Subgroups — C₂×C₆₇×#3515 #30742030

Order 17152.

7142 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3515	C₂	1	32	yes	maximal, direct product factor
2	C₂×#557×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#554×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	2	yes	maximal, complemented
6	C₂×#552×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂×#552×C₆₇	C₂	1	4	yes	maximal, complemented
8	C₂×#552×C₆₇	C₂	1	2	yes	maximal, complemented
9	C₂×#547×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#547×C₆₇	C₂	1	2	yes	maximal, complemented
11	C₂×#541×C₆₇	C₂	1	2	yes	maximal, complemented
12	C₂×#539×C₆₇	C₂	1	4	yes	maximal, complemented
13	C₂×#533×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#529×C₆₇	C₂	1	2	yes	maximal, complemented
15	C₂×#529×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#125×C₆₇	C₂	1	2	yes	maximal, complemented
17	C₂×#520×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	—
21	#557×C₆₇	C₂²	1	16	yes	complemented
22	#554×C₆₇	C₂²	1	16	yes	complemented
23	#554×C₆₇	C₂²	1	16	yes	complemented
24	#553×C₆₇	C₂²	1	32	yes	complemented
25	#552×C₆₇	C₂²	1	32	yes	complemented
26	#552×C₆₇	C₂²	1	64	yes	complemented
27	#552×C₆₇	C₂²	1	32	yes	complemented
28	#547×C₆₇	C₂²	1	16	yes	complemented
29	#547×C₆₇	C₂²	1	32	yes	complemented
30	#541×C₆₇	C₂²	1	32	yes	complemented
31	#539×C₆₇	C₂²	1	64	yes	complemented
32	#533×C₆₇	C₂²	1	16	yes	complemented
33	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	—
36	#529×C₆₇	C₂²	1	32	yes	complemented
37	#529×C₆₇	C₂²	1	16	yes	complemented
38	C₂×#126×C₆₇	C₂²	1	4	yes	—
39	C₂×#126×C₆₇	C₂²	1	2	yes	—
40	C₂×#126×C₆₇	C₂²	1	4	yes	—
41	C₂×#126×C₆₇	C₂²	1	4	yes	—
42	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#125×C₆₇	C₂²	1	2	yes	—
44	C₂×#125×C₆₇	C₂²	1	4	yes	—
45	C₂×#125×C₆₇	C₂²	1	4	yes	—
46	C₂×#125×C₆₇	C₂²	1	2	yes	—
47	C₂×#125×C₆₇	C₂²	1	2	yes	—
48	C₂×#125×C₆₇	C₂²	1	4	yes	—
49	C₂×#125×C₆₇	C₂²	1	4	yes	—
50	C₂×#125×C₆₇	C₂²	1	2	yes	—
51	C₂×#125×C₆₇	C₂²	1	32	yes	complemented
52	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
53	C₂×#123×C₆₇	C₂²	1	2	yes	—
54	C₂×#123×C₆₇	C₂²	1	4	yes	—
55	C₂×#123×C₆₇	C₂²	1	4	yes	—
56	C₂×#123×C₆₇	C₂²	1	4	yes	—
57	C₂×#123×C₆₇	C₂²	1	4	yes	—
58	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
59	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
60	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
61	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
62	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
63	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	4	yes	—
64	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
65	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
66	C₂×#121×C₆₇	C₂²	1	2	yes	—
67	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
68	C₂×#121×C₆₇	C₂²	1	4	yes	—
69	#520×C₆₇	C₂²	1	32	yes	complemented
70	C₄×#41×C₆₇	C₂²	1	16	yes	complemented
71	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
72	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
73	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
74	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
75	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
76	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
77	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
78	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
79	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
80	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
81	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
82	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
83	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
84	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	—
85	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
86	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
87	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
88	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
89	C₂×#117×C₆₇	C₂²	1	2	yes	—
90	C₂×#117×C₆₇	C₂²	1	2	yes	—
91	C₂×#117×C₆₇	C₂²	1	4	yes	—
92	C₂×#117×C₆₇	C₂²	1	4	yes	—
93	C₂×#117×C₆₇	C₂²	1	2	yes	—
94	C₂²×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
95	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
96	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
97	C₂²×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
98	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
99	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
100	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
101	C₂×#41×C₆₇	—	2	8	no	—
102	C₂×#41×C₆₇	—	2	16	no	—
103	C₂×#41×C₆₇	C₂³	1	8	yes	—
104	C₂×#41×C₆₇	C₂³	1	16	yes	—
105	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
106	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
107	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
108	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
109	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
111	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
112	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
113	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
115	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
116	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
119	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
120	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
121	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
123	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
124	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	—
125	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	—
126	C₄⋊Q₈×C₆₇	C₂³	1	16	yes	—
127	#126×C₆₇	C₂³	1	32	yes	—
128	#126×C₆₇	C₂³	1	16	yes	—
129	#126×C₆₇	C₂³	1	32	yes	—
130	#126×C₆₇	C₂³	1	32	yes	—
131	#125×C₆₇	C₂³	1	8	yes	—
132	#125×C₆₇	C₂³	1	16	yes	—
133	#125×C₆₇	C₂³	1	32	yes	—
134	#125×C₆₇	C₂³	1	32	yes	—
135	#125×C₆₇	C₂³	1	16	yes	—
136	#125×C₆₇	C₂³	1	16	yes	—
137	#125×C₆₇	C₂³	1	32	yes	—
138	#125×C₆₇	C₂³	1	32	yes	—
139	#125×C₆₇	C₂³	1	16	yes	—
140	#124×C₆₇	C₂³	1	8	yes	—
141	#123×C₆₇	C₂³	1	16	yes	—
142	#123×C₆₇	C₂³	1	32	yes	—
143	#123×C₆₇	C₂³	1	32	yes	—
144	#123×C₆₇	C₂³	1	32	yes	—
145	#123×C₆₇	C₂³	1	32	yes	—
146	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
147	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
148	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
149	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
150	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	—
151	C₂²⋊Q₈×C₆₇	C₂³	1	32	yes	—
152	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
153	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
154	#121×C₆₇	C₂³	1	16	yes	—
155	#121×C₆₇	C₂³	1	8	yes	—
156	#121×C₆₇	C₂³	1	32	yes	—
157	C₄×Q₈×C₆₇	C₂³	1	8	yes	—
158	C₄×Q₈×C₆₇	C₂³	1	8	yes	—
159	C₄×Q₈×C₆₇	C₂³	1	16	yes	—
160	C₄×Q₈×C₆₇	C₂³	1	16	yes	—
161	C₄×Q₈×C₆₇	C₂³	1	16	yes	—
162	C₄×Q₈×C₆₇	C₂³	1	8	yes	—
163	C₄×Q₈×C₆₇	C₂³	1	16	yes	—
164	C₄×D₄×C₆₇	C₂³	1	8	yes	—
165	C₄×D₄×C₆₇	C₂³	1	16	yes	—
166	C₄×D₄×C₆₇	C₂³	1	8	yes	—
167	C₄×D₄×C₆₇	C₂³	1	16	yes	—
168	C₄×D₄×C₆₇	C₂³	1	32	yes	—
169	C₄×D₄×C₆₇	C₂³	1	16	yes	—
170	C₄×D₄×C₆₇	C₂³	1	32	yes	—
171	C₄×D₄×C₆₇	C₂³	1	16	yes	—
172	C₄×D₄×C₆₇	C₂³	1	8	yes	—
173	C₄×D₄×C₆₇	C₂³	1	16	yes	—
174	#117×C₆₇	C₂³	1	8	yes	—
175	#117×C₆₇	C₂³	1	16	yes	—
176	#117×C₆₇	C₂³	1	16	yes	—
177	#117×C₆₇	C₂³	1	32	yes	—
178	#117×C₆₇	C₂³	1	32	yes	—
179	#117×C₆₇	C₂³	1	16	yes	—
180	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
182	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
189	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
191	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
192	C₂×C₄⋊C₄×C₆₇	C₂³	1	32	yes	—
193	C₂×C₄⋊C₄×C₆₇	C₂³	1	16	yes	—
194	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
195	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
196	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
197	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
198	C₂×C₄⋊C₄×C₆₇	C₂³	1	16	yes	—
199	C₂×C₄⋊C₄×C₆₇	C₂³	1	32	yes	—
200	C₂×C₄⋊C₄×C₆₇	C₂³	1	16	yes	—
201	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
203	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
205	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
206	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
207	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
208	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
209	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
213	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
216	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
217	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	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	2	yes	—
221	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
223	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
226	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
228	C₂×C₄²×C₆₇	C₂³	1	16	yes	—
229	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
230	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
231	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
232	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
233	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
234	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
235	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
236	#41×C₆₇	—	2	32	no	—
237	#41×C₆₇	—	2	64	no	—
238	C₂×Q₈×C₆₇	—	2	4	no	—
239	C₂×Q₈×C₆₇	—	2	8	no	—
240	C₂×Q₈×C₆₇	—	2	4	no	—
241	C₂×Q₈×C₆₇	—	4	4	no	—
242	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
243	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
244	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
245	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
246	C₂×D₄×C₆₇	—	2	8	no	—
247	C₂×D₄×C₆₇	—	2	16	no	—
248	C₂×D₄×C₆₇	—	2	4	no	—
249	C₂×D₄×C₆₇	—	4	4	no	—
250	C₂×D₄×C₆₇	#41	1	8	yes	—
251	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
252	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
253	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
254	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
255	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
256	C₂²×C₄×C₆₇	—	2	8	no	—
257	C₂²×C₄×C₆₇	—	2	16	no	—
258	C₂²×C₄×C₆₇	—	2	4	no	—
259	C₂²×C₄×C₆₇	—	2	8	no	—
260	C₂²×C₄×C₆₇	—	2	8	no	—
261	C₂²×C₄×C₆₇	—	2	4	no	—
262	C₂²×C₄×C₆₇	—	4	4	no	—
263	C₂²×C₄×C₆₇	—	4	8	no	—
264	C₂²×C₄×C₆₇	—	4	2	no	—
265	C₂²×C₄×C₆₇	—	4	8	no	—
266	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
267	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
268	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
269	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
270	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
271	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
272	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
281	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
282	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
285	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
286	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
287	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
288	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
290	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
291	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
292	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
293	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
294	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
295	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
296	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
297	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
298	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
299	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
300	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
301	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
302	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
303	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
304	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
305	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
306	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
307	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
308	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
309	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
310	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
311	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
312	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
313	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
314	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
315	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
316	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
317	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
318	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
319	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
320	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
321	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
322	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
323	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
324	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
325	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
326	C₄²×C₆₇	C₂⁴	1	4	yes	—
327	C₄²×C₆₇	C₂⁴	1	8	yes	—
328	C₄²×C₆₇	C₂⁴	1	4	yes	—
329	C₄²×C₆₇	C₂⁴	1	4	yes	—
330	C₄²×C₆₇	C₂⁴	1	8	yes	—
331	C₄²×C₆₇	C₂⁴	1	4	yes	—
332	C₄²×C₆₇	C₂⁴	1	8	yes	—
333	C₄²×C₆₇	C₂⁴	1	16	yes	—
334	C₄²×C₆₇	C₂⁴	1	16	yes	—
335	C₄²×C₆₇	C₂⁴	1	8	yes	—
336	C₂³×C₆₇	—	2	4	no	—
337	C₂³×C₆₇	—	2	4	no	—
338	C₂³×C₆₇	—	2	2	no	—
339	C₂³×C₆₇	—	2	4	no	—
340	C₂³×C₆₇	—	2	2	no	—
341	C₂³×C₆₇	—	2	4	no	—
342	C₂³×C₆₇	—	2	4	no	—
343	C₂³×C₆₇	—	2	2	no	—
344	C₂³×C₆₇	C₂×#41	1	8	yes	—
345	C₂³×C₆₇	C₂⁵	1	2	yes	—
346	C₂³×C₆₇	C₂⁵	1	4	yes	—
347	C₂³×C₆₇	C₂⁵	1	4	yes	—
348	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
349	Q₈×C₆₇	—	2	8	no	—
350	Q₈×C₆₇	—	2	16	no	—
351	Q₈×C₆₇	—	2	8	no	—
352	Q₈×C₆₇	—	4	8	no	—
353	D₄×C₆₇	—	2	16	no	—
354	D₄×C₆₇	—	2	32	no	—
355	D₄×C₆₇	—	2	8	no	—
356	D₄×C₆₇	—	4	8	no	—
357	D₄×C₆₇	C₂×#41	1	16	yes	—
358	C₂×C₄×C₆₇	—	2	2	no	—
359	C₂×C₄×C₆₇	—	2	4	no	—
360	C₂×C₄×C₆₇	—	2	4	no	—
361	C₂×C₄×C₆₇	—	2	8	no	—
362	C₂×C₄×C₆₇	—	2	16	no	—
363	C₂×C₄×C₆₇	—	2	32	no	—
364	C₂×C₄×C₆₇	—	2	2	no	—
365	C₂×C₄×C₆₇	—	2	4	no	—
366	C₂×C₄×C₆₇	—	2	4	no	—
367	C₂×C₄×C₆₇	—	2	2	no	—
368	C₂×C₄×C₆₇	—	2	4	no	—
369	C₂×C₄×C₆₇	—	2	4	no	—
370	C₂×C₄×C₆₇	—	2	8	no	—
371	C₂×C₄×C₆₇	—	2	2	no	—
372	C₂×C₄×C₆₇	—	2	8	no	—
373	C₂×C₄×C₆₇	—	2	16	no	—
374	C₂×C₄×C₆₇	—	2	16	no	—
375	C₂×C₄×C₆₇	—	2	8	no	—
376	C₂×C₄×C₆₇	—	4	8	no	—
377	C₂×C₄×C₆₇	—	4	16	no	—
378	C₂×C₄×C₆₇	—	4	4	no	—
379	C₂×C₄×C₆₇	—	4	16	no	—
380	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
381	C₂×C₄×C₆₇	2₋¹⁺⁴	1	4	yes	—
382	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
383	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
384	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
385	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
386	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
387	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
388	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
389	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
390	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
391	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
392	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
393	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
394	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
395	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
396	C₂²×C₆₇	—	2	4	no	—
397	C₂²×C₆₇	—	2	4	no	—
398	C₂²×C₆₇	—	2	16	no	—
399	C₂²×C₆₇	—	2	2	no	—
400	C₂²×C₆₇	—	2	4	no	—
401	C₂²×C₆₇	—	2	2	no	—
402	C₂²×C₆₇	—	2	4	no	—
403	C₂²×C₆₇	—	2	4	no	—
404	C₂²×C₆₇	—	2	2	no	—
405	C₂²×C₆₇	—	4	4	no	—
406	C₂²×C₆₇	—	4	8	no	—
407	C₂²×C₆₇	C₂²×#41	1	8	yes	—
408	C₂²×C₆₇	C₂²×#41	1	2	yes	—
409	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	2	yes	—
410	C₂²×C₆₇	#585	1	2	yes	—
411	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
412	C₄×C₆₇	—	2	2	no	—
413	C₄×C₆₇	—	2	4	no	—
414	C₄×C₆₇	—	2	4	no	—
415	C₄×C₆₇	—	2	8	no	—
416	C₄×C₆₇	—	2	2	no	—
417	C₄×C₆₇	—	2	4	no	—
418	C₄×C₆₇	—	2	4	no	—
419	C₄×C₆₇	—	2	2	no	—
420	C₄×C₆₇	—	2	4	no	—
421	C₄×C₆₇	—	2	4	no	—
422	C₄×C₆₇	—	2	8	no	—
423	C₄×C₆₇	—	2	2	no	—
424	C₄×C₆₇	C₂²×#41	1	4	yes	—
425	C₄×C₆₇	C₂×2₋¹⁺⁴	1	4	yes	—
426	C₂×#3515	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
427	C₂×C₆₇	—	2	8	no	—
428	C₂×C₆₇	—	4	2	no	—
429	C₂×C₆₇	—	4	4	no	—
430	C₂×C₆₇	#3515	1	4	yes	direct product factor
431	C₂×C₆₇	C₂³×#41	1	1	yes	characteristic
432	C₂×C₆₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
433	C₂×C₆₇	C₂×#585	1	1	yes	characteristic
434	#3515	C₂×C₆₇	1	32	yes	direct product factor
435	C₂×#557	C₂×C₆₇	1	1	yes	characteristic, complemented
436	C₂×#554	C₂×C₆₇	1	1	yes	characteristic, complemented
437	C₂×#554	C₂×C₆₇	1	1	yes	characteristic, complemented
438	C₂×#553	C₂×C₆₇	1	2	yes	complemented
439	C₂×#552	C₂×C₆₇	1	2	yes	complemented
440	C₂×#552	C₂×C₆₇	1	4	yes	complemented
441	C₂×#552	C₂×C₆₇	1	2	yes	complemented
442	C₂×#547	C₂×C₆₇	1	1	yes	characteristic, complemented
443	C₂×#547	C₂×C₆₇	1	2	yes	complemented
444	C₂×#541	C₂×C₆₇	1	2	yes	complemented
445	C₂×#539	C₂×C₆₇	1	4	yes	complemented
446	C₂×#533	C₂×C₆₇	1	1	yes	characteristic, complemented
447	C₂×#529	C₂×C₆₇	1	1	yes	characteristic, complemented
448	C₂×#529	C₂×C₆₇	1	2	yes	complemented
449	C₂²×#125	C₂×C₆₇	1	2	yes	complemented
450	C₂×#520	C₂×C₆₇	1	2	yes	complemented
451	C₂×C₄×#41	C₂×C₆₇	1	1	yes	characteristic, complemented
452	C₆₇	C₂×#3515	1	1	yes	characteristic, direct product factor, Sylow
453	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
454	C₂²×#41	C₂²×C₆₇	1	2	yes	—
455	#557	C₂²×C₆₇	1	16	yes	complemented
456	#554	C₂²×C₆₇	1	16	yes	complemented
457	#554	C₂²×C₆₇	1	16	yes	complemented
458	#553	C₂²×C₆₇	1	32	yes	complemented
459	#552	C₂²×C₆₇	1	32	yes	complemented
460	#552	C₂²×C₆₇	1	64	yes	complemented
461	#552	C₂²×C₆₇	1	32	yes	complemented
462	#547	C₂²×C₆₇	1	16	yes	complemented
463	#547	C₂²×C₆₇	1	32	yes	complemented
464	#541	C₂²×C₆₇	1	32	yes	complemented
465	#539	C₂²×C₆₇	1	64	yes	complemented
466	#533	C₂²×C₆₇	1	16	yes	complemented
467	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
468	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
469	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
470	#529	C₂²×C₆₇	1	32	yes	complemented
471	#529	C₂²×C₆₇	1	16	yes	complemented
472	C₂×#126	C₂²×C₆₇	1	4	yes	—
473	C₂×#126	C₂²×C₆₇	1	2	yes	—
474	C₂×#126	C₂²×C₆₇	1	4	yes	—
475	C₂×#126	C₂²×C₆₇	1	4	yes	—
476	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic
477	C₂×#125	C₂²×C₆₇	1	2	yes	—
478	C₂×#125	C₂²×C₆₇	1	4	yes	—
479	C₂×#125	C₂²×C₆₇	1	4	yes	—
480	C₂×#125	C₂²×C₆₇	1	2	yes	—
481	C₂×#125	C₂²×C₆₇	1	2	yes	—
482	C₂×#125	C₂²×C₆₇	1	4	yes	—
483	C₂×#125	C₂²×C₆₇	1	4	yes	—
484	C₂×#125	C₂²×C₆₇	1	2	yes	—
485	C₂×#125	C₂²×C₆₇	1	32	yes	complemented
486	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
487	C₂×#123	C₂²×C₆₇	1	2	yes	—
488	C₂×#123	C₂²×C₆₇	1	4	yes	—
489	C₂×#123	C₂²×C₆₇	1	4	yes	—
490	C₂×#123	C₂²×C₆₇	1	4	yes	—
491	C₂×#123	C₂²×C₆₇	1	4	yes	—
492	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
493	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
494	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
495	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
496	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
497	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	4	yes	—
498	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
499	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
500	C₂×#121	C₂²×C₆₇	1	2	yes	—
501	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
502	C₂×#121	C₂²×C₆₇	1	4	yes	—
503	#520	C₂²×C₆₇	1	32	yes	complemented
504	C₄×#41	C₂²×C₆₇	1	16	yes	complemented
505	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
506	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
507	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
508	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
509	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
510	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
511	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
512	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
513	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
514	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
515	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
516	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
517	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
518	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	—
519	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
520	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
521	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
522	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
523	C₂×#117	C₂²×C₆₇	1	2	yes	—
524	C₂×#117	C₂²×C₆₇	1	2	yes	—
525	C₂×#117	C₂²×C₆₇	1	4	yes	—
526	C₂×#117	C₂²×C₆₇	1	4	yes	—
527	C₂×#117	C₂²×C₆₇	1	2	yes	—
528	C₂²×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
529	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
530	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
531	C₂²×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
532	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
533	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
534	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
535	C₂×#41	—	2	8	no	—
536	C₂×#41	—	2	16	no	—
537	C₂×#41	C₂³×C₆₇	1	8	yes	—
538	C₂×#41	C₂³×C₆₇	1	16	yes	—
539	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
540	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
541	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
542	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
543	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
544	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
545	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
546	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
547	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
548	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
549	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
550	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
551	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
552	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
553	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
554	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
555	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
556	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
557	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
558	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	—
559	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	—
560	C₄⋊Q₈	C₂³×C₆₇	1	16	yes	—
561	#126	C₂³×C₆₇	1	32	yes	—
562	#126	C₂³×C₆₇	1	16	yes	—
563	#126	C₂³×C₆₇	1	32	yes	—
564	#126	C₂³×C₆₇	1	32	yes	—
565	#125	C₂³×C₆₇	1	8	yes	—
566	#125	C₂³×C₆₇	1	16	yes	—
567	#125	C₂³×C₆₇	1	32	yes	—
568	#125	C₂³×C₆₇	1	32	yes	—
569	#125	C₂³×C₆₇	1	16	yes	—
570	#125	C₂³×C₆₇	1	16	yes	—
571	#125	C₂³×C₆₇	1	32	yes	—
572	#125	C₂³×C₆₇	1	32	yes	—
573	#125	C₂³×C₆₇	1	16	yes	—
574	#124	C₂³×C₆₇	1	8	yes	—
575	#123	C₂³×C₆₇	1	16	yes	—
576	#123	C₂³×C₆₇	1	32	yes	—
577	#123	C₂³×C₆₇	1	32	yes	—
578	#123	C₂³×C₆₇	1	32	yes	—
579	#123	C₂³×C₆₇	1	32	yes	—
580	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
581	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
582	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
583	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
584	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	—
585	C₂²⋊Q₈	C₂³×C₆₇	1	32	yes	—
586	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
587	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
588	#121	C₂³×C₆₇	1	16	yes	—
589	#121	C₂³×C₆₇	1	8	yes	—
590	#121	C₂³×C₆₇	1	32	yes	—
591	C₄×Q₈	C₂³×C₆₇	1	8	yes	—
592	C₄×Q₈	C₂³×C₆₇	1	8	yes	—
593	C₄×Q₈	C₂³×C₆₇	1	16	yes	—
594	C₄×Q₈	C₂³×C₆₇	1	16	yes	—
595	C₄×Q₈	C₂³×C₆₇	1	16	yes	—
596	C₄×Q₈	C₂³×C₆₇	1	8	yes	—
597	C₄×Q₈	C₂³×C₆₇	1	16	yes	—
598	C₄×D₄	C₂³×C₆₇	1	8	yes	—
599	C₄×D₄	C₂³×C₆₇	1	16	yes	—
600	C₄×D₄	C₂³×C₆₇	1	8	yes	—
601	C₄×D₄	C₂³×C₆₇	1	16	yes	—
602	C₄×D₄	C₂³×C₆₇	1	32	yes	—
603	C₄×D₄	C₂³×C₆₇	1	16	yes	—
604	C₄×D₄	C₂³×C₆₇	1	32	yes	—
605	C₄×D₄	C₂³×C₆₇	1	16	yes	—
606	C₄×D₄	C₂³×C₆₇	1	8	yes	—
607	C₄×D₄	C₂³×C₆₇	1	16	yes	—
608	#117	C₂³×C₆₇	1	8	yes	—
609	#117	C₂³×C₆₇	1	16	yes	—
610	#117	C₂³×C₆₇	1	16	yes	—
611	#117	C₂³×C₆₇	1	32	yes	—
612	#117	C₂³×C₆₇	1	32	yes	—
613	#117	C₂³×C₆₇	1	16	yes	—
614	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
616	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
623	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
625	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
626	C₂×C₄⋊C₄	C₂³×C₆₇	1	32	yes	—
627	C₂×C₄⋊C₄	C₂³×C₆₇	1	16	yes	—
628	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
629	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
630	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
631	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
632	C₂×C₄⋊C₄	C₂³×C₆₇	1	16	yes	—
633	C₂×C₄⋊C₄	C₂³×C₆₇	1	32	yes	—
634	C₂×C₄⋊C₄	C₂³×C₆₇	1	16	yes	—
635	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
640	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
655	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
656	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
658	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
659	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
660	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
661	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
662	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
664	C₂×C₄²	C₂³×C₆₇	1	16	yes	—
665	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
666	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
667	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
668	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
669	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
670	#41	—	2	32	no	—
671	#41	—	2	64	no	—
672	C₂×Q₈	—	2	4	no	—
673	C₂×Q₈	—	2	8	no	—
674	C₂×Q₈	—	2	4	no	—
675	C₂×Q₈	—	4	4	no	—
676	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
677	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
678	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
679	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
680	C₂×D₄	—	2	8	no	—
681	C₂×D₄	—	2	16	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	4	4	no	—
684	C₂×D₄	#41×C₆₇	1	8	yes	—
685	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
686	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
687	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
688	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
689	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
690	C₂²×C₄	—	2	16	no	—
691	C₂²×C₄	—	2	8	no	—
692	C₂²×C₄	—	2	8	no	—
693	C₂²×C₄	—	2	4	no	—
694	C₂²×C₄	—	2	8	no	—
695	C₂²×C₄	—	2	4	no	—
696	C₂²×C₄	—	4	4	no	—
697	C₂²×C₄	—	4	8	no	—
698	C₂²×C₄	—	4	2	no	—
699	C₂²×C₄	—	4	8	no	—
700	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
701	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
702	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
704	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
708	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
710	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
711	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
712	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
713	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
714	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
717	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
718	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
719	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
720	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
721	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
722	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
724	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
725	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
726	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
727	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
728	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
729	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
730	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
731	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
732	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
733	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
734	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
735	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
736	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
737	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
738	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
739	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
740	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
741	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
742	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
743	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
744	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
745	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
746	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
747	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
748	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
749	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
750	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
751	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
752	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
753	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
754	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
755	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
756	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
757	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
758	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
759	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
760	C₄²	C₂⁴×C₆₇	1	4	yes	—
761	C₄²	C₂⁴×C₆₇	1	8	yes	—
762	C₄²	C₂⁴×C₆₇	1	4	yes	—
763	C₄²	C₂⁴×C₆₇	1	4	yes	—
764	C₄²	C₂⁴×C₆₇	1	8	yes	—
765	C₄²	C₂⁴×C₆₇	1	4	yes	—
766	C₄²	C₂⁴×C₆₇	1	8	yes	—
767	C₄²	C₂⁴×C₆₇	1	16	yes	—
768	C₄²	C₂⁴×C₆₇	1	16	yes	—
769	C₄²	C₂⁴×C₆₇	1	8	yes	—
770	C₂³	—	2	4	no	—
771	C₂³	—	2	4	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	4	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	4	no	—
776	C₂³	—	2	4	no	—
777	C₂³	—	2	2	no	—
778	C₂³	C₂×#41×C₆₇	1	8	yes	—
779	C₂³	C₂⁵×C₆₇	1	2	yes	—
780	C₂³	C₂⁵×C₆₇	1	4	yes	—
781	C₂³	C₂⁵×C₆₇	1	4	yes	—
782	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
783	Q₈	—	2	8	no	—
784	Q₈	—	2	16	no	—
785	Q₈	—	2	8	no	—
786	Q₈	—	4	8	no	—
787	D₄	—	2	16	no	—
788	D₄	—	2	32	no	—
789	D₄	—	2	8	no	—
790	D₄	—	4	8	no	—
791	D₄	C₂×#41×C₆₇	1	16	yes	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	4	no	—
794	C₂×C₄	—	2	8	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	16	no	—
797	C₂×C₄	—	2	32	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	4	no	—
804	C₂×C₄	—	2	8	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	8	no	—
807	C₂×C₄	—	2	16	no	—
808	C₂×C₄	—	2	16	no	—
809	C₂×C₄	—	2	8	no	—
810	C₂×C₄	—	4	8	no	—
811	C₂×C₄	—	4	16	no	—
812	C₂×C₄	—	4	4	no	—
813	C₂×C₄	—	4	16	no	—
814	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
815	C₂×C₄	2₋¹⁺⁴×C₆₇	1	4	yes	—
816	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
817	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
818	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
819	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
820	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
821	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
822	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
823	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
824	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
825	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
826	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
827	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
828	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
829	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
830	C₂²	—	2	4	no	—
831	C₂²	—	2	4	no	—
832	C₂²	—	2	16	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	4	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	2	4	no	—
837	C₂²	—	2	4	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	4	4	no	—
840	C₂²	—	4	8	no	—
841	C₂²	C₂²×#41×C₆₇	1	8	yes	—
842	C₂²	C₂²×#41×C₆₇	1	2	yes	—
843	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	2	yes	—
844	C₂²	#585×C₆₇	1	2	yes	—
845	C₂²	C₂⁶×C₆₇	1	1	yes	characteristic
846	C₄	—	2	2	no	—
847	C₄	—	2	4	no	—
848	C₄	—	2	4	no	—
849	C₄	—	2	8	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	4	no	—
852	C₄	—	2	4	no	—
853	C₄	—	2	2	no	—
854	C₄	—	2	4	no	—
855	C₄	—	2	4	no	—
856	C₄	—	2	8	no	—
857	C₄	—	2	2	no	—
858	C₄	C₂²×#41×C₆₇	1	4	yes	—
859	C₄	C₂×2₋¹⁺⁴×C₆₇	1	4	yes	—
860	C₂	—	2	8	no	—
861	C₂	—	4	2	no	—
862	C₂	—	4	4	no	—
863	C₂	C₆₇×#3515	1	4	yes	direct product factor
864	C₂	C₂³×#41×C₆₇	1	1	yes	characteristic
865	C₂	C₂²×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
866	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×#3515	C₂	direct (N × H)
2. C₂×#557×C₆₇	C₂	semidirect
3. C₂×#554×C₆₇	C₂	semidirect
4. C₂×#554×C₆₇	C₂	semidirect
5. C₂×#553×C₆₇	C₂	semidirect
6. C₂×#552×C₆₇	C₂	semidirect
7. C₂×#552×C₆₇	C₂	semidirect
8. C₂×#552×C₆₇	C₂	semidirect
9. C₂×#547×C₆₇	C₂	semidirect
10. C₂×#547×C₆₇	C₂	semidirect
11. C₂×#541×C₆₇	C₂	semidirect
12. C₂×#539×C₆₇	C₂	semidirect
13. C₂×#533×C₆₇	C₂	semidirect
14. C₂×#529×C₆₇	C₂	semidirect
15. C₂×#529×C₆₇	C₂	semidirect
16. C₂²×#125×C₆₇	C₂	semidirect
17. C₂×#520×C₆₇	C₂	semidirect
18. C₂×C₄×#41×C₆₇	C₂	semidirect
21. #557×C₆₇	C₂²	semidirect
22. #554×C₆₇	C₂²	semidirect
23. #554×C₆₇	C₂²	semidirect
24. #553×C₆₇	C₂²	semidirect
25. #552×C₆₇	C₂²	semidirect
26. #552×C₆₇	C₂²	semidirect
27. #552×C₆₇	C₂²	semidirect
28. #547×C₆₇	C₂²	semidirect
29. #547×C₆₇	C₂²	semidirect
30. #541×C₆₇	C₂²	semidirect
31. #539×C₆₇	C₂²	semidirect
32. #533×C₆₇	C₂²	semidirect
36. #529×C₆₇	C₂²	semidirect
37. #529×C₆₇	C₂²	semidirect
51. C₂×#125×C₆₇	C₂²	semidirect
69. #520×C₆₇	C₂²	semidirect
70. C₄×#41×C₆₇	C₂²	semidirect
426. C₂×#3515	C₆₇	direct (N × H)
430. C₂×C₆₇	#3515	direct (N × H)
434. #3515	C₂×C₆₇	direct (N × H)
435. C₂×#557	C₂×C₆₇	semidirect
436. C₂×#554	C₂×C₆₇	semidirect
437. C₂×#554	C₂×C₆₇	semidirect
438. C₂×#553	C₂×C₆₇	semidirect
439. C₂×#552	C₂×C₆₇	semidirect
440. C₂×#552	C₂×C₆₇	semidirect
441. C₂×#552	C₂×C₆₇	semidirect
442. C₂×#547	C₂×C₆₇	semidirect
443. C₂×#547	C₂×C₆₇	semidirect
444. C₂×#541	C₂×C₆₇	semidirect
445. C₂×#539	C₂×C₆₇	semidirect
446. C₂×#533	C₂×C₆₇	semidirect
447. C₂×#529	C₂×C₆₇	semidirect
448. C₂×#529	C₂×C₆₇	semidirect
449. C₂²×#125	C₂×C₆₇	semidirect
450. C₂×#520	C₂×C₆₇	semidirect
451. C₂×C₄×#41	C₂×C₆₇	semidirect
452. C₆₇	C₂×#3515	direct (N × H)
455. #557	C₂²×C₆₇	semidirect
456. #554	C₂²×C₆₇	semidirect
457. #554	C₂²×C₆₇	semidirect
458. #553	C₂²×C₆₇	semidirect
459. #552	C₂²×C₆₇	semidirect
460. #552	C₂²×C₆₇	semidirect
461. #552	C₂²×C₆₇	semidirect
462. #547	C₂²×C₆₇	semidirect
463. #547	C₂²×C₆₇	semidirect
464. #541	C₂²×C₆₇	semidirect
465. #539	C₂²×C₆₇	semidirect
466. #533	C₂²×C₆₇	semidirect
470. #529	C₂²×C₆₇	semidirect
471. #529	C₂²×C₆₇	semidirect
485. C₂×#125	C₂²×C₆₇	semidirect
503. #520	C₂²×C₆₇	semidirect
504. C₄×#41	C₂²×C₆₇	semidirect
863. C₂	C₆₇×#3515	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×#3515	2
C₂×#557×C₆₇	2
C₂×#554×C₆₇	2
C₂×#553×C₆₇	2
C₂×#552×C₆₇	2
C₂×#547×C₆₇	2
C₂×#541×C₆₇	2
C₂×#539×C₆₇	2
C₂×#533×C₆₇	2
C₂×#529×C₆₇	2
C₂²×#125×C₆₇	2
C₂×#520×C₆₇	2
C₂×C₄×#41×C₆₇	2
C₂×#3515	67

Subgroups — C2×C67×#3515 #30742030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3515 #30742030