Subgroups — #26122005

Order 12032.

894 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688885	C₂	1	2	yes	maximal
3	C₂×#15688885	C₂	1	2	yes	maximal
4	#20241618	C₂	1	1	yes	maximal, characteristic
5	C₄₇×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
7	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
9	C₂×C₄×C₄₇⋊C₈	—	2	4	no	—
10	C₂×C₄×C₄₇⋊C₈	C₄	1	4	yes	complemented
11	C₂×C₄₇⋊#95	—	2	1	no	—
12	C₂×C₄₇⋊#95	—	2	1	no	—
13	#15688885	—	2	4	no	—
14	#15688885	C₄	1	8	yes	complemented
15	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×#95×C₄₇	—	2	1	no	—
18	C₂×#95×C₄₇	—	2	1	no	—
19	C₂³×Dic₄₇	—	2	2	no	—
20	C₂²×C₄₇⋊C₈	—	2	2	no	—
21	C₂²×C₄₇⋊C₈	—	2	1	no	—
22	C₂²×C₄₇⋊C₈	—	2	1	no	—
23	C₂²×C₄₇⋊C₈	—	2	1	no	—
24	C₂²×C₄₇⋊C₈	—	2	1	no	—
25	C₂²×C₄₇⋊C₈	—	2	2	no	—
26	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
27	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
28	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
29	C₂²×C₄₇⋊C₈	D₄	1	4	yes	—
30	C₂×C₄⋊Dic₄₇	—	2	2	no	—
31	C₂×C₄⋊Dic₄₇	—	2	2	no	—
32	C₂×C₄⋊Dic₄₇	—	2	2	no	—
33	C₂×C₄⋊Dic₄₇	—	2	2	no	—
34	C₂×C₄⋊Dic₄₇	—	2	2	no	—
35	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
36	C₄×C₄₇⋊C₈	—	2	8	no	—
37	C₄₇⋊#95	—	4	2	no	—
38	C₄₇⋊#95	—	4	2	no	—
39	C₂³×C₄×C₄₇	—	2	2	no	—
40	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
43	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
45	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
48	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
49	C₂×C₄²×C₄₇	—	2	2	no	—
50	C₂×C₄²×C₄₇	—	2	2	no	—
51	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₄₇	Q₈	1	2	yes	—
53	#95×C₄₇	—	4	2	no	—
54	#95×C₄₇	—	4	2	no	—
55	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₄₇	—	2	2	no	—
57	C₂²×C₄×C₄₇	—	2	2	no	—
58	C₂²×C₄×C₄₇	—	2	2	no	—
59	C₂²×C₄×C₄₇	—	2	2	no	—
60	C₂²×C₄×C₄₇	—	2	4	no	—
61	C₂²×C₄×C₄₇	—	4	2	no	—
62	C₂²×C₄×C₄₇	—	4	2	no	—
63	C₂²×C₄×C₄₇	—	4	2	no	—
64	C₂²×C₄×C₄₇	—	4	2	no	—
65	C₂²×C₄×C₄₇	—	4	2	no	—
66	C₂²×C₄×C₄₇	—	4	2	no	—
67	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
68	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
69	C₂²×C₄×C₄₇	D₈	1	2	yes	—
70	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
71	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
72	C₂²×C₄×C₄₇	Q₁₆	1	2	yes	—
73	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
75	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
76	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	#41	1	2	yes	—
78	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	#41	1	2	yes	—
83	C₂²×Dic₄₇	—	2	4	no	—
84	C₂²×Dic₄₇	—	4	2	no	—
85	C₂²×Dic₄₇	—	4	2	no	—
86	C₂²×Dic₄₇	—	4	2	no	—
87	C₂²×Dic₄₇	—	4	2	no	—
88	C₂²×Dic₄₇	—	4	2	no	—
89	C₂²×Dic₄₇	—	4	2	no	—
90	C₄⋊C₄×C₄₇	—	2	4	no	—
91	C₄⋊C₄×C₄₇	—	2	4	no	—
92	C₄⋊C₄×C₄₇	—	4	2	no	—
93	C₄⋊C₄×C₄₇	—	4	2	no	—
94	C₄²×C₄₇	—	2	2	no	—
95	C₄²×C₄₇	—	2	2	no	—
96	C₄²×C₄₇	—	2	4	no	—
97	C₄⋊Dic₄₇	—	2	4	no	—
98	C₄⋊Dic₄₇	—	2	4	no	—
99	C₄⋊Dic₄₇	—	4	2	no	—
100	C₄⋊Dic₄₇	—	4	2	no	—
101	C₂×C₄₇⋊C₈	—	2	2	no	—
102	C₂×C₄₇⋊C₈	—	2	2	no	—
103	C₂×C₄₇⋊C₈	—	2	2	no	—
104	C₂×C₄₇⋊C₈	—	2	2	no	—
105	C₂×C₄₇⋊C₈	—	2	4	no	—
106	C₂×C₄₇⋊C₈	—	2	4	no	—
107	C₂×C₄₇⋊C₈	—	2	4	no	—
108	C₂×C₄₇⋊C₈	—	2	4	no	—
109	C₂×C₄₇⋊C₈	C₄²	1	4	yes	—
110	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	4	yes	—
111	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
112	C₂³×C₄₇	C₄×D₄	1	2	yes	—
113	C₂³×C₄₇	#121	1	2	yes	—
114	C₂³×C₄₇	#124	1	1	yes	characteristic
115	C₂³×C₄₇	#124	1	1	yes	characteristic
116	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
117	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
118	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
119	C₂³×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
120	C₂³×C₄₇	#135	1	2	yes	—
121	C₂³×C₄₇	#135	1	2	yes	—
122	C₂×C₄×C₄₇	—	2	2	no	—
123	C₂×C₄×C₄₇	—	2	2	no	—
124	C₂×C₄×C₄₇	—	2	2	no	—
125	C₂×C₄×C₄₇	—	2	2	no	—
126	C₂×C₄×C₄₇	—	2	4	no	—
127	C₂×C₄×C₄₇	—	2	4	no	—
128	C₂×C₄×C₄₇	—	2	4	no	—
129	C₂×C₄×C₄₇	—	2	4	no	—
130	C₂×C₄×C₄₇	—	4	4	no	—
131	C₂×C₄×C₄₇	—	4	4	no	—
132	C₂×C₄×C₄₇	—	4	4	no	—
133	C₂×C₄×C₄₇	—	8	2	no	—
134	C₂×C₄×C₄₇	—	8	2	no	—
135	C₂×C₄×C₄₇	—	8	2	no	—
136	C₂×C₄×C₄₇	—	8	2	no	—
137	C₂×C₄×C₄₇	#106	1	4	yes	—
138	C₂×C₄×C₄₇	#107	1	4	yes	—
139	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
140	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
142	C₂×C₄×C₄₇	#117	1	2	yes	—
143	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
144	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
145	C₂×C₄×C₄₇	#117	1	2	yes	—
146	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
148	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
149	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
150	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
151	C₂×C₄×C₄₇	#123	1	2	yes	—
152	C₂×C₄×C₄₇	#123	1	2	yes	—
153	C₂×C₄×C₄₇	#125	1	1	yes	characteristic
154	C₂×C₄×C₄₇	#125	1	1	yes	characteristic
155	C₂×C₄×C₄₇	#126	1	2	yes	—
156	C₂×C₄×C₄₇	#126	1	2	yes	—
157	C₂×Dic₄₇	—	4	4	no	—
158	C₂×Dic₄₇	—	4	4	no	—
159	C₂×Dic₄₇	—	4	4	no	—
160	C₂×Dic₄₇	—	8	2	no	—
161	C₂×Dic₄₇	—	8	2	no	—
162	C₂×Dic₄₇	—	8	2	no	—
163	C₂×Dic₄₇	—	8	2	no	—
164	C₄₇⋊C₈	—	2	4	no	—
165	C₄₇⋊C₈	—	2	4	no	—
166	#10820	—	47	1	no	maximal, Sylow
167	C₂²×C₄₇	C₄×C₄⋊C₄	1	1	yes	characteristic
168	C₂²×C₄₇	#380	1	1	yes	characteristic
169	C₂²×C₄₇	#382	1	1	yes	characteristic
170	C₂²×C₄₇	#388	1	2	yes	—
171	C₂²×C₄₇	#388	1	2	yes	—
172	C₂²×C₄₇	C₂×#106	1	1	yes	characteristic
173	C₂²×C₄₇	C₂×#107	1	1	yes	characteristic
174	C₂²×C₄₇	#427	1	1	yes	characteristic
175	C₂²×C₄₇	#427	1	1	yes	characteristic
176	C₂²×C₄₇	C₄×D₈	1	2	yes	—
177	C₂²×C₄₇	C₄×SD₁₆	1	2	yes	—
178	C₂²×C₄₇	C₄×SD₁₆	1	2	yes	—
179	C₂²×C₄₇	C₄×Q₁₆	1	2	yes	—
180	C₂²×C₄₇	#465	1	2	yes	—
181	C₂²×C₄₇	#465	1	2	yes	—
182	C₂²×C₄₇	#466	1	2	yes	—
183	C₂²×C₄₇	#467	1	2	yes	—
184	C₂²×C₄₇	#486	1	1	yes	characteristic
185	C₂²×C₄₇	#486	1	1	yes	characteristic
186	C₂²×C₄₇	#487	1	1	yes	characteristic
187	C₂²×C₄₇	#487	1	1	yes	characteristic
188	C₂²×C₄₇	#488	1	2	yes	—
189	C₂²×C₄₇	#488	1	2	yes	—
190	C₄×C₄₇	—	2	4	no	—
191	C₄×C₄₇	—	2	4	no	—
192	C₄×C₄₇	—	8	4	no	—
193	C₄×C₄₇	#376	1	1	yes	characteristic
194	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
195	C₄×C₄₇	#381	1	1	yes	characteristic
196	C₄×C₄₇	#383	1	1	yes	characteristic
197	C₄×C₄₇	#387	1	2	yes	—
198	C₄×C₄₇	#387	1	2	yes	—
199	Dic₄₇	—	8	4	no	—
200	C₂²×C₄×C₈	—	47	1	no	—
201	C₂×#340	—	47	2	no	—
202	C₂×#340	—	47	2	no	—
203	C₄⋊#95	—	47	1	no	—
204	C₄⋊#95	D₄₇	1	1	yes	characteristic
205	C₂×C₄₇	#1434	1	1	yes	characteristic
206	C₂×C₄₇	C₄×#106	1	1	yes	characteristic
207	C₂×C₄₇	C₄×#107	1	1	yes	characteristic
208	C₂×C₄₇	#1807	1	1	yes	characteristic
209	C₂×C₄₇	#1808	1	1	yes	characteristic
210	C₂×C₄₇	#1834	1	1	yes	characteristic
211	C₂×C₄₇	#1835	1	1	yes	characteristic
212	C₂×C₄₇	#1933	1	2	yes	—
213	C₂×C₄₇	#1933	1	2	yes	—
214	C₂×C₄₇	#1934	1	2	yes	—
215	C₂×C₄₇	#1934	1	2	yes	—
216	C₂³×C₈	—	47	1	no	—
217	C₂³×C₈	—	47	1	no	—
218	C₂²×C₄⋊C₄	—	47	2	no	—
219	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
220	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
221	C₂×C₄×C₈	—	47	4	no	—
222	C₂×C₄×C₈	—	94	4	no	—
223	C₂×#95	—	2	1	no	—
224	C₂×#95	—	2	1	no	—
225	C₂×#95	—	94	1	no	—
226	C₂×#95	—	94	1	no	—
227	#340	—	47	8	no	—
228	#340	—	94	4	no	—
229	C₄₇	#10820	1	1	yes	characteristic, complemented, Sylow
230	C₂³×C₄	—	2	2	no	—
231	C₂³×C₄	—	94	2	no	—
232	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
233	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
234	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
235	C₂²×C₈	—	47	4	no	—
236	C₂²×C₈	—	47	2	no	—
237	C₂²×C₈	—	47	2	no	—
238	C₂²×C₈	—	47	4	no	—
239	C₂²×C₈	—	94	2	no	—
240	C₂²×C₈	—	94	2	no	—
241	C₂²×C₈	—	94	1	no	—
242	C₂²×C₈	—	94	1	no	—
243	C₂²×C₈	—	94	1	no	—
244	C₂²×C₈	—	94	1	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	47	4	no	—
251	C₂×C₄⋊C₄	—	94	2	no	—
252	C₂×C₄⋊C₄	—	94	2	no	—
253	C₂×C₄⋊C₄	—	94	2	no	—
254	C₂×C₄⋊C₄	—	94	2	no	—
255	C₂×C₄⋊C₄	—	94	2	no	—
256	C₂×C₄⋊C₄	C₄×D₄₇	1	4	yes	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	—	2	2	no	—
259	C₂×C₄²	Dic₉₄	1	2	yes	—
260	C₂×C₄²	C₄×D₄₇	1	2	yes	—
261	C₄×C₈	—	94	8	no	—
262	#95	—	4	2	no	—
263	#95	—	4	2	no	—
264	#95	—	188	2	no	—
265	#95	—	188	2	no	—
266	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	94	4	no	—
279	C₂²×C₄	—	188	2	no	—
280	C₂²×C₄	—	188	2	no	—
281	C₂²×C₄	—	188	2	no	—
282	C₂²×C₄	—	188	2	no	—
283	C₂²×C₄	—	188	2	no	—
284	C₂²×C₄	—	188	2	no	—
285	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
286	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
287	C₂²×C₄	#10625334	1	2	yes	—
288	C₂²×C₄	#10625335	1	2	yes	—
289	C₂²×C₄	#10625336	1	2	yes	—
290	C₂²×C₄	#10625337	1	2	yes	—
291	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
294	C₂²×C₄	#10625350	1	2	yes	—
295	C₂²×C₄	D₄×D₄₇	1	2	yes	—
296	C₂²×C₄	#10625352	1	2	yes	—
297	C₂²×C₄	#10625352	1	1	yes	characteristic
298	C₂²×C₄	#10625352	1	1	yes	characteristic
299	C₂²×C₄	#10625354	1	1	yes	characteristic
300	C₂²×C₄	#10625354	1	1	yes	characteristic
301	C₂×C₈	—	47	4	no	—
302	C₂×C₈	—	47	4	no	—
303	C₂×C₈	—	94	2	no	—
304	C₂×C₈	—	94	2	no	—
305	C₂×C₈	—	94	2	no	—
306	C₂×C₈	—	94	2	no	—
307	C₂×C₈	—	94	4	no	—
308	C₂×C₈	—	94	4	no	—
309	C₂×C₈	—	94	4	no	—
310	C₂×C₈	—	94	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	—	94	4	no	—
316	C₄⋊C₄	—	94	4	no	—
317	C₄⋊C₄	—	188	2	no	—
318	C₄⋊C₄	—	188	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	4	no	—
322	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
323	C₂³	C₄×C₂²⋊D₄₇	1	2	yes	—
324	C₂³	#13093996	1	2	yes	—
325	C₂³	#13094011	1	1	yes	characteristic
326	C₂³	#13094013	1	1	yes	characteristic
327	C₂³	C₂×#10625334	1	1	yes	characteristic
328	C₂³	C₂×#10625336	1	1	yes	characteristic
329	C₂³	C₂×#10625335	1	1	yes	characteristic
330	C₂³	C₂×#10625337	1	1	yes	characteristic
331	C₂³	#13094044	1	2	yes	—
332	C₂³	#13094044	1	2	yes	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	8	2	no	—
345	C₂×C₄	—	8	2	no	—
346	C₂×C₄	—	8	2	no	—
347	C₂×C₄	—	8	2	no	—
348	C₂×C₄	—	376	2	no	—
349	C₂×C₄	—	376	2	no	—
350	C₂×C₄	—	376	2	no	—
351	C₂×C₄	—	376	2	no	—
352	C₂×C₄	—	188	4	no	—
353	C₂×C₄	—	188	4	no	—
354	C₂×C₄	—	188	4	no	—
355	C₂×C₄	#13093955	1	4	yes	—
356	C₂×C₄	#13093957	1	4	yes	—
357	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
358	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
359	C₂×C₄	#13093980	1	1	yes	characteristic
360	C₂×C₄	#13093980	1	2	yes	—
361	C₂×C₄	#13093981	1	1	yes	characteristic
362	C₂×C₄	#13093982	1	1	yes	characteristic
363	C₂×C₄	#13093982	1	2	yes	—
364	C₂×C₄	#13093982	1	1	yes	characteristic
365	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
366	C₂×C₄	#13093986	1	2	yes	—
367	C₂×C₄	C₄×Dic₉₄	1	2	yes	—
368	C₂×C₄	#13094001	1	2	yes	—
369	C₂×C₄	#13094006	1	2	yes	—
370	C₂×C₄	#13094009	1	2	yes	—
371	C₂×C₄	#13094015	1	1	yes	characteristic
372	C₂×C₄	#13094015	1	1	yes	characteristic
373	C₂×C₄	#13094017	1	2	yes	—
374	C₂×C₄	#13094019	1	2	yes	—
375	C₈	—	94	4	no	—
376	C₈	—	94	4	no	—
377	C₂²	C₄×Dic₄₇⋊C₄	1	1	yes	characteristic
378	C₂²	#15688981	1	1	yes	characteristic
379	C₂²	#15688988	1	1	yes	characteristic
380	C₂²	#15689013	1	2	yes	—
381	C₂²	#15689017	1	2	yes	—
382	C₂²	C₂×#13093955	1	1	yes	characteristic
383	C₂²	C₂×#13093957	1	1	yes	characteristic
384	C₂²	#15689159	1	1	yes	characteristic
385	C₂²	#15689159	1	1	yes	characteristic
386	C₂²	C₄×#10625334	1	2	yes	—
387	C₂²	C₄×#10625335	1	2	yes	—
388	C₂²	C₄×#10625336	1	2	yes	—
389	C₂²	C₄×#10625337	1	2	yes	—
390	C₂²	#15689350	1	2	yes	—
391	C₂²	#15689354	1	2	yes	—
392	C₂²	#15689357	1	2	yes	—
393	C₂²	#15689362	1	2	yes	—
394	C₂²	#15689469	1	1	yes	characteristic
395	C₂²	#15689471	1	1	yes	characteristic
396	C₂²	#15689473	1	1	yes	characteristic
397	C₂²	#15689475	1	1	yes	characteristic
398	C₂²	#15689477	1	2	yes	—
399	C₂²	#15689480	1	2	yes	—
400	C₄	—	2	4	no	—
401	C₄	—	2	4	no	—
402	C₄	—	8	4	no	—
403	C₄	—	376	4	no	—
404	C₄	#15688968	1	1	yes	characteristic
405	C₄	#15688970	1	1	yes	characteristic
406	C₄	#15688985	1	1	yes	characteristic
407	C₄	#15688990	1	1	yes	characteristic
408	C₄	#15689006	1	2	yes	—
409	C₄	#15689010	1	2	yes	—
410	C₂	#20241614	1	1	yes	characteristic
411	C₂	C₄×#13093955	1	1	yes	characteristic
412	C₂	C₄×#13093957	1	1	yes	characteristic
413	C₂	#20243411	1	1	yes	characteristic
414	C₂	#20243415	1	1	yes	characteristic
415	C₂	#20243515	1	1	yes	characteristic
416	C₂	#20243518	1	1	yes	characteristic
417	C₂	#20244063	1	2	yes	—
418	C₂	#20244067	1	2	yes	—
419	C₂	#20244070	1	2	yes	—
420	C₂	#20244074	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₄₇×C₄⋊#95	C₂
socle, prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₄⋊#95	D₄₇
hypocenter	C₄₇	#10820
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₄⋊#95

Complements

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

N	H ≅ G/N	type
10. C₂×C₄×C₄₇⋊C₈	C₄	semidirect
14. #15688885	C₄	semidirect
229. C₄₇	#10820	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₄₇⋊C₈	2
C₂×#15688885	2
#20241618	2
C₄₇×C₄⋊#95	2
#10820	47