Subgroups — C₄₇×#14345 #26054043

Order 12032.

2150 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	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#383	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#382	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1445	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1439	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1438	C₂	1	2	yes	maximal
7	C₄₇×C₂²⋊#95	C₂	1	4	yes	maximal, complemented
8	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
10	C₂×C₄×D₄×C₄₇	—	2	4	no	—
11	C₂×C₄×D₄×C₄₇	—	2	4	no	—
12	C₂×C₄×D₄×C₄₇	C₄	1	8	yes	complemented
13	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
15	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	8	yes	—
17	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#383	—	2	4	no	—
19	C₄₇×#382	—	2	4	no	—
20	C₂×#95×C₄₇	C₂²	1	2	yes	—
21	C₂×#95×C₄₇	C₂²	1	2	yes	—
22	C₂×#95×C₄₇	C₂²	1	2	yes	—
23	C₂×#95×C₄₇	C₂²	1	2	yes	—
24	C₂×#95×C₄₇	C₂²	1	2	yes	—
25	C₂×#95×C₄₇	C₂²	1	8	yes	—
26	C₂⁵×C₄₇	C₂³	1	2	yes	—
27	C₂²×D₄×C₄₇	—	2	8	no	—
28	C₂²×D₄×C₄₇	—	2	2	no	—
29	C₂²×D₄×C₄₇	—	2	2	no	—
30	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	—
31	C₂³×C₄×C₄₇	—	2	4	no	—
32	C₂³×C₄×C₄₇	—	2	4	no	—
33	C₂³×C₄×C₄₇	—	4	8	no	—
34	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	—
35	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
36	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
37	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
38	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
41	C₄×D₄×C₄₇	—	2	32	no	—
42	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
43	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
45	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
46	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
47	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
48	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
49	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
50	C₂×C₂²⋊C₄×C₄₇	—	4	8	no	—
51	C₂×C₂²⋊C₄×C₄₇	—	4	8	no	—
52	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
53	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
54	C₂×C₄²×C₄₇	D₄	1	4	yes	—
55	C₂×C₄²×C₄₇	D₄	1	4	yes	—
56	#95×C₄₇	—	2	4	no	—
57	#95×C₄₇	—	2	4	no	—
58	#95×C₄₇	—	2	4	no	—
59	#95×C₄₇	—	2	4	no	—
60	#95×C₄₇	—	2	4	no	—
61	#95×C₄₇	—	4	8	no	—
62	C₂⁴×C₄₇	—	2	2	no	—
63	C₂⁴×C₄₇	—	2	2	no	—
64	C₂⁴×C₄₇	—	2	4	no	—
65	C₂⁴×C₄₇	—	2	4	no	—
66	C₂⁴×C₄₇	—	2	8	no	—
67	C₂⁴×C₄₇	—	2	4	no	—
68	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
69	C₂⁴×C₄₇	#41	1	8	yes	—
70	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
71	C₂×D₄×C₄₇	—	2	16	no	—
72	C₂×D₄×C₄₇	—	2	16	no	—
73	C₂×D₄×C₄₇	—	2	16	no	—
74	C₂×D₄×C₄₇	—	2	8	no	—
75	C₂²×C₄×C₄₇	—	2	4	no	—
76	C₂²×C₄×C₄₇	—	2	2	no	—
77	C₂²×C₄×C₄₇	—	2	4	no	—
78	C₂²×C₄×C₄₇	—	2	2	no	—
79	C₂²×C₄×C₄₇	—	2	2	no	—
80	C₂²×C₄×C₄₇	—	2	2	no	—
81	C₂²×C₄×C₄₇	—	2	8	no	—
82	C₂²×C₄×C₄₇	—	2	16	no	—
83	C₂²×C₄×C₄₇	—	2	4	no	—
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	2	8	no	—
86	C₂²×C₄×C₄₇	—	2	8	no	—
87	C₂²×C₄×C₄₇	—	2	4	no	—
88	C₂²×C₄×C₄₇	—	2	4	no	—
89	C₂²×C₄×C₄₇	—	2	8	no	—
90	C₂²×C₄×C₄₇	—	2	8	no	—
91	C₂²×C₄×C₄₇	—	2	4	no	—
92	C₂²×C₄×C₄₇	—	2	4	no	—
93	C₂²×C₄×C₄₇	—	4	16	no	—
94	C₂²×C₄×C₄₇	—	4	16	no	—
95	C₂²×C₄×C₄₇	—	4	16	no	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
106	C₄⋊C₄×C₄₇	—	2	8	no	—
107	C₄⋊C₄×C₄₇	—	4	8	no	—
108	C₂²⋊C₄×C₄₇	—	2	16	no	—
109	C₂²⋊C₄×C₄₇	—	4	32	no	—
110	C₄²×C₄₇	C₂²⋊C₄	1	16	yes	complemented
111	C₂³×C₄₇	—	2	4	no	—
112	C₂³×C₄₇	—	2	4	no	—
113	C₂³×C₄₇	—	2	8	no	—
114	C₂³×C₄₇	—	2	8	no	—
115	C₂³×C₄₇	—	2	8	no	—
116	C₂³×C₄₇	—	2	8	no	—
117	C₂³×C₄₇	—	2	16	no	—
118	C₂³×C₄₇	—	2	16	no	—
119	C₂³×C₄₇	—	4	4	no	—
120	C₂³×C₄₇	—	4	4	no	—
121	C₂³×C₄₇	—	4	2	no	—
122	C₂³×C₄₇	—	4	2	no	—
123	C₂³×C₄₇	—	4	4	no	—
124	C₂³×C₄₇	—	4	8	no	—
125	C₂³×C₄₇	—	4	8	no	—
126	C₂³×C₄₇	#117	1	8	yes	—
127	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
128	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
129	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
130	C₂³×C₄₇	C₂×#41	1	4	yes	—
131	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
132	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
133	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
134	D₄×C₄₇	—	2	32	no	—
135	C₂×C₄×C₄₇	—	2	4	no	—
136	C₂×C₄×C₄₇	—	2	4	no	—
137	C₂×C₄×C₄₇	—	2	4	no	—
138	C₂×C₄×C₄₇	—	2	4	no	—
139	C₂×C₄×C₄₇	—	2	4	no	—
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	2	4	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	4	no	—
145	C₂×C₄×C₄₇	—	2	4	no	—
146	C₂×C₄×C₄₇	—	2	8	no	—
147	C₂×C₄×C₄₇	—	4	32	no	—
148	C₂×C₄×C₄₇	—	4	4	no	—
149	C₂×C₄×C₄₇	—	4	4	no	—
150	C₂×C₄×C₄₇	—	4	4	no	—
151	C₂×C₄×C₄₇	—	4	4	no	—
152	C₂×C₄×C₄₇	—	4	4	no	—
153	C₂×C₄×C₄₇	—	4	4	no	—
154	C₂×C₄×C₄₇	—	4	4	no	—
155	C₂×C₄×C₄₇	—	4	4	no	—
156	C₂×C₄×C₄₇	—	4	8	no	—
157	C₂×C₄×C₄₇	—	4	8	no	—
158	C₂×C₄×C₄₇	—	4	8	no	—
159	C₂×C₄×C₄₇	—	4	8	no	—
160	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
161	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
162	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
163	#14345	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂²×C₄₇	—	2	16	no	—
165	C₂²×C₄₇	—	2	8	no	—
166	C₂²×C₄₇	—	4	4	no	—
167	C₂²×C₄₇	—	4	4	no	—
168	C₂²×C₄₇	—	4	8	no	—
169	C₂²×C₄₇	—	4	8	no	—
170	C₂²×C₄₇	—	4	8	no	—
171	C₂²×C₄₇	—	4	16	no	—
172	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
173	C₂²×C₄₇	C₂×#117	1	2	yes	—
174	C₂²×C₄₇	#518	1	2	yes	—
175	C₂²×C₄₇	#520	1	2	yes	—
176	C₂²×C₄₇	#525	1	2	yes	—
177	C₂²×C₄₇	#525	1	2	yes	—
178	C₂²×C₄₇	#535	1	2	yes	—
179	C₂²×C₄₇	#535	1	2	yes	—
180	C₂²×C₄₇	#535	1	1	yes	characteristic
181	C₂²×C₄₇	#536	1	1	yes	characteristic
182	C₂²×C₄₇	#537	1	2	yes	—
183	C₂²×C₄₇	#538	1	8	yes	—
184	C₂²×C₄₇	#539	1	8	yes	—
185	C₄×C₄₇	—	2	4	no	—
186	C₄×C₄₇	—	2	4	no	—
187	C₄×C₄₇	—	2	4	no	—
188	C₄×C₄₇	—	4	4	no	—
189	C₄×C₄₇	—	8	4	no	—
190	C₄×C₄₇	—	8	4	no	—
191	C₂²×C₄×D₄	C₂×C₄₇	1	1	yes	characteristic
192	C₂×#383	C₂×C₄₇	1	1	yes	characteristic, complemented
193	C₂×#382	C₂×C₄₇	1	1	yes	characteristic, complemented
194	#1445	C₂×C₄₇	1	2	yes	complemented
195	#1439	C₂×C₄₇	1	4	yes	complemented
196	#1438	C₂×C₄₇	1	2	yes	—
197	C₂²⋊#95	C₂×C₄₇	1	4	yes	complemented
198	C₂×C₄₇	—	4	8	no	—
199	C₂×C₄₇	#2280	1	1	yes	characteristic
200	C₂×C₄₇	#2309	1	1	yes	characteristic
201	C₂×C₄₇	#2311	1	1	yes	characteristic
202	C₂×C₄₇	#2318	1	4	yes	—
203	C₂×C₄₇	#2631	1	2	yes	—
204	C₂×C₄₇	#2633	1	2	yes	—
205	C₂×C₄₇	#2636	1	4	yes	—
206	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
207	C₂⁴×C₄	C₂²×C₄₇	1	2	yes	—
208	C₂×C₄×D₄	—	2	4	no	—
209	C₂×C₄×D₄	—	2	4	no	—
210	C₂×C₄×D₄	C₄×C₄₇	1	8	yes	complemented
211	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
212	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
213	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
214	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	8	yes	—
215	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
216	#383	—	2	4	no	—
217	#382	—	2	4	no	—
218	C₂×#95	C₂²×C₄₇	1	2	yes	—
219	C₂×#95	C₂²×C₄₇	1	2	yes	—
220	C₂×#95	C₂²×C₄₇	1	2	yes	—
221	C₂×#95	C₂²×C₄₇	1	2	yes	—
222	C₂×#95	C₂²×C₄₇	1	2	yes	—
223	C₂×#95	C₂²×C₄₇	1	8	yes	—
224	C₄₇	#14345	1	1	yes	characteristic, direct product factor, Sylow
225	C₂⁵	C₂³×C₄₇	1	2	yes	—
226	C₂²×D₄	—	2	8	no	—
227	C₂²×D₄	—	2	2	no	—
228	C₂²×D₄	—	2	2	no	—
229	C₂²×D₄	C₂×C₄×C₄₇	1	4	yes	—
230	C₂³×C₄	—	2	4	no	—
231	C₂³×C₄	—	2	4	no	—
232	C₂³×C₄	—	4	8	no	—
233	C₂³×C₄	C₂×C₄×C₄₇	1	8	yes	—
234	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
235	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
236	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
237	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
238	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
239	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
240	C₄×D₄	—	2	32	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	4	no	—
244	C₂×C₄⋊C₄	—	4	4	no	—
245	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
246	C₂×C₂²⋊C₄	—	2	4	no	—
247	C₂×C₂²⋊C₄	—	2	4	no	—
248	C₂×C₂²⋊C₄	—	2	16	no	—
249	C₂×C₂²⋊C₄	—	4	8	no	—
250	C₂×C₂²⋊C₄	—	4	8	no	—
251	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	8	yes	—
252	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
253	C₂×C₄²	D₄×C₄₇	1	4	yes	—
254	C₂×C₄²	D₄×C₄₇	1	4	yes	—
255	#95	—	2	4	no	—
256	#95	—	2	4	no	—
257	#95	—	2	4	no	—
258	#95	—	2	4	no	—
259	#95	—	2	4	no	—
260	#95	—	4	8	no	—
261	C₂⁴	—	2	2	no	—
262	C₂⁴	—	2	2	no	—
263	C₂⁴	—	2	4	no	—
264	C₂⁴	—	2	4	no	—
265	C₂⁴	—	2	8	no	—
266	C₂⁴	—	2	4	no	—
267	C₂⁴	C₂²×C₄×C₄₇	1	4	yes	—
268	C₂⁴	#41×C₄₇	1	8	yes	—
269	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
270	C₂×D₄	—	2	16	no	—
271	C₂×D₄	—	2	16	no	—
272	C₂×D₄	—	2	16	no	—
273	C₂×D₄	—	2	8	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	8	no	—
281	C₂²×C₄	—	2	16	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	8	no	—
285	C₂²×C₄	—	2	8	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	8	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	8	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	4	16	no	—
293	C₂²×C₄	—	4	16	no	—
294	C₂²×C₄	—	4	16	no	—
295	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
296	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
297	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
298	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
299	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
300	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
305	C₄⋊C₄	—	2	8	no	—
306	C₄⋊C₄	—	4	8	no	—
307	C₂²⋊C₄	—	2	16	no	—
308	C₂²⋊C₄	—	4	32	no	—
309	C₄²	C₂²⋊C₄×C₄₇	1	16	yes	complemented
310	C₂³	—	2	4	no	—
311	C₂³	—	2	4	no	—
312	C₂³	—	2	8	no	—
313	C₂³	—	2	8	no	—
314	C₂³	—	2	8	no	—
315	C₂³	—	2	8	no	—
316	C₂³	—	2	16	no	—
317	C₂³	—	2	16	no	—
318	C₂³	—	4	4	no	—
319	C₂³	—	4	4	no	—
320	C₂³	—	4	2	no	—
321	C₂³	—	4	2	no	—
322	C₂³	—	4	4	no	—
323	C₂³	—	4	8	no	—
324	C₂³	—	4	8	no	—
325	C₂³	#117×C₄₇	1	8	yes	—
326	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
327	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
328	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
329	C₂³	C₂×#41×C₄₇	1	4	yes	—
330	C₂³	H(5,𝔽₂)×C₄₇	1	4	yes	—
331	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
332	C₂³	2₋¹⁺⁴×C₄₇	1	2	yes	—
333	D₄	—	2	32	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	8	no	—
346	C₂×C₄	—	4	32	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	8	no	—
356	C₂×C₄	—	4	8	no	—
357	C₂×C₄	—	4	8	no	—
358	C₂×C₄	—	4	8	no	—
359	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
360	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
361	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
362	C₂²	—	2	8	no	—
363	C₂²	—	2	16	no	—
364	C₂²	—	4	4	no	—
365	C₂²	—	4	4	no	—
366	C₂²	—	4	8	no	—
367	C₂²	—	4	8	no	—
368	C₂²	—	4	8	no	—
369	C₂²	—	4	16	no	—
370	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
371	C₂²	C₂×#117×C₄₇	1	2	yes	—
372	C₂²	C₄₇×#518	1	2	yes	—
373	C₂²	C₄₇×#520	1	2	yes	—
374	C₂²	C₄₇×#525	1	2	yes	—
375	C₂²	C₄₇×#525	1	2	yes	—
376	C₂²	C₄₇×#535	1	2	yes	—
377	C₂²	C₄₇×#535	1	2	yes	—
378	C₂²	C₄₇×#535	1	1	yes	characteristic
379	C₂²	C₄₇×#536	1	1	yes	characteristic
380	C₂²	C₄₇×#537	1	2	yes	—
381	C₂²	C₄₇×#538	1	8	yes	—
382	C₂²	C₄₇×#539	1	8	yes	—
383	C₄	—	2	4	no	—
384	C₄	—	2	4	no	—
385	C₄	—	2	4	no	—
386	C₄	—	4	4	no	—
387	C₄	—	8	4	no	—
388	C₄	—	8	4	no	—
389	C₂	—	4	8	no	—
390	C₂	C₄₇×#2280	1	1	yes	characteristic
391	C₂	C₄₇×#2309	1	1	yes	characteristic
392	C₂	C₄₇×#2311	1	1	yes	characteristic
393	C₂	C₄₇×#2318	1	4	yes	—
394	C₂	C₄₇×#2631	1	2	yes	—
395	C₂	C₄₇×#2633	1	2	yes	—
396	C₂	C₄₇×#2636	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₇
Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
prime radical	C₂³×D₄×C₄₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#383	C₂	semidirect
3. C₂×C₄₇×#382	C₂	semidirect
4. C₄₇×#1445	C₂	semidirect
5. C₄₇×#1439	C₂	semidirect
7. C₄₇×C₂²⋊#95	C₂	semidirect
12. C₂×C₄×D₄×C₄₇	C₄	semidirect
110. C₄²×C₄₇	C₂²⋊C₄	semidirect
163. #14345	C₄₇	direct (N × H)
192. C₂×#383	C₂×C₄₇	semidirect
193. C₂×#382	C₂×C₄₇	semidirect
194. #1445	C₂×C₄₇	semidirect
195. #1439	C₂×C₄₇	semidirect
197. C₂²⋊#95	C₂×C₄₇	semidirect
210. C₂×C₄×D₄	C₄×C₄₇	semidirect
224. C₄₇	#14345	direct (N × H)
309. C₄²	C₂²⋊C₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₄₇	2
C₂×C₄₇×#383	2
C₂×C₄₇×#382	2
C₄₇×#1445	2
C₄₇×#1439	2
C₄₇×#1438	2
C₄₇×C₂²⋊#95	2
#14345	47

Subgroups — C47×#14345 #26054043

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#14345 #26054043