Subgroups — #22573903

Order 8576.

1052 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864084	C₂	1	2	yes	maximal, complemented
2	#16864082	C₂	1	2	yes	maximal, complemented
3	#16864080	C₂	1	2	yes	maximal, complemented
4	#16864078	C₂	1	2	yes	maximal, complemented
5	#16864074	C₂	1	2	yes	maximal, complemented
6	#16864073	C₂	1	2	yes	maximal, complemented
7	#16864071	C₂	1	2	yes	maximal, complemented
8	#16864069	C₂	1	2	yes	maximal, complemented
9	#16864021	C₂	1	1	yes	maximal, characteristic, complemented
10	#16863993	C₂	1	1	yes	maximal, characteristic, complemented
11	#16863990	C₂	1	2	yes	maximal, complemented
12	#16863954	C₂	1	1	yes	maximal, characteristic
13	#16863932	C₂	1	1	yes	maximal, characteristic, complemented
14	#16863927	C₂	1	1	yes	maximal, characteristic, complemented
15	#16863926	C₂	1	2	yes	maximal, complemented
16	#123×D₆₇	C₂	1	2	yes	maximal, complemented
17	#16863868	C₂	1	2	yes	maximal, complemented
18	C₂×#14524001	C₂	1	1	yes	maximal, characteristic, complemented
19	#539×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×D₄×D₆₇	C₂²	1	2	yes	—
21	C₂²×C₄×D₆₇	C₂²	1	1	yes	characteristic
22	#14524038	C₂²	1	2	yes	complemented
23	#14524038	C₂²	1	2	yes	complemented
24	#14524038	C₂²	1	2	yes	complemented
25	#14524038	C₂²	1	2	yes	complemented
26	#14524036	C₂²	1	2	yes	complemented
27	#14524036	C₂²	1	2	yes	complemented
28	#14524036	C₂²	1	2	yes	complemented
29	#14524034	C₂²	1	2	yes	complemented
30	#14524034	C₂²	1	1	yes	characteristic, complemented
31	#14524034	C₂²	1	1	yes	characteristic, complemented
32	#14524033	C₂²	1	2	yes	complemented
33	#14524033	C₂²	1	2	yes	complemented
34	#14524033	C₂²	1	2	yes	complemented
35	#14524032	C₂²	1	1	yes	characteristic, complemented
36	#14524030	C₂²	1	1	yes	characteristic, complemented
37	#14524029	C₂²	1	2	yes	complemented
38	#14524028	C₂²	1	2	yes	—
39	#14524028	C₂²	1	2	yes	—
40	#14524028	C₂²	1	2	yes	—
41	#14524028	C₂²	1	2	yes	complemented
42	#14524027	C₂²	1	2	yes	complemented
43	#14524027	C₂²	1	2	yes	complemented
44	#14524026	C₂²	1	2	yes	complemented
45	#14524025	C₂²	1	2	yes	—
46	#14524025	C₂²	1	2	yes	—
47	#14524025	C₂²	1	2	yes	—
48	#14524025	C₂²	1	2	yes	complemented
49	#14524024	C₂²	1	2	yes	complemented
50	#14524023	C₂²	1	2	yes	complemented
51	#14524023	C₂²	1	2	yes	complemented
52	#14524022	C₂²	1	1	yes	characteristic, complemented
53	#14524021	C₂²	1	2	yes	complemented
54	#14524021	C₂²	1	2	yes	complemented
55	#14524021	C₂²	1	2	yes	complemented
56	#14524020	C₂²	1	2	yes	complemented
57	#14524020	C₂²	1	2	yes	complemented
58	#14524019	C₂²	1	2	yes	complemented
59	#14524017	C₂²	1	1	yes	characteristic
60	#14524015	C₂²	1	2	yes	—
61	#14524013	C₂²	1	2	yes	—
62	#14524011	C₂²	1	2	yes	—
63	Q₈×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
64	C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
65	#14524008	C₂²	1	1	yes	characteristic, complemented
66	C₄×D₂₆₈	C₂²	1	2	yes	—
67	D₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
68	D₄×Dic₆₇	C₂²	1	2	yes	complemented
69	#14524005	C₂²	1	2	yes	—
70	#14524005	C₂²	1	1	yes	characteristic, complemented
71	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
72	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
73	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	complemented
74	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
75	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	complemented
76	#14524002	C₂²	1	2	yes	complemented
77	#14524001	C₂²	1	2	yes	complemented
78	#14524001	C₂²	1	2	yes	complemented
79	#14524001	C₂²	1	2	yes	complemented
80	#14524001	C₂²	1	2	yes	complemented
81	#14524001	C₂²	1	2	yes	complemented
82	#14524001	C₂²	1	2	yes	complemented
83	#14524000	C₂²	1	2	yes	complemented
84	#14524000	C₂²	1	2	yes	complemented
85	#14523999	C₂²	1	2	yes	complemented
86	C₂×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic, complemented
87	C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
88	C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
89	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
90	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
91	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	2	yes	complemented
92	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
93	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	complemented
96	C₂×C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
97	C₂×C₄×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
98	#126×C₆₇	C₂²	1	2	yes	complemented
99	#125×C₆₇	C₂²	1	2	yes	complemented
100	#123×C₆₇	C₂²	1	2	yes	complemented
101	#123×C₆₇	C₂²	1	2	yes	complemented
102	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
104	#121×C₆₇	C₂²	1	1	yes	characteristic
105	C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
106	C₂×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₆₇	C₂³	1	2	yes	—
108	C₂³×D₆₇	C₂³	1	1	yes	characteristic
109	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
110	C₂×Dic₁₃₄	C₂³	1	2	yes	—
111	C₂×D₂₆₈	C₂³	1	2	yes	—
112	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
113	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
114	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
115	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
116	D₄×D₆₇	—	2	8	no	—
117	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
118	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
119	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
120	C₂²×Dic₆₇	C₂³	1	2	yes	—
121	C₂×C₄×D₆₇	—	2	4	no	—
122	C₂×C₄×D₆₇	C₂³	1	2	yes	—
123	C₂×C₄×D₆₇	C₂³	1	2	yes	—
124	C₂×C₄×D₆₇	C₂³	1	2	yes	—
125	C₂×C₄×D₆₇	C₂³	1	2	yes	—
126	C₂×C₄×D₆₇	C₂³	1	2	yes	—
127	C₂×C₄×D₆₇	C₂³	1	2	yes	—
128	C₂×C₄×D₆₇	C₂³	1	2	yes	—
129	C₄⋊Dic₆₇	C₂³	1	2	yes	—
130	C₄⋊Dic₆₇	C₂³	1	2	yes	—
131	C₄⋊Dic₆₇	C₂³	1	2	yes	—
132	C₄⋊Dic₆₇	C₂³	1	2	yes	—
133	C₄⋊Dic₆₇	C₂³	1	2	yes	—
134	C₄⋊Dic₆₇	C₂³	1	2	yes	—
135	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
136	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
137	Dic₆₇⋊C₄	C₂³	1	2	yes	—
138	Dic₆₇⋊C₄	C₂³	1	2	yes	—
139	Dic₆₇⋊C₄	C₂³	1	2	yes	—
140	Dic₆₇⋊C₄	C₂³	1	2	yes	—
141	Dic₆₇⋊C₄	C₂³	1	2	yes	—
142	Dic₆₇⋊C₄	C₂³	1	2	yes	—
143	Dic₆₇⋊C₄	C₂³	1	2	yes	—
144	Dic₆₇⋊C₄	C₂³	1	2	yes	—
145	Dic₆₇⋊C₄	C₂³	1	2	yes	—
146	Dic₆₇⋊C₄	C₂³	1	2	yes	—
147	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
148	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
149	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
150	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
151	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
152	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
153	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
154	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
155	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
156	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
157	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
158	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
159	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
160	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
161	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
162	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
163	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
164	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
165	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
166	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
167	C₄×Dic₆₇	C₂³	1	2	yes	—
168	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
169	C₄×Dic₆₇	C₂³	1	2	yes	—
170	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
171	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
172	C₄×Dic₆₇	C₂³	1	2	yes	—
173	C₄×Dic₆₇	C₂³	1	2	yes	—
174	C₄×Dic₆₇	C₂³	1	2	yes	—
175	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×D₄×C₆₇	C₂³	1	2	yes	—
177	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
178	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
182	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
186	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
189	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
191	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
195	C₄²×C₆₇	C₂³	1	2	yes	—
196	C₂³×C₆₇	C₂⁴	1	2	yes	—
197	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
198	C₂²×D₆₇	—	2	4	no	—
199	C₂²×D₆₇	—	4	1	no	—
200	C₂²×D₆₇	—	4	1	no	—
201	C₂²×D₆₇	—	4	2	no	—
202	C₂²×D₆₇	—	4	2	no	—
203	C₂²×D₆₇	#41	1	4	yes	—
204	C₂²×D₆₇	C₂⁴	1	2	yes	—
205	C₂²×D₆₇	C₂⁴	1	2	yes	—
206	Q₈×C₆₇	—	4	1	no	—
207	D₄×C₆₇	—	2	4	no	—
208	D₄×C₆₇	—	4	1	no	—
209	C₂×C₄×C₆₇	—	2	2	no	—
210	C₂×C₄×C₆₇	—	4	1	no	—
211	C₂×C₄×C₆₇	—	4	1	no	—
212	C₂×C₄×C₆₇	—	4	2	no	—
213	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
214	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
215	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
216	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
217	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
218	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
219	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
220	C₂²⋊D₆₇	—	2	4	no	—
221	C₂²⋊D₆₇	—	2	4	no	—
222	C₂²⋊D₆₇	—	4	2	no	—
223	C₂×Dic₆₇	—	2	2	no	—
224	C₂×Dic₆₇	—	4	2	no	—
225	C₂×Dic₆₇	—	4	1	no	—
226	C₂×Dic₆₇	—	4	1	no	—
227	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
228	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
229	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
230	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
231	C₂×Dic₆₇	C₂⁴	1	2	yes	—
232	C₂×Dic₆₇	C₂⁴	1	2	yes	—
233	C₂×Dic₆₇	C₂⁴	1	2	yes	—
234	C₂×Dic₆₇	C₂⁴	1	2	yes	—
235	D₂₆₈	—	2	4	no	—
236	D₂₆₈	—	4	1	no	—
237	C₄×D₆₇	—	2	4	no	—
238	C₄×D₆₇	—	2	4	no	—
239	C₄×D₆₇	—	2	4	no	—
240	C₄×D₆₇	—	4	2	no	—
241	C₄×D₆₇	—	4	2	no	—
242	C₄×D₆₇	—	4	2	no	—
243	C₄×D₆₇	—	4	2	no	—
244	Dic₁₃₄	—	4	1	no	—
245	Dic₁₃₄	—	4	2	no	—
246	C₂²×C₆₇	—	2	1	no	—
247	C₂²×C₆₇	—	2	1	no	—
248	C₂²×C₆₇	—	2	2	no	—
249	C₂²×C₆₇	—	2	2	no	—
250	C₂²×C₆₇	—	2	2	no	—
251	C₂²×C₆₇	C₂×#41	1	2	yes	—
252	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
253	C₂×D₆₇	—	2	2	no	—
254	C₂×D₆₇	—	2	2	no	—
255	C₂×D₆₇	—	2	2	no	—
256	C₂×D₆₇	—	2	2	no	—
257	C₂×D₆₇	—	2	2	no	—
258	C₂×D₆₇	—	4	4	no	—
259	C₂×D₆₇	—	8	4	no	—
260	C₂×D₆₇	C₂×#41	1	4	yes	—
261	C₄×C₆₇	—	2	2	no	—
262	C₄×C₆₇	—	2	2	no	—
263	C₄×C₆₇	—	2	2	no	—
264	C₄×C₆₇	—	2	1	no	—
265	C₄×C₆₇	—	2	2	no	—
266	C₄×C₆₇	—	2	2	no	—
267	C₄×C₆₇	—	2	1	no	—
268	Dic₆₇	—	2	1	no	—
269	Dic₆₇	—	2	1	no	—
270	Dic₆₇	—	2	2	no	—
271	Dic₆₇	—	2	2	no	—
272	Dic₆₇	—	2	2	no	—
273	Dic₆₇	—	2	2	no	—
274	Dic₆₇	—	2	1	no	—
275	Dic₆₇	—	2	1	no	—
276	C₂×C₆₇	—	2	2	no	—
277	C₂×C₆₇	—	4	2	no	—
278	C₂×C₆₇	C₂²×#41	1	1	yes	characteristic
279	C₂×C₆₇	#585	1	1	yes	characteristic
280	C₂×C₆₇	#585	1	1	yes	characteristic
281	D₆₇	—	2	4	no	—
282	D₆₇	—	4	2	no	—
283	#3491	—	67	1	no	maximal, Sylow
284	C₆₇	#3491	1	1	yes	characteristic, complemented, Sylow
285	#552	—	67	2	no	—
286	#552	—	67	2	no	—
287	#552	—	67	2	no	—
288	#552	—	67	2	no	—
289	#551	—	67	2	no	—
290	#551	—	67	2	no	—
291	#551	—	67	2	no	—
292	#551	—	67	2	no	—
293	#543	—	67	1	no	—
294	#539	—	67	2	no	—
295	#539	—	67	1	no	—
296	#539	D₆₇	1	1	yes	characteristic, complemented
297	#534	—	67	1	no	—
298	#529	—	67	1	no	—
299	#529	—	67	1	no	—
300	#529	—	67	2	no	—
301	C₂×#123	—	67	2	no	—
302	#518	—	67	2	no	—
303	C₂×#117	—	67	1	no	—
304	C₂²×D₄	—	67	2	no	—
305	C₂³×C₄	—	67	1	no	—
306	#126	—	67	2	no	—
307	#126	—	67	2	no	—
308	#126	—	67	2	no	—
309	#126	—	67	2	no	—
310	#126	—	67	2	no	—
311	#126	—	67	2	no	—
312	#126	—	67	2	no	—
313	#126	C₂×D₆₇	1	2	yes	complemented
314	#125	—	67	2	no	—
315	#125	—	67	1	no	—
316	#125	—	67	1	no	—
317	#125	—	67	2	no	—
318	#125	—	67	2	no	—
319	#125	—	67	2	no	—
320	#125	C₂×D₆₇	1	2	yes	complemented
321	#124	—	67	1	no	—
322	#124	—	67	1	no	—
323	#124	—	67	2	no	—
324	#123	—	67	2	no	—
325	#123	—	67	2	no	—
326	#123	—	67	2	no	—
327	#123	—	67	2	no	—
328	#123	—	67	2	no	—
329	#123	—	67	2	no	—
330	#123	—	67	2	no	—
331	#123	—	67	2	no	—
332	#123	—	67	2	no	—
333	#123	—	67	2	no	—
334	#123	—	67	2	no	—
335	#123	—	67	2	no	—
336	#123	C₂×D₆₇	1	2	yes	complemented
337	#123	C₂×D₆₇	1	2	yes	complemented
338	C₂²⋊Q₈	—	67	2	no	—
339	C₂²⋊Q₈	—	67	1	no	—
340	C₂²⋊Q₈	—	67	2	no	—
341	C₂²⋊Q₈	—	67	2	no	—
342	C₂²⋊Q₈	—	67	2	no	—
343	C₂²⋊Q₈	—	67	2	no	—
344	C₂²⋊Q₈	—	67	2	no	—
345	C₂²⋊Q₈	—	67	2	no	—
346	C₂²⋊Q₈	—	67	2	no	—
347	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
348	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	complemented
349	#121	—	67	2	no	—
350	#121	—	67	1	no	—
351	#121	C₂×D₆₇	1	1	yes	characteristic
352	#120	—	67	2	no	—
353	#120	—	67	2	no	—
354	C₄×Q₈	—	67	1	no	—
355	C₄×Q₈	—	67	1	no	—
356	C₄×Q₈	—	67	2	no	—
357	C₄×D₄	—	67	2	no	—
358	C₄×D₄	—	67	1	no	—
359	C₄×D₄	—	67	2	no	—
360	C₄×D₄	—	67	2	no	—
361	C₄×D₄	—	67	2	no	—
362	C₄×D₄	—	67	2	no	—
363	C₄×D₄	—	67	1	no	—
364	C₄×D₄	—	67	2	no	—
365	C₄×D₄	—	67	2	no	—
366	C₄×D₄	—	67	2	no	—
367	C₄×D₄	C₂×D₆₇	1	2	yes	complemented
368	#117	—	67	2	no	—
369	#117	—	67	2	no	—
370	#117	—	67	2	no	—
371	#117	—	67	2	no	—
372	#117	—	67	2	no	—
373	#117	—	67	2	no	—
374	#117	—	67	2	no	—
375	#117	—	67	2	no	—
376	#117	—	67	2	no	—
377	#117	—	67	2	no	—
378	C₂×C₄⋊C₄	—	67	1	no	—
379	C₂×C₄⋊C₄	—	67	2	no	—
380	C₂×C₄⋊C₄	—	67	2	no	—
381	C₂×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic, complemented
382	C₂×C₂²⋊C₄	—	67	1	no	—
383	C₂×C₂²⋊C₄	—	67	1	no	—
384	C₂×C₂²⋊C₄	—	67	2	no	—
385	C₂×C₂²⋊C₄	—	67	2	no	—
386	C₂×C₂²⋊C₄	—	67	2	no	—
387	C₂×C₂²⋊C₄	—	67	2	no	—
388	C₂×C₂²⋊C₄	—	67	2	no	—
389	C₂×C₄²	—	67	1	no	—
390	C₂×C₄²	—	67	1	no	—
391	C₂⁴	—	67	1	no	—
392	C₂⁴	—	67	2	no	—
393	C₂×Q₈	—	67	2	no	—
394	C₂×Q₈	—	67	1	no	—
395	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
396	C₂×D₄	—	67	2	no	—
397	C₂×D₄	—	67	2	no	—
398	C₂×D₄	—	67	2	no	—
399	C₂×D₄	—	67	1	no	—
400	C₂×D₄	—	67	2	no	—
401	C₂×D₄	—	134	8	no	—
402	C₂×D₄	C₂²×D₆₇	1	2	yes	—
403	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
404	C₂²×C₄	—	67	1	no	—
405	C₂²×C₄	—	67	1	no	—
406	C₂²×C₄	—	67	2	no	—
407	C₂²×C₄	—	67	2	no	—
408	C₂²×C₄	—	67	2	no	—
409	C₂²×C₄	—	67	2	no	—
410	C₂²×C₄	—	67	2	no	—
411	C₂²×C₄	—	67	1	no	—
412	C₂²×C₄	—	67	2	no	—
413	C₂²×C₄	—	67	2	no	—
414	C₂²×C₄	—	67	2	no	—
415	C₂²×C₄	—	134	4	no	—
416	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
417	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
418	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
419	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
420	C₄⋊C₄	—	67	2	no	—
421	C₄⋊C₄	—	67	2	no	—
422	C₄⋊C₄	—	67	2	no	—
423	C₄⋊C₄	—	67	2	no	—
424	C₄⋊C₄	—	67	2	no	—
425	C₄⋊C₄	—	67	2	no	—
426	C₄⋊C₄	—	67	2	no	—
427	C₄⋊C₄	—	67	2	no	—
428	C₄⋊C₄	—	67	2	no	—
429	C₄⋊C₄	—	67	2	no	—
430	C₄⋊C₄	—	67	2	no	—
431	C₄⋊C₄	—	67	2	no	—
432	C₄⋊C₄	—	67	2	no	—
433	C₄⋊C₄	—	67	2	no	—
434	C₄⋊C₄	—	67	2	no	—
435	C₄⋊C₄	—	67	1	no	—
436	C₄⋊C₄	—	67	2	no	—
437	C₄⋊C₄	—	67	1	no	—
438	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
439	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
440	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
441	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
442	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
443	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
444	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
445	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
446	C₂²⋊C₄	—	67	2	no	—
447	C₂²⋊C₄	—	67	2	no	—
448	C₂²⋊C₄	—	67	2	no	—
449	C₂²⋊C₄	—	67	2	no	—
450	C₂²⋊C₄	—	67	2	no	—
451	C₂²⋊C₄	—	67	2	no	—
452	C₂²⋊C₄	—	67	2	no	—
453	C₂²⋊C₄	—	67	2	no	—
454	C₂²⋊C₄	—	67	2	no	—
455	C₂²⋊C₄	—	67	2	no	—
456	C₂²⋊C₄	—	67	2	no	—
457	C₂²⋊C₄	—	67	2	no	—
458	C₂²⋊C₄	—	67	2	no	—
459	C₂²⋊C₄	—	67	2	no	—
460	C₂²⋊C₄	—	67	2	no	—
461	C₂²⋊C₄	—	67	2	no	—
462	C₂²⋊C₄	—	67	2	no	—
463	C₂²⋊C₄	—	67	2	no	—
464	C₂²⋊C₄	—	67	2	no	—
465	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
466	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
467	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
468	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
469	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
470	C₄²	—	67	1	no	—
471	C₄²	—	67	1	no	—
472	C₄²	—	67	2	no	—
473	C₄²	—	67	1	no	—
474	C₄²	—	67	1	no	—
475	C₄²	—	67	2	no	—
476	C₄²	—	67	2	no	—
477	C₄²	—	67	2	no	—
478	C₄²	—	67	2	no	—
479	C₄²	C₂²×D₆₇	1	2	yes	—
480	C₂³	—	268	1	no	—
481	C₂³	—	268	1	no	—
482	C₂³	—	268	2	no	—
483	C₂³	—	268	2	no	—
484	C₂³	—	67	4	no	—
485	C₂³	—	67	2	no	—
486	C₂³	—	67	2	no	—
487	C₂³	—	134	4	no	—
488	C₂³	C₂³×D₆₇	1	2	yes	—
489	C₂³	C₂³×D₆₇	1	1	yes	characteristic
490	Q₈	—	4	1	no	—
491	Q₈	—	268	1	no	—
492	Q₈	—	268	2	no	—
493	D₄	—	2	4	no	—
494	D₄	—	4	1	no	—
495	D₄	—	268	1	no	—
496	D₄	—	268	2	no	—
497	D₄	—	134	4	no	—
498	D₄	—	134	4	no	—
499	D₄	—	134	4	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	268	2	no	—
505	C₂×C₄	—	268	2	no	—
506	C₂×C₄	—	268	2	no	—
507	C₂×C₄	—	268	2	no	—
508	C₂×C₄	—	268	1	no	—
509	C₂×C₄	—	268	2	no	—
510	C₂×C₄	—	268	1	no	—
511	C₂×C₄	—	67	1	no	—
512	C₂×C₄	—	67	1	no	—
513	C₂×C₄	—	67	1	no	—
514	C₂×C₄	—	67	1	no	—
515	C₂×C₄	—	67	2	no	—
516	C₂×C₄	—	67	2	no	—
517	C₂×C₄	—	67	2	no	—
518	C₂×C₄	—	67	2	no	—
519	C₂×C₄	—	134	4	no	—
520	C₂×C₄	—	134	4	no	—
521	C₂×C₄	—	134	4	no	—
522	C₂×C₄	—	134	2	no	—
523	C₂×C₄	C₂³×D₆₇	1	2	yes	—
524	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
525	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
526	C₂×C₄	C₂³×D₆₇	1	2	yes	—
527	C₂×C₄	C₂³×D₆₇	1	2	yes	—
528	C₂×C₄	C₂³×D₆₇	1	2	yes	—
529	C₂×C₄	C₂³×D₆₇	1	2	yes	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	268	4	no	—
536	C₂²	—	536	4	no	—
537	C₂²	—	67	4	no	—
538	C₂²	—	134	2	no	—
539	C₂²	—	134	2	no	—
540	C₂²	—	134	2	no	—
541	C₂²	—	134	2	no	—
542	C₂²	—	134	2	no	—
543	C₂²	#41×D₆₇	1	2	yes	—
544	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
545	C₄	—	2	2	no	—
546	C₄	—	2	2	no	—
547	C₄	—	2	2	no	—
548	C₄	—	2	2	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	2	no	—
552	C₄	—	134	1	no	—
553	C₄	—	134	1	no	—
554	C₄	—	134	2	no	—
555	C₄	—	134	2	no	—
556	C₄	—	134	1	no	—
557	C₄	—	134	1	no	—
558	C₄	—	134	2	no	—
559	C₄	—	134	2	no	—
560	C₂	—	2	2	no	—
561	C₂	—	4	2	no	—
562	C₂	—	268	2	no	—
563	C₂	—	134	4	no	—
564	C₂	C₂×#41×D₆₇	1	1	yes	characteristic
565	C₂	#16864231	1	1	yes	characteristic
566	C₂	#16864233	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#539×C₆₇	C₂
hypercenter	#539	D₆₇
hypocenter	C₆₇	#3491
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #539

Complements

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

N	H ≅ G/N	type
1. #16864084	C₂	semidirect
2. #16864082	C₂	semidirect
3. #16864080	C₂	semidirect
4. #16864078	C₂	semidirect
5. #16864074	C₂	semidirect
6. #16864073	C₂	semidirect
7. #16864071	C₂	semidirect
8. #16864069	C₂	semidirect
9. #16864021	C₂	semidirect
10. #16863993	C₂	semidirect
11. #16863990	C₂	semidirect
13. #16863932	C₂	semidirect
14. #16863927	C₂	semidirect
15. #16863926	C₂	semidirect
16. #123×D₆₇	C₂	semidirect
17. #16863868	C₂	semidirect
18. C₂×#14524001	C₂	semidirect
19. #539×C₆₇	C₂	semidirect
22. #14524038	C₂²	semidirect
23. #14524038	C₂²	semidirect
24. #14524038	C₂²	semidirect
25. #14524038	C₂²	semidirect
26. #14524036	C₂²	semidirect
27. #14524036	C₂²	semidirect
28. #14524036	C₂²	semidirect
29. #14524034	C₂²	semidirect
30. #14524034	C₂²	semidirect
31. #14524034	C₂²	semidirect
32. #14524033	C₂²	semidirect
33. #14524033	C₂²	semidirect
34. #14524033	C₂²	semidirect
35. #14524032	C₂²	semidirect
36. #14524030	C₂²	semidirect
37. #14524029	C₂²	semidirect
41. #14524028	C₂²	semidirect
42. #14524027	C₂²	semidirect
43. #14524027	C₂²	semidirect
44. #14524026	C₂²	semidirect
48. #14524025	C₂²	semidirect
49. #14524024	C₂²	semidirect
50. #14524023	C₂²	semidirect
51. #14524023	C₂²	semidirect
52. #14524022	C₂²	semidirect
53. #14524021	C₂²	semidirect
54. #14524021	C₂²	semidirect
55. #14524021	C₂²	semidirect
56. #14524020	C₂²	semidirect
57. #14524020	C₂²	semidirect
58. #14524019	C₂²	semidirect
63. Q₈×Dic₆₇	C₂²	semidirect
64. C₄×Dic₁₃₄	C₂²	semidirect
65. #14524008	C₂²	semidirect
67. D₄×Dic₆₇	C₂²	semidirect
68. D₄×Dic₆₇	C₂²	semidirect
70. #14524005	C₂²	semidirect
72. C₄×C₂²⋊D₆₇	C₂²	semidirect
73. C₄×C₂²⋊D₆₇	C₂²	semidirect
75. (C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
76. #14524002	C₂²	semidirect
77. #14524001	C₂²	semidirect
78. #14524001	C₂²	semidirect
79. #14524001	C₂²	semidirect
80. #14524001	C₂²	semidirect
81. #14524001	C₂²	semidirect
82. #14524001	C₂²	semidirect
83. #14524000	C₂²	semidirect
84. #14524000	C₂²	semidirect
85. #14523999	C₂²	semidirect
86. C₂×C₄⋊Dic₆₇	C₂²	semidirect
87. C₄⋊C₄×D₆₇	C₂²	semidirect
88. C₄⋊C₄×D₆₇	C₂²	semidirect
91. C₂×(C₂×D₆₇)⋊C₄	C₂²	semidirect
93. C₂²⋊C₄×D₆₇	C₂²	semidirect
94. C₂²⋊C₄×D₆₇	C₂²	semidirect
95. C₂²⋊C₄×D₆₇	C₂²	semidirect
96. C₂×C₄×Dic₆₇	C₂²	semidirect
97. C₂×C₄×Dic₆₇	C₂²	semidirect
98. #126×C₆₇	C₂²	semidirect
99. #125×C₆₇	C₂²	semidirect
100. #123×C₆₇	C₂²	semidirect
101. #123×C₆₇	C₂²	semidirect
102. C₂²⋊Q₈×C₆₇	C₂²	semidirect
103. C₂²⋊Q₈×C₆₇	C₂²	semidirect
105. C₄×D₄×C₆₇	C₂²	semidirect
106. C₂×C₄⋊C₄×C₆₇	C₂²	semidirect
284. C₆₇	#3491	semidirect
296. #539	D₆₇	semidirect
313. #126	C₂×D₆₇	semidirect
320. #125	C₂×D₆₇	semidirect
336. #123	C₂×D₆₇	semidirect
337. #123	C₂×D₆₇	semidirect
347. C₂²⋊Q₈	C₂×D₆₇	semidirect
348. C₂²⋊Q₈	C₂×D₆₇	semidirect
367. C₄×D₄	C₂×D₆₇	semidirect
381. C₂×C₄⋊C₄	C₂×D₆₇	semidirect