Subgroups — #26235186

Order 12032.

740 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	C₂×#15689254	C₂	1	1	yes	maximal, characteristic
2	#20245866	C₂	1	1	yes	maximal, characteristic
3	#20244109	C₂	1	2	yes	maximal
4	#20244106	C₂	1	1	yes	maximal, characteristic
5	#20244106	C₂	1	2	yes	maximal
6	#20244104	C₂	1	1	yes	maximal, characteristic
7	#20243507	C₂	1	2	yes	maximal
8	#20243504	C₂	1	1	yes	maximal, characteristic
9	#20243246	C₂	1	2	yes	maximal
10	C₄×Dic₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
11	C₂×C₈×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
12	#15689254	—	2	4	no	—
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
15	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
18	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
19	C₂×#13093935	C₂²	1	2	yes	—
20	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
21	#15689030	C₄	1	1	yes	characteristic
22	#15689030	C₄	1	1	yes	characteristic
23	#15689022	C₄	1	1	yes	characteristic
24	#15689022	C₄	1	1	yes	characteristic
25	#15689009	C₄	1	2	yes	—
26	#15689009	C₄	1	2	yes	—
27	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
29	#15688969	C₂²	1	2	yes	—
30	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
31	#15688877	C₂²	1	1	yes	characteristic
32	#15688877	C₂²	1	1	yes	characteristic
33	#15688877	C₂²	1	2	yes	—
34	#15688877	C₂²	1	2	yes	—
35	#15688877	C₂²	1	2	yes	—
36	#15688877	C₂²	1	2	yes	—
37	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₈×Q₈×C₄₇	—	2	4	no	—
39	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
41	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
43	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
50	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
55	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
56	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
57	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
58	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
59	Dic₄₇⋊C₈	—	2	2	no	—
60	Dic₄₇⋊C₈	—	2	4	no	—
61	Dic₄₇⋊C₈	—	2	2	no	—
62	Dic₄₇⋊C₈	—	2	4	no	—
63	#13093935	—	2	4	no	—
64	C₄×C₄₇⋊C₈	—	2	2	no	—
65	C₄₇⋊#95	C₂×C₄	1	2	yes	—
66	C₄₇⋊#95	C₂×C₄	1	2	yes	—
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×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
75	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
76	C₄×Q₈×C₄₇	D₄	1	4	yes	—
77	C₄×Q₈×C₄₇	Q₈	1	4	yes	—
78	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
79	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
82	C₄⋊C₈×C₄₇	—	2	2	no	—
83	C₄⋊C₈×C₄₇	—	2	4	no	—
84	C₄×C₈×C₄₇	—	2	2	no	—
85	C₄×C₈×C₄₇	—	2	4	no	—
86	C₂×Q₈×C₄₇	—	2	2	no	—
87	C₂×Q₈×C₄₇	—	2	2	no	—
88	C₂×Q₈×C₄₇	C₄⋊C₄	1	4	yes	—
89	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
97	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
98	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₄₇	—	2	1	no	—
101	C₂×C₈×C₄₇	—	2	1	no	—
102	C₂×C₈×C₄₇	—	2	2	no	—
103	C₂×C₈×C₄₇	—	2	1	no	—
104	C₂×C₈×C₄₇	—	2	1	no	—
105	C₂×C₈×C₄₇	—	2	2	no	—
106	C₂×C₈×C₄₇	—	2	1	no	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	#41	1	2	yes	—
109	C₄⋊C₄×C₄₇	C₄⋊C₄	1	8	yes	—
110	C₄⋊C₄×C₄₇	C₄⋊C₄	1	4	yes	—
111	C₄²×C₄₇	C₂×D₄	1	2	yes	—
112	C₄²×C₄₇	C₂×D₄	1	4	yes	—
113	C₄²×C₄₇	C₂×Q₈	1	4	yes	—
114	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
115	C₄⋊Dic₄₇	—	2	2	no	—
116	C₄⋊Dic₄₇	—	2	2	no	—
117	C₄⋊Dic₄₇	—	2	4	no	—
118	C₄⋊Dic₄₇	—	4	2	no	—
119	C₄×Dic₄₇	—	2	2	no	—
120	C₄×Dic₄₇	—	2	2	no	—
121	C₄×Dic₄₇	—	2	1	no	—
122	C₄×Dic₄₇	—	2	1	no	—
123	C₄×Dic₄₇	—	2	2	no	—
124	C₄×Dic₄₇	—	2	2	no	—
125	C₄×Dic₄₇	—	2	1	no	—
126	C₄×Dic₄₇	—	2	1	no	—
127	C₄×Dic₄₇	—	2	2	no	—
128	C₄×Dic₄₇	—	4	1	no	—
129	C₂×C₄₇⋊C₈	—	2	1	no	—
130	C₂×C₄₇⋊C₈	—	2	1	no	—
131	C₂×C₄₇⋊C₈	—	2	1	no	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	—	2	1	no	—
134	C₂×C₄₇⋊C₈	—	2	2	no	—
135	C₂×C₄₇⋊C₈	—	2	1	no	—
136	C₂×C₄₇⋊C₈	—	2	2	no	—
137	C₂×C₄₇⋊C₈	#41	1	2	yes	—
138	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
139	Q₈×C₄₇	—	2	8	no	—
140	C₂×C₄×C₄₇	—	2	1	no	—
141	C₂×C₄×C₄₇	—	2	2	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	1	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
147	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
148	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
149	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
150	C₂×C₄×C₄₇	#131	1	2	yes	—
151	C₂×C₄×C₄₇	#131	1	2	yes	—
152	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
157	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
158	C₂×Dic₄₇	—	2	1	no	—
159	C₂×Dic₄₇	—	2	1	no	—
160	C₂×Dic₄₇	—	2	2	no	—
161	C₂×Dic₄₇	—	2	2	no	—
162	C₂×Dic₄₇	—	2	1	no	—
163	C₂×Dic₄₇	—	2	1	no	—
164	C₂×Dic₄₇	—	2	1	no	—
165	C₂×Dic₄₇	—	2	1	no	—
166	C₂×Dic₄₇	—	2	1	no	—
167	C₂×Dic₄₇	—	2	1	no	—
168	C₂×Dic₄₇	—	2	1	no	—
169	C₂×Dic₄₇	—	2	2	no	—
170	C₂×Dic₄₇	—	2	2	no	—
171	C₂×Dic₄₇	—	2	2	no	—
172	C₂×Dic₄₇	—	2	1	no	—
173	C₂×Dic₄₇	—	2	1	no	—
174	C₂×Dic₄₇	—	2	2	no	—
175	C₂×Dic₄₇	#131	1	2	yes	—
176	C₈×C₄₇	—	2	2	no	—
177	C₈×C₄₇	—	4	2	no	—
178	C₈×C₄₇	—	4	1	no	—
179	C₄₇⋊C₈	—	2	2	no	—
180	C₄₇⋊C₈	—	4	1	no	—
181	C₄₇⋊C₈	—	4	2	no	—
182	#22735	—	47	1	no	maximal, Sylow
183	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
184	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
185	C₂²×C₄₇	#519	1	1	yes	characteristic
186	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
187	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
188	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
189	C₂²×C₄₇	#568	1	1	yes	characteristic
190	C₄×C₄₇	—	2	4	no	—
191	C₄×C₄₇	—	2	2	no	—
192	C₄×C₄₇	—	2	4	no	—
193	C₄×C₄₇	#424	1	4	yes	—
194	C₄×C₄₇	#548	1	1	yes	characteristic
195	C₄×C₄₇	#548	1	1	yes	characteristic
196	C₄×C₄₇	#557	1	1	yes	characteristic
197	C₄×C₄₇	#557	1	1	yes	characteristic
198	Dic₄₇	—	2	2	no	—
199	Dic₄₇	—	4	2	no	—
200	Dic₄₇	—	4	1	no	—
201	Dic₄₇	—	4	2	no	—
202	Dic₄₇	—	4	1	no	—
203	Dic₄₇	—	4	1	no	—
204	C₂×#446	—	47	1	no	—
205	C₂×C₈×Q₈	D₄₇	1	1	yes	characteristic
206	#2295	—	47	1	no	—
207	#1940	—	47	2	no	—
208	#1939	—	47	1	no	—
209	#1939	—	47	2	no	—
210	#1939	—	47	1	no	—
211	#1832	—	47	2	no	—
212	#1831	—	47	1	no	—
213	#1768	—	47	2	no	—
214	C₄×C₄⋊C₈	—	47	1	no	—
215	C₂×C₄₇	#2351	1	1	yes	characteristic
216	C₂×C₄₇	C₂×#424	1	1	yes	characteristic
217	C₂×C₄₇	#2906	1	1	yes	characteristic
218	C₂×C₄₇	#2966	1	1	yes	characteristic
219	C₂×C₄₇	#2969	1	1	yes	characteristic
220	C₂×C₄₇	#2985	1	1	yes	characteristic
221	C₂×C₄₇	#2986	1	1	yes	characteristic
222	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
223	#446	—	94	4	no	—
224	C₈×Q₈	—	2	4	no	—
225	C₂×C₄⋊C₈	—	47	1	no	—
226	C₂×C₄⋊C₈	—	47	2	no	—
227	C₂×C₄⋊C₈	—	47	2	no	—
228	C₂×C₄⋊C₈	—	47	1	no	—
229	C₂×C₄⋊C₈	—	47	1	no	—
230	C₂×C₄⋊C₈	—	47	2	no	—
231	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
232	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
233	C₂×#97	—	47	2	no	—
234	C₂×C₄×C₈	—	47	1	no	—
235	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
236	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
237	#391	—	47	1	no	—
238	#391	—	47	1	no	—
239	#389	—	47	1	no	—
240	#389	—	47	1	no	—
241	#387	—	47	2	no	—
242	#387	—	47	2	no	—
243	C₄×C₄⋊C₄	—	47	1	no	—
244	C₄×C₄⋊C₄	—	47	2	no	—
245	#376	—	47	2	no	—
246	C₄³	—	47	1	no	—
247	#336	—	47	2	no	—
248	#336	—	47	2	no	—
249	#336	—	47	1	no	—
250	#336	—	47	2	no	—
251	#336	—	47	2	no	—
252	#336	—	47	1	no	—
253	C₄₇	#22735	1	1	yes	characteristic, complemented, Sylow
254	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
255	C₂²×C₈	—	47	1	no	—
256	C₂²×C₈	—	47	1	no	—
257	C₂²×C₈	—	47	2	no	—
258	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
259	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
260	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
261	C₄×Q₈	Dic₉₄	1	4	yes	—
262	C₄×Q₈	C₂²⋊D₄₇	1	4	yes	—
263	C₂×C₄⋊C₄	—	47	2	no	—
264	C₂×C₄⋊C₄	—	47	1	no	—
265	C₂×C₄⋊C₄	—	47	1	no	—
266	C₂×C₄⋊C₄	—	47	2	no	—
267	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
268	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
269	C₂×C₄²	—	47	1	no	—
270	C₂×C₄²	—	47	1	no	—
271	C₂×C₄²	—	47	1	no	—
272	C₂×C₄²	—	47	1	no	—
273	C₂×C₄²	—	47	1	no	—
274	C₂×C₄²	—	47	2	no	—
275	C₂×C₄²	—	47	1	no	—
276	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
277	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
278	C₄⋊C₈	—	2	2	no	—
279	C₄⋊C₈	—	2	4	no	—
280	C₄⋊C₈	—	94	4	no	—
281	C₄⋊C₈	—	94	2	no	—
282	C₄⋊C₈	—	94	2	no	—
283	C₄⋊C₈	—	94	4	no	—
284	C₄⋊C₈	—	94	2	no	—
285	C₄⋊C₈	—	94	4	no	—
286	#97	—	94	4	no	—
287	C₄×C₈	—	2	2	no	—
288	C₄×C₈	—	2	4	no	—
289	C₄×C₈	—	94	2	no	—
290	#95	—	47	2	no	—
291	#95	—	47	2	no	—
292	#95	—	47	2	no	—
293	#95	—	47	2	no	—
294	#95	—	47	2	no	—
295	#95	—	47	2	no	—
296	#95	—	47	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	Dic₄₇⋊C₄	1	4	yes	—
300	C₂²×C₄	—	47	1	no	—
301	C₂²×C₄	—	47	1	no	—
302	C₂²×C₄	—	47	1	no	—
303	C₂²×C₄	—	47	2	no	—
304	C₂²×C₄	—	47	2	no	—
305	C₂²×C₄	—	47	1	no	—
306	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
307	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
309	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
310	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	47	2	no	—
320	C₂×C₈	—	94	1	no	—
321	C₂×C₈	—	94	1	no	—
322	C₂×C₈	—	94	1	no	—
323	C₂×C₈	—	94	2	no	—
324	C₂×C₈	—	94	1	no	—
325	C₂×C₈	—	94	2	no	—
326	C₂×C₈	—	94	1	no	—
327	C₂×C₈	—	94	2	no	—
328	C₂×C₈	#10625354	1	2	yes	—
329	C₄⋊C₄	—	94	4	no	—
330	C₄⋊C₄	—	94	2	no	—
331	C₄⋊C₄	—	94	2	no	—
332	C₄⋊C₄	—	188	2	no	—
333	C₄⋊C₄	Dic₄₇⋊C₄	1	8	yes	—
334	C₄⋊C₄	Dic₄₇⋊C₄	1	4	yes	—
335	C₄²	—	94	2	no	—
336	C₄²	—	94	2	no	—
337	C₄²	—	94	2	no	—
338	C₄²	—	94	1	no	—
339	C₄²	—	94	2	no	—
340	C₄²	—	94	1	no	—
341	C₄²	—	94	2	no	—
342	C₄²	—	94	1	no	—
343	C₄²	—	94	1	no	—
344	C₄²	—	188	1	no	—
345	C₄²	C₂×Dic₉₄	1	4	yes	—
346	C₄²	C₂×Dic₉₄	1	2	yes	—
347	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
348	C₄²	C₂×C₂²⋊D₄₇	1	4	yes	—
349	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
350	Q₈	—	2	8	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	47	2	no	—
358	C₂×C₄	—	94	1	no	—
359	C₂×C₄	—	94	1	no	—
360	C₂×C₄	—	94	2	no	—
361	C₂×C₄	—	94	2	no	—
362	C₂×C₄	—	94	1	no	—
363	C₂×C₄	—	94	1	no	—
364	C₂×C₄	—	94	1	no	—
365	C₂×C₄	—	94	1	no	—
366	C₂×C₄	—	94	2	no	—
367	C₂×C₄	—	94	1	no	—
368	C₂×C₄	—	94	1	no	—
369	C₂×C₄	—	94	1	no	—
370	C₂×C₄	—	94	2	no	—
371	C₂×C₄	—	94	2	no	—
372	C₂×C₄	—	94	1	no	—
373	C₂×C₄	—	94	1	no	—
374	C₂×C₄	—	94	2	no	—
375	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
376	C₂×C₄	C₂×Dic₄₇⋊C₄	1	4	yes	—
377	C₂×C₄	C₂×Dic₄₇⋊C₄	1	4	yes	—
378	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
379	C₂×C₄	#13094030	1	2	yes	—
380	C₂×C₄	#13094030	1	2	yes	—
381	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
382	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
383	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
384	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
385	C₂×C₄	#13094071	1	1	yes	characteristic
386	C₂×C₄	#13094072	1	1	yes	characteristic
387	C₈	—	2	2	no	—
388	C₈	—	4	1	no	—
389	C₈	—	4	2	no	—
390	C₈	—	94	2	no	—
391	C₈	—	188	1	no	—
392	C₈	—	188	2	no	—
393	C₂²	C₂²×Dic₄₇⋊C₄	1	1	yes	characteristic
394	C₂²	C₄×#10625354	1	1	yes	characteristic
395	C₂²	#15689599	1	1	yes	characteristic
396	C₂²	#131×D₄₇	1	1	yes	characteristic
397	C₂²	C₂×#13094030	1	1	yes	characteristic
398	C₂²	C₂×#13094030	1	1	yes	characteristic
399	C₂²	#15689888	1	1	yes	characteristic
400	C₄	—	2	4	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	4	no	—
403	C₄	—	94	2	no	—
404	C₄	—	188	1	no	—
405	C₄	—	188	1	no	—
406	C₄	—	188	2	no	—
407	C₄	—	188	1	no	—
408	C₄	—	188	2	no	—
409	C₄	#15689149	1	4	yes	—
410	C₄	#15689780	1	1	yes	characteristic
411	C₄	#15689784	1	1	yes	characteristic
412	C₄	#15689849	1	1	yes	characteristic
413	C₄	#15689852	1	1	yes	characteristic
414	C₂	#20246306	1	1	yes	characteristic
415	C₂	C₂×#15689149	1	1	yes	characteristic
416	C₂	#20251954	1	1	yes	characteristic
417	C₂	#20252365	1	1	yes	characteristic
418	C₂	#20252391	1	1	yes	characteristic
419	C₂	#20252479	1	1	yes	characteristic
420	C₂	#20252488	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle, prime radical	C₂³×C₄₇	C₂³×C₄
Fitting	C₂×C₈×Q₈×C₄₇	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₈×Q₈	D₄₇
hypocenter	C₄₇	#22735
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₈×Q₈

Complements

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

N	H ≅ G/N	type
253. C₄₇	#22735	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689254	2
#20245866	2
#20244109	2
#20244106	2
#20244104	2
#20243507	2
#20243504	2
#20243246	2
C₄×Dic₄₇⋊C₈	2
C₂×C₈×Q₈×C₄₇	2
#22735	47