Subgroups — #22573936

Order 8576.

1142 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864110	C₂	1	2	yes	maximal, complemented
2	#16864091	C₂	1	2	yes	maximal, complemented
3	#16864089	C₂	1	2	yes	maximal, complemented
4	#16864074	C₂	1	2	yes	maximal, complemented
5	#16864069	C₂	1	2	yes	maximal, complemented
6	#16864044	C₂	1	2	yes	maximal, complemented
7	#16864043	C₂	1	2	yes	maximal, complemented
8	#16864035	C₂	1	2	yes	maximal, complemented
9	#16864026	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864017	C₂	1	1	yes	maximal, characteristic, complemented
11	#16864013	C₂	1	1	yes	maximal, characteristic, complemented
12	#16863999	C₂	1	1	yes	maximal, characteristic, complemented
13	#16863959	C₂	1	1	yes	maximal, characteristic, complemented
14	#16863944	C₂	1	1	yes	maximal, characteristic, complemented
15	#16863943	C₂	1	1	yes	maximal, characteristic, complemented
16	#16863931	C₂	1	1	yes	maximal, characteristic, complemented
17	#16863928	C₂	1	1	yes	maximal, characteristic, complemented
18	#16863906	C₂	1	1	yes	maximal, characteristic, complemented
19	#121×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	#16863875	C₂	1	1	yes	maximal, characteristic, complemented
21	#16863868	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₆₇	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×#11761627	C₂²	1	1	yes	characteristic
26	C₂×#11761627	C₂²	1	2	yes	complemented
27	C₂×D₄×D₆₇	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₆₇	C₂²	1	2	yes	—
29	C₂²×C₄×D₆₇	C₂²	1	1	yes	characteristic
30	#14524043	C₂²	1	1	yes	characteristic, complemented
31	#14524042	C₂²	1	1	yes	characteristic, complemented
32	#14524042	C₂²	1	2	yes	complemented
33	#14524039	C₂²	1	1	yes	characteristic, complemented
34	#14524038	C₂²	1	2	yes	complemented
35	#14524038	C₂²	1	2	yes	complemented
36	#14524036	C₂²	1	2	yes	complemented
37	#14524036	C₂²	1	2	yes	complemented
38	#14524034	C₂²	1	1	yes	characteristic, complemented
39	#14524033	C₂²	1	2	yes	complemented
40	#14524031	C₂²	1	1	yes	characteristic, complemented
41	#14524030	C₂²	1	2	yes	complemented
42	#14524030	C₂²	1	1	yes	characteristic, complemented
43	#14524030	C₂²	1	2	yes	complemented
44	#14524029	C₂²	1	2	yes	complemented
45	#14524029	C₂²	1	2	yes	complemented
46	#14524028	C₂²	1	2	yes	complemented
47	#14524027	C₂²	1	2	yes	complemented
48	#14524025	C₂²	1	2	yes	—
49	#14524025	C₂²	1	2	yes	complemented
50	#14524025	C₂²	1	2	yes	complemented
51	#14524025	C₂²	1	2	yes	complemented
52	#14524024	C₂²	1	2	yes	complemented
53	#14524023	C₂²	1	2	yes	—
54	#14524023	C₂²	1	1	yes	characteristic, complemented
55	#14524022	C₂²	1	1	yes	characteristic, complemented
56	#14524021	C₂²	1	2	yes	—
57	#14524021	C₂²	1	2	yes	complemented
58	#14524020	C₂²	1	2	yes	complemented
59	#14524018	C₂²	1	1	yes	characteristic
60	#14524017	C₂²	1	1	yes	characteristic
61	#14524016	C₂²	1	2	yes	—
62	#14524016	C₂²	1	2	yes	complemented
63	#14524015	C₂²	1	2	yes	—
64	#14524015	C₂²	1	2	yes	complemented
65	#14524015	C₂²	1	2	yes	complemented
66	#14524015	C₂²	1	2	yes	complemented
67	#14524014	C₂²	1	1	yes	characteristic
68	#14524014	C₂²	1	2	yes	complemented
69	#14524014	C₂²	1	2	yes	complemented
70	#14524014	C₂²	1	1	yes	characteristic, complemented
71	#14524011	C₂²	1	2	yes	—
72	#14524011	C₂²	1	2	yes	—
73	#14524011	C₂²	1	2	yes	—
74	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
75	#14524008	C₂²	1	1	yes	characteristic, complemented
76	C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
77	D₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
78	D₄×Dic₆₇	C₂²	1	2	yes	complemented
79	D₄×Dic₆₇	C₂²	1	2	yes	complemented
80	D₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
81	#14524005	C₂²	1	2	yes	complemented
82	#14524005	C₂²	1	1	yes	characteristic, complemented
83	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
84	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
86	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
87	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
88	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
89	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
90	#14524002	C₂²	1	1	yes	characteristic, complemented
91	#14524002	C₂²	1	2	yes	complemented
92	#14524001	C₂²	1	1	yes	characteristic
93	#14524001	C₂²	1	1	yes	characteristic
94	#14524001	C₂²	1	1	yes	characteristic
95	#14524001	C₂²	1	2	yes	complemented
96	#14524000	C₂²	1	1	yes	characteristic
97	#14524000	C₂²	1	1	yes	characteristic
98	#14523999	C₂²	1	1	yes	characteristic, complemented
99	#14523999	C₂²	1	2	yes	complemented
100	#14523999	C₂²	1	1	yes	characteristic, complemented
101	C₂×Dic₆₇⋊C₄	C₂²	1	2	yes	complemented
102	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
103	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
104	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
105	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	—
106	C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
107	C₂²⋊C₄×D₆₇	C₂²	1	1	yes	characteristic
108	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
110	C₄²×D₆₇	C₂²	1	1	yes	characteristic, 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
117	#121×C₆₇	C₂²	1	2	yes	complemented
118	#121×C₆₇	C₂²	1	2	yes	complemented
119	#121×C₆₇	C₂²	1	1	yes	characteristic, 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	1	yes	characteristic
124	C₂³×D₆₇	C₂³	1	2	yes	—
125	#11761628	—	4	4	no	—
126	#11761627	—	2	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×D₂₆₈	C₂³	1	1	yes	characteristic
132	C₂×D₂₆₈	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
140	D₄×D₆₇	—	2	4	no	—
141	D₄×D₆₇	—	4	4	no	—
142	C₂²×Dic₆₇	C₂³	1	2	yes	—
143	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
144	C₂²×Dic₆₇	C₂³	1	2	yes	—
145	C₂²×Dic₆₇	C₂³	1	2	yes	—
146	C₂×C₄×D₆₇	—	2	4	no	—
147	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
158	C₄⋊Dic₆₇	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	1	yes	characteristic
162	C₄⋊Dic₆₇	C₂³	1	2	yes	—
163	C₄⋊Dic₆₇	C₂³	1	2	yes	—
164	C₄⋊Dic₆₇	C₂³	1	2	yes	—
165	Dic₆₇⋊C₄	C₂³	1	2	yes	—
166	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
167	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
168	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
169	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
175	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₆₇	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	2	yes	—
182	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
183	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
184	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
185	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
186	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
188	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
190	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
196	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
197	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
198	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
199	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
200	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
201	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
202	C₄×Dic₆₇	C₂³	1	2	yes	—
203	C₄×Dic₆₇	C₂³	1	2	yes	—
204	C₄×Dic₆₇	C₂³	1	2	yes	—
205	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₆₇	C₂³	1	2	yes	—
208	C₂×D₄×C₆₇	C₂³	1	2	yes	—
209	C₂×D₄×C₆₇	C₂³	1	2	yes	—
210	C₂×D₄×C₆₇	C₂³	1	2	yes	—
211	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
213	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
214	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
219	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
221	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
226	C₄²×C₆₇	C₂³	1	1	yes	characteristic
227	C₄²×C₆₇	C₂³	1	1	yes	characteristic
228	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
229	C₂³×C₆₇	C₂⁴	1	2	yes	—
230	C₂³×C₆₇	C₂⁴	1	2	yes	—
231	C₂²×D₆₇	—	2	2	no	—
232	C₂²×D₆₇	—	2	2	no	—
233	C₂²×D₆₇	—	2	4	no	—
234	C₂²×D₆₇	—	4	1	no	—
235	C₂²×D₆₇	—	4	2	no	—
236	C₂²×D₆₇	—	4	2	no	—
237	C₂²×D₆₇	C₂⁴	1	2	yes	—
238	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
239	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
240	D₄×C₆₇	—	2	2	no	—
241	D₄×C₆₇	—	2	2	no	—
242	D₄×C₆₇	—	4	2	no	—
243	D₄×C₆₇	—	4	2	no	—
244	D₄×C₆₇	—	4	2	no	—
245	D₄×C₆₇	—	4	2	no	—
246	C₂×C₄×C₆₇	—	2	2	no	—
247	C₂×C₄×C₆₇	—	4	2	no	—
248	C₂×C₄×C₆₇	—	4	2	no	—
249	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
255	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
256	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₂²⋊D₆₇	—	2	4	no	—
258	C₂²⋊D₆₇	—	2	4	no	—
259	C₂²⋊D₆₇	—	2	4	no	—
260	C₂²⋊D₆₇	—	2	4	no	—
261	C₂²⋊D₆₇	—	4	2	no	—
262	C₂²⋊D₆₇	—	4	2	no	—
263	C₂²⋊D₆₇	—	4	2	no	—
264	C₂×Dic₆₇	—	2	2	no	—
265	C₂×Dic₆₇	—	2	4	no	—
266	C₂×Dic₆₇	—	4	2	no	—
267	C₂×Dic₆₇	—	4	2	no	—
268	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₆₇	C₂⁴	1	2	yes	—
271	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₆₇	C₂⁴	1	2	yes	—
275	C₂×Dic₆₇	C₂⁴	1	2	yes	—
276	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
277	D₂₆₈	—	2	4	no	—
278	D₂₆₈	—	2	2	no	—
279	C₄×D₆₇	—	2	2	no	—
280	C₄×D₆₇	—	2	2	no	—
281	C₄×D₆₇	—	2	2	no	—
282	C₄×D₆₇	—	2	2	no	—
283	C₄×D₆₇	—	2	2	no	—
284	C₄×D₆₇	—	4	2	no	—
285	C₄×D₆₇	—	4	1	no	—
286	C₄×D₆₇	—	4	1	no	—
287	C₄×D₆₇	—	4	2	no	—
288	C₄×D₆₇	—	4	2	no	—
289	C₄×D₆₇	#41	1	4	yes	complemented
290	Dic₁₃₄	—	2	2	no	—
291	Dic₁₃₄	—	4	2	no	—
292	Dic₁₃₄	—	4	2	no	—
293	C₂²×C₆₇	—	2	2	no	—
294	C₂²×C₆₇	—	2	1	no	—
295	C₂²×C₆₇	—	2	2	no	—
296	C₂²×C₆₇	—	2	2	no	—
297	C₂²×C₆₇	—	2	2	no	—
298	C₂²×C₆₇	—	2	1	no	—
299	C₂²×C₆₇	—	2	2	no	—
300	C₂²×C₆₇	—	2	2	no	—
301	C₂²×C₆₇	—	2	1	no	—
302	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
303	C₂×D₆₇	—	2	1	no	—
304	C₂×D₆₇	—	2	1	no	—
305	C₂×D₆₇	—	2	1	no	—
306	C₂×D₆₇	—	2	1	no	—
307	C₂×D₆₇	—	2	2	no	—
308	C₂×D₆₇	—	2	2	no	—
309	C₂×D₆₇	—	2	2	no	—
310	C₂×D₆₇	—	4	4	no	—
311	C₂×D₆₇	—	8	4	no	—
312	C₂×D₆₇	C₂×#41	1	2	yes	—
313	C₂×D₆₇	H(5,𝔽₂)	1	2	yes	—
314	C₄×C₆₇	—	2	1	no	—
315	C₄×C₆₇	—	2	1	no	—
316	C₄×C₆₇	—	2	2	no	—
317	C₄×C₆₇	—	2	1	no	—
318	C₄×C₆₇	—	2	1	no	—
319	C₄×C₆₇	—	2	2	no	—
320	C₄×C₆₇	—	2	1	no	—
321	C₄×C₆₇	C₂×#41	1	2	yes	—
322	Dic₆₇	—	2	2	no	—
323	Dic₆₇	—	2	1	no	—
324	Dic₆₇	—	2	1	no	—
325	Dic₆₇	—	2	2	no	—
326	Dic₆₇	—	2	2	no	—
327	Dic₆₇	—	2	1	no	—
328	Dic₆₇	—	2	1	no	—
329	Dic₆₇	—	2	1	no	—
330	Dic₆₇	C₂×#41	1	2	yes	—
331	C₂×C₆₇	—	4	1	no	—
332	C₂×C₆₇	—	4	2	no	—
333	C₂×C₆₇	—	4	2	no	—
334	C₂×C₆₇	C₂²×#41	1	1	yes	characteristic
335	C₂×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
336	C₂×C₆₇	#585	1	1	yes	characteristic
337	D₆₇	—	2	2	no	—
338	D₆₇	—	2	2	no	—
339	D₆₇	—	4	2	no	—
340	#3494	—	67	1	no	maximal, Sylow
341	C₆₇	#3494	1	1	yes	characteristic, complemented, Sylow
342	#555	—	67	2	no	—
343	#553	—	67	2	no	—
344	#553	—	67	2	no	—
345	#551	—	67	2	no	—
346	#551	—	67	2	no	—
347	#547	—	67	2	no	—
348	#546	—	67	2	no	—
349	#546	—	67	2	no	—
350	#544	—	67	1	no	—
351	#542	—	67	1	no	—
352	#542	—	67	1	no	—
353	#540	—	67	1	no	—
354	#540	D₆₇	1	1	yes	characteristic, complemented
355	#535	—	67	1	no	—
356	#532	—	67	1	no	—
357	#532	—	67	1	no	—
358	#529	—	67	1	no	—
359	#529	—	67	1	no	—
360	#525	—	67	1	no	—
361	C₂×#121	—	67	1	no	—
362	#520	—	67	1	no	—
363	#518	—	67	1	no	—
364	C₂×#117	—	67	1	no	—
365	C₂×#41	—	67	2	no	—
366	C₂×#41	—	67	1	no	—
367	C₂×#41	—	67	2	no	—
368	C₂²×D₄	—	67	2	no	—
369	C₂²×D₄	—	67	1	no	—
370	C₂³×C₄	—	67	1	no	—
371	C₄⋊Q₈	—	67	1	no	—
372	C₄⋊Q₈	—	67	2	no	—
373	C₄⋊Q₈	—	67	1	no	—
374	#127	—	67	1	no	—
375	#127	C₂×D₆₇	1	1	yes	characteristic, complemented
376	#126	—	67	2	no	—
377	#126	—	67	2	no	—
378	#126	—	67	2	no	—
379	#126	—	67	2	no	—
380	#125	—	67	1	no	—
381	#125	—	67	2	no	—
382	#125	C₂×D₆₇	1	1	yes	characteristic, complemented
383	#124	—	67	1	no	—
384	#124	—	67	2	no	—
385	#124	—	67	2	no	—
386	#124	—	67	2	no	—
387	#124	—	67	2	no	—
388	#124	—	67	1	no	—
389	#123	—	67	2	no	—
390	#123	—	67	2	no	—
391	#123	—	67	2	no	—
392	#123	—	67	2	no	—
393	#123	—	67	2	no	—
394	#123	—	67	2	no	—
395	#123	—	67	2	no	—
396	#123	C₂×D₆₇	1	2	yes	complemented
397	#123	C₂×D₆₇	1	2	yes	complemented
398	C₂²⋊Q₈	—	67	1	no	—
399	C₂²⋊Q₈	—	67	1	no	—
400	C₂²⋊Q₈	—	67	2	no	—
401	C₂²⋊Q₈	—	67	2	no	—
402	C₂²⋊Q₈	—	67	2	no	—
403	C₂²⋊Q₈	—	67	2	no	—
404	#121	—	67	1	no	—
405	#121	—	67	2	no	—
406	#121	—	67	1	no	—
407	#121	—	67	2	no	—
408	#121	—	67	2	no	—
409	#121	—	67	2	no	—
410	#121	—	67	2	no	—
411	#121	—	67	2	no	—
412	#121	—	67	1	no	—
413	#121	—	67	1	no	—
414	#121	—	67	2	no	—
415	#121	—	67	2	no	—
416	#121	C₂×D₆₇	1	1	yes	characteristic
417	#121	C₂×D₆₇	1	1	yes	characteristic, complemented
418	#121	C₂×D₆₇	1	2	yes	complemented
419	#121	C₂×D₆₇	1	2	yes	complemented
420	#120	—	67	2	no	—
421	#120	—	67	2	no	—
422	#120	—	67	2	no	—
423	C₄×Q₈	—	67	1	no	—
424	C₄×Q₈	—	67	1	no	—
425	C₄×D₄	—	67	1	no	—
426	C₄×D₄	—	67	1	no	—
427	C₄×D₄	—	67	2	no	—
428	C₄×D₄	—	67	2	no	—
429	C₄×D₄	—	67	2	no	—
430	C₄×D₄	—	67	2	no	—
431	C₄×D₄	—	67	2	no	—
432	C₄×D₄	—	67	2	no	—
433	C₄×D₄	—	67	1	no	—
434	C₄×D₄	—	67	2	no	—
435	C₄×D₄	—	67	2	no	—
436	C₄×D₄	—	67	2	no	—
437	C₄×D₄	—	67	2	no	—
438	C₄×D₄	—	67	1	no	—
439	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
440	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic, complemented
441	#117	—	67	1	no	—
442	#117	—	67	2	no	—
443	#117	—	67	1	no	—
444	#117	—	67	1	no	—
445	#117	—	67	1	no	—
446	#117	—	67	2	no	—
447	#117	—	67	1	no	—
448	#117	—	67	1	no	—
449	#117	—	67	2	no	—
450	#117	—	67	1	no	—
451	#117	—	67	1	no	—
452	#117	C₂×D₆₇	1	1	yes	characteristic, complemented
453	C₂×C₄⋊C₄	—	67	2	no	—
454	C₂×C₄⋊C₄	—	67	1	no	—
455	C₂×C₄⋊C₄	—	67	1	no	—
456	C₂×C₄⋊C₄	—	67	1	no	—
457	C₂×C₂²⋊C₄	—	67	2	no	—
458	C₂×C₂²⋊C₄	—	67	1	no	—
459	C₂×C₂²⋊C₄	—	67	1	no	—
460	C₂×C₂²⋊C₄	—	67	2	no	—
461	C₂×C₂²⋊C₄	—	67	2	no	—
462	C₂×C₄²	—	67	1	no	—
463	C₂×C₄²	—	67	1	no	—
464	C₂⁴	—	67	2	no	—
465	C₂⁴	—	67	1	no	—
466	#41	—	268	4	no	—
467	#41	—	268	4	no	—
468	#41	—	134	4	no	—
469	C₂×Q₈	—	67	2	no	—
470	C₂×Q₈	—	67	2	no	—
471	C₂×Q₈	—	67	1	no	—
472	C₂×D₄	—	268	4	no	—
473	C₂×D₄	—	67	2	no	—
474	C₂×D₄	—	67	2	no	—
475	C₂×D₄	—	67	2	no	—
476	C₂×D₄	—	67	2	no	—
477	C₂×D₄	—	67	2	no	—
478	C₂×D₄	—	67	2	no	—
479	C₂×D₄	—	67	2	no	—
480	C₂×D₄	—	67	1	no	—
481	C₂×D₄	—	67	2	no	—
482	C₂×D₄	—	134	4	no	—
483	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
484	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
485	C₂×D₄	C₂²×D₆₇	1	2	yes	—
486	C₂×D₄	C₂²×D₆₇	1	2	yes	—
487	C₂×D₄	C₂²×D₆₇	1	2	yes	—
488	C₂×D₄	C₂²×D₆₇	1	2	yes	—
489	C₂²×C₄	—	67	2	no	—
490	C₂²×C₄	—	67	2	no	—
491	C₂²×C₄	—	67	1	no	—
492	C₂²×C₄	—	67	1	no	—
493	C₂²×C₄	—	67	2	no	—
494	C₂²×C₄	—	67	2	no	—
495	C₂²×C₄	—	67	2	no	—
496	C₂²×C₄	—	67	1	no	—
497	C₂²×C₄	—	67	2	no	—
498	C₂²×C₄	—	67	1	no	—
499	C₂²×C₄	—	67	1	no	—
500	C₂²×C₄	—	67	1	no	—
501	C₂²×C₄	—	67	1	no	—
502	C₂²×C₄	—	67	1	no	—
503	C₂²×C₄	—	67	1	no	—
504	C₂²×C₄	—	134	4	no	—
505	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
506	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
507	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
508	C₄⋊C₄	—	67	1	no	—
509	C₄⋊C₄	—	67	2	no	—
510	C₄⋊C₄	—	67	1	no	—
511	C₄⋊C₄	—	67	1	no	—
512	C₄⋊C₄	—	67	1	no	—
513	C₄⋊C₄	—	67	1	no	—
514	C₄⋊C₄	—	67	1	no	—
515	C₄⋊C₄	—	67	1	no	—
516	C₄⋊C₄	—	67	2	no	—
517	C₄⋊C₄	—	67	2	no	—
518	C₄⋊C₄	—	67	2	no	—
519	C₄⋊C₄	—	67	1	no	—
520	C₄⋊C₄	—	67	2	no	—
521	C₄⋊C₄	—	67	2	no	—
522	C₄⋊C₄	—	67	2	no	—
523	C₄⋊C₄	—	67	2	no	—
524	C₄⋊C₄	—	67	2	no	—
525	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
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	C₂²⋊C₄	—	67	1	no	—
532	C₂²⋊C₄	—	67	1	no	—
533	C₂²⋊C₄	—	67	2	no	—
534	C₂²⋊C₄	—	67	2	no	—
535	C₂²⋊C₄	—	67	2	no	—
536	C₂²⋊C₄	—	67	2	no	—
537	C₂²⋊C₄	—	67	2	no	—
538	C₂²⋊C₄	—	67	2	no	—
539	C₂²⋊C₄	—	67	2	no	—
540	C₂²⋊C₄	—	67	1	no	—
541	C₂²⋊C₄	—	67	1	no	—
542	C₂²⋊C₄	—	67	2	no	—
543	C₂²⋊C₄	—	67	1	no	—
544	C₂²⋊C₄	—	67	1	no	—
545	C₂²⋊C₄	—	67	2	no	—
546	C₂²⋊C₄	—	67	2	no	—
547	C₂²⋊C₄	—	67	2	no	—
548	C₂²⋊C₄	—	67	2	no	—
549	C₂²⋊C₄	—	67	2	no	—
550	C₂²⋊C₄	—	67	2	no	—
551	C₂²⋊C₄	—	67	2	no	—
552	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
553	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
554	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
557	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
558	C₄²	—	67	1	no	—
559	C₄²	—	67	1	no	—
560	C₄²	—	67	1	no	—
561	C₄²	—	67	1	no	—
562	C₄²	—	67	1	no	—
563	C₄²	—	67	1	no	—
564	C₄²	—	67	2	no	—
565	C₄²	—	67	2	no	—
566	C₄²	—	67	2	no	—
567	C₄²	C₂²×D₆₇	1	1	yes	characteristic
568	C₄²	C₂²×D₆₇	1	1	yes	characteristic
569	C₂³	—	268	1	no	—
570	C₂³	—	268	2	no	—
571	C₂³	—	268	2	no	—
572	C₂³	—	67	1	no	—
573	C₂³	—	67	1	no	—
574	C₂³	—	67	2	no	—
575	C₂³	—	134	2	no	—
576	C₂³	—	134	2	no	—
577	C₂³	—	134	4	no	—
578	C₂³	C₂³×D₆₇	1	1	yes	characteristic
579	C₂³	C₂³×D₆₇	1	2	yes	—
580	C₂³	C₂³×D₆₇	1	2	yes	—
581	Q₈	—	268	2	no	—
582	Q₈	—	268	2	no	—
583	Q₈	—	134	2	no	—
584	D₄	—	2	2	no	—
585	D₄	—	2	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	4	2	no	—
588	D₄	—	4	2	no	—
589	D₄	—	4	2	no	—
590	D₄	—	268	2	no	—
591	D₄	—	268	2	no	—
592	D₄	—	268	2	no	—
593	D₄	—	134	4	no	—
594	D₄	—	134	4	no	—
595	D₄	—	134	4	no	—
596	D₄	—	134	4	no	—
597	D₄	—	134	4	no	—
598	D₄	—	134	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	268	2	no	—
603	C₂×C₄	—	268	2	no	—
604	C₂×C₄	—	268	1	no	—
605	C₂×C₄	—	268	2	no	—
606	C₂×C₄	—	268	1	no	—
607	C₂×C₄	—	268	2	no	—
608	C₂×C₄	—	268	2	no	—
609	C₂×C₄	—	67	1	no	—
610	C₂×C₄	—	67	4	no	—
611	C₂×C₄	—	67	1	no	—
612	C₂×C₄	—	67	1	no	—
613	C₂×C₄	—	67	2	no	—
614	C₂×C₄	—	67	1	no	—
615	C₂×C₄	—	67	1	no	—
616	C₂×C₄	—	67	1	no	—
617	C₂×C₄	—	67	2	no	—
618	C₂×C₄	—	67	2	no	—
619	C₂×C₄	—	134	2	no	—
620	C₂×C₄	—	134	2	no	—
621	C₂×C₄	—	134	2	no	—
622	C₂×C₄	—	134	2	no	—
623	C₂×C₄	—	134	2	no	—
624	C₂×C₄	—	134	4	no	—
625	C₂×C₄	—	134	2	no	—
626	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
630	C₂×C₄	C₂³×D₆₇	1	2	yes	—
631	C₂×C₄	C₂³×D₆₇	1	2	yes	—
632	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
634	C₂²	—	2	1	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	268	4	no	—
644	C₂²	—	536	4	no	—
645	C₂²	—	67	2	no	—
646	C₂²	—	67	2	no	—
647	C₂²	—	134	2	no	—
648	C₂²	—	134	2	no	—
649	C₂²	—	134	2	no	—
650	C₂²	—	134	1	no	—
651	C₂²	—	134	1	no	—
652	C₂²	—	134	1	no	—
653	C₂²	—	134	1	no	—
654	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	1	no	—
662	C₄	—	67	2	no	—
663	C₄	—	134	1	no	—
664	C₄	—	134	2	no	—
665	C₄	—	134	1	no	—
666	C₄	—	134	2	no	—
667	C₄	—	134	2	no	—
668	C₄	—	134	1	no	—
669	C₄	—	134	1	no	—
670	C₄	—	134	1	no	—
671	C₄	#41×D₆₇	1	2	yes	—
672	C₂	—	4	1	no	—
673	C₂	—	4	2	no	—
674	C₂	—	4	2	no	—
675	C₂	—	268	2	no	—
676	C₂	—	134	2	no	—
677	C₂	—	134	2	no	—
678	C₂	C₂×#41×D₆₇	1	1	yes	characteristic
679	C₂	H(5,𝔽₂)×D₆₇	1	1	yes	characteristic
680	C₂	#16864231	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	#3494
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. #16864110	C₂	semidirect
2. #16864091	C₂	semidirect
3. #16864089	C₂	semidirect
4. #16864074	C₂	semidirect
5. #16864069	C₂	semidirect
6. #16864044	C₂	semidirect
7. #16864043	C₂	semidirect
8. #16864035	C₂	semidirect
9. #16864026	C₂	semidirect
10. #16864017	C₂	semidirect
11. #16864013	C₂	semidirect
12. #16863999	C₂	semidirect
13. #16863959	C₂	semidirect
14. #16863944	C₂	semidirect
15. #16863943	C₂	semidirect
16. #16863931	C₂	semidirect
17. #16863928	C₂	semidirect
18. #16863906	C₂	semidirect
19. #121×D₆₇	C₂	semidirect
20. #16863875	C₂	semidirect
21. #16863868	C₂	semidirect
22. #117×D₆₇	C₂	semidirect
23. #540×C₆₇	C₂	semidirect
24. C₂×#11761628	C₂²	semidirect
26. C₂×#11761627	C₂²	semidirect
30. #14524043	C₂²	semidirect
31. #14524042	C₂²	semidirect
32. #14524042	C₂²	semidirect
33. #14524039	C₂²	semidirect
34. #14524038	C₂²	semidirect
35. #14524038	C₂²	semidirect
36. #14524036	C₂²	semidirect
37. #14524036	C₂²	semidirect
38. #14524034	C₂²	semidirect
39. #14524033	C₂²	semidirect
40. #14524031	C₂²	semidirect
41. #14524030	C₂²	semidirect
42. #14524030	C₂²	semidirect
43. #14524030	C₂²	semidirect
44. #14524029	C₂²	semidirect
45. #14524029	C₂²	semidirect
46. #14524028	C₂²	semidirect
47. #14524027	C₂²	semidirect
49. #14524025	C₂²	semidirect
50. #14524025	C₂²	semidirect
51. #14524025	C₂²	semidirect
52. #14524024	C₂²	semidirect
54. #14524023	C₂²	semidirect
55. #14524022	C₂²	semidirect
57. #14524021	C₂²	semidirect
58. #14524020	C₂²	semidirect
62. #14524016	C₂²	semidirect
64. #14524015	C₂²	semidirect
65. #14524015	C₂²	semidirect
66. #14524015	C₂²	semidirect
68. #14524014	C₂²	semidirect
69. #14524014	C₂²	semidirect
70. #14524014	C₂²	semidirect
74. C₄×Dic₁₃₄	C₂²	semidirect
75. #14524008	C₂²	semidirect
76. C₄×D₂₆₈	C₂²	semidirect
77. D₄×Dic₆₇	C₂²	semidirect
78. D₄×Dic₆₇	C₂²	semidirect
79. D₄×Dic₆₇	C₂²	semidirect
80. D₄×Dic₆₇	C₂²	semidirect
81. #14524005	C₂²	semidirect
82. #14524005	C₂²	semidirect
84. C₄×C₂²⋊D₆₇	C₂²	semidirect
85. C₄×C₂²⋊D₆₇	C₂²	semidirect
86. C₄×C₂²⋊D₆₇	C₂²	semidirect
88. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
89. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
90. #14524002	C₂²	semidirect
91. #14524002	C₂²	semidirect
95. #14524001	C₂²	semidirect
98. #14523999	C₂²	semidirect
99. #14523999	C₂²	semidirect
100. #14523999	C₂²	semidirect
101. C₂×Dic₆₇⋊C₄	C₂²	semidirect
103. C₄⋊C₄×D₆₇	C₂²	semidirect
104. C₄⋊C₄×D₆₇	C₂²	semidirect
110. C₄²×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
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
289. C₄×D₆₇	#41	semidirect
341. C₆₇	#3494	semidirect
354. #540	D₆₇	semidirect
375. #127	C₂×D₆₇	semidirect
382. #125	C₂×D₆₇	semidirect
396. #123	C₂×D₆₇	semidirect
397. #123	C₂×D₆₇	semidirect
417. #121	C₂×D₆₇	semidirect
418. #121	C₂×D₆₇	semidirect
419. #121	C₂×D₆₇	semidirect
439. C₄×D₄	C₂×D₆₇	semidirect
440. C₄×D₄	C₂×D₆₇	semidirect
452. #117	C₂×D₆₇	semidirect