Subgroups — #26104343

Order 12032.

578 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	#20243368	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×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
8	C₂×C₂²⋊(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	C₄⋊(C₄₇⋊C₈)	—	4	2	no	—
29	C₂²⋊(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	1	no	—
65	C₂²×C₄×C₄₇	—	2	1	no	—
66	C₂²×C₄×C₄₇	—	2	1	no	—
67	C₂²×C₄×C₄₇	—	2	1	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	—	4	1	no	—
74	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	C₂×C₈	1	2	yes	—
78	C₂²×C₄×C₄₇	M₁₆	1	2	yes	—
79	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
80	C₂²×C₄×C₄₇	Q₁₆	1	2	yes	—
81	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
84	C₄⋊C₄×C₄₇	—	2	4	no	—
85	C₄⋊C₄×C₄₇	—	2	1	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	—	4	1	no	—
90	C₄⋊C₄×C₄₇	—	4	1	no	—
91	C₄⋊C₄×C₄₇	C₂×C₈	1	2	yes	complemented
92	C₂²⋊C₄×C₄₇	—	2	4	no	—
93	C₂²⋊C₄×C₄₇	—	4	2	no	—
94	C₄²×C₄₇	—	2	2	no	—
95	C₄²×C₄₇	—	2	2	no	—
96	C₄²×C₄₇	—	4	1	no	—
97	C₄²×C₄₇	—	4	1	no	—
98	C₄²×C₄₇	—	4	2	no	—
99	C₄²×C₄₇	—	4	2	no	—
100	C₂×C₄₇⋊C₈	—	2	4	no	—
101	C₂×C₄₇⋊C₈	—	4	8	no	—
102	C₂×C₄₇⋊C₈	—	4	2	no	—
103	C₂×C₄₇⋊C₈	—	4	2	no	—
104	C₂×C₄₇⋊C₈	—	4	2	no	—
105	C₂×C₄₇⋊C₈	—	4	2	no	—
106	C₂×C₄₇⋊C₈	—	4	2	no	—
107	C₂³×C₄₇	—	2	1	no	—
108	C₂³×C₄₇	—	2	1	no	—
109	C₂³×C₄₇	—	2	1	no	—
110	C₂³×C₄₇	—	2	1	no	—
111	C₂³×C₄₇	C₂²⋊C₈	1	2	yes	—
112	C₂³×C₄₇	#103	1	2	yes	—
113	C₂³×C₄₇	#104	1	2	yes	—
114	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	Q₈×C₄₇	—	4	2	no	—
116	Q₈×C₄₇	—	4	2	no	—
117	C₂×C₄×C₄₇	—	2	4	no	—
118	C₂×C₄×C₄₇	—	2	4	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	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	1	no	—
129	C₂×C₄×C₄₇	—	2	1	no	—
130	C₂×C₄×C₄₇	—	2	1	no	—
131	C₂×C₄×C₄₇	—	2	2	no	—
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	4	2	no	—
134	C₂×C₄×C₄₇	—	4	2	no	—
135	C₂×C₄×C₄₇	—	4	2	no	—
136	C₂×C₄×C₄₇	—	4	2	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	—	4	1	no	—
144	C₂×C₄×C₄₇	—	4	1	no	—
145	C₂×C₄×C₄₇	—	4	1	no	—
146	C₂×C₄×C₄₇	—	4	1	no	—
147	C₂×C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
148	C₂×C₄×C₄₇	#99	1	2	yes	—
149	C₂×C₄×C₄₇	#103	1	2	yes	—
150	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
154	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
156	C₄₇⋊C₈	—	4	4	no	—
157	C₄₇⋊C₈	—	8	2	no	—
158	#7589	—	47	1	no	maximal, Sylow
159	C₂²×C₄₇	—	2	2	no	—
160	C₂²×C₄₇	—	2	2	no	—
161	C₂²×C₄₇	—	2	2	no	—
162	C₂²×C₄₇	—	2	2	no	—
163	C₂²×C₄₇	—	2	2	no	—
164	C₂²×C₄₇	—	2	2	no	—
165	C₂²×C₄₇	Q₈⋊C₈	1	4	yes	—
166	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
167	C₂²×C₄₇	C₂×#99	1	1	yes	characteristic
168	C₂²×C₄₇	#413	1	1	yes	characteristic
169	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
170	C₂²×C₄₇	#417	1	1	yes	characteristic
171	C₂²×C₄₇	C₂×#104	1	1	yes	characteristic
172	C₂²×C₄₇	#421	1	1	yes	characteristic
173	C₄×C₄₇	—	2	2	no	—
174	C₄×C₄₇	—	2	1	no	—
175	C₄×C₄₇	—	2	1	no	—
176	C₄×C₄₇	—	2	1	no	—
177	C₄×C₄₇	—	2	2	no	—
178	C₄×C₄₇	—	2	1	no	—
179	C₄×C₄₇	—	2	1	no	—
180	C₄×C₄₇	—	2	2	no	—
181	C₄×C₄₇	—	2	1	no	—
182	C₄×C₄₇	—	4	2	no	—
183	C₄×C₄₇	—	4	2	no	—
184	C₄×C₄₇	—	8	1	no	—
185	C₄×C₄₇	—	8	1	no	—
186	C₄×C₂²⋊Q₈	D₄₇	1	1	yes	characteristic
187	#1797	—	47	1	no	—
188	C₂×#336	—	47	1	no	—
189	#1272	—	47	2	no	—
190	#1271	—	47	2	no	—
191	C₂×C₄₇	—	2	4	no	—
192	C₂×C₄₇	#1459	1	1	yes	characteristic
193	C₂×C₄₇	C₂×Q₈⋊C₈	1	1	yes	characteristic
194	C₂×C₄₇	#1477	1	1	yes	characteristic
195	C₂×C₄₇	#1504	1	1	yes	characteristic
196	C₂×C₄₇	#1520	1	1	yes	characteristic
197	C₂×C₄₇	#1532	1	1	yes	characteristic
198	C₂×C₄₇	#1550	1	1	yes	characteristic
199	C₂³×C₈	—	94	1	no	—
200	C₂×C₂²⋊Q₈	Dic₄₇	1	1	yes	characteristic
201	C₂×C₄×Q₈	Dic₄₇	1	1	yes	characteristic
202	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
203	C₂×C₄⋊C₈	—	94	1	no	—
204	C₂×C₂²⋊C₈	—	94	1	no	—
205	#391	C₂×D₄₇	1	1	yes	characteristic
206	#389	C₂×D₄₇	1	1	yes	characteristic
207	#387	—	2	1	no	—
208	#385	—	2	1	no	—
209	#380	Dic₄₇	1	1	yes	characteristic
210	C₄×C₄⋊C₄	—	2	1	no	—
211	C₄×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
212	C₄×C₂²⋊C₄	—	2	1	no	—
213	#336	—	47	2	no	—
214	#336	—	47	2	no	—
215	#336	—	94	1	no	—
216	C₄₇	#7589	1	1	yes	characteristic, complemented, Sylow
217	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
218	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
219	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
220	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
221	C₂²×C₈	—	94	4	no	—
222	C₂²×C₈	—	94	2	no	—
223	C₂²×C₈	—	94	2	no	—
224	C₂²×C₈	—	188	2	no	—
225	C₂²×C₈	—	188	2	no	—
226	C₂²⋊Q₈	—	2	2	no	—
227	C₂²⋊Q₈	C₄₇⋊C₈	1	4	yes	complemented
228	C₄×Q₈	—	4	2	no	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₄⋊C₄	—	2	1	no	—
231	C₂×C₄⋊C₄	—	2	1	no	—
232	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
235	C₂×C₂²⋊C₄	—	2	1	no	—
236	C₂×C₂²⋊C₄	—	2	1	no	—
237	C₂×C₄²	—	2	1	no	—
238	C₂×C₄²	—	2	1	no	—
239	C₂×C₄²	—	4	2	no	—
240	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
241	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
242	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
243	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
244	C₄⋊C₈	—	188	2	no	—
245	C₂²⋊C₈	—	188	2	no	—
246	#95	—	2	1	no	—
247	#95	—	2	1	no	—
248	#95	—	2	1	no	—
249	#95	—	2	1	no	—
250	#95	—	2	1	no	—
251	C₂⁴	C₂²⋊Dic₄₇	1	1	yes	characteristic
252	C₂×Q₈	—	2	1	no	—
253	C₂×Q₈	—	4	1	no	—
254	C₂×Q₈	—	4	1	no	—
255	C₂×Q₈	C₂×C₄₇⋊C₈	1	2	yes	complemented
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	2	1	no	—
261	C₂²×C₄	—	2	1	no	—
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	4	1	no	—
265	C₂²×C₄	—	4	1	no	—
266	C₂²×C₄	—	4	1	no	—
267	C₂²×C₄	—	4	1	no	—
268	C₂²×C₄	C₂×C₄₇⋊C₈	1	2	yes	—
269	C₂²×C₄	#10625329	1	2	yes	—
270	C₂²×C₄	#10625336	1	2	yes	—
271	C₂²×C₄	#10625337	1	2	yes	—
272	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
273	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
274	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
275	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
278	C₂×C₈	—	94	4	no	—
279	C₂×C₈	—	188	2	no	—
280	C₂×C₈	—	188	2	no	—
281	C₂×C₈	—	188	2	no	—
282	C₂×C₈	—	188	8	no	—
283	C₂×C₈	—	188	2	no	—
284	C₂×C₈	—	188	2	no	—
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	—	2	1	no	—
287	C₄⋊C₄	—	4	1	no	—
288	C₄⋊C₄	—	4	1	no	—
289	C₄⋊C₄	—	4	2	no	—
290	C₄⋊C₄	—	4	1	no	—
291	C₄⋊C₄	—	4	1	no	—
292	C₄⋊C₄	C₂×C₄₇⋊C₈	1	2	yes	complemented
293	C₂²⋊C₄	—	2	4	no	—
294	C₂²⋊C₄	—	4	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	4	1	no	—
298	C₄²	—	4	1	no	—
299	C₄²	—	4	2	no	—
300	C₄²	—	4	2	no	—
301	C₂³	—	2	1	no	—
302	C₂³	—	2	1	no	—
303	C₂³	—	2	1	no	—
304	C₂³	—	2	1	no	—
305	C₂³	C₂²⋊(C₄₇⋊C₈)	1	2	yes	—
306	C₂³	#13093948	1	2	yes	—
307	C₂³	#13093951	1	2	yes	—
308	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
309	Q₈	—	4	2	no	—
310	Q₈	—	4	2	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	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	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	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	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	C₂²⋊(C₄₇⋊C₈)	1	2	yes	—
342	C₂×C₄	#13093939	1	2	yes	—
343	C₂×C₄	#13093948	1	2	yes	—
344	C₂×C₄	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
345	C₂×C₄	C₂×#10625329	1	1	yes	characteristic
346	C₂×C₄	C₂×#10625336	1	1	yes	characteristic
347	C₂×C₄	C₂×#10625337	1	1	yes	characteristic
348	C₂×C₄	#13094049	1	1	yes	characteristic
349	C₂×C₄	#13094054	1	1	yes	characteristic
350	C₈	—	376	2	no	—
351	C₈	—	188	4	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	Q₈⋊(C₄₇⋊C₈)	1	4	yes	—
359	C₂²	C₂×C₂²⋊(C₄₇⋊C₈)	1	1	yes	characteristic
360	C₂²	C₂×#13093939	1	1	yes	characteristic
361	C₂²	#15689107	1	1	yes	characteristic
362	C₂²	C₂×#13093948	1	1	yes	characteristic
363	C₂²	#15689124	1	1	yes	characteristic
364	C₂²	C₂×#13093951	1	1	yes	characteristic
365	C₂²	#15689140	1	1	yes	characteristic
366	C₄	—	2	1	no	—
367	C₄	—	2	2	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	2	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	1	no	—
375	C₄	—	4	2	no	—
376	C₄	—	4	2	no	—
377	C₄	—	8	1	no	—
378	C₄	—	8	1	no	—
379	C₂	—	2	4	no	—
380	C₂	#20241706	1	1	yes	characteristic
381	C₂	C₂×Q₈⋊(C₄₇⋊C₈)	1	1	yes	characteristic
382	C₂	#20241775	1	1	yes	characteristic
383	C₂	#20241892	1	1	yes	characteristic
384	C₂	#20241960	1	1	yes	characteristic
385	C₂	#20242008	1	1	yes	characteristic
386	C₂	#20242078	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×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	#7589
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ 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
91. C₄⋊C₄×C₄₇	C₂×C₈	semidirect
216. C₄₇	#7589	semidirect
227. C₂²⋊Q₈	C₄₇⋊C₈	semidirect
255. C₂×Q₈	C₂×C₄₇⋊C₈	semidirect
292. 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
#20243368	2
C₂×#15688878	2
#20241214	2
#20241211	2
C₄×C₂²⋊Q₈×C₄₇	2
#7589	47