Subgroups — #26224580

Order 12032.

742 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13094015	C₂	1	1	yes	maximal, characteristic
2	#20244106	C₂	1	1	yes	maximal, characteristic
3	#20243946	C₂	1	2	yes	maximal
4	#20243942	C₂	1	2	yes	maximal
5	#20243504	C₂	1	1	yes	maximal, characteristic
6	#20243253	C₂	1	1	yes	maximal, characteristic
7	#20243253	C₂	1	2	yes	maximal
8	C₄⋊C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
9	#20243249	C₂	1	2	yes	maximal
10	C₄×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1939	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094015	C₄	1	1	yes	characteristic
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
15	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
16	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
19	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
20	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
21	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
22	#15689022	C₄	1	1	yes	characteristic
23	#15689019	C₄	1	1	yes	characteristic
24	#15689010	C₄	1	2	yes	—
25	#15689006	C₄	1	2	yes	—
26	#15688988	C₄	1	1	yes	characteristic
27	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
28	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
29	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
30	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
31	#15688878	C₂²	1	2	yes	—
32	#15688877	C₂²	1	2	yes	—
33	#15688877	C₂²	1	2	yes	—
34	#15688877	C₂²	1	2	yes	—
35	#15688877	C₂²	1	2	yes	—
36	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#336	C₂²	1	2	yes	—
41	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
42	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
43	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
44	#13094015	C₈	1	8	yes	complemented
45	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
50	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
56	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
57	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
58	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
59	Dic₄₇⋊C₈	—	2	4	no	—
60	C₄×C₄₇⋊C₈	—	2	4	no	—
61	C₄×C₄₇⋊C₈	Q₈	1	4	yes	—
62	C₈×Dic₄₇	—	2	2	no	—
63	C₈×Dic₄₇	—	2	2	no	—
64	C₈×Dic₄₇	—	2	2	no	—
65	C₈×Dic₄₇	—	2	4	no	—
66	C₈×Dic₄₇	—	2	2	no	—
67	C₄₇⋊#95	C₂×C₄	1	2	yes	—
68	C₄₇⋊#95	C₂×C₄	1	2	yes	—
69	C₄₇⋊#95	C₂×C₄	1	2	yes	—
70	C₄₇⋊#95	C₂×C₄	1	2	yes	—
71	C₄₇⋊#95	C₂×C₄	1	2	yes	—
72	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
73	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₄₇	—	2	4	no	—
80	C₄⋊C₈×C₄₇	—	2	2	no	—
81	C₄×C₈×C₄₇	—	2	2	no	—
82	#95×C₄₇	C₂×C₄	1	2	yes	—
83	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
88	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
89	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
92	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₈×C₄₇	—	2	1	no	—
95	C₂×C₈×C₄₇	—	2	1	no	—
96	C₂×C₈×C₄₇	—	2	1	no	—
97	C₂×C₈×C₄₇	—	2	1	no	—
98	C₂×C₈×C₄₇	—	2	2	no	—
99	C₂×C₈×C₄₇	—	2	2	no	—
100	C₂×C₈×C₄₇	—	2	2	no	—
101	C₂×C₈×C₄₇	#41	1	2	yes	—
102	C₂×C₈×C₄₇	#41	1	2	yes	—
103	C₄⋊C₄×C₄₇	—	2	2	no	—
104	C₄⋊C₄×C₄₇	C₂×C₈	1	4	yes	—
105	C₄²×C₄₇	—	2	2	no	—
106	C₄²×C₄₇	—	2	2	no	—
107	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
108	C₄²×C₄₇	#41	1	2	yes	—
109	C₄⋊Dic₄₇	—	2	2	no	—
110	C₄⋊Dic₄₇	—	2	4	no	—
111	C₄⋊Dic₄₇	C₂×C₈	1	8	yes	—
112	C₄⋊Dic₄₇	C₂×C₈	1	4	yes	—
113	Dic₄₇⋊C₄	—	2	4	no	—
114	Dic₄₇⋊C₄	C₂×C₈	1	8	yes	—
115	C₄×Dic₄₇	—	2	2	no	—
116	C₄×Dic₄₇	—	2	1	no	—
117	C₄×Dic₄₇	—	2	1	no	—
118	C₄×Dic₄₇	—	2	1	no	—
119	C₄×Dic₄₇	—	2	1	no	—
120	C₄×Dic₄₇	—	2	2	no	—
121	C₄×Dic₄₇	—	2	2	no	—
122	C₄×Dic₄₇	—	2	2	no	—
123	C₄×Dic₄₇	—	2	2	no	—
124	C₄×Dic₄₇	C₂×C₈	1	4	yes	—
125	C₂×C₄₇⋊C₈	—	2	1	no	—
126	C₂×C₄₇⋊C₈	—	2	1	no	—
127	C₂×C₄₇⋊C₈	—	2	2	no	—
128	C₂×C₄₇⋊C₈	—	2	2	no	—
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
131	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
132	C₂×C₄₇⋊C₈	#41	1	2	yes	—
133	C₂×C₄₇⋊C₈	#41	1	2	yes	—
134	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
135	C₂×C₄×C₄₇	—	2	2	no	—
136	C₂×C₄×C₄₇	—	2	1	no	—
137	C₂×C₄×C₄₇	—	2	1	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	2	2	no	—
142	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
143	C₂×C₄×C₄₇	C₄×Q₈	1	2	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	2	yes	—
147	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
153	C₂×Dic₄₇	—	2	1	no	—
154	C₂×Dic₄₇	—	2	1	no	—
155	C₂×Dic₄₇	—	2	1	no	—
156	C₂×Dic₄₇	—	2	2	no	—
157	C₂×Dic₄₇	—	2	1	no	—
158	C₂×Dic₄₇	—	2	1	no	—
159	C₂×Dic₄₇	—	2	1	no	—
160	C₂×Dic₄₇	—	2	1	no	—
161	C₂×Dic₄₇	—	2	1	no	—
162	C₂×Dic₄₇	—	2	2	no	—
163	C₂×Dic₄₇	—	2	2	no	—
164	C₂×Dic₄₇	—	2	2	no	—
165	C₂×Dic₄₇	—	2	2	no	—
166	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
167	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
168	C₂×Dic₄₇	C₂²×C₈	1	4	yes	—
169	C₂×Dic₄₇	#131	1	2	yes	—
170	C₂×Dic₄₇	#131	1	2	yes	—
171	C₈×C₄₇	—	2	2	no	—
172	C₈×C₄₇	—	2	2	no	—
173	C₈×C₄₇	—	4	2	no	—
174	C₄₇⋊C₈	—	2	2	no	—
175	C₄₇⋊C₈	—	4	2	no	—
176	C₄₇⋊C₈	#125	1	4	yes	complemented
177	C₈×#125	—	47	1	no	maximal, Sylow
178	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
179	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
180	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
181	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
182	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
183	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
184	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
185	C₄×C₄₇	—	2	2	no	—
186	C₄×C₄₇	—	2	4	no	—
187	C₄×C₄₇	—	4	2	no	—
188	C₄×C₄₇	C₈×Q₈	1	4	yes	—
189	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
190	C₄×C₄₇	#529	1	1	yes	characteristic
191	C₄×C₄₇	#529	1	1	yes	characteristic
192	C₄×C₄₇	#533	1	1	yes	characteristic
193	Dic₄₇	—	2	2	no	—
194	Dic₄₇	—	2	2	no	—
195	Dic₄₇	—	2	4	no	—
196	Dic₄₇	—	2	2	no	—
197	Dic₄₇	—	2	2	no	—
198	Dic₄₇	—	4	2	no	—
199	C₄×#125	—	47	1	no	—
200	#1939	—	47	1	no	—
201	#1939	D₄₇	1	1	yes	characteristic
202	#1916	—	47	2	no	—
203	#1916	—	47	2	no	—
204	#1831	—	47	1	no	—
205	C₈×C₄⋊C₄	—	47	2	no	—
206	C₈×C₄⋊C₄	—	47	1	no	—
207	C₈×C₄⋊C₄	—	47	1	no	—
208	C₈×C₄⋊C₄	—	47	2	no	—
209	C₄²×C₈	—	47	1	no	—
210	C₂×C₄₇	C₄×#125	1	1	yes	characteristic
211	C₂×C₄₇	C₂×C₈×Q₈	1	1	yes	characteristic
212	C₂×C₄₇	#2960	1	1	yes	characteristic
213	C₂×C₄₇	C₈×#41	1	1	yes	characteristic
214	C₂×C₄₇	C₈×#41	1	1	yes	characteristic
215	C₂×C₄₇	#2966	1	1	yes	characteristic
216	C₂×C₄₇	#2966	1	1	yes	characteristic
217	C₂×#125	—	47	1	no	—
218	C₂×C₄⋊C₈	—	47	2	no	—
219	C₂×C₄⋊C₈	—	47	1	no	—
220	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
221	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
222	C₂×C₄×C₈	—	47	1	no	—
223	C₂×C₄×C₈	—	47	1	no	—
224	C₂×C₄×C₈	—	47	1	no	—
225	C₂×C₄×C₈	—	47	1	no	—
226	C₂×C₄×C₈	—	47	1	no	—
227	C₂×C₄×C₈	—	47	2	no	—
228	C₂×C₄×C₈	—	47	2	no	—
229	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
230	#389	—	47	1	no	—
231	#389	—	47	1	no	—
232	#387	—	47	2	no	—
233	#387	—	47	2	no	—
234	#382	—	47	1	no	—
235	C₄×C₄⋊C₄	—	47	2	no	—
236	C₄×C₄⋊C₄	—	47	1	no	—
237	C₄×C₄⋊C₄	—	47	2	no	—
238	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
239	C₄³	—	47	1	no	—
240	#336	—	47	2	no	—
241	#336	—	47	2	no	—
242	#336	—	47	2	no	—
243	#336	—	47	2	no	—
244	#336	—	47	2	no	—
245	#336	C₂×D₄₇	1	2	yes	—
246	C₄₇	C₈×#125	1	1	yes	characteristic, complemented, Sylow
247	C₂²×C₈	—	47	1	no	—
248	C₂²×C₈	—	47	1	no	—
249	C₂²×C₈	—	47	2	no	—
250	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
251	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
252	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
253	#125	—	47	8	no	—
254	C₂×C₄⋊C₄	—	47	2	no	—
255	C₂×C₄⋊C₄	—	47	2	no	—
256	C₂×C₄⋊C₄	—	47	1	no	—
257	C₂×C₄⋊C₄	—	47	2	no	—
258	C₂×C₄⋊C₄	—	47	1	no	—
259	C₂×C₄⋊C₄	—	47	2	no	—
260	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
262	C₂×C₄²	—	47	1	no	—
263	C₂×C₄²	—	47	1	no	—
264	C₂×C₄²	—	47	1	no	—
265	C₂×C₄²	—	47	1	no	—
266	C₂×C₄²	—	47	1	no	—
267	C₂×C₄²	—	47	1	no	—
268	C₂×C₄²	—	47	2	no	—
269	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
270	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
271	C₄⋊C₈	—	2	4	no	—
272	C₄⋊C₈	—	2	2	no	—
273	C₄⋊C₈	—	94	4	no	—
274	C₄⋊C₈	—	94	2	no	—
275	C₄×C₈	—	2	2	no	—
276	C₄×C₈	—	47	4	no	—
277	C₄×C₈	—	94	4	no	—
278	C₄×C₈	—	94	2	no	—
279	C₄×C₈	—	94	2	no	—
280	C₄×C₈	—	94	4	no	—
281	C₄×C₈	—	94	2	no	—
282	C₄×C₈	—	94	2	no	—
283	#95	—	47	2	no	—
284	#95	—	47	2	no	—
285	#95	—	47	2	no	—
286	#95	—	47	2	no	—
287	#95	—	47	2	no	—
288	#95	C₄×D₄₇	1	2	yes	—
289	C₂²×C₄	—	47	1	no	—
290	C₂²×C₄	—	47	1	no	—
291	C₂²×C₄	—	47	1	no	—
292	C₂²×C₄	—	47	1	no	—
293	C₂²×C₄	—	47	2	no	—
294	C₂²×C₄	—	47	2	no	—
295	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
296	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
297	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
298	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
299	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	47	2	no	—
308	C₂×C₈	—	47	2	no	—
309	C₂×C₈	—	47	2	no	—
310	C₂×C₈	—	47	2	no	—
311	C₂×C₈	—	94	1	no	—
312	C₂×C₈	—	94	1	no	—
313	C₂×C₈	—	94	2	no	—
314	C₂×C₈	—	94	2	no	—
315	C₂×C₈	—	94	2	no	—
316	C₂×C₈	#10625352	1	2	yes	—
317	C₂×C₈	#10625354	1	2	yes	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	47	8	no	—
320	C₄⋊C₄	—	47	8	no	—
321	C₄⋊C₄	—	47	4	no	—
322	C₄⋊C₄	—	94	4	no	—
323	C₄⋊C₄	—	94	4	no	—
324	C₄⋊C₄	—	94	2	no	—
325	C₄⋊C₄	C₈×D₄₇	1	4	yes	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	47	4	no	—
329	C₄²	—	94	2	no	—
330	C₄²	—	94	2	no	—
331	C₄²	—	94	2	no	—
332	C₄²	—	94	1	no	—
333	C₄²	—	94	1	no	—
334	C₄²	—	94	2	no	—
335	C₄²	—	94	1	no	—
336	C₄²	—	94	1	no	—
337	C₄²	—	94	2	no	—
338	C₄²	#10625352	1	2	yes	—
339	C₄²	Q₈×D₄₇	1	2	yes	—
340	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	47	2	no	—
349	C₂×C₄	—	47	2	no	—
350	C₂×C₄	—	47	4	no	—
351	C₂×C₄	—	47	2	no	—
352	C₂×C₄	—	47	2	no	—
353	C₂×C₄	—	94	1	no	—
354	C₂×C₄	—	94	1	no	—
355	C₂×C₄	—	94	1	no	—
356	C₂×C₄	—	94	2	no	—
357	C₂×C₄	—	94	1	no	—
358	C₂×C₄	—	94	1	no	—
359	C₂×C₄	—	94	1	no	—
360	C₂×C₄	—	94	2	no	—
361	C₂×C₄	—	94	1	no	—
362	C₂×C₄	—	94	1	no	—
363	C₂×C₄	—	94	2	no	—
364	C₂×C₄	—	94	2	no	—
365	C₂×C₄	—	94	2	no	—
366	C₂×C₄	#13093989	1	2	yes	—
367	C₂×C₄	#13093989	1	2	yes	—
368	C₂×C₄	C₂×C₈×D₄₇	1	4	yes	—
369	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
370	C₂×C₄	#13094032	1	2	yes	—
371	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
372	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
373	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
374	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
375	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
376	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
377	C₈	—	2	2	no	—
378	C₈	—	2	2	no	—
379	C₈	—	4	2	no	—
380	C₈	—	47	4	no	—
381	C₈	—	94	2	no	—
382	C₈	—	188	2	no	—
383	C₂²	C₂×#13093989	1	1	yes	characteristic
384	C₂²	C₄×#10625352	1	1	yes	characteristic
385	C₂²	C₄×#10625354	1	1	yes	characteristic
386	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
387	C₂²	#131×D₄₇	1	1	yes	characteristic
388	C₂²	#131×D₄₇	1	1	yes	characteristic
389	C₂²	C₂×#13094032	1	1	yes	characteristic
390	C₄	—	2	2	no	—
391	C₄	—	2	4	no	—
392	C₄	—	4	2	no	—
393	C₄	—	94	2	no	—
394	C₄	—	94	2	no	—
395	C₄	—	94	4	no	—
396	C₄	—	94	2	no	—
397	C₄	—	94	2	no	—
398	C₄	—	188	2	no	—
399	C₄	#15689247	1	4	yes	—
400	C₄	#125×D₄₇	1	1	yes	characteristic
401	C₄	#15689654	1	1	yes	characteristic
402	C₄	#15689659	1	1	yes	characteristic
403	C₄	#15689678	1	1	yes	characteristic
404	C₂	#20245947	1	1	yes	characteristic
405	C₂	C₂×#15689247	1	1	yes	characteristic
406	C₂	#20252321	1	1	yes	characteristic
407	C₂	C₈×#10625352	1	1	yes	characteristic
408	C₂	C₈×#10625354	1	1	yes	characteristic
409	C₂	#20252362	1	1	yes	characteristic
410	C₂	#20252366	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Fitting	C₄₇×#1939	C₂
socle, prime radical	C₂³×C₄₇	C₂³×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1939	D₄₇
hypocenter	C₄₇	C₈×#125
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1939

Complements

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

N	H ≅ G/N	type
44. #13094015	C₈	semidirect
176. C₄₇⋊C₈	#125	semidirect
246. C₄₇	C₈×#125	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13094015	2
#20244106	2
#20243946	2
#20243942	2
#20243504	2
#20243253	2
C₄⋊C₄×C₄₇⋊C₈	2
#20243249	2
C₄×C₈×Dic₄₇	2
C₄₇×#1939	2
C₈×#125	47