Subgroups — C₄₇×#18092 #26057790

Order 12032.

598 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3168	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#2994	C₂	1	2	yes	maximal, complemented
3	C₄₇×#1592	C₂	1	2	yes	maximal, complemented
4	C₄₇×#1584	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1581	C₂	1	2	yes	maximal, complemented
6	C₄₇×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
7	C₂×C₄₇×#335	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1483	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1451	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#529	C₂²	1	2	yes	—
11	C₄₇×#499	C₄	1	1	yes	characteristic
12	C₄₇×#495	C₄	1	1	yes	characteristic
13	C₄₇×#488	C₄	1	2	yes	—
14	C₄₇×#467	C₄	1	1	yes	characteristic
15	C₄₇×#466	C₄	1	1	yes	characteristic
16	C₄₇×#465	C₄	1	2	yes	—
17	C₄₇×#446	C₂²	1	2	yes	—
18	C₈×Q₈×C₄₇	C₂²	1	2	yes	—
19	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
20	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	—
21	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
22	C₄₇×#436	C₂²	1	2	yes	—
23	C₄₇×#435	—	2	2	no	—
24	C₈×D₄×C₄₇	—	2	2	no	—
25	C₈×D₄×C₄₇	C₂²	1	2	yes	—
26	C₄₇×#433	—	2	2	no	—
27	C₄₇×#431	C₂²	1	1	yes	characteristic
28	C₄₇×#424	—	2	2	no	—
29	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
30	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#335	C₂²	1	1	yes	characteristic
33	C₄₇×#335	C₂²	1	2	yes	—
34	C₄₇×#335	C₂²	1	1	yes	characteristic
35	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
36	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
37	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
38	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
39	C₄₇×#322	C₂²	1	2	yes	—
40	C₄₇×#322	C₂²	1	2	yes	—
41	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
42	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
43	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂×M₁₆×C₄₇	—	2	1	no	—
45	C₂×M₁₆×C₄₇	—	2	2	no	—
46	C₂²×C₈×C₄₇	—	2	2	no	—
47	C₂²×C₈×C₄₇	—	2	2	no	—
48	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
50	#126×C₄₇	—	2	2	no	—
51	#125×C₄₇	C₂×C₄	1	2	yes	—
52	#124×C₄₇	C₂×C₄	1	2	yes	—
53	#123×C₄₇	—	2	2	no	—
54	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
55	#121×C₄₇	C₂×C₄	1	2	yes	—
56	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
57	C₄×D₄×C₄₇	—	2	2	no	—
58	C₄×D₄×C₄₇	C₂³	1	2	yes	—
59	#117×C₄₇	—	2	2	no	—
60	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
61	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
62	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
63	#106×C₄₇	C₂×C₄	1	2	yes	—
64	C₄⋊C₈×C₄₇	—	2	2	no	—
65	C₄⋊C₈×C₄₇	—	2	2	no	—
66	C₄⋊C₈×C₄₇	—	2	2	no	—
67	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
68	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
69	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
70	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
71	#103×C₄₇	C₂×C₄	1	2	yes	—
72	#103×C₄₇	C₂×C₄	1	2	yes	—
73	#102×C₄₇	C₂×C₄	1	2	yes	—
74	#102×C₄₇	C₂×C₄	1	2	yes	—
75	C₂²⋊C₈×C₄₇	—	2	2	no	—
76	C₂²⋊C₈×C₄₇	—	2	2	no	—
77	C₂²⋊C₈×C₄₇	D₄	1	2	yes	—
78	#97×C₄₇	—	2	2	no	—
79	#97×C₄₇	—	2	1	no	—
80	C₄×C₈×C₄₇	—	2	2	no	—
81	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
83	C₄×C₈×C₄₇	C₂³	1	2	yes	—
84	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₄₇	C₂³	1	2	yes	—
87	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
94	Q₁₆×C₄₇	—	4	1	no	—
95	SD₁₆×C₄₇	—	2	4	no	—
96	D₈×C₄₇	—	4	1	no	—
97	M₁₆×C₄₇	—	4	2	no	—
98	M₁₆×C₄₇	—	8	2	no	—
99	C₂×C₈×C₄₇	—	2	2	no	—
100	C₂×C₈×C₄₇	—	2	2	no	—
101	C₂×C₈×C₄₇	—	2	2	no	—
102	C₂×C₈×C₄₇	—	2	2	no	—
103	C₂×C₈×C₄₇	—	4	1	no	—
104	C₂×C₈×C₄₇	—	8	2	no	—
105	C₂×C₈×C₄₇	—	8	2	no	—
106	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
112	C₄⋊C₄×C₄₇	—	2	2	no	—
113	C₄⋊C₄×C₄₇	—	2	2	no	—
114	C₄⋊C₄×C₄₇	—	2	2	no	—
115	C₄⋊C₄×C₄₇	—	2	2	no	—
116	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
117	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
118	C₂²⋊C₄×C₄₇	—	2	2	no	—
119	C₂²⋊C₄×C₄₇	—	2	2	no	—
120	C₂²⋊C₄×C₄₇	—	2	2	no	—
121	C₂²⋊C₄×C₄₇	—	2	2	no	—
122	C₂²⋊C₄×C₄₇	—	2	2	no	—
123	C₄²×C₄₇	—	2	2	no	—
124	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₄₇	#41	1	1	yes	characteristic
127	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
128	C₂³×C₄₇	—	2	2	no	—
129	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
130	Q₈×C₄₇	—	2	2	no	—
131	Q₈×C₄₇	—	2	2	no	—
132	D₄×C₄₇	—	2	2	no	—
133	D₄×C₄₇	—	2	2	no	—
134	D₄×C₄₇	—	4	4	no	—
135	C₂×C₄×C₄₇	—	2	2	no	—
136	C₂×C₄×C₄₇	—	2	1	no	—
137	C₂×C₄×C₄₇	—	2	1	no	—
138	C₂×C₄×C₄₇	—	2	1	no	—
139	C₂×C₄×C₄₇	—	2	1	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	—	4	2	no	—
144	C₂×C₄×C₄₇	—	4	2	no	—
145	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
151	C₈×C₄₇	—	2	1	no	—
152	C₈×C₄₇	—	2	1	no	—
153	C₈×C₄₇	—	2	1	no	—
154	C₈×C₄₇	—	2	2	no	—
155	C₈×C₄₇	—	2	2	no	—
156	C₈×C₄₇	—	4	2	no	—
157	C₈×C₄₇	—	4	2	no	—
158	C₈×C₄₇	—	4	2	no	—
159	C₈×C₄₇	#131	1	2	yes	—
160	#18092	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂²×C₄₇	—	2	1	no	—
162	C₂²×C₄₇	—	2	1	no	—
163	C₂²×C₄₇	—	4	2	no	—
164	C₂²×C₄₇	—	4	2	no	—
165	C₂²×C₄₇	—	4	2	no	—
166	C₂²×C₄₇	#444	1	2	yes	—
167	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
168	C₄×C₄₇	—	2	1	no	—
169	C₄×C₄₇	—	2	1	no	—
170	C₄×C₄₇	—	2	1	no	—
171	C₄×C₄₇	—	2	1	no	—
172	C₄×C₄₇	—	4	2	no	—
173	C₄×C₄₇	—	4	2	no	—
174	C₄×C₄₇	—	4	2	no	—
175	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
176	C₄×C₄₇	#568	1	1	yes	characteristic
177	C₄×C₄₇	#576	1	1	yes	characteristic
178	C₄×C₄₇	#578	1	1	yes	characteristic
179	#3168	C₂×C₄₇	1	1	yes	characteristic
180	#2994	C₂×C₄₇	1	2	yes	complemented
181	#1592	C₂×C₄₇	1	2	yes	complemented
182	#1584	C₂×C₄₇	1	2	yes	complemented
183	#1581	C₂×C₄₇	1	2	yes	complemented
184	SD₁₆⋊C₈	C₂×C₄₇	1	2	yes	complemented
185	C₂×#335	C₂×C₄₇	1	1	yes	characteristic, complemented
186	#1483	C₂×C₄₇	1	2	yes	complemented
187	#1451	C₂×C₄₇	1	1	yes	characteristic, complemented
188	C₂×C₄₇	—	2	2	no	—
189	C₂×C₄₇	—	8	2	no	—
190	C₂×C₄₇	#2935	1	1	yes	characteristic
191	C₂×C₄₇	#2951	1	1	yes	characteristic
192	C₂×C₄₇	C₂×#444	1	1	yes	characteristic
193	#529	C₂²×C₄₇	1	2	yes	—
194	#499	C₄×C₄₇	1	1	yes	characteristic
195	#495	C₄×C₄₇	1	1	yes	characteristic
196	#488	C₄×C₄₇	1	2	yes	—
197	#467	C₄×C₄₇	1	1	yes	characteristic
198	#466	C₄×C₄₇	1	1	yes	characteristic
199	#465	C₄×C₄₇	1	2	yes	—
200	#446	C₂²×C₄₇	1	2	yes	—
201	C₈×Q₈	C₂²×C₄₇	1	2	yes	—
202	C₄×Q₁₆	C₂²×C₄₇	1	1	yes	characteristic
203	C₄×SD₁₆	C₂²×C₄₇	1	2	yes	—
204	C₄×D₈	C₂²×C₄₇	1	1	yes	characteristic
205	#436	C₂²×C₄₇	1	2	yes	—
206	#435	—	2	2	no	—
207	C₈×D₄	—	2	2	no	—
208	C₈×D₄	C₂²×C₄₇	1	2	yes	—
209	#433	—	2	2	no	—
210	#431	C₂²×C₄₇	1	1	yes	characteristic
211	#424	—	2	2	no	—
212	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
213	C₄×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
214	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
215	#335	C₂²×C₄₇	1	1	yes	characteristic
216	#335	C₂²×C₄₇	1	2	yes	—
217	#335	C₂²×C₄₇	1	1	yes	characteristic
218	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	—
219	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	—
220	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
221	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
222	#322	C₂²×C₄₇	1	2	yes	—
223	#322	C₂²×C₄₇	1	2	yes	—
224	C₄₇	#18092	1	1	yes	characteristic, direct product factor, Sylow
225	C₂×Q₁₆	C₂×C₄×C₄₇	1	1	yes	characteristic
226	C₂×SD₁₆	C₂×C₄×C₄₇	1	2	yes	—
227	C₂×D₈	C₂×C₄×C₄₇	1	1	yes	characteristic
228	C₂×M₁₆	—	2	1	no	—
229	C₂×M₁₆	—	2	2	no	—
230	C₂²×C₈	—	2	2	no	—
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
233	C₂²×C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
234	#126	—	2	2	no	—
235	#125	C₂×C₄×C₄₇	1	2	yes	—
236	#124	C₂×C₄×C₄₇	1	2	yes	—
237	#123	—	2	2	no	—
238	C₂²⋊Q₈	C₂×C₄×C₄₇	1	2	yes	—
239	#121	C₂×C₄×C₄₇	1	2	yes	—
240	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
241	C₄×D₄	—	2	2	no	—
242	C₄×D₄	C₂³×C₄₇	1	2	yes	—
243	#117	—	2	2	no	—
244	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
245	#107	C₂×C₄×C₄₇	1	1	yes	characteristic
246	#107	C₂×C₄×C₄₇	1	1	yes	characteristic
247	#106	C₂×C₄×C₄₇	1	2	yes	—
248	C₄⋊C₈	—	2	2	no	—
249	C₄⋊C₈	—	2	2	no	—
250	C₄⋊C₈	—	2	2	no	—
251	C₄⋊C₈	D₄×C₄₇	1	1	yes	characteristic
252	C₄⋊C₈	D₄×C₄₇	1	1	yes	characteristic
253	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
254	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
255	#103	C₂×C₄×C₄₇	1	2	yes	—
256	#103	C₂×C₄×C₄₇	1	2	yes	—
257	#102	C₂×C₄×C₄₇	1	2	yes	—
258	#102	C₂×C₄×C₄₇	1	2	yes	—
259	C₂²⋊C₈	—	2	2	no	—
260	C₂²⋊C₈	—	2	2	no	—
261	C₂²⋊C₈	D₄×C₄₇	1	2	yes	—
262	#97	—	2	2	no	—
263	#97	—	2	1	no	—
264	C₄×C₈	—	2	2	no	—
265	C₄×C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
266	C₄×C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
267	C₄×C₈	C₂³×C₄₇	1	2	yes	—
268	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
269	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
270	C₄×C₈	C₂³×C₄₇	1	2	yes	—
271	C₂×Q₈	C₂²×C₄×C₄₇	1	2	yes	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
277	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
278	Q₁₆	—	4	1	no	—
279	SD₁₆	—	2	4	no	—
280	D₈	—	4	1	no	—
281	M₁₆	—	4	2	no	—
282	M₁₆	—	8	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	4	1	no	—
288	C₂×C₈	—	8	2	no	—
289	C₂×C₈	—	8	2	no	—
290	C₂×C₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
291	C₂×C₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
292	C₂×C₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
293	C₂×C₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
294	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
295	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
301	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
302	C₂²⋊C₄	—	2	2	no	—
303	C₂²⋊C₄	—	2	2	no	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₂²⋊C₄	—	2	2	no	—
307	C₄²	—	2	2	no	—
308	C₄²	C₂²×C₄×C₄₇	1	1	yes	characteristic
309	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
310	C₄²	#41×C₄₇	1	1	yes	characteristic
311	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
312	C₂³	—	2	2	no	—
313	C₂³	C₄×D₄×C₄₇	1	1	yes	characteristic
314	Q₈	—	2	2	no	—
315	Q₈	—	2	2	no	—
316	D₄	—	2	2	no	—
317	D₄	—	2	2	no	—
318	D₄	—	4	4	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
330	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
331	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
332	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
333	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
334	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
335	C₈	—	2	1	no	—
336	C₈	—	2	1	no	—
337	C₈	—	2	1	no	—
338	C₈	—	2	2	no	—
339	C₈	—	2	2	no	—
340	C₈	—	4	2	no	—
341	C₈	—	4	2	no	—
342	C₈	—	4	2	no	—
343	C₈	#131×C₄₇	1	2	yes	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	4	2	no	—
347	C₂²	—	4	2	no	—
348	C₂²	—	4	2	no	—
349	C₂²	C₄₇×#444	1	2	yes	—
350	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	4	2	no	—
356	C₄	—	4	2	no	—
357	C₄	—	4	2	no	—
358	C₄	C₂×#131×C₄₇	1	1	yes	characteristic
359	C₄	C₄₇×#568	1	1	yes	characteristic
360	C₄	C₄₇×#576	1	1	yes	characteristic
361	C₄	C₄₇×#578	1	1	yes	characteristic
362	C₂	—	2	2	no	—
363	C₂	—	8	2	no	—
364	C₂	C₄₇×#2935	1	1	yes	characteristic
365	C₂	C₄₇×#2951	1	1	yes	characteristic
366	C₂	C₂×C₄₇×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₄²	C₂⁴×C₄₇
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₄₇×#466	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₇ ◁ C₄₇×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#2994	C₂	semidirect
3. C₄₇×#1592	C₂	semidirect
4. C₄₇×#1584	C₂	semidirect
5. C₄₇×#1581	C₂	semidirect
6. C₄₇×SD₁₆⋊C₈	C₂	semidirect
7. C₂×C₄₇×#335	C₂	semidirect
8. C₄₇×#1483	C₂	semidirect
9. C₄₇×#1451	C₂	semidirect
160. #18092	C₄₇	direct (N × H)
180. #2994	C₂×C₄₇	semidirect
181. #1592	C₂×C₄₇	semidirect
182. #1584	C₂×C₄₇	semidirect
183. #1581	C₂×C₄₇	semidirect
184. SD₁₆⋊C₈	C₂×C₄₇	semidirect
185. C₂×#335	C₂×C₄₇	semidirect
186. #1483	C₂×C₄₇	semidirect
187. #1451	C₂×C₄₇	semidirect
224. C₄₇	#18092	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₇×#3168	2
C₄₇×#2994	2
C₄₇×#1592	2
C₄₇×#1584	2
C₄₇×#1581	2
C₄₇×SD₁₆⋊C₈	2
C₂×C₄₇×#335	2
C₄₇×#1483	2
C₄₇×#1451	2
#18092	47

Subgroups — C47×#18092 #26057790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#18092 #26057790