Subgroups — #124×C₄₇⋊C₈ #26224144

Order 12032.

974 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#20244325	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244183	C₂	1	1	yes	maximal, characteristic
5	#20243996	C₂	1	4	yes	maximal, complemented
6	#20243505	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²⋊C₄×C₄₇⋊C₈	C₂	1	4	yes	maximal, complemented
8	C₄²×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#124×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
11	Q₈×C₄₇⋊C₈	—	2	4	no	—
12	D₄×C₄₇⋊C₈	—	2	4	no	—
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
18	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
19	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
21	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
22	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
23	#15688878	C₂²	1	4	yes	—
24	#15688878	C₂²	1	4	yes	—
25	C₂×#124×C₄₇	C₄	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
28	C₄₇×#391	C₄	1	1	yes	characteristic
29	C₄₇×#390	C₄	1	1	yes	characteristic
30	C₄₇×#388	C₄	1	4	yes	—
31	C₄₇×#382	C₄	1	1	yes	characteristic
32	C₄×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	—
33	C₄³×C₄₇	C₂²	1	1	yes	characteristic
34	C₂²×C₄₇⋊C₈	—	2	4	no	—
35	C₂²×C₄₇⋊C₈	—	2	8	no	—
36	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
37	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
38	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
39	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
40	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
41	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
42	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
43	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
44	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
45	C₂²⋊(C₄₇⋊C₈)	—	2	8	no	—
46	C₄×C₄₇⋊C₈	—	2	2	no	—
47	C₄×C₄₇⋊C₈	—	2	4	no	—
48	C₄×C₄₇⋊C₈	—	2	4	no	—
49	C₄×C₄₇⋊C₈	—	2	4	no	—
50	C₄×C₄₇⋊C₈	D₄	1	4	yes	—
51	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
54	#124×C₄₇	C₈	1	8	yes	complemented
55	C₄×Q₈×C₄₇	—	2	2	no	—
56	C₄×Q₈×C₄₇	—	2	2	no	—
57	C₄×D₄×C₄₇	—	2	2	no	—
58	C₄×D₄×C₄₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
62	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
64	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
65	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
69	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
70	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
71	#95×C₄₇	C₂×C₄	1	4	yes	—
72	#95×C₄₇	C₂×C₄	1	4	yes	—
73	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
74	C₂×Q₈×C₄₇	—	2	2	no	—
75	C₂×Q₈×C₄₇	—	2	2	no	—
76	C₂×Q₈×C₄₇	C₂×C₈	1	4	yes	complemented
77	C₂×D₄×C₄₇	—	2	2	no	—
78	C₂×D₄×C₄₇	—	2	2	no	—
79	C₂×D₄×C₄₇	C₂×C₈	1	4	yes	—
80	C₂²×C₄×C₄₇	—	2	2	no	—
81	C₂²×C₄×C₄₇	—	2	2	no	—
82	C₂²×C₄×C₄₇	—	2	4	no	—
83	C₂²×C₄×C₄₇	—	2	4	no	—
84	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
92	C₄⋊C₄×C₄₇	—	2	2	no	—
93	C₄⋊C₄×C₄₇	—	2	4	no	—
94	C₄⋊C₄×C₄₇	—	2	2	no	—
95	C₂²⋊C₄×C₄₇	—	2	4	no	—
96	C₂²⋊C₄×C₄₇	—	2	8	no	—
97	C₂²⋊C₄×C₄₇	C₂×C₈	1	16	yes	complemented
98	C₄²×C₄₇	—	2	4	no	—
99	C₄²×C₄₇	—	2	2	no	—
100	C₄²×C₄₇	—	2	2	no	—
101	C₄²×C₄₇	—	2	2	no	—
102	C₄²×C₄₇	—	2	2	no	—
103	C₄²×C₄₇	—	2	2	no	—
104	C₄²×C₄₇	C₂×C₈	1	4	yes	complemented
105	C₄²×C₄₇	C₂×D₄	1	2	yes	—
106	C₄²×C₄₇	#41	1	2	yes	—
107	C₂×C₄₇⋊C₈	—	2	2	no	—
108	C₂×C₄₇⋊C₈	—	2	2	no	—
109	C₂×C₄₇⋊C₈	—	2	2	no	—
110	C₂×C₄₇⋊C₈	—	2	2	no	—
111	C₂×C₄₇⋊C₈	—	2	2	no	—
112	C₂×C₄₇⋊C₈	—	2	4	no	—
113	C₂×C₄₇⋊C₈	—	2	4	no	—
114	C₂×C₄₇⋊C₈	—	4	8	no	—
115	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
116	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
117	C₂×C₄₇⋊C₈	#41	1	4	yes	—
118	C₂×C₄₇⋊C₈	#41	1	4	yes	—
119	C₂³×C₄₇	—	2	2	no	—
120	C₂³×C₄₇	—	2	4	no	—
121	C₂³×C₄₇	—	2	4	no	—
122	C₂³×C₄₇	—	2	2	no	—
123	C₂³×C₄₇	C₂²×C₈	1	4	yes	—
124	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
125	Q₈×C₄₇	—	2	8	no	—
126	D₄×C₄₇	—	2	8	no	—
127	C₂×C₄×C₄₇	—	2	2	no	—
128	C₂×C₄×C₄₇	—	2	2	no	—
129	C₂×C₄×C₄₇	—	2	2	no	—
130	C₂×C₄×C₄₇	—	2	2	no	—
131	C₂×C₄×C₄₇	—	2	2	no	—
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	—	2	2	no	—
135	C₂×C₄×C₄₇	—	2	2	no	—
136	C₂×C₄×C₄₇	—	2	4	no	—
137	C₂×C₄×C₄₇	—	2	4	no	—
138	C₂×C₄×C₄₇	—	4	2	no	—
139	C₂×C₄×C₄₇	—	4	4	no	—
140	C₂×C₄×C₄₇	—	4	2	no	—
141	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
142	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
143	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
144	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
145	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
146	C₂×C₄×C₄₇	#131	1	4	yes	—
147	C₂×C₄×C₄₇	#131	1	2	yes	—
148	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
150	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
151	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
152	C₄₇⋊C₈	—	2	4	no	—
153	C₄₇⋊C₈	—	2	2	no	—
154	C₄₇⋊C₈	—	4	2	no	—
155	C₄₇⋊C₈	—	4	2	no	—
156	C₄₇⋊C₈	#124	1	4	yes	direct product factor
157	C₈×#124	—	47	1	no	maximal, Sylow
158	C₂²×C₄₇	—	2	4	no	—
159	C₂²×C₄₇	—	2	8	no	—
160	C₂²×C₄₇	—	4	2	no	—
161	C₂²×C₄₇	—	4	4	no	—
162	C₂²×C₄₇	—	4	2	no	—
163	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
164	C₂²×C₄₇	C₄×#41	1	2	yes	—
165	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
166	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
167	C₂²×C₄₇	C₂×#131	1	2	yes	—
168	C₄×C₄₇	—	2	4	no	—
169	C₄×C₄₇	—	2	2	no	—
170	C₄×C₄₇	—	2	4	no	—
171	C₄×C₄₇	—	2	4	no	—
172	C₄×C₄₇	—	4	2	no	—
173	C₄×C₄₇	—	4	2	no	—
174	C₄×C₄₇	C₈×D₄	1	4	yes	—
175	C₄×C₄₇	C₂×#124	1	1	yes	characteristic
176	C₄×C₄₇	#529	1	2	yes	—
177	C₄×C₄₇	#532	1	1	yes	characteristic
178	C₂×C₈×Q₈	—	47	1	no	—
179	C₂×C₈×D₄	—	47	1	no	—
180	C₄×#124	D₄₇	1	1	yes	characteristic
181	#1984	—	47	1	no	—
182	#1954	—	47	1	no	—
183	#1923	—	47	4	no	—
184	#1831	—	47	1	no	—
185	C₈×C₂²⋊C₄	—	47	4	no	—
186	C₄²×C₈	—	47	1	no	—
187	C₂×C₄₇	—	4	4	no	—
188	C₂×C₄₇	C₄×#124	1	1	yes	characteristic
189	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
190	C₂×C₄₇	#2931	1	1	yes	characteristic
191	C₂×C₄₇	C₈×#41	1	2	yes	—
192	C₂×C₄₇	#2966	1	2	yes	—
193	C₂³×C₈	—	47	2	no	—
194	C₂×#124	Dic₄₇	1	1	yes	characteristic
195	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
196	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
197	C₈×Q₈	—	94	4	no	—
198	C₈×D₄	—	94	4	no	—
199	C₂×C₄⋊C₈	—	47	1	no	—
200	C₂×C₄⋊C₈	—	47	1	no	—
201	C₂×C₄⋊C₈	—	47	2	no	—
202	C₂×C₂²⋊C₈	—	47	2	no	—
203	C₂×C₂²⋊C₈	—	47	4	no	—
204	C₂×C₄×C₈	—	47	1	no	—
205	C₂×C₄×C₈	—	47	2	no	—
206	C₂×C₄×C₈	—	47	2	no	—
207	C₂×C₄×C₈	—	47	1	no	—
208	C₂×C₄×C₈	—	47	2	no	—
209	#391	Dic₄₇	1	1	yes	characteristic
210	#390	Dic₄₇	1	1	yes	characteristic
211	#388	Dic₄₇	1	4	yes	—
212	#382	Dic₄₇	1	1	yes	characteristic
213	C₄×C₂²⋊C₄	C₂×D₄₇	1	4	yes	—
214	C₄³	C₂×D₄₇	1	1	yes	characteristic
215	#336	—	47	4	no	—
216	#336	—	47	4	no	—
217	C₄₇	C₈×#124	1	1	yes	characteristic, complemented, Sylow
218	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
219	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
220	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
221	C₂²×C₈	—	47	1	no	—
222	C₂²×C₈	—	47	2	no	—
223	C₂²×C₈	—	47	1	no	—
224	C₂²×C₈	—	47	2	no	—
225	C₂²×C₈	—	47	2	no	—
226	C₂²×C₈	—	94	8	no	—
227	C₂²×C₈	—	94	4	no	—
228	#124	C₄₇⋊C₈	1	8	yes	direct product factor
229	C₄×Q₈	—	2	2	no	—
230	C₄×Q₈	—	2	2	no	—
231	C₄×D₄	—	2	2	no	—
232	C₄×D₄	—	2	2	no	—
233	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
236	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
237	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	4	yes	—
238	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	4	yes	—
239	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
240	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
241	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
242	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
243	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
244	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
245	C₄⋊C₈	—	94	4	no	—
246	C₄⋊C₈	—	94	2	no	—
247	C₄⋊C₈	—	94	2	no	—
248	C₂²⋊C₈	—	94	8	no	—
249	C₂²⋊C₈	—	94	4	no	—
250	C₄×C₈	—	47	4	no	—
251	C₄×C₈	—	94	4	no	—
252	C₄×C₈	—	94	4	no	—
253	C₄×C₈	—	94	4	no	—
254	C₄×C₈	—	94	2	no	—
255	#95	C₂×Dic₄₇	1	4	yes	—
256	#95	C₂×Dic₄₇	1	4	yes	—
257	C₂⁴	C₂²×Dic₄₇	1	2	yes	—
258	C₂×Q₈	—	2	2	no	—
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	C₂×C₄₇⋊C₈	1	4	yes	complemented
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	—	2	2	no	—
263	C₂×D₄	C₂×C₄₇⋊C₈	1	4	yes	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
269	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
270	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
271	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
272	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
273	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
274	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
275	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
276	C₂×C₈	—	47	2	no	—
277	C₂×C₈	—	47	4	no	—
278	C₂×C₈	—	47	2	no	—
279	C₂×C₈	—	47	4	no	—
280	C₂×C₈	—	94	2	no	—
281	C₂×C₈	—	94	2	no	—
282	C₂×C₈	—	94	2	no	—
283	C₂×C₈	—	94	2	no	—
284	C₂×C₈	—	94	2	no	—
285	C₂×C₈	—	94	4	no	—
286	C₂×C₈	—	94	4	no	—
287	C₂×C₈	—	188	8	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₂²⋊C₄	—	2	4	no	—
292	C₂²⋊C₄	—	2	8	no	—
293	C₂²⋊C₄	C₂×C₄₇⋊C₈	1	16	yes	complemented
294	C₄²	—	2	4	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	2	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	2	no	—
300	C₄²	C₂×C₄₇⋊C₈	1	4	yes	complemented
301	C₄²	D₄×D₄₇	1	2	yes	—
302	C₄²	#10625352	1	2	yes	—
303	C₂³	—	2	2	no	—
304	C₂³	—	2	4	no	—
305	C₂³	—	2	4	no	—
306	C₂³	—	2	2	no	—
307	C₂³	C₂²×C₄₇⋊C₈	1	4	yes	—
308	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
309	Q₈	—	2	8	no	—
310	D₄	—	2	8	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
326	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
327	C₂×C₄	C₂²×C₄₇⋊C₈	1	4	yes	—
328	C₂×C₄	C₂²×C₄₇⋊C₈	1	4	yes	—
329	C₂×C₄	C₂²×C₄₇⋊C₈	1	2	yes	—
330	C₂×C₄	#13094031	1	4	yes	—
331	C₂×C₄	#13094031	1	2	yes	—
332	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
333	C₂×C₄	#41×D₄₇	1	2	yes	—
334	C₂×C₄	#41×D₄₇	1	2	yes	—
335	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
336	C₈	—	47	4	no	—
337	C₈	—	94	4	no	—
338	C₈	—	94	2	no	—
339	C₈	—	188	2	no	—
340	C₈	—	188	2	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	2	8	no	—
343	C₂²	—	4	2	no	—
344	C₂²	—	4	2	no	—
345	C₂²	—	4	4	no	—
346	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
347	C₂²	#41×Dic₄₇	1	2	yes	—
348	C₂²	C₂³×C₄₇⋊C₈	1	1	yes	characteristic
349	C₂²	C₂×#13094031	1	1	yes	characteristic
350	C₂²	C₂×#13094031	1	2	yes	—
351	C₄	—	2	4	no	—
352	C₄	—	2	4	no	—
353	C₄	—	2	2	no	—
354	C₄	—	2	4	no	—
355	C₄	—	4	2	no	—
356	C₄	—	4	2	no	—
357	C₄	D₄×C₄₇⋊C₈	1	4	yes	—
358	C₄	#124×D₄₇	1	1	yes	characteristic
359	C₄	#15689652	1	2	yes	—
360	C₄	#15689672	1	1	yes	characteristic
361	C₂	—	4	4	no	—
362	C₂	#124×Dic₄₇	1	1	yes	characteristic
363	C₂	C₂×D₄×C₄₇⋊C₈	1	1	yes	characteristic
364	C₂	#20252100	1	1	yes	characteristic
365	C₂	#41×C₄₇⋊C₈	1	2	yes	—
366	C₂	#20252364	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Fitting	C₄×#124×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×D₄×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×#124	D₄₇
hypocenter	C₄₇	C₈×#124
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#124

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×C₄₇⋊C₈	C₂	semidirect
3. #20244325	C₂	semidirect
5. #20243996	C₂	semidirect
6. #20243505	C₂	semidirect
7. C₂²⋊C₄×C₄₇⋊C₈	C₂	semidirect
8. C₄²×C₄₇⋊C₈	C₂	semidirect
54. #124×C₄₇	C₈	semidirect
76. C₂×Q₈×C₄₇	C₂×C₈	semidirect
97. C₂²⋊C₄×C₄₇	C₂×C₈	semidirect
104. C₄²×C₄₇	C₂×C₈	semidirect
156. C₄₇⋊C₈	#124	direct (N × H)
217. C₄₇	C₈×#124	semidirect
228. #124	C₄₇⋊C₈	direct (N × H)
260. C₂×Q₈	C₂×C₄₇⋊C₈	semidirect
293. C₂²⋊C₄	C₂×C₄₇⋊C₈	semidirect
300. C₄²	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
C₂×Q₈×C₄₇⋊C₈	2
C₂×D₄×C₄₇⋊C₈	2
#20244325	2
#20244183	2
#20243996	2
#20243505	2
C₂²⋊C₄×C₄₇⋊C₈	2
C₄²×C₄₇⋊C₈	2
C₄×#124×C₄₇	2
C₈×#124	47

Subgroups — #124×C47⋊C8 #26224144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #124×C₄₇⋊C₈ #26224144