Subgroups — #22574139

Order 8576.

1152 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864130	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864100	C₂	1	1	yes	maximal, characteristic, complemented
3	#16864099	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864097	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864089	C₂	1	1	yes	maximal, characteristic, complemented
6	#16864078	C₂	1	1	yes	maximal, characteristic, complemented
7	#16864073	C₂	1	1	yes	maximal, characteristic, complemented
8	#16864071	C₂	1	1	yes	maximal, characteristic, complemented
9	#16864069	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864069	C₂	1	1	yes	maximal, characteristic, complemented
11	#16864048	C₂	1	1	yes	maximal, characteristic, complemented
12	#16864038	C₂	1	1	yes	maximal, characteristic, complemented
13	#16864038	C₂	1	1	yes	maximal, characteristic, complemented
14	#16864038	C₂	1	1	yes	maximal, characteristic, complemented
15	#16864037	C₂	1	1	yes	maximal, characteristic, complemented
16	#16864030	C₂	1	1	yes	maximal, characteristic, complemented
17	#16864016	C₂	1	1	yes	maximal, characteristic, complemented
18	#16863998	C₂	1	1	yes	maximal, characteristic, complemented
19	#16863994	C₂	1	1	yes	maximal, characteristic, complemented
20	#16863985	C₂	1	1	yes	maximal, characteristic, complemented
21	#16863979	C₂	1	1	yes	maximal, characteristic, complemented
22	#16863931	C₂	1	1	yes	maximal, characteristic, complemented
23	#16863929	C₂	1	1	yes	maximal, characteristic, complemented
24	#16863909	C₂	1	1	yes	maximal, characteristic, complemented
25	#16863905	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×#14524028	C₂	1	1	yes	maximal, characteristic, complemented
27	#123×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
28	#16863877	C₂	1	1	yes	maximal, characteristic, complemented
29	#16863868	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×D₄×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
31	#539×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#11761629	C₂²	1	1	yes	characteristic, complemented
33	C₂×#11761628	C₂²	1	1	yes	characteristic
34	C₂×#11761628	C₂²	1	1	yes	characteristic, complemented
35	C₂²×D₂₆₈	C₂²	1	1	yes	characteristic
36	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic
37	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic
38	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic
39	C₂²×C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
41	#14524041	C₂²	1	1	yes	characteristic, complemented
42	#14524039	C₂²	1	1	yes	characteristic
43	#14524038	C₂²	1	1	yes	characteristic, complemented
44	#14524038	C₂²	1	1	yes	characteristic, complemented
45	#14524038	C₂²	1	1	yes	characteristic, complemented
46	#14524038	C₂²	1	1	yes	characteristic, complemented
47	#14524038	C₂²	1	1	yes	characteristic, complemented
48	#14524038	C₂²	1	1	yes	characteristic, complemented
49	#14524037	C₂²	1	1	yes	characteristic, complemented
50	#14524036	C₂²	1	1	yes	characteristic, complemented
51	#14524033	C₂²	1	1	yes	characteristic, complemented
52	#14524033	C₂²	1	1	yes	characteristic, complemented
53	#14524033	C₂²	1	1	yes	characteristic, complemented
54	#14524032	C₂²	1	1	yes	characteristic, complemented
55	#14524031	C₂²	1	1	yes	characteristic, complemented
56	#14524029	C₂²	1	1	yes	characteristic, complemented
57	#14524029	C₂²	1	1	yes	characteristic, complemented
58	#14524029	C₂²	1	1	yes	characteristic, complemented
59	#14524029	C₂²	1	1	yes	characteristic, complemented
60	#14524029	C₂²	1	1	yes	characteristic, complemented
61	#14524028	C₂²	1	1	yes	characteristic
62	#14524028	C₂²	1	1	yes	characteristic
63	#14524028	C₂²	1	1	yes	characteristic
64	#14524028	C₂²	1	1	yes	characteristic, complemented
65	#14524028	C₂²	1	1	yes	characteristic, complemented
66	#14524028	C₂²	1	1	yes	characteristic, complemented
67	#14524028	C₂²	1	1	yes	characteristic, complemented
68	#14524028	C₂²	1	1	yes	characteristic, complemented
69	#14524028	C₂²	1	1	yes	characteristic, complemented
70	#14524028	C₂²	1	1	yes	characteristic, complemented
71	#14524028	C₂²	1	1	yes	characteristic, complemented
72	#14524028	C₂²	1	1	yes	characteristic, complemented
73	#14524028	C₂²	1	1	yes	characteristic, complemented
74	#14524028	C₂²	1	1	yes	characteristic, complemented
75	#14524027	C₂²	1	1	yes	characteristic, complemented
76	#14524027	C₂²	1	1	yes	characteristic, complemented
77	#14524026	C₂²	1	1	yes	characteristic, complemented
78	#14524025	C₂²	1	1	yes	characteristic, complemented
79	#14524025	C₂²	1	1	yes	characteristic, complemented
80	#14524025	C₂²	1	1	yes	characteristic, complemented
81	#14524025	C₂²	1	1	yes	characteristic, complemented
82	#14524024	C₂²	1	1	yes	characteristic, complemented
83	#14524023	C₂²	1	1	yes	characteristic, complemented
84	#14524023	C₂²	1	1	yes	characteristic, complemented
85	#14524021	C₂²	1	1	yes	characteristic, complemented
86	#14524021	C₂²	1	1	yes	characteristic, complemented
87	#14524021	C₂²	1	1	yes	characteristic, complemented
88	#14524021	C₂²	1	1	yes	characteristic, complemented
89	#14524021	C₂²	1	1	yes	characteristic, complemented
90	#14524020	C₂²	1	1	yes	characteristic, complemented
91	#14524020	C₂²	1	1	yes	characteristic, complemented
92	#14524019	C₂²	1	1	yes	characteristic, complemented
93	#14524018	C₂²	1	1	yes	characteristic
94	#14524018	C₂²	1	1	yes	characteristic
95	#14524018	C₂²	1	1	yes	characteristic, complemented
96	#14524018	C₂²	1	1	yes	characteristic, complemented
97	#14524018	C₂²	1	1	yes	characteristic, complemented
98	#14524018	C₂²	1	1	yes	characteristic, complemented
99	#14524017	C₂²	1	1	yes	characteristic, complemented
100	#14524016	C₂²	1	1	yes	characteristic
101	#14524016	C₂²	1	1	yes	characteristic
102	#14524016	C₂²	1	1	yes	characteristic, complemented
103	#14524016	C₂²	1	1	yes	characteristic, complemented
104	#14524016	C₂²	1	1	yes	characteristic, complemented
105	#14524016	C₂²	1	1	yes	characteristic, complemented
106	#14524015	C₂²	1	1	yes	characteristic, complemented
107	#14524015	C₂²	1	1	yes	characteristic, complemented
108	#14524015	C₂²	1	1	yes	characteristic, complemented
109	#14524013	C₂²	1	1	yes	characteristic
110	#14524013	C₂²	1	1	yes	characteristic
111	#14524013	C₂²	1	1	yes	characteristic, complemented
112	#14524013	C₂²	1	1	yes	characteristic, complemented
113	#14524013	C₂²	1	1	yes	characteristic, complemented
114	#14524013	C₂²	1	1	yes	characteristic, complemented
115	#14524011	C₂²	1	1	yes	characteristic
116	#14524011	C₂²	1	1	yes	characteristic
117	#14524008	C₂²	1	1	yes	characteristic, complemented
118	#14524008	C₂²	1	1	yes	characteristic, complemented
119	#14524008	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
123	D₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
124	D₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
125	#14524005	C₂²	1	1	yes	characteristic
126	#14524005	C₂²	1	1	yes	characteristic, complemented
127	#14524005	C₂²	1	1	yes	characteristic, complemented
128	#14524005	C₂²	1	1	yes	characteristic, complemented
129	#14524005	C₂²	1	1	yes	characteristic, complemented
130	#14524005	C₂²	1	1	yes	characteristic, complemented
131	#14524005	C₂²	1	1	yes	characteristic, complemented
132	#14524005	C₂²	1	1	yes	characteristic, complemented
133	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
134	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
135	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
136	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
137	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
138	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
139	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
140	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
141	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
142	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
143	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
144	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
145	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
146	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
147	#14524002	C₂²	1	1	yes	characteristic, complemented
148	#14524001	C₂²	1	1	yes	characteristic, complemented
149	#14524001	C₂²	1	1	yes	characteristic, complemented
150	#14524001	C₂²	1	1	yes	characteristic, complemented
151	#14524001	C₂²	1	1	yes	characteristic, complemented
152	#14524001	C₂²	1	1	yes	characteristic, complemented
153	#14524000	C₂²	1	1	yes	characteristic, complemented
154	#14524000	C₂²	1	1	yes	characteristic, complemented
155	#14523999	C₂²	1	1	yes	characteristic, complemented
156	C₂×Dic₆₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
157	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
158	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
159	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
160	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
161	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
162	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
163	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
164	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
165	C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
166	C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
167	C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
168	C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
169	C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
170	C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
171	C₄²×D₆₇	C₂²	1	1	yes	characteristic, complemented
172	#126×C₆₇	C₂²	1	1	yes	characteristic, complemented
173	#126×C₆₇	C₂²	1	1	yes	characteristic, complemented
174	#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
175	#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
176	#123×C₆₇	C₂²	1	1	yes	characteristic, complemented
177	#123×C₆₇	C₂²	1	1	yes	characteristic, complemented
178	#123×C₆₇	C₂²	1	1	yes	characteristic, complemented
179	#123×C₆₇	C₂²	1	1	yes	characteristic, complemented
180	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
181	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
182	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
183	#121×C₆₇	C₂²	1	1	yes	characteristic
184	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
185	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
186	C₂×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₆₇	C₂³	1	1	yes	characteristic
188	C₂³×D₆₇	C₂³	1	1	yes	characteristic
189	C₂³×D₆₇	C₂³	1	1	yes	characteristic
190	C₂³×D₆₇	C₂³	1	1	yes	characteristic
191	#11761629	—	4	2	no	—
192	#11761628	—	2	4	no	—
193	#11761628	—	4	2	no	—
194	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
195	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
196	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
197	C₂×D₂₆₈	—	4	2	no	—
198	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
199	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
200	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
201	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
202	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
203	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
204	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
205	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
206	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
207	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
208	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
216	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
217	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
218	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
219	D₄×D₆₇	—	2	4	no	—
220	D₄×D₆₇	—	2	4	no	—
221	D₄×D₆₇	—	4	2	no	—
222	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
223	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
224	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
225	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₆₇	—	4	2	no	—
227	C₂×C₄×D₆₇	—	4	2	no	—
228	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
240	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
243	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
244	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
245	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
246	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
247	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
248	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
249	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
250	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
251	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
252	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
253	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
254	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
255	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
256	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
257	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
258	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
259	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
260	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
261	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
262	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
263	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
264	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
265	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
266	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
267	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
273	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
274	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
275	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
276	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
277	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
278	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
279	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
280	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
281	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
282	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
283	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
284	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
285	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
286	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
287	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
288	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
289	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
293	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
294	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
295	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
296	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
297	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
298	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
299	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
300	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
301	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
302	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
303	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
304	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
305	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
306	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
307	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
308	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
309	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
310	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
311	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
312	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
313	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
314	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
315	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
316	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
317	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
318	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
319	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
320	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
321	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
322	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
323	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
324	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
325	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
326	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
327	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
328	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
329	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
330	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
331	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
332	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
333	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
334	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
335	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
336	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
337	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
338	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
339	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
340	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
341	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
342	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
343	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
344	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
345	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
346	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
347	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
348	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
349	C₄²×C₆₇	C₂³	1	1	yes	characteristic
350	C₄²×C₆₇	C₂³	1	1	yes	characteristic
351	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
352	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
353	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
354	C₂²×D₆₇	—	2	2	no	—
355	C₂²×D₆₇	—	2	2	no	—
356	C₂²×D₆₇	—	2	2	no	—
357	C₂²×D₆₇	—	2	2	no	—
358	C₂²×D₆₇	—	2	2	no	—
359	C₂²×D₆₇	—	2	2	no	—
360	C₂²×D₆₇	—	4	1	no	—
361	C₂²×D₆₇	—	4	1	no	—
362	C₂²×D₆₇	—	4	1	no	—
363	C₂²×D₆₇	—	4	1	no	—
364	C₂²×D₆₇	—	4	1	no	—
365	C₂²×D₆₇	—	4	1	no	—
366	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
367	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
368	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
369	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
370	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
371	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
372	Q₈×C₆₇	—	4	1	no	—
373	D₄×C₆₇	—	2	2	no	—
374	D₄×C₆₇	—	2	2	no	—
375	D₄×C₆₇	—	4	1	no	—
376	C₂×C₄×C₆₇	—	2	2	no	—
377	C₂×C₄×C₆₇	—	4	1	no	—
378	C₂×C₄×C₆₇	—	4	1	no	—
379	C₂×C₄×C₆₇	—	4	1	no	—
380	C₂×C₄×C₆₇	—	4	1	no	—
381	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
382	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
383	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
384	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
385	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
386	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
387	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
388	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
389	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
390	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
391	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
392	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
393	C₂²⋊D₆₇	—	2	2	no	—
394	C₂²⋊D₆₇	—	2	2	no	—
395	C₂²⋊D₆₇	—	2	2	no	—
396	C₂²⋊D₆₇	—	2	2	no	—
397	C₂²⋊D₆₇	—	4	1	no	—
398	C₂²⋊D₆₇	—	4	1	no	—
399	C₂²⋊D₆₇	—	4	1	no	—
400	C₂²⋊D₆₇	—	4	1	no	—
401	C₂²⋊D₆₇	—	4	1	no	—
402	C₂²⋊D₆₇	#41	1	4	yes	complemented
403	C₂×Dic₆₇	—	4	1	no	—
404	C₂×Dic₆₇	—	4	1	no	—
405	C₂×Dic₆₇	—	4	1	no	—
406	C₂×Dic₆₇	—	4	1	no	—
407	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
408	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
409	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
410	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
411	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
412	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
413	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
414	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
415	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
416	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
417	D₂₆₈	—	2	2	no	—
418	D₂₆₈	—	2	2	no	—
419	D₂₆₈	—	2	2	no	—
420	D₂₆₈	—	2	2	no	—
421	D₂₆₈	—	2	2	no	—
422	D₂₆₈	—	2	2	no	—
423	D₂₆₈	—	4	1	no	—
424	D₂₆₈	—	4	1	no	—
425	D₂₆₈	—	4	1	no	—
426	D₂₆₈	—	4	1	no	—
427	D₂₆₈	—	4	1	no	—
428	C₄×D₆₇	—	2	2	no	—
429	C₄×D₆₇	—	2	2	no	—
430	C₄×D₆₇	—	2	2	no	—
431	C₄×D₆₇	—	2	2	no	—
432	C₄×D₆₇	—	2	2	no	—
433	C₄×D₆₇	—	2	2	no	—
434	C₄×D₆₇	—	2	2	no	—
435	C₄×D₆₇	—	4	1	no	—
436	C₄×D₆₇	—	4	1	no	—
437	C₄×D₆₇	—	4	1	no	—
438	C₄×D₆₇	—	4	1	no	—
439	C₄×D₆₇	—	4	1	no	—
440	C₄×D₆₇	—	4	1	no	—
441	C₄×D₆₇	—	4	1	no	—
442	C₄×D₆₇	—	4	1	no	—
443	C₄×D₆₇	—	4	1	no	—
444	C₄×D₆₇	—	4	1	no	—
445	C₄×D₆₇	—	4	1	no	—
446	Dic₁₃₄	—	2	2	no	—
447	Dic₁₃₄	—	4	1	no	—
448	Dic₁₃₄	—	4	1	no	—
449	C₂²×C₆₇	—	2	1	no	—
450	C₂²×C₆₇	—	2	1	no	—
451	C₂²×C₆₇	—	2	1	no	—
452	C₂²×C₆₇	—	2	1	no	—
453	C₂²×C₆₇	—	2	1	no	—
454	C₂²×C₆₇	—	2	1	no	—
455	C₂²×C₆₇	—	2	1	no	—
456	C₂²×C₆₇	—	2	1	no	—
457	C₂²×C₆₇	C₂×#41	1	2	yes	—
458	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
459	C₂×D₆₇	—	2	1	no	—
460	C₂×D₆₇	—	2	1	no	—
461	C₂×D₆₇	—	2	1	no	—
462	C₂×D₆₇	—	2	1	no	—
463	C₂×D₆₇	—	2	1	no	—
464	C₂×D₆₇	—	2	1	no	—
465	C₂×D₆₇	—	2	1	no	—
466	C₂×D₆₇	—	2	1	no	—
467	C₂×D₆₇	—	2	1	no	—
468	C₂×D₆₇	—	2	1	no	—
469	C₂×D₆₇	—	2	1	no	—
470	C₂×D₆₇	—	2	1	no	—
471	C₂×D₆₇	—	2	1	no	—
472	C₂×D₆₇	—	2	1	no	—
473	C₂×D₆₇	—	2	1	no	—
474	C₂×D₆₇	—	2	1	no	—
475	C₂×D₆₇	—	4	4	no	—
476	C₂×D₆₇	—	4	4	no	—
477	C₂×D₆₇	—	8	2	no	—
478	C₂×D₆₇	—	8	2	no	—
479	C₂×D₆₇	C₂×#41	1	2	yes	—
480	C₂×D₆₇	H(5,𝔽₂)	1	2	yes	—
481	C₄×C₆₇	—	2	1	no	—
482	C₄×C₆₇	—	2	1	no	—
483	C₄×C₆₇	—	2	1	no	—
484	C₄×C₆₇	—	2	1	no	—
485	C₄×C₆₇	—	2	1	no	—
486	C₄×C₆₇	—	2	1	no	—
487	C₄×C₆₇	—	2	1	no	—
488	C₄×C₆₇	—	2	1	no	—
489	C₄×C₆₇	—	2	1	no	—
490	C₄×C₆₇	—	2	1	no	—
491	C₄×C₆₇	—	2	1	no	—
492	C₄×C₆₇	—	2	1	no	—
493	Dic₆₇	—	2	1	no	—
494	Dic₆₇	—	2	1	no	—
495	Dic₆₇	—	2	1	no	—
496	Dic₆₇	—	2	1	no	—
497	Dic₆₇	—	2	1	no	—
498	Dic₆₇	—	2	1	no	—
499	Dic₆₇	—	2	1	no	—
500	Dic₆₇	—	2	1	no	—
501	Dic₆₇	—	2	1	no	—
502	Dic₆₇	C₂×#41	1	2	yes	—
503	C₂×C₆₇	—	2	2	no	—
504	C₂×C₆₇	—	4	1	no	—
505	C₂×C₆₇	—	4	1	no	—
506	C₂×C₆₇	C₂²×#41	1	1	yes	characteristic
507	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
508	C₂×C₆₇	#585	1	1	yes	characteristic
509	D₆₇	—	2	2	no	—
510	D₆₇	—	2	2	no	—
511	D₆₇	—	4	1	no	—
512	D₆₇	—	4	1	no	—
513	D₆₇	—	4	1	no	—
514	D₆₇	—	4	1	no	—
515	#3513	—	67	1	no	maximal, Sylow
516	C₆₇	#3513	1	1	yes	characteristic, complemented, Sylow
517	#559	—	67	1	no	—
518	#554	—	67	1	no	—
519	#553	—	67	1	no	—
520	#553	—	67	1	no	—
521	#553	—	67	1	no	—
522	#552	—	67	1	no	—
523	#551	—	67	1	no	—
524	#551	—	67	1	no	—
525	#551	—	67	1	no	—
526	#551	—	67	1	no	—
527	#547	—	67	1	no	—
528	#546	—	67	1	no	—
529	#546	—	67	1	no	—
530	#546	—	67	1	no	—
531	#546	—	67	1	no	—
532	D₄²	—	67	1	no	—
533	#542	—	67	1	no	—
534	#540	—	67	1	no	—
535	#539	—	67	1	no	—
536	#539	D₆₇	1	1	yes	characteristic, complemented
537	#538	—	67	1	no	—
538	#538	—	67	1	no	—
539	#529	—	67	1	no	—
540	#529	—	67	1	no	—
541	#525	—	67	1	no	—
542	#525	—	67	1	no	—
543	C₂×#123	—	67	1	no	—
544	C₂×#123	—	67	1	no	—
545	#520	—	67	1	no	—
546	#518	—	67	1	no	—
547	C₂×C₄×D₄	—	67	1	no	—
548	C₂×#41	—	67	1	no	—
549	C₂×#41	—	67	1	no	—
550	C₂×#41	—	67	1	no	—
551	C₂²×D₄	—	67	1	no	—
552	C₂²×D₄	—	67	1	no	—
553	C₂²×D₄	—	67	1	no	—
554	C₂²×D₄	—	67	1	no	—
555	C₂³×C₄	—	67	1	no	—
556	C₂³×C₄	—	67	1	no	—
557	C₄⋊Q₈	—	67	1	no	—
558	#127	—	67	1	no	—
559	#126	—	67	1	no	—
560	#126	—	67	1	no	—
561	#126	—	67	1	no	—
562	#126	—	67	1	no	—
563	#126	—	67	1	no	—
564	#126	—	67	1	no	—
565	#126	—	67	1	no	—
566	#126	—	67	1	no	—
567	#126	C₂×D₆₇	1	1	yes	characteristic, complemented
568	#126	C₂×D₆₇	1	1	yes	characteristic, complemented
569	#125	—	67	1	no	—
570	#125	—	67	1	no	—
571	#125	—	67	1	no	—
572	#125	C₂×D₆₇	1	1	yes	characteristic, complemented
573	#125	C₂×D₆₇	1	1	yes	characteristic, complemented
574	#124	—	67	1	no	—
575	#124	—	67	1	no	—
576	#124	—	67	1	no	—
577	#124	—	67	1	no	—
578	#124	—	67	1	no	—
579	#124	—	67	1	no	—
580	#124	—	67	1	no	—
581	#123	—	67	1	no	—
582	#123	—	67	1	no	—
583	#123	—	67	1	no	—
584	#123	—	67	1	no	—
585	#123	—	67	1	no	—
586	#123	—	67	1	no	—
587	#123	—	67	1	no	—
588	#123	—	67	1	no	—
589	#123	—	67	1	no	—
590	#123	—	67	1	no	—
591	#123	—	67	1	no	—
592	#123	—	67	1	no	—
593	#123	—	67	1	no	—
594	#123	—	67	1	no	—
595	#123	—	67	1	no	—
596	#123	—	67	1	no	—
597	#123	—	67	1	no	—
598	#123	—	67	1	no	—
599	#123	—	67	1	no	—
600	#123	—	67	1	no	—
601	#123	—	67	1	no	—
602	#123	—	67	1	no	—
603	#123	C₂×D₆₇	1	1	yes	characteristic, complemented
604	#123	C₂×D₆₇	1	1	yes	characteristic, complemented
605	#123	C₂×D₆₇	1	1	yes	characteristic, complemented
606	#123	C₂×D₆₇	1	1	yes	characteristic, complemented
607	C₂²⋊Q₈	—	67	1	no	—
608	C₂²⋊Q₈	—	67	1	no	—
609	C₂²⋊Q₈	—	67	1	no	—
610	C₂²⋊Q₈	—	67	1	no	—
611	C₂²⋊Q₈	—	67	1	no	—
612	C₂²⋊Q₈	—	67	1	no	—
613	C₂²⋊Q₈	—	67	1	no	—
614	C₂²⋊Q₈	—	67	1	no	—
615	C₂²⋊Q₈	—	67	1	no	—
616	C₂²⋊Q₈	—	67	1	no	—
617	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
618	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
619	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
620	#121	—	67	1	no	—
621	#121	—	67	1	no	—
622	#121	—	67	1	no	—
623	#121	—	67	1	no	—
624	#121	—	67	1	no	—
625	#121	—	67	1	no	—
626	#121	—	67	1	no	—
627	#121	—	67	1	no	—
628	#121	—	67	1	no	—
629	#121	—	67	1	no	—
630	#121	—	67	1	no	—
631	#121	—	67	1	no	—
632	#121	—	67	1	no	—
633	#121	—	67	1	no	—
634	#121	—	67	1	no	—
635	#121	—	67	1	no	—
636	#121	C₂×D₆₇	1	1	yes	characteristic
637	#120	—	67	1	no	—
638	#120	—	67	1	no	—
639	#120	—	67	1	no	—
640	#120	—	67	1	no	—
641	#120	—	67	1	no	—
642	#120	—	67	1	no	—
643	#120	—	67	1	no	—
644	#120	—	67	1	no	—
645	C₄×Q₈	—	67	1	no	—
646	C₄×Q₈	—	67	1	no	—
647	C₄×Q₈	—	67	1	no	—
648	C₄×D₄	—	67	1	no	—
649	C₄×D₄	—	67	1	no	—
650	C₄×D₄	—	67	1	no	—
651	C₄×D₄	—	67	1	no	—
652	C₄×D₄	—	67	1	no	—
653	C₄×D₄	—	67	1	no	—
654	C₄×D₄	—	67	1	no	—
655	C₄×D₄	—	67	1	no	—
656	C₄×D₄	—	67	1	no	—
657	C₄×D₄	—	67	1	no	—
658	C₄×D₄	—	67	1	no	—
659	C₄×D₄	—	67	1	no	—
660	C₄×D₄	—	67	1	no	—
661	C₄×D₄	—	67	1	no	—
662	C₄×D₄	—	67	1	no	—
663	C₄×D₄	—	67	1	no	—
664	C₄×D₄	—	67	1	no	—
665	C₄×D₄	—	67	1	no	—
666	C₄×D₄	—	67	1	no	—
667	C₄×D₄	—	67	1	no	—
668	C₄×D₄	—	67	1	no	—
669	C₄×D₄	—	67	1	no	—
670	C₄×D₄	—	67	1	no	—
671	C₄×D₄	—	67	1	no	—
672	C₄×D₄	—	67	1	no	—
673	C₄×D₄	—	67	1	no	—
674	C₄×D₄	—	67	1	no	—
675	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
676	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
677	#117	—	67	1	no	—
678	#117	—	67	1	no	—
679	#117	—	67	1	no	—
680	#117	—	67	1	no	—
681	#117	—	67	1	no	—
682	#117	—	67	1	no	—
683	#117	—	67	1	no	—
684	#117	—	67	1	no	—
685	#117	—	67	1	no	—
686	C₂×C₄⋊C₄	—	67	1	no	—
687	C₂×C₄⋊C₄	—	67	1	no	—
688	C₂×C₄⋊C₄	—	67	1	no	—
689	C₂×C₄⋊C₄	—	67	1	no	—
690	C₂×C₄⋊C₄	—	67	1	no	—
691	C₂×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
692	C₂×C₂²⋊C₄	—	67	1	no	—
693	C₂×C₂²⋊C₄	—	67	1	no	—
694	C₂×C₂²⋊C₄	—	67	1	no	—
695	C₂×C₂²⋊C₄	—	67	1	no	—
696	C₂×C₂²⋊C₄	—	67	1	no	—
697	C₂×C₂²⋊C₄	—	67	1	no	—
698	C₂×C₂²⋊C₄	—	67	1	no	—
699	C₂×C₂²⋊C₄	—	67	1	no	—
700	C₂×C₂²⋊C₄	—	67	1	no	—
701	C₂×C₂²⋊C₄	—	67	1	no	—
702	C₂×C₄²	—	67	1	no	—
703	C₂⁴	—	67	1	no	—
704	C₂⁴	—	67	1	no	—
705	C₂⁴	—	67	1	no	—
706	C₂⁴	—	67	1	no	—
707	#41	—	268	2	no	—
708	#41	—	268	2	no	—
709	#41	—	134	4	no	—
710	C₂×Q₈	—	67	1	no	—
711	C₂×Q₈	—	67	1	no	—
712	C₂×Q₈	—	67	1	no	—
713	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
714	C₂×D₄	—	268	2	no	—
715	C₂×D₄	—	268	2	no	—
716	C₂×D₄	—	67	1	no	—
717	C₂×D₄	—	67	1	no	—
718	C₂×D₄	—	67	1	no	—
719	C₂×D₄	—	67	1	no	—
720	C₂×D₄	—	67	1	no	—
721	C₂×D₄	—	67	1	no	—
722	C₂×D₄	—	67	1	no	—
723	C₂×D₄	—	67	1	no	—
724	C₂×D₄	—	67	1	no	—
725	C₂×D₄	—	67	1	no	—
726	C₂×D₄	—	67	1	no	—
727	C₂×D₄	—	67	1	no	—
728	C₂×D₄	—	67	1	no	—
729	C₂×D₄	—	67	1	no	—
730	C₂×D₄	—	67	1	no	—
731	C₂×D₄	—	67	1	no	—
732	C₂×D₄	—	67	1	no	—
733	C₂×D₄	—	67	1	no	—
734	C₂×D₄	—	67	1	no	—
735	C₂×D₄	—	67	1	no	—
736	C₂×D₄	—	67	1	no	—
737	C₂×D₄	—	134	4	no	—
738	C₂×D₄	—	134	4	no	—
739	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
740	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
741	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
742	C₂²×C₄	—	268	2	no	—
743	C₂²×C₄	—	268	2	no	—
744	C₂²×C₄	—	67	1	no	—
745	C₂²×C₄	—	67	1	no	—
746	C₂²×C₄	—	67	1	no	—
747	C₂²×C₄	—	67	1	no	—
748	C₂²×C₄	—	67	1	no	—
749	C₂²×C₄	—	67	1	no	—
750	C₂²×C₄	—	67	1	no	—
751	C₂²×C₄	—	67	1	no	—
752	C₂²×C₄	—	67	1	no	—
753	C₂²×C₄	—	67	1	no	—
754	C₂²×C₄	—	67	1	no	—
755	C₂²×C₄	—	67	1	no	—
756	C₂²×C₄	—	67	1	no	—
757	C₂²×C₄	—	67	1	no	—
758	C₂²×C₄	—	67	1	no	—
759	C₂²×C₄	—	67	1	no	—
760	C₂²×C₄	—	67	1	no	—
761	C₂²×C₄	—	67	1	no	—
762	C₂²×C₄	—	67	1	no	—
763	C₂²×C₄	—	67	1	no	—
764	C₂²×C₄	—	67	1	no	—
765	C₂²×C₄	—	67	1	no	—
766	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
767	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
768	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
769	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
770	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
771	C₄⋊C₄	—	67	1	no	—
772	C₄⋊C₄	—	67	1	no	—
773	C₄⋊C₄	—	67	1	no	—
774	C₄⋊C₄	—	67	1	no	—
775	C₄⋊C₄	—	67	1	no	—
776	C₄⋊C₄	—	67	1	no	—
777	C₄⋊C₄	—	67	1	no	—
778	C₄⋊C₄	—	67	1	no	—
779	C₄⋊C₄	—	67	1	no	—
780	C₄⋊C₄	—	67	1	no	—
781	C₄⋊C₄	—	67	1	no	—
782	C₄⋊C₄	—	67	1	no	—
783	C₄⋊C₄	—	67	1	no	—
784	C₄⋊C₄	—	67	1	no	—
785	C₄⋊C₄	—	67	1	no	—
786	C₄⋊C₄	—	67	1	no	—
787	C₄⋊C₄	—	67	1	no	—
788	C₄⋊C₄	—	67	1	no	—
789	C₄⋊C₄	—	67	1	no	—
790	C₄⋊C₄	—	67	1	no	—
791	C₄⋊C₄	—	67	1	no	—
792	C₄⋊C₄	—	67	1	no	—
793	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
794	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
795	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
796	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
797	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
798	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
799	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
800	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
801	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
802	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
803	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
804	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
805	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
806	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
807	C₂²⋊C₄	—	67	1	no	—
808	C₂²⋊C₄	—	67	1	no	—
809	C₂²⋊C₄	—	67	1	no	—
810	C₂²⋊C₄	—	67	1	no	—
811	C₂²⋊C₄	—	67	1	no	—
812	C₂²⋊C₄	—	67	1	no	—
813	C₂²⋊C₄	—	67	1	no	—
814	C₂²⋊C₄	—	67	1	no	—
815	C₂²⋊C₄	—	67	1	no	—
816	C₂²⋊C₄	—	67	1	no	—
817	C₂²⋊C₄	—	67	1	no	—
818	C₂²⋊C₄	—	67	1	no	—
819	C₂²⋊C₄	—	67	1	no	—
820	C₂²⋊C₄	—	67	1	no	—
821	C₂²⋊C₄	—	67	1	no	—
822	C₂²⋊C₄	—	67	1	no	—
823	C₂²⋊C₄	—	67	1	no	—
824	C₂²⋊C₄	—	67	1	no	—
825	C₂²⋊C₄	—	67	1	no	—
826	C₂²⋊C₄	—	67	1	no	—
827	C₂²⋊C₄	—	67	1	no	—
828	C₂²⋊C₄	—	67	1	no	—
829	C₂²⋊C₄	—	67	1	no	—
830	C₂²⋊C₄	—	67	1	no	—
831	C₂²⋊C₄	—	67	1	no	—
832	C₂²⋊C₄	—	67	1	no	—
833	C₂²⋊C₄	—	67	1	no	—
834	C₂²⋊C₄	—	67	1	no	—
835	C₂²⋊C₄	—	67	1	no	—
836	C₂²⋊C₄	—	67	1	no	—
837	C₂²⋊C₄	—	67	1	no	—
838	C₂²⋊C₄	—	67	1	no	—
839	C₂²⋊C₄	—	67	1	no	—
840	C₂²⋊C₄	—	67	1	no	—
841	C₂²⋊C₄	—	67	1	no	—
842	C₂²⋊C₄	—	67	1	no	—
843	C₂²⋊C₄	—	67	1	no	—
844	C₂²⋊C₄	—	67	1	no	—
845	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
846	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
847	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
848	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
849	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
850	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
851	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
852	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
853	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
854	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
855	C₄²	—	67	1	no	—
856	C₄²	—	67	1	no	—
857	C₄²	—	67	1	no	—
858	C₄²	—	67	1	no	—
859	C₄²	—	67	1	no	—
860	C₄²	—	67	1	no	—
861	C₄²	—	67	1	no	—
862	C₄²	—	67	1	no	—
863	C₄²	—	67	1	no	—
864	C₄²	—	67	1	no	—
865	C₄²	C₂²×D₆₇	1	1	yes	characteristic
866	C₄²	C₂²×D₆₇	1	1	yes	characteristic
867	C₂³	—	268	1	no	—
868	C₂³	—	268	1	no	—
869	C₂³	—	268	1	no	—
870	C₂³	—	268	1	no	—
871	C₂³	—	268	1	no	—
872	C₂³	—	268	1	no	—
873	C₂³	—	67	1	no	—
874	C₂³	—	67	1	no	—
875	C₂³	—	67	1	no	—
876	C₂³	—	67	1	no	—
877	C₂³	—	67	1	no	—
878	C₂³	—	67	1	no	—
879	C₂³	—	134	2	no	—
880	C₂³	—	134	2	no	—
881	C₂³	—	134	2	no	—
882	C₂³	—	134	2	no	—
883	C₂³	—	134	2	no	—
884	C₂³	—	134	2	no	—
885	C₂³	C₂³×D₆₇	1	1	yes	characteristic
886	C₂³	C₂³×D₆₇	1	1	yes	characteristic
887	C₂³	C₂³×D₆₇	1	1	yes	characteristic
888	Q₈	—	4	1	no	—
889	Q₈	—	268	1	no	—
890	Q₈	—	268	1	no	—
891	Q₈	—	134	2	no	—
892	D₄	—	2	2	no	—
893	D₄	—	2	2	no	—
894	D₄	—	4	1	no	—
895	D₄	—	268	1	no	—
896	D₄	—	268	1	no	—
897	D₄	—	268	1	no	—
898	D₄	—	268	1	no	—
899	D₄	—	268	1	no	—
900	D₄	—	268	1	no	—
901	D₄	—	268	1	no	—
902	D₄	—	268	1	no	—
903	D₄	—	268	1	no	—
904	D₄	—	268	1	no	—
905	D₄	—	67	4	no	—
906	D₄	—	134	2	no	—
907	D₄	—	134	2	no	—
908	D₄	—	134	2	no	—
909	D₄	—	134	2	no	—
910	D₄	—	134	2	no	—
911	D₄	—	134	2	no	—
912	D₄	—	134	2	no	—
913	D₄	—	134	2	no	—
914	D₄	—	134	2	no	—
915	D₄	—	134	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	4	1	no	—
918	C₂×C₄	—	4	1	no	—
919	C₂×C₄	—	4	1	no	—
920	C₂×C₄	—	4	1	no	—
921	C₂×C₄	—	268	1	no	—
922	C₂×C₄	—	268	1	no	—
923	C₂×C₄	—	268	1	no	—
924	C₂×C₄	—	268	1	no	—
925	C₂×C₄	—	268	1	no	—
926	C₂×C₄	—	268	1	no	—
927	C₂×C₄	—	268	1	no	—
928	C₂×C₄	—	268	1	no	—
929	C₂×C₄	—	268	1	no	—
930	C₂×C₄	—	268	1	no	—
931	C₂×C₄	—	268	1	no	—
932	C₂×C₄	—	268	1	no	—
933	C₂×C₄	—	268	1	no	—
934	C₂×C₄	—	268	1	no	—
935	C₂×C₄	—	268	1	no	—
936	C₂×C₄	—	67	1	no	—
937	C₂×C₄	—	67	1	no	—
938	C₂×C₄	—	67	1	no	—
939	C₂×C₄	—	67	1	no	—
940	C₂×C₄	—	67	1	no	—
941	C₂×C₄	—	67	1	no	—
942	C₂×C₄	—	67	1	no	—
943	C₂×C₄	—	67	1	no	—
944	C₂×C₄	—	67	1	no	—
945	C₂×C₄	—	67	1	no	—
946	C₂×C₄	—	134	2	no	—
947	C₂×C₄	—	134	2	no	—
948	C₂×C₄	—	134	2	no	—
949	C₂×C₄	—	134	2	no	—
950	C₂×C₄	—	134	2	no	—
951	C₂×C₄	—	134	2	no	—
952	C₂×C₄	—	134	2	no	—
953	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
954	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
955	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
956	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
957	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
958	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
959	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
960	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
961	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
962	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
963	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
964	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
965	C₂²	—	2	1	no	—
966	C₂²	—	2	1	no	—
967	C₂²	—	2	1	no	—
968	C₂²	—	2	1	no	—
969	C₂²	—	2	1	no	—
970	C₂²	—	2	1	no	—
971	C₂²	—	2	1	no	—
972	C₂²	—	2	1	no	—
973	C₂²	—	268	4	no	—
974	C₂²	—	268	4	no	—
975	C₂²	—	536	2	no	—
976	C₂²	—	536	2	no	—
977	C₂²	—	67	2	no	—
978	C₂²	—	67	2	no	—
979	C₂²	—	134	1	no	—
980	C₂²	—	134	1	no	—
981	C₂²	—	134	1	no	—
982	C₂²	—	134	1	no	—
983	C₂²	—	134	1	no	—
984	C₂²	—	134	1	no	—
985	C₂²	—	134	1	no	—
986	C₂²	—	134	1	no	—
987	C₂²	—	134	1	no	—
988	C₂²	—	134	1	no	—
989	C₂²	—	134	1	no	—
990	C₂²	—	134	1	no	—
991	C₂²	—	134	1	no	—
992	C₂²	—	134	1	no	—
993	C₂²	—	134	1	no	—
994	C₂²	—	134	1	no	—
995	C₂²	#41×D₆₇	1	2	yes	—
996	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
997	C₄	—	2	1	no	—
998	C₄	—	2	1	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	2	1	no	—
1001	C₄	—	2	1	no	—
1002	C₄	—	2	1	no	—
1003	C₄	—	2	1	no	—
1004	C₄	—	2	1	no	—
1005	C₄	—	2	1	no	—
1006	C₄	—	2	1	no	—
1007	C₄	—	2	1	no	—
1008	C₄	—	2	1	no	—
1009	C₄	—	67	2	no	—
1010	C₄	—	134	1	no	—
1011	C₄	—	134	1	no	—
1012	C₄	—	134	1	no	—
1013	C₄	—	134	1	no	—
1014	C₄	—	134	1	no	—
1015	C₄	—	134	1	no	—
1016	C₄	—	134	1	no	—
1017	C₄	—	134	1	no	—
1018	C₄	—	134	1	no	—
1019	C₂	—	2	2	no	—
1020	C₂	—	4	1	no	—
1021	C₂	—	4	1	no	—
1022	C₂	—	268	1	no	—
1023	C₂	—	268	1	no	—
1024	C₂	—	268	1	no	—
1025	C₂	—	268	1	no	—
1026	C₂	—	134	2	no	—
1027	C₂	—	134	2	no	—
1028	C₂	C₂×#41×D₆₇	1	1	yes	characteristic
1029	C₂	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
1030	C₂	#16864233	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#539×C₆₇	C₂
hypercenter	#539	D₆₇
hypocenter	C₆₇	#3513
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #539

Complements

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

N	H ≅ G/N	type
1. #16864130	C₂	semidirect
2. #16864100	C₂	semidirect
3. #16864099	C₂	semidirect
4. #16864097	C₂	semidirect
5. #16864089	C₂	semidirect
6. #16864078	C₂	semidirect
7. #16864073	C₂	semidirect
8. #16864071	C₂	semidirect
9. #16864069	C₂	semidirect
10. #16864069	C₂	semidirect
11. #16864048	C₂	semidirect
12. #16864038	C₂	semidirect
13. #16864038	C₂	semidirect
14. #16864038	C₂	semidirect
15. #16864037	C₂	semidirect
16. #16864030	C₂	semidirect
17. #16864016	C₂	semidirect
18. #16863998	C₂	semidirect
19. #16863994	C₂	semidirect
20. #16863985	C₂	semidirect
21. #16863979	C₂	semidirect
22. #16863931	C₂	semidirect
23. #16863929	C₂	semidirect
24. #16863909	C₂	semidirect
25. #16863905	C₂	semidirect
26. C₂×#14524028	C₂	semidirect
27. #123×D₆₇	C₂	semidirect
28. #16863877	C₂	semidirect
29. #16863868	C₂	semidirect
30. C₄×D₄×D₆₇	C₂	semidirect
31. #539×C₆₇	C₂	semidirect
32. C₂×#11761629	C₂²	semidirect
34. C₂×#11761628	C₂²	semidirect
39. C₂²×C₄×D₆₇	C₂²	semidirect
40. C₂²×C₄×D₆₇	C₂²	semidirect
41. #14524041	C₂²	semidirect
43. #14524038	C₂²	semidirect
44. #14524038	C₂²	semidirect
45. #14524038	C₂²	semidirect
46. #14524038	C₂²	semidirect
47. #14524038	C₂²	semidirect
48. #14524038	C₂²	semidirect
49. #14524037	C₂²	semidirect
50. #14524036	C₂²	semidirect
51. #14524033	C₂²	semidirect
52. #14524033	C₂²	semidirect
53. #14524033	C₂²	semidirect
54. #14524032	C₂²	semidirect
55. #14524031	C₂²	semidirect
56. #14524029	C₂²	semidirect
57. #14524029	C₂²	semidirect
58. #14524029	C₂²	semidirect
59. #14524029	C₂²	semidirect
60. #14524029	C₂²	semidirect
64. #14524028	C₂²	semidirect
65. #14524028	C₂²	semidirect
66. #14524028	C₂²	semidirect
67. #14524028	C₂²	semidirect
68. #14524028	C₂²	semidirect
69. #14524028	C₂²	semidirect
70. #14524028	C₂²	semidirect
71. #14524028	C₂²	semidirect
72. #14524028	C₂²	semidirect
73. #14524028	C₂²	semidirect
74. #14524028	C₂²	semidirect
75. #14524027	C₂²	semidirect
76. #14524027	C₂²	semidirect
77. #14524026	C₂²	semidirect
78. #14524025	C₂²	semidirect
79. #14524025	C₂²	semidirect
80. #14524025	C₂²	semidirect
81. #14524025	C₂²	semidirect
82. #14524024	C₂²	semidirect
83. #14524023	C₂²	semidirect
84. #14524023	C₂²	semidirect
85. #14524021	C₂²	semidirect
86. #14524021	C₂²	semidirect
87. #14524021	C₂²	semidirect
88. #14524021	C₂²	semidirect
89. #14524021	C₂²	semidirect
90. #14524020	C₂²	semidirect
91. #14524020	C₂²	semidirect
92. #14524019	C₂²	semidirect
95. #14524018	C₂²	semidirect
96. #14524018	C₂²	semidirect
97. #14524018	C₂²	semidirect
98. #14524018	C₂²	semidirect
99. #14524017	C₂²	semidirect
102. #14524016	C₂²	semidirect
103. #14524016	C₂²	semidirect
104. #14524016	C₂²	semidirect
105. #14524016	C₂²	semidirect
106. #14524015	C₂²	semidirect
107. #14524015	C₂²	semidirect
108. #14524015	C₂²	semidirect
111. #14524013	C₂²	semidirect
112. #14524013	C₂²	semidirect
113. #14524013	C₂²	semidirect
114. #14524013	C₂²	semidirect
117. #14524008	C₂²	semidirect
118. #14524008	C₂²	semidirect
119. #14524008	C₂²	semidirect
120. C₄×D₂₆₈	C₂²	semidirect
121. C₄×D₂₆₈	C₂²	semidirect
122. C₄×D₂₆₈	C₂²	semidirect
123. D₄×Dic₆₇	C₂²	semidirect
124. D₄×Dic₆₇	C₂²	semidirect
126. #14524005	C₂²	semidirect
127. #14524005	C₂²	semidirect
128. #14524005	C₂²	semidirect
129. #14524005	C₂²	semidirect
130. #14524005	C₂²	semidirect
131. #14524005	C₂²	semidirect
132. #14524005	C₂²	semidirect
135. C₄×C₂²⋊D₆₇	C₂²	semidirect
136. C₄×C₂²⋊D₆₇	C₂²	semidirect
137. C₄×C₂²⋊D₆₇	C₂²	semidirect
138. C₄×C₂²⋊D₆₇	C₂²	semidirect
139. C₄×C₂²⋊D₆₇	C₂²	semidirect
142. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
143. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
144. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
145. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
146. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
147. #14524002	C₂²	semidirect
148. #14524001	C₂²	semidirect
149. #14524001	C₂²	semidirect
150. #14524001	C₂²	semidirect
151. #14524001	C₂²	semidirect
152. #14524001	C₂²	semidirect
153. #14524000	C₂²	semidirect
154. #14524000	C₂²	semidirect
155. #14523999	C₂²	semidirect
156. C₂×Dic₆₇⋊C₄	C₂²	semidirect
157. C₄⋊C₄×D₆₇	C₂²	semidirect
158. C₄⋊C₄×D₆₇	C₂²	semidirect
159. C₄⋊C₄×D₆₇	C₂²	semidirect
160. C₄⋊C₄×D₆₇	C₂²	semidirect
161. C₂×(C₂×D₆₇)⋊C₄	C₂²	semidirect
162. C₂×(C₂×D₆₇)⋊C₄	C₂²	semidirect
163. C₂×(C₂×D₆₇)⋊C₄	C₂²	semidirect
164. C₂×(C₂×D₆₇)⋊C₄	C₂²	semidirect
165. C₂²⋊C₄×D₆₇	C₂²	semidirect
166. C₂²⋊C₄×D₆₇	C₂²	semidirect
167. C₂²⋊C₄×D₆₇	C₂²	semidirect
168. C₂²⋊C₄×D₆₇	C₂²	semidirect
169. C₂²⋊C₄×D₆₇	C₂²	semidirect
170. C₂²⋊C₄×D₆₇	C₂²	semidirect
171. C₄²×D₆₇	C₂²	semidirect
172. #126×C₆₇	C₂²	semidirect
173. #126×C₆₇	C₂²	semidirect
174. #125×C₆₇	C₂²	semidirect
175. #125×C₆₇	C₂²	semidirect
176. #123×C₆₇	C₂²	semidirect
177. #123×C₆₇	C₂²	semidirect
178. #123×C₆₇	C₂²	semidirect
179. #123×C₆₇	C₂²	semidirect
180. C₂²⋊Q₈×C₆₇	C₂²	semidirect
181. C₂²⋊Q₈×C₆₇	C₂²	semidirect
182. C₂²⋊Q₈×C₆₇	C₂²	semidirect
184. C₄×D₄×C₆₇	C₂²	semidirect
185. C₄×D₄×C₆₇	C₂²	semidirect
186. C₂×C₄⋊C₄×C₆₇	C₂²	semidirect
402. C₂²⋊D₆₇	#41	semidirect
516. C₆₇	#3513	semidirect
536. #539	D₆₇	semidirect
567. #126	C₂×D₆₇	semidirect
568. #126	C₂×D₆₇	semidirect
572. #125	C₂×D₆₇	semidirect
573. #125	C₂×D₆₇	semidirect
603. #123	C₂×D₆₇	semidirect
604. #123	C₂×D₆₇	semidirect
605. #123	C₂×D₆₇	semidirect
606. #123	C₂×D₆₇	semidirect
617. C₂²⋊Q₈	C₂×D₆₇	semidirect
618. C₂²⋊Q₈	C₂×D₆₇	semidirect
619. C₂²⋊Q₈	C₂×D₆₇	semidirect
675. C₄×D₄	C₂×D₆₇	semidirect
676. C₄×D₄	C₂×D₆₇	semidirect
691. C₂×C₄⋊C₄	C₂×D₆₇	semidirect