Subgroups — #22574282

Order 8576.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864118	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864107	C₂	1	1	yes	maximal, characteristic, complemented
3	#16864097	C₂	1	2	yes	maximal, complemented
4	#16864090	C₂	1	1	yes	maximal, characteristic, complemented
5	#16864087	C₂	1	2	yes	maximal, complemented
6	#16864085	C₂	1	1	yes	maximal, characteristic, complemented
7	#16864076	C₂	1	2	yes	maximal, complemented
8	#16864071	C₂	1	2	yes	maximal, complemented
9	#16864048	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	#16864020	C₂	1	1	yes	maximal, characteristic, complemented
13	#16864006	C₂	1	1	yes	maximal, characteristic, complemented
14	#16863987	C₂	1	2	yes	maximal, complemented
15	#16863980	C₂	1	2	yes	maximal, complemented
16	#16863933	C₂	1	2	yes	maximal, complemented
17	#16863932	C₂	1	1	yes	maximal, characteristic, complemented
18	#16863926	C₂	1	1	yes	maximal, characteristic, complemented
19	#126×D₆₇	C₂	1	2	yes	maximal, complemented
20	#16863878	C₂	1	1	yes	maximal, characteristic, complemented
21	#16863870	C₂	1	1	yes	maximal, characteristic, complemented
22	#16863864	C₂	1	1	yes	maximal, characteristic, complemented
23	#556×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	C₂²×D₂₆₈	C₂²	1	1	yes	characteristic
27	#14524041	C₂²	1	1	yes	characteristic, complemented
28	#14524038	C₂²	1	2	yes	complemented
29	#14524038	C₂²	1	2	yes	complemented
30	#14524038	C₂²	1	2	yes	complemented
31	#14524038	C₂²	1	1	yes	characteristic, complemented
32	#14524037	C₂²	1	2	yes	complemented
33	#14524037	C₂²	1	2	yes	complemented
34	#14524036	C₂²	1	2	yes	—
35	#14524036	C₂²	1	2	yes	—
36	#14524036	C₂²	1	2	yes	—
37	#14524036	C₂²	1	1	yes	characteristic
38	#14524035	C₂²	1	2	yes	complemented
39	#14524034	C₂²	1	1	yes	characteristic, complemented
40	#14524034	C₂²	1	2	yes	complemented
41	#14524034	C₂²	1	1	yes	characteristic, complemented
42	#14524033	C₂²	1	2	yes	complemented
43	#14524033	C₂²	1	1	yes	characteristic, complemented
44	#14524032	C₂²	1	1	yes	characteristic
45	#14524032	C₂²	1	2	yes	complemented
46	#14524031	C₂²	1	1	yes	characteristic
47	#14524029	C₂²	1	1	yes	characteristic
48	#14524028	C₂²	1	2	yes	—
49	#14524028	C₂²	1	2	yes	—
50	#14524028	C₂²	1	2	yes	complemented
51	#14524028	C₂²	1	2	yes	complemented
52	#14524027	C₂²	1	1	yes	characteristic, complemented
53	#14524027	C₂²	1	2	yes	complemented
54	#14524025	C₂²	1	2	yes	—
55	#14524025	C₂²	1	2	yes	complemented
56	#14524025	C₂²	1	2	yes	complemented
57	#14524024	C₂²	1	1	yes	characteristic
58	#14524023	C₂²	1	1	yes	characteristic, complemented
59	#14524023	C₂²	1	2	yes	complemented
60	#14524022	C₂²	1	1	yes	characteristic
61	#14524021	C₂²	1	2	yes	complemented
62	#14524020	C₂²	1	1	yes	characteristic, complemented
63	#14524019	C₂²	1	2	yes	complemented
64	#14524019	C₂²	1	2	yes	complemented
65	#14524019	C₂²	1	2	yes	complemented
66	#14524018	C₂²	1	1	yes	characteristic
67	#14524018	C₂²	1	2	yes	—
68	#14524017	C₂²	1	1	yes	characteristic
69	#14524016	C₂²	1	2	yes	—
70	#14524016	C₂²	1	2	yes	complemented
71	#14524016	C₂²	1	2	yes	complemented
72	#14524015	C₂²	1	1	yes	characteristic
73	#14524013	C₂²	1	2	yes	—
74	#14524011	C₂²	1	2	yes	—
75	Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
76	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
77	#14524008	C₂²	1	1	yes	characteristic, complemented
78	#14524008	C₂²	1	1	yes	characteristic, complemented
79	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
80	C₄×D₂₆₈	C₂²	1	2	yes	—
81	C₄×D₂₆₈	C₂²	1	2	yes	—
82	C₄×D₂₆₈	C₂²	1	2	yes	complemented
83	C₄×D₂₆₈	C₂²	1	2	yes	complemented
84	#14524005	C₂²	1	1	yes	characteristic
85	#14524005	C₂²	1	1	yes	characteristic
86	#14524005	C₂²	1	1	yes	characteristic
87	#14524005	C₂²	1	1	yes	characteristic
88	#14524005	C₂²	1	1	yes	characteristic
89	#14524005	C₂²	1	2	yes	complemented
90	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
91	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic, complemented
92	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
93	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
94	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
95	#14524002	C₂²	1	1	yes	characteristic
96	#14524001	C₂²	1	2	yes	complemented
97	#14524000	C₂²	1	1	yes	characteristic, complemented
98	#14524000	C₂²	1	2	yes	complemented
99	#14524000	C₂²	1	2	yes	complemented
100	#14524000	C₂²	1	2	yes	complemented
101	#14524000	C₂²	1	2	yes	complemented
102	C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
103	C₄⋊C₄×D₆₇	C₂²	1	1	yes	characteristic, complemented
104	C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
105	C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
106	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
110	C₂×C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
111	C₄²×D₆₇	C₂²	1	2	yes	complemented
112	C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	#126×C₆₇	C₂²	1	2	yes	—
114	#126×C₆₇	C₂²	1	2	yes	complemented
115	#124×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	2	yes	complemented
119	C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
121	#117×C₆₇	C₂²	1	1	yes	characteristic
122	#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₆₇	C₂³	1	2	yes	—
124	#11761629	—	2	4	no	—
125	#11761628	—	2	4	no	—
126	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
127	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
128	C₂×D₂₆₈	—	2	4	no	—
129	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
130	C₂×D₂₆₈	C₂³	1	2	yes	—
131	C₂×D₂₆₈	C₂³	1	2	yes	—
132	C₂×D₂₆₈	C₂³	1	2	yes	—
133	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
138	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
139	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₆₇	C₂³	1	2	yes	—
141	C₂×C₄×D₆₇	C₂³	1	2	yes	—
142	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₆₇	C₂³	1	2	yes	—
144	C₂×C₄×D₆₇	C₂³	1	2	yes	—
145	C₂×C₄×D₆₇	C₂³	1	2	yes	—
146	C₂×C₄×D₆₇	C₂³	1	2	yes	—
147	C₂×C₄×D₆₇	C₂³	1	2	yes	—
148	C₂×C₄×D₆₇	C₂³	1	2	yes	—
149	C₂×C₄×D₆₇	C₂³	1	2	yes	—
150	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
152	C₄⋊Dic₆₇	C₂³	1	2	yes	—
153	C₄⋊Dic₆₇	C₂³	1	2	yes	—
154	C₄⋊Dic₆₇	C₂³	1	2	yes	—
155	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
156	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₆₇	C₂³	1	2	yes	—
158	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
159	Dic₆₇⋊C₄	C₂³	1	2	yes	—
160	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
161	Dic₆₇⋊C₄	C₂³	1	2	yes	—
162	Dic₆₇⋊C₄	C₂³	1	2	yes	—
163	Dic₆₇⋊C₄	C₂³	1	2	yes	—
164	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
165	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
171	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
176	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
177	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
178	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
179	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
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	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	2	yes	—
193	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
194	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
195	C₄×Dic₆₇	C₂³	1	2	yes	—
196	C₄×Dic₆₇	C₂³	1	2	yes	—
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	2	yes	—
201	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
202	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
203	C₂×Q₈×C₆₇	C₂³	1	2	yes	—
204	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
205	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
207	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
208	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
209	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
212	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
213	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
214	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
215	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
216	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
218	C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
219	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
221	C₄²×C₆₇	C₂³	1	2	yes	—
222	C₄²×C₆₇	C₂³	1	2	yes	—
223	C₄²×C₆₇	C₂³	1	1	yes	characteristic
224	C₄²×C₆₇	C₂³	1	2	yes	—
225	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
226	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
227	C₂²×D₆₇	—	2	4	no	—
228	C₂²×D₆₇	—	4	2	no	—
229	C₂²×D₆₇	—	4	2	no	—
230	C₂²×D₆₇	C₂⁴	1	2	yes	—
231	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
232	C₂²×D₆₇	C₂⁴	1	2	yes	—
233	Q₈×C₆₇	—	2	2	no	—
234	Q₈×C₆₇	—	4	2	no	—
235	D₄×C₆₇	—	4	1	no	—
236	C₂×C₄×C₆₇	—	2	2	no	—
237	C₂×C₄×C₆₇	—	2	2	no	—
238	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
239	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
244	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
245	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
246	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₂²⋊D₆₇	—	2	4	no	—
248	C₂²⋊D₆₇	—	4	1	no	—
249	C₂²⋊D₆₇	—	4	2	no	—
250	C₂²⋊D₆₇	—	4	1	no	—
251	C₂×Dic₆₇	—	4	1	no	—
252	C₂×Dic₆₇	—	4	1	no	—
253	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₆₇	C₂⁴	1	2	yes	—
258	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₆₇	C₂⁴	1	2	yes	—
261	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
262	D₂₆₈	—	2	4	no	—
263	D₂₆₈	—	2	4	no	—
264	D₂₆₈	—	2	2	no	—
265	D₂₆₈	—	4	2	no	—
266	D₂₆₈	#41	1	4	yes	—
267	C₄×D₆₇	—	2	4	no	—
268	C₄×D₆₇	—	2	4	no	—
269	C₄×D₆₇	—	2	2	no	—
270	C₄×D₆₇	—	4	2	no	—
271	C₄×D₆₇	—	4	2	no	—
272	C₄×D₆₇	—	4	2	no	—
273	C₄×D₆₇	—	4	2	no	—
274	C₄×D₆₇	—	4	2	no	—
275	C₄×D₆₇	—	4	2	no	—
276	C₄×D₆₇	—	4	2	no	—
277	Dic₁₃₄	—	2	2	no	—
278	Dic₁₃₄	—	4	1	no	—
279	C₂²×C₆₇	—	2	1	no	—
280	C₂²×C₆₇	—	2	1	no	—
281	C₂²×C₆₇	—	2	1	no	—
282	C₂²×C₆₇	—	2	1	no	—
283	C₂²×C₆₇	—	2	1	no	—
284	C₂²×C₆₇	—	2	1	no	—
285	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
286	C₂×D₆₇	—	2	2	no	—
287	C₂×D₆₇	—	2	2	no	—
288	C₂×D₆₇	—	2	1	no	—
289	C₂×D₆₇	—	2	2	no	—
290	C₂×D₆₇	—	2	1	no	—
291	C₂×D₆₇	—	2	2	no	—
292	C₂×D₆₇	—	2	2	no	—
293	C₂×D₆₇	—	2	1	no	—
294	C₂×D₆₇	—	8	4	no	—
295	C₂×D₆₇	C₂×#41	1	4	yes	—
296	C₄×C₆₇	—	2	1	no	—
297	C₄×C₆₇	—	2	2	no	—
298	C₄×C₆₇	—	2	1	no	—
299	C₄×C₆₇	—	2	1	no	—
300	C₄×C₆₇	—	2	2	no	—
301	C₄×C₆₇	—	2	2	no	—
302	C₄×C₆₇	—	2	2	no	—
303	C₄×C₆₇	—	2	1	no	—
304	C₄×C₆₇	C₂×#41	1	2	yes	—
305	Dic₆₇	—	2	2	no	—
306	Dic₆₇	—	2	1	no	—
307	Dic₆₇	—	2	1	no	—
308	Dic₆₇	—	2	1	no	—
309	Dic₆₇	—	2	1	no	—
310	Dic₆₇	—	2	1	no	—
311	Dic₆₇	—	2	1	no	—
312	Dic₆₇	—	2	1	no	—
313	Dic₆₇	—	2	2	no	—
314	C₂×C₆₇	—	4	1	no	—
315	C₂×C₆₇	—	4	1	no	—
316	C₂×C₆₇	C₂²×#41	1	1	yes	characteristic
317	C₂×C₆₇	#585	1	1	yes	characteristic
318	C₂×C₆₇	#585	1	1	yes	characteristic
319	D₆₇	—	2	4	no	—
320	D₆₇	—	4	1	no	—
321	D₆₇	—	4	2	no	—
322	#3521	—	67	1	no	maximal, Sylow
323	C₆₇	#3521	1	1	yes	characteristic, complemented, Sylow
324	#556	—	67	1	no	—
325	#556	D₆₇	1	1	yes	characteristic, complemented
326	#554	—	67	1	no	—
327	#553	—	67	2	no	—
328	#553	—	67	1	no	—
329	#552	—	67	2	no	—
330	#552	—	67	1	no	—
331	#551	—	67	2	no	—
332	#551	—	67	2	no	—
333	#547	—	67	1	no	—
334	#546	—	67	1	no	—
335	#546	—	67	1	no	—
336	#542	—	67	1	no	—
337	#541	—	67	1	no	—
338	#539	—	67	2	no	—
339	#538	—	67	2	no	—
340	#529	—	67	1	no	—
341	#529	—	67	2	no	—
342	#529	—	67	1	no	—
343	C₂×#126	—	67	2	no	—
344	#520	—	67	1	no	—
345	#518	—	67	1	no	—
346	C₄×#41	—	67	1	no	—
347	C₂×#41	—	67	1	no	—
348	C₂×#41	—	67	1	no	—
349	C₂²×D₄	—	67	1	no	—
350	C₄⋊Q₈	—	67	1	no	—
351	C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
352	#126	—	67	2	no	—
353	#126	—	67	2	no	—
354	#126	—	67	2	no	—
355	#126	—	67	1	no	—
356	#126	—	67	1	no	—
357	#126	—	67	2	no	—
358	#126	—	67	2	no	—
359	#126	—	67	2	no	—
360	#126	—	67	2	no	—
361	#126	—	67	2	no	—
362	#126	C₂×D₆₇	1	2	yes	—
363	#126	C₂×D₆₇	1	2	yes	complemented
364	#125	—	67	2	no	—
365	#125	—	67	1	no	—
366	#125	—	67	1	no	—
367	#125	—	67	2	no	—
368	#125	—	67	1	no	—
369	#125	—	67	2	no	—
370	#124	—	67	2	no	—
371	#124	—	67	1	no	—
372	#124	—	67	1	no	—
373	#124	—	67	1	no	—
374	#124	C₂×D₆₇	1	2	yes	—
375	#123	—	67	1	no	—
376	#123	—	67	2	no	—
377	#123	—	67	2	no	—
378	#123	—	67	2	no	—
379	#123	—	67	2	no	—
380	#123	—	67	2	no	—
381	#123	—	67	1	no	—
382	#123	—	67	2	no	—
383	#123	—	67	2	no	—
384	#123	—	67	2	no	—
385	C₂²⋊Q₈	—	67	2	no	—
386	C₂²⋊Q₈	—	67	2	no	—
387	C₂²⋊Q₈	—	67	2	no	—
388	C₂²⋊Q₈	—	67	1	no	—
389	C₂²⋊Q₈	—	67	2	no	—
390	C₂²⋊Q₈	—	67	2	no	—
391	C₂²⋊Q₈	—	67	1	no	—
392	C₂²⋊Q₈	—	67	1	no	—
393	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
394	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
395	#121	—	67	1	no	—
396	#121	—	67	1	no	—
397	#121	—	67	2	no	—
398	#121	—	67	1	no	—
399	#121	—	67	2	no	—
400	#121	—	67	2	no	—
401	#121	—	67	2	no	—
402	#120	—	67	2	no	—
403	#120	—	67	2	no	—
404	C₄×Q₈	—	67	1	no	—
405	C₄×Q₈	—	67	1	no	—
406	C₄×Q₈	—	67	1	no	—
407	C₄×Q₈	—	67	1	no	—
408	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
409	C₄×Q₈	C₂×D₆₇	1	2	yes	complemented
410	C₄×D₄	—	67	1	no	—
411	C₄×D₄	—	67	1	no	—
412	C₄×D₄	—	67	1	no	—
413	C₄×D₄	—	67	1	no	—
414	C₄×D₄	—	67	1	no	—
415	C₄×D₄	—	67	1	no	—
416	C₄×D₄	—	67	1	no	—
417	C₄×D₄	—	67	2	no	—
418	C₄×D₄	—	67	2	no	—
419	C₄×D₄	—	67	2	no	—
420	C₄×D₄	—	67	2	no	—
421	C₄×D₄	—	67	2	no	—
422	C₄×D₄	—	67	2	no	—
423	C₄×D₄	—	67	2	no	—
424	C₄×D₄	—	67	1	no	—
425	C₄×D₄	—	67	2	no	—
426	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
427	#117	—	67	1	no	—
428	#117	—	67	2	no	—
429	#117	—	67	2	no	—
430	#117	—	67	1	no	—
431	#117	—	67	2	no	—
432	#117	—	67	2	no	—
433	#117	—	67	2	no	—
434	#117	C₂×D₆₇	1	1	yes	characteristic
435	#117	C₂×D₆₇	1	1	yes	characteristic, complemented
436	C₂×C₄⋊C₄	—	67	2	no	—
437	C₂×C₄⋊C₄	—	67	1	no	—
438	C₂×C₄⋊C₄	—	67	2	no	—
439	C₂×C₄⋊C₄	—	67	2	no	—
440	C₂×C₂²⋊C₄	—	67	2	no	—
441	C₂×C₂²⋊C₄	—	67	2	no	—
442	C₂×C₂²⋊C₄	—	67	2	no	—
443	C₂×C₂²⋊C₄	—	67	2	no	—
444	C₂×C₄²	—	67	1	no	—
445	C₂×C₄²	—	67	2	no	—
446	C₂⁴	—	67	2	no	—
447	#41	—	134	4	no	—
448	#41	—	134	4	no	—
449	C₂×Q₈	—	67	1	no	—
450	C₂×Q₈	—	67	1	no	—
451	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
452	C₂×Q₈	C₂²×D₆₇	1	2	yes	—
453	C₂×D₄	—	67	1	no	—
454	C₂×D₄	—	67	2	no	—
455	C₂×D₄	—	67	1	no	—
456	C₂×D₄	—	67	2	no	—
457	C₂×D₄	—	67	2	no	—
458	C₂×D₄	—	67	1	no	—
459	C₂×D₄	—	67	2	no	—
460	C₂×D₄	—	67	2	no	—
461	C₂×D₄	—	67	1	no	—
462	C₂×D₄	—	134	4	no	—
463	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
464	C₂²×C₄	—	67	1	no	—
465	C₂²×C₄	—	67	1	no	—
466	C₂²×C₄	—	67	2	no	—
467	C₂²×C₄	—	67	2	no	—
468	C₂²×C₄	—	67	2	no	—
469	C₂²×C₄	—	67	2	no	—
470	C₂²×C₄	—	67	2	no	—
471	C₂²×C₄	—	67	2	no	—
472	C₂²×C₄	—	67	2	no	—
473	C₂²×C₄	—	67	2	no	—
474	C₂²×C₄	—	67	2	no	—
475	C₂²×C₄	—	67	1	no	—
476	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
477	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
478	C₄⋊C₄	—	67	1	no	—
479	C₄⋊C₄	—	67	2	no	—
480	C₄⋊C₄	—	67	1	no	—
481	C₄⋊C₄	—	67	1	no	—
482	C₄⋊C₄	—	67	2	no	—
483	C₄⋊C₄	—	67	1	no	—
484	C₄⋊C₄	—	67	2	no	—
485	C₄⋊C₄	—	67	2	no	—
486	C₄⋊C₄	—	67	2	no	—
487	C₄⋊C₄	—	67	2	no	—
488	C₄⋊C₄	—	67	1	no	—
489	C₄⋊C₄	—	67	1	no	—
490	C₄⋊C₄	—	67	1	no	—
491	C₄⋊C₄	—	67	1	no	—
492	C₄⋊C₄	—	67	2	no	—
493	C₄⋊C₄	—	67	2	no	—
494	C₄⋊C₄	—	67	2	no	—
495	C₄⋊C₄	—	67	2	no	—
496	C₄⋊C₄	—	67	2	no	—
497	C₄⋊C₄	—	67	2	no	—
498	C₄⋊C₄	—	67	1	no	—
499	C₄⋊C₄	—	67	1	no	—
500	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
501	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
503	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
504	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
507	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
508	C₂²⋊C₄	—	67	1	no	—
509	C₂²⋊C₄	—	67	1	no	—
510	C₂²⋊C₄	—	67	1	no	—
511	C₂²⋊C₄	—	67	2	no	—
512	C₂²⋊C₄	—	67	1	no	—
513	C₂²⋊C₄	—	67	2	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	2	no	—
519	C₂²⋊C₄	—	67	2	no	—
520	C₂²⋊C₄	—	67	2	no	—
521	C₂²⋊C₄	—	67	1	no	—
522	C₂²⋊C₄	—	67	2	no	—
523	C₂²⋊C₄	—	67	2	no	—
524	C₂²⋊C₄	—	67	1	no	—
525	C₂²⋊C₄	—	67	1	no	—
526	C₂²⋊C₄	—	67	2	no	—
527	C₂²⋊C₄	—	67	2	no	—
528	C₂²⋊C₄	—	67	2	no	—
529	C₂²⋊C₄	—	67	1	no	—
530	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
531	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
532	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
535	C₂²⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
536	C₄²	—	67	1	no	—
537	C₄²	—	67	1	no	—
538	C₄²	—	67	1	no	—
539	C₄²	—	67	2	no	—
540	C₄²	—	67	1	no	—
541	C₄²	—	67	2	no	—
542	C₄²	—	67	2	no	—
543	C₄²	—	67	1	no	—
544	C₄²	C₂²×D₆₇	1	2	yes	—
545	C₄²	C₂²×D₆₇	1	2	yes	—
546	C₄²	C₂²×D₆₇	1	2	yes	—
547	C₄²	C₂²×D₆₇	1	1	yes	characteristic
548	C₂³	—	268	2	no	—
549	C₂³	—	268	2	no	—
550	C₂³	—	67	2	no	—
551	C₂³	—	67	2	no	—
552	C₂³	—	67	1	no	—
553	C₂³	—	134	4	no	—
554	C₂³	C₂³×D₆₇	1	1	yes	characteristic
555	C₂³	C₂³×D₆₇	1	1	yes	characteristic
556	Q₈	—	2	2	no	—
557	Q₈	—	4	2	no	—
558	Q₈	—	268	1	no	—
559	Q₈	—	134	2	no	—
560	D₄	—	4	1	no	—
561	D₄	—	268	2	no	—
562	D₄	—	268	1	no	—
563	D₄	—	268	2	no	—
564	D₄	—	268	1	no	—
565	D₄	—	67	4	no	—
566	D₄	—	134	4	no	—
567	D₄	—	134	4	no	—
568	D₄	—	134	4	no	—
569	D₄	—	134	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	268	2	no	—
573	C₂×C₄	—	268	2	no	—
574	C₂×C₄	—	268	2	no	—
575	C₂×C₄	—	268	2	no	—
576	C₂×C₄	—	268	2	no	—
577	C₂×C₄	—	268	2	no	—
578	C₂×C₄	—	268	2	no	—
579	C₂×C₄	—	268	1	no	—
580	C₂×C₄	—	268	1	no	—
581	C₂×C₄	—	67	1	no	—
582	C₂×C₄	—	67	1	no	—
583	C₂×C₄	—	67	1	no	—
584	C₂×C₄	—	67	2	no	—
585	C₂×C₄	—	67	1	no	—
586	C₂×C₄	—	67	1	no	—
587	C₂×C₄	—	67	1	no	—
588	C₂×C₄	—	67	2	no	—
589	C₂×C₄	—	67	1	no	—
590	C₂×C₄	—	134	4	no	—
591	C₂×C₄	—	134	4	no	—
592	C₂×C₄	—	134	2	no	—
593	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
594	C₂×C₄	C₂³×D₆₇	1	2	yes	—
595	C₂×C₄	C₂³×D₆₇	1	2	yes	—
596	C₂×C₄	C₂³×D₆₇	1	2	yes	—
597	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₆₇	1	2	yes	—
600	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
601	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	536	4	no	—
609	C₂²	—	67	4	no	—
610	C₂²	—	134	1	no	—
611	C₂²	—	134	2	no	—
612	C₂²	—	134	2	no	—
613	C₂²	—	134	1	no	—
614	C₂²	—	134	1	no	—
615	C₂²	—	134	2	no	—
616	C₂²	—	134	2	no	—
617	C₂²	—	134	2	no	—
618	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	1	no	—
627	C₄	—	134	1	no	—
628	C₄	—	134	2	no	—
629	C₄	—	134	1	no	—
630	C₄	—	134	1	no	—
631	C₄	—	134	1	no	—
632	C₄	—	134	1	no	—
633	C₄	—	134	2	no	—
634	C₄	—	134	1	no	—
635	C₄	—	134	1	no	—
636	C₄	#41×D₆₇	1	2	yes	—
637	C₂	—	4	1	no	—
638	C₂	—	4	1	no	—
639	C₂	—	268	2	no	—
640	C₂	—	268	1	no	—
641	C₂	—	134	4	no	—
642	C₂	C₂×#41×D₆₇	1	1	yes	characteristic
643	C₂	#16864232	1	1	yes	characteristic
644	C₂	#16864233	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#556×C₆₇	C₂
hypercenter	#556	D₆₇
hypocenter	C₆₇	#3521
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #16864118	C₂	semidirect
2. #16864107	C₂	semidirect
3. #16864097	C₂	semidirect
4. #16864090	C₂	semidirect
5. #16864087	C₂	semidirect
6. #16864085	C₂	semidirect
7. #16864076	C₂	semidirect
8. #16864071	C₂	semidirect
9. #16864048	C₂	semidirect
10. #16864042	C₂	semidirect
11. #16864037	C₂	semidirect
12. #16864020	C₂	semidirect
13. #16864006	C₂	semidirect
14. #16863987	C₂	semidirect
15. #16863980	C₂	semidirect
16. #16863933	C₂	semidirect
17. #16863932	C₂	semidirect
18. #16863926	C₂	semidirect
19. #126×D₆₇	C₂	semidirect
20. #16863878	C₂	semidirect
21. #16863870	C₂	semidirect
22. #16863864	C₂	semidirect
23. #556×C₆₇	C₂	semidirect
27. #14524041	C₂²	semidirect
28. #14524038	C₂²	semidirect
29. #14524038	C₂²	semidirect
30. #14524038	C₂²	semidirect
31. #14524038	C₂²	semidirect
32. #14524037	C₂²	semidirect
33. #14524037	C₂²	semidirect
38. #14524035	C₂²	semidirect
39. #14524034	C₂²	semidirect
40. #14524034	C₂²	semidirect
41. #14524034	C₂²	semidirect
42. #14524033	C₂²	semidirect
43. #14524033	C₂²	semidirect
45. #14524032	C₂²	semidirect
50. #14524028	C₂²	semidirect
51. #14524028	C₂²	semidirect
52. #14524027	C₂²	semidirect
53. #14524027	C₂²	semidirect
55. #14524025	C₂²	semidirect
56. #14524025	C₂²	semidirect
58. #14524023	C₂²	semidirect
59. #14524023	C₂²	semidirect
61. #14524021	C₂²	semidirect
62. #14524020	C₂²	semidirect
63. #14524019	C₂²	semidirect
64. #14524019	C₂²	semidirect
65. #14524019	C₂²	semidirect
70. #14524016	C₂²	semidirect
71. #14524016	C₂²	semidirect
75. Q₈×Dic₆₇	C₂²	semidirect
76. C₄×Dic₁₃₄	C₂²	semidirect
77. #14524008	C₂²	semidirect
78. #14524008	C₂²	semidirect
82. C₄×D₂₆₈	C₂²	semidirect
83. C₄×D₂₆₈	C₂²	semidirect
89. #14524005	C₂²	semidirect
91. C₄×C₂²⋊D₆₇	C₂²	semidirect
92. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
93. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
94. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
96. #14524001	C₂²	semidirect
97. #14524000	C₂²	semidirect
98. #14524000	C₂²	semidirect
99. #14524000	C₂²	semidirect
100. #14524000	C₂²	semidirect
101. #14524000	C₂²	semidirect
102. C₄⋊C₄×D₆₇	C₂²	semidirect
103. C₄⋊C₄×D₆₇	C₂²	semidirect
104. C₄⋊C₄×D₆₇	C₂²	semidirect
105. C₄⋊C₄×D₆₇	C₂²	semidirect
110. C₂×C₄×Dic₆₇	C₂²	semidirect
111. C₄²×D₆₇	C₂²	semidirect
112. C₄⋊Q₈×C₆₇	C₂²	semidirect
114. #126×C₆₇	C₂²	semidirect
117. C₂²⋊Q₈×C₆₇	C₂²	semidirect
118. C₄×Q₈×C₆₇	C₂²	semidirect
119. C₄×Q₈×C₆₇	C₂²	semidirect
122. #117×C₆₇	C₂²	semidirect
323. C₆₇	#3521	semidirect
325. #556	D₆₇	semidirect
351. C₄⋊Q₈	C₂×D₆₇	semidirect
363. #126	C₂×D₆₇	semidirect
394. C₂²⋊Q₈	C₂×D₆₇	semidirect
408. C₄×Q₈	C₂×D₆₇	semidirect
409. C₄×Q₈	C₂×D₆₇	semidirect
435. #117	C₂×D₆₇	semidirect