Subgroups — #30825974

Order 17152.

638 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22569304	C₂	1	1	yes	maximal, characteristic, complemented
2	#22569233	C₂	1	1	yes	maximal, characteristic
3	#22559067	C₂	1	2	yes	maximal, complemented
4	#22559046	C₂	1	2	yes	maximal, complemented
5	SD₁₆⋊(C₆₇⋊C₈)	C₂	1	2	yes	maximal, complemented
6	SD₁₆×C₆₇⋊C₈	C₂	1	2	yes	maximal, complemented
7	#22558989	C₂	1	1	yes	maximal, characteristic, complemented
8	#22558652	C₂	1	1	yes	maximal, characteristic
9	#22558630	C₂	1	1	yes	maximal, characteristic, complemented
10	#22558504	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3101	C₂	1	1	yes	maximal, characteristic
12	#16863527	—	2	2	no	—
13	#16863527	C₂²	1	2	yes	complemented
14	Q₈×C₆₇⋊C₈	C₂²	1	2	yes	complemented
15	D₄×C₆₇⋊C₈	—	2	2	no	—
16	D₄×C₆₇⋊C₈	C₂²	1	2	yes	—
17	D₄×C₆₇⋊C₈	C₂²	1	2	yes	—
18	#16863457	—	2	2	no	—
19	#16863453	C₂²	1	1	yes	characteristic
20	#16863449	C₂²	1	1	yes	characteristic
21	#16863449	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
23	C₄×#11761612	C₂²	1	1	yes	characteristic
24	#16863149	C₂²	1	2	yes	complemented
25	#16863147	C₂²	1	2	yes	complemented
26	Q₈⋊(C₆₇⋊C₈)	C₂²	1	2	yes	complemented
27	Q₈⋊(C₆₇⋊C₈)	C₂²	1	2	yes	complemented
28	D₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
29	D₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
30	#16863118	C₂²	1	1	yes	characteristic, complemented
31	#16863118	C₂²	1	1	yes	characteristic, complemented
32	#16863117	C₂²	1	1	yes	characteristic, complemented
33	C₈×C₆₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
34	#533×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
36	#483×C₆₇	C₄	1	2	yes	—
37	#476×C₆₇	C₄	1	2	yes	—
38	#461×C₆₇	C₄	1	2	yes	—
39	#450×C₆₇	C₄	1	2	yes	—
40	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
41	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
42	#431×C₆₇	C₂²	1	1	yes	characteristic
43	C₂×#11761612	—	2	1	no	—
44	C₂²×C₆₇⋊C₈	—	2	2	no	—
45	C₂²×C₆₇⋊C₈	—	2	2	no	—
46	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
47	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
48	C₄⋊(C₆₇⋊C₈)	D₄	1	2	yes	—
49	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
50	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
51	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
52	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
53	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
54	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
55	C₂²⋊(C₆₇⋊C₈)	D₄	1	2	yes	—
56	#14523954	—	2	2	no	—
57	#14523954	—	2	1	no	—
58	#14523954	—	2	1	no	—
59	C₄×C₆₇⋊C₈	—	2	2	no	—
60	C₄×C₆₇⋊C₈	—	2	1	no	—
61	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
62	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
63	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
64	C₄×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
65	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₆₇	—	2	1	no	—
67	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	—
68	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	—
69	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
70	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
71	#125×C₆₇	—	2	1	no	—
72	C₂²⋊Q₈×C₆₇	—	2	1	no	—
73	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
74	C₄×Q₈×C₆₇	—	2	1	no	—
75	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
76	C₄×D₄×C₆₇	—	2	1	no	—
77	C₄×D₄×C₆₇	—	2	1	no	—
78	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
79	C₄×D₄×C₆₇	C₂³	1	2	yes	—
80	#117×C₆₇	—	2	1	no	—
81	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
83	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
84	#106×C₆₇	C₂×C₄	1	2	yes	—
85	#106×C₆₇	C₂×C₄	1	2	yes	—
86	C₄⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
87	#103×C₆₇	C₂×C₄	1	2	yes	—
88	#103×C₆₇	C₂×C₄	1	2	yes	—
89	#102×C₆₇	C₂×C₄	1	2	yes	—
90	#102×C₆₇	C₂×C₄	1	2	yes	—
91	C₂²⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
92	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	#11761612	—	4	2	no	—
95	C₂×C₆₇⋊C₈	—	2	1	no	—
96	C₂×C₆₇⋊C₈	—	2	2	no	—
97	C₂×C₆₇⋊C₈	—	2	2	no	—
98	C₂×C₆₇⋊C₈	—	2	1	no	—
99	C₂×C₆₇⋊C₈	—	8	2	no	—
100	C₂×C₆₇⋊C₈	—	8	2	no	—
101	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
102	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
103	C₂⁴×C₆₇	—	2	1	no	—
104	C₂×Q₈×C₆₇	—	2	1	no	—
105	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
106	C₂×D₄×C₆₇	—	2	4	no	—
107	C₂×D₄×C₆₇	—	2	1	no	—
108	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₆₇	—	2	1	no	—
110	C₂²×C₄×C₆₇	—	2	2	no	—
111	C₂²×C₄×C₆₇	—	2	2	no	—
112	C₂²×C₄×C₆₇	—	8	2	no	—
113	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
116	SD₁₆×C₆₇	—	2	4	no	—
117	SD₁₆×C₆₇	—	2	4	no	—
118	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
120	C₄⋊C₄×C₆₇	—	2	1	no	—
121	C₄⋊C₄×C₆₇	—	2	1	no	—
122	C₄⋊C₄×C₆₇	—	2	1	no	—
123	C₄⋊C₄×C₆₇	—	2	1	no	—
124	C₄⋊C₄×C₆₇	—	2	2	no	—
125	C₄⋊C₄×C₆₇	—	2	2	no	—
126	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
127	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
128	C₂²⋊C₄×C₆₇	—	2	2	no	—
129	C₂²⋊C₄×C₆₇	—	2	2	no	—
130	C₂²⋊C₄×C₆₇	—	2	2	no	—
131	C₄²×C₆₇	—	2	2	no	—
132	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₆₇	#41	1	1	yes	characteristic
135	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
136	C₂³×C₆₇	—	2	4	no	—
137	C₂³×C₆₇	—	2	2	no	—
138	C₂³×C₆₇	—	8	1	no	—
139	C₂³×C₆₇	—	8	1	no	—
140	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
141	Q₈×C₆₇	—	2	2	no	—
142	Q₈×C₆₇	—	2	2	no	—
143	Q₈×C₆₇	—	8	1	no	—
144	D₄×C₆₇	—	2	4	no	—
145	D₄×C₆₇	—	2	2	no	—
146	D₄×C₆₇	#131	1	4	yes	—
147	C₂×C₄×C₆₇	—	2	2	no	—
148	C₂×C₄×C₆₇	—	2	2	no	—
149	C₂×C₄×C₆₇	—	2	2	no	—
150	C₂×C₄×C₆₇	—	2	2	no	—
151	C₂×C₄×C₆₇	—	2	2	no	—
152	C₂×C₄×C₆₇	—	4	1	no	—
153	C₂×C₄×C₆₇	—	4	2	no	—
154	C₂×C₄×C₆₇	—	4	2	no	—
155	C₂×C₄×C₆₇	—	8	2	no	—
156	C₂×C₄×C₆₇	—	8	1	no	—
157	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
163	C₈×C₆₇	—	2	2	no	—
164	C₈×C₆₇	—	2	2	no	—
165	C₆₇⋊C₈	—	2	2	no	—
166	C₆₇⋊C₈	—	2	2	no	—
167	C₆₇⋊C₈	—	2	2	no	—
168	C₆₇⋊C₈	—	4	1	no	—
169	C₆₇⋊C₈	—	4	2	no	—
170	C₆₇⋊C₈	—	4	2	no	—
171	C₂²×C₆₇	—	2	1	no	—
172	C₂²×C₆₇	—	2	4	no	—
173	C₂²×C₆₇	—	2	1	no	—
174	C₂²×C₆₇	—	2	1	no	—
175	C₂²×C₆₇	—	4	2	no	—
176	C₂²×C₆₇	—	4	2	no	—
177	C₂²×C₆₇	—	8	4	no	—
178	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
179	C₄×C₆₇	—	2	1	no	—
180	C₄×C₆₇	—	2	1	no	—
181	C₄×C₆₇	—	2	1	no	—
182	C₄×C₆₇	—	2	1	no	—
183	C₄×C₆₇	—	4	2	no	—
184	C₄×C₆₇	—	4	2	no	—
185	C₄×C₆₇	—	4	2	no	—
186	C₄×C₆₇	C₂×#131	1	2	yes	—
187	C₄×C₆₇	#577	1	2	yes	—
188	#17924	—	67	1	no	maximal, Sylow
189	C₂×C₆₇	—	4	1	no	—
190	C₂×C₆₇	—	4	4	no	—
191	C₂×C₆₇	#2929	1	1	yes	characteristic
192	C₂×C₆₇	#2949	1	1	yes	characteristic
193	C₂×C₆₇	#2956	1	1	yes	characteristic
194	#3101	D₆₇	1	1	yes	characteristic
195	#2985	—	67	1	no	—
196	#2972	—	67	1	no	—
197	#1585	—	67	2	no	—
198	#1582	—	67	2	no	—
199	SD₁₆⋊C₈	—	67	2	no	—
200	C₈×SD₁₆	—	67	2	no	—
201	#1572	—	67	1	no	—
202	#1490	—	67	1	no	—
203	#1485	—	67	1	no	—
204	#1453	—	67	1	no	—
205	C₆₇	#17924	1	1	yes	characteristic, complemented, Sylow
206	#533	C₂×D₆₇	1	1	yes	characteristic
207	C₂×C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
208	#483	Dic₆₇	1	2	yes	—
209	#476	Dic₆₇	1	2	yes	—
210	#461	Dic₆₇	1	2	yes	—
211	#450	Dic₆₇	1	2	yes	—
212	#446	—	67	2	no	—
213	#446	—	134	2	no	—
214	C₈×Q₈	—	67	2	no	—
215	C₄×SD₁₆	C₂×D₆₇	1	2	yes	—
216	C₄×SD₁₆	C₂×D₆₇	1	2	yes	—
217	C₈×D₄	—	67	2	no	—
218	C₈×D₄	—	67	2	no	—
219	C₈×D₄	—	134	2	no	—
220	#433	—	134	2	no	—
221	#432	—	67	1	no	—
222	#431	—	67	1	no	—
223	#431	—	67	1	no	—
224	#431	C₂×D₆₇	1	1	yes	characteristic
225	C₂×C₂²⋊C₈	—	134	2	no	—
226	C₄×M₁₆	—	67	1	no	—
227	#335	—	67	2	no	—
228	#334	—	67	2	no	—
229	Q₈⋊C₈	—	67	2	no	—
230	Q₈⋊C₈	—	67	2	no	—
231	D₄⋊C₈	—	67	2	no	—
232	D₄⋊C₈	—	67	2	no	—
233	#322	—	67	1	no	—
234	#322	—	67	1	no	—
235	#322	—	67	1	no	—
236	C₈²	—	67	1	no	—
237	C₂²×D₄	C₂×Dic₆₇	1	1	yes	characteristic
238	C₂³×C₄	—	2	1	no	—
239	C₂×SD₁₆	C₂×Dic₆₇	1	2	yes	—
240	C₂×SD₁₆	C₂×Dic₆₇	1	2	yes	—
241	C₂×M₁₆	—	134	1	no	—
242	C₂²×C₈	—	134	2	no	—
243	C₂²×C₈	—	134	2	no	—
244	C₄⋊Q₈	C₂×Dic₆₇	1	1	yes	characteristic
245	C₄⋊Q₈	C₂×Dic₆₇	1	1	yes	characteristic
246	#125	—	2	1	no	—
247	C₂²⋊Q₈	—	2	1	no	—
248	C₂²⋊Q₈	C₂×Dic₆₇	1	2	yes	—
249	C₄×Q₈	—	2	1	no	—
250	C₄×Q₈	C₂²×D₆₇	1	2	yes	—
251	C₄×D₄	—	2	1	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	C₂×Dic₆₇	1	2	yes	—
254	C₄×D₄	C₂²×D₆₇	1	2	yes	—
255	#117	—	2	1	no	—
256	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	—	2	1	no	—
258	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
259	#106	C₂×Dic₆₇	1	2	yes	—
260	#106	C₂×Dic₆₇	1	2	yes	—
261	C₄⋊C₈	—	67	2	no	—
262	C₄⋊C₈	—	67	2	no	—
263	C₄⋊C₈	—	67	2	no	—
264	C₄⋊C₈	—	134	2	no	—
265	C₄⋊C₈	—	134	2	no	—
266	C₄⋊C₈	C₂×Dic₆₇	1	2	yes	—
267	#103	C₂×Dic₆₇	1	2	yes	—
268	#103	C₂×Dic₆₇	1	2	yes	—
269	#102	C₂×Dic₆₇	1	2	yes	—
270	#102	C₂×Dic₆₇	1	2	yes	—
271	C₂²⋊C₈	—	67	2	no	—
272	C₂²⋊C₈	—	134	2	no	—
273	C₂²⋊C₈	—	134	2	no	—
274	C₂²⋊C₈	—	134	1	no	—
275	C₂²⋊C₈	—	134	1	no	—
276	C₂²⋊C₈	C₂×Dic₆₇	1	2	yes	—
277	#97	—	134	2	no	—
278	#97	—	134	1	no	—
279	#97	—	134	1	no	—
280	C₄×C₈	—	67	1	no	—
281	C₄×C₈	—	67	1	no	—
282	C₄×C₈	—	67	1	no	—
283	C₄×C₈	—	67	1	no	—
284	C₄×C₈	—	134	2	no	—
285	C₄×C₈	—	134	1	no	—
286	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
287	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
288	C₂⁴	—	2	1	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	C₂²×Dic₆₇	1	2	yes	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	1	no	—
293	C₂×D₄	C₂²×Dic₆₇	1	2	yes	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	8	2	no	—
298	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
299	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
300	C₂²×C₄	#11761627	1	1	yes	characteristic
301	SD₁₆	—	2	4	no	—
302	SD₁₆	—	2	4	no	—
303	M₁₆	—	268	2	no	—
304	C₂×C₈	—	536	2	no	—
305	C₂×C₈	—	536	2	no	—
306	C₂×C₈	—	67	2	no	—
307	C₂×C₈	—	67	2	no	—
308	C₂×C₈	—	134	2	no	—
309	C₂×C₈	—	134	2	no	—
310	C₂×C₈	—	134	1	no	—
311	C₂×C₈	—	134	1	no	—
312	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
313	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
321	C₄⋊C₄	C₂²×Dic₆₇	1	2	yes	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₂²⋊C₄	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
327	C₄²	D₄×D₆₇	1	1	yes	characteristic
328	C₄²	#11761627	1	1	yes	characteristic
329	C₄²	C₂³×D₆₇	1	1	yes	characteristic
330	C₂³	—	2	4	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	8	1	no	—
333	C₂³	—	8	1	no	—
334	C₂³	D₄×Dic₆₇	1	1	yes	characteristic
335	Q₈	—	2	2	no	—
336	Q₈	—	2	2	no	—
337	Q₈	—	8	1	no	—
338	D₄	—	2	4	no	—
339	D₄	—	2	2	no	—
340	D₄	#14524050	1	4	yes	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	—	8	1	no	—
351	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
352	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
353	C₂×C₄	D₄×Dic₆₇	1	1	yes	characteristic
354	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
355	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
356	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
357	C₈	—	2	2	no	—
358	C₈	—	2	2	no	—
359	C₈	—	268	1	no	—
360	C₈	—	268	2	no	—
361	C₈	—	268	2	no	—
362	C₈	—	134	2	no	—
363	C₈	—	134	2	no	—
364	C₈	—	134	2	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	4	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	8	4	no	—
372	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	2	no	—
379	C₄	—	4	2	no	—
380	C₄	C₂×#14524050	1	2	yes	—
381	C₄	#16864202	1	2	yes	—
382	C₂	—	4	1	no	—
383	C₂	—	4	4	no	—
384	C₂	#22568904	1	1	yes	characteristic
385	C₂	#22569069	1	1	yes	characteristic
386	C₂	#22569119	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#3101	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂²×D₄×C₆₇	C₂×C₄
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	#3101	D₆₇
hypocenter	C₆₇	#17924
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3101

Complements

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

N	H ≅ G/N	type
1. #22569304	C₂	semidirect
3. #22559067	C₂	semidirect
4. #22559046	C₂	semidirect
5. SD₁₆⋊(C₆₇⋊C₈)	C₂	semidirect
6. SD₁₆×C₆₇⋊C₈	C₂	semidirect
7. #22558989	C₂	semidirect
9. #22558630	C₂	semidirect
10. #22558504	C₂	semidirect
13. #16863527	C₂²	semidirect
14. Q₈×C₆₇⋊C₈	C₂²	semidirect
24. #16863149	C₂²	semidirect
25. #16863147	C₂²	semidirect
26. Q₈⋊(C₆₇⋊C₈)	C₂²	semidirect
27. Q₈⋊(C₆₇⋊C₈)	C₂²	semidirect
30. #16863118	C₂²	semidirect
31. #16863118	C₂²	semidirect
32. #16863117	C₂²	semidirect
33. C₈×C₆₇⋊C₈	C₂²	semidirect
205. C₆₇	#17924	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#22569304	2
#22569233	2
#22559067	2
#22559046	2
SD₁₆⋊(C₆₇⋊C₈)	2
SD₁₆×C₆₇⋊C₈	2
#22558989	2
#22558652	2
#22558630	2
#22558504	2
C₆₇×#3101	2
#17924	67