Subgroups — #26235091

Order 12032.

832 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689253	C₂	1	2	yes	maximal
2	C₄²×Dic₉₄	C₂	1	1	yes	maximal, characteristic
3	#20244110	C₂	1	4	yes	maximal
4	#20244106	C₂	1	2	yes	maximal
5	#20243540	C₂	1	1	yes	maximal, characteristic
6	#20243539	C₂	1	2	yes	maximal
7	#20243243	C₂	1	2	yes	maximal
8	C₄×C₄⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×Dic₉₄	C₄	1	1	yes	characteristic
10	C₂×C₄×Dic₉₄	C₄	1	1	yes	characteristic
11	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
12	#15689253	—	2	8	no	—
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
16	C₂×Dic₄₇⋊C₈	C₂²	1	4	yes	—
17	C₂×Dic₄₇⋊C₈	C₂²	1	4	yes	—
18	C₂×#13093934	C₂²	1	4	yes	—
19	C₄×Dic₄₇⋊C₄	C₄	1	2	yes	—
20	C₄×Dic₄₇⋊C₄	C₄	1	2	yes	—
21	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
22	C₄×C₄⋊Dic₄₇	C₄	1	1	yes	characteristic
23	C₄×C₄⋊Dic₄₇	C₄	1	1	yes	characteristic
24	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
25	C₄²×Dic₄₇	C₂²	1	2	yes	—
26	#15688877	C₂²	1	4	yes	—
27	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
30	C₄³×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#336	C₂²	1	2	yes	—
32	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
34	C₄×Dic₉₄	—	2	4	no	—
35	C₄×Dic₉₄	—	2	4	no	—
36	C₄×Dic₉₄	D₄	1	4	yes	—
37	C₄×Dic₉₄	Q₈	1	4	yes	—
38	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
41	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
42	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
43	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
44	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
45	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
46	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
47	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
48	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
49	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
50	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
51	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
52	C₄⋊(C₄₇⋊C₈)	—	4	2	no	—
53	Dic₄₇⋊C₈	—	2	8	no	—
54	Dic₄₇⋊C₈	—	4	4	no	—
55	#13093934	—	2	8	no	—
56	C₄₇⋊#95	C₂×C₄	1	2	yes	—
57	C₄₇⋊#95	C₂×C₄	1	2	yes	—
58	C₄₇⋊#95	C₂×C₄	1	2	yes	—
59	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
60	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
61	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₄₇	—	2	2	no	—
69	C₄⋊C₈×C₄₇	Q₈	1	4	yes	complemented
70	C₄×C₈×C₄₇	—	2	4	no	—
71	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
78	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
79	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
80	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
81	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
82	C₂×Dic₉₄	—	2	2	no	—
83	C₂×Dic₉₄	—	2	2	no	—
84	C₂×Dic₉₄	C₄⋊C₄	1	4	yes	—
85	C₂×C₈×C₄₇	—	2	2	no	—
86	C₂×C₈×C₄₇	—	2	2	no	—
87	C₂×C₈×C₄₇	—	2	2	no	—
88	C₂×C₈×C₄₇	—	2	2	no	—
89	C₂×C₈×C₄₇	—	2	2	no	—
90	C₂×C₈×C₄₇	C₂×Q₈	1	4	yes	—
91	C₄²×C₄₇	—	2	2	no	—
92	C₄²×C₄₇	—	2	2	no	—
93	C₄²×C₄₇	—	2	1	no	—
94	C₄²×C₄₇	—	2	1	no	—
95	C₄²×C₄₇	—	4	1	no	—
96	C₄²×C₄₇	M₁₆	1	4	yes	—
97	C₄²×C₄₇	C₂×D₄	1	2	yes	—
98	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
99	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
100	C₄²×C₄₇	#41	1	2	yes	—
101	C₄⋊Dic₄₇	—	2	2	no	—
102	C₄⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
103	C₄⋊Dic₄₇	M₁₆	1	4	yes	—
104	Dic₄₇⋊C₄	—	2	4	no	—
105	Dic₄₇⋊C₄	—	2	4	no	—
106	Dic₄₇⋊C₄	C₄⋊C₄	1	8	yes	—
107	C₄×Dic₄₇	—	2	4	no	—
108	C₄×Dic₄₇	—	2	4	no	—
109	C₄×Dic₄₇	—	2	2	no	—
110	C₄×Dic₄₇	—	2	2	no	—
111	C₄×Dic₄₇	—	2	4	no	—
112	C₄×Dic₄₇	—	4	2	no	—
113	C₄×Dic₄₇	C₂×D₄	1	4	yes	—
114	C₄×Dic₄₇	C₂×Q₈	1	4	yes	—
115	C₂×C₄₇⋊C₈	—	2	4	no	—
116	C₂×C₄₇⋊C₈	—	2	4	no	—
117	C₂×C₄₇⋊C₈	—	2	4	no	—
118	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
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	C₂×C₄⋊C₄	1	2	yes	—
129	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
130	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
131	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
132	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
133	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
134	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
135	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
136	C₂×C₄×C₄₇	#131	1	2	yes	—
137	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
138	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
139	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
140	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
141	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
142	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
143	C₂×Dic₄₇	—	2	2	no	—
144	C₂×Dic₄₇	—	2	2	no	—
145	C₂×Dic₄₇	—	2	2	no	—
146	C₂×Dic₄₇	—	2	2	no	—
147	C₂×Dic₄₇	—	2	2	no	—
148	C₂×Dic₄₇	—	2	2	no	—
149	C₂×Dic₄₇	—	2	2	no	—
150	C₂×Dic₄₇	—	2	2	no	—
151	C₂×Dic₄₇	—	2	2	no	—
152	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
153	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
154	C₂×Dic₄₇	C₂×M₁₆	1	4	yes	—
155	Dic₉₄	—	2	8	no	—
156	C₈×C₄₇	—	2	4	no	—
157	C₈×C₄₇	—	4	2	no	—
158	C₄₇⋊C₈	—	4	4	no	—
159	#22722	—	47	1	no	maximal, Sylow
160	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
161	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
162	C₂²×C₄₇	#520	1	1	yes	characteristic
163	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
164	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
165	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
166	C₂²×C₄₇	#568	1	1	yes	characteristic
167	C₄×C₄₇	—	2	2	no	—
168	C₄×C₄₇	—	2	2	no	—
169	C₄×C₄₇	—	2	2	no	—
170	C₄×C₄₇	—	4	1	no	—
171	C₄×C₄₇	#423	1	4	yes	—
172	C₄×C₄₇	#446	1	4	yes	complemented
173	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
174	C₄×C₄₇	#550	1	1	yes	characteristic
175	C₄×C₄₇	#557	1	1	yes	characteristic
176	C₄×C₄₇	Q₈²	1	1	yes	characteristic
177	Dic₄₇	—	2	4	no	—
178	Dic₄₇	—	2	4	no	—
179	Dic₄₇	—	2	4	no	—
180	Dic₄₇	—	4	2	no	—
181	C₂×#446	—	47	2	no	—
182	C₄²×Q₈	—	47	1	no	—
183	#1940	—	47	4	no	—
184	#1939	—	47	2	no	—
185	#1842	—	47	2	no	—
186	#1842	—	47	1	no	—
187	#1767	—	47	2	no	—
188	C₄×C₄⋊C₈	D₄₇	1	1	yes	characteristic
189	C₂×C₄₇	Q₈×C₄⋊C₄	1	1	yes	characteristic
190	C₂×C₄₇	C₂×#423	1	1	yes	characteristic
191	C₂×C₄₇	#2906	1	1	yes	characteristic
192	C₂×C₄₇	C₂×#446	1	1	yes	characteristic
193	C₂×C₄₇	Q₈×M₁₆	1	1	yes	characteristic
194	C₂×C₄₇	#2989	1	1	yes	characteristic
195	C₂×C₄₇	#2990	1	1	yes	characteristic
196	C₂×C₄×Q₈	—	47	1	no	—
197	C₂×C₄×Q₈	—	47	1	no	—
198	C₂×C₄×Q₈	—	47	1	no	—
199	#446	—	94	8	no	—
200	C₂×C₄⋊C₈	—	47	4	no	—
201	C₂×C₄⋊C₈	—	47	2	no	—
202	C₂×C₄⋊C₈	—	47	2	no	—
203	C₂×C₄⋊C₈	—	47	4	no	—
204	C₂×C₄⋊C₈	—	47	2	no	—
205	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
206	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
207	C₂×#97	—	47	4	no	—
208	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
209	C₄×C₄⋊C₄	—	47	1	no	—
210	C₄×C₄⋊C₄	—	47	1	no	—
211	C₄×C₄⋊C₄	—	47	2	no	—
212	C₄×C₄⋊C₄	—	47	2	no	—
213	C₄×C₄⋊C₄	—	47	1	no	—
214	C₄×C₄⋊C₄	—	47	2	no	—
215	C₄³	—	47	2	no	—
216	C₄³	C₂×D₄₇	1	1	yes	characteristic
217	#336	—	47	4	no	—
218	#336	C₂×D₄₇	1	2	yes	—
219	C₄₇	#22722	1	1	yes	characteristic, complemented, Sylow
220	C₂²×Q₈	—	47	1	no	—
221	C₂²×C₈	—	47	4	no	—
222	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
223	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
224	C₄×Q₈	—	47	4	no	—
225	C₄×Q₈	—	47	4	no	—
226	C₄×Q₈	—	94	4	no	—
227	C₄×Q₈	—	94	4	no	—
228	C₂×C₄⋊C₄	—	47	2	no	—
229	C₂×C₄⋊C₄	—	47	1	no	—
230	C₂×C₄⋊C₄	—	47	1	no	—
231	C₂×C₄⋊C₄	—	47	2	no	—
232	C₂×C₄⋊C₄	—	47	2	no	—
233	C₂×C₄⋊C₄	—	47	1	no	—
234	C₂×C₄²	—	47	2	no	—
235	C₂×C₄²	—	47	2	no	—
236	C₂×C₄²	—	47	2	no	—
237	C₂×C₄²	—	47	2	no	—
238	C₂×C₄²	—	47	2	no	—
239	C₂×C₄²	—	47	2	no	—
240	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
241	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
242	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
243	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
244	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
245	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
246	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
247	C₄⋊C₈	—	2	2	no	—
248	C₄⋊C₈	—	94	8	no	—
249	C₄⋊C₈	—	94	4	no	—
250	C₄⋊C₈	—	94	4	no	—
251	C₄⋊C₈	—	188	2	no	—
252	C₄⋊C₈	—	188	4	no	—
253	C₄⋊C₈	Dic₉₄	1	4	yes	complemented
254	#97	—	94	8	no	—
255	C₄×C₈	—	2	4	no	—
256	#95	—	47	2	no	—
257	#95	—	47	2	no	—
258	#95	—	47	2	no	—
259	C₂×Q₈	—	47	4	no	—
260	C₂×Q₈	—	94	2	no	—
261	C₂×Q₈	—	94	2	no	—
262	C₂²×C₄	—	47	2	no	—
263	C₂²×C₄	—	47	2	no	—
264	C₂²×C₄	—	47	2	no	—
265	C₂²×C₄	—	47	2	no	—
266	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
267	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
272	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	2	2	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	94	4	no	—
279	C₂×C₈	—	94	4	no	—
280	C₂×C₈	—	94	4	no	—
281	C₂×C₈	C₂×Dic₉₄	1	4	yes	—
282	C₄⋊C₄	—	47	8	no	—
283	C₄⋊C₄	—	47	4	no	—
284	C₄⋊C₄	—	47	4	no	—
285	C₄⋊C₄	—	94	4	no	—
286	C₄⋊C₄	—	94	4	no	—
287	C₄⋊C₄	—	94	2	no	—
288	C₄²	—	2	2	no	—
289	C₄²	—	2	2	no	—
290	C₄²	—	2	1	no	—
291	C₄²	—	2	1	no	—
292	C₄²	—	4	1	no	—
293	C₄²	—	47	4	no	—
294	C₄²	—	47	4	no	—
295	C₄²	—	94	4	no	—
296	C₄²	—	94	4	no	—
297	C₄²	—	94	4	no	—
298	C₄²	—	94	2	no	—
299	C₄²	—	94	2	no	—
300	C₄²	—	188	2	no	—
301	C₄²	#10625324	1	4	yes	—
302	C₄²	C₂×Dic₉₄	1	2	yes	—
303	C₄²	#10625350	1	2	yes	—
304	C₄²	D₄×D₄₇	1	2	yes	—
305	C₄²	Q₈×D₄₇	1	2	yes	—
306	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
307	Q₈	—	94	8	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	1	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	—	47	4	no	—
318	C₂×C₄	—	47	4	no	—
319	C₂×C₄	—	47	4	no	—
320	C₂×C₄	—	94	2	no	—
321	C₂×C₄	—	94	2	no	—
322	C₂×C₄	—	94	2	no	—
323	C₂×C₄	—	94	2	no	—
324	C₂×C₄	—	94	2	no	—
325	C₂×C₄	—	94	2	no	—
326	C₂×C₄	—	94	2	no	—
327	C₂×C₄	—	94	2	no	—
328	C₂×C₄	—	94	2	no	—
329	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
330	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
331	C₂×C₄	C₄×Dic₉₄	1	2	yes	—
332	C₂×C₄	C₄×Dic₉₄	1	2	yes	—
333	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
334	C₂×C₄	C₂×#10625324	1	2	yes	—
335	C₂×C₄	C₂×#10625324	1	2	yes	—
336	C₂×C₄	C₂×#10625324	1	2	yes	—
337	C₂×C₄	#13094030	1	2	yes	—
338	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
339	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
340	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
341	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
342	C₂×C₄	#13094070	1	1	yes	characteristic
343	C₂×C₄	#13094071	1	1	yes	characteristic
344	C₈	—	2	4	no	—
345	C₈	—	4	2	no	—
346	C₈	—	188	4	no	—
347	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
348	C₂²	C₂×C₄×Dic₉₄	1	1	yes	characteristic
349	C₂²	#15689603	1	1	yes	characteristic
350	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
351	C₂²	C₂²×#10625324	1	1	yes	characteristic
352	C₂²	C₂×#13094030	1	1	yes	characteristic
353	C₂²	#15689889	1	1	yes	characteristic
354	C₄	—	2	2	no	—
355	C₄	—	2	2	no	—
356	C₄	—	2	2	no	—
357	C₄	—	4	1	no	—
358	C₄	—	94	4	no	—
359	C₄	—	94	4	no	—
360	C₄	—	94	4	no	—
361	C₄	—	188	2	no	—
362	C₄	#15689145	1	4	yes	—
363	C₄	#15689253	1	4	yes	complemented
364	C₄	D₄×Dic₉₄	1	1	yes	characteristic
365	C₄	#15689794	1	1	yes	characteristic
366	C₄	#15689851	1	1	yes	characteristic
367	C₄	Q₈×Dic₉₄	1	1	yes	characteristic
368	C₂	C₄⋊C₄×Dic₉₄	1	1	yes	characteristic
369	C₂	C₂×#15689145	1	1	yes	characteristic
370	C₂	#20251953	1	1	yes	characteristic
371	C₂	C₂×#15689253	1	1	yes	characteristic
372	C₂	M₁₆×Dic₉₄	1	1	yes	characteristic
373	C₂	#20252501	1	1	yes	characteristic
374	C₂	#20252509	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle, prime radical	C₂³×C₄₇	C₂³×C₄
Fitting	C₄×C₄⋊C₈×C₄₇	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×C₄⋊C₈	D₄₇
hypocenter	C₄₇	#22722
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
69. C₄⋊C₈×C₄₇	Q₈	semidirect
172. C₄×C₄₇	#446	semidirect
219. C₄₇	#22722	semidirect
253. C₄⋊C₈	Dic₉₄	semidirect
363. C₄	#15689253	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689253	2
C₄²×Dic₉₄	2
#20244110	2
#20244106	2
#20243540	2
#20243539	2
#20243243	2
C₄×C₄⋊C₈×C₄₇	2
#22722	47