Subgroups — #26220393

Order 12032.

1046 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689176	C₂	1	2	yes	maximal, complemented
2	#20244183	C₂	1	2	yes	maximal
3	#20244107	C₂	1	2	yes	maximal, complemented
4	#20243996	C₂	1	4	yes	maximal, complemented
5	C₄×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×C₂²⋊(C₄₇⋊C₈)	C₂	1	2	yes	maximal, complemented
7	C₄²×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄²×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
9	#15689176	—	2	8	no	—
10	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
11	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
12	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
13	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
14	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
15	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
16	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
17	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	#15688878	C₂²	1	2	yes	—
20	#15688878	C₂²	1	4	yes	—
21	C₂×C₄×D₄×C₄₇	C₄	1	1	yes	characteristic
22	C₂×C₄×D₄×C₄₇	C₄	1	1	yes	characteristic
23	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
25	C₄×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
28	C₄×C₂²⋊C₄×C₄₇	C₄	1	2	yes	—
29	C₄×C₂²⋊C₄×C₄₇	C₄	1	2	yes	—
30	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
31	C₄³×C₄₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
33	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
34	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
35	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
36	C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
37	C₂²⋊(C₄₇⋊C₈)	—	2	8	no	—
38	C₂²⋊(C₄₇⋊C₈)	—	2	8	no	—
39	C₄×C₄₇⋊C₈	—	2	4	no	—
40	C₄×C₄₇⋊C₈	—	2	4	no	—
41	C₄×C₄₇⋊C₈	—	2	2	no	—
42	C₄×C₄₇⋊C₈	—	2	4	no	—
43	C₄×C₄₇⋊C₈	D₄	1	4	yes	complemented
44	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
48	C₄×D₄×C₄₇	—	2	4	no	—
49	C₄×D₄×C₄₇	—	2	4	no	—
50	C₄×D₄×C₄₇	C₈	1	8	yes	complemented
51	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
55	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
56	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₄₇	—	2	4	no	—
58	C₂×C₄²×C₄₇	—	2	4	no	—
59	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
60	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
61	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
66	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
69	#95×C₄₇	C₂×C₄	1	2	yes	—
70	#95×C₄₇	C₂×C₄	1	2	yes	—
71	#95×C₄₇	C₂×C₄	1	2	yes	—
72	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
73	C₂×D₄×C₄₇	—	2	2	no	—
74	C₂×D₄×C₄₇	—	2	2	no	—
75	C₂×D₄×C₄₇	C₂×C₈	1	4	yes	—
76	C₂²×C₄×C₄₇	—	2	4	no	—
77	C₂²×C₄×C₄₇	—	2	4	no	—
78	C₂²×C₄×C₄₇	—	2	4	no	—
79	C₂²×C₄×C₄₇	—	2	4	no	—
80	C₂²×C₄×C₄₇	—	2	4	no	—
81	C₂²×C₄×C₄₇	—	2	2	no	—
82	C₂²×C₄×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	—	2	4	no	—
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	C₂×C₈	1	8	yes	—
86	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
96	C₄⋊C₄×C₄₇	—	2	2	no	—
97	C₄⋊C₄×C₄₇	—	2	2	no	—
98	C₄⋊C₄×C₄₇	C₂×C₈	1	4	yes	—
99	C₂²⋊C₄×C₄₇	—	2	4	no	—
100	C₂²⋊C₄×C₄₇	—	2	4	no	—
101	C₂²⋊C₄×C₄₇	C₂×C₈	1	8	yes	—
102	C₄²×C₄₇	—	2	4	no	—
103	C₄²×C₄₇	—	2	4	no	—
104	C₄²×C₄₇	—	2	2	no	—
105	C₄²×C₄₇	—	2	2	no	—
106	C₄²×C₄₇	—	2	2	no	—
107	C₄²×C₄₇	—	2	2	no	—
108	C₄²×C₄₇	—	2	2	no	—
109	C₄²×C₄₇	C₂×C₈	1	4	yes	—
110	C₄²×C₄₇	M₁₆	1	4	yes	—
111	C₄²×C₄₇	C₂×D₄	1	2	yes	—
112	C₄²×C₄₇	#41	1	4	yes	—
113	C₄²×C₄₇	#41	1	2	yes	—
114	C₂×C₄₇⋊C₈	—	2	2	no	—
115	C₂×C₄₇⋊C₈	—	2	2	no	—
116	C₂×C₄₇⋊C₈	—	2	2	no	—
117	C₂×C₄₇⋊C₈	—	2	2	no	—
118	C₂×C₄₇⋊C₈	—	2	4	no	—
119	C₂×C₄₇⋊C₈	—	2	4	no	—
120	C₂×C₄₇⋊C₈	—	2	4	no	—
121	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
122	C₂×C₄₇⋊C₈	#41	1	4	yes	—
123	C₂³×C₄₇	—	2	2	no	—
124	C₂³×C₄₇	—	2	2	no	—
125	C₂³×C₄₇	—	2	2	no	—
126	C₂³×C₄₇	—	2	2	no	—
127	C₂³×C₄₇	—	2	2	no	—
128	C₂³×C₄₇	—	2	2	no	—
129	C₂³×C₄₇	C₂²×C₈	1	4	yes	—
130	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
131	D₄×C₄₇	—	2	8	no	—
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	2	1	no	—
134	C₂×C₄×C₄₇	—	2	1	no	—
135	C₂×C₄×C₄₇	—	2	1	no	—
136	C₂×C₄×C₄₇	—	2	1	no	—
137	C₂×C₄×C₄₇	—	2	1	no	—
138	C₂×C₄×C₄₇	—	2	1	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	16	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	2	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	4	4	no	—
148	C₂×C₄×C₄₇	—	4	4	no	—
149	C₂×C₄×C₄₇	—	4	8	no	—
150	C₂×C₄×C₄₇	#117	1	2	yes	—
151	C₂×C₄×C₄₇	#117	1	2	yes	—
152	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
153	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
154	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
155	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
156	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
157	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
158	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
159	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
160	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
161	C₂×C₄×C₄₇	#131	1	2	yes	—
162	C₂×C₄×C₄₇	#131	1	2	yes	—
163	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
165	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
167	C₄₇⋊C₈	—	2	4	no	—
168	C₄₇⋊C₈	—	2	4	no	—
169	C₄₇⋊C₈	—	4	4	no	—
170	#21264	—	47	1	no	maximal, Sylow
171	C₂²×C₄₇	—	2	4	no	—
172	C₂²×C₄₇	—	2	4	no	—
173	C₂²×C₄₇	—	2	4	no	—
174	C₂²×C₄₇	—	4	2	no	—
175	C₂²×C₄₇	—	4	2	no	—
176	C₂²×C₄₇	—	4	2	no	—
177	C₂²×C₄₇	—	4	2	no	—
178	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
179	C₂²×C₄₇	C₂×C₄×D₄	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	C₂²×M₁₆	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	—	2	2	no	—
188	C₄×C₄₇	—	2	2	no	—
189	C₄×C₄₇	—	4	2	no	—
190	C₄×C₄₇	—	4	2	no	—
191	C₄×C₄₇	#431	1	4	yes	complemented
192	C₄×C₄₇	C₈×D₄	1	4	yes	—
193	C₄×C₄₇	#436	1	4	yes	—
194	C₄×C₄₇	#529	1	2	yes	—
195	C₄×C₄₇	#532	1	2	yes	—
196	C₂×#431	—	47	2	no	—
197	C₄²×D₄	D₄₇	1	1	yes	characteristic
198	#1954	—	47	2	no	—
199	#1939	—	47	2	no	—
200	#1923	—	47	4	no	—
201	C₄×C₄⋊C₈	—	47	1	no	—
202	C₄×C₂²⋊C₈	—	47	2	no	—
203	C₄²×C₈	—	47	1	no	—
204	C₂×C₄₇	—	4	4	no	—
205	C₂×C₄₇	#2293	1	1	yes	characteristic
206	C₂×C₄₇	C₂×#431	1	1	yes	characteristic
207	C₂×C₄₇	#2922	1	1	yes	characteristic
208	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
209	C₂×C₄₇	C₂×#436	1	1	yes	characteristic
210	C₂×C₄₇	C₈×#41	1	1	yes	characteristic
211	C₂×C₄₇	#2965	1	1	yes	characteristic
212	C₂×C₄×D₄	Dic₄₇	1	1	yes	characteristic
213	C₂×C₄×D₄	Dic₄₇	1	1	yes	characteristic
214	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
215	C₂²×C₄²	C₂×D₄₇	1	2	yes	—
216	#431	—	94	8	no	—
217	C₂×C₄⋊C₈	—	47	4	no	—
218	C₂×C₄⋊C₈	—	47	2	no	—
219	C₂×C₂²⋊C₈	—	47	4	no	—
220	C₂×C₂²⋊C₈	—	47	4	no	—
221	C₂×C₄×C₈	—	47	1	no	—
222	C₂×C₄×C₈	—	47	2	no	—
223	C₂×C₄×C₈	—	47	2	no	—
224	C₂×C₄×C₈	—	47	2	no	—
225	C₂×C₄×C₈	—	47	1	no	—
226	C₄×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
227	C₄×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
228	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
229	C₄×C₂²⋊C₄	Dic₄₇	1	2	yes	—
230	C₄×C₂²⋊C₄	Dic₄₇	1	2	yes	—
231	C₄×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
232	C₄³	C₂×D₄₇	1	1	yes	characteristic
233	#336	—	47	2	no	—
234	#336	—	47	4	no	—
235	C₄₇	#21264	1	1	yes	characteristic, complemented, Sylow
236	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
237	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
238	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
239	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
240	C₂²×C₈	—	47	2	no	—
241	C₂²×C₈	—	47	2	no	—
242	C₂²×C₈	—	47	4	no	—
243	C₄×D₄	—	2	4	no	—
244	C₄×D₄	—	2	4	no	—
245	C₄×D₄	C₄₇⋊C₈	1	8	yes	complemented
246	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
250	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
251	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
252	C₂×C₄²	—	2	4	no	—
253	C₂×C₄²	—	2	4	no	—
254	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
255	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
256	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
257	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
258	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
259	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
260	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
261	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
262	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
263	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
264	C₄⋊C₈	—	94	8	no	—
265	C₄⋊C₈	—	94	4	no	—
266	C₂²⋊C₈	—	94	8	no	—
267	C₂²⋊C₈	—	94	8	no	—
268	C₄×C₈	—	47	4	no	—
269	C₄×C₈	—	94	4	no	—
270	C₄×C₈	—	94	4	no	—
271	C₄×C₈	—	94	4	no	—
272	C₄×C₈	—	94	2	no	—
273	#95	C₂×Dic₄₇	1	2	yes	—
274	#95	C₂×Dic₄₇	1	2	yes	—
275	#95	C₂×Dic₄₇	1	2	yes	—
276	C₂⁴	C₂²×Dic₄₇	1	2	yes	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	C₂×C₄₇⋊C₈	1	4	yes	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	C₂×C₄₇⋊C₈	1	8	yes	—
290	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
291	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
292	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
293	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
294	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
295	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
296	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
297	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
298	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
299	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
300	C₂×C₈	—	47	4	no	—
301	C₂×C₈	—	47	4	no	—
302	C₂×C₈	—	94	2	no	—
303	C₂×C₈	—	94	2	no	—
304	C₂×C₈	—	94	2	no	—
305	C₂×C₈	—	94	2	no	—
306	C₂×C₈	—	94	4	no	—
307	C₂×C₈	—	94	4	no	—
308	C₂×C₈	—	94	4	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	C₂×C₄₇⋊C₈	1	4	yes	—
312	C₂²⋊C₄	—	2	4	no	—
313	C₂²⋊C₄	—	2	4	no	—
314	C₂²⋊C₄	C₂×C₄₇⋊C₈	1	8	yes	—
315	C₄²	—	2	4	no	—
316	C₄²	—	2	4	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	2	no	—
322	C₄²	C₂×C₄₇⋊C₈	1	4	yes	—
323	C₄²	#10625329	1	4	yes	—
324	C₄²	#10625350	1	4	yes	—
325	C₄²	D₄×D₄₇	1	2	yes	—
326	C₄²	#10625352	1	2	yes	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	C₂²×C₄₇⋊C₈	1	4	yes	—
334	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
335	D₄	—	2	8	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	16	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	8	no	—
354	C₂×C₄	#13093983	1	2	yes	—
355	C₂×C₄	#13093983	1	2	yes	—
356	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
357	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
358	C₂×C₄	C₂²×C₄₇⋊C₈	1	2	yes	—
359	C₂×C₄	C₂²×C₄₇⋊C₈	1	4	yes	—
360	C₂×C₄	C₂²×C₄₇⋊C₈	1	2	yes	—
361	C₂×C₄	C₂²×C₄₇⋊C₈	1	2	yes	—
362	C₂×C₄	C₂×#10625329	1	2	yes	—
363	C₂×C₄	C₂×#10625329	1	2	yes	—
364	C₂×C₄	C₂×#10625329	1	2	yes	—
365	C₂×C₄	#13094031	1	2	yes	—
366	C₂×C₄	#13094031	1	2	yes	—
367	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
368	C₂×C₄	#41×D₄₇	1	2	yes	—
369	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
370	C₂×C₄	C₂×#10625350	1	2	yes	—
371	C₈	—	94	4	no	—
372	C₈	—	94	4	no	—
373	C₈	—	188	4	no	—
374	C₂²	—	2	4	no	—
375	C₂²	—	2	4	no	—
376	C₂²	—	2	4	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	C₂×#13093983	1	1	yes	characteristic
382	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
383	C₂²	#41×Dic₄₇	1	1	yes	characteristic
384	C₂²	C₂³×C₄₇⋊C₈	1	1	yes	characteristic
385	C₂²	C₂²×#10625329	1	1	yes	characteristic
386	C₂²	C₂×#13094031	1	1	yes	characteristic
387	C₂²	C₂×#13094031	1	1	yes	characteristic
388	C₄	—	2	2	no	—
389	C₄	—	2	4	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	2	no	—
394	C₄	#15689176	1	4	yes	complemented
395	C₄	D₄×C₄₇⋊C₈	1	4	yes	—
396	C₄	#15689201	1	4	yes	—
397	C₄	#15689655	1	2	yes	—
398	C₄	#15689670	1	2	yes	—
399	C₂	—	4	4	no	—
400	C₂	#20245853	1	1	yes	characteristic
401	C₂	C₂×#15689176	1	1	yes	characteristic
402	C₂	#20252032	1	1	yes	characteristic
403	C₂	C₂×D₄×C₄₇⋊C₈	1	1	yes	characteristic
404	C₂	C₂×#15689201	1	1	yes	characteristic
405	C₂	#41×C₄₇⋊C₈	1	1	yes	characteristic
406	C₂	#20252355	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄²×D₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×D₄×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄²×D₄	D₄₇
hypocenter	C₄₇	#21264
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄² ◁ C₄²×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#15689176	C₂	semidirect
3. #20244107	C₂	semidirect
4. #20243996	C₂	semidirect
5. C₄×C₄⋊(C₄₇⋊C₈)	C₂	semidirect
6. C₄×C₂²⋊(C₄₇⋊C₈)	C₂	semidirect
7. C₄²×C₄₇⋊C₈	C₂	semidirect
43. C₄×C₄₇⋊C₈	D₄	semidirect
50. C₄×D₄×C₄₇	C₈	semidirect
191. C₄×C₄₇	#431	semidirect
235. C₄₇	#21264	semidirect
245. C₄×D₄	C₄₇⋊C₈	semidirect
394. C₄	#15689176	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689176	2
#20244183	2
#20244107	2
#20243996	2
C₄×C₄⋊(C₄₇⋊C₈)	2
C₄×C₂²⋊(C₄₇⋊C₈)	2
C₄²×C₄₇⋊C₈	2
C₄²×D₄×C₄₇	2
#21264	47