Subgroups — #22574837

Order 8576.

936 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864145	C₂	1	2	yes	maximal, complemented
2	#16864145	C₂	1	2	yes	maximal, complemented
3	#16864118	C₂	1	2	yes	maximal, complemented
4	#16864100	C₂	1	2	yes	maximal, complemented
5	#16864087	C₂	1	2	yes	maximal, complemented
6	#16864079	C₂	1	2	yes	maximal, complemented
7	#16864073	C₂	1	2	yes	maximal, complemented
8	#16864070	C₂	1	2	yes	maximal, complemented
9	#16864025	C₂	1	1	yes	maximal, characteristic, complemented
10	#16864021	C₂	1	1	yes	maximal, characteristic, complemented
11	#16864018	C₂	1	2	yes	maximal, complemented
12	#16864005	C₂	1	2	yes	maximal, complemented
13	#16864004	C₂	1	2	yes	maximal, complemented
14	#16863995	C₂	1	1	yes	maximal, characteristic, complemented
15	#16863994	C₂	1	2	yes	maximal, complemented
16	#16863986	C₂	1	1	yes	maximal, characteristic
17	#16863930	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14524037	C₂	1	1	yes	maximal, characteristic, complemented
19	#533×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	#14524042	C₂²	1	2	yes	complemented
21	#14524041	C₂²	1	2	yes	complemented
22	#14524041	C₂²	1	2	yes	complemented
23	#14524038	C₂²	1	2	yes	—
24	#14524038	C₂²	1	2	yes	—
25	#14524038	C₂²	1	2	yes	—
26	#14524038	C₂²	1	2	yes	—
27	#14524038	C₂²	1	2	yes	complemented
28	#14524038	C₂²	1	2	yes	complemented
29	#14524037	C₂²	1	2	yes	—
30	#14524037	C₂²	1	2	yes	—
31	#14524037	C₂²	1	2	yes	—
32	#14524037	C₂²	1	2	yes	—
33	#14524037	C₂²	1	2	yes	—
34	#14524037	C₂²	1	2	yes	complemented
35	#14524037	C₂²	1	2	yes	complemented
36	#14524035	C₂²	1	1	yes	characteristic, complemented
37	#14524035	C₂²	1	2	yes	complemented
38	#14524034	C₂²	1	2	yes	complemented
39	#14524033	C₂²	1	2	yes	complemented
40	#14524033	C₂²	1	2	yes	complemented
41	#14524033	C₂²	1	2	yes	complemented
42	#14524033	C₂²	1	2	yes	complemented
43	#14524033	C₂²	1	2	yes	complemented
44	#14524033	C₂²	1	2	yes	complemented
45	#14524032	C₂²	1	2	yes	—
46	#14524032	C₂²	1	2	yes	—
47	#14524031	C₂²	1	2	yes	—
48	#14524031	C₂²	1	1	yes	characteristic, complemented
49	#14524028	C₂²	1	2	yes	—
50	#14524028	C₂²	1	2	yes	—
51	#14524028	C₂²	1	2	yes	—
52	#14524028	C₂²	1	2	yes	—
53	#14524028	C₂²	1	2	yes	—
54	#14524028	C₂²	1	2	yes	complemented
55	#14524027	C₂²	1	2	yes	—
56	#14524026	C₂²	1	2	yes	—
57	#14524023	C₂²	1	2	yes	—
58	#14524022	C₂²	1	1	yes	characteristic
59	#14524021	C₂²	1	2	yes	—
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	#14524021	C₂²	1	2	yes	complemented
65	#14524020	C₂²	1	2	yes	—
66	#14524020	C₂²	1	2	yes	—
67	#14524019	C₂²	1	2	yes	—
68	#14524019	C₂²	1	2	yes	—
69	#14524019	C₂²	1	2	yes	complemented
70	#14524019	C₂²	1	2	yes	complemented
71	#14524018	C₂²	1	2	yes	—
72	#14524017	C₂²	1	1	yes	characteristic
73	#14524013	C₂²	1	2	yes	—
74	C₄×Dic₁₃₄	C₂²	1	2	yes	complemented
75	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic, complemented
76	#14524008	C₂²	1	2	yes	complemented
77	C₄×D₂₆₈	C₂²	1	2	yes	—
78	C₄×D₂₆₈	C₂²	1	1	yes	characteristic, complemented
79	#14524005	C₂²	1	2	yes	—
80	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
81	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
82	(C₂²⋊D₆₇)⋊C₄	C₂²	1	2	yes	—
83	#14524001	C₂²	1	2	yes	—
84	#14524000	C₂²	1	2	yes	—
85	#14524000	C₂²	1	2	yes	complemented
86	#14524000	C₂²	1	2	yes	complemented
87	#14523999	C₂²	1	2	yes	—
88	C₂×Dic₆₇⋊C₄	C₂²	1	1	yes	characteristic
89	C₂×Dic₆₇⋊C₄	C₂²	1	1	yes	characteristic
90	C₂×Dic₆₇⋊C₄	C₂²	1	1	yes	characteristic
91	C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
92	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
93	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
94	C₂×(C₂×D₆₇)⋊C₄	C₂²	1	1	yes	characteristic
95	C₂²⋊C₄×D₆₇	C₂²	1	2	yes	—
96	C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
97	C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	#125×C₆₇	C₂²	1	2	yes	complemented
99	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
100	C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
101	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
102	C₄×Q₈×C₆₇	C₂²	1	2	yes	complemented
103	C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
104	C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
105	#117×C₆₇	C₂²	1	2	yes	—
106	C₂×C₄²×C₆₇	C₂²	1	1	yes	characteristic
107	C₂³×D₆₇	C₂³	1	1	yes	characteristic
108	C₂×Dic₁₃₄	C₂³	1	2	yes	—
109	C₂×Dic₁₃₄	C₂³	1	2	yes	—
110	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
111	C₂×D₂₆₈	C₂³	1	2	yes	—
112	C₂×D₂₆₈	C₂³	1	2	yes	—
113	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
115	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
116	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
117	C₂²×Dic₆₇	C₂³	1	1	yes	characteristic
118	C₂×C₄×D₆₇	C₂³	1	2	yes	—
119	C₂×C₄×D₆₇	C₂³	1	2	yes	—
120	C₂×C₄×D₆₇	C₂³	1	2	yes	—
121	C₂×C₄×D₆₇	C₂³	1	2	yes	—
122	C₂×C₄×D₆₇	C₂³	1	2	yes	—
123	C₄⋊Dic₆₇	C₂³	1	2	yes	—
124	C₄⋊Dic₆₇	C₂³	1	2	yes	—
125	C₄⋊Dic₆₇	C₂³	1	2	yes	—
126	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
127	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
128	C₄⋊Dic₆₇	C₂³	1	2	yes	—
129	Dic₆₇⋊C₄	C₂³	1	2	yes	—
130	Dic₆₇⋊C₄	C₂³	1	2	yes	—
131	Dic₆₇⋊C₄	C₂³	1	2	yes	—
132	Dic₆₇⋊C₄	C₂³	1	2	yes	—
133	Dic₆₇⋊C₄	C₂³	1	2	yes	—
134	Dic₆₇⋊C₄	C₂³	1	2	yes	—
135	Dic₆₇⋊C₄	C₂³	1	2	yes	—
136	Dic₆₇⋊C₄	C₂³	1	2	yes	—
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	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
149	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
150	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
151	(C₂×D₆₇)⋊C₄	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	2	yes	—
167	C₄×Dic₆₇	C₂³	1	2	yes	—
168	C₄×Dic₆₇	C₂³	1	2	yes	—
169	C₄×Dic₆₇	C₂³	1	2	yes	—
170	C₄×Dic₆₇	C₂³	1	2	yes	—
171	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×Q₈×C₆₇	C₂³	1	2	yes	—
173	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
174	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
177	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
182	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
184	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
186	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₄²×C₆₇	C₂³	1	1	yes	characteristic
189	C₄²×C₆₇	C₂³	1	1	yes	characteristic
190	C₄²×C₆₇	C₂³	1	1	yes	characteristic
191	C₄²×C₆₇	C₂³	1	1	yes	characteristic
192	C₄²×C₆₇	C₂³	1	2	yes	—
193	C₄²×C₆₇	C₂³	1	2	yes	—
194	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
195	C₂²×D₆₇	—	2	2	no	—
196	C₂²×D₆₇	—	4	1	no	—
197	C₂²×D₆₇	—	4	1	no	—
198	C₂²×D₆₇	C₂⁴	1	2	yes	—
199	C₂²×D₆₇	C₂⁴	1	2	yes	—
200	Q₈×C₆₇	—	4	2	no	—
201	Q₈×C₆₇	—	4	1	no	—
202	Q₈×C₆₇	—	4	1	no	—
203	C₂×C₄×C₆₇	—	2	2	no	—
204	C₂×C₄×C₆₇	—	4	1	no	—
205	C₂×C₄×C₆₇	—	4	1	no	—
206	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
207	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
208	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
209	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
210	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
211	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
212	C₂×C₄×C₆₇	C₂⁴	1	2	yes	—
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	C₂²⋊D₆₇	—	2	4	no	—
217	C₂×Dic₆₇	—	2	2	no	—
218	C₂×Dic₆₇	—	4	1	no	—
219	C₂×Dic₆₇	—	4	1	no	—
220	C₂×Dic₆₇	C₂⁴	1	2	yes	—
221	C₂×Dic₆₇	C₂⁴	1	2	yes	—
222	C₂×Dic₆₇	C₂⁴	1	2	yes	—
223	C₂×Dic₆₇	C₂⁴	1	2	yes	—
224	C₂×Dic₆₇	C₂⁴	1	2	yes	—
225	C₂×Dic₆₇	C₂⁴	1	2	yes	—
226	D₂₆₈	—	4	1	no	—
227	D₂₆₈	—	4	2	no	—
228	D₂₆₈	—	4	2	no	—
229	C₄×D₆₇	—	4	2	no	—
230	C₄×D₆₇	—	4	2	no	—
231	C₄×D₆₇	—	4	2	no	—
232	C₄×D₆₇	—	4	2	no	—
233	C₄×D₆₇	—	4	2	no	—
234	Dic₁₃₄	—	4	1	no	—
235	Dic₁₃₄	—	4	2	no	—
236	Dic₁₃₄	—	4	2	no	—
237	C₂²×C₆₇	—	2	1	no	—
238	C₂²×C₆₇	—	2	1	no	—
239	C₂²×C₆₇	2₋¹⁺⁴	1	2	yes	—
240	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
241	C₂×D₆₇	—	2	2	no	—
242	C₂×D₆₇	—	2	2	no	—
243	C₂×D₆₇	—	2	2	no	—
244	C₂×D₆₇	—	2	2	no	—
245	C₂×D₆₇	—	2	2	no	—
246	C₂×D₆₇	—	2	2	no	—
247	C₂×D₆₇	—	8	2	no	—
248	C₄×C₆₇	—	2	1	no	—
249	C₄×C₆₇	—	2	1	no	—
250	C₄×C₆₇	—	2	2	no	—
251	C₄×C₆₇	—	2	1	no	—
252	C₄×C₆₇	—	2	2	no	—
253	C₄×C₆₇	—	2	1	no	—
254	C₄×C₆₇	—	2	2	no	—
255	C₄×C₆₇	—	2	2	no	—
256	C₄×C₆₇	—	2	1	no	—
257	C₄×C₆₇	—	2	1	no	—
258	Dic₆₇	—	2	2	no	—
259	Dic₆₇	—	2	2	no	—
260	Dic₆₇	—	2	2	no	—
261	Dic₆₇	—	2	2	no	—
262	Dic₆₇	—	2	2	no	—
263	Dic₆₇	—	2	2	no	—
264	C₂×C₆₇	—	2	2	no	—
265	C₂×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
266	C₂×C₆₇	#585	1	1	yes	characteristic
267	C₂×C₆₇	#585	1	1	yes	characteristic
268	D₆₇	—	4	2	no	—
269	D₆₇	—	4	2	no	—
270	#3564	—	67	1	no	maximal, Sylow
271	C₆₇	#3564	1	1	yes	characteristic, complemented, Sylow
272	#563	—	67	2	no	—
273	#563	—	67	2	no	—
274	#556	—	67	2	no	—
275	#554	—	67	2	no	—
276	#552	—	67	2	no	—
277	#552	—	67	2	no	—
278	#551	—	67	2	no	—
279	#551	—	67	2	no	—
280	#544	—	67	1	no	—
281	#543	—	67	1	no	—
282	#542	—	67	2	no	—
283	#541	—	67	2	no	—
284	#541	—	67	2	no	—
285	#539	—	67	2	no	—
286	#539	—	67	1	no	—
287	#538	—	67	1	no	—
288	#533	D₆₇	1	1	yes	characteristic, complemented
289	#529	—	67	1	no	—
290	C₂×#126	—	67	1	no	—
291	C₄⋊Q₈	—	67	2	no	—
292	C₄⋊Q₈	—	67	2	no	—
293	C₄⋊Q₈	—	67	2	no	—
294	C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
295	C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
296	#126	—	67	2	no	—
297	#126	—	67	2	no	—
298	#126	—	67	2	no	—
299	#126	—	67	2	no	—
300	#126	—	67	2	no	—
301	#126	—	67	2	no	—
302	#126	—	67	2	no	—
303	#126	—	67	2	no	—
304	#126	—	67	2	no	—
305	#126	—	67	2	no	—
306	#126	—	67	2	no	—
307	#126	—	67	2	no	—
308	#126	—	67	2	no	—
309	#125	—	67	2	no	—
310	#125	—	67	2	no	—
311	#125	—	67	2	no	—
312	#125	—	67	2	no	—
313	#125	—	67	2	no	—
314	#125	—	67	2	no	—
315	#125	—	67	2	no	—
316	#125	—	67	1	no	—
317	#125	—	67	2	no	—
318	#125	C₂×D₆₇	1	2	yes	complemented
319	#124	—	67	2	no	—
320	#124	—	67	2	no	—
321	#124	—	67	1	no	—
322	#124	—	67	2	no	—
323	#123	—	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	C₂²⋊Q₈	—	67	2	no	—
332	C₂²⋊Q₈	—	67	2	no	—
333	C₂²⋊Q₈	—	67	2	no	—
334	C₂²⋊Q₈	—	67	2	no	—
335	C₂²⋊Q₈	—	67	1	no	—
336	C₂²⋊Q₈	—	67	2	no	—
337	C₂²⋊Q₈	—	67	2	no	—
338	C₂²⋊Q₈	—	67	2	no	—
339	C₂²⋊Q₈	—	67	2	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	C₂×D₆₇	1	1	yes	characteristic
346	C₂²⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
347	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	—
348	#121	—	67	1	no	—
349	#121	—	67	2	no	—
350	#120	—	67	2	no	—
351	C₄×Q₈	—	67	2	no	—
352	C₄×Q₈	—	67	1	no	—
353	C₄×Q₈	—	67	2	no	—
354	C₄×Q₈	C₂×D₆₇	1	2	yes	complemented
355	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
356	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic, complemented
357	C₄×D₄	—	67	2	no	—
358	C₄×D₄	—	67	2	no	—
359	C₄×D₄	—	67	2	no	—
360	C₄×D₄	—	67	2	no	—
361	C₄×D₄	—	67	1	no	—
362	C₄×D₄	—	67	2	no	—
363	#117	—	67	2	no	—
364	#117	—	67	2	no	—
365	#117	—	67	2	no	—
366	#117	—	67	2	no	—
367	#117	—	67	2	no	—
368	#117	C₂×D₆₇	1	2	yes	—
369	C₂×C₄⋊C₄	—	67	1	no	—
370	C₂×C₄⋊C₄	—	67	1	no	—
371	C₂×C₄⋊C₄	—	67	1	no	—
372	C₂×C₄⋊C₄	—	67	2	no	—
373	C₂×C₂²⋊C₄	—	67	1	no	—
374	C₂×C₂²⋊C₄	—	67	1	no	—
375	C₂×C₂²⋊C₄	—	67	1	no	—
376	C₂×C₂²⋊C₄	—	67	2	no	—
377	C₂×C₄²	C₂×D₆₇	1	1	yes	characteristic
378	C₂⁴	—	67	1	no	—
379	C₂×Q₈	—	67	2	no	—
380	C₂×Q₈	—	67	1	no	—
381	C₂×Q₈	—	67	2	no	—
382	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
383	C₂×Q₈	C₂²×D₆₇	1	2	yes	—
384	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
385	C₂×D₄	—	67	2	no	—
386	C₂×D₄	—	67	2	no	—
387	C₂×D₄	—	67	2	no	—
388	C₂×D₄	—	67	1	no	—
389	C₂²×C₄	—	67	1	no	—
390	C₂²×C₄	—	67	1	no	—
391	C₂²×C₄	—	67	2	no	—
392	C₂²×C₄	—	67	2	no	—
393	C₂²×C₄	—	67	2	no	—
394	C₂²×C₄	—	67	2	no	—
395	C₂²×C₄	—	67	2	no	—
396	C₂²×C₄	—	67	1	no	—
397	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
398	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
399	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
400	C₄⋊C₄	—	67	2	no	—
401	C₄⋊C₄	—	67	2	no	—
402	C₄⋊C₄	—	67	2	no	—
403	C₄⋊C₄	—	67	2	no	—
404	C₄⋊C₄	—	67	2	no	—
405	C₄⋊C₄	—	67	2	no	—
406	C₄⋊C₄	—	67	2	no	—
407	C₄⋊C₄	—	67	2	no	—
408	C₄⋊C₄	—	67	2	no	—
409	C₄⋊C₄	—	67	2	no	—
410	C₄⋊C₄	—	67	2	no	—
411	C₄⋊C₄	—	67	2	no	—
412	C₄⋊C₄	—	67	2	no	—
413	C₄⋊C₄	—	67	2	no	—
414	C₄⋊C₄	—	67	2	no	—
415	C₄⋊C₄	—	67	1	no	—
416	C₄⋊C₄	—	67	2	no	—
417	C₄⋊C₄	—	67	2	no	—
418	C₄⋊C₄	—	67	2	no	—
419	C₄⋊C₄	—	67	2	no	—
420	C₄⋊C₄	—	67	1	no	—
421	C₄⋊C₄	—	67	2	no	—
422	C₄⋊C₄	—	67	2	no	—
423	C₄⋊C₄	—	67	2	no	—
424	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
425	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
426	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
427	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
428	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
429	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
430	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
431	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
432	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
433	C₂²⋊C₄	—	67	2	no	—
434	C₂²⋊C₄	—	67	2	no	—
435	C₂²⋊C₄	—	67	2	no	—
436	C₂²⋊C₄	—	67	2	no	—
437	C₂²⋊C₄	—	67	2	no	—
438	C₂²⋊C₄	—	67	2	no	—
439	C₂²⋊C₄	—	67	2	no	—
440	C₂²⋊C₄	—	67	2	no	—
441	C₂²⋊C₄	—	67	2	no	—
442	C₂²⋊C₄	—	67	2	no	—
443	C₂²⋊C₄	—	67	2	no	—
444	C₂²⋊C₄	—	67	2	no	—
445	C₂²⋊C₄	—	67	2	no	—
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	C₂²×D₆₇	1	2	yes	—
453	C₂²⋊C₄	C₂²×D₆₇	1	2	yes	—
454	C₄²	—	67	2	no	—
455	C₄²	—	67	2	no	—
456	C₄²	—	67	2	no	—
457	C₄²	—	67	2	no	—
458	C₄²	—	67	2	no	—
459	C₄²	C₂²×D₆₇	1	1	yes	characteristic
460	C₄²	C₂²×D₆₇	1	1	yes	characteristic
461	C₄²	C₂²×D₆₇	1	1	yes	characteristic
462	C₄²	C₂²×D₆₇	1	1	yes	characteristic
463	C₄²	C₂²×D₆₇	1	2	yes	—
464	C₄²	C₂²×D₆₇	1	2	yes	—
465	C₂³	—	268	1	no	—
466	C₂³	—	268	1	no	—
467	C₂³	—	67	2	no	—
468	C₂³	—	67	2	no	—
469	C₂³	—	134	2	no	—
470	C₂³	C₂³×D₆₇	1	1	yes	characteristic
471	Q₈	—	4	1	no	—
472	Q₈	—	4	2	no	—
473	Q₈	—	4	1	no	—
474	Q₈	—	268	1	no	—
475	Q₈	—	268	2	no	—
476	Q₈	—	268	2	no	—
477	D₄	—	268	1	no	—
478	D₄	—	268	2	no	—
479	D₄	—	268	2	no	—
480	D₄	—	134	4	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	268	2	no	—
485	C₂×C₄	—	268	2	no	—
486	C₂×C₄	—	268	2	no	—
487	C₂×C₄	—	268	2	no	—
488	C₂×C₄	—	268	2	no	—
489	C₂×C₄	—	268	1	no	—
490	C₂×C₄	—	268	1	no	—
491	C₂×C₄	—	67	2	no	—
492	C₂×C₄	—	67	2	no	—
493	C₂×C₄	—	67	2	no	—
494	C₂×C₄	—	67	2	no	—
495	C₂×C₄	—	67	2	no	—
496	C₂×C₄	—	67	2	no	—
497	C₂×C₄	—	134	2	no	—
498	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
499	C₂×C₄	C₂³×D₆₇	1	2	yes	—
500	C₂×C₄	C₂³×D₆₇	1	2	yes	—
501	C₂×C₄	C₂³×D₆₇	1	2	yes	—
502	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
503	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
504	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
505	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
506	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
507	C₂×C₄	C₂³×D₆₇	1	2	yes	—
508	C₂²	—	2	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	536	2	no	—
511	C₂²	—	134	2	no	—
512	C₂²	—	134	2	no	—
513	C₂²	—	134	2	no	—
514	C₂²	—	134	2	no	—
515	C₂²	—	134	2	no	—
516	C₂²	—	134	2	no	—
517	C₂²	#14524091	1	2	yes	—
518	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	1	no	—
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	2	1	no	—
525	C₄	—	2	2	no	—
526	C₄	—	2	2	no	—
527	C₄	—	2	2	no	—
528	C₄	—	2	2	no	—
529	C₄	—	134	2	no	—
530	C₄	—	134	2	no	—
531	C₄	—	134	2	no	—
532	C₄	—	134	2	no	—
533	C₄	—	134	2	no	—
534	C₄	—	134	2	no	—
535	C₂	—	2	2	no	—
536	C₂	—	268	2	no	—
537	C₂	—	268	2	no	—
538	C₂	C₂×#14524091	1	1	yes	characteristic
539	C₂	#16864232	1	1	yes	characteristic
540	C₂	#16864232	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	#533×C₆₇	C₂
hypercenter	#533	D₆₇
hypocenter	C₆₇	#3564
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ #533

Complements

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

N	H ≅ G/N	type
1. #16864145	C₂	semidirect
2. #16864145	C₂	semidirect
3. #16864118	C₂	semidirect
4. #16864100	C₂	semidirect
5. #16864087	C₂	semidirect
6. #16864079	C₂	semidirect
7. #16864073	C₂	semidirect
8. #16864070	C₂	semidirect
9. #16864025	C₂	semidirect
10. #16864021	C₂	semidirect
11. #16864018	C₂	semidirect
12. #16864005	C₂	semidirect
13. #16864004	C₂	semidirect
14. #16863995	C₂	semidirect
15. #16863994	C₂	semidirect
17. #16863930	C₂	semidirect
18. C₂×#14524037	C₂	semidirect
19. #533×C₆₇	C₂	semidirect
20. #14524042	C₂²	semidirect
21. #14524041	C₂²	semidirect
22. #14524041	C₂²	semidirect
27. #14524038	C₂²	semidirect
28. #14524038	C₂²	semidirect
34. #14524037	C₂²	semidirect
35. #14524037	C₂²	semidirect
36. #14524035	C₂²	semidirect
37. #14524035	C₂²	semidirect
38. #14524034	C₂²	semidirect
39. #14524033	C₂²	semidirect
40. #14524033	C₂²	semidirect
41. #14524033	C₂²	semidirect
42. #14524033	C₂²	semidirect
43. #14524033	C₂²	semidirect
44. #14524033	C₂²	semidirect
48. #14524031	C₂²	semidirect
54. #14524028	C₂²	semidirect
62. #14524021	C₂²	semidirect
63. #14524021	C₂²	semidirect
64. #14524021	C₂²	semidirect
69. #14524019	C₂²	semidirect
70. #14524019	C₂²	semidirect
74. C₄×Dic₁₃₄	C₂²	semidirect
75. C₄×Dic₁₃₄	C₂²	semidirect
76. #14524008	C₂²	semidirect
78. C₄×D₂₆₈	C₂²	semidirect
85. #14524000	C₂²	semidirect
86. #14524000	C₂²	semidirect
91. C₄⋊C₄×D₆₇	C₂²	semidirect
96. C₄⋊Q₈×C₆₇	C₂²	semidirect
97. C₄⋊Q₈×C₆₇	C₂²	semidirect
98. #125×C₆₇	C₂²	semidirect
102. C₄×Q₈×C₆₇	C₂²	semidirect
103. C₄×Q₈×C₆₇	C₂²	semidirect
104. C₄×Q₈×C₆₇	C₂²	semidirect
271. C₆₇	#3564	semidirect
288. #533	D₆₇	semidirect
294. C₄⋊Q₈	C₂×D₆₇	semidirect
295. C₄⋊Q₈	C₂×D₆₇	semidirect
318. #125	C₂×D₆₇	semidirect
354. C₄×Q₈	C₂×D₆₇	semidirect
355. C₄×Q₈	C₂×D₆₇	semidirect
356. C₄×Q₈	C₂×D₆₇	semidirect