Subgroups — C₄₇×#15073 #26054771

Order 12032.

2118 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#385	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₇×#381	C₂	1	2	yes	maximal
4	C₂×C₄₇×#381	C₂	1	2	yes	maximal
5	C₄₇×#1442	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1441	C₂	1	4	yes	maximal, complemented
7	C₄₇×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic
8	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
9	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₄₇	—	2	8	no	—
11	C₂²×C₄⋊C₄×C₄₇	—	2	4	no	—
12	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
14	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₄₇×#385	—	2	4	no	—
18	C₄₇×#381	—	2	8	no	—
19	C₄₇×#381	—	2	8	no	—
20	C₂×#95×C₄₇	C₂²	1	4	yes	—
21	C₂×#95×C₄₇	C₂²	1	8	yes	—
22	C₂×#95×C₄₇	C₂²	1	4	yes	—
23	C₂×#95×C₄₇	C₂²	1	2	yes	—
24	C₂×#95×C₄₇	C₂²	1	4	yes	—
25	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
26	C₂³×C₄×C₄₇	—	2	4	no	—
27	C₂³×C₄×C₄₇	—	2	8	no	—
28	C₂³×C₄×C₄₇	—	2	4	no	—
29	C₂³×C₄×C₄₇	—	2	4	no	—
30	C₂³×C₄×C₄₇	—	2	4	no	—
31	C₂³×C₄×C₄₇	—	2	4	no	—
32	C₂³×C₄×C₄₇	—	2	4	no	—
33	C₂³×C₄×C₄₇	—	2	4	no	—
34	C₂³×C₄×C₄₇	D₄	1	8	yes	—
35	C₂³×C₄×C₄₇	D₄	1	4	yes	—
36	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
39	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
40	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
41	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
42	C₂×C₄⋊C₄×C₄₇	—	2	32	no	—
43	C₂×C₄⋊C₄×C₄₇	—	2	16	no	—
44	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
45	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
47	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
49	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
50	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
51	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
52	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
53	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
54	C₂×C₂²⋊C₄×C₄₇	D₄	1	4	yes	—
55	#95×C₄₇	—	2	16	no	—
56	#95×C₄₇	—	2	8	no	—
57	#95×C₄₇	—	2	8	no	—
58	#95×C₄₇	—	2	4	no	—
59	#95×C₄₇	—	2	8	no	—
60	C₂⁴×C₄₇	—	2	4	no	—
61	C₂⁴×C₄₇	—	2	4	no	—
62	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
63	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
64	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
65	C₂⁴×C₄₇	#41	1	2	yes	—
66	C₂⁴×C₄₇	#41	1	4	yes	—
67	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
68	C₂²×C₄×C₄₇	—	2	32	no	—
69	C₂²×C₄×C₄₇	—	2	8	no	—
70	C₂²×C₄×C₄₇	—	2	4	no	—
71	C₂²×C₄×C₄₇	—	2	4	no	—
72	C₂²×C₄×C₄₇	—	2	16	no	—
73	C₂²×C₄×C₄₇	—	2	16	no	—
74	C₂²×C₄×C₄₇	—	2	16	no	—
75	C₂²×C₄×C₄₇	—	2	16	no	—
76	C₂²×C₄×C₄₇	—	2	2	no	—
77	C₂²×C₄×C₄₇	—	2	4	no	—
78	C₂²×C₄×C₄₇	—	2	4	no	—
79	C₂²×C₄×C₄₇	—	2	4	no	—
80	C₂²×C₄×C₄₇	—	2	2	no	—
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	1	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	1	no	—
89	C₂²×C₄×C₄₇	—	2	2	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	8	no	—
95	C₂²×C₄×C₄₇	—	2	4	no	—
96	C₂²×C₄×C₄₇	—	2	8	no	—
97	C₂²×C₄×C₄₇	—	4	8	no	—
98	C₂²×C₄×C₄₇	—	4	8	no	—
99	C₂²×C₄×C₄₇	—	4	8	no	—
100	C₂²×C₄×C₄₇	—	4	8	no	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₄₇	#41	1	8	yes	—
105	C₄⋊C₄×C₄₇	—	2	32	no	—
106	C₄⋊C₄×C₄₇	—	4	8	no	—
107	C₂²⋊C₄×C₄₇	—	2	8	no	—
108	C₂²⋊C₄×C₄₇	—	4	4	no	—
109	C₂²⋊C₄×C₄₇	—	4	8	no	—
110	C₂³×C₄₇	—	2	4	no	—
111	C₂³×C₄₇	—	2	8	no	—
112	C₂³×C₄₇	—	2	8	no	—
113	C₂³×C₄₇	—	2	4	no	—
114	C₂³×C₄₇	—	2	8	no	—
115	C₂³×C₄₇	—	2	16	no	—
116	C₂³×C₄₇	—	2	8	no	—
117	C₂³×C₄₇	#120	1	4	yes	—
118	C₂³×C₄₇	#121	1	4	yes	—
119	C₂³×C₄₇	#121	1	8	yes	—
120	C₂³×C₄₇	#123	1	8	yes	—
121	C₂³×C₄₇	#124	1	4	yes	—
122	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
123	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
124	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
125	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
126	C₂³×C₄₇	C₂×#41	1	2	yes	—
127	C₂³×C₄₇	C₂×#41	1	4	yes	—
128	C₂³×C₄₇	2₋¹⁺⁴	1	4	yes	—
129	C₂×C₄×C₄₇	—	2	32	no	—
130	C₂×C₄×C₄₇	—	2	4	no	—
131	C₂×C₄×C₄₇	—	2	4	no	—
132	C₂×C₄×C₄₇	—	2	16	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	—	4	4	no	—
139	C₂×C₄×C₄₇	—	4	4	no	—
140	C₂×C₄×C₄₇	—	4	2	no	—
141	C₂×C₄×C₄₇	—	4	4	no	—
142	C₂×C₄×C₄₇	—	4	4	no	—
143	C₂×C₄×C₄₇	—	4	2	no	—
144	C₂×C₄×C₄₇	—	4	4	no	—
145	C₂×C₄×C₄₇	—	4	32	no	—
146	C₂×C₄×C₄₇	—	4	1	no	—
147	C₂×C₄×C₄₇	—	4	1	no	—
148	C₂×C₄×C₄₇	—	4	4	no	—
149	C₂×C₄×C₄₇	—	4	2	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	2	no	—
154	C₂×C₄×C₄₇	—	4	4	no	—
155	C₂×C₄×C₄₇	—	4	8	no	—
156	C₂×C₄×C₄₇	—	4	8	no	—
157	C₂×C₄×C₄₇	#123	1	8	yes	—
158	#15073	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂²×C₄₇	—	2	4	no	—
160	C₂²×C₄₇	—	2	4	no	—
161	C₂²×C₄₇	—	2	16	no	—
162	C₂²×C₄₇	—	2	16	no	—
163	C₂²×C₄₇	—	2	8	no	—
164	C₂²×C₄₇	—	2	8	no	—
165	C₂²×C₄₇	#394	1	8	yes	—
166	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
167	C₂²×C₄₇	C₂×#121	1	2	yes	—
168	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
169	C₂²×C₄₇	C₂×#123	1	2	yes	—
170	C₂²×C₄₇	C₂×#123	1	2	yes	—
171	C₂²×C₄₇	#525	1	4	yes	—
172	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
173	C₂²×C₄₇	#536	1	4	yes	—
174	C₂²×C₄₇	#536	1	2	yes	—
175	C₂²×C₄₇	#547	1	4	yes	—
176	C₂²×C₄₇	#552	1	8	yes	—
177	C₂²×C₄₇	#552	1	4	yes	—
178	C₄×C₄₇	—	2	8	no	—
179	C₄×C₄₇	—	4	8	no	—
180	C₄×C₄₇	—	4	4	no	—
181	C₄×C₄₇	—	8	1	no	—
182	C₄×C₄₇	—	8	1	no	—
183	C₄×C₄₇	—	8	4	no	—
184	C₂³×C₄⋊C₄	C₂×C₄₇	1	1	yes	characteristic
185	C₂×#385	C₂×C₄₇	1	1	yes	characteristic
186	C₂×#381	C₂×C₄₇	1	2	yes	—
187	C₂×#381	C₂×C₄₇	1	2	yes	—
188	#1442	C₂×C₄₇	1	4	yes	complemented
189	#1441	C₂×C₄₇	1	4	yes	complemented
190	C₂²⋊#95	C₂×C₄₇	1	1	yes	characteristic
191	C₂×C₄₇	—	2	8	no	—
192	C₂×C₄₇	C₂×#394	1	1	yes	characteristic
193	C₂×C₄₇	#2413	1	4	yes	—
194	C₂×C₄₇	#2484	1	4	yes	—
195	C₂×C₄₇	#2486	1	2	yes	—
196	C₂×C₄₇	#2503	1	2	yes	—
197	C₂×C₄₇	#2614	1	1	yes	characteristic
198	C₂×C₄₇	#2849	1	1	yes	characteristic
199	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
200	C₂⁴×C₄	C₂²×C₄₇	1	2	yes	—
201	C₂²×C₄⋊C₄	—	2	8	no	—
202	C₂²×C₄⋊C₄	—	2	4	no	—
203	C₂²×C₄⋊C₄	C₂²×C₄₇	1	4	yes	—
204	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
205	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
206	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
207	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
208	#385	—	2	4	no	—
209	#381	—	2	8	no	—
210	#381	—	2	8	no	—
211	C₂×#95	C₂²×C₄₇	1	4	yes	—
212	C₂×#95	C₂²×C₄₇	1	4	yes	—
213	C₂×#95	C₂²×C₄₇	1	8	yes	—
214	C₂×#95	C₂²×C₄₇	1	4	yes	—
215	C₂×#95	C₂²×C₄₇	1	2	yes	—
216	C₄₇	#15073	1	1	yes	characteristic, direct product factor, Sylow
217	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
218	C₂³×C₄	—	2	4	no	—
219	C₂³×C₄	—	2	8	no	—
220	C₂³×C₄	—	2	4	no	—
221	C₂³×C₄	—	2	4	no	—
222	C₂³×C₄	—	2	4	no	—
223	C₂³×C₄	—	2	4	no	—
224	C₂³×C₄	—	2	4	no	—
225	C₂³×C₄	—	2	4	no	—
226	C₂³×C₄	D₄×C₄₇	1	8	yes	—
227	C₂³×C₄	D₄×C₄₇	1	4	yes	—
228	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
229	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
230	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
231	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
232	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
233	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
234	C₂×C₄⋊C₄	—	2	32	no	—
235	C₂×C₄⋊C₄	—	2	16	no	—
236	C₂×C₄⋊C₄	—	2	8	no	—
237	C₂×C₄⋊C₄	—	2	4	no	—
238	C₂×C₄⋊C₄	—	2	8	no	—
239	C₂×C₂²⋊C₄	—	2	2	no	—
240	C₂×C₂²⋊C₄	—	2	2	no	—
241	C₂×C₂²⋊C₄	—	2	4	no	—
242	C₂×C₂²⋊C₄	—	2	4	no	—
243	C₂×C₂²⋊C₄	—	2	4	no	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₂²⋊C₄	—	2	4	no	—
246	C₂×C₂²⋊C₄	D₄×C₄₇	1	4	yes	—
247	#95	—	2	16	no	—
248	#95	—	2	8	no	—
249	#95	—	2	8	no	—
250	#95	—	2	4	no	—
251	#95	—	2	8	no	—
252	C₂⁴	—	2	4	no	—
253	C₂⁴	—	2	4	no	—
254	C₂⁴	C₂×D₄×C₄₇	1	4	yes	—
255	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
256	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
257	C₂⁴	#41×C₄₇	1	2	yes	—
258	C₂⁴	#41×C₄₇	1	4	yes	—
259	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
260	C₂²×C₄	—	2	32	no	—
261	C₂²×C₄	—	2	8	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	16	no	—
265	C₂²×C₄	—	2	16	no	—
266	C₂²×C₄	—	2	16	no	—
267	C₂²×C₄	—	2	16	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	8	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	8	no	—
289	C₂²×C₄	—	4	8	no	—
290	C₂²×C₄	—	4	8	no	—
291	C₂²×C₄	—	4	8	no	—
292	C₂²×C₄	—	4	8	no	—
293	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
294	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
295	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
296	C₂²×C₄	#41×C₄₇	1	8	yes	—
297	C₄⋊C₄	—	2	32	no	—
298	C₄⋊C₄	—	4	8	no	—
299	C₂²⋊C₄	—	2	8	no	—
300	C₂²⋊C₄	—	4	4	no	—
301	C₂²⋊C₄	—	4	8	no	—
302	C₂³	—	2	4	no	—
303	C₂³	—	2	8	no	—
304	C₂³	—	2	8	no	—
305	C₂³	—	2	4	no	—
306	C₂³	—	2	8	no	—
307	C₂³	—	2	16	no	—
308	C₂³	—	2	8	no	—
309	C₂³	#120×C₄₇	1	4	yes	—
310	C₂³	#121×C₄₇	1	4	yes	—
311	C₂³	#121×C₄₇	1	8	yes	—
312	C₂³	#123×C₄₇	1	8	yes	—
313	C₂³	#124×C₄₇	1	4	yes	—
314	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
315	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
316	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
317	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
318	C₂³	C₂×#41×C₄₇	1	2	yes	—
319	C₂³	C₂×#41×C₄₇	1	4	yes	—
320	C₂³	2₋¹⁺⁴×C₄₇	1	4	yes	—
321	C₂×C₄	—	2	32	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	16	no	—
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	4	no	—
337	C₂×C₄	—	4	32	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	4	8	no	—
348	C₂×C₄	—	4	8	no	—
349	C₂×C₄	#123×C₄₇	1	8	yes	—
350	C₂²	—	2	4	no	—
351	C₂²	—	2	4	no	—
352	C₂²	—	2	16	no	—
353	C₂²	—	2	16	no	—
354	C₂²	—	2	8	no	—
355	C₂²	—	2	8	no	—
356	C₂²	C₄₇×#394	1	8	yes	—
357	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
358	C₂²	C₂×#121×C₄₇	1	2	yes	—
359	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
360	C₂²	C₂×#123×C₄₇	1	2	yes	—
361	C₂²	C₂×#123×C₄₇	1	2	yes	—
362	C₂²	C₄₇×#525	1	4	yes	—
363	C₂²	C₂×#124×C₄₇	1	1	yes	characteristic
364	C₂²	C₄₇×#536	1	4	yes	—
365	C₂²	C₄₇×#536	1	2	yes	—
366	C₂²	C₄₇×#547	1	4	yes	—
367	C₂²	C₄₇×#552	1	8	yes	—
368	C₂²	C₄₇×#552	1	4	yes	—
369	C₄	—	2	8	no	—
370	C₄	—	4	8	no	—
371	C₄	—	4	4	no	—
372	C₄	—	8	1	no	—
373	C₄	—	8	1	no	—
374	C₄	—	8	4	no	—
375	C₂	—	2	8	no	—
376	C₂	C₂×C₄₇×#394	1	1	yes	characteristic
377	C₂	C₄₇×#2413	1	4	yes	—
378	C₂	C₄₇×#2484	1	4	yes	—
379	C₂	C₄₇×#2486	1	2	yes	—
380	C₂	C₄₇×#2503	1	2	yes	—
381	C₂	C₄₇×#2614	1	1	yes	characteristic
382	C₂	C₄₇×#2849	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
prime radical	C₂⁵×C₄₇	C₂³
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₄₇×#1442	C₂	semidirect
6. C₄₇×#1441	C₂	semidirect
158. #15073	C₄₇	direct (N × H)
188. #1442	C₂×C₄₇	semidirect
189. #1441	C₂×C₄₇	semidirect
216. C₄₇	#15073	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄⋊C₄×C₄₇	2
C₂×C₄₇×#385	2
C₂×C₄₇×#381	2
C₄₇×#1442	2
C₄₇×#1441	2
C₄₇×C₂²⋊#95	2
#15073	47

Subgroups — C47×#15073 #26054771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#15073 #26054771