Subgroups — #26110820

Order 12032.

604 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689180	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈⋊(C₄₇⋊C₈)	C₂	1	2	yes	maximal, complemented
4	#20241229	C₂	1	2	yes	maximal, complemented
5	C₄×C₂²⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
6	#15689180	—	2	4	no	—
7	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
8	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
9	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
10	C₂×#13093935	—	2	1	no	—
11	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
12	#15688878	—	2	1	no	—
13	Q₈⋊(C₄₇⋊C₈)	—	2	4	no	—
14	C₂×C₂²⋊Q₈×C₄₇	C₄	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
17	C₄₇×#391	C₄	1	1	yes	characteristic
18	C₄₇×#389	C₄	1	1	yes	characteristic
19	C₄₇×#387	—	2	1	no	—
20	C₄₇×#385	—	2	1	no	—
21	C₄₇×#380	C₄	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
23	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
25	C₂²×C₄₇⋊C₈	—	2	2	no	—
26	C₂²×C₄₇⋊C₈	—	2	2	no	—
27	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
28	C₄⋊(C₄₇⋊C₈)	D₄	1	4	yes	—
29	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
30	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
31	#13093935	—	2	4	no	—
32	C₄×C₄₇⋊C₈	—	2	2	no	—
33	C₄×C₄₇⋊C₈	—	2	2	no	—
34	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
38	C₂²⋊Q₈×C₄₇	—	2	2	no	—
39	C₂²⋊Q₈×C₄₇	—	2	2	no	—
40	C₄×Q₈×C₄₇	—	2	2	no	—
41	C₄×Q₈×C₄₇	—	2	2	no	—
42	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
43	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
44	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
45	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
49	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
50	C₂×C₄²×C₄₇	—	2	2	no	—
51	C₂×C₄²×C₄₇	—	2	2	no	—
52	C₂×C₄²×C₄₇	—	2	1	no	—
53	C₂×C₄²×C₄₇	—	2	1	no	—
54	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
58	#95×C₄₇	—	2	1	no	—
59	#95×C₄₇	—	2	1	no	—
60	#95×C₄₇	—	2	1	no	—
61	#95×C₄₇	—	2	1	no	—
62	#95×C₄₇	—	2	1	no	—
63	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×Q₈×C₄₇	—	2	1	no	—
65	C₂×Q₈×C₄₇	—	2	2	no	—
66	C₂×Q₈×C₄₇	—	2	2	no	—
67	C₂×Q₈×C₄₇	M₁₆	1	2	yes	—
68	C₂²×C₄×C₄₇	—	2	2	no	—
69	C₂²×C₄×C₄₇	—	2	1	no	—
70	C₂²×C₄×C₄₇	—	2	1	no	—
71	C₂²×C₄×C₄₇	—	2	2	no	—
72	C₂²×C₄×C₄₇	—	2	1	no	—
73	C₂²×C₄×C₄₇	—	2	2	no	—
74	C₂²×C₄×C₄₇	—	2	1	no	—
75	C₂²×C₄×C₄₇	—	2	1	no	—
76	C₂²×C₄×C₄₇	—	2	1	no	—
77	C₂²×C₄×C₄₇	—	2	2	no	—
78	C₂²×C₄×C₄₇	—	2	2	no	—
79	C₂²×C₄×C₄₇	—	2	2	no	—
80	C₂²×C₄×C₄₇	—	2	1	no	—
81	C₂²×C₄×C₄₇	—	2	1	no	—
82	C₂²×C₄×C₄₇	—	4	1	no	—
83	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
89	C₄⋊C₄×C₄₇	—	2	4	no	—
90	C₄⋊C₄×C₄₇	—	2	1	no	—
91	C₄⋊C₄×C₄₇	—	2	2	no	—
92	C₄⋊C₄×C₄₇	—	2	2	no	—
93	C₄⋊C₄×C₄₇	—	4	2	no	—
94	C₄⋊C₄×C₄₇	—	4	2	no	—
95	C₄⋊C₄×C₄₇	M₁₆	1	2	yes	—
96	C₂²⋊C₄×C₄₇	—	2	4	no	—
97	C₂²⋊C₄×C₄₇	—	4	2	no	—
98	C₄²×C₄₇	—	2	2	no	—
99	C₄²×C₄₇	—	2	1	no	—
100	C₄²×C₄₇	—	2	2	no	—
101	C₄²×C₄₇	—	2	1	no	—
102	C₄²×C₄₇	—	4	1	no	—
103	C₄²×C₄₇	—	4	1	no	—
104	C₄²×C₄₇	—	4	2	no	—
105	C₄²×C₄₇	C₂×D₄	1	2	yes	—
106	C₄²×C₄₇	#41	1	2	yes	—
107	C₂×C₄₇⋊C₈	—	2	4	no	—
108	C₂×C₄₇⋊C₈	—	2	4	no	—
109	C₂×C₄₇⋊C₈	—	4	2	no	—
110	C₂×C₄₇⋊C₈	—	4	2	no	—
111	C₂×C₄₇⋊C₈	—	4	2	no	—
112	C₂×C₄₇⋊C₈	—	4	2	no	—
113	C₂³×C₄₇	—	2	1	no	—
114	C₂³×C₄₇	—	2	1	no	—
115	C₂³×C₄₇	—	2	1	no	—
116	C₂³×C₄₇	—	2	1	no	—
117	C₂³×C₄₇	—	2	1	no	—
118	C₂³×C₄₇	—	2	1	no	—
119	C₂³×C₄₇	#104	1	2	yes	—
120	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	Q₈×C₄₇	—	2	4	no	—
122	Q₈×C₄₇	—	4	2	no	—
123	C₂×C₄×C₄₇	—	2	1	no	—
124	C₂×C₄×C₄₇	—	2	1	no	—
125	C₂×C₄×C₄₇	—	2	1	no	—
126	C₂×C₄×C₄₇	—	2	1	no	—
127	C₂×C₄×C₄₇	—	2	1	no	—
128	C₂×C₄×C₄₇	—	2	2	no	—
129	C₂×C₄×C₄₇	—	2	2	no	—
130	C₂×C₄×C₄₇	—	2	1	no	—
131	C₂×C₄×C₄₇	—	2	1	no	—
132	C₂×C₄×C₄₇	—	2	1	no	—
133	C₂×C₄×C₄₇	—	2	1	no	—
134	C₂×C₄×C₄₇	—	2	1	no	—
135	C₂×C₄×C₄₇	—	2	1	no	—
136	C₂×C₄×C₄₇	—	4	4	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	2	no	—
142	C₂×C₄×C₄₇	—	4	2	no	—
143	C₂×C₄×C₄₇	—	4	2	no	—
144	C₂×C₄×C₄₇	—	4	2	no	—
145	C₂×C₄×C₄₇	—	4	1	no	—
146	C₂×C₄×C₄₇	—	4	1	no	—
147	C₂×C₄×C₄₇	—	4	1	no	—
148	C₂×C₄×C₄₇	—	4	1	no	—
149	C₂×C₄×C₄₇	—	4	1	no	—
150	C₂×C₄×C₄₇	—	4	1	no	—
151	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
152	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
153	C₂×C₄×C₄₇	#121	1	2	yes	—
154	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
157	C₂×C₄×C₄₇	#131	1	2	yes	—
158	C₂×C₄×C₄₇	#135	1	2	yes	—
159	C₂×C₄×C₄₇	#137	1	2	yes	—
160	C₄₇⋊C₈	—	4	4	no	—
161	C₄₇⋊C₈	—	4	4	no	—
162	#8941	—	47	1	no	maximal, Sylow
163	C₂²×C₄₇	—	2	2	no	—
164	C₂²×C₄₇	—	2	2	no	—
165	C₂²×C₄₇	—	2	2	no	—
166	C₂²×C₄₇	—	4	1	no	—
167	C₂²×C₄₇	—	4	1	no	—
168	C₂²×C₄₇	—	4	1	no	—
169	C₂²×C₄₇	—	4	1	no	—
170	C₂²×C₄₇	#386	1	1	yes	characteristic
171	C₂²×C₄₇	#407	1	1	yes	characteristic
172	C₂²×C₄₇	#408	1	1	yes	characteristic
173	C₂²×C₄₇	#416	1	1	yes	characteristic
174	C₂²×C₄₇	#419	1	1	yes	characteristic
175	C₂²×C₄₇	C₂×#104	1	1	yes	characteristic
176	C₂²×C₄₇	#421	1	1	yes	characteristic
177	C₄×C₄₇	—	2	2	no	—
178	C₄×C₄₇	—	4	1	no	—
179	C₄×C₄₇	—	4	2	no	—
180	C₄×C₄₇	—	4	1	no	—
181	C₄×C₄₇	—	4	1	no	—
182	C₄×C₄₇	—	4	2	no	—
183	C₄×C₄₇	—	8	1	no	—
184	C₄×C₄₇	—	8	1	no	—
185	C₄×C₄₇	#435	1	2	yes	—
186	C₄×C₄₇	#436	1	2	yes	—
187	C₄×C₄₇	#452	1	2	yes	—
188	C₄×C₄₇	#485	1	2	yes	—
189	C₂×#432	—	47	1	no	—
190	C₄×C₂²⋊Q₈	D₄₇	1	1	yes	characteristic
191	C₄×C₂²⋊C₈	—	47	1	no	—
192	C₂×Q₈⋊C₈	—	47	2	no	—
193	#1279	—	47	2	no	—
194	C₂×C₄₇	—	4	2	no	—
195	C₂×C₄₇	#1488	1	1	yes	characteristic
196	C₂×C₄₇	#1491	1	1	yes	characteristic
197	C₂×C₄₇	#1494	1	1	yes	characteristic
198	C₂×C₄₇	#1497	1	1	yes	characteristic
199	C₂×C₄₇	#1870	1	1	yes	characteristic
200	C₂×C₄₇	#1871	1	1	yes	characteristic
201	C₂×C₄₇	#1873	1	1	yes	characteristic
202	C₂×C₂²⋊Q₈	Dic₄₇	1	1	yes	characteristic
203	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
204	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
205	#432	—	94	4	no	—
206	C₂×C₄⋊C₈	—	47	2	no	—
207	C₂×C₂²⋊C₈	—	94	1	no	—
208	C₂×C₂²⋊C₈	—	94	1	no	—
209	C₂×#97	—	94	1	no	—
210	C₂×C₄×C₈	—	47	2	no	—
211	#391	Dic₄₇	1	1	yes	characteristic
212	#389	Dic₄₇	1	1	yes	characteristic
213	#387	—	2	1	no	—
214	#385	—	2	1	no	—
215	#380	Dic₄₇	1	1	yes	characteristic
216	C₄×C₄⋊C₄	—	2	1	no	—
217	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
218	C₄×C₂²⋊C₄	—	2	1	no	—
219	#336	—	94	1	no	—
220	Q₈⋊C₈	—	94	4	no	—
221	C₄₇	#8941	1	1	yes	characteristic, complemented, Sylow
222	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
223	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
224	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
225	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
226	C₂²×C₈	—	94	2	no	—
227	C₂²×C₈	—	94	2	no	—
228	C₂²⋊Q₈	—	2	2	no	—
229	C₂²⋊Q₈	—	2	2	no	—
230	C₄×Q₈	—	2	2	no	—
231	C₄×Q₈	—	2	2	no	—
232	C₂×C₄⋊C₄	—	2	1	no	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	—	2	1	no	—
235	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
237	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
238	C₂×C₂²⋊C₄	—	2	1	no	—
239	C₂×C₂²⋊C₄	—	2	1	no	—
240	C₂×C₄²	—	2	2	no	—
241	C₂×C₄²	—	2	2	no	—
242	C₂×C₄²	—	2	1	no	—
243	C₂×C₄²	—	2	1	no	—
244	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
245	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
246	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
247	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
248	C₄⋊C₈	—	47	4	no	—
249	C₄⋊C₈	—	94	2	no	—
250	C₂²⋊C₈	—	94	4	no	—
251	C₂²⋊C₈	—	94	4	no	—
252	#97	—	94	4	no	—
253	C₄×C₈	—	94	2	no	—
254	C₄×C₈	—	94	2	no	—
255	#95	—	2	1	no	—
256	#95	—	2	1	no	—
257	#95	—	2	1	no	—
258	#95	—	2	1	no	—
259	#95	—	2	1	no	—
260	C₂⁴	C₂²⋊Dic₄₇	1	1	yes	characteristic
261	C₂×Q₈	—	2	1	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	2	2	no	—
264	C₂×Q₈	#10625329	1	2	yes	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
281	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
282	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
283	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
286	C₂×C₈	—	94	4	no	—
287	C₂×C₈	—	94	4	no	—
288	C₂×C₈	—	188	2	no	—
289	C₂×C₈	—	188	2	no	—
290	C₂×C₈	—	188	2	no	—
291	C₂×C₈	—	188	2	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	1	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	4	2	no	—
297	C₄⋊C₄	—	4	2	no	—
298	C₄⋊C₄	#10625329	1	2	yes	—
299	C₂²⋊C₄	—	2	4	no	—
300	C₂²⋊C₄	—	4	2	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	1	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	1	no	—
305	C₄²	—	4	1	no	—
306	C₄²	—	4	1	no	—
307	C₄²	—	4	2	no	—
308	C₄²	D₄×D₄₇	1	2	yes	—
309	C₄²	#10625352	1	2	yes	—
310	C₂³	—	2	1	no	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	1	no	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	1	no	—
316	C₂³	#13093951	1	2	yes	—
317	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
318	Q₈	—	2	4	no	—
319	Q₈	—	4	2	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
349	C₂×C₄	#13093992	1	1	yes	characteristic
350	C₂×C₄	#13093996	1	2	yes	—
351	C₂×C₄	#13094005	1	1	yes	characteristic
352	C₂×C₄	C₂×#10625329	1	1	yes	characteristic
353	C₂×C₄	C₂×#10625329	1	1	yes	characteristic
354	C₂×C₄	#13094031	1	2	yes	—
355	C₂×C₄	#13094044	1	2	yes	—
356	C₂×C₄	#13094055	1	2	yes	—
357	C₈	—	188	4	no	—
358	C₈	—	188	4	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	4	1	no	—
363	C₂²	—	4	1	no	—
364	C₂²	—	4	1	no	—
365	C₂²	—	4	1	no	—
366	C₂²	#15689003	1	1	yes	characteristic
367	C₂²	#15689087	1	1	yes	characteristic
368	C₂²	#15689090	1	1	yes	characteristic
369	C₂²	#15689119	1	1	yes	characteristic
370	C₂²	#15689132	1	1	yes	characteristic
371	C₂²	C₂×#13093951	1	1	yes	characteristic
372	C₂²	#15689140	1	1	yes	characteristic
373	C₄	—	2	2	no	—
374	C₄	—	4	2	no	—
375	C₄	—	4	1	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	1	no	—
378	C₄	—	4	1	no	—
379	C₄	—	8	1	no	—
380	C₄	—	8	1	no	—
381	C₄	#15689195	1	2	yes	—
382	C₄	#15689201	1	2	yes	—
383	C₄	#15689283	1	2	yes	—
384	C₄	#15689461	1	2	yes	—
385	C₂	—	4	2	no	—
386	C₂	#20241822	1	1	yes	characteristic
387	C₂	#20241835	1	1	yes	characteristic
388	C₂	#20241848	1	1	yes	characteristic
389	C₂	#20241861	1	1	yes	characteristic
390	C₂	#20243686	1	1	yes	characteristic
391	C₂	#20243691	1	1	yes	characteristic
392	C₂	#20243701	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂²×C₄×C₄₇	C₂²×C₄
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	#8941
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×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. C₂×Q₈⋊(C₄₇⋊C₈)	C₂	semidirect
4. #20241229	C₂	semidirect
221. C₄₇	#8941	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689180	2
C₄×C₂²⋊(C₄₇⋊C₈)	2
C₂×Q₈⋊(C₄₇⋊C₈)	2
#20241229	2
C₄×C₂²⋊Q₈×C₄₇	2
#8941	47