Subgroups — #26185754

Order 12032.

714 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252495	C₂	1	2	yes	maximal, complemented
2	C₄×#13094043	C₂	1	1	yes	maximal, characteristic
3	#20242200	C₂	1	2	yes	maximal, complemented
4	#20242197	C₂	1	2	yes	maximal, complemented
5	C₈×Dic₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#20242194	C₂	1	1	yes	maximal, characteristic, complemented
7	D₈×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#335×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241772	C₂	1	2	yes	maximal, complemented
10	#20241670	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094043	C₄	1	1	yes	characteristic
13	C₄×#10625352	C₂²	1	2	yes	—
14	C₈×Dic₉₄	C₂²	1	2	yes	—
15	#15689247	C₂²	1	2	yes	—
16	C₄×Dic₁₈₈	C₂²	1	1	yes	characteristic
17	#15689217	C₄	1	1	yes	characteristic
18	#15689214	C₄	1	2	yes	—
19	C₄×#10625335	C₂²	1	2	yes	—
20	D₈×Dic₄₇	C₄	1	1	yes	characteristic
21	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
22	C₈×C₂²⋊D₄₇	—	2	2	no	—
23	(C₂²⋊D₄₇)⋊C₈	—	2	2	no	—
24	#15689174	C₂²	1	1	yes	characteristic
25	#15689174	C₂²	1	1	yes	characteristic
26	#15689173	—	2	2	no	—
27	#15689160	C₄	1	1	yes	characteristic
28	C₂×Dic₄₇⋊C₈	—	2	2	no	—
29	C₄⋊C₈×D₄₇	C₂²	1	2	yes	—
30	#15689116	C₄	1	2	yes	—
31	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
32	#15688876	C₂²	1	1	yes	characteristic
33	#15688875	C₂²	1	2	yes	—
34	#15688855	C₂²	1	2	yes	—
35	#15688853	C₂²	1	2	yes	—
36	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
37	#15688845	C₂²	1	1	yes	characteristic
38	#15688845	C₂²	1	1	yes	characteristic
39	C₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
40	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₄₇	C₂²	1	2	yes	—
42	C₄₇×#335	C₂²	1	1	yes	characteristic
43	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
44	C₈²×C₄₇	C₂²	1	1	yes	characteristic
45	C₂×#10625352	C₂×C₄	1	2	yes	—
46	#13094043	C₈	1	8	yes	complemented
47	C₂×Dic₁₈₈	C₂×C₄	1	1	yes	characteristic
48	C₂×#10625335	C₂×C₄	1	2	yes	—
49	C₂²×C₄₇⋊C₈	—	2	2	no	—
50	C₂×C₈×D₄₇	—	2	2	no	—
51	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
53	C₄×Dic₉₄	C₂³	1	2	yes	—
54	#13093989	C₂×C₄	1	2	yes	—
55	D₄×Dic₄₇	C₂×C₄	1	2	yes	—
56	C₄×C₂²⋊D₄₇	—	2	2	no	—
57	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
58	#13093982	C₂×C₄	1	2	yes	—
59	#13093980	—	2	2	no	—
60	C₂×C₄×Dic₄₇	—	2	2	no	—
61	C₄²×D₄₇	C₂³	1	1	yes	characteristic
62	#13093958	C₂×C₄	1	1	yes	characteristic
63	#13093955	C₂×C₄	1	2	yes	—
64	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
65	Dic₄₇⋊C₈	—	2	2	no	—
66	Dic₄₇⋊C₈	—	2	2	no	—
67	Dic₄₇⋊C₈	—	2	1	no	—
68	Dic₄₇⋊C₈	—	2	2	no	—
69	Dic₄₇⋊C₈	D₄	1	1	yes	characteristic
70	Dic₄₇⋊C₈	D₄	1	1	yes	characteristic
71	#13093949	C₂×C₄	1	2	yes	—
72	#13093947	C₂×C₄	1	2	yes	—
73	#13093945	C₂×C₄	1	2	yes	—
74	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
75	(C₂×D₄₇)⋊C₈	—	2	1	no	—
76	(C₂×D₄₇)⋊C₈	D₄	1	1	yes	characteristic
77	(C₂×D₄₇)⋊C₈	D₄	1	1	yes	characteristic
78	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
79	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
80	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
81	C₈×Dic₄₇	—	2	2	no	—
82	C₈×Dic₄₇	—	2	2	no	—
83	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
85	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₈×C₄₇	—	2	2	no	—
87	C₄×D₄×C₄₇	C₂³	1	2	yes	—
88	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
89	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
90	#102×C₄₇	C₂×C₄	1	2	yes	—
91	C₂²⋊C₈×C₄₇	—	2	2	no	—
92	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
95	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂×C₂²⋊D₄₇	—	2	2	no	—
98	C₂²×Dic₄₇	—	2	2	no	—
99	C₂²×Dic₄₇	—	2	2	no	—
100	#10625352	—	2	4	no	—
101	#10625352	C₂×C₈	1	8	yes	complemented
102	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂×C₄×D₄₇	#41	1	1	yes	characteristic
105	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
106	D₈×C₄₇	C₂×C₈	1	4	yes	complemented
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	—	2	1	no	—
109	C₂×C₈×C₄₇	—	8	2	no	—
110	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
115	C₂²⋊C₄×C₄₇	—	2	2	no	—
116	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
117	C₂²⋊Dic₄₇	—	2	2	no	—
118	#10625335	C₂×C₈	1	8	yes	complemented
119	(C₂×D₄₇)⋊C₄	—	2	2	no	—
120	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
121	Dic₄₇⋊C₄	—	2	2	no	—
122	Dic₄₇⋊C₄	—	2	2	no	—
123	C₄×Dic₄₇	—	2	2	no	—
124	C₄×Dic₄₇	—	2	2	no	—
125	C₄×Dic₄₇	—	2	2	no	—
126	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
128	C₄×Dic₄₇	#41	1	1	yes	characteristic
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	—	2	1	no	—
131	C₂×C₄₇⋊C₈	—	8	2	no	—
132	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
135	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
136	Dic₁₈₈	C₂×C₈	1	4	yes	complemented
137	C₈×D₄₇	—	2	2	no	—
138	C₈×D₄₇	—	8	2	no	—
139	C₈×D₄₇	C₂×C₈	1	4	yes	complemented
140	C₂³×C₄₇	—	2	2	no	—
141	C₂²×D₄₇	C₄×D₄	1	1	yes	characteristic
142	D₄×C₄₇	—	2	2	no	—
143	D₄×C₄₇	C₂²×C₈	1	4	yes	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
150	C₂²⋊D₄₇	—	2	8	no	—
151	C₂×Dic₄₇	—	2	2	no	—
152	C₂×Dic₄₇	—	2	8	no	—
153	C₂×Dic₄₇	—	2	2	no	—
154	C₂×Dic₄₇	—	8	2	no	—
155	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
156	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
157	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
158	C₄×D₄₇	—	2	1	no	—
159	C₄×D₄₇	—	2	1	no	—
160	C₄×D₄₇	—	4	1	no	—
161	C₄×D₄₇	C₂²×C₈	1	2	yes	—
162	C₄×D₄₇	#131	1	2	yes	—
163	Dic₉₄	—	2	2	no	—
164	Dic₉₄	C₂²×C₈	1	4	yes	—
165	C₈×C₄₇	—	2	1	no	—
166	C₈×C₄₇	—	2	1	no	—
167	C₈×C₄₇	—	2	1	no	—
168	C₈×C₄₇	—	4	1	no	—
169	C₈×C₄₇	—	4	2	no	—
170	C₈×C₄₇	C₂²×C₈	1	2	yes	—
171	C₄₇⋊C₈	—	2	1	no	—
172	C₄₇⋊C₈	—	2	1	no	—
173	C₄₇⋊C₈	—	2	1	no	—
174	C₄₇⋊C₈	—	4	1	no	—
175	C₄₇⋊C₈	—	4	2	no	—
176	C₄₇⋊C₈	C₂²×C₈	1	2	yes	—
177	#17857	—	47	1	no	maximal, Sylow
178	C₂²×C₄₇	—	2	4	no	—
179	C₂²×C₄₇	—	4	2	no	—
180	C₂²×C₄₇	—	4	2	no	—
181	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
182	C₂×D₄₇	—	2	1	no	—
183	C₂×D₄₇	—	2	1	no	—
184	C₂×D₄₇	C₈×D₄	1	2	yes	—
185	C₄×C₄₇	—	2	1	no	—
186	C₄×C₄₇	—	4	2	no	—
187	C₄×C₄₇	C₂³×C₈	1	1	yes	characteristic
188	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
189	C₄×C₄₇	#576	1	1	yes	characteristic
190	C₄×C₄₇	#578	1	1	yes	characteristic
191	Dic₄₇	—	2	4	no	—
192	Dic₄₇	—	2	1	no	—
193	Dic₄₇	—	2	1	no	—
194	Dic₄₇	—	4	2	no	—
195	Dic₄₇	C₈×D₄	1	2	yes	—
196	#2988	—	47	2	no	—
197	C₄×#135	—	47	1	no	—
198	SD₁₆⋊C₈	—	47	2	no	—
199	SD₁₆⋊C₈	—	47	2	no	—
200	C₈×Q₁₆	—	47	1	no	—
201	C₈×Q₁₆	—	47	1	no	—
202	C₈×D₈	—	47	1	no	—
203	C₈×D₈	D₄₇	1	1	yes	characteristic, complemented
204	C₂×#335	—	47	1	no	—
205	#1477	—	47	2	no	—
206	#1450	—	47	1	no	—
207	C₂×C₄₇	—	4	4	no	—
208	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
209	C₂×C₄₇	#2951	1	1	yes	characteristic
210	C₂×C₄₇	#2957	1	1	yes	characteristic
211	D₄₇	—	2	2	no	—
212	C₂×#135	—	47	1	no	—
213	C₄×#41	—	47	2	no	—
214	C₈×Q₈	—	47	2	no	—
215	C₈×Q₈	—	47	2	no	—
216	C₄×Q₁₆	—	47	1	no	—
217	C₄×Q₁₆	—	47	1	no	—
218	C₄×SD₁₆	—	47	2	no	—
219	C₄×SD₁₆	—	47	2	no	—
220	C₄×D₈	—	47	1	no	—
221	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
222	C₈×D₄	—	47	2	no	—
223	C₈×D₄	—	94	2	no	—
224	C₈×D₄	—	94	2	no	—
225	C₈×D₄	C₂×D₄₇	1	2	yes	—
226	#431	—	47	1	no	—
227	#431	—	47	1	no	—
228	#431	—	94	2	no	—
229	#427	—	47	1	no	—
230	C₂×C₄⋊C₈	—	47	2	no	—
231	C₂×C₄⋊C₈	—	94	2	no	—
232	#416	—	47	2	no	—
233	C₂×C₄×C₈	—	47	1	no	—
234	#335	—	47	2	no	—
235	#335	—	47	1	no	—
236	#335	C₂×D₄₇	1	1	yes	characteristic
237	Q₈⋊C₈	—	47	2	no	—
238	Q₈⋊C₈	—	47	2	no	—
239	D₄⋊C₈	—	47	2	no	—
240	D₄⋊C₈	C₂×D₄₇	1	2	yes	—
241	#322	—	47	1	no	—
242	#322	—	47	1	no	—
243	C₈²	—	47	1	no	—
244	C₈²	C₂×D₄₇	1	1	yes	characteristic
245	C₄₇	#17857	1	1	yes	characteristic, complemented, Sylow
246	C₂×#41	—	47	2	no	—
247	#135	—	47	8	no	—
248	C₂×Q₁₆	—	47	1	no	—
249	C₂×SD₁₆	—	47	2	no	—
250	C₂×D₈	C₄×D₄₇	1	1	yes	characteristic
251	C₂²×C₈	—	2	2	no	—
252	C₂²×C₈	—	47	1	no	—
253	C₂²×C₈	—	47	1	no	—
254	C₂²×C₈	—	94	2	no	—
255	C₂²×C₈	—	94	2	no	—
256	C₄×Q₈	—	47	2	no	—
257	C₄×Q₈	—	47	2	no	—
258	C₄×D₄	—	47	2	no	—
259	C₄×D₄	—	94	2	no	—
260	C₄×D₄	—	94	2	no	—
261	C₄×D₄	C₂²×D₄₇	1	2	yes	—
262	#117	—	47	2	no	—
263	#117	—	94	2	no	—
264	C₂×C₄²	—	47	1	no	—
265	C₂×C₄²	—	94	2	no	—
266	#107	—	47	1	no	—
267	#107	C₄×D₄₇	1	1	yes	characteristic
268	#106	—	47	2	no	—
269	C₄⋊C₈	—	47	1	no	—
270	C₄⋊C₈	—	47	1	no	—
271	C₄⋊C₈	—	47	2	no	—
272	C₄⋊C₈	—	94	2	no	—
273	C₄⋊C₈	—	94	1	no	—
274	C₄⋊C₈	—	94	2	no	—
275	C₄⋊C₈	—	94	2	no	—
276	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
277	#103	—	47	2	no	—
278	#103	—	47	2	no	—
279	#102	—	47	2	no	—
280	#102	C₄×D₄₇	1	2	yes	—
281	C₂²⋊C₈	—	2	2	no	—
282	C₂²⋊C₈	—	47	1	no	—
283	C₂²⋊C₈	—	47	1	no	—
284	C₂²⋊C₈	—	94	1	no	—
285	C₂²⋊C₈	—	94	2	no	—
286	C₄×C₈	—	47	1	no	—
287	C₄×C₈	—	47	1	no	—
288	C₄×C₈	—	47	1	no	—
289	C₄×C₈	—	47	1	no	—
290	C₄×C₈	—	47	1	no	—
291	C₄×C₈	—	94	2	no	—
292	C₄×C₈	—	94	2	no	—
293	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
294	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
295	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
296	#41	—	47	8	no	—
297	#41	—	94	4	no	—
298	C₂×Q₈	—	47	2	no	—
299	C₂×D₄	—	94	2	no	—
300	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	47	1	no	—
303	C₂²×C₄	—	47	1	no	—
304	C₂²×C₄	—	47	1	no	—
305	C₂²×C₄	—	94	2	no	—
306	C₂²×C₄	—	94	2	no	—
307	Q₁₆	—	47	4	no	—
308	SD₁₆	—	47	8	no	—
309	D₈	C₈×D₄₇	1	4	yes	complemented
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	8	2	no	—
313	C₂×C₈	—	47	1	no	—
314	C₂×C₈	—	47	4	no	—
315	C₂×C₈	—	47	1	no	—
316	C₂×C₈	—	47	1	no	—
317	C₂×C₈	—	47	1	no	—
318	C₂×C₈	—	94	2	no	—
319	C₂×C₈	—	94	2	no	—
320	C₂×C₈	—	94	1	no	—
321	C₂×C₈	—	376	2	no	—
322	C₂×C₈	—	376	2	no	—
323	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
324	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
325	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
326	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
327	C₄⋊C₄	—	47	2	no	—
328	C₄⋊C₄	—	94	2	no	—
329	C₄⋊C₄	—	94	2	no	—
330	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	94	2	no	—
333	C₂²⋊C₄	—	94	2	no	—
334	C₄²	—	47	1	no	—
335	C₄²	—	47	1	no	—
336	C₄²	—	47	1	no	—
337	C₄²	—	94	2	no	—
338	C₄²	—	94	2	no	—
339	C₄²	—	94	2	no	—
340	C₄²	C₂³×D₄₇	1	1	yes	characteristic
341	C₂³	—	2	2	no	—
342	C₂³	—	47	1	no	—
343	Q₈	—	47	4	no	—
344	Q₈	—	94	2	no	—
345	D₄	—	2	2	no	—
346	D₄	—	94	8	no	—
347	D₄	C₂×C₈×D₄₇	1	4	yes	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	47	1	no	—
352	C₂×C₄	—	47	2	no	—
353	C₂×C₄	—	47	2	no	—
354	C₂×C₄	—	47	1	no	—
355	C₂×C₄	—	47	1	no	—
356	C₂×C₄	—	94	8	no	—
357	C₂×C₄	—	94	2	no	—
358	C₂×C₄	—	94	1	no	—
359	C₂×C₄	—	94	1	no	—
360	C₂×C₄	—	94	2	no	—
361	C₂×C₄	—	376	2	no	—
362	C₂×C₄	—	188	1	no	—
363	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
364	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
365	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
366	C₈	—	2	1	no	—
367	C₈	—	2	1	no	—
368	C₈	—	2	1	no	—
369	C₈	—	4	1	no	—
370	C₈	—	4	2	no	—
371	C₈	—	47	2	no	—
372	C₈	—	94	1	no	—
373	C₈	—	94	1	no	—
374	C₈	—	94	1	no	—
375	C₈	—	188	1	no	—
376	C₈	—	188	2	no	—
377	C₈	C₂×C₈×D₄₇	1	2	yes	—
378	C₂²	—	2	4	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	47	2	no	—
382	C₂²	—	94	1	no	—
383	C₂²	—	94	1	no	—
384	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
385	C₄	—	2	1	no	—
386	C₄	—	4	2	no	—
387	C₄	—	47	2	no	—
388	C₄	—	94	1	no	—
389	C₄	—	94	1	no	—
390	C₄	—	94	4	no	—
391	C₄	—	188	2	no	—
392	C₄	C₂²×C₈×D₄₇	1	1	yes	characteristic
393	C₄	#131×D₄₇	1	1	yes	characteristic
394	C₄	#15689924	1	1	yes	characteristic
395	C₄	#15689937	1	1	yes	characteristic
396	C₂	—	4	4	no	—
397	C₂	—	94	2	no	—
398	C₂	C₈×D₄×D₄₇	1	1	yes	characteristic
399	C₂	#20252258	1	1	yes	characteristic
400	C₂	#20252300	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂³×C₈
Frattini	C₄²	C₂³×D₄₇
Fitting	C₈×D₈×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#13094043	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₈×D₈	D₄₇
hypocenter	C₄₇	#17857
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈×D₈

Complements

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

N	H ≅ G/N	type
1. #20252495	C₂	semidirect
3. #20242200	C₂	semidirect
4. #20242197	C₂	semidirect
5. C₈×Dic₁₈₈	C₂	semidirect
6. #20242194	C₂	semidirect
7. D₈×C₄₇⋊C₈	C₂	semidirect
8. #335×D₄₇	C₂	semidirect
9. #20241772	C₂	semidirect
10. #20241670	C₂	semidirect
11. C₈×D₈×C₄₇	C₂	semidirect
46. #13094043	C₈	semidirect
101. #10625352	C₂×C₈	semidirect
106. D₈×C₄₇	C₂×C₈	semidirect
118. #10625335	C₂×C₈	semidirect
136. Dic₁₈₈	C₂×C₈	semidirect
139. C₈×D₄₇	C₂×C₈	semidirect
203. C₈×D₈	D₄₇	semidirect
245. C₄₇	#17857	semidirect
309. D₈	C₈×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20252495	2
C₄×#13094043	2
#20242200	2
#20242197	2
C₈×Dic₁₈₈	2
#20242194	2
D₈×C₄₇⋊C₈	2
#335×D₄₇	2
#20241772	2
#20241670	2
C₈×D₈×C₄₇	2
#17857	47