Subgroups — #26104242

Order 12032.

596 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688878	C₂	1	1	yes	maximal, characteristic
3	#20241214	C₂	1	2	yes	maximal, complemented
4	#20241211	C₂	1	2	yes	maximal, complemented
5	C₄×C₂²⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₇⋊C₈	—	2	1	no	—
7	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
8	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
9	#15688878	—	2	1	no	—
10	#15688878	C₂²	1	2	yes	—
11	#15688878	C₂²	1	2	yes	—
12	C₂×C₂²⋊Q₈×C₄₇	C₄	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₄₇	C₄	1	1	yes	characteristic
14	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
15	C₄₇×#391	C₂²	1	1	yes	characteristic
16	C₄₇×#389	C₂²	1	1	yes	characteristic
17	C₄₇×#387	—	2	1	no	—
18	C₄₇×#385	—	2	1	no	—
19	C₄₇×#380	C₄	1	1	yes	characteristic
20	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
21	C₄×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
22	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
23	C₂²×C₄₇⋊C₈	—	2	4	no	—
24	C₂²×C₄₇⋊C₈	—	2	2	no	—
25	C₂²×C₄₇⋊C₈	—	2	2	no	—
26	C₂²×C₄₇⋊C₈	—	4	2	no	—
27	C₂²×C₄₇⋊C₈	—	4	2	no	—
28	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
29	C₄×C₄₇⋊C₈	—	4	2	no	—
30	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
34	C₂²⋊Q₈×C₄₇	—	2	2	no	—
35	C₂²⋊Q₈×C₄₇	C₈	1	4	yes	complemented
36	C₄×Q₈×C₄₇	—	4	2	no	—
37	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
38	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
39	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
40	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
43	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
44	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
45	C₂×C₄²×C₄₇	—	2	1	no	—
46	C₂×C₄²×C₄₇	—	2	1	no	—
47	C₂×C₄²×C₄₇	—	4	2	no	—
48	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
52	#95×C₄₇	—	2	1	no	—
53	#95×C₄₇	—	2	1	no	—
54	#95×C₄₇	—	2	1	no	—
55	#95×C₄₇	—	2	1	no	—
56	#95×C₄₇	—	2	1	no	—
57	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
58	C₂×Q₈×C₄₇	—	2	1	no	—
59	C₂×Q₈×C₄₇	—	4	1	no	—
60	C₂×Q₈×C₄₇	—	4	1	no	—
61	C₂×Q₈×C₄₇	C₂×C₈	1	2	yes	complemented
62	C₂²×C₄×C₄₇	—	2	2	no	—
63	C₂²×C₄×C₄₇	—	2	2	no	—
64	C₂²×C₄×C₄₇	—	2	2	no	—
65	C₂²×C₄×C₄₇	—	2	1	no	—
66	C₂²×C₄×C₄₇	—	2	1	no	—
67	C₂²×C₄×C₄₇	—	2	2	no	—
68	C₂²×C₄×C₄₇	—	2	1	no	—
69	C₂²×C₄×C₄₇	—	2	1	no	—
70	C₂²×C₄×C₄₇	—	4	1	no	—
71	C₂²×C₄×C₄₇	—	4	1	no	—
72	C₂²×C₄×C₄₇	—	4	1	no	—
73	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₇	C₂×C₈	1	2	yes	—
77	C₂²×C₄×C₄₇	M₁₆	1	2	yes	—
78	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
79	C₂²×C₄×C₄₇	Q₁₆	1	2	yes	—
80	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
83	C₄⋊C₄×C₄₇	—	2	4	no	—
84	C₄⋊C₄×C₄₇	—	2	1	no	—
85	C₄⋊C₄×C₄₇	—	4	2	no	—
86	C₄⋊C₄×C₄₇	—	4	1	no	—
87	C₄⋊C₄×C₄₇	—	4	1	no	—
88	C₄⋊C₄×C₄₇	—	4	2	no	—
89	C₄⋊C₄×C₄₇	C₂×C₈	1	2	yes	complemented
90	C₂²⋊C₄×C₄₇	—	2	4	no	—
91	C₂²⋊C₄×C₄₇	—	4	2	no	—
92	C₄²×C₄₇	—	2	2	no	—
93	C₄²×C₄₇	—	2	2	no	—
94	C₄²×C₄₇	—	4	1	no	—
95	C₄²×C₄₇	—	4	1	no	—
96	C₄²×C₄₇	—	4	2	no	—
97	C₄²×C₄₇	—	4	2	no	—
98	C₂×C₄₇⋊C₈	—	2	4	no	—
99	C₂×C₄₇⋊C₈	—	2	4	no	—
100	C₂×C₄₇⋊C₈	—	4	2	no	—
101	C₂×C₄₇⋊C₈	—	4	2	no	—
102	C₂×C₄₇⋊C₈	—	4	8	no	—
103	C₂×C₄₇⋊C₈	—	4	2	no	—
104	C₂×C₄₇⋊C₈	—	4	2	no	—
105	C₂³×C₄₇	—	2	1	no	—
106	C₂³×C₄₇	—	2	1	no	—
107	C₂³×C₄₇	—	2	1	no	—
108	C₂³×C₄₇	—	2	1	no	—
109	C₂³×C₄₇	C₂²⋊C₈	1	2	yes	—
110	C₂³×C₄₇	#103	1	2	yes	—
111	C₂³×C₄₇	#104	1	2	yes	—
112	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
113	Q₈×C₄₇	—	4	2	no	—
114	Q₈×C₄₇	—	4	2	no	—
115	C₂×C₄×C₄₇	—	2	1	no	—
116	C₂×C₄×C₄₇	—	2	1	no	—
117	C₂×C₄×C₄₇	—	2	1	no	—
118	C₂×C₄×C₄₇	—	2	1	no	—
119	C₂×C₄×C₄₇	—	2	1	no	—
120	C₂×C₄×C₄₇	—	2	1	no	—
121	C₂×C₄×C₄₇	—	2	1	no	—
122	C₂×C₄×C₄₇	—	2	1	no	—
123	C₂×C₄×C₄₇	—	2	4	no	—
124	C₂×C₄×C₄₇	—	2	4	no	—
125	C₂×C₄×C₄₇	—	2	2	no	—
126	C₂×C₄×C₄₇	—	2	2	no	—
127	C₂×C₄×C₄₇	—	2	1	no	—
128	C₂×C₄×C₄₇	—	2	1	no	—
129	C₂×C₄×C₄₇	—	2	1	no	—
130	C₂×C₄×C₄₇	—	4	2	no	—
131	C₂×C₄×C₄₇	—	4	2	no	—
132	C₂×C₄×C₄₇	—	4	4	no	—
133	C₂×C₄×C₄₇	—	4	1	no	—
134	C₂×C₄×C₄₇	—	4	1	no	—
135	C₂×C₄×C₄₇	—	4	1	no	—
136	C₂×C₄×C₄₇	—	4	1	no	—
137	C₂×C₄×C₄₇	—	4	1	no	—
138	C₂×C₄×C₄₇	—	4	1	no	—
139	C₂×C₄×C₄₇	—	4	1	no	—
140	C₂×C₄×C₄₇	—	4	1	no	—
141	C₂×C₄×C₄₇	—	4	1	no	—
142	C₂×C₄×C₄₇	—	4	1	no	—
143	C₂×C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
144	C₂×C₄×C₄₇	#99	1	2	yes	—
145	C₂×C₄×C₄₇	#103	1	2	yes	—
146	C₂×C₄×C₄₇	#104	1	2	yes	—
147	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
151	C₂×C₄×C₄₇	#135	1	2	yes	—
152	C₄₇⋊C₈	—	4	4	no	—
153	C₄₇⋊C₈	—	4	4	no	—
154	#7566	—	47	1	no	maximal, Sylow
155	C₂²×C₄₇	—	2	2	no	—
156	C₂²×C₄₇	—	2	2	no	—
157	C₂²×C₄₇	—	2	2	no	—
158	C₂²×C₄₇	—	2	2	no	—
159	C₂²×C₄₇	—	2	2	no	—
160	C₂²×C₄₇	—	2	2	no	—
161	C₂²×C₄₇	Q₈⋊C₈	1	4	yes	—
162	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
163	C₂²×C₄₇	C₂×#99	1	1	yes	characteristic
164	C₂²×C₄₇	#413	1	1	yes	characteristic
165	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
166	C₂²×C₄₇	#416	1	1	yes	characteristic
167	C₂²×C₄₇	C₂×#104	1	1	yes	characteristic
168	C₂²×C₄₇	C₂×#104	1	1	yes	characteristic
169	C₄×C₄₇	—	2	2	no	—
170	C₄×C₄₇	—	2	1	no	—
171	C₄×C₄₇	—	2	1	no	—
172	C₄×C₄₇	—	2	1	no	—
173	C₄×C₄₇	—	2	1	no	—
174	C₄×C₄₇	—	2	2	no	—
175	C₄×C₄₇	—	4	2	no	—
176	C₄×C₄₇	—	4	2	no	—
177	C₄×C₄₇	—	4	1	no	—
178	C₄×C₄₇	—	8	1	no	—
179	C₄×C₄₇	—	8	1	no	—
180	C₄×C₄₇	#328	1	4	yes	—
181	C₄×C₂²⋊Q₈	D₄₇	1	1	yes	characteristic
182	C₄×C₂²⋊C₈	—	47	1	no	—
183	C₂×#336	—	47	1	no	—
184	#1272	—	47	2	no	—
185	#1271	—	47	2	no	—
186	C₂×C₄₇	—	2	4	no	—
187	C₂×C₄₇	#1459	1	1	yes	characteristic
188	C₂×C₄₇	C₂×Q₈⋊C₈	1	1	yes	characteristic
189	C₂×C₄₇	#1476	1	1	yes	characteristic
190	C₂×C₄₇	C₂×#328	1	1	yes	characteristic
191	C₂×C₄₇	#1501	1	1	yes	characteristic
192	C₂×C₄₇	#1524	1	1	yes	characteristic
193	C₂×C₄₇	#1542	1	1	yes	characteristic
194	C₂³×C₈	—	94	1	no	—
195	C₂×C₂²⋊Q₈	Dic₄₇	1	1	yes	characteristic
196	C₂×C₄×Q₈	Dic₄₇	1	1	yes	characteristic
197	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
198	C₂×C₂²⋊C₈	—	94	1	no	—
199	C₂×C₄×C₈	—	94	1	no	—
200	#391	C₂×D₄₇	1	1	yes	characteristic
201	#389	C₂×D₄₇	1	1	yes	characteristic
202	#387	—	2	1	no	—
203	#385	—	2	1	no	—
204	#380	Dic₄₇	1	1	yes	characteristic
205	C₄×C₄⋊C₄	—	2	1	no	—
206	C₄×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
207	C₄×C₂²⋊C₄	—	2	1	no	—
208	#336	—	47	2	no	—
209	#336	—	47	2	no	—
210	#336	—	94	1	no	—
211	C₄₇	#7566	1	1	yes	characteristic, complemented, Sylow
212	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
213	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
214	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
215	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
216	C₂²×C₈	—	94	4	no	—
217	C₂²×C₈	—	94	2	no	—
218	C₂²×C₈	—	94	2	no	—
219	C₂²×C₈	—	188	2	no	—
220	C₂²×C₈	—	188	2	no	—
221	C₂²⋊Q₈	—	2	2	no	—
222	C₂²⋊Q₈	C₄₇⋊C₈	1	4	yes	complemented
223	C₄×Q₈	—	4	2	no	—
224	C₂×C₄⋊C₄	—	2	1	no	—
225	C₂×C₄⋊C₄	—	2	1	no	—
226	C₂×C₄⋊C₄	—	2	1	no	—
227	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
230	C₂×C₂²⋊C₄	—	2	1	no	—
231	C₂×C₂²⋊C₄	—	2	1	no	—
232	C₂×C₄²	—	2	1	no	—
233	C₂×C₄²	—	2	1	no	—
234	C₂×C₄²	—	4	2	no	—
235	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
236	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
237	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
238	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
239	C₂²⋊C₈	—	94	4	no	—
240	C₄×C₈	—	188	2	no	—
241	#95	—	2	1	no	—
242	#95	—	2	1	no	—
243	#95	—	2	1	no	—
244	#95	—	2	1	no	—
245	#95	—	2	1	no	—
246	C₂⁴	C₂²⋊Dic₄₇	1	1	yes	characteristic
247	C₂×Q₈	—	2	1	no	—
248	C₂×Q₈	—	4	1	no	—
249	C₂×Q₈	—	4	1	no	—
250	C₂×Q₈	C₂×C₄₇⋊C₈	1	2	yes	complemented
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	—	2	1	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	1	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	4	1	no	—
260	C₂²×C₄	—	4	1	no	—
261	C₂²×C₄	—	4	1	no	—
262	C₂²×C₄	C₂×C₄₇⋊C₈	1	2	yes	—
263	C₂²×C₄	#10625329	1	2	yes	—
264	C₂²×C₄	#10625336	1	2	yes	—
265	C₂²×C₄	#10625337	1	2	yes	—
266	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
267	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
268	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
269	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
272	C₂×C₈	—	94	4	no	—
273	C₂×C₈	—	94	4	no	—
274	C₂×C₈	—	188	2	no	—
275	C₂×C₈	—	188	2	no	—
276	C₂×C₈	—	188	8	no	—
277	C₂×C₈	—	188	2	no	—
278	C₂×C₈	—	188	2	no	—
279	C₄⋊C₄	—	2	4	no	—
280	C₄⋊C₄	—	2	1	no	—
281	C₄⋊C₄	—	4	1	no	—
282	C₄⋊C₄	—	4	1	no	—
283	C₄⋊C₄	—	4	2	no	—
284	C₄⋊C₄	—	4	2	no	—
285	C₄⋊C₄	C₂×C₄₇⋊C₈	1	2	yes	complemented
286	C₂²⋊C₄	—	2	4	no	—
287	C₂²⋊C₄	—	4	2	no	—
288	C₄²	—	2	2	no	—
289	C₄²	—	2	2	no	—
290	C₄²	—	4	1	no	—
291	C₄²	—	4	1	no	—
292	C₄²	—	4	2	no	—
293	C₄²	—	4	2	no	—
294	C₂³	—	2	1	no	—
295	C₂³	—	2	1	no	—
296	C₂³	—	2	1	no	—
297	C₂³	—	2	1	no	—
298	C₂³	C₂²⋊(C₄₇⋊C₈)	1	2	yes	—
299	C₂³	#13093948	1	2	yes	—
300	C₂³	#13093951	1	2	yes	—
301	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
302	Q₈	—	4	2	no	—
303	Q₈	—	4	2	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	C₂²⋊(C₄₇⋊C₈)	1	2	yes	—
333	C₂×C₄	#13093939	1	2	yes	—
334	C₂×C₄	#13093948	1	2	yes	—
335	C₂×C₄	#13093951	1	2	yes	—
336	C₂×C₄	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
337	C₂×C₄	C₂×#10625329	1	1	yes	characteristic
338	C₂×C₄	C₂×#10625336	1	1	yes	characteristic
339	C₂×C₄	C₂×#10625337	1	1	yes	characteristic
340	C₂×C₄	#13094044	1	2	yes	—
341	C₈	—	188	4	no	—
342	C₈	—	188	4	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	2	2	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	2	2	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	2	2	no	—
349	C₂²	Q₈⋊(C₄₇⋊C₈)	1	4	yes	—
350	C₂²	C₂×C₂²⋊(C₄₇⋊C₈)	1	1	yes	characteristic
351	C₂²	C₂×#13093939	1	1	yes	characteristic
352	C₂²	#15689107	1	1	yes	characteristic
353	C₂²	C₂×#13093948	1	1	yes	characteristic
354	C₂²	#15689119	1	1	yes	characteristic
355	C₂²	C₂×#13093951	1	1	yes	characteristic
356	C₂²	C₂×#13093951	1	1	yes	characteristic
357	C₄	—	2	2	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	—	2	2	no	—
363	C₄	—	4	2	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	1	no	—
366	C₄	—	8	1	no	—
367	C₄	—	8	1	no	—
368	C₄	#15688860	1	4	yes	—
369	C₂	—	2	4	no	—
370	C₂	#20241706	1	1	yes	characteristic
371	C₂	C₂×Q₈⋊(C₄₇⋊C₈)	1	1	yes	characteristic
372	C₂	#20241770	1	1	yes	characteristic
373	C₂	C₂×#15688860	1	1	yes	characteristic
374	C₂	#20241879	1	1	yes	characteristic
375	C₂	#20241976	1	1	yes	characteristic
376	C₂	#20242045	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄×C₂²⋊Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₄×C₂²⋊Q₈	D₄₇
hypocenter	C₄₇	#7566
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₄×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
3. #20241214	C₂	semidirect
4. #20241211	C₂	semidirect
35. C₂²⋊Q₈×C₄₇	C₈	semidirect
61. C₂×Q₈×C₄₇	C₂×C₈	semidirect
89. C₄⋊C₄×C₄₇	C₂×C₈	semidirect
211. C₄₇	#7566	semidirect
222. C₂²⋊Q₈	C₄₇⋊C₈	semidirect
250. C₂×Q₈	C₂×C₄₇⋊C₈	semidirect
285. C₄⋊C₄	C₂×C₄₇⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₂²⋊(C₄₇⋊C₈)	2
C₂×#15688878	2
#20241214	2
#20241211	2
C₄×C₂²⋊Q₈×C₄₇	2
#7566	47