Subgroups — #26121503

Order 12032.

1670 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688878	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₄₇⋊C₈	—	2	8	no	—
6	C₂³×C₄₇⋊C₈	—	2	2	no	—
7	C₂³×C₄₇⋊C₈	—	2	2	no	—
8	C₂³×C₄₇⋊C₈	C₄	1	4	yes	complemented
9	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
10	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
11	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
12	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
13	C₂×C₂²⋊(C₄₇⋊C₈)	C₄	1	4	yes	complemented
14	#15688878	—	2	8	no	—
15	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊C₄×C₄₇	C₄	1	2	yes	—
17	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
18	C₄×C₂²⋊C₄×C₄₇	—	2	2	no	—
19	C₄×C₂²⋊C₄×C₄₇	—	2	2	no	—
20	C₂×#95×C₄₇	C₄	1	2	yes	—
21	C₂²×C₄₇⋊C₈	—	2	16	no	—
22	C₂²×C₄₇⋊C₈	—	2	16	no	—
23	C₂²×C₄₇⋊C₈	—	2	8	no	—
24	C₂²×C₄₇⋊C₈	—	2	2	no	—
25	C₂²×C₄₇⋊C₈	—	2	2	no	—
26	C₂²×C₄₇⋊C₈	—	2	4	no	—
27	C₂²×C₄₇⋊C₈	—	2	16	no	—
28	C₂²×C₄₇⋊C₈	—	2	2	no	—
29	C₂²×C₄₇⋊C₈	—	2	2	no	—
30	C₂²×C₄₇⋊C₈	—	2	4	no	—
31	C₂²×C₄₇⋊C₈	—	2	4	no	—
32	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
33	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
34	C₂²×C₄₇⋊C₈	D₄	1	8	yes	—
35	C₂²⋊(C₄₇⋊C₈)	—	2	8	no	—
36	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₇	—	2	4	no	—
38	C₂³×C₄×C₄₇	—	2	4	no	—
39	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
40	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
42	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
43	C₂³×C₄×C₄₇	D₄	1	2	yes	—
44	C₂³×C₄×C₄₇	D₄	1	2	yes	—
45	C₂³×C₄×C₄₇	D₄	1	2	yes	—
46	C₂³×C₄×C₄₇	Q₈	1	2	yes	—
47	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
48	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
49	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
50	C₂×C₂²⋊C₄×C₄₇	C₈	1	8	yes	complemented
51	C₂×C₄²×C₄₇	—	2	4	no	—
52	C₂×C₄²×C₄₇	—	2	2	no	—
53	C₂×C₄²×C₄₇	—	2	2	no	—
54	C₂×C₄²×C₄₇	—	2	4	no	—
55	#95×C₄₇	—	2	4	no	—
56	C₂⁴×C₄₇	—	2	4	no	—
57	C₂⁴×C₄₇	—	2	4	no	—
58	C₂⁴×C₄₇	C₄²	1	2	yes	—
59	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
60	C₂⁴×C₄₇	C₄⋊C₄	1	2	yes	—
61	C₂⁴×C₄₇	C₂×C₈	1	4	yes	—
62	C₂⁴×C₄₇	M₁₆	1	4	yes	—
63	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₄₇	—	2	4	no	—
65	C₂²×C₄×C₄₇	—	2	4	no	—
66	C₂²×C₄×C₄₇	—	2	4	no	—
67	C₂²×C₄×C₄₇	—	2	8	no	—
68	C₂²×C₄×C₄₇	—	2	4	no	—
69	C₂²×C₄×C₄₇	—	2	4	no	—
70	C₂²×C₄×C₄₇	—	2	8	no	—
71	C₂²×C₄×C₄₇	—	2	8	no	—
72	C₂²×C₄×C₄₇	—	2	4	no	—
73	C₂²×C₄×C₄₇	—	2	4	no	—
74	C₂²×C₄×C₄₇	—	2	4	no	—
75	C₂²×C₄×C₄₇	—	2	8	no	—
76	C₂²×C₄×C₄₇	—	2	4	no	—
77	C₂²×C₄×C₄₇	—	2	8	no	—
78	C₂²×C₄×C₄₇	C₄²	1	2	yes	—
79	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
80	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
81	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
82	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
83	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
84	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
85	C₂²×C₄×C₄₇	C₂×C₈	1	8	yes	complemented
86	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
92	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	#41	1	4	yes	—
94	C₂²⋊C₄×C₄₇	—	2	16	no	—
95	C₄²×C₄₇	—	4	2	no	—
96	C₄²×C₄₇	—	4	4	no	—
97	C₄²×C₄₇	—	4	2	no	—
98	C₂×C₄₇⋊C₈	—	2	32	no	—
99	C₂×C₄₇⋊C₈	—	2	4	no	—
100	C₂×C₄₇⋊C₈	—	2	4	no	—
101	C₂×C₄₇⋊C₈	—	2	8	no	—
102	C₂×C₄₇⋊C₈	—	2	8	no	—
103	C₂×C₄₇⋊C₈	—	2	4	no	—
104	C₂×C₄₇⋊C₈	—	2	8	no	—
105	C₂×C₄₇⋊C₈	—	4	2	no	—
106	C₂×C₄₇⋊C₈	—	4	4	no	—
107	C₂×C₄₇⋊C₈	—	4	2	no	—
108	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	8	yes	complemented
109	C₂³×C₄₇	—	2	4	no	—
110	C₂³×C₄₇	—	2	4	no	—
111	C₂³×C₄₇	—	2	4	no	—
112	C₂³×C₄₇	—	2	4	no	—
113	C₂³×C₄₇	—	2	4	no	—
114	C₂³×C₄₇	—	2	4	no	—
115	C₂³×C₄₇	—	2	16	no	—
116	C₂³×C₄₇	—	2	16	no	—
117	C₂³×C₄₇	#95	1	4	yes	—
118	C₂³×C₄₇	C₄×C₈	1	4	yes	—
119	C₂³×C₄₇	#97	1	4	yes	—
120	C₂³×C₄₇	C₂²⋊C₈	1	8	yes	—
121	C₂³×C₄₇	C₄⋊C₈	1	8	yes	—
122	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
123	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
124	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
125	C₂³×C₄₇	C₄×D₄	1	4	yes	—
126	C₂³×C₄₇	C₂²×C₈	1	2	yes	—
127	C₂³×C₄₇	C₂×M₁₆	1	2	yes	—
128	C₂³×C₄₇	#131	1	4	yes	—
129	C₂×C₄×C₄₇	—	2	4	no	—
130	C₂×C₄×C₄₇	—	2	4	no	—
131	C₂×C₄×C₄₇	—	2	4	no	—
132	C₂×C₄×C₄₇	—	2	4	no	—
133	C₂×C₄×C₄₇	—	2	8	no	—
134	C₂×C₄×C₄₇	—	2	4	no	—
135	C₂×C₄×C₄₇	—	2	8	no	—
136	C₂×C₄×C₄₇	—	2	8	no	—
137	C₂×C₄×C₄₇	—	2	8	no	—
138	C₂×C₄×C₄₇	—	2	16	no	—
139	C₂×C₄×C₄₇	—	4	4	no	—
140	C₂×C₄×C₄₇	—	4	4	no	—
141	C₂×C₄×C₄₇	—	4	8	no	—
142	C₂×C₄×C₄₇	#95	1	4	yes	—
143	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
144	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₄₇	#117	1	2	yes	—
149	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
150	C₂×C₄×C₄₇	#120	1	2	yes	—
151	C₂×C₄×C₄₇	#120	1	2	yes	—
152	C₂×C₄×C₄₇	#121	1	4	yes	—
153	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
154	C₂×C₄×C₄₇	#123	1	2	yes	—
155	C₂×C₄×C₄₇	#123	1	2	yes	—
156	C₄₇⋊C₈	—	2	8	no	—
157	C₄₇⋊C₈	—	4	4	no	—
158	#10714	—	47	1	no	maximal, Sylow
159	C₂²×C₄₇	—	2	16	no	—
160	C₂²×C₄₇	—	2	16	no	—
161	C₂²×C₄₇	—	2	4	no	—
162	C₂²×C₄₇	—	2	4	no	—
163	C₂²×C₄₇	—	2	8	no	—
164	C₂²×C₄₇	—	2	8	no	—
165	C₂²×C₄₇	#336	1	8	yes	complemented
166	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
167	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
168	C₂²×C₄₇	#385	1	2	yes	—
169	C₂²×C₄₇	#386	1	2	yes	—
170	C₂²×C₄₇	C₂×C₄×C₈	1	1	yes	characteristic
171	C₂²×C₄₇	C₂×#97	1	1	yes	characteristic
172	C₂²×C₄₇	#405	1	2	yes	—
173	C₂²×C₄₇	C₂×C₂²⋊C₈	1	2	yes	—
174	C₂²×C₄₇	#408	1	2	yes	—
175	C₂²×C₄₇	C₂×C₄⋊C₈	1	2	yes	—
176	C₂²×C₄₇	#424	1	2	yes	—
177	C₂²×C₄₇	C₈×D₄	1	8	yes	—
178	C₂²×C₄₇	#435	1	8	yes	—
179	C₄×C₄₇	—	2	4	no	—
180	C₄×C₄₇	—	4	8	no	—
181	C₄×C₄₇	#379	1	1	yes	characteristic
182	C₄×C₄₇	#380	1	2	yes	—
183	C₄×C₄₇	#381	1	1	yes	characteristic
184	C₄×C₄₇	#385	1	2	yes	—
185	C₄×C₄₇	#386	1	2	yes	—
186	C₂⁴×C₈	—	47	1	no	—
187	C₂²×C₂²⋊C₈	—	47	1	no	—
188	C₂×C₄×C₂²⋊C₄	D₄₇	1	1	yes	characteristic
189	C₂×#336	—	47	4	no	—
190	C₂×C₄₇	—	2	8	no	—
191	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
192	C₂×C₄₇	C₂×#336	1	1	yes	characteristic
193	C₂×C₄₇	#1729	1	1	yes	characteristic
194	C₂×C₄₇	C₈×C₂²⋊C₄	1	2	yes	—
195	C₂×C₄₇	#1752	1	2	yes	—
196	C₂×C₄₇	#1850	1	4	yes	—
197	C₂×C₄₇	#1869	1	4	yes	—
198	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
199	C₂³×C₈	—	47	2	no	—
200	C₂³×C₈	—	47	4	no	—
201	C₂³×C₈	—	47	2	no	—
202	C₂³×C₈	—	94	8	no	—
203	C₂³×C₈	—	94	2	no	—
204	C₂³×C₈	—	94	2	no	—
205	C₂²×C₂²⋊C₄	Dic₄₇	1	2	yes	—
206	C₂²×C₄²	C₂×D₄₇	1	2	yes	—
207	C₂×C₂²⋊C₈	—	47	4	no	—
208	C₂×C₂²⋊C₈	—	94	2	no	—
209	C₂×C₂²⋊C₈	—	94	2	no	—
210	C₄×C₂²⋊C₄	—	2	2	no	—
211	C₄×C₂²⋊C₄	—	2	2	no	—
212	C₂×#95	Dic₄₇	1	2	yes	—
213	#336	—	94	8	no	—
214	C₄₇	#10714	1	1	yes	characteristic, complemented, Sylow
215	C₂⁵	C₂×Dic₄₇	1	1	yes	characteristic
216	C₂³×C₄	—	2	4	no	—
217	C₂³×C₄	—	2	4	no	—
218	C₂³×C₄	Dic₉₄	1	2	yes	—
219	C₂³×C₄	C₄×D₄₇	1	2	yes	—
220	C₂³×C₄	C₄×D₄₇	1	2	yes	—
221	C₂³×C₄	D₁₈₈	1	2	yes	—
222	C₂³×C₄	C₂×Dic₄₇	1	4	yes	—
223	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
224	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
225	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
226	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
227	C₂²×C₈	—	47	4	no	—
228	C₂²×C₈	—	47	8	no	—
229	C₂²×C₈	—	47	4	no	—
230	C₂²×C₈	—	94	16	no	—
231	C₂²×C₈	—	94	16	no	—
232	C₂²×C₈	—	94	16	no	—
233	C₂²×C₈	—	94	8	no	—
234	C₂²×C₈	—	94	2	no	—
235	C₂²×C₈	—	94	4	no	—
236	C₂²×C₈	—	94	2	no	—
237	C₂²×C₈	—	94	2	no	—
238	C₂²×C₈	—	94	4	no	—
239	C₂²×C₈	—	94	4	no	—
240	C₂²×C₈	—	94	2	no	—
241	C₂×C₂²⋊C₄	—	2	4	no	—
242	C₂×C₂²⋊C₄	—	2	4	no	—
243	C₂×C₂²⋊C₄	C₄₇⋊C₈	1	8	yes	complemented
244	C₂×C₄²	—	2	4	no	—
245	C₂×C₄²	—	2	4	no	—
246	C₂×C₄²	—	2	2	no	—
247	C₂×C₄²	—	2	2	no	—
248	C₂²⋊C₈	—	94	8	no	—
249	#95	—	2	4	no	—
250	C₂⁴	—	2	4	no	—
251	C₂⁴	—	2	4	no	—
252	C₂⁴	C₂×C₄₇⋊C₈	1	4	yes	—
253	C₂⁴	#10625329	1	4	yes	—
254	C₂⁴	C₄×Dic₄₇	1	2	yes	—
255	C₂⁴	C₄⋊Dic₄₇	1	2	yes	—
256	C₂⁴	C₂²⋊Dic₄₇	1	2	yes	—
257	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	8	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	8	no	—
265	C₂²×C₄	—	2	8	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	8	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	8	no	—
272	C₂²×C₄	C₂×C₄₇⋊C₈	1	8	yes	complemented
273	C₂²×C₄	C₄×Dic₄₇	1	2	yes	—
274	C₂²×C₄	Dic₄₇⋊C₄	1	4	yes	—
275	C₂²×C₄	Dic₄₇⋊C₄	1	4	yes	—
276	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
277	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	4	yes	—
278	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	4	yes	—
279	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
280	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
284	C₂²×C₄	D₄×D₄₇	1	4	yes	—
285	C₂²×C₄	#10625352	1	4	yes	—
286	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
288	C₂×C₈	—	47	8	no	—
289	C₂×C₈	—	94	32	no	—
290	C₂×C₈	—	94	4	no	—
291	C₂×C₈	—	94	4	no	—
292	C₂×C₈	—	94	8	no	—
293	C₂×C₈	—	94	8	no	—
294	C₂×C₈	—	94	4	no	—
295	C₂×C₈	—	94	8	no	—
296	C₂×C₈	—	188	2	no	—
297	C₂×C₈	—	188	4	no	—
298	C₂×C₈	—	188	2	no	—
299	C₂²⋊C₄	—	2	16	no	—
300	C₄²	—	4	2	no	—
301	C₄²	—	4	4	no	—
302	C₄²	—	4	2	no	—
303	C₂³	—	2	4	no	—
304	C₂³	—	2	4	no	—
305	C₂³	—	2	4	no	—
306	C₂³	—	2	4	no	—
307	C₂³	—	2	4	no	—
308	C₂³	—	2	4	no	—
309	C₂³	—	2	16	no	—
310	C₂³	—	2	16	no	—
311	C₂³	C₄₇⋊#95	1	4	yes	—
312	C₂³	C₄×C₄₇⋊C₈	1	4	yes	—
313	C₂³	#13093935	1	4	yes	—
314	C₂³	C₂²⋊(C₄₇⋊C₈)	1	8	yes	—
315	C₂³	C₄⋊(C₄₇⋊C₈)	1	8	yes	—
316	C₂³	C₂×C₄×Dic₄₇	1	1	yes	characteristic
317	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
318	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
319	C₂³	D₄×Dic₄₇	1	4	yes	—
320	C₂³	C₂²×C₄₇⋊C₈	1	2	yes	—
321	C₂³	C₂×#10625329	1	2	yes	—
322	C₂³	#13094031	1	4	yes	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	2	16	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	4	8	no	—
336	C₂×C₄	C₄₇⋊#95	1	4	yes	—
337	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
338	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
339	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
340	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
341	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
342	C₂×C₄	#13093980	1	2	yes	—
343	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	4	yes	—
344	C₂×C₄	#13093992	1	2	yes	—
345	C₂×C₄	#13093994	1	2	yes	—
346	C₂×C₄	#13093996	1	4	yes	—
347	C₂×C₄	#13094001	1	4	yes	—
348	C₂×C₄	#13094005	1	2	yes	—
349	C₂×C₄	#13094008	1	2	yes	—
350	C₈	—	94	8	no	—
351	C₈	—	188	4	no	—
352	C₂²	—	2	16	no	—
353	C₂²	—	2	4	no	—
354	C₂²	—	2	4	no	—
355	C₂²	—	2	8	no	—
356	C₂²	—	2	8	no	—
357	C₂²	—	2	16	no	—
358	C₂²	#15688878	1	8	yes	complemented
359	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
360	C₂²	C₂²⋊C₄×Dic₄₇	1	2	yes	—
361	C₂²	#15688998	1	2	yes	—
362	C₂²	#15689003	1	2	yes	—
363	C₂²	C₂×C₄×C₄₇⋊C₈	1	1	yes	characteristic
364	C₂²	C₂×#13093935	1	1	yes	characteristic
365	C₂²	#15689079	1	2	yes	—
366	C₂²	C₂×C₂²⋊(C₄₇⋊C₈)	1	2	yes	—
367	C₂²	#15689090	1	2	yes	—
368	C₂²	C₂×C₄⋊(C₄₇⋊C₈)	1	2	yes	—
369	C₂²	#15689150	1	2	yes	—
370	C₂²	D₄×C₄₇⋊C₈	1	8	yes	—
371	C₂²	#15689195	1	8	yes	—
372	C₄	—	2	4	no	—
373	C₄	—	4	8	no	—
374	C₄	#15688978	1	1	yes	characteristic
375	C₄	#15688981	1	2	yes	—
376	C₄	#15688984	1	1	yes	characteristic
377	C₄	#15688995	1	2	yes	—
378	C₄	#15689000	1	2	yes	—
379	C₂	—	2	8	no	—
380	C₂	#20241610	1	1	yes	characteristic
381	C₂	C₂×#15688878	1	1	yes	characteristic
382	C₂	#20243085	1	1	yes	characteristic
383	C₂	C₂²⋊C₄×C₄₇⋊C₈	1	2	yes	—
384	C₂	#20243166	1	2	yes	—
385	C₂	#20243568	1	4	yes	—
386	C₂	#20243681	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂×C₄×C₈
Fitting	C₂×C₄×C₂²⋊C₄×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂²×C₄
prime radical	C₂⁵×C₄₇	C₂×C₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×C₄×C₂²⋊C₄	D₄₇
hypocenter	C₄₇	#10714
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×C₄×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
3. C₂×#15688878	C₂	semidirect
8. C₂³×C₄₇⋊C₈	C₄	semidirect
13. C₂×C₂²⋊(C₄₇⋊C₈)	C₄	semidirect
50. C₂×C₂²⋊C₄×C₄₇	C₈	semidirect
85. C₂²×C₄×C₄₇	C₂×C₈	semidirect
108. C₂×C₄₇⋊C₈	C₂²⋊C₄	semidirect
165. C₂²×C₄₇	#336	semidirect
214. C₄₇	#10714	semidirect
243. C₂×C₂²⋊C₄	C₄₇⋊C₈	semidirect
272. C₂²×C₄	C₂×C₄₇⋊C₈	semidirect
358. C₂²	#15688878	semidirect

Maximal subgroups

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

subgroup	index
C₂⁴×C₄₇⋊C₈	2
C₂²×C₂²⋊(C₄₇⋊C₈)	2
C₂×#15688878	2
C₂×C₄×C₂²⋊C₄×C₄₇	2
#10714	47