Subgroups — #26223312

Order 12032.

906 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689079	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244003	C₂	1	2	yes	maximal, complemented
4	#20243954	C₂	1	2	yes	maximal, complemented
5	#20243686	C₂	1	1	yes	maximal, characteristic
6	#20243573	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243459	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄⋊C₄×C₄₇⋊C₈	C₂	1	2	yes	maximal, complemented
9	C₂²⋊C₄×C₄₇⋊C₈	C₂	1	2	yes	maximal, complemented
10	C₂²⋊C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2395	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625329	C₂²	1	1	yes	characteristic
13	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
15	D₄×C₄₇⋊C₈	—	2	4	no	—
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
22	#15689079	—	2	4	no	—
23	C₂×#13093935	C₂²	1	2	yes	—
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
27	#15688878	C₂²	1	2	yes	—
28	#15688878	C₂²	1	2	yes	—
29	#15688878	C₂²	1	2	yes	—
30	#15688878	C₂²	1	2	yes	—
31	#15688878	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
34	C₄₇×#400	C₄	1	1	yes	characteristic
35	C₄₇×#399	C₄	1	1	yes	characteristic
36	C₄₇×#398	C₄	1	1	yes	characteristic
37	C₄₇×#397	C₄	1	2	yes	—
38	C₄₇×#397	C₄	1	1	yes	characteristic
39	C₄₇×#394	C₄	1	2	yes	—
40	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
41	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
42	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₂×#10625329	—	2	2	no	—
44	C₂×#10625329	—	2	4	no	—
45	C₂²×C₄₇⋊C₈	—	2	4	no	—
46	C₂²×C₄₇⋊C₈	—	2	2	no	—
47	C₂²×C₄₇⋊C₈	—	2	4	no	—
48	C₂²×C₄₇⋊C₈	D₄	1	4	yes	—
49	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
50	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
54	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
55	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
56	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
57	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
58	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
59	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
60	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
61	#13093935	—	2	4	no	—
62	C₄×C₄₇⋊C₈	—	2	4	no	—
63	C₄×C₄₇⋊C₈	—	2	2	no	—
64	C₄×C₄₇⋊C₈	—	2	4	no	—
65	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₄×D₄×C₄₇	—	2	2	no	—
69	C₄×D₄×C₄₇	—	2	2	no	—
70	#117×C₄₇	—	2	2	no	—
71	#117×C₄₇	—	2	2	no	—
72	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
76	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
77	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
78	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
81	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
82	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
83	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
84	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
86	#95×C₄₇	C₂×C₄	1	2	yes	—
87	#95×C₄₇	C₂×C₄	1	2	yes	—
88	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
89	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
90	#95×C₄₇	C₂×C₄	1	2	yes	—
91	#95×C₄₇	C₂×C₄	1	2	yes	—
92	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂×D₄×C₄₇	—	2	2	no	—
95	C₂×D₄×C₄₇	—	2	2	no	—
96	C₂×D₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	—	2	1	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₄₇	#41	1	2	yes	—
113	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
114	C₄⋊C₄×C₄₇	—	2	2	no	—
115	C₄⋊C₄×C₄₇	—	2	2	no	—
116	C₄⋊C₄×C₄₇	—	2	2	no	—
117	C₄⋊C₄×C₄₇	—	2	4	no	—
118	C₄⋊C₄×C₄₇	—	2	4	no	—
119	C₂²⋊C₄×C₄₇	—	2	4	no	—
120	C₂²⋊C₄×C₄₇	—	2	2	no	—
121	C₂²⋊C₄×C₄₇	—	2	4	no	—
122	C₂²⋊C₄×C₄₇	—	2	2	no	—
123	C₂²⋊C₄×C₄₇	—	2	4	no	—
124	C₂²⋊C₄×C₄₇	—	2	4	no	—
125	C₄²×C₄₇	—	2	2	no	—
126	C₄²×C₄₇	—	2	1	no	—
127	C₄²×C₄₇	—	2	2	no	—
128	C₄²×C₄₇	—	2	1	no	—
129	C₄²×C₄₇	—	2	2	no	—
130	C₄²×C₄₇	—	2	2	no	—
131	#10625329	—	2	8	no	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	—	2	2	no	—
134	C₂×C₄₇⋊C₈	—	2	2	no	—
135	C₂×C₄₇⋊C₈	—	2	8	no	—
136	C₂×C₄₇⋊C₈	—	2	1	no	—
137	C₂×C₄₇⋊C₈	—	2	1	no	—
138	C₂×C₄₇⋊C₈	—	2	2	no	—
139	C₂×C₄₇⋊C₈	—	2	2	no	—
140	C₂×C₄₇⋊C₈	—	2	2	no	—
141	C₂×C₄₇⋊C₈	—	2	2	no	—
142	C₂×C₄₇⋊C₈	—	2	2	no	—
143	C₂×C₄₇⋊C₈	—	4	4	no	—
144	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
145	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
146	C₂×C₄₇⋊C₈	#41	1	4	yes	—
147	C₂×C₄₇⋊C₈	#41	1	4	yes	—
148	C₂³×C₄₇	—	2	1	no	—
149	C₂³×C₄₇	—	2	2	no	—
150	C₂³×C₄₇	—	2	2	no	—
151	C₂³×C₄₇	—	2	2	no	—
152	C₂³×C₄₇	—	2	2	no	—
153	C₂³×C₄₇	—	2	1	no	—
154	C₂³×C₄₇	—	2	1	no	—
155	C₂³×C₄₇	—	2	1	no	—
156	C₂³×C₄₇	C₄×D₄	1	2	yes	—
157	C₂³×C₄₇	#131	1	2	yes	—
158	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
159	D₄×C₄₇	—	2	8	no	—
160	C₂×C₄×C₄₇	—	2	1	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	4	no	—
168	C₂×C₄×C₄₇	—	2	1	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	2	2	no	—
180	C₂×C₄×C₄₇	—	2	2	no	—
181	C₂×C₄×C₄₇	—	4	1	no	—
182	C₂×C₄×C₄₇	—	4	1	no	—
183	C₂×C₄×C₄₇	—	4	2	no	—
184	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
185	C₂×C₄×C₄₇	#131	1	4	yes	—
186	C₂×C₄×C₄₇	#131	1	2	yes	—
187	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
189	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
190	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
191	C₄₇⋊C₈	—	2	2	no	—
192	C₄₇⋊C₈	—	2	4	no	—
193	C₄₇⋊C₈	—	4	1	no	—
194	C₄₇⋊C₈	—	4	1	no	—
195	C₄₇⋊C₈	—	4	2	no	—
196	C₄₇⋊C₈	#123	1	4	yes	—
197	#21566	—	47	1	no	maximal, Sylow
198	C₂²×C₄₇	—	2	2	no	—
199	C₂²×C₄₇	—	2	2	no	—
200	C₂²×C₄₇	—	2	2	no	—
201	C₂²×C₄₇	—	2	4	no	—
202	C₂²×C₄₇	—	2	2	no	—
203	C₂²×C₄₇	—	4	1	no	—
204	C₂²×C₄₇	—	4	2	no	—
205	C₂²×C₄₇	—	4	2	no	—
206	C₂²×C₄₇	—	4	2	no	—
207	C₂²×C₄₇	—	4	1	no	—
208	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
209	C₂²×C₄₇	C₄×#41	1	2	yes	—
210	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
211	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
212	C₂²×C₄₇	C₂×#131	1	2	yes	—
213	C₄×C₄₇	—	2	2	no	—
214	C₄×C₄₇	—	2	4	no	—
215	C₄×C₄₇	—	2	2	no	—
216	C₄×C₄₇	—	4	2	no	—
217	C₄×C₄₇	—	4	1	no	—
218	C₄×C₄₇	—	4	2	no	—
219	C₄×C₄₇	—	4	2	no	—
220	C₄×C₄₇	—	4	1	no	—
221	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
222	C₄×C₄₇	#525	1	1	yes	characteristic
223	C₄×C₄₇	#529	1	2	yes	—
224	C₂×C₈×D₄	—	47	1	no	—
225	C₂×#405	—	47	1	no	—
226	#2395	D₄₇	1	1	yes	characteristic
227	#1924	—	47	2	no	—
228	#1917	—	47	2	no	—
229	#1870	—	47	1	no	—
230	#1851	—	47	1	no	—
231	#1818	—	47	1	no	—
232	C₈×C₄⋊C₄	—	47	2	no	—
233	C₈×C₂²⋊C₄	—	47	1	no	—
234	C₈×C₂²⋊C₄	—	47	2	no	—
235	C₂×C₄₇	—	4	2	no	—
236	C₂×C₄₇	—	4	2	no	—
237	C₂×C₄₇	C₄×#123	1	1	yes	characteristic
238	C₂×C₄₇	#2929	1	1	yes	characteristic
239	C₂×C₄₇	#2931	1	1	yes	characteristic
240	C₂×C₄₇	#2966	1	2	yes	—
241	C₂×C₄₇	#2966	1	2	yes	—
242	C₂²×M₁₆	—	47	1	no	—
243	C₂³×C₈	—	47	1	no	—
244	C₂³×C₈	—	47	1	no	—
245	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
246	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
247	C₈×D₄	—	94	4	no	—
248	C₂×C₄⋊C₈	—	47	2	no	—
249	C₂×C₄⋊C₈	—	47	1	no	—
250	C₂×C₂²⋊C₈	—	47	1	no	—
251	C₂×C₂²⋊C₈	—	47	1	no	—
252	C₂×C₂²⋊C₈	—	47	2	no	—
253	C₂×C₂²⋊C₈	—	47	1	no	—
254	#405	—	94	4	no	—
255	C₂×#97	—	47	2	no	—
256	C₂×C₄×C₈	—	47	2	no	—
257	C₂×C₄×C₈	—	47	1	no	—
258	C₂×C₄×C₈	—	47	2	no	—
259	#400	Dic₄₇	1	1	yes	characteristic
260	#399	Dic₄₇	1	1	yes	characteristic
261	#398	Dic₄₇	1	1	yes	characteristic
262	#397	Dic₄₇	1	2	yes	—
263	#397	Dic₄₇	1	1	yes	characteristic
264	#394	Dic₄₇	1	2	yes	—
265	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
266	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
267	C₄×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
268	#336	—	47	2	no	—
269	#336	—	47	2	no	—
270	#336	—	47	2	no	—
271	#336	—	47	2	no	—
272	#336	—	47	2	no	—
273	C₄₇	#21566	1	1	yes	characteristic, complemented, Sylow
274	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
275	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
276	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
277	C₂×M₁₆	—	94	4	no	—
278	C₂×M₁₆	—	94	2	no	—
279	C₂²×C₈	—	47	1	no	—
280	C₂²×C₈	—	47	4	no	—
281	C₂²×C₈	—	47	1	no	—
282	C₂²×C₈	—	47	2	no	—
283	C₂²×C₈	—	47	1	no	—
284	C₂²×C₈	—	47	2	no	—
285	C₂²×C₈	—	47	1	no	—
286	C₂²×C₈	—	94	4	no	—
287	C₂²×C₈	—	94	4	no	—
288	C₂²×C₈	—	94	2	no	—
289	C₄×D₄	—	2	2	no	—
290	C₄×D₄	—	2	2	no	—
291	#117	—	2	2	no	—
292	#117	—	2	2	no	—
293	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
297	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
298	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
299	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
302	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
303	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
304	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
305	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
306	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
307	C₄⋊C₈	—	94	4	no	—
308	C₄⋊C₈	—	94	2	no	—
309	C₂²⋊C₈	—	94	4	no	—
310	C₂²⋊C₈	—	94	2	no	—
311	C₂²⋊C₈	—	94	2	no	—
312	C₂²⋊C₈	—	94	2	no	—
313	#97	—	94	4	no	—
314	C₄×C₈	—	94	4	no	—
315	C₄×C₈	—	94	4	no	—
316	C₄×C₈	—	94	2	no	—
317	#95	C₂×Dic₄₇	1	2	yes	—
318	#95	C₂×Dic₄₇	1	1	yes	characteristic
319	#95	C₂×Dic₄₇	1	2	yes	—
320	#95	C₂×Dic₄₇	1	1	yes	characteristic
321	#95	C₂×Dic₄₇	1	2	yes	—
322	#95	C₂×Dic₄₇	1	2	yes	—
323	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
324	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	D₄×D₄₇	1	2	yes	—
335	C₂²×C₄	#10625352	1	2	yes	—
336	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
337	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
338	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
339	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
340	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
341	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
342	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
343	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
344	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
345	M₁₆	—	94	8	no	—
346	C₂×C₈	—	47	2	no	—
347	C₂×C₈	—	47	4	no	—
348	C₂×C₈	—	47	2	no	—
349	C₂×C₈	—	47	4	no	—
350	C₂×C₈	—	94	8	no	—
351	C₂×C₈	—	94	2	no	—
352	C₂×C₈	—	94	2	no	—
353	C₂×C₈	—	94	2	no	—
354	C₂×C₈	—	94	1	no	—
355	C₂×C₈	—	94	1	no	—
356	C₂×C₈	—	94	2	no	—
357	C₂×C₈	—	94	2	no	—
358	C₂×C₈	—	94	2	no	—
359	C₂×C₈	—	94	2	no	—
360	C₂×C₈	—	94	2	no	—
361	C₂×C₈	—	188	4	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	1	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	D₄×Dic₄₇	1	2	yes	—
388	C₂³	#13094031	1	2	yes	—
389	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
390	D₄	—	2	8	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
416	C₂×C₄	#13094031	1	4	yes	—
417	C₂×C₄	#13094031	1	2	yes	—
418	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
419	C₂×C₄	#41×D₄₇	1	2	yes	—
420	C₂×C₄	#41×D₄₇	1	2	yes	—
421	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
422	C₈	—	47	4	no	—
423	C₈	—	94	2	no	—
424	C₈	—	94	4	no	—
425	C₈	—	188	1	no	—
426	C₈	—	188	1	no	—
427	C₈	—	188	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
439	C₂²	#41×Dic₄₇	1	2	yes	—
440	C₂²	C₂×#13094031	1	1	yes	characteristic
441	C₂²	C₂×#13094031	1	1	yes	characteristic
442	C₂²	C₂×#13094031	1	2	yes	—
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	4	no	—
446	C₄	—	4	1	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	1	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	2	no	—
451	C₄	#123×D₄₇	1	1	yes	characteristic
452	C₄	#15689631	1	1	yes	characteristic
453	C₄	#15689650	1	2	yes	—
454	C₂	—	4	2	no	—
455	C₂	—	4	2	no	—
456	C₂	#123×Dic₄₇	1	1	yes	characteristic
457	C₂	#20252083	1	1	yes	characteristic
458	C₂	#20252100	1	1	yes	characteristic
459	C₂	#20252364	1	2	yes	—
460	C₂	#20252364	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#2395	C₂
prime radical	C₂²×D₄×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2395	D₄₇
hypocenter	C₄₇	#21566
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #2395

Complements

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

N	H ≅ G/N	type
2. C₂×#15689079	C₂	semidirect
3. #20244003	C₂	semidirect
4. #20243954	C₂	semidirect
6. #20243573	C₂	semidirect
7. #20243459	C₂	semidirect
8. C₄⋊C₄×C₄₇⋊C₈	C₂	semidirect
9. C₂²⋊C₄×C₄₇⋊C₈	C₂	semidirect
10. C₂²⋊C₄×C₄₇⋊C₈	C₂	semidirect
273. C₄₇	#21566	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×C₄₇⋊C₈	2
C₂×#15689079	2
#20244003	2
#20243954	2
#20243686	2
#20243573	2
#20243459	2
C₄⋊C₄×C₄₇⋊C₈	2
C₂²⋊C₄×C₄₇⋊C₈	2
C₄₇×#2395	2
#21566	47