Subgroups — #26215251

Order 12032.

1002 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689201	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#20243257	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄⋊C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243172	C₂	1	2	yes	maximal, complemented
7	C₂²⋊C₄×C₄₇⋊C₈	C₂	1	2	yes	maximal, complemented
8	#20243154	C₂	1	2	yes	maximal, complemented
9	#20243134	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243085	C₂	1	2	yes	maximal, complemented
11	C₄₇×#2293	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625329	C₂²	1	2	yes	—
13	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
14	#15689201	C₄	1	8	yes	complemented
15	D₄×C₄₇⋊C₈	C₄	1	8	yes	complemented
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
19	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
20	C₂×#13093935	C₂²	1	2	yes	—
21	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
22	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
23	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	#15688878	C₂²	1	2	yes	—
26	#15688878	C₂²	1	2	yes	—
27	#15688878	C₂²	1	2	yes	—
28	#15688878	C₂²	1	1	yes	characteristic
29	#15688878	C₂²	1	1	yes	characteristic
30	#15688878	C₂²	1	1	yes	characteristic
31	#15688878	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×#117×C₄₇	C₂²	1	2	yes	—
34	C₄₇×#390	C₄	1	2	yes	—
35	C₄₇×#389	C₄	1	2	yes	—
36	C₄₇×#388	C₄	1	4	yes	—
37	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
39	C₄³×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×#10625329	—	4	2	no	—
41	C₂×#10625329	—	4	2	no	—
42	C₂×#10625329	C₂×C₄	1	8	yes	—
43	C₂²×C₄₇⋊C₈	—	4	2	no	—
44	C₂²×C₄₇⋊C₈	—	4	2	no	—
45	C₂²×C₄₇⋊C₈	C₂×C₄	1	8	yes	—
46	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
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	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
53	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
54	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	—
55	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	—
56	#13093935	—	4	2	no	—
57	C₄×C₄₇⋊C₈	—	4	2	no	—
58	C₄×C₄₇⋊C₈	—	4	2	no	—
59	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
60	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
61	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
63	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
64	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
65	#117×C₄₇	—	4	2	no	—
66	#117×C₄₇	—	4	2	no	—
67	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
69	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
71	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
72	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
74	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
75	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	#95×C₄₇	C₂×C₄	1	4	yes	—
80	#95×C₄₇	C₂×C₄	1	2	yes	—
81	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
82	C₂×D₄×C₄₇	—	2	4	no	—
83	C₂×D₄×C₄₇	C₄²	1	4	yes	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
94	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
97	C₄⋊C₄×C₄₇	—	2	4	no	—
98	C₄⋊C₄×C₄₇	—	4	4	no	—
99	C₄⋊C₄×C₄₇	C₄²	1	4	yes	—
100	C₂²⋊C₄×C₄₇	—	2	8	no	—
101	C₂²⋊C₄×C₄₇	—	4	4	no	—
102	C₂²⋊C₄×C₄₇	C₄²	1	8	yes	—
103	C₄²×C₄₇	—	2	4	no	—
104	C₄²×C₄₇	—	2	4	no	—
105	C₄²×C₄₇	—	2	1	no	—
106	C₄²×C₄₇	—	2	1	no	—
107	C₄²×C₄₇	—	2	2	no	—
108	C₄²×C₄₇	—	2	2	no	—
109	C₄²×C₄₇	—	2	1	no	—
110	C₄²×C₄₇	—	2	1	no	—
111	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
112	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
113	#10625329	—	4	8	no	—
114	C₂×C₄₇⋊C₈	—	2	1	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	1	no	—
119	C₂×C₄₇⋊C₈	—	2	2	no	—
120	C₂×C₄₇⋊C₈	—	2	1	no	—
121	C₂×C₄₇⋊C₈	—	2	1	no	—
122	C₂×C₄₇⋊C₈	—	2	1	no	—
123	C₂×C₄₇⋊C₈	—	2	1	no	—
124	C₂×C₄₇⋊C₈	—	2	1	no	—
125	C₂×C₄₇⋊C₈	—	2	1	no	—
126	C₂×C₄₇⋊C₈	—	4	8	no	—
127	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
128	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
129	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
130	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
131	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
132	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
133	C₂³×C₄₇	—	2	2	no	—
134	C₂³×C₄₇	—	2	2	no	—
135	C₂³×C₄₇	—	2	4	no	—
136	C₂³×C₄₇	—	2	4	no	—
137	C₂³×C₄₇	C₂×C₄²	1	4	yes	—
138	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
139	D₄×C₄₇	—	2	8	no	—
140	C₂×C₄×C₄₇	—	2	2	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	4	no	—
146	C₂×C₄×C₄₇	—	2	4	no	—
147	C₂×C₄×C₄₇	—	2	4	no	—
148	C₂×C₄×C₄₇	—	2	4	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	4	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	2	4	no	—
155	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
156	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
157	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
158	C₂×C₄×C₄₇	#131	1	4	yes	—
159	C₂×C₄×C₄₇	#131	1	4	yes	—
160	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
163	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
164	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
165	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
166	C₄₇⋊C₈	—	2	2	no	—
167	C₄₇⋊C₈	—	2	4	no	—
168	C₄₇⋊C₈	—	2	4	no	—
169	C₄₇⋊C₈	—	2	2	no	—
170	C₄₇⋊C₈	—	2	2	no	—
171	C₄₇⋊C₈	—	2	2	no	—
172	#20562	—	47	1	no	maximal, Sylow
173	C₂²×C₄₇	—	2	4	no	—
174	C₂²×C₄₇	—	2	4	no	—
175	C₂²×C₄₇	—	2	4	no	—
176	C₂²×C₄₇	—	4	4	no	—
177	C₂²×C₄₇	—	4	4	no	—
178	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
179	C₂²×C₄₇	#518	1	1	yes	characteristic
180	C₂²×C₄₇	#520	1	1	yes	characteristic
181	C₂²×C₄₇	C₂×#131	1	2	yes	—
182	C₂²×C₄₇	C₂×#131	1	2	yes	—
183	C₄×C₄₇	—	2	2	no	—
184	C₄×C₄₇	—	2	4	no	—
185	C₄×C₄₇	—	2	4	no	—
186	C₄×C₄₇	—	4	2	no	—
187	C₄×C₄₇	—	4	4	no	—
188	C₄×C₄₇	#405	1	4	yes	—
189	C₄×C₄₇	#518	1	1	yes	characteristic
190	C₄×C₄₇	#518	1	1	yes	characteristic
191	C₄×C₄₇	#520	1	1	yes	characteristic
192	C₄×C₄₇	#520	1	1	yes	characteristic
193	C₂×#436	—	47	1	no	—
194	C₂×C₈×D₄	—	47	1	no	—
195	#2293	D₄₇	1	1	yes	characteristic
196	#1770	—	47	1	no	—
197	C₈×C₄⋊C₄	—	47	1	no	—
198	C₄×C₄⋊C₈	—	47	1	no	—
199	#1753	—	47	2	no	—
200	C₈×C₂²⋊C₄	—	47	2	no	—
201	#1750	—	47	2	no	—
202	#1744	—	47	1	no	—
203	#1729	—	47	2	no	—
204	C₂×C₄₇	—	4	4	no	—
205	C₂×C₄₇	#2275	1	1	yes	characteristic
206	C₂×C₄₇	C₂×#405	1	1	yes	characteristic
207	C₂×C₄₇	C₄×#131	1	1	yes	characteristic
208	C₂×C₄₇	#2979	1	2	yes	—
209	C₂×C₄₇	#2994	1	2	yes	—
210	C₂²×M₁₆	—	47	2	no	—
211	C₂³×C₈	—	47	2	no	—
212	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
213	C₂×#117	C₂×D₄₇	1	2	yes	—
214	#436	—	47	8	no	—
215	C₈×D₄	—	47	8	no	—
216	C₂×C₄⋊C₈	—	47	1	no	—
217	C₂×C₄⋊C₈	—	47	1	no	—
218	C₂×C₂²⋊C₈	—	47	2	no	—
219	C₂×C₂²⋊C₈	—	47	2	no	—
220	C₂×#97	—	47	2	no	—
221	C₂×C₄×C₈	—	47	1	no	—
222	C₂×C₄×C₈	—	47	1	no	—
223	C₂×C₄×C₈	—	47	2	no	—
224	C₂×C₄×C₈	—	47	2	no	—
225	#390	Dic₄₇	1	2	yes	—
226	#389	Dic₄₇	1	2	yes	—
227	#388	Dic₄₇	1	4	yes	—
228	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
229	C₄×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
230	C₄³	C₂×D₄₇	1	1	yes	characteristic
231	#336	—	47	1	no	—
232	#336	—	47	2	no	—
233	#336	—	47	2	no	—
234	#336	—	47	2	no	—
235	#336	—	47	1	no	—
236	#336	—	47	1	no	—
237	#336	—	47	1	no	—
238	C₄₇	#20562	1	1	yes	characteristic, complemented, Sylow
239	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
240	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
241	C₂×M₁₆	—	47	8	no	—
242	C₂×M₁₆	—	188	2	no	—
243	C₂×M₁₆	—	188	2	no	—
244	C₂²×C₈	—	47	1	no	—
245	C₂²×C₈	—	47	2	no	—
246	C₂²×C₈	—	47	1	no	—
247	C₂²×C₈	—	47	2	no	—
248	C₂²×C₈	—	47	1	no	—
249	C₂²×C₈	—	47	1	no	—
250	C₂²×C₈	—	47	8	no	—
251	C₂²×C₈	—	188	2	no	—
252	C₂²×C₈	—	188	2	no	—
253	C₄×D₄	C₄×D₄₇	1	4	yes	—
254	C₄×D₄	C₄×D₄₇	1	4	yes	—
255	#117	—	4	2	no	—
256	#117	—	4	2	no	—
257	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
258	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
259	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	4	yes	—
261	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	4	yes	—
262	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
263	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
264	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
265	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
266	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
267	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
268	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
269	C₄⋊C₈	—	47	4	no	—
270	C₄⋊C₈	—	47	4	no	—
271	C₂²⋊C₈	—	47	8	no	—
272	C₂²⋊C₈	—	47	8	no	—
273	#97	—	188	2	no	—
274	C₄×C₈	—	47	4	no	—
275	C₄×C₈	—	47	4	no	—
276	C₄×C₈	—	188	2	no	—
277	C₄×C₈	—	188	2	no	—
278	#95	C₂×Dic₄₇	1	4	yes	—
279	#95	C₂×Dic₄₇	1	2	yes	—
280	C₂⁴	C₂²×Dic₄₇	1	2	yes	—
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	C₄×Dic₄₇	1	4	yes	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
288	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
289	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
290	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
291	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
292	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
293	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
294	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
295	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
296	M₁₆	—	188	8	no	—
297	C₂×C₈	—	47	2	no	—
298	C₂×C₈	—	47	2	no	—
299	C₂×C₈	—	47	2	no	—
300	C₂×C₈	—	47	2	no	—
301	C₂×C₈	—	47	4	no	—
302	C₂×C₈	—	47	4	no	—
303	C₂×C₈	—	94	1	no	—
304	C₂×C₈	—	94	2	no	—
305	C₂×C₈	—	94	1	no	—
306	C₂×C₈	—	94	2	no	—
307	C₂×C₈	—	94	1	no	—
308	C₂×C₈	—	94	1	no	—
309	C₂×C₈	—	94	2	no	—
310	C₂×C₈	—	94	2	no	—
311	C₂×C₈	—	94	1	no	—
312	C₂×C₈	—	94	1	no	—
313	C₂×C₈	—	94	1	no	—
314	C₂×C₈	—	94	1	no	—
315	C₂×C₈	—	188	8	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	4	4	no	—
318	C₄⋊C₄	C₄×Dic₄₇	1	4	yes	—
319	C₂²⋊C₄	—	2	8	no	—
320	C₂²⋊C₄	—	4	4	no	—
321	C₂²⋊C₄	C₄×Dic₄₇	1	8	yes	—
322	C₄²	—	2	4	no	—
323	C₄²	—	2	4	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	1	no	—
327	C₄²	—	2	1	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	2	1	no	—
330	C₄²	C₂×C₄×D₄₇	1	2	yes	—
331	C₄²	C₂×C₄×D₄₇	1	2	yes	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	4	no	—
335	C₂³	—	2	4	no	—
336	C₂³	C₂×C₄×Dic₄₇	1	4	yes	—
337	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
338	D₄	—	2	8	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
355	C₂×C₄	C₂×C₄×Dic₄₇	1	4	yes	—
356	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
357	C₂×C₄	#13094031	1	4	yes	—
358	C₂×C₄	#13094031	1	4	yes	—
359	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
360	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
361	C₂×C₄	#13094069	1	1	yes	characteristic
362	C₂×C₄	#13094069	1	1	yes	characteristic
363	C₂×C₄	#13094070	1	1	yes	characteristic
364	C₂×C₄	#13094071	1	1	yes	characteristic
365	C₈	—	94	4	no	—
366	C₈	—	94	2	no	—
367	C₈	—	94	4	no	—
368	C₈	—	94	2	no	—
369	C₈	—	94	2	no	—
370	C₈	—	94	2	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	4	4	no	—
375	C₂²	—	4	4	no	—
376	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
377	C₂²	#15689598	1	1	yes	characteristic
378	C₂²	#15689606	1	1	yes	characteristic
379	C₂²	C₂×#13094031	1	2	yes	—
380	C₂²	C₂×#13094031	1	2	yes	—
381	C₄	—	2	4	no	—
382	C₄	—	2	2	no	—
383	C₄	—	2	4	no	—
384	C₄	—	4	2	no	—
385	C₄	—	4	4	no	—
386	C₄	#15689079	1	4	yes	—
387	C₄	#15689595	1	1	yes	characteristic
388	C₄	#15689595	1	1	yes	characteristic
389	C₄	#15689602	1	1	yes	characteristic
390	C₄	#15689602	1	1	yes	characteristic
391	C₂	—	4	4	no	—
392	C₂	#20245749	1	1	yes	characteristic
393	C₂	C₂×#15689079	1	1	yes	characteristic
394	C₂	C₄×#13094031	1	1	yes	characteristic
395	C₂	#20252455	1	2	yes	—
396	C₂	#20252548	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₄₇×#2293	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×D₄×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2293	D₄₇
hypocenter	C₄₇	#20562
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #2293

Complements

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

N	H ≅ G/N	type
3. #20243257	C₂	semidirect
4. C₄⋊C₄×C₄₇⋊C₈	C₂	semidirect
5. C₄×C₄⋊(C₄₇⋊C₈)	C₂	semidirect
6. #20243172	C₂	semidirect
7. C₂²⋊C₄×C₄₇⋊C₈	C₂	semidirect
8. #20243154	C₂	semidirect
9. #20243134	C₂	semidirect
10. #20243085	C₂	semidirect
14. #15689201	C₄	semidirect
15. D₄×C₄₇⋊C₈	C₄	semidirect
238. C₄₇	#20562	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689201	2
C₂×D₄×C₄₇⋊C₈	2
#20243257	2
C₄⋊C₄×C₄₇⋊C₈	2
C₄×C₄⋊(C₄₇⋊C₈)	2
#20243172	2
C₂²⋊C₄×C₄₇⋊C₈	2
#20243154	2
#20243134	2
#20243085	2
C₄₇×#2293	2
#20562	47