Subgroups — #22574427

Order 8576.

1134 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864141	C₂	1	2	yes	maximal, complemented
2	#16864141	C₂	1	2	yes	maximal, complemented
3	#16864104	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864101	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864056	C₂	1	1	yes	maximal, characteristic, complemented
6	#16864053	C₂	1	1	yes	maximal, characteristic, complemented
7	#16864047	C₂	1	1	yes	maximal, characteristic, complemented
8	#16864046	C₂	1	1	yes	maximal, characteristic, complemented
9	#16864043	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864043	C₂	1	2	yes	maximal, complemented
11	#16864035	C₂	1	2	yes	maximal, complemented
12	#16864034	C₂	1	1	yes	maximal, characteristic, complemented
13	#16864021	C₂	1	2	yes	maximal, complemented
14	#16864019	C₂	1	1	yes	maximal, characteristic, complemented
15	#16864013	C₂	1	1	yes	maximal, characteristic, complemented
16	#16863992	C₂	1	2	yes	maximal, complemented
17	#16863978	C₂	1	2	yes	maximal, complemented
18	#16863975	C₂	1	2	yes	maximal, complemented
19	#16863974	C₂	1	1	yes	maximal, characteristic, complemented
20	#16863903	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂²⋊Q₈×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	#121×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	#537×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11761628	C₂²	1	2	yes	complemented
25	C₂×#11761628	C₂²	1	1	yes	characteristic, complemented
26	C₂×#11761627	C₂²	1	2	yes	complemented
27	C₂×Q₈×D₆₇	C₂²	1	1	yes	characteristic, complemented
28	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic
29	C₂×D₄×D₆₇	C₂²	1	2	yes	—
30	C₂²×C₄×D₆₇	C₂²	1	1	yes	characteristic
31	#14524042	C₂²	1	1	yes	characteristic, complemented
32	#14524042	C₂²	1	1	yes	characteristic, complemented
33	#14524038	C₂²	1	2	yes	complemented
34	#14524036	C₂²	1	2	yes	complemented
35	#14524033	C₂²	1	2	yes	complemented
36	#14524033	C₂²	1	2	yes	complemented
37	#14524032	C₂²	1	1	yes	characteristic, complemented
38	#14524030	C₂²	1	1	yes	characteristic, complemented
39	#14524030	C₂²	1	2	yes	complemented
40	#14524030	C₂²	1	2	yes	complemented
41	#14524029	C₂²	1	2	yes	complemented
42	#14524029	C₂²	1	2	yes	complemented
43	#14524028	C₂²	1	2	yes	complemented
44	#14524026	C₂²	1	2	yes	complemented
45	#14524026	C₂²	1	2	yes	complemented
46	#14524025	C₂²	1	2	yes	complemented
47	#14524025	C₂²	1	2	yes	complemented
48	#14524025	C₂²	1	2	yes	complemented
49	#14524024	C₂²	1	2	yes	complemented
50	#14524024	C₂²	1	2	yes	complemented
51	#14524024	C₂²	1	1	yes	characteristic, complemented
52	#14524024	C₂²	1	1	yes	characteristic, complemented
53	#14524023	C₂²	1	2	yes	—
54	#14524023	C₂²	1	1	yes	characteristic
55	#14524023	C₂²	1	2	yes	complemented
56	#14524022	C₂²	1	1	yes	characteristic, complemented
57	#14524022	C₂²	1	2	yes	complemented
58	#14524022	C₂²	1	1	yes	characteristic, complemented
59	#14524022	C₂²	1	2	yes	complemented
60	#14524021	C₂²	1	2	yes	—
61	#14524021	C₂²	1	2	yes	—
62	#14524021	C₂²	1	2	yes	complemented
63	#14524021	C₂²	1	2	yes	complemented
64	#14524020	C₂²	1	2	yes	complemented
65	#14524020	C₂²	1	2	yes	complemented
66	#14524020	C₂²	1	2	yes	complemented
67	#14524020	C₂²	1	2	yes	complemented
68	#14524019	C₂²	1	1	yes	characteristic
69	#14524019	C₂²	1	1	yes	characteristic
70	#14524019	C₂²	1	2	yes	complemented
71	#14524019	C₂²	1	1	yes	characteristic, complemented
72	#14524018	C₂²	1	1	yes	characteristic
73	#14524017	C₂²	1	1	yes	characteristic
74	#14524017	C₂²	1	1	yes	characteristic, complemented
75	#14524016	C₂²	1	2	yes	—
76	#14524016	C₂²	1	2	yes	complemented
77	#14524015	C₂²	1	2	yes	—
78	#14524015	C₂²	1	2	yes	complemented
79	#14524015	C₂²	1	2	yes	complemented
80	#14524015	C₂²	1	2	yes	complemented
81	#14524014	C₂²	1	1	yes	characteristic
82	#14524014	C₂²	1	1	yes	characteristic
83	#14524014	C₂²	1	2	yes	complemented
84	#14524014	C₂²	1	2	yes	complemented
85	#14524014	C₂²	1	2	yes	complemented
86	#14524014	C₂²	1	1	yes	characteristic, complemented
87	#14524011	C₂²	1	2	yes	—
88	#14524011	C₂²	1	1	yes	characteristic
89	#14524011	C₂²	1	2	yes	—
90	#14524011	C₂²	1	1	yes	characteristic
91	Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
92	#14524008	C₂²	1	1	yes	characteristic, complemented
93	D₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
94	#14524005	C₂²	1	1	yes	characteristic, complemented
95	#14524005	C₂²	1	2	yes	complemented
96	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
98	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
102	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
103	#14524002	C₂²	1	1	yes	characteristic, complemented
104	C₂×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic, complemented
105	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
106	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
107	C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
108	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
111	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
112	C₂×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	C₂×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	#121×C₆₇	C₂²	1	1	yes	characteristic
118	#121×C₆₇	C₂²	1	2	yes	complemented
119	#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	#121×C₆₇	C₂²	1	2	yes	complemented
121	#121×C₆₇	C₂²	1	2	yes	complemented
122	C₂×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₆₇	C₂³	1	1	yes	characteristic
124	C₂³×D₆₇	C₂³	1	2	yes	—
125	#11761628	—	4	2	no	—
126	#11761628	—	4	4	no	—
127	#11761627	—	4	4	no	—
128	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
129	C₂×Dic₁₃₄	C₂³	1	2	yes	—
130	C₂×Dic₁₃₄	C₂³	1	2	yes	—
131	C₂×Dic₁₃₄	C₂³	1	2	yes	—
132	Q₈×D₆₇	—	4	2	no	—
133	C₂×D₂₆₈	C₂³	1	2	yes	—
134	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
144	D₄×D₆₇	—	4	2	no	—
145	D₄×D₆₇	—	4	4	no	—
146	C₂²×Dic₆₇	C₂³	1	2	yes	—
147	C₂²×Dic₆₇	C₂³	1	2	yes	—
148	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₆₇	—	4	2	no	—
150	C₂×C₄×D₆₇	C₂³	1	2	yes	—
151	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₆₇	C₂³	1	2	yes	—
155	C₂×C₄×D₆₇	C₂³	1	2	yes	—
156	C₂×C₄×D₆₇	C₂³	1	2	yes	—
157	C₂×C₄×D₆₇	C₂³	1	2	yes	—
158	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₆₇	C₂³	1	2	yes	—
162	C₄⋊Dic₆₇	C₂³	1	2	yes	—
163	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
164	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
165	C₄⋊Dic₆₇	C₂³	1	2	yes	—
166	Dic₆₇⋊C₄	C₂³	1	2	yes	—
167	Dic₆₇⋊C₄	C₂³	1	2	yes	—
168	Dic₆₇⋊C₄	C₂³	1	2	yes	—
169	Dic₆₇⋊C₄	C₂³	1	2	yes	—
170	Dic₆₇⋊C₄	C₂³	1	2	yes	—
171	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
172	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
173	Dic₆₇⋊C₄	C₂³	1	2	yes	—
174	Dic₆₇⋊C₄	C₂³	1	2	yes	—
175	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
176	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
177	Dic₆₇⋊C₄	C₂³	1	2	yes	—
178	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
179	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
180	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
181	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
185	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
186	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
187	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
189	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
190	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
196	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
199	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
200	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
202	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
203	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
204	C₄×Dic₆₇	C₂³	1	2	yes	—
205	C₄×Dic₆₇	C₂³	1	2	yes	—
206	#41×C₆₇	—	4	2	no	—
207	#41×C₆₇	—	4	2	no	—
208	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
209	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
210	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₆₇	C₂³	1	2	yes	—
212	C₂×D₄×C₆₇	C₂³	1	2	yes	—
213	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×D₄×C₆₇	C₂³	1	2	yes	—
215	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
216	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
217	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
218	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
219	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
220	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
221	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
222	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
223	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
224	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
225	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
226	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
228	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
229	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
230	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
231	C₂³×C₆₇	C₂⁴	1	2	yes	—
232	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
233	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
234	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
235	C₂²×D₆₇	—	2	2	no	—
236	C₂²×D₆₇	—	2	2	no	—
237	C₂²×D₆₇	—	2	4	no	—
238	C₂²×D₆₇	—	4	1	no	—
239	C₂²×D₆₇	—	4	2	no	—
240	C₂²×D₆₇	—	4	2	no	—
241	C₂²×D₆₇	C₂⁴	1	2	yes	—
242	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
243	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
244	Q₈×C₆₇	—	2	2	no	—
245	Q₈×C₆₇	—	4	1	no	—
246	D₄×C₆₇	—	2	2	no	—
247	D₄×C₆₇	—	4	2	no	—
248	D₄×C₆₇	—	4	1	no	—
249	D₄×C₆₇	—	4	1	no	—
250	D₄×C₆₇	—	4	1	no	—
251	D₄×C₆₇	—	4	2	no	—
252	D₄×C₆₇	—	4	2	no	—
253	C₂×C₄×C₆₇	—	2	2	no	—
254	C₂×C₄×C₆₇	—	2	2	no	—
255	C₂×C₄×C₆₇	—	2	2	no	—
256	C₂×C₄×C₆₇	—	4	2	no	—
257	C₂×C₄×C₆₇	—	4	2	no	—
258	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
259	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
260	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
261	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
265	C₂²⋊D₆₇	—	2	4	no	—
266	C₂²⋊D₆₇	—	2	2	no	—
267	C₂²⋊D₆₇	—	2	2	no	—
268	C₂²⋊D₆₇	—	2	2	no	—
269	C₂²⋊D₆₇	—	2	2	no	—
270	C₂²⋊D₆₇	—	4	2	no	—
271	C₂²⋊D₆₇	—	4	2	no	—
272	C₂²⋊D₆₇	—	4	2	no	—
273	C₂²⋊D₆₇	—	4	2	no	—
274	C₂×Dic₆₇	—	4	1	no	—
275	C₂×Dic₆₇	—	4	2	no	—
276	C₂×Dic₆₇	—	4	2	no	—
277	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₆₇	C₂⁴	1	2	yes	—
281	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
282	C₂×Dic₆₇	C₂⁴	1	2	yes	—
283	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₆₇	C₂⁴	1	2	yes	—
285	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
286	D₂₆₈	—	2	4	no	—
287	D₂₆₈	—	2	2	no	—
288	C₄×D₆₇	—	2	4	no	—
289	C₄×D₆₇	—	2	2	no	—
290	C₄×D₆₇	—	2	2	no	—
291	C₄×D₆₇	—	4	1	no	—
292	C₄×D₆₇	—	4	1	no	—
293	C₄×D₆₇	—	4	2	no	—
294	C₄×D₆₇	—	4	2	no	—
295	C₄×D₆₇	—	4	2	no	—
296	C₄×D₆₇	—	4	2	no	—
297	Dic₁₃₄	—	2	2	no	—
298	Dic₁₃₄	—	4	2	no	—
299	Dic₁₃₄	—	4	2	no	—
300	Dic₁₃₄	—	4	2	no	—
301	C₂²×C₆₇	—	2	1	no	—
302	C₂²×C₆₇	—	2	2	no	—
303	C₂²×C₆₇	—	2	1	no	—
304	C₂²×C₆₇	—	2	1	no	—
305	C₂²×C₆₇	—	2	1	no	—
306	C₂²×C₆₇	—	2	1	no	—
307	C₂²×C₆₇	—	2	2	no	—
308	C₂²×C₆₇	—	2	1	no	—
309	C₂²×C₆₇	—	2	1	no	—
310	C₂²×C₆₇	—	2	1	no	—
311	C₂²×C₆₇	—	2	1	no	—
312	C₂²×C₆₇	—	2	2	no	—
313	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
314	C₂×D₆₇	—	2	1	no	—
315	C₂×D₆₇	—	2	1	no	—
316	C₂×D₆₇	—	2	1	no	—
317	C₂×D₆₇	—	2	1	no	—
318	C₂×D₆₇	—	2	2	no	—
319	C₂×D₆₇	—	2	2	no	—
320	C₂×D₆₇	—	2	2	no	—
321	C₂×D₆₇	—	4	4	no	—
322	C₂×D₆₇	—	8	4	no	—
323	C₂×D₆₇	H(5,𝔽₂)	1	2	yes	—
324	C₂×D₆₇	2₋¹⁺⁴	1	2	yes	—
325	C₄×C₆₇	—	2	2	no	—
326	C₄×C₆₇	—	2	2	no	—
327	C₄×C₆₇	—	2	2	no	—
328	C₄×C₆₇	—	2	1	no	—
329	C₄×C₆₇	—	2	1	no	—
330	C₄×C₆₇	—	2	1	no	—
331	C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
332	Dic₆₇	—	2	2	no	—
333	Dic₆₇	—	2	1	no	—
334	Dic₆₇	—	2	1	no	—
335	Dic₆₇	—	2	1	no	—
336	Dic₆₇	—	2	2	no	—
337	Dic₆₇	—	2	2	no	—
338	Dic₆₇	—	2	1	no	—
339	Dic₆₇	—	2	1	no	—
340	Dic₆₇	—	2	1	no	—
341	C₂×C₆₇	—	4	1	no	—
342	C₂×C₆₇	—	4	2	no	—
343	C₂×C₆₇	—	4	1	no	—
344	C₂×C₆₇	—	4	1	no	—
345	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
346	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
347	C₂×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
348	D₆₇	—	2	2	no	—
349	D₆₇	—	2	2	no	—
350	D₆₇	—	4	2	no	—
351	#3536	—	67	1	no	maximal, Sylow
352	C₆₇	#3536	1	1	yes	characteristic, complemented, Sylow
353	#562	—	67	2	no	—
354	#562	—	67	2	no	—
355	#554	—	67	1	no	—
356	#554	—	67	1	no	—
357	#548	—	67	1	no	—
358	#548	—	67	1	no	—
359	#547	—	67	1	no	—
360	#547	—	67	1	no	—
361	#546	—	67	1	no	—
362	#546	—	67	2	no	—
363	#546	—	67	2	no	—
364	#546	—	67	1	no	—
365	#543	—	67	2	no	—
366	#542	—	67	1	no	—
367	#542	—	67	1	no	—
368	#539	—	67	2	no	—
369	#538	—	67	2	no	—
370	#537	—	67	1	no	—
371	#537	—	67	2	no	—
372	#537	D₆₇	1	1	yes	characteristic, complemented
373	#525	—	67	1	no	—
374	C₂×C₂²⋊Q₈	—	67	1	no	—
375	C₂×#121	—	67	1	no	—
376	C₂×#41	—	67	2	no	—
377	C₂×#41	—	67	2	no	—
378	C₂×#41	—	67	1	no	—
379	C₂×#41	C₂×D₆₇	1	1	yes	characteristic, complemented
380	C₂×#41	C₂×D₆₇	1	1	yes	characteristic, complemented
381	C₂²×Q₈	—	67	1	no	—
382	C₂²×D₄	—	67	2	no	—
383	C₂²×D₄	—	67	1	no	—
384	C₂³×C₄	—	67	1	no	—
385	C₄⋊Q₈	—	67	1	no	—
386	C₄⋊Q₈	—	67	1	no	—
387	#126	—	67	2	no	—
388	#126	—	67	2	no	—
389	#125	—	67	2	no	—
390	#125	—	67	2	no	—
391	#124	—	67	1	no	—
392	#124	—	67	2	no	—
393	#124	—	67	1	no	—
394	#124	—	67	2	no	—
395	#124	—	67	2	no	—
396	#124	—	67	2	no	—
397	#123	—	67	1	no	—
398	#123	—	67	1	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	—	67	2	no	—
406	#123	—	67	2	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	1	no	—
412	C₂²⋊Q₈	—	67	1	no	—
413	C₂²⋊Q₈	—	67	2	no	—
414	C₂²⋊Q₈	—	67	2	no	—
415	C₂²⋊Q₈	—	67	2	no	—
416	C₂²⋊Q₈	—	67	1	no	—
417	C₂²⋊Q₈	—	67	2	no	—
418	C₂²⋊Q₈	—	67	2	no	—
419	C₂²⋊Q₈	—	67	2	no	—
420	C₂²⋊Q₈	—	67	2	no	—
421	C₂²⋊Q₈	—	67	2	no	—
422	C₂²⋊Q₈	—	67	2	no	—
423	C₂²⋊Q₈	—	67	2	no	—
424	C₂²⋊Q₈	—	67	2	no	—
425	C₂²⋊Q₈	—	67	2	no	—
426	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
427	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
428	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
429	#121	—	67	1	no	—
430	#121	—	67	2	no	—
431	#121	—	67	1	no	—
432	#121	—	67	1	no	—
433	#121	—	67	2	no	—
434	#121	—	67	2	no	—
435	#121	—	67	2	no	—
436	#121	—	67	2	no	—
437	#121	—	67	2	no	—
438	#121	—	67	2	no	—
439	#121	—	67	1	no	—
440	#121	—	67	1	no	—
441	#121	—	67	1	no	—
442	#121	—	67	2	no	—
443	#121	—	67	2	no	—
444	#121	C₂×D₆₇	1	1	yes	characteristic
445	#121	C₂×D₆₇	1	2	yes	complemented
446	#121	C₂×D₆₇	1	1	yes	characteristic, complemented
447	#121	C₂×D₆₇	1	2	yes	complemented
448	#121	C₂×D₆₇	1	2	yes	complemented
449	#120	—	67	1	no	—
450	#120	—	67	1	no	—
451	#120	—	67	2	no	—
452	#120	—	67	2	no	—
453	C₄×Q₈	—	67	1	no	—
454	C₄×Q₈	—	67	1	no	—
455	C₄×D₄	—	67	1	no	—
456	C₄×D₄	—	67	1	no	—
457	C₄×D₄	—	67	1	no	—
458	C₄×D₄	—	67	1	no	—
459	C₄×D₄	—	67	1	no	—
460	C₄×D₄	—	67	2	no	—
461	C₄×D₄	—	67	2	no	—
462	C₄×D₄	—	67	2	no	—
463	C₄×D₄	—	67	1	no	—
464	C₄×D₄	—	67	2	no	—
465	#117	—	67	1	no	—
466	C₂×C₄⋊C₄	—	67	1	no	—
467	C₂×C₄⋊C₄	—	67	1	no	—
468	C₂×C₄⋊C₄	—	67	2	no	—
469	C₂×C₄⋊C₄	—	67	1	no	—
470	C₂×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
471	C₂×C₂²⋊C₄	—	67	2	no	—
472	C₂×C₂²⋊C₄	—	67	2	no	—
473	C₂×C₂²⋊C₄	—	67	2	no	—
474	C₂×C₂²⋊C₄	—	67	2	no	—
475	C₂⁴	—	67	2	no	—
476	C₂⁴	—	67	1	no	—
477	#41	—	4	2	no	—
478	#41	—	4	2	no	—
479	#41	—	268	2	no	—
480	#41	—	268	4	no	—
481	#41	—	268	4	no	—
482	C₂×Q₈	—	268	2	no	—
483	C₂×Q₈	—	67	2	no	—
484	C₂×Q₈	—	67	2	no	—
485	C₂×Q₈	—	67	2	no	—
486	C₂×Q₈	—	67	1	no	—
487	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
488	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
489	C₂×D₄	—	268	4	no	—
490	C₂×D₄	—	268	2	no	—
491	C₂×D₄	—	67	2	no	—
492	C₂×D₄	—	67	2	no	—
493	C₂×D₄	—	67	2	no	—
494	C₂×D₄	—	67	2	no	—
495	C₂×D₄	—	67	1	no	—
496	C₂×D₄	—	67	1	no	—
497	C₂×D₄	—	67	1	no	—
498	C₂×D₄	—	67	1	no	—
499	C₂×D₄	—	67	2	no	—
500	C₂×D₄	—	67	2	no	—
501	C₂×D₄	—	67	1	no	—
502	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
503	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
504	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
505	C₂×D₄	C₂²×D₆₇	1	2	yes	—
506	C₂×D₄	C₂²×D₆₇	1	2	yes	—
507	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
508	C₂×D₄	C₂²×D₆₇	1	2	yes	—
509	C₂²×C₄	—	268	2	no	—
510	C₂²×C₄	—	67	2	no	—
511	C₂²×C₄	—	67	2	no	—
512	C₂²×C₄	—	67	1	no	—
513	C₂²×C₄	—	67	1	no	—
514	C₂²×C₄	—	67	2	no	—
515	C₂²×C₄	—	67	2	no	—
516	C₂²×C₄	—	67	2	no	—
517	C₂²×C₄	—	67	2	no	—
518	C₂²×C₄	—	67	1	no	—
519	C₂²×C₄	—	67	2	no	—
520	C₂²×C₄	—	67	1	no	—
521	C₂²×C₄	—	67	1	no	—
522	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
523	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
524	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
525	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
526	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
527	C₄⋊C₄	—	67	1	no	—
528	C₄⋊C₄	—	67	1	no	—
529	C₄⋊C₄	—	67	2	no	—
530	C₄⋊C₄	—	67	2	no	—
531	C₄⋊C₄	—	67	2	no	—
532	C₄⋊C₄	—	67	2	no	—
533	C₄⋊C₄	—	67	2	no	—
534	C₄⋊C₄	—	67	2	no	—
535	C₄⋊C₄	—	67	1	no	—
536	C₄⋊C₄	—	67	1	no	—
537	C₄⋊C₄	—	67	2	no	—
538	C₄⋊C₄	—	67	1	no	—
539	C₄⋊C₄	—	67	1	no	—
540	C₄⋊C₄	—	67	1	no	—
541	C₄⋊C₄	—	67	1	no	—
542	C₄⋊C₄	—	67	2	no	—
543	C₄⋊C₄	—	67	2	no	—
544	C₄⋊C₄	—	67	2	no	—
545	C₄⋊C₄	—	67	2	no	—
546	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
547	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
548	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
549	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
550	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
551	C₂²⋊C₄	—	67	2	no	—
552	C₂²⋊C₄	—	67	2	no	—
553	C₂²⋊C₄	—	67	2	no	—
554	C₂²⋊C₄	—	67	1	no	—
555	C₂²⋊C₄	—	67	1	no	—
556	C₂²⋊C₄	—	67	2	no	—
557	C₂²⋊C₄	—	67	2	no	—
558	C₂²⋊C₄	—	67	1	no	—
559	C₂²⋊C₄	—	67	1	no	—
560	C₂²⋊C₄	—	67	2	no	—
561	C₂²⋊C₄	—	67	1	no	—
562	C₂²⋊C₄	—	67	1	no	—
563	C₂²⋊C₄	—	67	1	no	—
564	C₂²⋊C₄	—	67	1	no	—
565	C₂²⋊C₄	—	67	2	no	—
566	C₂²⋊C₄	—	67	2	no	—
567	C₂²⋊C₄	—	67	2	no	—
568	C₂²⋊C₄	—	67	2	no	—
569	C₂²⋊C₄	—	67	2	no	—
570	C₂²⋊C₄	—	67	2	no	—
571	C₂²⋊C₄	—	67	1	no	—
572	C₂²⋊C₄	—	67	1	no	—
573	C₂²⋊C₄	—	67	2	no	—
574	C₂²⋊C₄	—	67	2	no	—
575	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
576	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
577	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
578	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
579	C₄²	—	67	1	no	—
580	C₄²	—	67	1	no	—
581	C₄²	—	67	2	no	—
582	C₄²	—	67	2	no	—
583	C₂³	—	268	1	no	—
584	C₂³	—	268	2	no	—
585	C₂³	—	268	2	no	—
586	C₂³	—	67	1	no	—
587	C₂³	—	67	1	no	—
588	C₂³	—	67	2	no	—
589	C₂³	—	134	2	no	—
590	C₂³	—	134	2	no	—
591	C₂³	—	134	4	no	—
592	C₂³	C₂³×D₆₇	1	2	yes	—
593	C₂³	C₂³×D₆₇	1	1	yes	characteristic
594	C₂³	C₂³×D₆₇	1	1	yes	characteristic
595	C₂³	C₂³×D₆₇	1	1	yes	characteristic
596	Q₈	—	2	2	no	—
597	Q₈	—	4	1	no	—
598	Q₈	—	268	2	no	—
599	Q₈	—	268	2	no	—
600	Q₈	—	268	2	no	—
601	Q₈	—	134	2	no	—
602	D₄	—	2	2	no	—
603	D₄	—	4	2	no	—
604	D₄	—	4	1	no	—
605	D₄	—	4	1	no	—
606	D₄	—	4	1	no	—
607	D₄	—	4	2	no	—
608	D₄	—	4	2	no	—
609	D₄	—	268	2	no	—
610	D₄	—	268	2	no	—
611	D₄	—	268	2	no	—
612	D₄	—	268	2	no	—
613	D₄	—	134	4	no	—
614	D₄	—	134	4	no	—
615	D₄	—	134	2	no	—
616	D₄	—	134	2	no	—
617	D₄	—	134	2	no	—
618	D₄	—	134	2	no	—
619	D₄	—	134	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	4	2	no	—
624	C₂×C₄	—	4	2	no	—
625	C₂×C₄	—	268	1	no	—
626	C₂×C₄	—	268	1	no	—
627	C₂×C₄	—	268	2	no	—
628	C₂×C₄	—	268	2	no	—
629	C₂×C₄	—	268	2	no	—
630	C₂×C₄	—	268	2	no	—
631	C₂×C₄	—	268	1	no	—
632	C₂×C₄	—	268	2	no	—
633	C₂×C₄	—	268	2	no	—
634	C₂×C₄	—	67	1	no	—
635	C₂×C₄	—	67	1	no	—
636	C₂×C₄	—	67	1	no	—
637	C₂×C₄	—	67	1	no	—
638	C₂×C₄	—	67	2	no	—
639	C₂×C₄	—	67	2	no	—
640	C₂×C₄	—	67	1	no	—
641	C₂×C₄	—	67	2	no	—
642	C₂×C₄	—	67	1	no	—
643	C₂×C₄	—	134	4	no	—
644	C₂×C₄	—	134	2	no	—
645	C₂×C₄	—	134	2	no	—
646	C₂×C₄	C₂³×D₆₇	1	2	yes	—
647	C₂×C₄	C₂³×D₆₇	1	2	yes	—
648	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
649	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
650	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₆₇	1	2	yes	—
652	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	268	4	no	—
666	C₂²	—	536	4	no	—
667	C₂²	—	67	2	no	—
668	C₂²	—	67	2	no	—
669	C₂²	—	134	2	no	—
670	C₂²	—	134	2	no	—
671	C₂²	—	134	2	no	—
672	C₂²	—	134	1	no	—
673	C₂²	—	134	1	no	—
674	C₂²	—	134	1	no	—
675	C₂²	—	134	1	no	—
676	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
677	C₄	—	2	2	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	2	no	—
683	C₄	—	134	2	no	—
684	C₄	—	134	2	no	—
685	C₄	—	134	1	no	—
686	C₄	—	134	1	no	—
687	C₄	—	134	1	no	—
688	C₄	—	134	1	no	—
689	C₄	—	134	2	no	—
690	C₄	—	134	1	no	—
691	C₄	—	134	1	no	—
692	C₄	#14524088	1	2	yes	—
693	C₂	—	4	1	no	—
694	C₂	—	4	2	no	—
695	C₂	—	4	1	no	—
696	C₂	—	4	1	no	—
697	C₂	—	268	2	no	—
698	C₂	—	134	2	no	—
699	C₂	—	134	2	no	—
700	C₂	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
701	C₂	C₂×#14524088	1	1	yes	characteristic
702	C₂	2₋¹⁺⁴×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#537×C₆₇	C₂
hypercenter	#537	D₆₇
hypocenter	C₆₇	#3536
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #537

Complements

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

N	H ≅ G/N	type
1. #16864141	C₂	semidirect
2. #16864141	C₂	semidirect
3. #16864104	C₂	semidirect
4. #16864101	C₂	semidirect
5. #16864056	C₂	semidirect
6. #16864053	C₂	semidirect
7. #16864047	C₂	semidirect
8. #16864046	C₂	semidirect
9. #16864043	C₂	semidirect
10. #16864043	C₂	semidirect
11. #16864035	C₂	semidirect
12. #16864034	C₂	semidirect
13. #16864021	C₂	semidirect
14. #16864019	C₂	semidirect
15. #16864013	C₂	semidirect
16. #16863992	C₂	semidirect
17. #16863978	C₂	semidirect
18. #16863975	C₂	semidirect
19. #16863974	C₂	semidirect
20. #16863903	C₂	semidirect
21. C₂²⋊Q₈×D₆₇	C₂	semidirect
22. #121×D₆₇	C₂	semidirect
23. #537×C₆₇	C₂	semidirect
24. C₂×#11761628	C₂²	semidirect
25. C₂×#11761628	C₂²	semidirect
26. C₂×#11761627	C₂²	semidirect
27. C₂×Q₈×D₆₇	C₂²	semidirect
31. #14524042	C₂²	semidirect
32. #14524042	C₂²	semidirect
33. #14524038	C₂²	semidirect
34. #14524036	C₂²	semidirect
35. #14524033	C₂²	semidirect
36. #14524033	C₂²	semidirect
37. #14524032	C₂²	semidirect
38. #14524030	C₂²	semidirect
39. #14524030	C₂²	semidirect
40. #14524030	C₂²	semidirect
41. #14524029	C₂²	semidirect
42. #14524029	C₂²	semidirect
43. #14524028	C₂²	semidirect
44. #14524026	C₂²	semidirect
45. #14524026	C₂²	semidirect
46. #14524025	C₂²	semidirect
47. #14524025	C₂²	semidirect
48. #14524025	C₂²	semidirect
49. #14524024	C₂²	semidirect
50. #14524024	C₂²	semidirect
51. #14524024	C₂²	semidirect
52. #14524024	C₂²	semidirect
55. #14524023	C₂²	semidirect
56. #14524022	C₂²	semidirect
57. #14524022	C₂²	semidirect
58. #14524022	C₂²	semidirect
59. #14524022	C₂²	semidirect
62. #14524021	C₂²	semidirect
63. #14524021	C₂²	semidirect
64. #14524020	C₂²	semidirect
65. #14524020	C₂²	semidirect
66. #14524020	C₂²	semidirect
67. #14524020	C₂²	semidirect
70. #14524019	C₂²	semidirect
71. #14524019	C₂²	semidirect
74. #14524017	C₂²	semidirect
76. #14524016	C₂²	semidirect
78. #14524015	C₂²	semidirect
79. #14524015	C₂²	semidirect
80. #14524015	C₂²	semidirect
83. #14524014	C₂²	semidirect
84. #14524014	C₂²	semidirect
85. #14524014	C₂²	semidirect
86. #14524014	C₂²	semidirect
91. Q₈×Dic₆₇	C₂²	semidirect
92. #14524008	C₂²	semidirect
93. D₄×Dic₆₇	C₂²	semidirect
94. #14524005	C₂²	semidirect
95. #14524005	C₂²	semidirect
99. C₄×C₂²⋊D₆₇	C₂²	semidirect
100. C₄×C₂²⋊D₆₇	C₂²	semidirect
101. C₄×C₂²⋊D₆₇	C₂²	semidirect
103. #14524002	C₂²	semidirect
104. C₂×C₄⋊Dic₆₇	C₂²	semidirect
106. C₄⋊C₄×D₆₇	C₂²	semidirect
107. C₄⋊C₄×D₆₇	C₂²	semidirect
112. C₂×#41×C₆₇	C₂²	semidirect
113. C₂×#41×C₆₇	C₂²	semidirect
114. C₂²⋊Q₈×C₆₇	C₂²	semidirect
115. C₂²⋊Q₈×C₆₇	C₂²	semidirect
116. C₂²⋊Q₈×C₆₇	C₂²	semidirect
118. #121×C₆₇	C₂²	semidirect
119. #121×C₆₇	C₂²	semidirect
120. #121×C₆₇	C₂²	semidirect
121. #121×C₆₇	C₂²	semidirect
122. C₂×C₄⋊C₄×C₆₇	C₂²	semidirect
352. C₆₇	#3536	semidirect
372. #537	D₆₇	semidirect
379. C₂×#41	C₂×D₆₇	semidirect
380. C₂×#41	C₂×D₆₇	semidirect
426. C₂²⋊Q₈	C₂×D₆₇	semidirect
427. C₂²⋊Q₈	C₂×D₆₇	semidirect
428. C₂²⋊Q₈	C₂×D₆₇	semidirect
445. #121	C₂×D₆₇	semidirect
446. #121	C₂×D₆₇	semidirect
447. #121	C₂×D₆₇	semidirect
448. #121	C₂×D₆₇	semidirect
470. C₂×C₄⋊C₄	C₂×D₆₇	semidirect