Subgroups — #26107961

Order 12032.

1034 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20243376	C₂	1	1	yes	maximal, characteristic
2	#20243323	C₂	1	2	yes	maximal, complemented
3	#20241960	C₂	1	2	yes	maximal, complemented
4	#20241706	C₂	1	1	yes	maximal, characteristic
5	C₂×D₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#13093948	—	2	4	no	—
7	C₂×#13093939	—	2	1	no	—
8	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
9	#15688983	C₂²	1	2	yes	—
10	#15688890	—	2	1	no	—
11	#15688860	—	2	4	no	—
12	#15688849	—	2	1	no	—
13	#15688847	—	2	1	no	—
14	C₂³×Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
15	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
16	D₄×Q₈×C₄₇	—	2	4	no	—
17	D₄×Q₈×C₄₇	—	2	4	no	—
18	C₂×C₄⋊Q₈×C₄₇	—	2	1	no	—
19	C₂×C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
20	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
21	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
22	C₂×C₂²⋊Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
23	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
25	C₂×C₄×D₄×C₄₇	—	2	1	no	—
26	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄₇⋊C₈	—	2	2	no	—
28	C₂×C₄⋊Dic₄₇	—	2	2	no	—
29	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
30	#13093948	—	4	8	no	—
31	#13093939	—	4	2	no	—
32	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
33	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
34	C₄₇⋊#95	—	2	2	no	—
35	C₂²×Q₈×C₄₇	—	2	2	no	—
36	C₂²×Q₈×C₄₇	—	2	2	no	—
37	C₂²×Q₈×C₄₇	—	2	1	no	—
38	C₂²×Q₈×C₄₇	—	2	1	no	—
39	C₂²×Q₈×C₄₇	—	2	2	no	—
40	C₂²×Q₈×C₄₇	—	4	4	no	—
41	C₂²×Q₈×C₄₇	—	4	4	no	—
42	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
43	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×Q₈×C₄₇	D₄	1	4	yes	—
46	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₇	—	2	1	no	—
48	C₂³×C₄×C₄₇	—	2	1	no	—
49	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
51	C₄⋊Q₈×C₄₇	—	2	8	no	—
52	C₄⋊Q₈×C₄₇	—	2	2	no	—
53	C₄⋊Q₈×C₄₇	—	2	2	no	—
54	C₂²⋊Q₈×C₄₇	—	2	8	no	—
55	C₂²⋊Q₈×C₄₇	—	2	8	no	—
56	C₂²⋊Q₈×C₄₇	—	2	2	no	—
57	C₂²⋊Q₈×C₄₇	—	2	2	no	—
58	C₂²⋊Q₈×C₄₇	—	2	2	no	—
59	C₂²⋊Q₈×C₄₇	D₄	1	4	yes	—
60	C₄×Q₈×C₄₇	—	2	2	no	—
61	C₄×Q₈×C₄₇	—	2	2	no	—
62	C₄×D₄×C₄₇	—	2	8	no	—
63	C₄×D₄×C₄₇	—	2	2	no	—
64	C₄×D₄×C₄₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₄₇	D₄	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₄₇	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₄₇	—	2	1	no	—
77	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
78	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
80	C₂×Q₈×C₄₇	—	2	4	no	—
81	C₂×Q₈×C₄₇	—	2	4	no	—
82	C₂×Q₈×C₄₇	—	2	1	no	—
83	C₂×Q₈×C₄₇	—	2	1	no	—
84	C₂×Q₈×C₄₇	—	2	1	no	—
85	C₂×Q₈×C₄₇	—	2	4	no	—
86	C₂×Q₈×C₄₇	—	2	8	no	—
87	C₂×Q₈×C₄₇	—	4	2	no	—
88	C₂×Q₈×C₄₇	—	4	4	no	—
89	C₂×Q₈×C₄₇	—	4	4	no	—
90	C₂×Q₈×C₄₇	—	4	4	no	—
91	C₂×Q₈×C₄₇	—	4	2	no	—
92	C₂×Q₈×C₄₇	—	4	8	no	—
93	C₂×Q₈×C₄₇	—	4	8	no	—
94	C₂×Q₈×C₄₇	—	4	4	no	—
95	C₂×Q₈×C₄₇	—	4	4	no	—
96	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
97	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
98	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
99	C₂×D₄×C₄₇	—	2	2	no	—
100	C₂×D₄×C₄₇	—	2	2	no	—
101	C₂×D₄×C₄₇	SD₁₆	1	2	yes	—
102	C₂×D₄×C₄₇	Q₁₆	1	2	yes	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	—	2	4	no	—
105	C₂²×C₄×C₄₇	—	2	1	no	—
106	C₂²×C₄×C₄₇	—	2	1	no	—
107	C₂²×C₄×C₄₇	—	2	1	no	—
108	C₂²×C₄×C₄₇	—	2	4	no	—
109	C₂²×C₄×C₄₇	—	2	1	no	—
110	C₂²×C₄×C₄₇	—	2	1	no	—
111	C₂²×C₄×C₄₇	—	4	2	no	—
112	C₂²×C₄×C₄₇	—	4	4	no	—
113	C₂²×C₄×C₄₇	—	4	4	no	—
114	C₂²×C₄×C₄₇	—	4	2	no	—
115	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×Dic₄₇	—	4	2	no	—
123	C₄⋊C₄×C₄₇	—	2	4	no	—
124	C₄⋊C₄×C₄₇	—	2	4	no	—
125	C₄⋊C₄×C₄₇	—	2	4	no	—
126	C₄⋊C₄×C₄₇	—	2	4	no	—
127	C₄⋊C₄×C₄₇	—	2	1	no	—
128	C₄⋊C₄×C₄₇	—	2	4	no	—
129	C₄⋊C₄×C₄₇	—	2	2	no	—
130	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
131	C₂²⋊C₄×C₄₇	—	2	4	no	—
132	C₂²⋊C₄×C₄₇	—	2	4	no	—
133	C₂²⋊C₄×C₄₇	—	2	2	no	—
134	C₂²⋊C₄×C₄₇	—	2	2	no	—
135	C₄²×C₄₇	—	2	4	no	—
136	C₄²×C₄₇	—	2	1	no	—
137	C₄²×C₄₇	—	2	1	no	—
138	C₂²⋊Dic₄₇	—	4	2	no	—
139	C₂²⋊Dic₄₇	—	4	2	no	—
140	C₄⋊Dic₄₇	—	4	4	no	—
141	C₂×C₄₇⋊C₈	—	4	4	no	—
142	C₂×C₄₇⋊C₈	—	4	2	no	—
143	C₂³×C₄₇	—	2	1	no	—
144	C₂³×C₄₇	—	2	1	no	—
145	C₂³×C₄₇	—	4	1	no	—
146	C₂³×C₄₇	—	4	1	no	—
147	C₂³×C₄₇	—	4	1	no	—
148	C₂³×C₄₇	—	4	1	no	—
149	C₂³×C₄₇	#103	1	2	yes	complemented
150	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂³×C₄₇	#120	1	2	yes	—
152	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
153	C₂³×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
154	C₂³×C₄₇	#137	1	2	yes	—
155	Q₈×C₄₇	—	2	4	no	—
156	Q₈×C₄₇	—	2	2	no	—
157	Q₈×C₄₇	—	2	4	no	—
158	Q₈×C₄₇	—	4	8	no	—
159	Q₈×C₄₇	—	4	2	no	—
160	Q₈×C₄₇	—	4	8	no	—
161	Q₈×C₄₇	—	4	2	no	—
162	Q₈×C₄₇	—	4	2	no	—
163	Q₈×C₄₇	#99	1	4	yes	complemented
164	D₄×C₄₇	—	2	4	no	—
165	D₄×C₄₇	—	2	4	no	—
166	C₂×C₄×C₄₇	—	2	4	no	—
167	C₂×C₄×C₄₇	—	2	1	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	1	no	—
170	C₂×C₄×C₄₇	—	2	4	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	1	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	1	no	—
177	C₂×C₄×C₄₇	—	4	1	no	—
178	C₂×C₄×C₄₇	—	4	2	no	—
179	C₂×C₄×C₄₇	—	4	8	no	—
180	C₂×C₄×C₄₇	—	4	8	no	—
181	C₂×C₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	—	4	2	no	—
183	C₂×C₄×C₄₇	—	4	2	no	—
184	C₂×C₄×C₄₇	—	4	2	no	—
185	C₂×C₄×C₄₇	—	4	2	no	—
186	C₂×C₄×C₄₇	—	4	1	no	—
187	C₂×C₄×C₄₇	—	4	1	no	—
188	C₂×C₄×C₄₇	#103	1	2	yes	complemented
189	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₄₇	#120	1	2	yes	—
192	C₂×Dic₄₇	—	8	2	no	—
193	C₂×Dic₄₇	—	8	2	no	—
194	C₂×Dic₄₇	—	8	2	no	—
195	C₄₇⋊C₈	—	8	2	no	—
196	#8379	—	47	1	no	maximal, Sylow
197	C₂²×C₄₇	—	2	2	no	—
198	C₂²×C₄₇	—	2	1	no	—
199	C₂²×C₄₇	—	2	2	no	—
200	C₂²×C₄₇	—	2	1	no	—
201	C₂²×C₄₇	—	2	2	no	—
202	C₂²×C₄₇	—	4	1	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	—	4	1	no	—
209	C₂²×C₄₇	#379	1	1	yes	characteristic
210	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
211	C₂²×C₄₇	#419	1	1	yes	characteristic
212	C₂²×C₄₇	#448	1	2	yes	—
213	C₂²×C₄₇	#451	1	2	yes	—
214	C₄×C₄₇	—	2	2	no	—
215	C₄×C₄₇	—	2	4	no	—
216	C₄×C₄₇	—	2	1	no	—
217	C₄×C₄₇	—	2	2	no	—
218	C₄×C₄₇	—	4	1	no	—
219	C₄×C₄₇	—	4	2	no	—
220	C₄×C₄₇	—	4	2	no	—
221	C₄×C₄₇	—	4	2	no	—
222	C₄×C₄₇	—	4	1	no	—
223	C₄×C₄₇	C₂×#99	1	2	yes	—
224	Dic₄₇	—	16	2	no	—
225	C₂×D₄×Q₈	D₄₇	1	1	yes	characteristic
226	#1799	—	47	1	no	—
227	#1787	—	47	2	no	—
228	#1520	—	47	2	no	—
229	#1459	—	47	1	no	—
230	C₂×C₄₇	—	2	2	no	—
231	C₂×C₄₇	—	2	1	no	—
232	C₂×C₄₇	—	2	1	no	—
233	C₂×C₄₇	—	2	2	no	—
234	C₂×C₄₇	—	4	2	no	—
235	C₂×C₄₇	#1781	1	1	yes	characteristic
236	C₂×C₄₇	#1787	1	1	yes	characteristic
237	C₂×C₄₇	#1796	1	1	yes	characteristic
238	C₂³×Q₈	Dic₄₇	1	1	yes	characteristic, complemented
239	C₂³×Q₈	C₂×D₄₇	1	1	yes	characteristic
240	D₄×Q₈	—	2	4	no	—
241	D₄×Q₈	—	2	4	no	—
242	C₂×C₄⋊Q₈	—	2	1	no	—
243	C₂×C₄⋊Q₈	Dic₄₇	1	1	yes	characteristic, complemented
244	C₂×C₂²⋊Q₈	—	2	1	no	—
245	C₂×C₂²⋊Q₈	—	2	1	no	—
246	C₂×C₂²⋊Q₈	Dic₄₇	1	1	yes	characteristic, complemented
247	C₂×C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
248	C₂×C₄×Q₈	Dic₄₇	1	1	yes	characteristic, complemented
249	C₂×C₄×D₄	—	2	1	no	—
250	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
251	C₂×#103	—	94	4	no	—
252	C₂×#99	—	94	1	no	—
253	C₂×C₂²⋊C₈	—	47	2	no	—
254	#380	—	47	2	no	—
255	#342	—	94	1	no	—
256	#328	—	94	4	no	—
257	#324	—	94	1	no	—
258	#323	—	94	1	no	—
259	C₄₇	#8379	1	1	yes	characteristic, complemented, Sylow
260	C₂²×Q₈	—	2	2	no	—
261	C₂²×Q₈	—	2	2	no	—
262	C₂²×Q₈	—	2	1	no	—
263	C₂²×Q₈	—	2	1	no	—
264	C₂²×Q₈	—	2	2	no	—
265	C₂²×Q₈	—	4	4	no	—
266	C₂²×Q₈	—	4	4	no	—
267	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
268	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
269	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
270	C₂²×Q₈	C₂²⋊D₄₇	1	4	yes	—
271	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
272	C₂³×C₄	—	2	1	no	—
273	C₂³×C₄	—	2	1	no	—
274	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
275	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
276	C₂²×C₈	—	94	2	no	—
277	C₄⋊Q₈	—	2	8	no	—
278	C₄⋊Q₈	—	2	2	no	—
279	C₄⋊Q₈	—	2	2	no	—
280	C₂²⋊Q₈	—	2	8	no	—
281	C₂²⋊Q₈	—	2	8	no	—
282	C₂²⋊Q₈	—	2	2	no	—
283	C₂²⋊Q₈	—	2	2	no	—
284	C₂²⋊Q₈	—	2	2	no	—
285	C₂²⋊Q₈	C₂²⋊D₄₇	1	4	yes	—
286	C₄×Q₈	—	2	2	no	—
287	C₄×Q₈	—	2	2	no	—
288	C₄×D₄	—	2	8	no	—
289	C₄×D₄	—	2	2	no	—
290	C₄×D₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	94	2	no	—
297	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₂²⋊C₄	—	94	2	no	—
302	C₂×C₂²⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
303	C₂×C₂²⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
304	C₂×C₄²	—	2	1	no	—
305	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
306	#103	—	188	8	no	—
307	#99	—	188	2	no	—
308	C₂²⋊C₈	—	94	2	no	—
309	C₂²⋊C₈	—	94	2	no	—
310	#95	—	94	2	no	—
311	C₂⁴	C₂²⋊Dic₄₇	1	1	yes	characteristic
312	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
313	C₂×Q₈	—	2	4	no	—
314	C₂×Q₈	—	2	4	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	4	no	—
319	C₂×Q₈	—	2	8	no	—
320	C₂×Q₈	—	4	2	no	—
321	C₂×Q₈	—	4	4	no	—
322	C₂×Q₈	—	4	2	no	—
323	C₂×Q₈	—	4	4	no	—
324	C₂×Q₈	—	4	4	no	—
325	C₂×Q₈	—	4	8	no	—
326	C₂×Q₈	—	4	8	no	—
327	C₂×Q₈	—	4	4	no	—
328	C₂×Q₈	—	4	4	no	—
329	C₂×Q₈	C₂²⋊Dic₄₇	1	2	yes	—
330	C₂×Q₈	C₂²⋊Dic₄₇	1	2	yes	—
331	C₂×Q₈	C₂²⋊Dic₄₇	1	2	yes	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	#10625336	1	2	yes	—
335	C₂×D₄	#10625337	1	2	yes	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	4	no	—
346	C₂²×C₄	—	4	4	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	188	2	no	—
349	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
350	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
351	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
352	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
353	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
354	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
355	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
356	C₂×C₈	—	188	4	no	—
357	C₂×C₈	—	188	2	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	188	4	no	—
366	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	188	2	no	—
372	C₂²⋊C₄	—	188	2	no	—
373	C₄²	—	2	4	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	1	no	—
382	C₂³	#13093948	1	2	yes	complemented
383	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
384	C₂³	#13093993	1	2	yes	—
385	C₂³	C₂×#10625336	1	1	yes	characteristic
386	C₂³	C₂×#10625337	1	1	yes	characteristic
387	C₂³	#13094055	1	2	yes	—
388	Q₈	—	2	4	no	—
389	Q₈	—	2	2	no	—
390	Q₈	—	2	4	no	—
391	Q₈	—	4	8	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	4	8	no	—
394	Q₈	—	4	2	no	—
395	Q₈	—	4	2	no	—
396	Q₈	#13093939	1	4	yes	complemented
397	D₄	—	2	4	no	—
398	D₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	8	no	—
413	C₂×C₄	—	4	8	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	376	2	no	—
422	C₂×C₄	—	376	2	no	—
423	C₂×C₄	—	376	2	no	—
424	C₂×C₄	#13093948	1	2	yes	complemented
425	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
426	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
427	C₂×C₄	#13093993	1	2	yes	—
428	C₈	—	376	2	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	#15688979	1	1	yes	characteristic
442	C₂²	C₂×#13093948	1	1	yes	characteristic
443	C₂²	#15689132	1	1	yes	characteristic
444	C₂²	#15689262	1	2	yes	—
445	C₂²	#15689279	1	2	yes	—
446	C₄	—	2	2	no	—
447	C₄	—	2	4	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	1	no	—
455	C₄	—	752	2	no	—
456	C₄	C₂×#13093939	1	2	yes	—
457	C₂	—	2	2	no	—
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	—	2	2	no	—
461	C₂	—	4	2	no	—
462	C₂	#20243303	1	1	yes	characteristic
463	C₂	#20243323	1	1	yes	characteristic
464	C₂	#20243363	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15688979
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×D₄×Q₈×C₄₇	C₂
socle	C₂²×C₄₇	#379
prime radical	C₂²×D₄×C₄₇	D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×D₄×Q₈	D₄₇
hypocenter	C₄₇	#8379
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×D₄×Q₈

Complements

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

N	H ≅ G/N	type
2. #20243323	C₂	semidirect
3. #20241960	C₂	semidirect
14. C₂³×Q₈×C₄₇	C₄	semidirect
19. C₂×C₄⋊Q₈×C₄₇	C₄	semidirect
22. C₂×C₂²⋊Q₈×C₄₇	C₄	semidirect
24. C₂×C₄×Q₈×C₄₇	C₄	semidirect
149. C₂³×C₄₇	#103	semidirect
163. Q₈×C₄₇	#99	semidirect
188. C₂×C₄×C₄₇	#103	semidirect
238. C₂³×Q₈	Dic₄₇	semidirect
243. C₂×C₄⋊Q₈	Dic₄₇	semidirect
246. C₂×C₂²⋊Q₈	Dic₄₇	semidirect
248. C₂×C₄×Q₈	Dic₄₇	semidirect
259. C₄₇	#8379	semidirect
382. C₂³	#13093948	semidirect
396. Q₈	#13093939	semidirect
424. C₂×C₄	#13093948	semidirect

Maximal subgroups

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

subgroup	index
#20243376	2
#20243323	2
#20241960	2
#20241706	2
C₂×D₄×Q₈×C₄₇	2
#8379	47