	C₂²×C₆₇	semidirect
558. C₂×#117	C₂²×C₆₇	semidirect
559. C₂×#117	C₂²×C₆₇	semidirect
560. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
561. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
562. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
563. C₂²×C₄²	C₂²×C₆₇	semidirect
564. C₂²×C₄²	C₂²×C₆₇	semidirect
569. C₂×#41	C₂³×C₆₇	semidirect
575. C₂²×Q₈	C₂³×C₆₇	semidirect
600. C₄⋊Q₈	C₂³×C₆₇	semidirect
601. C₄⋊Q₈	C₂³×C₆₇	semidirect
603. #126	C₂³×C₆₇	semidirect
604. #126	C₂³×C₆₇	semidirect
605. #126	C₂³×C₆₇	semidirect
606. #125	C₂³×C₆₇	semidirect
609. #124	C₂³×C₆₇	semidirect
610. #124	C₂³×C₆₇	semidirect
611. #124	C₂³×C₆₇	semidirect
612. #124	C₂³×C₆₇	semidirect
613. #124	C₂³×C₆₇	semidirect
614. #124	C₂³×C₆₇	semidirect
615. #123	C₂³×C₆₇	semidirect
616. #123	C₂³×C₆₇	semidirect
617. #123	C₂³×C₆₇	semidirect
618. #123	C₂³×C₆₇	semidirect
619. C₂²⋊Q₈	C₂³×C₆₇	semidirect
620. C₂²⋊Q₈	C₂³×C₆₇	semidirect
621. C₂²⋊Q₈	C₂³×C₆₇	semidirect
622. C₂²⋊Q₈	C₂³×C₆₇	semidirect
623. C₂²⋊Q₈	C₂³×C₆₇	semidirect
627. #121	C₂³×C₆₇	semidirect
628. #121	C₂³×C₆₇	semidirect
629. #121	C₂³×C₆₇	semidirect
630. #121	C₂³×C₆₇	semidirect
632. #120	C₂³×C₆₇	semidirect
633. C₄×Q₈	C₂³×C₆₇	semidirect
634. C₄×Q₈	C₂³×C₆₇	semidirect
635. C₄×Q₈	C₂³×C₆₇	semidirect
636. C₄×Q₈	C₂³×C₆₇	semidirect
641. C₄×D₄	C₂³×C₆₇	semidirect
642. C₄×D₄	C₂³×C₆₇	semidirect
643. C₄×D₄	C₂³×C₆₇	semidirect
644. C₄×D₄	C₂³×C₆₇	semidirect
645. C₄×D₄	C₂³×C₆₇	semidirect
646. C₄×D₄	C₂³×C₆₇	semidirect
647. C₄×D₄	C₂³×C₆₇	semidirect
648. C₄×D₄	C₂³×C₆₇	semidirect
649. C₄×D₄	C₂³×C₆₇	semidirect
650. #117	C₂³×C₆₇	semidirect
651. #117	C₂³×C₆₇	semidirect
652. #117	C₂³×C₆₇	semidirect
653. #117	C₂³×C₆₇	semidirect
654. #117	C₂³×C₆₇	semidirect
686. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
687. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
688. C₂×C₂²⋊C₄	C₂³×C₆₇	semidirect
698. C₂×C₄²	C₂³×C₆₇	semidirect
699. C₂×C₄²	C₂³×C₆₇	semidirect
730. C₂×D₄	#41×C₆₇	semidirect
848. D₄	C₂×#41×C₆₇	semidirect
923. C₂	C₆₇×#3514	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×#3514	2
C₂×#559×C₆₇	2
C₂×#556×C₆₇	2
C₂×#555×C₆₇	2
C₂×#551×C₆₇	2
C₂×D₄×Q₈×C₆₇	2
C₂×#548×C₆₇	2
C₂×#546×C₆₇	2
C₂×D₄²×C₆₇	2
C₂×#542×C₆₇	2
C₂×#538×C₆₇	2
C₂×#532×C₆₇	2
C₂×#529×C₆₇	2
C₂²×#124×C₆₇	2
C₂×#518×C₆₇	2
C₂×C₄×#41×C₆₇	2
C₂×#3514	67

Subgroups — C2×C67×#3514 #30742029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3514 #30742029