Subgroups — C₄₇×#13952 #26053650

Order 12032.

1342 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	C₂×C₄₇×#383	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₇×#376	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#1444	C₂	1	2	yes	maximal
5	C₄₇×#1442	C₂	1	2	yes	maximal
6	C₄₇×#1436	C₂	1	4	yes	maximal
7	C₄₇×C₄⋊#95	C₂	1	2	yes	maximal
8	C₄₇×#1434	C₂	1	2	yes	maximal
9	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
10	C₂²×C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
11	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
12	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
13	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
14	C₄₇×#383	—	2	4	no	—
15	C₄×C₄⋊C₄×C₄₇	—	2	4	no	—
16	C₄₇×#376	C₄	1	8	yes	complemented
17	C₂×#95×C₄₇	C₂²	1	2	yes	—
18	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
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	4	yes	—
24	C₂×#95×C₄₇	C₂²	1	4	yes	—
25	C₂×#95×C₄₇	C₂²	1	2	yes	—
26	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
28	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
29	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
30	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
31	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
32	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
33	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
34	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
36	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
37	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
38	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
39	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
40	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
41	C₂×C₄²×C₄₇	—	2	8	no	—
42	C₂×C₄²×C₄₇	—	2	4	no	—
43	C₂×C₄²×C₄₇	—	4	2	no	—
44	C₂×C₄²×C₄₇	—	4	2	no	—
45	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	—
46	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
47	C₂×C₄²×C₄₇	D₄	1	4	yes	—
48	C₂×C₄²×C₄₇	Q₈	1	4	yes	—
49	#95×C₄₇	—	2	4	no	—
50	#95×C₄₇	—	2	4	no	—
51	#95×C₄₇	—	2	4	no	—
52	#95×C₄₇	—	2	2	no	—
53	#95×C₄₇	—	2	2	no	—
54	#95×C₄₇	—	2	8	no	—
55	#95×C₄₇	—	2	8	no	—
56	#95×C₄₇	—	4	4	no	—
57	#95×C₄₇	C₂×C₄	1	4	yes	—
58	#95×C₄₇	C₂×C₄	1	8	yes	—
59	#95×C₄₇	C₂×C₄	1	4	yes	—
60	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
61	C₂²×C₄×C₄₇	—	2	4	no	—
62	C₂²×C₄×C₄₇	—	2	4	no	—
63	C₂²×C₄×C₄₇	—	2	4	no	—
64	C₂²×C₄×C₄₇	—	2	1	no	—
65	C₂²×C₄×C₄₇	—	2	1	no	—
66	C₂²×C₄×C₄₇	—	2	2	no	—
67	C₂²×C₄×C₄₇	—	2	1	no	—
68	C₂²×C₄×C₄₇	—	2	1	no	—
69	C₂²×C₄×C₄₇	—	2	2	no	—
70	C₂²×C₄×C₄₇	—	2	4	no	—
71	C₂²×C₄×C₄₇	—	2	4	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	4	no	—
76	C₂²×C₄×C₄₇	—	2	4	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	2	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	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
95	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
101	C₂²×C₄×C₄₇	#41	1	8	yes	—
102	C₂²×C₄×C₄₇	#41	1	8	yes	—
103	C₄⋊C₄×C₄₇	—	2	16	no	—
104	C₄⋊C₄×C₄₇	—	4	16	no	—
105	C₄²×C₄₇	—	2	16	no	—
106	C₄²×C₄₇	—	4	8	no	—
107	C₄²×C₄₇	C₄⋊C₄	1	16	yes	complemented
108	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
109	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
110	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
111	C₂³×C₄₇	C₂×#41	1	4	yes	—
112	C₂³×C₄₇	C₂×#41	1	4	yes	—
113	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
114	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
115	C₂³×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
116	C₂³×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
117	C₂×C₄×C₄₇	—	2	4	no	—
118	C₂×C₄×C₄₇	—	2	4	no	—
119	C₂×C₄×C₄₇	—	2	4	no	—
120	C₂×C₄×C₄₇	—	2	2	no	—
121	C₂×C₄×C₄₇	—	2	2	no	—
122	C₂×C₄×C₄₇	—	2	4	no	—
123	C₂×C₄×C₄₇	—	2	4	no	—
124	C₂×C₄×C₄₇	—	2	4	no	—
125	C₂×C₄×C₄₇	—	2	4	no	—
126	C₂×C₄×C₄₇	—	2	4	no	—
127	C₂×C₄×C₄₇	—	2	2	no	—
128	C₂×C₄×C₄₇	—	2	2	no	—
129	C₂×C₄×C₄₇	—	2	2	no	—
130	C₂×C₄×C₄₇	—	2	2	no	—
131	C₂×C₄×C₄₇	—	2	8	no	—
132	C₂×C₄×C₄₇	—	2	8	no	—
133	C₂×C₄×C₄₇	—	2	4	no	—
134	C₂×C₄×C₄₇	—	2	4	no	—
135	C₂×C₄×C₄₇	—	2	4	no	—
136	C₂×C₄×C₄₇	—	2	8	no	—
137	C₂×C₄×C₄₇	—	2	8	no	—
138	C₂×C₄×C₄₇	—	2	8	no	—
139	C₂×C₄×C₄₇	—	4	4	no	—
140	C₂×C₄×C₄₇	—	4	4	no	—
141	C₂×C₄×C₄₇	—	4	4	no	—
142	C₂×C₄×C₄₇	—	4	4	no	—
143	C₂×C₄×C₄₇	—	4	4	no	—
144	C₂×C₄×C₄₇	—	4	4	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	—	4	2	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	C₂×C₄⋊C₄	1	4	yes	—
156	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
157	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
158	C₂×C₄×C₄₇	#117	1	8	yes	—
159	#13952	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
161	C₂²×C₄₇	C₂×#117	1	2	yes	—
162	C₂²×C₄₇	C₄×#41	1	2	yes	—
163	C₂²×C₄₇	#520	1	1	yes	characteristic
164	C₂²×C₄₇	#520	1	1	yes	characteristic
165	C₂²×C₄₇	#525	1	2	yes	—
166	C₂²×C₄₇	#532	1	2	yes	—
167	C₂²×C₄₇	#533	1	2	yes	—
168	C₂²×C₄₇	#533	1	2	yes	—
169	C₂²×C₄₇	#535	1	1	yes	characteristic
170	C₂²×C₄₇	#536	1	1	yes	characteristic
171	C₂²×C₄₇	#544	1	1	yes	characteristic
172	C₂²×C₄₇	#544	1	1	yes	characteristic
173	C₂²×C₄₇	#551	1	4	yes	—
174	C₂²×C₄₇	#552	1	4	yes	—
175	C₂²×C₄₇	#553	1	4	yes	—
176	C₂²×C₄₇	#556	1	4	yes	—
177	C₄×C₄₇	—	2	4	no	—
178	C₄×C₄₇	—	2	8	no	—
179	C₄×C₄₇	—	2	4	no	—
180	C₄×C₄₇	—	2	4	no	—
181	C₄×C₄₇	—	4	4	no	—
182	C₄×C₄₇	—	4	8	no	—
183	C₄×C₄₇	—	8	2	no	—
184	C₄×C₄₇	—	8	2	no	—
185	C₂×#383	C₂×C₄₇	1	1	yes	characteristic
186	C₂×C₄×C₄⋊C₄	C₂×C₄₇	1	1	yes	characteristic
187	C₂×#376	C₂×C₄₇	1	1	yes	characteristic
188	#1444	C₂×C₄₇	1	2	yes	—
189	#1442	C₂×C₄₇	1	2	yes	—
190	#1436	C₂×C₄₇	1	4	yes	—
191	C₄⋊#95	C₂×C₄₇	1	2	yes	—
192	#1434	C₂×C₄₇	1	2	yes	—
193	C₂×C₄₇	#2285	1	1	yes	characteristic
194	C₂×C₄₇	#2296	1	1	yes	characteristic
195	C₂×C₄₇	#2317	1	1	yes	characteristic
196	C₂×C₄₇	#2343	1	2	yes	—
197	C₂×C₄₇	#2347	1	2	yes	—
198	C₂×C₄₇	#2603	1	2	yes	—
199	C₂×C₄₇	#2604	1	2	yes	—
200	C₂×C₄₇	#2605	1	2	yes	—
201	C₂×C₄₇	#2606	1	2	yes	—
202	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
203	C₂²×C₄⋊C₄	C₂²×C₄₇	1	4	yes	—
204	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
205	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
206	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
207	#383	—	2	4	no	—
208	C₄×C₄⋊C₄	—	2	4	no	—
209	#376	C₄×C₄₇	1	8	yes	complemented
210	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
211	C₂×#95	C₂²×C₄₇	1	2	yes	—
212	C₂×#95	C₂²×C₄₇	1	4	yes	—
213	C₂×#95	C₂²×C₄₇	1	4	yes	—
214	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
215	C₂×#95	C₂²×C₄₇	1	2	yes	—
216	C₂×#95	C₂²×C₄₇	1	2	yes	—
217	C₂×#95	C₂²×C₄₇	1	4	yes	—
218	C₂×#95	C₂²×C₄₇	1	2	yes	—
219	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
220	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
221	C₄₇	#13952	1	1	yes	characteristic, direct product factor, Sylow
222	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
223	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
224	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
225	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
226	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
227	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
228	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
229	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
230	C₂×C₄⋊C₄	—	2	4	no	—
231	C₂×C₄⋊C₄	—	2	8	no	—
232	C₂×C₄⋊C₄	—	2	8	no	—
233	C₂×C₄⋊C₄	—	2	8	no	—
234	C₂×C₄⋊C₄	—	4	4	no	—
235	C₂×C₄²	—	2	8	no	—
236	C₂×C₄²	—	2	4	no	—
237	C₂×C₄²	—	4	2	no	—
238	C₂×C₄²	—	4	2	no	—
239	C₂×C₄²	C₂×C₄×C₄₇	1	8	yes	—
240	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
241	C₂×C₄²	D₄×C₄₇	1	4	yes	—
242	C₂×C₄²	Q₈×C₄₇	1	4	yes	—
243	#95	—	2	4	no	—
244	#95	—	2	2	no	—
245	#95	—	2	2	no	—
246	#95	—	2	4	no	—
247	#95	—	2	4	no	—
248	#95	—	2	8	no	—
249	#95	—	2	8	no	—
250	#95	—	4	4	no	—
251	#95	C₂×C₄×C₄₇	1	4	yes	—
252	#95	C₂×C₄×C₄₇	1	8	yes	—
253	#95	C₂×C₄×C₄₇	1	4	yes	—
254	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	1	no	—
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
285	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
286	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
287	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
288	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
289	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
290	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
291	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
292	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
293	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
294	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
295	C₂²×C₄	#41×C₄₇	1	8	yes	—
296	C₂²×C₄	#41×C₄₇	1	8	yes	—
297	C₄⋊C₄	—	2	16	no	—
298	C₄⋊C₄	—	4	16	no	—
299	C₄²	—	2	16	no	—
300	C₄²	—	4	8	no	—
301	C₄²	C₄⋊C₄×C₄₇	1	16	yes	complemented
302	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
303	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
304	C₂³	C₂²×Q₈×C₄₇	1	1	yes	characteristic
305	C₂³	C₂×#41×C₄₇	1	4	yes	—
306	C₂³	C₂×#41×C₄₇	1	4	yes	—
307	C₂³	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
308	C₂³	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
309	C₂³	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
310	C₂³	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	2	8	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	—	4	4	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	4	yes	—
350	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	4	yes	—
351	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	4	yes	—
352	C₂×C₄	#117×C₄₇	1	8	yes	—
353	C₂²	C₂²×C₄⋊C₄×C₄₇	1	1	yes	characteristic
354	C₂²	C₂×#117×C₄₇	1	2	yes	—
355	C₂²	C₄×#41×C₄₇	1	2	yes	—
356	C₂²	C₄₇×#520	1	1	yes	characteristic
357	C₂²	C₄₇×#520	1	1	yes	characteristic
358	C₂²	C₄₇×#525	1	2	yes	—
359	C₂²	C₄₇×#532	1	2	yes	—
360	C₂²	C₄₇×#533	1	2	yes	—
361	C₂²	C₄₇×#533	1	2	yes	—
362	C₂²	C₄₇×#535	1	1	yes	characteristic
363	C₂²	C₄₇×#536	1	1	yes	characteristic
364	C₂²	C₄₇×#544	1	1	yes	characteristic
365	C₂²	C₄₇×#544	1	1	yes	characteristic
366	C₂²	C₄₇×#551	1	4	yes	—
367	C₂²	C₄₇×#552	1	4	yes	—
368	C₂²	C₄₇×#553	1	4	yes	—
369	C₂²	C₄₇×#556	1	4	yes	—
370	C₄	—	2	4	no	—
371	C₄	—	2	4	no	—
372	C₄	—	2	4	no	—
373	C₄	—	2	8	no	—
374	C₄	—	4	4	no	—
375	C₄	—	4	8	no	—
376	C₄	—	8	2	no	—
377	C₄	—	8	2	no	—
378	C₂	C₄₇×#2285	1	1	yes	characteristic
379	C₂	C₄₇×#2296	1	1	yes	characteristic
380	C₂	C₄₇×#2317	1	1	yes	characteristic
381	C₂	C₄₇×#2343	1	2	yes	—
382	C₂	C₄₇×#2347	1	2	yes	—
383	C₂	C₄₇×#2603	1	2	yes	—
384	C₂	C₄₇×#2604	1	2	yes	—
385	C₂	C₄₇×#2605	1	2	yes	—
386	C₂	C₄₇×#2606	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₄₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₇
Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
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
16. C₄₇×#376	C₄	semidirect
107. C₄²×C₄₇	C₄⋊C₄	semidirect
159. #13952	C₄₇	direct (N × H)
209. #376	C₄×C₄₇	semidirect
221. C₄₇	#13952	direct (N × H)
301. C₄²	C₄⋊C₄×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×#383	2
C₂×C₄×C₄⋊C₄×C₄₇	2
C₂×C₄₇×#376	2
C₄₇×#1444	2
C₄₇×#1442	2
C₄₇×#1436	2
C₄₇×C₄⋊#95	2
C₄₇×#1434	2
#13952	47

Subgroups — C47×#13952 #26053650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#13952 #26053650