Subgroups — #22574565

Order 8576.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864148	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864143	C₂	1	1	yes	maximal, characteristic, complemented
3	#16864142	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864138	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864111	C₂	1	1	yes	maximal, characteristic, complemented
6	#16864109	C₂	1	1	yes	maximal, characteristic, complemented
7	#16864073	C₂	1	1	yes	maximal, characteristic, complemented
8	#16864072	C₂	1	1	yes	maximal, characteristic, complemented
9	#16864071	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864070	C₂	1	1	yes	maximal, characteristic, complemented
11	#16864069	C₂	1	1	yes	maximal, characteristic, complemented
12	#16864041	C₂	1	1	yes	maximal, characteristic, complemented
13	#16864038	C₂	1	1	yes	maximal, characteristic, complemented
14	#16864036	C₂	1	1	yes	maximal, characteristic, complemented
15	#16864033	C₂	1	1	yes	maximal, characteristic, complemented
16	#16864019	C₂	1	1	yes	maximal, characteristic, complemented
17	#16864017	C₂	1	1	yes	maximal, characteristic, complemented
18	#16864015	C₂	1	1	yes	maximal, characteristic, complemented
19	#16864012	C₂	1	1	yes	maximal, characteristic, complemented
20	#16863985	C₂	1	1	yes	maximal, characteristic, complemented
21	#16863982	C₂	1	1	yes	maximal, characteristic, complemented
22	#16863982	C₂	1	1	yes	maximal, characteristic, complemented
23	#16863979	C₂	1	1	yes	maximal, characteristic, complemented
24	#16863972	C₂	1	1	yes	maximal, characteristic, complemented
25	#16863968	C₂	1	1	yes	maximal, characteristic, complemented
26	#16863958	C₂	1	1	yes	maximal, characteristic, complemented
27	#16863956	C₂	1	1	yes	maximal, characteristic, complemented
28	#16863932	C₂	1	1	yes	maximal, characteristic, complemented
29	#16863926	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#14524029	C₂	1	1	yes	maximal, characteristic, complemented
31	#551×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#11761628	C₂²	1	1	yes	characteristic
33	C₂×#11761627	C₂²	1	1	yes	characteristic
34	C₂²×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
37	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
38	#14524043	C₂²	1	1	yes	characteristic, complemented
39	#14524043	C₂²	1	1	yes	characteristic, complemented
40	#14524042	C₂²	1	1	yes	characteristic, complemented
41	#14524042	C₂²	1	1	yes	characteristic, complemented
42	#14524038	C₂²	1	1	yes	characteristic, complemented
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	#14524037	C₂²	1	1	yes	characteristic, complemented
49	#14524036	C₂²	1	1	yes	characteristic, complemented
50	#14524036	C₂²	1	1	yes	characteristic, complemented
51	#14524036	C₂²	1	1	yes	characteristic, complemented
52	#14524034	C₂²	1	1	yes	characteristic, complemented
53	#14524033	C₂²	1	1	yes	characteristic, complemented
54	#14524032	C₂²	1	1	yes	characteristic, complemented
55	#14524032	C₂²	1	1	yes	characteristic, complemented
56	#14524031	C₂²	1	1	yes	characteristic, complemented
57	#14524031	C₂²	1	1	yes	characteristic, complemented
58	#14524031	C₂²	1	1	yes	characteristic, complemented
59	#14524031	C₂²	1	1	yes	characteristic, complemented
60	#14524029	C₂²	1	1	yes	characteristic
61	#14524029	C₂²	1	1	yes	characteristic
62	#14524029	C₂²	1	1	yes	characteristic, complemented
63	#14524029	C₂²	1	1	yes	characteristic, complemented
64	#14524029	C₂²	1	1	yes	characteristic, complemented
65	#14524029	C₂²	1	1	yes	characteristic, complemented
66	#14524029	C₂²	1	1	yes	characteristic, complemented
67	#14524029	C₂²	1	1	yes	characteristic, complemented
68	#14524029	C₂²	1	1	yes	characteristic, complemented
69	#14524029	C₂²	1	1	yes	characteristic, complemented
70	#14524029	C₂²	1	1	yes	characteristic, complemented
71	#14524029	C₂²	1	1	yes	characteristic, complemented
72	#14524029	C₂²	1	1	yes	characteristic, complemented
73	#14524029	C₂²	1	1	yes	characteristic, complemented
74	#14524029	C₂²	1	1	yes	characteristic, complemented
75	#14524028	C₂²	1	1	yes	characteristic, complemented
76	#14524028	C₂²	1	1	yes	characteristic, complemented
77	#14524028	C₂²	1	1	yes	characteristic, complemented
78	#14524028	C₂²	1	1	yes	characteristic, complemented
79	#14524028	C₂²	1	1	yes	characteristic, complemented
80	#14524027	C₂²	1	1	yes	characteristic
81	#14524027	C₂²	1	1	yes	characteristic, complemented
82	#14524027	C₂²	1	1	yes	characteristic, complemented
83	#14524027	C₂²	1	1	yes	characteristic, complemented
84	#14524027	C₂²	1	1	yes	characteristic, complemented
85	#14524027	C₂²	1	1	yes	characteristic, complemented
86	#14524027	C₂²	1	1	yes	characteristic, complemented
87	#14524027	C₂²	1	1	yes	characteristic, complemented
88	#14524026	C₂²	1	1	yes	characteristic, complemented
89	#14524026	C₂²	1	1	yes	characteristic, complemented
90	#14524025	C₂²	1	1	yes	characteristic
91	#14524025	C₂²	1	1	yes	characteristic, complemented
92	#14524025	C₂²	1	1	yes	characteristic, complemented
93	#14524025	C₂²	1	1	yes	characteristic, complemented
94	#14524025	C₂²	1	1	yes	characteristic, complemented
95	#14524024	C₂²	1	1	yes	characteristic, complemented
96	#14524023	C₂²	1	1	yes	characteristic, complemented
97	#14524023	C₂²	1	1	yes	characteristic, complemented
98	#14524023	C₂²	1	1	yes	characteristic, complemented
99	#14524023	C₂²	1	1	yes	characteristic, complemented
100	#14524023	C₂²	1	1	yes	characteristic, complemented
101	#14524022	C₂²	1	1	yes	characteristic, complemented
102	#14524021	C₂²	1	1	yes	characteristic, complemented
103	#14524021	C₂²	1	1	yes	characteristic, complemented
104	#14524021	C₂²	1	1	yes	characteristic, complemented
105	#14524021	C₂²	1	1	yes	characteristic, complemented
106	#14524020	C₂²	1	1	yes	characteristic, complemented
107	#14524020	C₂²	1	1	yes	characteristic, complemented
108	#14524020	C₂²	1	1	yes	characteristic, complemented
109	#14524020	C₂²	1	1	yes	characteristic, complemented
110	#14524020	C₂²	1	1	yes	characteristic, complemented
111	#14524019	C₂²	1	1	yes	characteristic, complemented
112	#14524018	C₂²	1	1	yes	characteristic, complemented
113	#14524018	C₂²	1	1	yes	characteristic, complemented
114	#14524017	C₂²	1	1	yes	characteristic
115	#14524017	C₂²	1	1	yes	characteristic
116	#14524017	C₂²	1	1	yes	characteristic
117	#14524017	C₂²	1	1	yes	characteristic, complemented
118	#14524017	C₂²	1	1	yes	characteristic, complemented
119	#14524017	C₂²	1	1	yes	characteristic, complemented
120	#14524016	C₂²	1	1	yes	characteristic
121	#14524016	C₂²	1	1	yes	characteristic, complemented
122	#14524016	C₂²	1	1	yes	characteristic, complemented
123	#14524016	C₂²	1	1	yes	characteristic, complemented
124	#14524016	C₂²	1	1	yes	characteristic, complemented
125	#14524015	C₂²	1	1	yes	characteristic
126	#14524015	C₂²	1	1	yes	characteristic, complemented
127	#14524014	C₂²	1	1	yes	characteristic
128	#14524014	C₂²	1	1	yes	characteristic, complemented
129	#14524014	C₂²	1	1	yes	characteristic, complemented
130	#14524013	C₂²	1	1	yes	characteristic
131	#14524013	C₂²	1	1	yes	characteristic
132	#14524013	C₂²	1	1	yes	characteristic
133	#14524013	C₂²	1	1	yes	characteristic, complemented
134	#14524013	C₂²	1	1	yes	characteristic, complemented
135	#14524013	C₂²	1	1	yes	characteristic, complemented
136	#14524013	C₂²	1	1	yes	characteristic, complemented
137	#14524012	C₂²	1	1	yes	characteristic
138	#14524011	C₂²	1	1	yes	characteristic
139	#14524011	C₂²	1	1	yes	characteristic, complemented
140	#14524011	C₂²	1	1	yes	characteristic, complemented
141	Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
142	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
143	C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
144	C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
145	D₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
146	#14524005	C₂²	1	1	yes	characteristic, complemented
147	#14524005	C₂²	1	1	yes	characteristic, complemented
148	#14524005	C₂²	1	1	yes	characteristic, complemented
149	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
150	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
151	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
152	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
153	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
154	(C₂²⋊D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
155	#14524002	C₂²	1	1	yes	characteristic, complemented
156	#14524002	C₂²	1	1	yes	characteristic, complemented
157	#14524001	C₂²	1	1	yes	characteristic, complemented
158	#14524001	C₂²	1	1	yes	characteristic, complemented
159	#14524001	C₂²	1	1	yes	characteristic, complemented
160	#14524000	C₂²	1	1	yes	characteristic, complemented
161	#14524000	C₂²	1	1	yes	characteristic, complemented
162	#14523999	C₂²	1	1	yes	characteristic, complemented
163	C₂×C₂²⋊Dic₆₇	C₂²	1	1	yes	characteristic, complemented
164	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
165	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
166	C₂×(C₂×D₆₇)⋊C₄	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	C₂×C₄×Dic₆₇	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	#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
175	#123×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	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
179	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
180	#120×C₆₇	C₂²	1	1	yes	characteristic
181	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
182	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
183	#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
184	#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
185	C₂×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
186	C₂×C₂²⋊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	#11761628	—	4	2	no	—
191	#11761627	—	4	2	no	—
192	C₂×Dic₁₃₄	—	4	2	no	—
193	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
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×Dic₁₃₄	C₂³	1	1	yes	characteristic
198	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
199	C₂×Dic₁₃₄	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×C₂²⋊D₆₇	—	4	2	no	—
208	C₂×C₂²⋊D₆₇	—	4	2	no	—
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	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
220	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
222	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
223	D₄×D₆₇	—	4	2	no	—
224	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
225	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
226	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
227	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
228	C₂²×Dic₆₇	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	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
239	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
240	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
241	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
242	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
243	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
244	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
245	C₄⋊Dic₆₇	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	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
251	Dic₆₇⋊C₄	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	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
263	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
264	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
265	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
266	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
267	C₂²⋊Dic₆₇	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	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
273	(C₂×D₆₇)⋊C₄	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	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
305	C₄×Dic₆₇	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	C₂⁴×C₆₇	C₂³	1	1	yes	characteristic
314	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
315	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
316	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
317	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
318	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
319	C₂²×C₄×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	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
324	C₄⋊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	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
332	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
333	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
334	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
335	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
336	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
337	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
338	C₂²⋊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	C₄²×C₆₇	C₂³	1	1	yes	characteristic
346	C₄²×C₆₇	C₂³	1	1	yes	characteristic
347	C₄²×C₆₇	C₂³	1	1	yes	characteristic
348	C₂³×C₆₇	—	2	2	no	—
349	C₂³×C₆₇	—	4	1	no	—
350	C₂³×C₆₇	—	4	1	no	—
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	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
355	C₂²×D₆₇	—	2	2	no	—
356	C₂²×D₆₇	—	4	1	no	—
357	C₂²×D₆₇	—	4	1	no	—
358	C₂²×D₆₇	—	4	1	no	—
359	C₂²×D₆₇	—	4	1	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	C₂⁴	1	1	yes	characteristic
365	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
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	Q₈×C₆₇	—	4	1	no	—
370	D₄×C₆₇	—	2	2	no	—
371	D₄×C₆₇	—	4	1	no	—
372	D₄×C₆₇	—	4	1	no	—
373	C₂×C₄×C₆₇	—	2	2	no	—
374	C₂×C₄×C₆₇	—	4	1	no	—
375	C₂×C₄×C₆₇	—	4	1	no	—
376	C₂×C₄×C₆₇	—	4	1	no	—
377	C₂×C₄×C₆₇	—	4	1	no	—
378	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
379	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
380	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
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	C₂²⋊D₆₇	—	2	2	no	—
390	C₂²⋊D₆₇	—	2	2	no	—
391	C₂²⋊D₆₇	—	2	2	no	—
392	C₂²⋊D₆₇	—	4	1	no	—
393	C₂²⋊D₆₇	—	4	1	no	—
394	C₂²⋊D₆₇	—	4	1	no	—
395	C₂²⋊D₆₇	—	4	1	no	—
396	C₂²⋊D₆₇	—	4	1	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	—	4	1	no	—
403	C₂×Dic₆₇	—	2	2	no	—
404	C₂×Dic₆₇	—	2	2	no	—
405	C₂×Dic₆₇	—	4	1	no	—
406	C₂×Dic₆₇	—	4	1	no	—
407	C₂×Dic₆₇	—	4	1	no	—
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	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
418	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
419	D₂₆₈	—	4	1	no	—
420	D₂₆₈	—	4	1	no	—
421	D₂₆₈	—	4	1	no	—
422	D₂₆₈	—	4	1	no	—
423	D₂₆₈	—	4	1	no	—
424	D₂₆₈	—	4	1	no	—
425	D₂₆₈	—	4	1	no	—
426	C₄×D₆₇	—	4	1	no	—
427	C₄×D₆₇	—	4	1	no	—
428	C₄×D₆₇	—	4	1	no	—
429	C₄×D₆₇	—	4	1	no	—
430	C₄×D₆₇	—	4	1	no	—
431	C₄×D₆₇	—	4	1	no	—
432	C₄×D₆₇	—	4	1	no	—
433	C₄×D₆₇	—	4	1	no	—
434	C₄×D₆₇	—	4	1	no	—
435	Dic₁₃₄	—	4	1	no	—
436	Dic₁₃₄	—	4	1	no	—
437	Dic₁₃₄	—	4	1	no	—
438	Dic₁₃₄	—	4	1	no	—
439	Dic₁₃₄	—	4	1	no	—
440	Dic₁₃₄	—	4	1	no	—
441	Dic₁₃₄	—	4	1	no	—
442	C₂²×C₆₇	—	2	1	no	—
443	C₂²×C₆₇	—	2	1	no	—
444	C₂²×C₆₇	—	2	1	no	—
445	C₂²×C₆₇	—	2	1	no	—
446	C₂²×C₆₇	—	2	1	no	—
447	C₂²×C₆₇	—	2	1	no	—
448	C₂²×C₆₇	—	2	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	—	8	2	no	—
454	C₂²×C₆₇	H(5,𝔽₂)	1	2	yes	—
455	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
456	C₂×D₆₇	—	2	1	no	—
457	C₂×D₆₇	—	2	1	no	—
458	C₂×D₆₇	—	2	1	no	—
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	—	8	2	no	—
472	C₂×D₆₇	—	8	2	no	—
473	C₂×D₆₇	—	8	2	no	—
474	C₄×C₆₇	—	2	1	no	—
475	C₄×C₆₇	—	2	1	no	—
476	C₄×C₆₇	—	2	1	no	—
477	C₄×C₆₇	—	2	1	no	—
478	C₄×C₆₇	—	2	1	no	—
479	C₄×C₆₇	—	2	1	no	—
480	C₄×C₆₇	—	2	1	no	—
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	Dic₆₇	—	2	1	no	—
486	Dic₆₇	—	2	1	no	—
487	Dic₆₇	—	2	1	no	—
488	Dic₆₇	—	2	1	no	—
489	Dic₆₇	—	2	1	no	—
490	Dic₆₇	—	2	1	no	—
491	Dic₆₇	—	2	1	no	—
492	Dic₆₇	—	2	1	no	—
493	Dic₆₇	—	2	1	no	—
494	Dic₆₇	—	2	1	no	—
495	Dic₆₇	—	2	1	no	—
496	C₂×C₆₇	—	2	2	no	—
497	C₂×C₆₇	—	4	1	no	—
498	C₂×C₆₇	—	4	1	no	—
499	C₂×C₆₇	—	4	1	no	—
500	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
501	C₂×C₆₇	#585	1	1	yes	characteristic
502	C₂×C₆₇	#585	1	1	yes	characteristic
503	D₆₇	—	4	1	no	—
504	D₆₇	—	4	1	no	—
505	D₆₇	—	4	1	no	—
506	D₆₇	—	4	1	no	—
507	D₆₇	—	4	1	no	—
508	#3545	—	67	1	no	maximal, Sylow
509	C₆₇	#3545	1	1	yes	characteristic, complemented, Sylow
510	#563	—	67	1	no	—
511	#562	—	67	1	no	—
512	#562	—	67	1	no	—
513	H(3,𝔽₄)	—	67	1	no	—
514	#555	—	67	1	no	—
515	#555	—	67	1	no	—
516	#551	—	67	1	no	—
517	#551	—	67	1	no	—
518	#551	—	67	1	no	—
519	#551	—	67	1	no	—
520	#551	—	67	1	no	—
521	#551	D₆₇	1	1	yes	characteristic, complemented
522	#546	—	67	1	no	—
523	#546	—	67	1	no	—
524	#546	—	67	1	no	—
525	#546	—	67	1	no	—
526	#542	—	67	1	no	—
527	#542	—	67	1	no	—
528	#542	—	67	1	no	—
529	#542	—	67	1	no	—
530	#538	—	67	1	no	—
531	#538	—	67	1	no	—
532	#538	—	67	1	no	—
533	#538	—	67	1	no	—
534	#536	—	67	1	no	—
535	#536	—	67	1	no	—
536	#534	—	67	1	no	—
537	#534	—	67	1	no	—
538	#529	—	67	1	no	—
539	#529	—	67	1	no	—
540	C₂×#124	—	67	1	no	—
541	C₂×#41	—	67	1	no	—
542	C₂×#41	—	67	1	no	—
543	C₂²×Q₈	—	67	1	no	—
544	C₂²×D₄	—	67	1	no	—
545	C₂²×D₄	—	67	1	no	—
546	C₂²×D₄	—	67	1	no	—
547	C₄⋊Q₈	—	67	1	no	—
548	C₄⋊Q₈	—	67	1	no	—
549	C₄⋊Q₈	—	67	1	no	—
550	C₄⋊Q₈	—	67	1	no	—
551	#126	—	67	1	no	—
552	#126	—	67	1	no	—
553	#126	—	67	1	no	—
554	#126	—	67	1	no	—
555	#126	—	67	1	no	—
556	#126	—	67	1	no	—
557	#126	—	67	1	no	—
558	#126	—	67	1	no	—
559	#126	—	67	1	no	—
560	#126	—	67	1	no	—
561	#126	C₂×D₆₇	1	1	yes	characteristic, complemented
562	#126	C₂×D₆₇	1	1	yes	characteristic, complemented
563	#125	—	67	1	no	—
564	#125	—	67	1	no	—
565	#124	—	67	1	no	—
566	#124	—	67	1	no	—
567	#124	—	67	1	no	—
568	#124	—	67	1	no	—
569	#124	—	67	1	no	—
570	#124	—	67	1	no	—
571	#124	—	67	1	no	—
572	#124	—	67	1	no	—
573	#124	—	67	1	no	—
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	#124	—	67	1	no	—
582	#124	—	67	1	no	—
583	#124	—	67	1	no	—
584	#124	—	67	1	no	—
585	#124	—	67	1	no	—
586	#124	C₂×D₆₇	1	1	yes	characteristic, complemented
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	—	67	1	no	—
604	#123	—	67	1	no	—
605	#123	—	67	1	no	—
606	#123	—	67	1	no	—
607	#123	—	67	1	no	—
608	#123	C₂×D₆₇	1	1	yes	characteristic, complemented
609	#123	C₂×D₆₇	1	1	yes	characteristic, complemented
610	#123	C₂×D₆₇	1	1	yes	characteristic, complemented
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	—	67	1	no	—
618	C₂²⋊Q₈	—	67	1	no	—
619	C₂²⋊Q₈	—	67	1	no	—
620	C₂²⋊Q₈	—	67	1	no	—
621	C₂²⋊Q₈	—	67	1	no	—
622	C₂²⋊Q₈	—	67	1	no	—
623	C₂²⋊Q₈	—	67	1	no	—
624	C₂²⋊Q₈	—	67	1	no	—
625	C₂²⋊Q₈	—	67	1	no	—
626	C₂²⋊Q₈	—	67	1	no	—
627	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
628	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
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	—	67	1	no	—
637	#121	—	67	1	no	—
638	#121	—	67	1	no	—
639	#121	—	67	1	no	—
640	#121	—	67	1	no	—
641	#121	—	67	1	no	—
642	#121	—	67	1	no	—
643	#121	—	67	1	no	—
644	#121	—	67	1	no	—
645	#121	—	67	1	no	—
646	#121	—	67	1	no	—
647	#120	—	67	1	no	—
648	#120	—	67	1	no	—
649	#120	—	67	1	no	—
650	#120	—	67	1	no	—
651	#120	—	67	1	no	—
652	#120	—	67	1	no	—
653	#120	—	67	1	no	—
654	#120	—	67	1	no	—
655	#120	—	67	1	no	—
656	#120	—	67	1	no	—
657	#120	—	67	1	no	—
658	#120	C₂×D₆₇	1	1	yes	characteristic
659	C₄×Q₈	—	67	1	no	—
660	C₄×Q₈	—	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	C₂×D₆₇	1	1	yes	characteristic, complemented
674	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
675	#117	—	67	1	no	—
676	#117	—	67	1	no	—
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	C₂×D₆₇	1	1	yes	characteristic, complemented
684	#117	C₂×D₆₇	1	1	yes	characteristic, complemented
685	C₂×C₂²⋊C₄	—	67	1	no	—
686	C₂×C₂²⋊C₄	—	67	1	no	—
687	C₂×C₂²⋊C₄	—	67	1	no	—
688	C₂×C₂²⋊C₄	—	67	1	no	—
689	C₂×C₂²⋊C₄	—	67	1	no	—
690	C₂×C₂²⋊C₄	—	67	1	no	—
691	C₂×C₂²⋊C₄	—	67	1	no	—
692	C₂×C₂²⋊C₄	—	67	1	no	—
693	C₂×C₂²⋊C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
694	C₂×C₂²⋊C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
695	C₂×C₄²	—	67	1	no	—
696	C₂⁴	—	67	1	no	—
697	C₂⁴	—	67	1	no	—
698	C₂⁴	—	67	1	no	—
699	C₂⁴	C₂²×D₆₇	1	1	yes	characteristic
700	#41	—	268	2	no	—
701	#41	—	268	2	no	—
702	C₂×Q₈	—	268	2	no	—
703	C₂×Q₈	—	67	1	no	—
704	C₂×Q₈	—	67	1	no	—
705	C₂×Q₈	—	67	1	no	—
706	C₂×Q₈	—	67	1	no	—
707	C₂×Q₈	—	67	1	no	—
708	C₂×Q₈	—	67	1	no	—
709	C₂×Q₈	—	67	1	no	—
710	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
711	C₂×D₄	—	268	2	no	—
712	C₂×D₄	—	268	2	no	—
713	C₂×D₄	—	268	2	no	—
714	C₂×D₄	—	67	1	no	—
715	C₂×D₄	—	67	1	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	C₂²×D₆₇	1	1	yes	characteristic
736	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
737	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
738	C₂²×C₄	—	67	1	no	—
739	C₂²×C₄	—	67	1	no	—
740	C₂²×C₄	—	67	1	no	—
741	C₂²×C₄	—	67	1	no	—
742	C₂²×C₄	—	67	1	no	—
743	C₂²×C₄	—	67	1	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	C₂²×D₆₇	1	1	yes	characteristic
753	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
754	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
755	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
756	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
757	C₄⋊C₄	—	67	1	no	—
758	C₄⋊C₄	—	67	1	no	—
759	C₄⋊C₄	—	67	1	no	—
760	C₄⋊C₄	—	67	1	no	—
761	C₄⋊C₄	—	67	1	no	—
762	C₄⋊C₄	—	67	1	no	—
763	C₄⋊C₄	—	67	1	no	—
764	C₄⋊C₄	—	67	1	no	—
765	C₄⋊C₄	—	67	1	no	—
766	C₄⋊C₄	—	67	1	no	—
767	C₄⋊C₄	—	67	1	no	—
768	C₄⋊C₄	—	67	1	no	—
769	C₄⋊C₄	—	67	1	no	—
770	C₄⋊C₄	—	67	1	no	—
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	C₂²×D₆₇	1	1	yes	characteristic
782	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
783	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
784	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
785	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
786	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
787	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
788	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
789	C₂²⋊C₄	—	67	1	no	—
790	C₂²⋊C₄	—	67	1	no	—
791	C₂²⋊C₄	—	67	1	no	—
792	C₂²⋊C₄	—	67	1	no	—
793	C₂²⋊C₄	—	67	1	no	—
794	C₂²⋊C₄	—	67	1	no	—
795	C₂²⋊C₄	—	67	1	no	—
796	C₂²⋊C₄	—	67	1	no	—
797	C₂²⋊C₄	—	67	1	no	—
798	C₂²⋊C₄	—	67	1	no	—
799	C₂²⋊C₄	—	67	1	no	—
800	C₂²⋊C₄	—	67	1	no	—
801	C₂²⋊C₄	—	67	1	no	—
802	C₂²⋊C₄	—	67	1	no	—
803	C₂²⋊C₄	—	67	1	no	—
804	C₂²⋊C₄	—	67	1	no	—
805	C₂²⋊C₄	—	67	1	no	—
806	C₂²⋊C₄	—	67	1	no	—
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	C₂²×D₆₇	1	1	yes	characteristic
832	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
833	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
834	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
835	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
836	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
837	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
838	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
839	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
840	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
841	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
842	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
843	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
844	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
845	C₄²	—	67	1	no	—
846	C₄²	—	67	1	no	—
847	C₄²	—	67	1	no	—
848	C₄²	—	67	1	no	—
849	C₄²	—	67	1	no	—
850	C₄²	—	67	1	no	—
851	C₄²	—	67	1	no	—
852	C₄²	—	67	1	no	—
853	C₄²	—	67	1	no	—
854	C₄²	C₂²×D₆₇	1	1	yes	characteristic
855	C₄²	C₂²×D₆₇	1	1	yes	characteristic
856	C₄²	C₂²×D₆₇	1	1	yes	characteristic
857	C₂³	—	2	2	no	—
858	C₂³	—	4	1	no	—
859	C₂³	—	4	1	no	—
860	C₂³	—	268	1	no	—
861	C₂³	—	268	1	no	—
862	C₂³	—	268	1	no	—
863	C₂³	—	268	1	no	—
864	C₂³	—	268	1	no	—
865	C₂³	—	268	1	no	—
866	C₂³	—	268	1	no	—
867	C₂³	—	268	1	no	—
868	C₂³	—	67	1	no	—
869	C₂³	—	67	1	no	—
870	C₂³	—	67	1	no	—
871	C₂³	—	67	1	no	—
872	C₂³	—	67	1	no	—
873	C₂³	—	134	2	no	—
874	C₂³	C₂³×D₆₇	1	1	yes	characteristic
875	C₂³	C₂³×D₆₇	1	1	yes	characteristic
876	C₂³	C₂³×D₆₇	1	1	yes	characteristic
877	C₂³	C₂³×D₆₇	1	1	yes	characteristic
878	Q₈	—	4	1	no	—
879	Q₈	—	268	1	no	—
880	Q₈	—	268	1	no	—
881	Q₈	—	268	1	no	—
882	Q₈	—	268	1	no	—
883	Q₈	—	268	1	no	—
884	Q₈	—	268	1	no	—
885	Q₈	—	268	1	no	—
886	D₄	—	2	2	no	—
887	D₄	—	4	1	no	—
888	D₄	—	4	1	no	—
889	D₄	—	268	1	no	—
890	D₄	—	268	1	no	—
891	D₄	—	268	1	no	—
892	D₄	—	268	1	no	—
893	D₄	—	268	1	no	—
894	D₄	—	268	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	—	268	1	no	—
906	D₄	—	268	1	no	—
907	D₄	—	134	2	no	—
908	D₄	—	134	2	no	—
909	D₄	—	134	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	4	1	no	—
912	C₂×C₄	—	4	1	no	—
913	C₂×C₄	—	4	1	no	—
914	C₂×C₄	—	4	1	no	—
915	C₂×C₄	—	268	1	no	—
916	C₂×C₄	—	268	1	no	—
917	C₂×C₄	—	268	1	no	—
918	C₂×C₄	—	268	1	no	—
919	C₂×C₄	—	268	1	no	—
920	C₂×C₄	—	268	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	—	67	1	no	—
928	C₂×C₄	—	67	1	no	—
929	C₂×C₄	—	67	1	no	—
930	C₂×C₄	—	67	1	no	—
931	C₂×C₄	—	67	1	no	—
932	C₂×C₄	—	67	1	no	—
933	C₂×C₄	—	67	1	no	—
934	C₂×C₄	—	67	1	no	—
935	C₂×C₄	—	67	1	no	—
936	C₂×C₄	—	67	1	no	—
937	C₂×C₄	—	67	1	no	—
938	C₂×C₄	—	134	2	no	—
939	C₂×C₄	—	134	2	no	—
940	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
941	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
942	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
943	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
944	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
945	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
946	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
947	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
948	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
949	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
950	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
951	C₂²	—	2	1	no	—
952	C₂²	—	2	1	no	—
953	C₂²	—	2	1	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	1	no	—
956	C₂²	—	2	1	no	—
957	C₂²	—	2	1	no	—
958	C₂²	—	2	1	no	—
959	C₂²	—	2	1	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	2	1	no	—
962	C₂²	—	8	2	no	—
963	C₂²	—	536	2	no	—
964	C₂²	—	536	2	no	—
965	C₂²	—	536	2	no	—
966	C₂²	—	134	1	no	—
967	C₂²	—	134	1	no	—
968	C₂²	—	134	1	no	—
969	C₂²	—	134	1	no	—
970	C₂²	—	134	1	no	—
971	C₂²	—	134	1	no	—
972	C₂²	—	134	1	no	—
973	C₂²	—	134	1	no	—
974	C₂²	—	134	1	no	—
975	C₂²	—	134	1	no	—
976	C₂²	—	134	1	no	—
977	C₂²	—	134	1	no	—
978	C₂²	—	134	1	no	—
979	C₂²	—	134	1	no	—
980	C₂²	—	134	1	no	—
981	C₂²	#14524089	1	2	yes	—
982	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	1	no	—
989	C₄	—	2	1	no	—
990	C₄	—	2	1	no	—
991	C₄	—	2	1	no	—
992	C₄	—	2	1	no	—
993	C₄	—	2	1	no	—
994	C₄	—	134	1	no	—
995	C₄	—	134	1	no	—
996	C₄	—	134	1	no	—
997	C₄	—	134	1	no	—
998	C₄	—	134	1	no	—
999	C₄	—	134	1	no	—
1000	C₄	—	134	1	no	—
1001	C₄	—	134	1	no	—
1002	C₄	—	134	1	no	—
1003	C₄	—	134	1	no	—
1004	C₄	—	134	1	no	—
1005	C₂	—	2	2	no	—
1006	C₂	—	4	1	no	—
1007	C₂	—	4	1	no	—
1008	C₂	—	4	1	no	—
1009	C₂	—	268	1	no	—
1010	C₂	—	268	1	no	—
1011	C₂	—	268	1	no	—
1012	C₂	—	268	1	no	—
1013	C₂	—	268	1	no	—
1014	C₂	C₂×#14524089	1	1	yes	characteristic
1015	C₂	#16864231	1	1	yes	characteristic
1016	C₂	#16864232	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#551×C₆₇	C₂
hypercenter	#551	D₆₇
hypocenter	C₆₇	#3545
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. #16864148	C₂	semidirect
2. #16864143	C₂	semidirect
3. #16864142	C₂	semidirect
4. #16864138	C₂	semidirect
5. #16864111	C₂	semidirect
6. #16864109	C₂	semidirect
7. #16864073	C₂	semidirect
8. #16864072	C₂	semidirect
9. #16864071	C₂	semidirect
10. #16864070	C₂	semidirect
11. #16864069	C₂	semidirect
12. #16864041	C₂	semidirect
13. #16864038	C₂	semidirect
14. #16864036	C₂	semidirect
15. #16864033	C₂	semidirect
16. #16864019	C₂	semidirect
17. #16864017	C₂	semidirect
18. #16864015	C₂	semidirect
19. #16864012	C₂	semidirect
20. #16863985	C₂	semidirect
21. #16863982	C₂	semidirect
22. #16863982	C₂	semidirect
23. #16863979	C₂	semidirect
24. #16863972	C₂	semidirect
25. #16863968	C₂	semidirect
26. #16863958	C₂	semidirect
27. #16863956	C₂	semidirect
28. #16863932	C₂	semidirect
29. #16863926	C₂	semidirect
30. C₂×#14524029	C₂	semidirect
31. #551×C₆₇	C₂	semidirect
34. C₂²×Dic₁₃₄	C₂²	semidirect
36. C₂²×C₂²⋊D₆₇	C₂²	semidirect
37. C₂×D₄×D₆₇	C₂²	semidirect
38. #14524043	C₂²	semidirect
39. #14524043	C₂²	semidirect
40. #14524042	C₂²	semidirect
41. #14524042	C₂²	semidirect
42. #14524038	C₂²	semidirect
43. #14524038	C₂²	semidirect
44. #14524038	C₂²	semidirect
45. #14524038	C₂²	semidirect
46. #14524038	C₂²	semidirect
47. #14524038	C₂²	semidirect
48. #14524037	C₂²	semidirect
49. #14524036	C₂²	semidirect
50. #14524036	C₂²	semidirect
51. #14524036	C₂²	semidirect
52. #14524034	C₂²	semidirect
53. #14524033	C₂²	semidirect
54. #14524032	C₂²	semidirect
55. #14524032	C₂²	semidirect
56. #14524031	C₂²	semidirect
57. #14524031	C₂²	semidirect
58. #14524031	C₂²	semidirect
59. #14524031	C₂²	semidirect
62. #14524029	C₂²	semidirect
63. #14524029	C₂²	semidirect
64. #14524029	C₂²	semidirect
65. #14524029	C₂²	semidirect
66. #14524029	C₂²	semidirect
67. #14524029	C₂²	semidirect
68. #14524029	C₂²	semidirect
69. #14524029	C₂²	semidirect
70. #14524029	C₂²	semidirect
71. #14524029	C₂²	semidirect
72. #14524029	C₂²	semidirect
73. #14524029	C₂²	semidirect
74. #14524029	C₂²	semidirect
75. #14524028	C₂²	semidirect
76. #14524028	C₂²	semidirect
77. #14524028	C₂²	semidirect
78. #14524028	C₂²	semidirect
79. #14524028	C₂²	semidirect
81. #14524027	C₂²	semidirect
82. #14524027	C₂²	semidirect
83. #14524027	C₂²	semidirect
84. #14524027	C₂²	semidirect
85. #14524027	C₂²	semidirect
86. #14524027	C₂²	semidirect
87. #14524027	C₂²	semidirect
88. #14524026	C₂²	semidirect
89. #14524026	C₂²	semidirect
91. #14524025	C₂²	semidirect
92. #14524025	C₂²	semidirect
93. #14524025	C₂²	semidirect
94. #14524025	C₂²	semidirect
95. #14524024	C₂²	semidirect
96. #14524023	C₂²	semidirect
97. #14524023	C₂²	semidirect
98. #14524023	C₂²	semidirect
99. #14524023	C₂²	semidirect
100. #14524023	C₂²	semidirect
101. #14524022	C₂²	semidirect
102. #14524021	C₂²	semidirect
103. #14524021	C₂²	semidirect
104. #14524021	C₂²	semidirect
105. #14524021	C₂²	semidirect
106. #14524020	C₂²	semidirect
107. #14524020	C₂²	semidirect
108. #14524020	C₂²	semidirect
109. #14524020	C₂²	semidirect
110. #14524020	C₂²	semidirect
111. #14524019	C₂²	semidirect
112. #14524018	C₂²	semidirect
113. #14524018	C₂²	semidirect
117. #14524017	C₂²	semidirect
118. #14524017	C₂²	semidirect
119. #14524017	C₂²	semidirect
121. #14524016	C₂²	semidirect
122. #14524016	C₂²	semidirect
123. #14524016	C₂²	semidirect
124. #14524016	C₂²	semidirect
126. #14524015	C₂²	semidirect
128. #14524014	C₂²	semidirect
129. #14524014	C₂²	semidirect
133. #14524013	C₂²	semidirect
134. #14524013	C₂²	semidirect
135. #14524013	C₂²	semidirect
136. #14524013	C₂²	semidirect
139. #14524011	C₂²	semidirect
140. #14524011	C₂²	semidirect
141. Q₈×Dic₆₇	C₂²	semidirect
142. C₄×Dic₁₃₄	C₂²	semidirect
143. C₄×D₂₆₈	C₂²	semidirect
144. C₄×D₂₆₈	C₂²	semidirect
145. D₄×Dic₆₇	C₂²	semidirect
146. #14524005	C₂²	semidirect
147. #14524005	C₂²	semidirect
148. #14524005	C₂²	semidirect
149. C₄×C₂²⋊D₆₇	C₂²	semidirect
150. C₄×C₂²⋊D₆₇	C₂²	semidirect
151. C₄×C₂²⋊D₆₇	C₂²	semidirect
152. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
153. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
154. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
155. #14524002	C₂²	semidirect
156. #14524002	C₂²	semidirect
157. #14524001	C₂²	semidirect
158. #14524001	C₂²	semidirect
159. #14524001	C₂²	semidirect
160. #14524000	C₂²	semidirect
161. #14524000	C₂²	semidirect
162. #14523999	C₂²	semidirect
163. C₂×C₂²⋊Dic₆₇	C₂²	semidirect
164. C₂×(C₂×D₆₇)⋊C₄	C₂²	semidirect
165. C₂×(C₂×D₆₇)⋊C₄	C₂²	semidirect
166. C₂×(C₂×D₆₇)⋊C₄	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. C₂×C₄×Dic₆₇	C₂²	semidirect
172. #126×C₆₇	C₂²	semidirect
173. #126×C₆₇	C₂²	semidirect
174. #124×C₆₇	C₂²	semidirect
175. #123×C₆₇	C₂²	semidirect
176. #123×C₆₇	C₂²	semidirect
177. #123×C₆₇	C₂²	semidirect
178. C₂²⋊Q₈×C₆₇	C₂²	semidirect
179. C₂²⋊Q₈×C₆₇	C₂²	semidirect
181. C₄×D₄×C₆₇	C₂²	semidirect
182. C₄×D₄×C₆₇	C₂²	semidirect
183. #117×C₆₇	C₂²	semidirect
184. #117×C₆₇	C₂²	semidirect
185. C₂×C₂²⋊C₄×C₆₇	C₂²	semidirect
186. C₂×C₂²⋊C₄×C₆₇	C₂²	semidirect
509. C₆₇	#3545	semidirect
521. #551	D₆₇	semidirect
561. #126	C₂×D₆₇	semidirect
562. #126	C₂×D₆₇	semidirect
586. #124	C₂×D₆₇	semidirect
608. #123	C₂×D₆₇	semidirect
609. #123	C₂×D₆₇	semidirect
610. #123	C₂×D₆₇	semidirect
627. C₂²⋊Q₈	C₂×D₆₇	semidirect
628. C₂²⋊Q₈	C₂×D₆₇	semidirect
673. C₄×D₄	C₂×D₆₇	semidirect
674. C₄×D₄	C₂×D₆₇	semidirect
683. #117	C₂×D₆₇	semidirect
684. #117	C₂×D₆₇	semidirect
693. C₂×C₂²⋊C₄	C₂×D₆₇	semidirect
694. C₂×C₂²⋊C₄	C₂×D₆₇	semidirect