Subgroups — #22574538

Order 8576.

1260 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864136	C₂	1	2	yes	maximal, complemented
2	#16864134	C₂	1	2	yes	maximal, complemented
3	#16864129	C₂	1	1	yes	maximal, characteristic, complemented
4	#16864067	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864064	C₂	1	1	yes	maximal, characteristic, complemented
6	#16864043	C₂	1	1	yes	maximal, characteristic, complemented
7	#16864041	C₂	1	1	yes	maximal, characteristic, complemented
8	#16864038	C₂	1	2	yes	maximal, complemented
9	D₄×D₂₆₈	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864030	C₂	1	2	yes	maximal, complemented
11	#16864030	C₂	1	1	yes	maximal, characteristic, complemented
12	#16864030	C₂	1	1	yes	maximal, characteristic, complemented
13	#16864002	C₂	1	1	yes	maximal, characteristic, complemented
14	#16863998	C₂	1	2	yes	maximal, complemented
15	#16863965	C₂	1	1	yes	maximal, characteristic, complemented
16	#16863962	C₂	1	2	yes	maximal, complemented
17	#16863959	C₂	1	1	yes	maximal, characteristic, complemented
18	#16863957	C₂	1	2	yes	maximal, complemented
19	#16863954	C₂	1	2	yes	maximal, complemented
20	#127×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	#16863931	C₂	1	1	yes	maximal, characteristic, complemented
22	#16863924	C₂	1	1	yes	maximal, characteristic, complemented
23	#540×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	1	yes	characteristic, complemented
27	C₂²×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
28	C₂²×D₂₆₈	C₂²	1	2	yes	complemented
29	C₂×D₄×D₆₇	C₂²	1	2	yes	complemented
30	C₂×D₄×D₆₇	C₂²	1	2	yes	complemented
31	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
32	C₂×D₄×D₆₇	C₂²	1	2	yes	complemented
33	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
34	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
35	C₂×D₄×D₆₇	C₂²	1	2	yes	complemented
36	#14524040	C₂²	1	1	yes	characteristic, complemented
37	#14524040	C₂²	1	1	yes	characteristic, complemented
38	#14524039	C₂²	1	1	yes	characteristic
39	#14524039	C₂²	1	2	yes	complemented
40	#14524039	C₂²	1	1	yes	characteristic, complemented
41	#14524039	C₂²	1	1	yes	characteristic, complemented
42	#14524039	C₂²	1	2	yes	complemented
43	#14524039	C₂²	1	2	yes	complemented
44	#14524038	C₂²	1	2	yes	complemented
45	#14524038	C₂²	1	1	yes	characteristic, complemented
46	#14524036	C₂²	1	1	yes	characteristic, complemented
47	#14524033	C₂²	1	1	yes	characteristic, complemented
48	#14524031	C₂²	1	1	yes	characteristic, complemented
49	#14524031	C₂²	1	1	yes	characteristic, complemented
50	#14524030	C₂²	1	1	yes	characteristic, complemented
51	#14524029	C₂²	1	2	yes	complemented
52	#14524029	C₂²	1	1	yes	characteristic, complemented
53	#14524028	C₂²	1	2	yes	complemented
54	#14524028	C₂²	1	2	yes	complemented
55	#14524028	C₂²	1	1	yes	characteristic, complemented
56	#14524028	C₂²	1	2	yes	complemented
57	#14524027	C₂²	1	2	yes	complemented
58	#14524026	C₂²	1	2	yes	complemented
59	#14524025	C₂²	1	2	yes	complemented
60	#14524025	C₂²	1	2	yes	complemented
61	#14524025	C₂²	1	1	yes	characteristic, complemented
62	#14524023	C₂²	1	1	yes	characteristic, complemented
63	#14524021	C₂²	1	1	yes	characteristic, complemented
64	#14524018	C₂²	1	1	yes	characteristic
65	#14524018	C₂²	1	1	yes	characteristic, complemented
66	#14524018	C₂²	1	2	yes	complemented
67	#14524018	C₂²	1	1	yes	characteristic, complemented
68	#14524018	C₂²	1	2	yes	complemented
69	#14524018	C₂²	1	2	yes	complemented
70	#14524018	C₂²	1	2	yes	complemented
71	#14524017	C₂²	1	2	yes	complemented
72	#14524017	C₂²	1	2	yes	complemented
73	#14524017	C₂²	1	2	yes	complemented
74	#14524016	C₂²	1	1	yes	characteristic
75	#14524016	C₂²	1	2	yes	complemented
76	#14524016	C₂²	1	2	yes	complemented
77	#14524016	C₂²	1	2	yes	complemented
78	#14524016	C₂²	1	2	yes	complemented
79	#14524016	C₂²	1	2	yes	complemented
80	#14524015	C₂²	1	2	yes	complemented
81	#14524015	C₂²	1	2	yes	complemented
82	#14524015	C₂²	1	2	yes	complemented
83	#14524014	C₂²	1	2	yes	complemented
84	#14524013	C₂²	1	2	yes	complemented
85	#14524013	C₂²	1	2	yes	complemented
86	#14524013	C₂²	1	2	yes	complemented
87	#14524013	C₂²	1	2	yes	complemented
88	#14524013	C₂²	1	2	yes	complemented
89	#14524013	C₂²	1	2	yes	complemented
90	#14524013	C₂²	1	2	yes	complemented
91	#14524011	C₂²	1	2	yes	complemented
92	#14524011	C₂²	1	2	yes	complemented
93	#14524011	C₂²	1	2	yes	complemented
94	#14524011	C₂²	1	2	yes	complemented
95	#14524011	C₂²	1	2	yes	complemented
96	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
97	#14524008	C₂²	1	1	yes	characteristic, complemented
98	C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
99	#14524005	C₂²	1	1	yes	characteristic, complemented
100	#14524005	C₂²	1	1	yes	characteristic, complemented
101	#14524005	C₂²	1	2	yes	complemented
102	#14524005	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
104	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
105	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
106	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
107	#14524001	C₂²	1	2	yes	complemented
108	#14524000	C₂²	1	1	yes	characteristic, complemented
109	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
111	C₄²×D₆₇	C₂²	1	1	yes	characteristic, complemented
112	#127×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	#123×C₆₇	C₂²	1	2	yes	complemented
115	#123×C₆₇	C₂²	1	2	yes	complemented
116	#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	#121×C₆₇	C₂²	1	2	yes	complemented
119	#121×C₆₇	C₂²	1	2	yes	complemented
120	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₆₇	C₂³	1	2	yes	—
124	C₂³×D₆₇	C₂³	1	2	yes	—
125	C₂³×D₆₇	C₂³	1	2	yes	—
126	C₂³×D₆₇	C₂³	1	2	yes	—
127	#11761628	—	4	4	no	—
128	#11761628	—	4	2	no	—
129	#11761627	—	4	2	no	—
130	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
131	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
132	C₂×D₂₆₈	—	4	2	no	—
133	C₂×D₂₆₈	—	4	4	no	—
134	C₂×D₂₆₈	C₂³	1	2	yes	—
135	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
136	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
137	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
138	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
139	C₂×D₂₆₈	C₂³	1	2	yes	—
140	C₂×D₂₆₈	C₂³	1	2	yes	—
141	C₂×D₂₆₈	C₂³	1	2	yes	—
142	C₂×D₂₆₈	C₂³	1	2	yes	—
143	C₂×D₂₆₈	C₂³	1	2	yes	—
144	C₂×D₂₆₈	C₂³	1	2	yes	—
145	C₂×D₂₆₈	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
155	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
156	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
157	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
158	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
159	D₄×D₆₇	—	4	2	no	—
160	D₄×D₆₇	—	4	2	no	—
161	D₄×D₆₇	—	4	2	no	—
162	D₄×D₆₇	—	4	4	no	—
163	D₄×D₆₇	—	4	4	no	—
164	D₄×D₆₇	—	4	4	no	—
165	D₄×D₆₇	—	4	4	no	—
166	C₂²×Dic₆₇	C₂³	1	2	yes	—
167	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
168	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
169	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
170	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
171	C₂×C₄×D₆₇	C₂³	1	2	yes	—
172	C₂×C₄×D₆₇	C₂³	1	2	yes	—
173	C₂×C₄×D₆₇	C₂³	1	2	yes	—
174	C₂×C₄×D₆₇	C₂³	1	2	yes	—
175	C₄⋊Dic₆₇	C₂³	1	2	yes	—
176	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
177	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
178	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
179	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
180	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
181	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
182	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
183	Dic₆₇⋊C₄	C₂³	1	2	yes	—
184	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
185	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
186	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
187	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₆₇	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	1	yes	characteristic
192	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
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	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
203	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
204	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
205	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
206	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
207	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
208	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
209	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
210	C₄×Dic₆₇	C₂³	1	2	yes	—
211	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
212	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
213	C₂×D₄×C₆₇	C₂³	1	2	yes	—
214	C₂×D₄×C₆₇	C₂³	1	2	yes	—
215	C₂×D₄×C₆₇	C₂³	1	2	yes	—
216	C₂×D₄×C₆₇	C₂³	1	2	yes	—
217	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
218	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
219	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
220	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
221	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
227	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
232	C₄²×C₆₇	C₂³	1	1	yes	characteristic
233	C₄²×C₆₇	C₂³	1	1	yes	characteristic
234	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
235	C₂³×C₆₇	C₂⁴	1	2	yes	—
236	C₂³×C₆₇	C₂⁴	1	2	yes	—
237	C₂²×D₆₇	—	2	4	no	—
238	C₂²×D₆₇	—	2	4	no	—
239	C₂²×D₆₇	—	4	2	no	—
240	C₂²×D₆₇	—	4	2	no	—
241	C₂²×D₆₇	—	4	2	no	—
242	C₂²×D₆₇	—	4	2	no	—
243	C₂²×D₆₇	—	4	2	no	—
244	C₂²×D₆₇	—	4	2	no	—
245	C₂²×D₆₇	—	4	2	no	—
246	C₂²×D₆₇	—	4	2	no	—
247	C₂²×D₆₇	—	4	2	no	—
248	C₂²×D₆₇	—	4	2	no	—
249	C₂²×D₆₇	C₂⁴	1	2	yes	—
250	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
251	C₂²×D₆₇	C₂⁴	1	2	yes	—
252	C₂²×D₆₇	C₂⁴	1	2	yes	—
253	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
254	D₄×C₆₇	—	2	2	no	—
255	D₄×C₆₇	—	2	2	no	—
256	D₄×C₆₇	—	4	2	no	—
257	D₄×C₆₇	—	4	2	no	—
258	D₄×C₆₇	—	4	2	no	—
259	D₄×C₆₇	—	4	2	no	—
260	C₂×C₄×C₆₇	—	2	2	no	—
261	C₂×C₄×C₆₇	—	4	2	no	—
262	C₂×C₄×C₆₇	—	4	2	no	—
263	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
265	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
266	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
267	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
268	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
269	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
270	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
271	C₂²⋊D₆₇	—	2	2	no	—
272	C₂²⋊D₆₇	—	2	2	no	—
273	C₂²⋊D₆₇	—	2	4	no	—
274	C₂²⋊D₆₇	—	2	4	no	—
275	C₂²⋊D₆₇	—	4	2	no	—
276	C₂²⋊D₆₇	—	4	2	no	—
277	C₂²⋊D₆₇	—	4	2	no	—
278	C₂²⋊D₆₇	—	4	2	no	—
279	C₂²⋊D₆₇	—	4	2	no	—
280	C₂²⋊D₆₇	—	4	2	no	—
281	C₂²⋊D₆₇	—	4	2	no	—
282	C₂²⋊D₆₇	—	4	2	no	—
283	C₂²⋊D₆₇	—	4	2	no	—
284	C₂×Dic₆₇	—	4	2	no	—
285	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
287	C₂×Dic₆₇	C₂⁴	1	2	yes	—
288	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
289	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
290	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
291	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
292	D₂₆₈	—	2	4	no	—
293	D₂₆₈	—	2	2	no	—
294	D₂₆₈	—	2	2	no	—
295	D₂₆₈	—	2	2	no	—
296	D₂₆₈	—	2	2	no	—
297	D₂₆₈	—	4	2	no	—
298	D₂₆₈	—	4	2	no	—
299	D₂₆₈	—	4	2	no	—
300	D₂₆₈	—	4	2	no	—
301	D₂₆₈	—	4	2	no	—
302	D₂₆₈	—	4	2	no	—
303	D₂₆₈	—	4	2	no	—
304	C₄×D₆₇	—	2	2	no	—
305	C₄×D₆₇	—	2	2	no	—
306	C₄×D₆₇	—	2	2	no	—
307	C₄×D₆₇	—	2	2	no	—
308	C₄×D₆₇	—	2	4	no	—
309	C₄×D₆₇	—	4	2	no	—
310	C₄×D₆₇	—	4	2	no	—
311	C₄×D₆₇	—	4	2	no	—
312	Dic₁₃₄	—	2	2	no	—
313	Dic₁₃₄	—	2	2	no	—
314	C₂²×C₆₇	—	2	2	no	—
315	C₂²×C₆₇	—	2	2	no	—
316	C₂²×C₆₇	—	2	1	no	—
317	C₂²×C₆₇	—	2	2	no	—
318	C₂²×C₆₇	—	2	1	no	—
319	C₂²×C₆₇	—	2	1	no	—
320	C₂²×C₆₇	—	2	2	no	—
321	C₂²×C₆₇	—	2	2	no	—
322	C₂²×C₆₇	—	2	2	no	—
323	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
324	C₂×D₆₇	—	2	1	no	—
325	C₂×D₆₇	—	2	1	no	—
326	C₂×D₆₇	—	2	2	no	—
327	C₂×D₆₇	—	2	1	no	—
328	C₂×D₆₇	—	2	2	no	—
329	C₂×D₆₇	—	2	2	no	—
330	C₂×D₆₇	—	2	2	no	—
331	C₂×D₆₇	—	2	1	no	—
332	C₂×D₆₇	—	2	2	no	—
333	C₂×D₆₇	—	2	2	no	—
334	C₂×D₆₇	—	2	2	no	—
335	C₂×D₆₇	—	2	2	no	—
336	C₂×D₆₇	—	2	1	no	—
337	C₂×D₆₇	—	2	2	no	—
338	C₂×D₆₇	—	8	4	no	—
339	C₂×D₆₇	—	8	4	no	—
340	C₂×D₆₇	—	8	4	no	—
341	C₂×D₆₇	—	8	4	no	—
342	C₂×D₆₇	H(5,𝔽₂)	1	2	yes	—
343	C₄×C₆₇	—	2	1	no	—
344	C₄×C₆₇	—	2	2	no	—
345	C₄×C₆₇	—	2	1	no	—
346	C₄×C₆₇	—	2	1	no	—
347	C₄×C₆₇	—	2	1	no	—
348	C₄×C₆₇	—	2	2	no	—
349	C₄×C₆₇	—	2	1	no	—
350	C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
351	Dic₆₇	—	2	1	no	—
352	Dic₆₇	—	2	2	no	—
353	Dic₆₇	—	2	1	no	—
354	Dic₆₇	—	2	1	no	—
355	Dic₆₇	—	2	1	no	—
356	Dic₆₇	—	2	1	no	—
357	Dic₆₇	H(5,𝔽₂)	1	2	yes	—
358	C₂×C₆₇	—	4	2	no	—
359	C₂×C₆₇	—	4	1	no	—
360	C₂×C₆₇	—	4	2	no	—
361	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
362	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
363	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
364	D₆₇	—	2	2	no	—
365	D₆₇	—	4	2	no	—
366	D₆₇	—	4	2	no	—
367	D₆₇	—	4	1	no	—
368	D₆₇	—	4	2	no	—
369	#3543	—	67	1	no	maximal, Sylow
370	C₆₇	#3543	1	1	yes	characteristic, complemented, Sylow
371	#560	—	67	2	no	—
372	#560	—	67	2	no	—
373	#559	—	67	1	no	—
374	#550	—	67	1	no	—
375	#550	—	67	1	no	—
376	#546	—	67	2	no	—
377	#546	—	67	1	no	—
378	#546	—	67	1	no	—
379	D₄²	—	67	1	no	—
380	D₄²	—	67	1	no	—
381	D₄²	—	67	2	no	—
382	D₄²	—	67	1	no	—
383	#540	—	67	1	no	—
384	#540	—	67	2	no	—
385	#540	D₆₇	1	1	yes	characteristic, complemented
386	#535	—	67	1	no	—
387	#535	—	67	2	no	—
388	#535	—	67	1	no	—
389	#534	—	67	2	no	—
390	#534	—	67	2	no	—
391	C₂×#127	—	67	1	no	—
392	#529	—	67	1	no	—
393	#529	—	67	1	no	—
394	C₂×#41	—	67	1	no	—
395	C₂×#41	—	67	1	no	—
396	C₂×#41	—	67	2	no	—
397	C₂²×D₄	—	67	2	no	—
398	C₂²×D₄	—	67	1	no	—
399	C₂²×D₄	—	67	1	no	—
400	C₂²×D₄	—	67	2	no	—
401	C₂²×D₄	—	67	2	no	—
402	C₂²×D₄	—	67	1	no	—
403	C₂²×D₄	—	67	2	no	—
404	C₂²×D₄	—	67	2	no	—
405	C₂²×D₄	—	67	1	no	—
406	#127	—	67	2	no	—
407	#127	—	67	1	no	—
408	#127	—	67	1	no	—
409	#127	—	67	2	no	—
410	#127	—	67	1	no	—
411	#127	—	67	2	no	—
412	#127	—	67	1	no	—
413	#127	—	67	1	no	—
414	#127	C₂×D₆₇	1	1	yes	characteristic, complemented
415	#126	—	67	2	no	—
416	#126	—	67	1	no	—
417	#126	—	67	1	no	—
418	#125	—	67	1	no	—
419	#125	C₂×D₆₇	1	1	yes	characteristic, complemented
420	#124	—	67	1	no	—
421	#124	—	67	1	no	—
422	#124	—	67	2	no	—
423	#124	—	67	1	no	—
424	#124	—	67	1	no	—
425	#123	—	67	2	no	—
426	#123	—	67	2	no	—
427	#123	—	67	1	no	—
428	#123	—	67	2	no	—
429	#123	—	67	2	no	—
430	#123	—	67	1	no	—
431	#123	—	67	2	no	—
432	#123	—	67	2	no	—
433	#123	—	67	2	no	—
434	#123	C₂×D₆₇	1	2	yes	complemented
435	#123	C₂×D₆₇	1	2	yes	complemented
436	C₂²⋊Q₈	—	67	1	no	—
437	C₂²⋊Q₈	—	67	1	no	—
438	#121	—	67	2	no	—
439	#121	—	67	2	no	—
440	#121	—	67	2	no	—
441	#121	—	67	2	no	—
442	#121	—	67	2	no	—
443	#121	—	67	2	no	—
444	#121	—	67	2	no	—
445	#121	—	67	1	no	—
446	#121	—	67	2	no	—
447	#121	—	67	2	no	—
448	#121	—	67	2	no	—
449	#121	—	67	1	no	—
450	#121	—	67	1	no	—
451	#121	—	67	2	no	—
452	#121	—	67	1	no	—
453	#121	—	67	2	no	—
454	#121	—	67	2	no	—
455	#121	—	67	2	no	—
456	#121	—	67	2	no	—
457	#121	—	67	2	no	—
458	#121	C₂×D₆₇	1	2	yes	complemented
459	#121	C₂×D₆₇	1	1	yes	characteristic, complemented
460	#121	C₂×D₆₇	1	1	yes	characteristic, complemented
461	#121	C₂×D₆₇	1	2	yes	complemented
462	#120	—	67	2	no	—
463	#120	—	67	2	no	—
464	#120	—	67	2	no	—
465	#120	—	67	2	no	—
466	#120	—	67	2	no	—
467	#120	—	67	2	no	—
468	#120	—	67	2	no	—
469	#120	—	67	2	no	—
470	#120	—	67	2	no	—
471	#120	—	67	2	no	—
472	#120	—	67	2	no	—
473	#120	—	67	2	no	—
474	C₄×Q₈	—	67	1	no	—
475	C₄×Q₈	—	67	1	no	—
476	C₄×D₄	—	67	1	no	—
477	C₄×D₄	—	67	1	no	—
478	C₄×D₄	—	67	2	no	—
479	C₄×D₄	—	67	2	no	—
480	C₄×D₄	—	67	1	no	—
481	C₄×D₄	—	67	1	no	—
482	C₄×D₄	—	67	1	no	—
483	C₄×D₄	—	67	2	no	—
484	C₄×D₄	—	67	1	no	—
485	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
486	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
487	#117	—	67	2	no	—
488	#117	—	67	1	no	—
489	#117	C₂×D₆₇	1	1	yes	characteristic, complemented
490	C₂×C₂²⋊C₄	—	67	2	no	—
491	C₂×C₂²⋊C₄	—	67	2	no	—
492	C₂×C₄²	—	67	1	no	—
493	C₂⁴	—	67	2	no	—
494	C₂⁴	—	67	2	no	—
495	C₂⁴	—	67	2	no	—
496	C₂⁴	—	67	2	no	—
497	#41	—	268	2	no	—
498	#41	—	268	4	no	—
499	#41	—	268	2	no	—
500	C₂×Q₈	—	67	1	no	—
501	C₂×Q₈	—	67	1	no	—
502	C₂×D₄	—	268	2	no	—
503	C₂×D₄	—	268	4	no	—
504	C₂×D₄	—	268	4	no	—
505	C₂×D₄	—	268	2	no	—
506	C₂×D₄	—	268	2	no	—
507	C₂×D₄	—	268	2	no	—
508	C₂×D₄	—	268	4	no	—
509	C₂×D₄	—	268	4	no	—
510	C₂×D₄	—	268	4	no	—
511	C₂×D₄	—	67	2	no	—
512	C₂×D₄	—	67	2	no	—
513	C₂×D₄	—	67	2	no	—
514	C₂×D₄	—	67	2	no	—
515	C₂×D₄	—	67	2	no	—
516	C₂×D₄	—	67	2	no	—
517	C₂×D₄	—	67	2	no	—
518	C₂×D₄	—	67	2	no	—
519	C₂×D₄	—	67	2	no	—
520	C₂×D₄	—	67	1	no	—
521	C₂×D₄	—	67	1	no	—
522	C₂×D₄	—	67	2	no	—
523	C₂×D₄	—	67	2	no	—
524	C₂×D₄	—	67	2	no	—
525	C₂×D₄	—	67	2	no	—
526	C₂×D₄	—	67	2	no	—
527	C₂×D₄	—	67	2	no	—
528	C₂×D₄	—	67	2	no	—
529	C₂×D₄	—	67	2	no	—
530	C₂×D₄	—	67	2	no	—
531	C₂×D₄	—	67	2	no	—
532	C₂×D₄	—	67	1	no	—
533	C₂×D₄	—	67	1	no	—
534	C₂×D₄	—	67	1	no	—
535	C₂×D₄	—	67	1	no	—
536	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
537	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
538	C₂×D₄	C₂²×D₆₇	1	2	yes	—
539	C₂×D₄	C₂²×D₆₇	1	2	yes	—
540	C₂×D₄	C₂²×D₆₇	1	2	yes	—
541	C₂×D₄	C₂²×D₆₇	1	2	yes	—
542	C₂²×C₄	—	67	2	no	—
543	C₂²×C₄	—	67	2	no	—
544	C₂²×C₄	—	67	2	no	—
545	C₂²×C₄	—	67	2	no	—
546	C₂²×C₄	—	67	1	no	—
547	C₂²×C₄	—	67	1	no	—
548	C₂²×C₄	—	67	1	no	—
549	C₂²×C₄	—	67	2	no	—
550	C₂²×C₄	—	67	1	no	—
551	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
552	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
553	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
554	C₄⋊C₄	—	67	1	no	—
555	C₄⋊C₄	—	67	2	no	—
556	C₄⋊C₄	—	67	1	no	—
557	C₄⋊C₄	—	67	1	no	—
558	C₄⋊C₄	—	67	1	no	—
559	C₄⋊C₄	—	67	1	no	—
560	C₄⋊C₄	—	67	1	no	—
561	C₄⋊C₄	—	67	2	no	—
562	C₄⋊C₄	—	67	1	no	—
563	C₄⋊C₄	—	67	1	no	—
564	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
565	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
566	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
567	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
568	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
569	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
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	—	67	1	no	—
576	C₂²⋊C₄	—	67	1	no	—
577	C₂²⋊C₄	—	67	2	no	—
578	C₂²⋊C₄	—	67	2	no	—
579	C₂²⋊C₄	—	67	2	no	—
580	C₂²⋊C₄	—	67	1	no	—
581	C₂²⋊C₄	—	67	2	no	—
582	C₂²⋊C₄	—	67	1	no	—
583	C₂²⋊C₄	—	67	2	no	—
584	C₂²⋊C₄	—	67	1	no	—
585	C₂²⋊C₄	—	67	1	no	—
586	C₂²⋊C₄	—	67	2	no	—
587	C₂²⋊C₄	—	67	2	no	—
588	C₂²⋊C₄	—	67	2	no	—
589	C₂²⋊C₄	—	67	2	no	—
590	C₂²⋊C₄	—	67	2	no	—
591	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
592	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
593	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
594	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
595	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
596	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
597	C₄²	—	67	1	no	—
598	C₄²	—	67	1	no	—
599	C₄²	—	67	1	no	—
600	C₄²	—	67	2	no	—
601	C₄²	—	67	1	no	—
602	C₄²	C₂²×D₆₇	1	1	yes	characteristic
603	C₄²	C₂²×D₆₇	1	1	yes	characteristic
604	C₂³	—	268	2	no	—
605	C₂³	—	268	2	no	—
606	C₂³	—	268	2	no	—
607	C₂³	—	268	2	no	—
608	C₂³	—	268	2	no	—
609	C₂³	—	268	2	no	—
610	C₂³	—	268	2	no	—
611	C₂³	—	268	2	no	—
612	C₂³	—	268	2	no	—
613	C₂³	—	268	2	no	—
614	C₂³	—	67	1	no	—
615	C₂³	—	67	2	no	—
616	C₂³	—	67	2	no	—
617	C₂³	—	67	1	no	—
618	C₂³	—	67	2	no	—
619	C₂³	—	134	4	no	—
620	C₂³	—	134	4	no	—
621	C₂³	C₂³×D₆₇	1	2	yes	—
622	C₂³	C₂³×D₆₇	1	1	yes	characteristic
623	C₂³	C₂³×D₆₇	1	2	yes	—
624	Q₈	—	134	2	no	—
625	Q₈	—	134	2	no	—
626	D₄	—	2	2	no	—
627	D₄	—	2	2	no	—
628	D₄	—	4	2	no	—
629	D₄	—	4	2	no	—
630	D₄	—	4	2	no	—
631	D₄	—	4	2	no	—
632	D₄	—	268	2	no	—
633	D₄	—	268	2	no	—
634	D₄	—	268	2	no	—
635	D₄	—	268	2	no	—
636	D₄	—	268	2	no	—
637	D₄	—	268	2	no	—
638	D₄	—	268	2	no	—
639	D₄	—	268	2	no	—
640	D₄	—	268	2	no	—
641	D₄	—	268	2	no	—
642	D₄	—	268	2	no	—
643	D₄	—	268	2	no	—
644	D₄	—	268	2	no	—
645	D₄	—	268	2	no	—
646	D₄	—	268	2	no	—
647	D₄	—	268	2	no	—
648	D₄	—	134	2	no	—
649	D₄	—	134	4	no	—
650	D₄	—	134	4	no	—
651	D₄	—	134	2	no	—
652	D₄	—	134	4	no	—
653	D₄	—	134	2	no	—
654	D₄	—	134	2	no	—
655	D₄	—	134	2	no	—
656	D₄	—	134	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	4	2	no	—
659	C₂×C₄	—	4	2	no	—
660	C₂×C₄	—	268	2	no	—
661	C₂×C₄	—	268	2	no	—
662	C₂×C₄	—	268	2	no	—
663	C₂×C₄	—	268	2	no	—
664	C₂×C₄	—	67	1	no	—
665	C₂×C₄	—	67	1	no	—
666	C₂×C₄	—	67	1	no	—
667	C₂×C₄	—	67	1	no	—
668	C₂×C₄	—	67	2	no	—
669	C₂×C₄	—	67	1	no	—
670	C₂×C₄	—	67	1	no	—
671	C₂×C₄	—	134	2	no	—
672	C₂×C₄	—	134	4	no	—
673	C₂×C₄	—	134	2	no	—
674	C₂×C₄	—	134	2	no	—
675	C₂×C₄	—	134	2	no	—
676	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
677	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
678	C₂×C₄	C₂³×D₆₇	1	2	yes	—
679	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
680	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
681	C₂×C₄	C₂³×D₆₇	1	2	yes	—
682	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
683	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
684	C₂²	—	2	2	no	—
685	C₂²	—	2	2	no	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	2	1	no	—
689	C₂²	—	2	1	no	—
690	C₂²	—	2	1	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	536	4	no	—
694	C₂²	—	536	4	no	—
695	C₂²	—	536	4	no	—
696	C₂²	—	536	4	no	—
697	C₂²	—	67	2	no	—
698	C₂²	—	134	2	no	—
699	C₂²	—	134	2	no	—
700	C₂²	—	134	2	no	—
701	C₂²	—	134	2	no	—
702	C₂²	—	134	1	no	—
703	C₂²	—	134	2	no	—
704	C₂²	—	134	1	no	—
705	C₂²	—	134	2	no	—
706	C₂²	—	134	2	no	—
707	C₂²	—	134	1	no	—
708	C₂²	—	134	2	no	—
709	C₂²	—	134	2	no	—
710	C₂²	—	134	1	no	—
711	C₂²	—	134	1	no	—
712	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
713	C₄	—	2	1	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	2	no	—
716	C₄	—	2	2	no	—
717	C₄	—	2	1	no	—
718	C₄	—	2	1	no	—
719	C₄	—	2	1	no	—
720	C₄	—	67	2	no	—
721	C₄	—	134	1	no	—
722	C₄	—	134	1	no	—
723	C₄	—	134	1	no	—
724	C₄	—	134	1	no	—
725	C₄	—	134	2	no	—
726	C₄	—	134	1	no	—
727	C₄	#14524089	1	2	yes	—
728	C₂	—	4	2	no	—
729	C₂	—	4	1	no	—
730	C₂	—	4	2	no	—
731	C₂	—	268	2	no	—
732	C₂	—	268	1	no	—
733	C₂	—	268	2	no	—
734	C₂	—	268	2	no	—
735	C₂	—	134	2	no	—
736	C₂	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
737	C₂	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
738	C₂	C₂×#14524089	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#540×C₆₇	C₂
hypercenter	#540	D₆₇
hypocenter	C₆₇	#3543
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #540

Complements

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

N	H ≅ G/N	type
1. #16864136	C₂	semidirect
2. #16864134	C₂	semidirect
3. #16864129	C₂	semidirect
4. #16864067	C₂	semidirect
5. #16864064	C₂	semidirect
6. #16864043	C₂	semidirect
7. #16864041	C₂	semidirect
8. #16864038	C₂	semidirect
9. D₄×D₂₆₈	C₂	semidirect
10. #16864030	C₂	semidirect
11. #16864030	C₂	semidirect
12. #16864030	C₂	semidirect
13. #16864002	C₂	semidirect
14. #16863998	C₂	semidirect
15. #16863965	C₂	semidirect
16. #16863962	C₂	semidirect
17. #16863959	C₂	semidirect
18. #16863957	C₂	semidirect
19. #16863954	C₂	semidirect
20. #127×D₆₇	C₂	semidirect
21. #16863931	C₂	semidirect
22. #16863924	C₂	semidirect
23. #540×C₆₇	C₂	semidirect
24. C₂×#11761628	C₂²	semidirect
25. C₂×#11761628	C₂²	semidirect
26. C₂×#11761627	C₂²	semidirect
27. C₂²×D₂₆₈	C₂²	semidirect
28. C₂²×D₂₆₈	C₂²	semidirect
29. C₂×D₄×D₆₇	C₂²	semidirect
30. C₂×D₄×D₆₇	C₂²	semidirect
31. C₂×D₄×D₆₇	C₂²	semidirect
32. C₂×D₄×D₆₇	C₂²	semidirect
33. C₂×D₄×D₆₇	C₂²	semidirect
34. C₂×D₄×D₆₇	C₂²	semidirect
35. C₂×D₄×D₆₇	C₂²	semidirect
36. #14524040	C₂²	semidirect
37. #14524040	C₂²	semidirect
39. #14524039	C₂²	semidirect
40. #14524039	C₂²	semidirect
41. #14524039	C₂²	semidirect
42. #14524039	C₂²	semidirect
43. #14524039	C₂²	semidirect
44. #14524038	C₂²	semidirect
45. #14524038	C₂²	semidirect
46. #14524036	C₂²	semidirect
47. #14524033	C₂²	semidirect
48. #14524031	C₂²	semidirect
49. #14524031	C₂²	semidirect
50. #14524030	C₂²	semidirect
51. #14524029	C₂²	semidirect
52. #14524029	C₂²	semidirect
53. #14524028	C₂²	semidirect
54. #14524028	C₂²	semidirect
55. #14524028	C₂²	semidirect
56. #14524028	C₂²	semidirect
57. #14524027	C₂²	semidirect
58. #14524026	C₂²	semidirect
59. #14524025	C₂²	semidirect
60. #14524025	C₂²	semidirect
61. #14524025	C₂²	semidirect
62. #14524023	C₂²	semidirect
63. #14524021	C₂²	semidirect
65. #14524018	C₂²	semidirect
66. #14524018	C₂²	semidirect
67. #14524018	C₂²	semidirect
68. #14524018	C₂²	semidirect
69. #14524018	C₂²	semidirect
70. #14524018	C₂²	semidirect
71. #14524017	C₂²	semidirect
72. #14524017	C₂²	semidirect
73. #14524017	C₂²	semidirect
75. #14524016	C₂²	semidirect
76. #14524016	C₂²	semidirect
77. #14524016	C₂²	semidirect
78. #14524016	C₂²	semidirect
79. #14524016	C₂²	semidirect
80. #14524015	C₂²	semidirect
81. #14524015	C₂²	semidirect
82. #14524015	C₂²	semidirect
83. #14524014	C₂²	semidirect
84. #14524013	C₂²	semidirect
85. #14524013	C₂²	semidirect
86. #14524013	C₂²	semidirect
87. #14524013	C₂²	semidirect
88. #14524013	C₂²	semidirect
89. #14524013	C₂²	semidirect
90. #14524013	C₂²	semidirect
91. #14524011	C₂²	semidirect
92. #14524011	C₂²	semidirect
93. #14524011	C₂²	semidirect
94. #14524011	C₂²	semidirect
95. #14524011	C₂²	semidirect
96. C₄×Dic₁₃₄	C₂²	semidirect
97. #14524008	C₂²	semidirect
98. C₄×D₂₆₈	C₂²	semidirect
99. #14524005	C₂²	semidirect
100. #14524005	C₂²	semidirect
101. #14524005	C₂²	semidirect
102. #14524005	C₂²	semidirect
103. C₄×C₂²⋊D₆₇	C₂²	semidirect
104. C₄×C₂²⋊D₆₇	C₂²	semidirect
105. C₄×C₂²⋊D₆₇	C₂²	semidirect
106. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
107. #14524001	C₂²	semidirect
108. #14524000	C₂²	semidirect
109. C₂×(C₂×D₆₇)⋊C₄	C₂²	semidirect
110. C₂²⋊C₄×D₆₇	C₂²	semidirect
111. C₄²×D₆₇	C₂²	semidirect
112. #127×C₆₇	C₂²	semidirect
113. #125×C₆₇	C₂²	semidirect
114. #123×C₆₇	C₂²	semidirect
115. #123×C₆₇	C₂²	semidirect
116. #121×C₆₇	C₂²	semidirect
117. #121×C₆₇	C₂²	semidirect
118. #121×C₆₇	C₂²	semidirect
119. #121×C₆₇	C₂²	semidirect
120. C₄×D₄×C₆₇	C₂²	semidirect
121. C₄×D₄×C₆₇	C₂²	semidirect
122. #117×C₆₇	C₂²	semidirect
370. C₆₇	#3543	semidirect
385. #540	D₆₇	semidirect
414. #127	C₂×D₆₇	semidirect
419. #125	C₂×D₆₇	semidirect
434. #123	C₂×D₆₇	semidirect
435. #123	C₂×D₆₇	semidirect
458. #121	C₂×D₆₇	semidirect
459. #121	C₂×D₆₇	semidirect
460. #121	C₂×D₆₇	semidirect
461. #121	C₂×D₆₇	semidirect
485. C₄×D₄	C₂×D₆₇	semidirect
486. C₄×D₄	C₂×D₆₇	semidirect
489. #117	C₂×D₆₇	semidirect