Subgroups — C₄₇×#13824 #26053522

Order 12032.

2390 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#390	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#386	C₂	1	2	yes	maximal
3	C₂×C₄×C₂²⋊C₄×C₄₇	C₂	1	4	yes	maximal, complemented
4	C₄₇×#1437	C₂	1	4	yes	maximal, complemented
5	C₄₇×#1436	C₂	1	2	yes	maximal, complemented
6	C₄×#95×C₄₇	C₂	1	2	yes	maximal, complemented
7	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
8	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
10	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	—
11	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	—
12	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
13	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
14	C₂²×C₄²×C₄₇	C₂²	1	4	yes	—
15	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
16	C₄₇×#390	C₄	1	8	yes	complemented
17	C₄₇×#386	C₄	1	16	yes	complemented
18	C₄×C₂²⋊C₄×C₄₇	—	2	16	no	—
19	C₂×#95×C₄₇	C₂²	1	4	yes	—
20	C₂×#95×C₄₇	C₂²	1	2	yes	—
21	C₂×#95×C₄₇	C₂²	1	2	yes	—
22	C₂×#95×C₄₇	C₂²	1	4	yes	—
23	C₂×#95×C₄₇	C₂²	1	2	yes	—
24	C₂⁵×C₄₇	C₂³	1	2	yes	—
25	C₂²×D₄×C₄₇	—	4	2	no	—
26	C₂²×D₄×C₄₇	—	4	1	no	—
27	C₂²×D₄×C₄₇	—	4	1	no	—
28	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
29	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	—
30	C₂³×C₄×C₄₇	—	2	8	no	—
31	C₂³×C₄×C₄₇	—	2	8	no	—
32	C₂³×C₄×C₄₇	—	4	2	no	—
33	C₂³×C₄×C₄₇	—	4	2	no	—
34	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	complemented
35	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
36	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
37	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
39	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
40	C₂×C₄⋊C₄×C₄₇	—	4	1	no	—
41	C₂×C₄⋊C₄×C₄₇	—	4	1	no	—
42	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	complemented
43	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
44	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
45	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
46	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
47	C₂×C₂²⋊C₄×C₄₇	—	4	2	no	—
48	C₂×C₂²⋊C₄×C₄₇	—	4	2	no	—
49	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	16	yes	—
50	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	16	yes	complemented
51	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
52	C₂×C₄²×C₄₇	—	2	8	no	—
53	C₂×C₄²×C₄₇	—	2	8	no	—
54	C₂×C₄²×C₄₇	—	2	8	no	—
55	C₂×C₄²×C₄₇	—	4	2	no	—
56	C₂×C₄²×C₄₇	—	4	4	no	—
57	C₂×C₄²×C₄₇	—	4	2	no	—
58	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	complemented
59	#95×C₄₇	—	2	8	no	—
60	#95×C₄₇	—	2	4	no	—
61	#95×C₄₇	—	4	2	no	—
62	#95×C₄₇	C₂×C₄	1	16	yes	complemented
63	#95×C₄₇	D₄	1	8	yes	complemented
64	C₂⁴×C₄₇	—	2	4	no	—
65	C₂⁴×C₄₇	—	2	4	no	—
66	C₂⁴×C₄₇	—	2	4	no	—
67	C₂⁴×C₄₇	—	2	4	no	—
68	C₂⁴×C₄₇	—	2	2	no	—
69	C₂⁴×C₄₇	—	2	2	no	—
70	C₂⁴×C₄₇	—	2	2	no	—
71	C₂⁴×C₄₇	—	2	2	no	—
72	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
73	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
74	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
75	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
76	C₂×D₄×C₄₇	—	4	4	no	—
77	C₂×D₄×C₄₇	—	4	4	no	—
78	C₂×D₄×C₄₇	—	4	8	no	—
79	C₂×D₄×C₄₇	—	4	8	no	—
80	C₂×D₄×C₄₇	C₄²	1	16	yes	complemented
81	C₂²×C₄×C₄₇	—	2	4	no	—
82	C₂²×C₄×C₄₇	—	2	4	no	—
83	C₂²×C₄×C₄₇	—	2	4	no	—
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	2	4	no	—
86	C₂²×C₄×C₄₇	—	2	4	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	1	no	—
89	C₂²×C₄×C₄₇	—	2	1	no	—
90	C₂²×C₄×C₄₇	—	2	4	no	—
91	C₂²×C₄×C₄₇	—	2	4	no	—
92	C₂²×C₄×C₄₇	—	2	4	no	—
93	C₂²×C₄×C₄₇	—	2	4	no	—
94	C₂²×C₄×C₄₇	—	2	4	no	—
95	C₂²×C₄×C₄₇	—	2	4	no	—
96	C₂²×C₄×C₄₇	—	2	4	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	4	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	32	no	—
101	C₂²×C₄×C₄₇	—	4	8	no	—
102	C₂²×C₄×C₄₇	—	4	8	no	—
103	C₂²×C₄×C₄₇	—	4	16	no	—
104	C₂²×C₄×C₄₇	—	4	8	no	—
105	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
106	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
107	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
109	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
110	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
111	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
112	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
113	C₂²×C₄×C₄₇	#41	1	8	yes	—
114	C₂²×C₄×C₄₇	#41	1	4	yes	—
115	C₄⋊C₄×C₄₇	—	4	4	no	—
116	C₂²⋊C₄×C₄₇	—	2	32	no	—
117	C₂²⋊C₄×C₄₇	—	2	32	no	—
118	C₂²⋊C₄×C₄₇	—	4	8	no	—
119	C₄²×C₄₇	—	4	4	no	—
120	C₄²×C₄₇	—	4	8	no	—
121	C₄²×C₄₇	—	4	16	no	—
122	C₂³×C₄₇	—	2	8	no	—
123	C₂³×C₄₇	—	2	8	no	—
124	C₂³×C₄₇	—	2	8	no	—
125	C₂³×C₄₇	—	2	8	no	—
126	C₂³×C₄₇	—	2	8	no	—
127	C₂³×C₄₇	—	2	8	no	—
128	C₂³×C₄₇	—	2	4	no	—
129	C₂³×C₄₇	—	2	4	no	—
130	C₂³×C₄₇	—	2	4	no	—
131	C₂³×C₄₇	—	2	4	no	—
132	C₂³×C₄₇	—	2	4	no	—
133	C₂³×C₄₇	—	2	4	no	—
134	C₂³×C₄₇	—	4	2	no	—
135	C₂³×C₄₇	—	4	4	no	—
136	C₂³×C₄₇	—	4	4	no	—
137	C₂³×C₄₇	—	4	4	no	—
138	C₂³×C₄₇	—	4	2	no	—
139	C₂³×C₄₇	—	4	2	no	—
140	C₂³×C₄₇	—	4	4	no	—
141	C₂³×C₄₇	—	4	4	no	—
142	C₂³×C₄₇	—	4	4	no	—
143	C₂³×C₄₇	—	4	2	no	—
144	C₂³×C₄₇	C₂×C₄²	1	8	yes	—
145	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
146	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
147	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
148	C₂³×C₄₇	C₂×#41	1	4	yes	—
149	C₂³×C₄₇	C₂×#41	1	2	yes	—
150	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
151	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
152	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
153	D₄×C₄₇	—	4	16	no	—
154	C₂×C₄×C₄₇	—	2	8	no	—
155	C₂×C₄×C₄₇	—	2	4	no	—
156	C₂×C₄×C₄₇	—	2	4	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	8	no	—
160	C₂×C₄×C₄₇	—	2	4	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	—	2	8	no	—
163	C₂×C₄×C₄₇	—	2	8	no	—
164	C₂×C₄×C₄₇	—	2	8	no	—
165	C₂×C₄×C₄₇	—	2	8	no	—
166	C₂×C₄×C₄₇	—	2	8	no	—
167	C₂×C₄×C₄₇	—	2	8	no	—
168	C₂×C₄×C₄₇	—	2	8	no	—
169	C₂×C₄×C₄₇	—	2	8	no	—
170	C₂×C₄×C₄₇	—	2	8	no	—
171	C₂×C₄×C₄₇	—	2	8	no	—
172	C₂×C₄×C₄₇	—	2	4	no	—
173	C₂×C₄×C₄₇	—	4	32	no	—
174	C₂×C₄×C₄₇	—	4	2	no	—
175	C₂×C₄×C₄₇	—	4	4	no	—
176	C₂×C₄×C₄₇	—	4	4	no	—
177	C₂×C₄×C₄₇	—	4	4	no	—
178	C₂×C₄×C₄₇	—	4	4	no	—
179	C₂×C₄×C₄₇	—	4	4	no	—
180	C₂×C₄×C₄₇	—	4	2	no	—
181	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
182	C₂×C₄×C₄₇	C₄×D₄	1	8	yes	—
183	C₂×C₄×C₄₇	C₄×D₄	1	16	yes	—
184	#13824	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂²×C₄₇	—	2	16	no	—
186	C₂²×C₄₇	—	2	8	no	—
187	C₂²×C₄₇	—	4	4	no	—
188	C₂²×C₄₇	—	4	4	no	—
189	C₂²×C₄₇	—	4	8	no	—
190	C₂²×C₄₇	—	4	8	no	—
191	C₂²×C₄₇	—	4	8	no	—
192	C₂²×C₄₇	—	4	4	no	—
193	C₂²×C₄₇	—	4	4	no	—
194	C₂²×C₄₇	—	4	4	no	—
195	C₂²×C₄₇	—	4	4	no	—
196	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
197	C₂²×C₄₇	C₂×C₄×D₄	1	4	yes	—
198	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
199	C₂²×C₄₇	C₄×#41	1	4	yes	—
200	C₂²×C₄₇	C₄×#41	1	2	yes	—
201	C₂²×C₄₇	#518	1	2	yes	—
202	C₂²×C₄₇	#518	1	2	yes	—
203	C₂²×C₄₇	#518	1	1	yes	characteristic
204	C₂²×C₄₇	#518	1	1	yes	characteristic
205	C₂²×C₄₇	D₄²	1	1	yes	characteristic
206	C₂²×C₄₇	#546	1	4	yes	—
207	C₂²×C₄₇	#550	1	2	yes	—
208	C₂²×C₄₇	#551	1	2	yes	—
209	C₂²×C₄₇	#553	1	4	yes	—
210	C₂²×C₄₇	#555	1	2	yes	—
211	C₂²×C₄₇	#559	1	1	yes	characteristic
212	C₄×C₄₇	—	2	16	no	—
213	C₄×C₄₇	—	2	8	no	—
214	C₄×C₄₇	—	2	4	no	—
215	C₄×C₄₇	—	4	8	no	—
216	C₄×C₄₇	—	4	4	no	—
217	C₂×#390	C₂×C₄₇	1	1	yes	characteristic
218	C₂×#386	C₂×C₄₇	1	2	yes	—
219	C₂×C₄×C₂²⋊C₄	C₂×C₄₇	1	4	yes	complemented
220	#1437	C₂×C₄₇	1	4	yes	complemented
221	#1436	C₂×C₄₇	1	2	yes	complemented
222	C₄×#95	C₂×C₄₇	1	2	yes	complemented
223	C₂×C₄₇	—	4	8	no	—
224	C₂×C₄₇	C₄²×D₄	1	2	yes	—
225	C₂×C₄₇	#2273	1	1	yes	characteristic
226	C₂×C₄₇	#2358	1	2	yes	—
227	C₂×C₄₇	#2363	1	4	yes	—
228	C₂×C₄₇	#2364	1	2	yes	—
229	C₂×C₄₇	#2366	1	1	yes	characteristic
230	C₂×C₄₇	#2372	1	1	yes	characteristic
231	C₂×C₄₇	#2374	1	2	yes	—
232	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
233	C₂⁴×C₄	C₂²×C₄₇	1	2	yes	—
234	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
235	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	4	yes	—
236	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	4	yes	—
237	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
238	C₂²×C₄²	C₂²×C₄₇	1	4	yes	—
239	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
240	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
241	#390	C₄×C₄₇	1	8	yes	complemented
242	#386	C₄×C₄₇	1	16	yes	complemented
243	C₄×C₂²⋊C₄	—	2	16	no	—
244	C₂×#95	C₂²×C₄₇	1	2	yes	—
245	C₂×#95	C₂²×C₄₇	1	4	yes	—
246	C₂×#95	C₂²×C₄₇	1	2	yes	—
247	C₂×#95	C₂²×C₄₇	1	4	yes	—
248	C₂×#95	C₂²×C₄₇	1	2	yes	—
249	C₄₇	#13824	1	1	yes	characteristic, direct product factor, Sylow
250	C₂⁵	C₂³×C₄₇	1	2	yes	—
251	C₂²×D₄	—	4	2	no	—
252	C₂²×D₄	—	4	1	no	—
253	C₂²×D₄	—	4	1	no	—
254	C₂²×D₄	C₂×C₄×C₄₇	1	8	yes	—
255	C₂²×D₄	C₂×C₄×C₄₇	1	4	yes	—
256	C₂³×C₄	—	2	8	no	—
257	C₂³×C₄	—	2	8	no	—
258	C₂³×C₄	—	4	2	no	—
259	C₂³×C₄	—	4	2	no	—
260	C₂³×C₄	C₂×C₄×C₄₇	1	8	yes	complemented
261	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
262	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
263	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
264	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
265	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
266	C₂×C₄⋊C₄	—	4	1	no	—
267	C₂×C₄⋊C₄	—	4	1	no	—
268	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	complemented
269	C₂×C₂²⋊C₄	—	2	8	no	—
270	C₂×C₂²⋊C₄	—	2	8	no	—
271	C₂×C₂²⋊C₄	—	2	8	no	—
272	C₂×C₂²⋊C₄	—	2	8	no	—
273	C₂×C₂²⋊C₄	—	4	2	no	—
274	C₂×C₂²⋊C₄	—	4	2	no	—
275	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	16	yes	—
276	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	16	yes	complemented
277	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	8	yes	complemented
278	C₂×C₄²	—	2	8	no	—
279	C₂×C₄²	—	2	8	no	—
280	C₂×C₄²	—	2	8	no	—
281	C₂×C₄²	—	4	2	no	—
282	C₂×C₄²	—	4	4	no	—
283	C₂×C₄²	—	4	2	no	—
284	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	complemented
285	#95	—	2	8	no	—
286	#95	—	2	4	no	—
287	#95	—	4	2	no	—
288	#95	C₂×C₄×C₄₇	1	16	yes	complemented
289	#95	D₄×C₄₇	1	8	yes	complemented
290	C₂⁴	—	2	4	no	—
291	C₂⁴	—	2	4	no	—
292	C₂⁴	—	2	4	no	—
293	C₂⁴	—	2	4	no	—
294	C₂⁴	—	2	2	no	—
295	C₂⁴	—	2	2	no	—
296	C₂⁴	—	2	2	no	—
297	C₂⁴	—	2	2	no	—
298	C₂⁴	C₂²×C₄×C₄₇	1	4	yes	—
299	C₂⁴	C₂²×C₄×C₄₇	1	4	yes	—
300	C₂⁴	C₂²×C₄×C₄₇	1	4	yes	—
301	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
302	C₂×D₄	—	4	4	no	—
303	C₂×D₄	—	4	4	no	—
304	C₂×D₄	—	4	8	no	—
305	C₂×D₄	—	4	8	no	—
306	C₂×D₄	C₄²×C₄₇	1	16	yes	complemented
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	32	no	—
327	C₂²×C₄	—	4	8	no	—
328	C₂²×C₄	—	4	8	no	—
329	C₂²×C₄	—	4	16	no	—
330	C₂²×C₄	—	4	8	no	—
331	C₂²×C₄	C₂²×C₄×C₄₇	1	8	yes	—
332	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
333	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
334	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
335	C₂²×C₄	C₂²×C₄×C₄₇	1	8	yes	—
336	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
337	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
338	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
339	C₂²×C₄	#41×C₄₇	1	4	yes	—
340	C₂²×C₄	#41×C₄₇	1	8	yes	—
341	C₄⋊C₄	—	4	4	no	—
342	C₂²⋊C₄	—	2	32	no	—
343	C₂²⋊C₄	—	2	32	no	—
344	C₂²⋊C₄	—	4	8	no	—
345	C₄²	—	4	4	no	—
346	C₄²	—	4	8	no	—
347	C₄²	—	4	16	no	—
348	C₂³	—	2	8	no	—
349	C₂³	—	2	8	no	—
350	C₂³	—	2	8	no	—
351	C₂³	—	2	8	no	—
352	C₂³	—	2	8	no	—
353	C₂³	—	2	8	no	—
354	C₂³	—	2	4	no	—
355	C₂³	—	2	4	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	2	4	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	4	4	no	—
362	C₂³	—	4	4	no	—
363	C₂³	—	4	4	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	4	no	—
367	C₂³	—	4	4	no	—
368	C₂³	—	4	4	no	—
369	C₂³	—	4	2	no	—
370	C₂³	C₂×C₄²×C₄₇	1	8	yes	—
371	C₂³	C₂³×C₄×C₄₇	1	2	yes	—
372	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
373	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
374	C₂³	C₂×#41×C₄₇	1	4	yes	—
375	C₂³	C₂×#41×C₄₇	1	2	yes	—
376	C₂³	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
377	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
378	C₂³	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
379	D₄	—	4	16	no	—
380	C₂×C₄	—	2	8	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	8	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	8	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	8	no	—
396	C₂×C₄	—	2	8	no	—
397	C₂×C₄	—	2	8	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	4	32	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	C₂×C₄²×C₄₇	1	4	yes	—
408	C₂×C₄	C₄×D₄×C₄₇	1	8	yes	—
409	C₂×C₄	C₄×D₄×C₄₇	1	16	yes	—
410	C₂²	—	2	16	no	—
411	C₂²	—	2	8	no	—
412	C₂²	—	4	4	no	—
413	C₂²	—	4	4	no	—
414	C₂²	—	4	8	no	—
415	C₂²	—	4	8	no	—
416	C₂²	—	4	8	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	4	4	no	—
420	C₂²	—	4	4	no	—
421	C₂²	C₂²×C₄²×C₄₇	1	1	yes	characteristic
422	C₂²	C₂×C₄×D₄×C₄₇	1	4	yes	—
423	C₂²	C₂×C₄×D₄×C₄₇	1	2	yes	—
424	C₂²	C₄×#41×C₄₇	1	4	yes	—
425	C₂²	C₄×#41×C₄₇	1	2	yes	—
426	C₂²	C₄₇×#518	1	2	yes	—
427	C₂²	C₄₇×#518	1	2	yes	—
428	C₂²	C₄₇×#518	1	1	yes	characteristic
429	C₂²	C₄₇×#518	1	1	yes	characteristic
430	C₂²	D₄²×C₄₇	1	1	yes	characteristic
431	C₂²	C₄₇×#546	1	4	yes	—
432	C₂²	C₄₇×#550	1	2	yes	—
433	C₂²	C₄₇×#551	1	2	yes	—
434	C₂²	C₄₇×#553	1	4	yes	—
435	C₂²	C₄₇×#555	1	2	yes	—
436	C₂²	C₄₇×#559	1	1	yes	characteristic
437	C₄	—	2	4	no	—
438	C₄	—	2	16	no	—
439	C₄	—	2	8	no	—
440	C₄	—	4	8	no	—
441	C₄	—	4	4	no	—
442	C₂	—	4	8	no	—
443	C₂	C₄²×D₄×C₄₇	1	2	yes	—
444	C₂	C₄₇×#2273	1	1	yes	characteristic
445	C₂	C₄₇×#2358	1	2	yes	—
446	C₂	C₄₇×#2363	1	4	yes	—
447	C₂	C₄₇×#2364	1	2	yes	—
448	C₂	C₄₇×#2366	1	1	yes	characteristic
449	C₂	C₄₇×#2372	1	1	yes	characteristic
450	C₂	C₄₇×#2374	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂⁴
commutator	C₂²	C₂²×C₄²×C₄₇
Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
prime radical	C₂³×D₄×C₄₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×C₂²⋊C₄×C₄₇	C₂	semidirect
4. C₄₇×#1437	C₂	semidirect
5. C₄₇×#1436	C₂	semidirect
6. C₄×#95×C₄₇	C₂	semidirect
16. C₄₇×#390	C₄	semidirect
17. C₄₇×#386	C₄	semidirect
34. C₂³×C₄×C₄₇	C₂×C₄	semidirect
42. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
50. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
51. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
58. C₂×C₄²×C₄₇	C₂×C₄	semidirect
62. #95×C₄₇	C₂×C₄	semidirect
63. #95×C₄₇	D₄	semidirect
80. C₂×D₄×C₄₇	C₄²	semidirect
184. #13824	C₄₇	direct (N × H)
219. C₂×C₄×C₂²⋊C₄	C₂×C₄₇	semidirect
220. #1437	C₂×C₄₇	semidirect
221. #1436	C₂×C₄₇	semidirect
222. C₄×#95	C₂×C₄₇	semidirect
241. #390	C₄×C₄₇	semidirect
242. #386	C₄×C₄₇	semidirect
249. C₄₇	#13824	direct (N × H)
260. C₂³×C₄	C₂×C₄×C₄₇	semidirect
268. C₂×C₄⋊C₄	C₂×C₄×C₄₇	semidirect
276. C₂×C₂²⋊C₄	C₂×C₄×C₄₇	semidirect
277. C₂×C₂²⋊C₄	C₂×C₄×C₄₇	semidirect
284. C₂×C₄²	C₂×C₄×C₄₇	semidirect
288. #95	C₂×C₄×C₄₇	semidirect
289. #95	D₄×C₄₇	semidirect
306. C₂×D₄	C₄²×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#390	2
C₂×C₄₇×#386	2
C₂×C₄×C₂²⋊C₄×C₄₇	2
C₄₇×#1437	2
C₄₇×#1436	2
C₄×#95×C₄₇	2
#13824	47

Subgroups — C47×#13824 #26053522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#13824 #26053522