Subgroups — #22573955

Order 8576.

1022 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864117	C₂	1	2	yes	maximal, complemented
2	#16864104	C₂	1	2	yes	maximal, complemented
3	#16864088	C₂	1	2	yes	maximal, complemented
4	#16864081	C₂	1	4	yes	maximal, complemented
5	#16864080	C₂	1	2	yes	maximal, complemented
6	#16864072	C₂	1	4	yes	maximal, complemented
7	#16864027	C₂	1	1	yes	maximal, characteristic, complemented
8	#16864019	C₂	1	2	yes	maximal, complemented
9	#16864006	C₂	1	2	yes	maximal, complemented
10	#16863970	C₂	1	1	yes	maximal, characteristic, complemented
11	#16863948	C₂	1	2	yes	maximal, complemented
12	#16863932	C₂	1	2	yes	maximal, complemented
13	#16863907	C₂	1	1	yes	maximal, characteristic
14	#16863877	C₂	1	1	yes	maximal, characteristic, complemented
15	#16863874	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14524002	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#11761628	C₂²	1	1	yes	characteristic
19	#14524042	C₂²	1	2	yes	complemented
20	#14524042	C₂²	1	2	yes	complemented
21	#14524041	C₂²	1	2	yes	complemented
22	#14524038	C₂²	1	4	yes	complemented
23	#14524038	C₂²	1	4	yes	complemented
24	#14524036	C₂²	1	4	yes	—
25	#14524036	C₂²	1	4	yes	—
26	#14524034	C₂²	1	2	yes	complemented
27	#14524034	C₂²	1	4	yes	complemented
28	#14524034	C₂²	1	2	yes	complemented
29	#14524033	C₂²	1	4	yes	complemented
30	#14524033	C₂²	1	4	yes	complemented
31	#14524032	C₂²	1	2	yes	complemented
32	#14524029	C₂²	1	4	yes	—
33	#14524027	C₂²	1	4	yes	—
34	#14524026	C₂²	1	4	yes	—
35	#14524026	C₂²	1	2	yes	—
36	#14524025	C₂²	1	4	yes	—
37	#14524023	C₂²	1	4	yes	complemented
38	#14524022	C₂²	1	1	yes	characteristic
39	#14524022	C₂²	1	4	yes	—
40	#14524022	C₂²	1	1	yes	characteristic
41	#14524020	C₂²	1	4	yes	—
42	#14524019	C₂²	1	2	yes	complemented
43	#14524019	C₂²	1	2	yes	complemented
44	#14524017	C₂²	1	1	yes	characteristic
45	#14524017	C₂²	1	1	yes	characteristic
46	#14524012	C₂²	1	2	yes	—
47	Q₈×Dic₆₇	C₂²	1	2	yes	complemented
48	Q₈×Dic₆₇	C₂²	1	2	yes	complemented
49	Q₈×Dic₆₇	C₂²	1	2	yes	complemented
50	Q₈×Dic₆₇	C₂²	1	2	yes	complemented
51	#14524008	C₂²	1	2	yes	complemented
52	#14524008	C₂²	1	4	yes	complemented
53	#14524005	C₂²	1	2	yes	complemented
54	C₄×C₂²⋊D₆₇	C₂²	1	4	yes	—
55	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
56	C₄×C₂²⋊D₆₇	C₂²	1	2	yes	—
57	(C₂²⋊D₆₇)⋊C₄	C₂²	1	4	yes	—
58	#14524002	C₂²	1	2	yes	—
59	#14524002	C₂²	1	1	yes	characteristic
60	#14524002	C₂²	1	1	yes	characteristic
61	#14524002	C₂²	1	4	yes	—
62	#14524002	C₂²	1	1	yes	characteristic
63	#14524002	C₂²	1	2	yes	—
64	#14524002	C₂²	1	1	yes	characteristic
65	#14524002	C₂²	1	1	yes	characteristic
66	#14524001	C₂²	1	4	yes	complemented
67	#14524001	C₂²	1	2	yes	complemented
68	#14523999	C₂²	1	4	yes	—
69	C₂×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
70	C₂×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
71	C₄⋊C₄×D₆₇	C₂²	1	2	yes	complemented
72	C₂×C₂²⋊Dic₆₇	C₂²	1	2	yes	—
73	C₂×C₄×Dic₆₇	C₂²	1	2	yes	—
74	C₂²×Q₈×C₆₇	C₂²	1	1	yes	characteristic
75	C₂³×C₄×C₆₇	C₂²	1	1	yes	characteristic
76	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
77	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
78	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
79	C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
80	C₂×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
82	C₂×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
83	#11761628	—	2	4	no	—
84	C₂×Dic₁₃₄	C₂³	1	1	yes	characteristic
85	C₂×Dic₁₃₄	C₂³	1	4	yes	—
86	C₂×D₂₆₈	C₂³	1	1	yes	characteristic
87	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
88	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
89	C₂×C₂²⋊D₆₇	C₂³	1	2	yes	—
90	C₂²×Dic₆₇	C₂³	1	2	yes	—
91	C₂²×Dic₆₇	C₂³	1	2	yes	—
92	C₂×C₄×D₆₇	C₂³	1	2	yes	—
93	C₂×C₄×D₆₇	C₂³	1	4	yes	—
94	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
95	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
96	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
97	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
98	C₄⋊Dic₆₇	C₂³	1	2	yes	—
99	C₄⋊Dic₆₇	C₂³	1	2	yes	—
100	C₄⋊Dic₆₇	C₂³	1	4	yes	—
101	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
102	C₄⋊Dic₆₇	C₂³	1	1	yes	characteristic
103	C₄⋊Dic₆₇	C₂³	1	4	yes	—
104	C₄⋊Dic₆₇	C₂³	1	4	yes	—
105	Dic₆₇⋊C₄	C₂³	1	4	yes	—
106	Dic₆₇⋊C₄	C₂³	1	4	yes	—
107	Dic₆₇⋊C₄	C₂³	1	4	yes	—
108	Dic₆₇⋊C₄	C₂³	1	4	yes	—
109	Dic₆₇⋊C₄	C₂³	1	2	yes	—
110	Dic₆₇⋊C₄	C₂³	1	2	yes	—
111	Dic₆₇⋊C₄	C₂³	1	4	yes	—
112	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
113	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
114	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
115	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
116	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
117	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
118	C₂²⋊Dic₆₇	C₂³	1	2	yes	—
119	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
120	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
121	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
122	(C₂×D₆₇)⋊C₄	C₂³	1	4	yes	—
123	(C₂×D₆₇)⋊C₄	C₂³	1	2	yes	—
124	C₄×Dic₆₇	C₂³	1	2	yes	—
125	C₄×Dic₆₇	C₂³	1	2	yes	—
126	C₄×Dic₆₇	C₂³	1	2	yes	—
127	C₄×Dic₆₇	C₂³	1	2	yes	—
128	C₄×Dic₆₇	C₂³	1	4	yes	—
129	C₄×Dic₆₇	C₂³	1	4	yes	—
130	C₄×Dic₆₇	C₂³	1	4	yes	—
131	C₄×Dic₆₇	C₂³	1	2	yes	—
132	C₂⁴×C₆₇	C₂³	1	1	yes	characteristic
133	C₂×Q₈×C₆₇	—	2	4	no	—
134	C₂×Q₈×C₆₇	C₂³	1	2	yes	—
135	C₂×Q₈×C₆₇	C₂³	1	2	yes	—
136	C₂²×C₄×C₆₇	—	2	4	no	—
137	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
138	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
141	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
143	C₂²×C₄×C₆₇	C₂³	1	2	yes	—
144	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
145	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
147	C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
149	C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
150	C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
151	C₂³×C₆₇	—	2	2	no	—
152	C₂³×C₆₇	—	2	2	no	—
153	C₂³×C₆₇	—	4	1	no	—
154	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
155	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
156	C₂³×C₆₇	C₂⁴	1	1	yes	characteristic
157	C₂²×D₆₇	C₂⁴	1	2	yes	—
158	Q₈×C₆₇	—	2	4	no	—
159	Q₈×C₆₇	—	2	4	no	—
160	C₂×C₄×C₆₇	—	2	2	no	—
161	C₂×C₄×C₆₇	—	2	4	no	—
162	C₂×C₄×C₆₇	—	2	2	no	—
163	C₂×C₄×C₆₇	—	2	2	no	—
164	C₂×C₄×C₆₇	—	2	2	no	—
165	C₂×C₄×C₆₇	—	2	2	no	—
166	C₂×C₄×C₆₇	—	4	2	no	—
167	C₂×C₄×C₆₇	#41	1	4	yes	—
168	C₂×C₄×C₆₇	C₂⁴	1	4	yes	—
169	C₂×C₄×C₆₇	C₂⁴	1	4	yes	—
170	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
174	C₂²⋊D₆₇	—	2	4	no	—
175	C₂²⋊D₆₇	—	2	4	no	—
176	C₂²⋊D₆₇	—	4	2	no	—
177	C₂×Dic₆₇	—	2	4	no	—
178	C₂×Dic₆₇	—	4	2	no	—
179	C₂×Dic₆₇	C₂⁴	1	2	yes	—
180	C₂×Dic₆₇	C₂⁴	1	2	yes	—
181	C₂×Dic₆₇	C₂⁴	1	2	yes	—
182	C₂×Dic₆₇	C₂⁴	1	2	yes	—
183	C₂×Dic₆₇	C₂⁴	1	2	yes	—
184	C₂×Dic₆₇	C₂⁴	1	2	yes	—
185	C₂×Dic₆₇	C₂⁴	1	2	yes	—
186	D₂₆₈	—	2	2	no	—
187	C₄×D₆₇	—	2	4	no	—
188	C₄×D₆₇	—	4	4	no	—
189	Dic₁₃₄	—	2	2	no	—
190	Dic₁₃₄	—	4	4	no	—
191	C₂²×C₆₇	—	2	1	no	—
192	C₂²×C₆₇	—	2	1	no	—
193	C₂²×C₆₇	—	2	1	no	—
194	C₂²×C₆₇	—	2	1	no	—
195	C₂²×C₆₇	—	2	1	no	—
196	C₂²×C₆₇	—	2	1	no	—
197	C₂²×C₆₇	—	2	1	no	—
198	C₂²×C₆₇	—	4	4	no	—
199	C₂²×C₆₇	C₂×#41	1	2	yes	—
200	C₂²×C₆₇	2₋¹⁺⁴	1	2	yes	—
201	C₂²×C₆₇	C₂⁵	1	1	yes	characteristic
202	C₂×D₆₇	—	2	2	no	—
203	C₂×D₆₇	—	2	2	no	—
204	C₂×D₆₇	—	2	2	no	—
205	C₄×C₆₇	—	2	1	no	—
206	C₄×C₆₇	—	2	1	no	—
207	C₄×C₆₇	—	2	4	no	—
208	C₄×C₆₇	—	2	4	no	—
209	C₄×C₆₇	C₂×#41	1	2	yes	—
210	C₄×C₆₇	C₂×#41	1	2	yes	—
211	Dic₆₇	—	2	2	no	—
212	Dic₆₇	—	2	2	no	—
213	Dic₆₇	—	2	2	no	—
214	Dic₆₇	—	2	2	no	—
215	Dic₆₇	—	2	2	no	—
216	Dic₆₇	—	2	2	no	—
217	Dic₆₇	—	2	2	no	—
218	C₂×C₆₇	—	2	2	no	—
219	C₂×C₆₇	—	2	2	no	—
220	C₂×C₆₇	—	4	1	no	—
221	C₂×C₆₇	C₂²×#41	1	1	yes	characteristic
222	C₂×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
223	C₂×C₆₇	#585	1	1	yes	characteristic
224	D₆₇	—	4	2	no	—
225	#3495	—	67	1	no	maximal, Sylow
226	C₆₇	#3495	1	1	yes	characteristic, complemented, Sylow
227	#556	—	67	2	no	—
228	#554	—	67	2	no	—
229	#552	—	67	2	no	—
230	#552	—	67	2	no	—
231	#552	—	67	4	no	—
232	#551	—	67	4	no	—
233	#544	—	67	1	no	—
234	#542	—	67	2	no	—
235	#541	—	67	2	no	—
236	#536	—	67	1	no	—
237	#533	—	67	2	no	—
238	#529	—	67	2	no	—
239	#525	—	67	1	no	—
240	C₂×C₂²⋊Q₈	D₆₇	1	1	yes	characteristic, complemented
241	#520	—	67	1	no	—
242	#519	—	67	1	no	—
243	C₂×#117	—	67	1	no	—
244	C₂×#41	—	67	1	no	—
245	C₂²×Q₈	C₂×D₆₇	1	1	yes	characteristic
246	C₂³×C₄	C₂×D₆₇	1	1	yes	characteristic
247	C₄⋊Q₈	—	67	2	no	—
248	C₄⋊Q₈	—	67	2	no	—
249	C₄⋊Q₈	—	67	2	no	—
250	#126	—	67	4	no	—
251	#126	—	67	4	no	—
252	#126	—	67	4	no	—
253	#126	—	67	4	no	—
254	#125	—	67	2	no	—
255	#125	—	67	4	no	—
256	#125	—	67	4	no	—
257	#125	—	67	4	no	—
258	#125	—	67	2	no	—
259	#124	—	67	2	no	—
260	#124	—	67	4	no	—
261	#123	—	67	2	no	—
262	#123	—	67	4	no	—
263	#123	—	67	4	no	—
264	#123	—	67	4	no	—
265	C₂²⋊Q₈	—	67	2	no	—
266	C₂²⋊Q₈	—	67	2	no	—
267	C₂²⋊Q₈	—	67	1	no	—
268	C₂²⋊Q₈	—	67	1	no	—
269	C₂²⋊Q₈	—	67	4	no	—
270	C₂²⋊Q₈	—	67	4	no	—
271	C₂²⋊Q₈	—	67	4	no	—
272	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	—
273	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	—
274	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	—
275	C₂²⋊Q₈	C₂×D₆₇	1	2	yes	—
276	#121	—	67	1	no	—
277	#121	—	67	1	no	—
278	#120	—	67	2	no	—
279	C₄×Q₈	—	67	2	no	—
280	C₄×Q₈	—	67	2	no	—
281	C₄×Q₈	—	67	2	no	—
282	C₄×Q₈	—	67	2	no	—
283	C₄×Q₈	—	67	2	no	—
284	C₄×Q₈	—	67	4	no	—
285	C₄×D₄	—	67	4	no	—
286	C₄×D₄	—	67	2	no	—
287	C₄×D₄	—	67	2	no	—
288	C₄×D₄	—	67	2	no	—
289	C₄×D₄	—	67	4	no	—
290	#117	—	67	1	no	—
291	#117	—	67	1	no	—
292	#117	—	67	2	no	—
293	#117	—	67	1	no	—
294	#117	—	67	2	no	—
295	#117	—	67	1	no	—
296	#117	—	67	1	no	—
297	#117	—	67	4	no	—
298	#117	—	67	2	no	—
299	#117	—	67	4	no	—
300	#117	—	67	4	no	—
301	C₂×C₄⋊C₄	—	67	1	no	—
302	C₂×C₄⋊C₄	—	67	1	no	—
303	C₂×C₄⋊C₄	—	67	2	no	—
304	C₂×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂×D₆₇	1	2	yes	—
306	C₂×C₂²⋊C₄	—	67	2	no	—
307	C₂×C₂²⋊C₄	C₂×D₆₇	1	2	yes	—
308	C₂×C₄²	—	67	2	no	—
309	C₂⁴	C₂²×D₆₇	1	1	yes	characteristic
310	#41	—	134	4	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	—	67	4	no	—
313	C₂×Q₈	—	67	1	no	—
314	C₂×Q₈	C₂²×D₆₇	1	2	yes	—
315	C₂×Q₈	C₂²×D₆₇	1	2	yes	—
316	C₂×D₄	—	67	2	no	—
317	C₂×D₄	—	67	2	no	—
318	C₂×D₄	—	67	2	no	—
319	C₂×D₄	—	67	1	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	67	2	no	—
322	C₂²×C₄	—	67	4	no	—
323	C₂²×C₄	—	67	2	no	—
324	C₂²×C₄	—	67	2	no	—
325	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
326	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
327	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
328	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
329	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
330	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
331	C₂²×C₄	C₂²×D₆₇	1	2	yes	—
332	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
333	C₄⋊C₄	—	67	1	no	—
334	C₄⋊C₄	—	67	1	no	—
335	C₄⋊C₄	—	67	2	no	—
336	C₄⋊C₄	—	67	1	no	—
337	C₄⋊C₄	—	67	1	no	—
338	C₄⋊C₄	—	67	2	no	—
339	C₄⋊C₄	—	67	4	no	—
340	C₄⋊C₄	—	67	1	no	—
341	C₄⋊C₄	—	67	1	no	—
342	C₄⋊C₄	—	67	4	no	—
343	C₄⋊C₄	—	67	4	no	—
344	C₄⋊C₄	—	67	4	no	—
345	C₄⋊C₄	—	67	4	no	—
346	C₄⋊C₄	—	67	4	no	—
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	C₂²×D₆₇	1	2	yes	—
352	C₄⋊C₄	C₂²×D₆₇	1	4	yes	—
353	C₄⋊C₄	C₂²×D₆₇	1	2	yes	—
354	C₄⋊C₄	C₂²×D₆₇	1	4	yes	—
355	C₂²⋊C₄	—	67	2	no	—
356	C₂²⋊C₄	—	67	2	no	—
357	C₂²⋊C₄	—	67	2	no	—
358	C₂²⋊C₄	—	67	2	no	—
359	C₂²⋊C₄	—	67	2	no	—
360	C₂²⋊C₄	—	67	2	no	—
361	C₂²⋊C₄	—	67	2	no	—
362	C₂²⋊C₄	—	67	2	no	—
363	C₂²⋊C₄	—	67	4	no	—
364	C₂²⋊C₄	—	67	4	no	—
365	C₂²⋊C₄	—	67	2	no	—
366	C₂²⋊C₄	—	67	4	no	—
367	C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
368	C₂²⋊C₄	C₂²×D₆₇	1	4	yes	—
369	C₄²	—	67	2	no	—
370	C₄²	—	67	2	no	—
371	C₄²	—	67	2	no	—
372	C₄²	—	67	2	no	—
373	C₄²	—	67	4	no	—
374	C₄²	—	67	4	no	—
375	C₄²	—	67	4	no	—
376	C₄²	—	67	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	67	2	no	—
381	C₂³	C₂³×D₆₇	1	1	yes	characteristic
382	C₂³	C₂³×D₆₇	1	1	yes	characteristic
383	C₂³	C₂³×D₆₇	1	1	yes	characteristic
384	Q₈	—	2	4	no	—
385	Q₈	—	2	4	no	—
386	Q₈	—	268	4	no	—
387	Q₈	—	134	2	no	—
388	D₄	—	268	2	no	—
389	D₄	—	134	4	no	—
390	D₄	—	134	4	no	—
391	D₄	—	134	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	268	4	no	—
400	C₂×C₄	—	268	2	no	—
401	C₂×C₄	—	67	2	no	—
402	C₂×C₄	—	67	2	no	—
403	C₂×C₄	—	67	2	no	—
404	C₂×C₄	—	67	2	no	—
405	C₂×C₄	—	67	2	no	—
406	C₂×C₄	—	67	2	no	—
407	C₂×C₄	—	67	2	no	—
408	C₂×C₄	—	134	4	no	—
409	C₂×C₄	—	134	4	no	—
410	C₂×C₄	#11761627	1	4	yes	—
411	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
412	C₂×C₄	C₂³×D₆₇	1	4	yes	—
413	C₂×C₄	C₂³×D₆₇	1	4	yes	—
414	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
415	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
416	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	134	2	no	—
426	C₂²	—	134	2	no	—
427	C₂²	—	134	2	no	—
428	C₂²	C₂×#11761627	1	2	yes	—
429	C₂²	#14524091	1	2	yes	—
430	C₂²	C₂⁴×D₆₇	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	4	no	—
434	C₄	—	2	4	no	—
435	C₄	—	134	2	no	—
436	C₄	—	134	2	no	—
437	C₄	—	134	2	no	—
438	C₄	—	134	2	no	—
439	C₄	—	134	2	no	—
440	C₄	—	134	2	no	—
441	C₄	—	134	2	no	—
442	C₄	C₂×#11761627	1	2	yes	—
443	C₄	C₂×#11761627	1	2	yes	—
444	C₂	—	2	2	no	—
445	C₂	—	2	2	no	—
446	C₂	—	4	1	no	—
447	C₂	—	268	2	no	—
448	C₂	C₂²×#11761627	1	1	yes	characteristic
449	C₂	C₂×#14524091	1	1	yes	characteristic
450	C₂	#16864232	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₇
commutator, socle	C₂²×C₆₇	C₂⁵
Fitting	C₂×C₂²⋊Q₈×C₆₇	C₂
hypercenter	C₂×C₂²⋊Q₈	D₆₇
hypocenter	C₆₇	#3495
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #16864117	C₂	semidirect
2. #16864104	C₂	semidirect
3. #16864088	C₂	semidirect
4. #16864081	C₂	semidirect
5. #16864080	C₂	semidirect
6. #16864072	C₂	semidirect
7. #16864027	C₂	semidirect
8. #16864019	C₂	semidirect
9. #16864006	C₂	semidirect
10. #16863970	C₂	semidirect
11. #16863948	C₂	semidirect
12. #16863932	C₂	semidirect
14. #16863877	C₂	semidirect
15. #16863874	C₂	semidirect
16. C₂×#14524002	C₂	semidirect
17. C₂×C₂²⋊Q₈×C₆₇	C₂	semidirect
19. #14524042	C₂²	semidirect
20. #14524042	C₂²	semidirect
21. #14524041	C₂²	semidirect
22. #14524038	C₂²	semidirect
23. #14524038	C₂²	semidirect
26. #14524034	C₂²	semidirect
27. #14524034	C₂²	semidirect
28. #14524034	C₂²	semidirect
29. #14524033	C₂²	semidirect
30. #14524033	C₂²	semidirect
31. #14524032	C₂²	semidirect
37. #14524023	C₂²	semidirect
42. #14524019	C₂²	semidirect
43. #14524019	C₂²	semidirect
47. Q₈×Dic₆₇	C₂²	semidirect
48. Q₈×Dic₆₇	C₂²	semidirect
49. Q₈×Dic₆₇	C₂²	semidirect
50. Q₈×Dic₆₇	C₂²	semidirect
51. #14524008	C₂²	semidirect
52. #14524008	C₂²	semidirect
53. #14524005	C₂²	semidirect
66. #14524001	C₂²	semidirect
67. #14524001	C₂²	semidirect
71. C₄⋊C₄×D₆₇	C₂²	semidirect
226. C₆₇	#3495	semidirect
240. C₂×C₂²⋊Q₈	D₆₇	semidirect