Subgroups — #22574088

Order 8576.

992 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864123	C₂	1	2	yes	maximal, complemented
2	#16864122	C₂	1	2	yes	maximal, complemented
3	#16864117	C₂	1	2	yes	maximal, complemented
4	#16864114	C₂	1	2	yes	maximal, complemented
5	#16864087	C₂	1	2	yes	maximal, complemented
6	#16864085	C₂	1	2	yes	maximal, complemented
7	#16864084	C₂	1	2	yes	maximal, complemented
8	#16864080	C₂	1	2	yes	maximal, complemented
9	#16864006	C₂	1	2	yes	maximal, complemented
10	#16864004	C₂	1	2	yes	maximal, complemented
11	#16863969	C₂	1	2	yes	maximal
12	#16863953	C₂	1	1	yes	maximal, characteristic, complemented
13	#16863951	C₂	1	1	yes	maximal, characteristic, complemented
14	#16863951	C₂	1	1	yes	maximal, characteristic, complemented
15	#16863951	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄⋊Q₈×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	#16863872	C₂	1	2	yes	maximal, complemented
18	C₄×#11761628	C₂	1	1	yes	maximal, characteristic
19	#533×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#11761628	C₂²	1	1	yes	characteristic
21	C₂×Q₈×D₆₇	C₂²	1	2	yes	—
22	#14524043	C₂²	1	1	yes	characteristic
23	#14524043	C₂²	1	1	yes	characteristic
24	#14524042	C₂²	1	2	yes	—
25	#14524042	C₂²	1	2	yes	—
26	#14524042	C₂²	1	4	yes	—
27	#14524041	C₂²	1	2	yes	—
28	#14524038	C₂²	1	4	yes	—
29	#14524037	C₂²	1	4	yes	—
30	#14524036	C₂²	1	4	yes	—
31	#14524036	C₂²	1	4	yes	—
32	#14524035	C₂²	1	4	yes	—
33	#14524035	C₂²	1	2	yes	—
34	#14524034	C₂²	1	2	yes	—
35	#14524034	C₂²	1	4	yes	—
36	#14524034	C₂²	1	2	yes	—
37	#14524034	C₂²	1	2	yes	—
38	#14524033	C₂²	1	4	yes	—
39	#14524033	C₂²	1	4	yes	—
40	#14524029	C₂²	1	4	yes	—
41	#14524028	C₂²	1	4	yes	—
42	#14524025	C₂²	1	4	yes	—
43	#14524023	C₂²	1	2	yes	—
44	#14524023	C₂²	1	2	yes	—
45	#14524023	C₂²	1	2	yes	—
46	#14524022	C₂²	1	2	yes	—
47	#14524022	C₂²	1	2	yes	—
48	#14524019	C₂²	1	2	yes	—
49	#14524019	C₂²	1	2	yes	—
50	#14524019	C₂²	1	2	yes	—
51	Q₈×Dic₆₇	C₂²	1	2	yes	—
52	Q₈×Dic₆₇	C₂²	1	2	yes	—
53	Q₈×Dic₆₇	C₂²	1	2	yes	—
54	C₄×Dic₁₃₄	C₂²	1	2	yes	—
55	C₄×Dic₁₃₄	C₂²	1	2	yes	—
56	C₄×Dic₁₃₄	C₂²	1	4	yes	—
57	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic
58	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic
59	#14524008	C₂²	1	2	yes	—
60	#14524008	C₂²	1	2	yes	—
61	#14524008	C₂²	1	2	yes	—
62	#14524008	C₂²	1	4	yes	—
63	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
64	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
65	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
66	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
67	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
68	C₄×C₂²⋊D₆₇	C₂²	1	1	yes	characteristic
69	#14524002	C₂²	1	1	yes	characteristic
70	#14524002	C₂²	1	2	yes	—
71	#14524001	C₂²	1	4	yes	—
72	#14524001	C₂²	1	2	yes	—
73	#14524001	C₂²	1	2	yes	—
74	#14524001	C₂²	1	2	yes	—
75	#14524000	C₂²	1	1	yes	characteristic
76	#14524000	C₂²	1	4	yes	—
77	#14524000	C₂²	1	1	yes	characteristic
78	C₄⋊C₄×D₆₇	C₂²	1	2	yes	—
79	C₄⋊C₄×D₆₇	C₂²	1	2	yes	—
80	C₄²×D₆₇	C₂²	1	1	yes	characteristic
81	C₄²×D₆₇	C₂²	1	1	yes	characteristic
82	C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
83	C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
84	#125×C₆₇	C₂²	1	2	yes	—
85	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
86	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
87	C₄×Q₈×C₆₇	C₂²	1	2	yes	—
88	C₄×Q₈×C₆₇	C₂²	1	2	yes	—
89	#117×C₆₇	C₂²	1	2	yes	—
90	C₂×C₄²×C₆₇	C₂²	1	1	yes	characteristic
91	#11761628	—	2	4	no	—
92	C₂×Dic₁₃₄	C₂³	1	2	yes	—
93	C₂×Dic₁₃₄	C₂³	1	2	yes	—
94	C₂×Dic₁₃₄	C₂³	1	4	yes	—
95	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
96	Q₈×D₆₇	—	2	8	no	—
97	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
98	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
99	C₂×C₂²⋊D₆₇	C₂³	1	1	yes	characteristic
100	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
101	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
103	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
104	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
105	C₂×C₄×D₆₇	C₂³	1	4	yes	—
106	C₂×C₄×D₆₇	C₂³	1	1	yes	characteristic
107	C₄⋊Dic₆₇	C₂³	1	2	yes	—
108	C₄⋊Dic₆₇	C₂³	1	2	yes	—
109	C₄⋊Dic₆₇	C₂³	1	2	yes	—
110	C₄⋊Dic₆₇	C₂³	1	2	yes	—
111	C₄⋊Dic₆₇	C₂³	1	4	yes	—
112	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
113	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
114	C₄⋊Dic₆₇	C₂³	1	4	yes	—
115	C₄⋊Dic₆₇	C₂³	1	4	yes	—
116	Dic₆₇⋊C₄	C₂³	1	4	yes	—
117	Dic₆₇⋊C₄	C₂³	1	4	yes	—
118	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
119	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
120	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
121	Dic₆₇⋊C₄	C₂³	1	1	yes	characteristic
122	Dic₆₇⋊C₄	C₂³	1	4	yes	—
123	Dic₆₇⋊C₄	C₂³	1	4	yes	—
124	Dic₆₇⋊C₄	C₂³	1	4	yes	—
125	Dic₆₇⋊C₄	C₂³	1	4	yes	—
126	Dic₆₇⋊C₄	C₂³	1	4	yes	—
127	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
128	C₂²⋊Dic₆₇	C₂³	1	1	yes	characteristic
129	C₂²⋊Dic₆₇	C₂³	1	4	yes	—
130	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
131	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
132	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
133	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
134	(C₂×D₆₇)⋊C₄	C₂³	1	1	yes	characteristic
135	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
136	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
137	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
138	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
139	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
140	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
141	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
142	C₄×Dic₆₇	C₂³	1	1	yes	characteristic
143	C₄×Dic₆₇	C₂³	1	4	yes	—
144	C₄×Dic₆₇	C₂³	1	4	yes	—
145	C₄×Dic₆₇	C₂³	1	4	yes	—
146	C₄×Dic₆₇	C₂³	1	4	yes	—
147	C₂×Q₈×C₆₇	C₂³	1	2	yes	—
148	C₂×Q₈×C₆₇	C₂³	1	2	yes	—
149	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
150	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
151	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
152	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
155	C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
156	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
159	C₄²×C₆₇	C₂³	1	1	yes	characteristic
160	C₄²×C₆₇	C₂³	1	1	yes	characteristic
161	C₄²×C₆₇	C₂³	1	1	yes	characteristic
162	C₄²×C₆₇	C₂³	1	1	yes	characteristic
163	C₄²×C₆₇	C₂³	1	4	yes	—
164	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
165	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
166	C₂²×D₆₇	C₂⁴	1	1	yes	characteristic
167	Q₈×C₆₇	—	2	4	no	—
168	Q₈×C₆₇	—	2	4	no	—
169	C₂×C₄×C₆₇	—	2	2	no	—
170	C₂×C₄×C₆₇	—	2	2	no	—
171	C₂×C₄×C₆₇	—	2	2	no	—
172	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
174	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₆₇	C₂⁴	1	4	yes	—
176	C₂×C₄×C₆₇	C₂⁴	1	4	yes	—
177	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
179	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
180	C₂²⋊D₆₇	—	2	2	no	—
181	C₂²⋊D₆₇	—	2	2	no	—
182	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
183	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
184	C₂×Dic₆₇	C₂⁴	1	4	yes	—
185	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
186	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
187	C₂×Dic₆₇	C₂⁴	1	4	yes	—
188	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
189	C₂×Dic₆₇	C₂⁴	1	1	yes	characteristic
190	D₂₆₈	—	2	2	no	—
191	C₄×D₆₇	—	2	8	no	—
192	C₄×D₆₇	—	2	2	no	—
193	C₄×D₆₇	—	2	2	no	—
194	C₄×D₆₇	—	2	2	no	—
195	C₄×D₆₇	—	2	2	no	—
196	C₄×D₆₇	—	2	2	no	—
197	C₄×D₆₇	#41	1	4	yes	—
198	Dic₁₃₄	—	2	4	no	—
199	Dic₁₃₄	—	2	4	no	—
200	Dic₁₃₄	—	2	8	no	—
201	Dic₁₃₄	—	2	2	no	—
202	C₂²×C₆₇	—	2	1	no	—
203	C₂²×C₆₇	—	2	1	no	—
204	C₂²×C₆₇	—	2	1	no	—
205	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
206	C₂×D₆₇	—	2	1	no	—
207	C₂×D₆₇	—	2	1	no	—
208	C₂×D₆₇	—	2	1	no	—
209	C₂×D₆₇	—	2	1	no	—
210	C₂×D₆₇	—	2	1	no	—
211	C₂×D₆₇	C₂×#41	1	2	yes	—
212	C₄×C₆₇	—	2	4	no	—
213	C₄×C₆₇	—	2	1	no	—
214	C₄×C₆₇	—	2	1	no	—
215	C₄×C₆₇	—	2	1	no	—
216	C₄×C₆₇	—	2	4	no	—
217	C₄×C₆₇	C₂×#41	1	2	yes	—
218	C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
219	C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
220	Dic₆₇	—	2	4	no	—
221	Dic₆₇	—	2	1	no	—
222	Dic₆₇	—	2	4	no	—
223	Dic₆₇	—	2	1	no	—
224	Dic₆₇	—	2	1	no	—
225	Dic₆₇	—	2	1	no	—
226	Dic₆₇	—	2	1	no	—
227	Dic₆₇	C₂×#41	1	2	yes	—
228	C₂×C₆₇	—	4	1	no	—
229	C₂×C₆₇	C₂²×#41	1	1	yes	characteristic
230	C₂×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
231	C₂×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
232	D₆₇	—	2	2	no	—
233	D₆₇	—	4	1	no	—
234	#3509	—	67	1	no	maximal, Sylow
235	C₆₇	#3509	1	1	yes	characteristic, complemented, Sylow
236	#557	—	67	2	no	—
237	#557	—	67	2	no	—
238	#556	—	67	2	no	—
239	#556	—	67	2	no	—
240	#552	—	67	2	no	—
241	#552	—	67	2	no	—
242	#552	—	67	2	no	—
243	#552	—	67	2	no	—
244	#541	—	67	2	no	—
245	#541	—	67	2	no	—
246	#536	—	67	2	no	—
247	#533	—	67	1	no	—
248	#533	—	67	1	no	—
249	#533	—	67	1	no	—
250	#533	—	67	1	no	—
251	#533	D₆₇	1	1	yes	characteristic, complemented
252	C₂×C₄⋊Q₈	—	67	1	no	—
253	#519	—	67	2	no	—
254	C₄×#41	—	67	1	no	—
255	C₂×#41	—	67	1	no	—
256	C₂²×Q₈	—	67	2	no	—
257	C₄⋊Q₈	—	67	2	no	—
258	C₄⋊Q₈	—	67	2	no	—
259	C₄⋊Q₈	—	67	2	no	—
260	C₄⋊Q₈	—	67	4	no	—
261	C₄⋊Q₈	—	67	1	no	—
262	C₄⋊Q₈	—	67	1	no	—
263	C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
264	C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
265	#126	—	67	4	no	—
266	#126	—	67	4	no	—
267	#126	—	67	4	no	—
268	#126	—	67	4	no	—
269	#125	—	67	2	no	—
270	#125	—	67	2	no	—
271	#125	—	67	2	no	—
272	#125	—	67	4	no	—
273	#125	—	67	4	no	—
274	#125	—	67	4	no	—
275	#125	—	67	2	no	—
276	#125	—	67	4	no	—
277	#125	C₂×D₆₇	1	2	yes	—
278	#124	—	67	4	no	—
279	#123	—	67	4	no	—
280	#123	—	67	4	no	—
281	C₂²⋊Q₈	—	67	2	no	—
282	C₂²⋊Q₈	—	67	2	no	—
283	C₂²⋊Q₈	—	67	2	no	—
284	C₂²⋊Q₈	—	67	2	no	—
285	C₂²⋊Q₈	—	67	2	no	—
286	C₂²⋊Q₈	—	67	2	no	—
287	C₂²⋊Q₈	—	67	2	no	—
288	C₂²⋊Q₈	—	67	2	no	—
289	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	—
290	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	—
291	C₄×Q₈	—	67	2	no	—
292	C₄×Q₈	—	67	2	no	—
293	C₄×Q₈	—	67	2	no	—
294	C₄×Q₈	—	67	2	no	—
295	C₄×Q₈	—	67	4	no	—
296	C₄×Q₈	—	67	2	no	—
297	C₄×Q₈	—	67	2	no	—
298	C₄×Q₈	—	67	1	no	—
299	C₄×Q₈	—	67	1	no	—
300	C₄×Q₈	—	67	2	no	—
301	C₄×Q₈	—	67	4	no	—
302	C₄×Q₈	—	67	2	no	—
303	C₄×Q₈	C₂×D₆₇	1	2	yes	—
304	C₄×Q₈	C₂×D₆₇	1	2	yes	—
305	C₄×D₄	—	67	1	no	—
306	C₄×D₄	—	67	1	no	—
307	C₄×D₄	—	67	1	no	—
308	C₄×D₄	—	67	1	no	—
309	C₄×D₄	—	67	1	no	—
310	C₄×D₄	—	67	1	no	—
311	#117	—	67	1	no	—
312	#117	—	67	2	no	—
313	#117	—	67	2	no	—
314	#117	—	67	4	no	—
315	#117	—	67	2	no	—
316	#117	—	67	2	no	—
317	#117	—	67	1	no	—
318	#117	—	67	1	no	—
319	#117	—	67	4	no	—
320	#117	C₂×D₆₇	1	2	yes	—
321	C₂×C₄⋊C₄	—	67	2	no	—
322	C₂×C₄⋊C₄	—	67	2	no	—
323	C₂×C₄²	—	67	1	no	—
324	C₂×C₄²	—	67	1	no	—
325	C₂×C₄²	C₂×D₆₇	1	1	yes	characteristic
326	#41	—	134	4	no	—
327	C₂×Q₈	—	67	2	no	—
328	C₂×Q₈	—	67	2	no	—
329	C₂×Q₈	—	67	4	no	—
330	C₂×Q₈	—	67	1	no	—
331	C₂×Q₈	—	134	8	no	—
332	C₂×Q₈	C₂²×D₆₇	1	2	yes	—
333	C₂×Q₈	C₂²×D₆₇	1	2	yes	—
334	C₂×D₄	—	67	1	no	—
335	C₂×D₄	—	67	1	no	—
336	C₂×D₄	—	67	1	no	—
337	C₂²×C₄	—	67	1	no	—
338	C₂²×C₄	—	67	1	no	—
339	C₂²×C₄	—	67	1	no	—
340	C₂²×C₄	—	67	1	no	—
341	C₂²×C₄	—	67	1	no	—
342	C₂²×C₄	—	67	1	no	—
343	C₂²×C₄	—	67	4	no	—
344	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
345	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
346	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
347	C₄⋊C₄	—	67	2	no	—
348	C₄⋊C₄	—	67	2	no	—
349	C₄⋊C₄	—	67	4	no	—
350	C₄⋊C₄	—	67	4	no	—
351	C₄⋊C₄	—	67	2	no	—
352	C₄⋊C₄	—	67	1	no	—
353	C₄⋊C₄	—	67	1	no	—
354	C₄⋊C₄	—	67	1	no	—
355	C₄⋊C₄	—	67	1	no	—
356	C₄⋊C₄	—	67	1	no	—
357	C₄⋊C₄	—	67	1	no	—
358	C₄⋊C₄	—	67	2	no	—
359	C₄⋊C₄	—	67	4	no	—
360	C₄⋊C₄	—	67	4	no	—
361	C₄⋊C₄	—	67	4	no	—
362	C₄⋊C₄	—	67	4	no	—
363	C₄⋊C₄	—	67	4	no	—
364	C₄⋊C₄	—	67	4	no	—
365	C₄⋊C₄	—	67	4	no	—
366	C₄⋊C₄	—	67	4	no	—
367	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
368	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
369	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
370	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
371	C₄⋊C₄	C₂²×D₆₇	1	4	yes	—
372	C₄⋊C₄	C₂²×D₆₇	1	4	yes	—
373	C₂²⋊C₄	—	67	1	no	—
374	C₂²⋊C₄	—	67	1	no	—
375	C₂²⋊C₄	—	67	4	no	—
376	C₂²⋊C₄	—	67	1	no	—
377	C₂²⋊C₄	—	67	1	no	—
378	C₂²⋊C₄	—	67	4	no	—
379	C₂²⋊C₄	—	67	1	no	—
380	C₂²⋊C₄	—	67	1	no	—
381	C₂²⋊C₄	—	67	4	no	—
382	C₂²⋊C₄	—	67	4	no	—
383	C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
384	C₄²	—	67	1	no	—
385	C₄²	—	67	1	no	—
386	C₄²	—	67	1	no	—
387	C₄²	—	67	1	no	—
388	C₄²	—	67	1	no	—
389	C₄²	—	67	1	no	—
390	C₄²	—	67	4	no	—
391	C₄²	—	67	4	no	—
392	C₄²	—	67	4	no	—
393	C₄²	—	67	4	no	—
394	C₄²	C₂²×D₆₇	1	1	yes	characteristic
395	C₄²	C₂²×D₆₇	1	1	yes	characteristic
396	C₄²	C₂²×D₆₇	1	1	yes	characteristic
397	C₄²	C₂²×D₆₇	1	1	yes	characteristic
398	C₄²	C₂²×D₆₇	1	4	yes	—
399	C₂³	—	67	1	no	—
400	C₂³	—	67	1	no	—
401	C₂³	C₂³×D₆₇	1	1	yes	characteristic
402	Q₈	—	2	4	no	—
403	Q₈	—	2	4	no	—
404	Q₈	—	134	8	no	—
405	Q₈	—	134	2	no	—
406	Q₈	—	134	4	no	—
407	Q₈	—	134	4	no	—
408	D₄	—	134	2	no	—
409	D₄	—	134	2	no	—
410	D₄	—	134	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	67	1	no	—
415	C₂×C₄	—	67	4	no	—
416	C₂×C₄	—	67	1	no	—
417	C₂×C₄	—	67	1	no	—
418	C₂×C₄	—	67	4	no	—
419	C₂×C₄	—	67	1	no	—
420	C₂×C₄	—	67	1	no	—
421	C₂×C₄	—	67	4	no	—
422	C₂×C₄	—	67	1	no	—
423	C₂×C₄	—	134	8	no	—
424	C₂×C₄	—	134	2	no	—
425	C₂×C₄	—	134	2	no	—
426	C₂×C₄	—	134	2	no	—
427	C₂×C₄	—	134	2	no	—
428	C₂×C₄	—	134	2	no	—
429	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
430	C₂×C₄	C₂³×D₆₇	1	4	yes	—
431	C₂×C₄	C₂³×D₆₇	1	4	yes	—
432	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
433	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
434	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
435	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
436	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	67	2	no	—
441	C₂²	—	134	1	no	—
442	C₂²	—	134	1	no	—
443	C₂²	—	134	1	no	—
444	C₂²	—	134	1	no	—
445	C₂²	—	134	1	no	—
446	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
447	C₄	—	2	1	no	—
448	C₄	—	2	4	no	—
449	C₄	—	2	1	no	—
450	C₄	—	2	4	no	—
451	C₄	—	2	1	no	—
452	C₄	—	67	2	no	—
453	C₄	—	134	1	no	—
454	C₄	—	134	4	no	—
455	C₄	—	134	1	no	—
456	C₄	—	134	1	no	—
457	C₄	—	134	1	no	—
458	C₄	—	134	1	no	—
459	C₄	—	134	4	no	—
460	C₄	#41×D₆₇	1	2	yes	—
461	C₄	#14524090	1	2	yes	—
462	C₄	#14524091	1	2	yes	—
463	C₂	—	4	1	no	—
464	C₂	—	268	1	no	—
465	C₂	—	134	2	no	—
466	C₂	C₂×#41×D₆₇	1	1	yes	characteristic
467	C₂	C₂×#14524090	1	1	yes	characteristic
468	C₂	C₂×#14524091	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	#3509
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. #16864123	C₂	semidirect
2. #16864122	C₂	semidirect
3. #16864117	C₂	semidirect
4. #16864114	C₂	semidirect
5. #16864087	C₂	semidirect
6. #16864085	C₂	semidirect
7. #16864084	C₂	semidirect
8. #16864080	C₂	semidirect
9. #16864006	C₂	semidirect
10. #16864004	C₂	semidirect
12. #16863953	C₂	semidirect
13. #16863951	C₂	semidirect
14. #16863951	C₂	semidirect
15. #16863951	C₂	semidirect
16. C₄⋊Q₈×D₆₇	C₂	semidirect
17. #16863872	C₂	semidirect
19. #533×C₆₇	C₂	semidirect
235. C₆₇	#3509	semidirect
251. #533	D₆₇	semidirect