Subgroups — #22574637

Order 8576.

1050 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864150	C₂	1	2	yes	maximal, complemented
2	#16864136	C₂	1	2	yes	maximal, complemented
3	#16864109	C₂	1	2	yes	maximal, complemented
4	#16864099	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864094	C₂	1	1	yes	maximal, characteristic, complemented
6	#16864085	C₂	1	1	yes	maximal, characteristic, complemented
7	#16864071	C₂	1	2	yes	maximal, complemented
8	#16864058	C₂	1	1	yes	maximal, characteristic, complemented
9	#16864056	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864042	C₂	1	1	yes	maximal, characteristic, complemented
11	#16864037	C₂	1	1	yes	maximal, characteristic, complemented
12	#16864002	C₂	1	2	yes	maximal, complemented
13	#16864001	C₂	1	2	yes	maximal, complemented
14	#16863985	C₂	1	2	yes	maximal, complemented
15	#16863982	C₂	1	2	yes	maximal, complemented
16	#16863977	C₂	1	1	yes	maximal, characteristic, complemented
17	#16863976	C₂	1	1	yes	maximal, characteristic, complemented
18	#16863969	C₂	1	1	yes	maximal, characteristic, complemented
19	#16863965	C₂	1	1	yes	maximal, characteristic, complemented
20	#16863943	C₂	1	1	yes	maximal, characteristic, complemented
21	#16863933	C₂	1	1	yes	maximal, characteristic, complemented
22	#16863931	C₂	1	1	yes	maximal, characteristic, complemented
23	#552×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11761629	C₂²	1	1	yes	characteristic
25	C₂×#11761628	C₂²	1	1	yes	characteristic
26	C₂×#11761628	C₂²	1	1	yes	characteristic
27	C₂×#11761628	C₂²	1	1	yes	characteristic, complemented
28	C₂×Q₈×D₆₇	C₂²	1	1	yes	characteristic, complemented
29	C₂²×D₂₆₈	C₂²	1	1	yes	characteristic
30	#14524042	C₂²	1	2	yes	complemented
31	#14524042	C₂²	1	1	yes	characteristic, complemented
32	#14524040	C₂²	1	2	yes	—
33	#14524039	C₂²	1	1	yes	characteristic
34	#14524038	C₂²	1	2	yes	complemented
35	#14524038	C₂²	1	2	yes	complemented
36	#14524038	C₂²	1	2	yes	complemented
37	#14524038	C₂²	1	2	yes	complemented
38	#14524036	C₂²	1	2	yes	—
39	#14524035	C₂²	1	2	yes	complemented
40	#14524034	C₂²	1	1	yes	characteristic, complemented
41	#14524032	C₂²	1	1	yes	characteristic
42	#14524031	C₂²	1	1	yes	characteristic
43	#14524031	C₂²	1	2	yes	—
44	#14524031	C₂²	1	2	yes	complemented
45	#14524029	C₂²	1	1	yes	characteristic
46	#14524029	C₂²	1	2	yes	—
47	#14524029	C₂²	1	2	yes	complemented
48	#14524029	C₂²	1	1	yes	characteristic, complemented
49	#14524028	C₂²	1	2	yes	—
50	#14524028	C₂²	1	2	yes	—
51	#14524028	C₂²	1	2	yes	complemented
52	#14524028	C₂²	1	2	yes	complemented
53	#14524028	C₂²	1	2	yes	complemented
54	#14524028	C₂²	1	2	yes	complemented
55	#14524028	C₂²	1	2	yes	complemented
56	#14524025	C₂²	1	2	yes	—
57	#14524025	C₂²	1	2	yes	—
58	#14524023	C₂²	1	1	yes	characteristic, complemented
59	#14524023	C₂²	1	2	yes	complemented
60	#14524023	C₂²	1	2	yes	complemented
61	#14524023	C₂²	1	1	yes	characteristic, complemented
62	#14524022	C₂²	1	1	yes	characteristic
63	#14524021	C₂²	1	2	yes	complemented
64	#14524021	C₂²	1	2	yes	complemented
65	#14524019	C₂²	1	1	yes	characteristic, complemented
66	#14524018	C₂²	1	2	yes	—
67	#14524018	C₂²	1	1	yes	characteristic
68	#14524018	C₂²	1	1	yes	characteristic
69	#14524018	C₂²	1	1	yes	characteristic
70	#14524018	C₂²	1	1	yes	characteristic
71	#14524018	C₂²	1	1	yes	characteristic
72	#14524018	C₂²	1	1	yes	characteristic, complemented
73	#14524018	C₂²	1	2	yes	complemented
74	#14524018	C₂²	1	2	yes	complemented
75	#14524018	C₂²	1	2	yes	complemented
76	#14524018	C₂²	1	2	yes	complemented
77	#14524017	C₂²	1	1	yes	characteristic
78	#14524017	C₂²	1	2	yes	complemented
79	#14524017	C₂²	1	2	yes	complemented
80	#14524017	C₂²	1	2	yes	complemented
81	#14524016	C₂²	1	2	yes	—
82	#14524016	C₂²	1	1	yes	characteristic
83	#14524016	C₂²	1	1	yes	characteristic, complemented
84	#14524016	C₂²	1	2	yes	complemented
85	#14524016	C₂²	1	2	yes	complemented
86	#14524016	C₂²	1	2	yes	complemented
87	#14524014	C₂²	1	1	yes	characteristic
88	#14524013	C₂²	1	2	yes	—
89	#14524013	C₂²	1	2	yes	—
90	#14524013	C₂²	1	2	yes	—
91	#14524011	C₂²	1	2	yes	—
92	#14524008	C₂²	1	1	yes	characteristic, complemented
93	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
94	C₄×D₂₆₈	C₂²	1	2	yes	complemented
95	C₄×D₂₆₈	C₂²	1	2	yes	complemented
96	C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
97	#14524005	C₂²	1	1	yes	characteristic
98	#14524005	C₂²	1	2	yes	complemented
99	#14524005	C₂²	1	2	yes	complemented
100	#14524005	C₂²	1	2	yes	complemented
101	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
104	#14524001	C₂²	1	2	yes	complemented
105	#14524001	C₂²	1	1	yes	characteristic, complemented
106	#14524000	C₂²	1	2	yes	complemented
107	#14524000	C₂²	1	2	yes	complemented
108	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
109	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
111	C₄²×D₆₇	C₂²	1	1	yes	characteristic, complemented
112	#126×C₆₇	C₂²	1	2	yes	—
113	#125×C₆₇	C₂²	1	2	yes	complemented
114	#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	#123×C₆₇	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
120	#117×C₆₇	C₂²	1	1	yes	characteristic
121	#117×C₆₇	C₂²	1	2	yes	complemented
122	C₂×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₆₇	C₂³	1	2	yes	—
124	#11761629	—	4	2	no	—
125	#11761628	—	4	2	no	—
126	#11761628	—	4	2	no	—
127	#11761628	—	4	2	no	—
128	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
129	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
130	C₂×Dic₁₃₄	C₂³	1	2	yes	—
131	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
132	Q₈×D₆₇	—	4	2	no	—
133	C₂×D₂₆₈	—	4	2	no	—
134	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
135	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
136	C₂×D₂₆₈	C₂³	1	2	yes	—
137	C₂×D₂₆₈	C₂³	1	2	yes	—
138	C₂×D₂₆₈	C₂³	1	2	yes	—
139	C₂×D₂₆₈	C₂³	1	2	yes	—
140	C₂×D₂₆₈	C₂³	1	2	yes	—
141	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
142	C₂×D₂₆₈	C₂³	1	2	yes	—
143	C₂×D₂₆₈	C₂³	1	2	yes	—
144	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
145	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
153	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₆₇	C₂³	1	2	yes	—
160	C₂×C₄×D₆₇	C₂³	1	2	yes	—
161	C₂×C₄×D₆₇	C₂³	1	2	yes	—
162	C₂×C₄×D₆₇	C₂³	1	2	yes	—
163	C₂×C₄×D₆₇	C₂³	1	2	yes	—
164	C₂×C₄×D₆₇	C₂³	1	2	yes	—
165	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
166	C₄⋊Dic₆₇	C₂³	1	2	yes	—
167	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
168	C₄⋊Dic₆₇	C₂³	1	2	yes	—
169	C₄⋊Dic₆₇	C₂³	1	2	yes	—
170	Dic₆₇⋊C₄	C₂³	1	2	yes	—
171	Dic₆₇⋊C₄	C₂³	1	2	yes	—
172	Dic₆₇⋊C₄	C₂³	1	2	yes	—
173	Dic₆₇⋊C₄	C₂³	1	2	yes	—
174	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
175	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
176	Dic₆₇⋊C₄	C₂³	1	2	yes	—
177	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
179	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
180	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
185	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
198	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
200	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
201	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
202	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
203	C₄×Dic₆₇	C₂³	1	2	yes	—
204	C₄×Dic₆₇	C₂³	1	2	yes	—
205	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
207	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
208	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
210	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
213	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
215	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
216	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
218	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
219	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
224	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
225	C₄²×C₆₇	C₂³	1	2	yes	—
226	C₄²×C₆₇	C₂³	1	2	yes	—
227	C₄²×C₆₇	C₂³	1	1	yes	characteristic
228	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
229	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
230	C₂²×D₆₇	—	4	2	no	—
231	C₂²×D₆₇	—	4	2	no	—
232	C₂²×D₆₇	—	4	2	no	—
233	C₂²×D₆₇	C₂⁴	1	2	yes	—
234	C₂²×D₆₇	C₂⁴	1	2	yes	—
235	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
236	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
237	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
238	Q₈×C₆₇	—	2	2	no	—
239	D₄×C₆₇	—	4	1	no	—
240	C₂×C₄×C₆₇	—	2	2	no	—
241	C₂×C₄×C₆₇	—	2	2	no	—
242	C₂×C₄×C₆₇	—	4	2	no	—
243	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
245	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
247	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
248	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
250	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
252	C₂²⋊D₆₇	—	4	2	no	—
253	C₂²⋊D₆₇	—	4	1	no	—
254	C₂²⋊D₆₇	—	4	1	no	—
255	C₂²⋊D₆₇	—	4	2	no	—
256	C₂²⋊D₆₇	—	4	1	no	—
257	C₂²⋊D₆₇	—	4	1	no	—
258	C₂²⋊D₆₇	—	4	1	no	—
259	C₂²⋊D₆₇	—	4	1	no	—
260	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₆₇	C₂⁴	1	2	yes	—
265	C₂×Dic₆₇	C₂⁴	1	2	yes	—
266	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
267	D₂₆₈	—	2	2	no	—
268	D₂₆₈	—	2	2	no	—
269	D₂₆₈	—	4	2	no	—
270	D₂₆₈	—	4	2	no	—
271	D₂₆₈	—	4	2	no	—
272	D₂₆₈	—	4	2	no	—
273	D₂₆₈	—	4	1	no	—
274	D₂₆₈	—	4	2	no	—
275	D₂₆₈	—	4	2	no	—
276	D₂₆₈	—	4	1	no	—
277	D₂₆₈	—	4	1	no	—
278	D₂₆₈	—	4	2	no	—
279	C₄×D₆₇	—	2	2	no	—
280	C₄×D₆₇	—	2	2	no	—
281	C₄×D₆₇	—	2	2	no	—
282	C₄×D₆₇	—	4	2	no	—
283	C₄×D₆₇	—	4	1	no	—
284	C₄×D₆₇	—	4	2	no	—
285	C₄×D₆₇	—	4	2	no	—
286	C₄×D₆₇	—	4	1	no	—
287	C₄×D₆₇	—	4	2	no	—
288	C₄×D₆₇	—	4	2	no	—
289	C₄×D₆₇	—	4	2	no	—
290	Dic₁₃₄	—	2	2	no	—
291	Dic₁₃₄	—	4	2	no	—
292	Dic₁₃₄	—	4	1	no	—
293	Dic₁₃₄	—	4	1	no	—
294	C₂²×C₆₇	—	2	1	no	—
295	C₂²×C₆₇	—	2	1	no	—
296	C₂²×C₆₇	—	2	1	no	—
297	C₂²×C₆₇	—	2	1	no	—
298	C₂²×C₆₇	—	2	1	no	—
299	C₂²×C₆₇	—	2	1	no	—
300	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
301	C₂×D₆₇	—	2	1	no	—
302	C₂×D₆₇	—	2	1	no	—
303	C₂×D₆₇	—	2	1	no	—
304	C₂×D₆₇	—	2	2	no	—
305	C₂×D₆₇	—	2	2	no	—
306	C₂×D₆₇	—	2	1	no	—
307	C₂×D₆₇	—	2	1	no	—
308	C₂×D₆₇	—	2	1	no	—
309	C₂×D₆₇	—	2	2	no	—
310	C₂×D₆₇	—	2	2	no	—
311	C₂×D₆₇	—	2	1	no	—
312	C₂×D₆₇	—	2	1	no	—
313	C₂×D₆₇	—	2	1	no	—
314	C₂×D₆₇	—	2	2	no	—
315	C₂×D₆₇	—	2	2	no	—
316	C₂×D₆₇	—	8	4	no	—
317	C₄×C₆₇	—	2	1	no	—
318	C₄×C₆₇	—	2	2	no	—
319	C₄×C₆₇	—	2	1	no	—
320	C₄×C₆₇	—	2	1	no	—
321	C₄×C₆₇	—	2	2	no	—
322	C₄×C₆₇	—	2	2	no	—
323	C₄×C₆₇	—	2	1	no	—
324	C₄×C₆₇	—	2	2	no	—
325	C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
326	Dic₆₇	—	2	2	no	—
327	Dic₆₇	—	2	1	no	—
328	Dic₆₇	—	2	1	no	—
329	Dic₆₇	—	2	1	no	—
330	Dic₆₇	—	2	1	no	—
331	Dic₆₇	—	2	2	no	—
332	Dic₆₇	—	2	1	no	—
333	C₂×C₆₇	—	4	1	no	—
334	C₂×C₆₇	—	4	1	no	—
335	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
336	C₂×C₆₇	#585	1	1	yes	characteristic
337	C₂×C₆₇	#585	1	1	yes	characteristic
338	D₆₇	—	4	1	no	—
339	D₆₇	—	4	1	no	—
340	D₆₇	—	4	1	no	—
341	D₆₇	—	4	2	no	—
342	D₆₇	—	4	2	no	—
343	#3551	—	67	1	no	maximal, Sylow
344	C₆₇	#3551	1	1	yes	characteristic, complemented, Sylow
345	#563	—	67	2	no	—
346	#560	—	67	2	no	—
347	#555	—	67	2	no	—
348	#553	—	67	1	no	—
349	#553	—	67	1	no	—
350	#552	—	67	1	no	—
351	#552	D₆₇	1	1	yes	characteristic, complemented
352	#551	—	67	2	no	—
353	#548	—	67	1	no	—
354	#548	—	67	1	no	—
355	#546	—	67	1	no	—
356	#546	—	67	1	no	—
357	#540	—	67	2	no	—
358	#540	—	67	2	no	—
359	#538	—	67	2	no	—
360	#538	—	67	2	no	—
361	#537	—	67	1	no	—
362	#537	—	67	1	no	—
363	#536	—	67	1	no	—
364	#535	—	67	1	no	—
365	#532	—	67	1	no	—
366	#529	—	67	1	no	—
367	#529	—	67	1	no	—
368	C₂×#41	—	67	1	no	—
369	C₂×#41	—	67	1	no	—
370	C₂×#41	—	67	1	no	—
371	C₂×#41	—	67	1	no	—
372	C₂²×Q₈	—	67	1	no	—
373	C₂²×D₄	—	67	1	no	—
374	C₄⋊Q₈	—	67	1	no	—
375	C₄⋊Q₈	—	67	2	no	—
376	#127	—	67	1	no	—
377	#127	—	67	2	no	—
378	#126	—	67	2	no	—
379	#126	—	67	2	no	—
380	#126	—	67	2	no	—
381	#126	—	67	2	no	—
382	#126	—	67	2	no	—
383	#126	C₂×D₆₇	1	2	yes	—
384	#125	—	67	1	no	—
385	#125	—	67	2	no	—
386	#125	C₂×D₆₇	1	1	yes	characteristic, complemented
387	#125	C₂×D₆₇	1	2	yes	complemented
388	#124	—	67	1	no	—
389	#124	—	67	1	no	—
390	#124	—	67	1	no	—
391	#124	—	67	2	no	—
392	#124	—	67	2	no	—
393	#124	—	67	1	no	—
394	#124	—	67	2	no	—
395	#124	—	67	2	no	—
396	#123	—	67	2	no	—
397	#123	—	67	2	no	—
398	#123	—	67	2	no	—
399	#123	—	67	2	no	—
400	#123	—	67	2	no	—
401	#123	—	67	2	no	—
402	#123	—	67	2	no	—
403	#123	—	67	2	no	—
404	#123	—	67	2	no	—
405	#123	C₂×D₆₇	1	2	yes	—
406	C₂²⋊Q₈	—	67	1	no	—
407	C₂²⋊Q₈	—	67	1	no	—
408	C₂²⋊Q₈	—	67	1	no	—
409	C₂²⋊Q₈	—	67	1	no	—
410	C₂²⋊Q₈	—	67	2	no	—
411	C₂²⋊Q₈	—	67	2	no	—
412	C₂²⋊Q₈	—	67	2	no	—
413	C₂²⋊Q₈	—	67	2	no	—
414	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
415	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
416	#121	—	67	1	no	—
417	#121	—	67	2	no	—
418	#121	—	67	1	no	—
419	#121	—	67	2	no	—
420	#121	—	67	2	no	—
421	#121	—	67	1	no	—
422	#121	—	67	1	no	—
423	#121	—	67	1	no	—
424	#121	—	67	1	no	—
425	#121	—	67	1	no	—
426	#121	—	67	2	no	—
427	#121	—	67	2	no	—
428	#121	—	67	1	no	—
429	#121	—	67	2	no	—
430	#121	—	67	2	no	—
431	#121	—	67	2	no	—
432	#121	—	67	1	no	—
433	#121	—	67	1	no	—
434	#121	—	67	2	no	—
435	#121	—	67	2	no	—
436	#121	—	67	2	no	—
437	#121	—	67	2	no	—
438	#120	—	67	2	no	—
439	#120	—	67	2	no	—
440	#120	—	67	2	no	—
441	#120	—	67	2	no	—
442	C₄×Q₈	—	67	1	no	—
443	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
444	C₄×D₄	—	67	1	no	—
445	C₄×D₄	—	67	1	no	—
446	C₄×D₄	—	67	2	no	—
447	C₄×D₄	—	67	2	no	—
448	C₄×D₄	—	67	1	no	—
449	C₄×D₄	—	67	2	no	—
450	C₄×D₄	—	67	2	no	—
451	C₄×D₄	—	67	2	no	—
452	C₄×D₄	—	67	1	no	—
453	C₄×D₄	—	67	1	no	—
454	C₄×D₄	—	67	2	no	—
455	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
456	#117	—	67	2	no	—
457	#117	—	67	1	no	—
458	#117	—	67	2	no	—
459	#117	—	67	2	no	—
460	#117	C₂×D₆₇	1	1	yes	characteristic
461	#117	C₂×D₆₇	1	2	yes	complemented
462	C₂×C₄⋊C₄	—	67	1	no	—
463	C₂×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
464	C₂×C₂²⋊C₄	—	67	2	no	—
465	C₂×C₂²⋊C₄	—	67	2	no	—
466	C₂×C₄²	—	67	1	no	—
467	C₂⁴	—	67	2	no	—
468	#41	—	268	2	no	—
469	#41	—	268	2	no	—
470	#41	—	268	2	no	—
471	#41	—	268	2	no	—
472	C₂×Q₈	—	268	2	no	—
473	C₂×Q₈	—	67	1	no	—
474	C₂×Q₈	—	67	2	no	—
475	C₂×Q₈	—	67	1	no	—
476	C₂×Q₈	—	67	1	no	—
477	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
478	C₂×D₄	—	268	2	no	—
479	C₂×D₄	—	67	1	no	—
480	C₂×D₄	—	67	2	no	—
481	C₂×D₄	—	67	1	no	—
482	C₂×D₄	—	67	1	no	—
483	C₂×D₄	—	67	1	no	—
484	C₂×D₄	—	67	2	no	—
485	C₂×D₄	—	67	1	no	—
486	C₂×D₄	—	67	1	no	—
487	C₂×D₄	—	67	2	no	—
488	C₂×D₄	—	67	2	no	—
489	C₂×D₄	—	67	2	no	—
490	C₂×D₄	—	67	2	no	—
491	C₂×D₄	—	67	2	no	—
492	C₂×D₄	—	67	1	no	—
493	C₂×D₄	—	67	2	no	—
494	C₂×D₄	—	67	1	no	—
495	C₂×D₄	—	67	2	no	—
496	C₂×D₄	—	67	1	no	—
497	C₂×D₄	—	67	1	no	—
498	C₂×D₄	—	67	1	no	—
499	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
500	C₂²×C₄	—	67	1	no	—
501	C₂²×C₄	—	67	1	no	—
502	C₂²×C₄	—	67	2	no	—
503	C₂²×C₄	—	67	2	no	—
504	C₂²×C₄	—	67	2	no	—
505	C₂²×C₄	—	67	2	no	—
506	C₂²×C₄	—	67	2	no	—
507	C₂²×C₄	—	67	2	no	—
508	C₂²×C₄	—	67	1	no	—
509	C₂²×C₄	—	67	1	no	—
510	C₂²×C₄	—	67	1	no	—
511	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
512	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
513	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
514	C₄⋊C₄	—	67	1	no	—
515	C₄⋊C₄	—	67	2	no	—
516	C₄⋊C₄	—	67	2	no	—
517	C₄⋊C₄	—	67	2	no	—
518	C₄⋊C₄	—	67	2	no	—
519	C₄⋊C₄	—	67	2	no	—
520	C₄⋊C₄	—	67	2	no	—
521	C₄⋊C₄	—	67	1	no	—
522	C₄⋊C₄	—	67	1	no	—
523	C₄⋊C₄	—	67	1	no	—
524	C₄⋊C₄	—	67	2	no	—
525	C₄⋊C₄	—	67	2	no	—
526	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
529	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
530	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
531	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
532	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
533	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
534	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
535	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
536	C₂²⋊C₄	—	67	1	no	—
537	C₂²⋊C₄	—	67	2	no	—
538	C₂²⋊C₄	—	67	1	no	—
539	C₂²⋊C₄	—	67	2	no	—
540	C₂²⋊C₄	—	67	2	no	—
541	C₂²⋊C₄	—	67	2	no	—
542	C₂²⋊C₄	—	67	2	no	—
543	C₂²⋊C₄	—	67	1	no	—
544	C₂²⋊C₄	—	67	2	no	—
545	C₂²⋊C₄	—	67	2	no	—
546	C₂²⋊C₄	—	67	2	no	—
547	C₂²⋊C₄	—	67	2	no	—
548	C₂²⋊C₄	—	67	1	no	—
549	C₂²⋊C₄	—	67	1	no	—
550	C₂²⋊C₄	—	67	1	no	—
551	C₂²⋊C₄	—	67	2	no	—
552	C₂²⋊C₄	—	67	2	no	—
553	C₂²⋊C₄	—	67	2	no	—
554	C₂²⋊C₄	—	67	2	no	—
555	C₂²⋊C₄	—	67	2	no	—
556	C₂²⋊C₄	—	67	2	no	—
557	C₂²⋊C₄	—	67	2	no	—
558	C₂²⋊C₄	—	67	2	no	—
559	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
560	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
563	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
564	C₄²	—	67	1	no	—
565	C₄²	—	67	1	no	—
566	C₄²	—	67	1	no	—
567	C₄²	—	67	2	no	—
568	C₄²	—	67	2	no	—
569	C₄²	C₂²×D₆₇	1	1	yes	characteristic
570	C₄²	C₂²×D₆₇	1	2	yes	—
571	C₄²	C₂²×D₆₇	1	2	yes	—
572	C₂³	—	268	2	no	—
573	C₂³	—	268	2	no	—
574	C₂³	—	268	2	no	—
575	C₂³	—	67	2	no	—
576	C₂³	—	67	2	no	—
577	C₂³	—	67	1	no	—
578	C₂³	—	67	1	no	—
579	C₂³	—	67	1	no	—
580	C₂³	C₂³×D₆₇	1	1	yes	characteristic
581	C₂³	C₂³×D₆₇	1	1	yes	characteristic
582	Q₈	—	2	2	no	—
583	Q₈	—	268	2	no	—
584	Q₈	—	268	1	no	—
585	Q₈	—	268	1	no	—
586	Q₈	—	134	2	no	—
587	D₄	—	4	1	no	—
588	D₄	—	268	2	no	—
589	D₄	—	268	1	no	—
590	D₄	—	268	1	no	—
591	D₄	—	268	2	no	—
592	D₄	—	268	2	no	—
593	D₄	—	268	2	no	—
594	D₄	—	268	2	no	—
595	D₄	—	268	1	no	—
596	D₄	—	268	2	no	—
597	D₄	—	268	2	no	—
598	D₄	—	268	1	no	—
599	D₄	—	268	2	no	—
600	D₄	—	268	1	no	—
601	D₄	—	268	1	no	—
602	D₄	—	268	1	no	—
603	D₄	—	268	2	no	—
604	D₄	—	268	1	no	—
605	D₄	—	268	1	no	—
606	D₄	—	134	2	no	—
607	D₄	—	134	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	268	2	no	—
612	C₂×C₄	—	268	2	no	—
613	C₂×C₄	—	268	2	no	—
614	C₂×C₄	—	268	2	no	—
615	C₂×C₄	—	268	1	no	—
616	C₂×C₄	—	268	2	no	—
617	C₂×C₄	—	268	1	no	—
618	C₂×C₄	—	268	2	no	—
619	C₂×C₄	—	67	1	no	—
620	C₂×C₄	—	67	1	no	—
621	C₂×C₄	—	67	1	no	—
622	C₂×C₄	—	67	1	no	—
623	C₂×C₄	—	67	2	no	—
624	C₂×C₄	—	67	2	no	—
625	C₂×C₄	—	67	1	no	—
626	C₂×C₄	—	134	2	no	—
627	C₂×C₄	—	134	2	no	—
628	C₂×C₄	—	134	2	no	—
629	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
630	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
631	C₂×C₄	C₂³×D₆₇	1	2	yes	—
632	C₂×C₄	C₂³×D₆₇	1	2	yes	—
633	C₂×C₄	C₂³×D₆₇	1	2	yes	—
634	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
635	C₂×C₄	C₂³×D₆₇	1	2	yes	—
636	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
638	C₂²	—	2	1	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	536	4	no	—
645	C₂²	—	134	1	no	—
646	C₂²	—	134	2	no	—
647	C₂²	—	134	2	no	—
648	C₂²	—	134	1	no	—
649	C₂²	—	134	1	no	—
650	C₂²	—	134	1	no	—
651	C₂²	—	134	2	no	—
652	C₂²	—	134	1	no	—
653	C₂²	—	134	1	no	—
654	C₂²	—	134	2	no	—
655	C₂²	—	134	1	no	—
656	C₂²	—	134	1	no	—
657	C₂²	—	134	2	no	—
658	C₂²	—	134	1	no	—
659	C₂²	—	134	2	no	—
660	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	2	no	—
669	C₄	—	134	1	no	—
670	C₄	—	134	2	no	—
671	C₄	—	134	1	no	—
672	C₄	—	134	1	no	—
673	C₄	—	134	1	no	—
674	C₄	—	134	2	no	—
675	C₄	—	134	1	no	—
676	C₄	#14524089	1	2	yes	—
677	C₂	—	4	1	no	—
678	C₂	—	4	1	no	—
679	C₂	—	268	2	no	—
680	C₂	—	268	2	no	—
681	C₂	—	268	1	no	—
682	C₂	—	268	1	no	—
683	C₂	—	268	1	no	—
684	C₂	C₂×#14524089	1	1	yes	characteristic
685	C₂	#16864232	1	1	yes	characteristic
686	C₂	#16864233	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#552×C₆₇	C₂
hypercenter	#552	D₆₇
hypocenter	C₆₇	#3551
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #16864150	C₂	semidirect
2. #16864136	C₂	semidirect
3. #16864109	C₂	semidirect
4. #16864099	C₂	semidirect
5. #16864094	C₂	semidirect
6. #16864085	C₂	semidirect
7. #16864071	C₂	semidirect
8. #16864058	C₂	semidirect
9. #16864056	C₂	semidirect
10. #16864042	C₂	semidirect
11. #16864037	C₂	semidirect
12. #16864002	C₂	semidirect
13. #16864001	C₂	semidirect
14. #16863985	C₂	semidirect
15. #16863982	C₂	semidirect
16. #16863977	C₂	semidirect
17. #16863976	C₂	semidirect
18. #16863969	C₂	semidirect
19. #16863965	C₂	semidirect
20. #16863943	C₂	semidirect
21. #16863933	C₂	semidirect
22. #16863931	C₂	semidirect
23. #552×C₆₇	C₂	semidirect
27. C₂×#11761628	C₂²	semidirect
28. C₂×Q₈×D₆₇	C₂²	semidirect
30. #14524042	C₂²	semidirect
31. #14524042	C₂²	semidirect
34. #14524038	C₂²	semidirect
35. #14524038	C₂²	semidirect
36. #14524038	C₂²	semidirect
37. #14524038	C₂²	semidirect
39. #14524035	C₂²	semidirect
40. #14524034	C₂²	semidirect
44. #14524031	C₂²	semidirect
47. #14524029	C₂²	semidirect
48. #14524029	C₂²	semidirect
51. #14524028	C₂²	semidirect
52. #14524028	C₂²	semidirect
53. #14524028	C₂²	semidirect
54. #14524028	C₂²	semidirect
55. #14524028	C₂²	semidirect
58. #14524023	C₂²	semidirect
59. #14524023	C₂²	semidirect
60. #14524023	C₂²	semidirect
61. #14524023	C₂²	semidirect
63. #14524021	C₂²	semidirect
64. #14524021	C₂²	semidirect
65. #14524019	C₂²	semidirect
72. #14524018	C₂²	semidirect
73. #14524018	C₂²	semidirect
74. #14524018	C₂²	semidirect
75. #14524018	C₂²	semidirect
76. #14524018	C₂²	semidirect
78. #14524017	C₂²	semidirect
79. #14524017	C₂²	semidirect
80. #14524017	C₂²	semidirect
83. #14524016	C₂²	semidirect
84. #14524016	C₂²	semidirect
85. #14524016	C₂²	semidirect
86. #14524016	C₂²	semidirect
92. #14524008	C₂²	semidirect
94. C₄×D₂₆₈	C₂²	semidirect
95. C₄×D₂₆₈	C₂²	semidirect
96. C₄×D₂₆₈	C₂²	semidirect
98. #14524005	C₂²	semidirect
99. #14524005	C₂²	semidirect
100. #14524005	C₂²	semidirect
102. C₄×C₂²⋊D₆₇	C₂²	semidirect
103. C₄×C₂²⋊D₆₇	C₂²	semidirect
104. #14524001	C₂²	semidirect
105. #14524001	C₂²	semidirect
106. #14524000	C₂²	semidirect
107. #14524000	C₂²	semidirect
108. C₄⋊C₄×D₆₇	C₂²	semidirect
111. C₄²×D₆₇	C₂²	semidirect
113. #125×C₆₇	C₂²	semidirect
114. #125×C₆₇	C₂²	semidirect
117. C₂²⋊Q₈×C₆₇	C₂²	semidirect
118. C₄×Q₈×C₆₇	C₂²	semidirect
121. #117×C₆₇	C₂²	semidirect
122. C₂×C₄⋊C₄×C₆₇	C₂²	semidirect
344. C₆₇	#3551	semidirect
351. #552	D₆₇	semidirect
386. #125	C₂×D₆₇	semidirect
387. #125	C₂×D₆₇	semidirect
415. C₂²⋊Q₈	C₂×D₆₇	semidirect
443. C₄×Q₈	C₂×D₆₇	semidirect
461. #117	C₂×D₆₇	semidirect
463. C₂×C₄⋊C₄	C₂×D₆₇	semidirect