Subgroups — C₄₇×#20630 #26060328

Order 12032.

1498 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#424	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₇×#408	C₂	1	2	yes	maximal
4	C₄₇×#1798	C₂	1	4	yes	maximal, complemented
5	C₄₇×#1797	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1728	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₇×#336	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
10	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
11	C₄×#41×C₄₇	—	2	8	no	—
12	C₂×C₄×Q₈×C₄₇	C₄	1	2	yes	—
13	C₂×C₄×D₄×C₄₇	C₄	1	2	yes	—
14	C₂×C₄×D₄×C₄₇	C₄	1	4	yes	—
15	C₂×#117×C₄₇	C₂²	1	2	yes	—
16	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
18	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#424	—	2	8	no	—
20	C₂×C₄⋊C₈×C₄₇	C₂²	1	8	yes	—
21	C₄₇×#408	—	2	8	no	—
22	C₂×C₂²⋊C₈×C₄₇	C₂²	1	8	yes	—
23	C₄₇×#336	C₂²	1	2	yes	—
24	C₄₇×#336	C₂²	1	2	yes	—
25	C₄₇×#336	C₂²	1	2	yes	—
26	C₄₇×#336	C₂²	1	2	yes	—
27	C₂×#41×C₄₇	—	2	4	no	—
28	C₂×#41×C₄₇	—	2	4	no	—
29	C₂×#41×C₄₇	D₄	1	4	yes	—
30	C₂×#41×C₄₇	Q₈	1	4	yes	—
31	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
32	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
33	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
36	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
37	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
38	C₂×M₁₆×C₄₇	—	2	4	no	—
39	C₂×M₁₆×C₄₇	—	2	4	no	—
40	C₂×M₁₆×C₄₇	—	2	4	no	—
41	C₂²×C₈×C₄₇	—	2	4	no	—
42	C₂²×C₈×C₄₇	—	2	4	no	—
43	C₂²×C₈×C₄₇	—	2	4	no	—
44	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
45	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
46	C₄×Q₈×C₄₇	—	2	8	no	—
47	C₄×D₄×C₄₇	—	2	8	no	—
48	C₄×D₄×C₄₇	—	2	16	no	—
49	#117×C₄₇	—	2	8	no	—
50	#117×C₄₇	D₄	1	8	yes	—
51	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
52	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
54	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₄₇	—	2	4	no	—
56	C₂×C₄²×C₄₇	—	2	8	no	—
57	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
59	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
62	C₄⋊C₈×C₄₇	—	2	16	no	—
63	C₂²⋊C₈×C₄₇	—	2	16	no	—
64	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
65	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
66	#41×C₄₇	—	2	16	no	—
67	#41×C₄₇	—	2	16	no	—
68	C₂×Q₈×C₄₇	—	2	2	no	—
69	C₂×Q₈×C₄₇	—	2	2	no	—
70	C₂×Q₈×C₄₇	C₄⋊C₄	1	4	yes	—
71	C₂×D₄×C₄₇	—	2	4	no	—
72	C₂×D₄×C₄₇	—	2	4	no	—
73	C₂×D₄×C₄₇	—	2	2	no	—
74	C₂×D₄×C₄₇	—	2	2	no	—
75	C₂×D₄×C₄₇	C₄⋊C₄	1	8	yes	—
76	C₂×D₄×C₄₇	C₄⋊C₄	1	4	yes	—
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	8	no	—
81	C₂²×C₄×C₄₇	—	2	8	no	—
82	C₂²×C₄×C₄₇	—	2	4	no	—
83	C₂²×C₄×C₄₇	—	4	4	no	—
84	C₂²×C₄×C₄₇	—	4	2	no	—
85	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
91	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
92	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
94	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
95	C₂²×C₄×C₄₇	#41	1	4	yes	—
96	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
97	M₁₆×C₄₇	—	4	8	no	—
98	C₂×C₈×C₄₇	—	2	4	no	—
99	C₂×C₈×C₄₇	—	2	4	no	—
100	C₂×C₈×C₄₇	—	2	4	no	—
101	C₂×C₈×C₄₇	—	2	4	no	—
102	C₂×C₈×C₄₇	—	2	4	no	—
103	C₂×C₈×C₄₇	—	2	4	no	—
104	C₂×C₈×C₄₇	—	4	8	no	—
105	C₄⋊C₄×C₄₇	—	2	8	no	—
106	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
107	C₂²⋊C₄×C₄₇	—	2	8	no	—
108	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
109	C₄²×C₄₇	—	2	8	no	—
110	C₄²×C₄₇	—	2	4	no	—
111	C₄²×C₄₇	—	2	2	no	—
112	C₄²×C₄₇	—	2	2	no	—
113	C₄²×C₄₇	C₂×D₄	1	8	yes	—
114	C₂³×C₄₇	—	2	2	no	—
115	C₂³×C₄₇	—	2	2	no	—
116	C₂³×C₄₇	—	2	2	no	—
117	C₂³×C₄₇	—	2	2	no	—
118	C₂³×C₄₇	—	2	4	no	—
119	C₂³×C₄₇	—	2	4	no	—
120	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
121	C₂³×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
122	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
123	C₂³×C₄₇	#117	1	2	yes	—
124	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
125	Q₈×C₄₇	—	2	8	no	—
126	D₄×C₄₇	—	2	16	no	—
127	D₄×C₄₇	—	2	8	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	4	no	—
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	2	4	no	—
134	C₂×C₄×C₄₇	—	2	8	no	—
135	C₂×C₄×C₄₇	—	2	8	no	—
136	C₂×C₄×C₄₇	—	2	2	no	—
137	C₂×C₄×C₄₇	—	2	2	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	4	16	no	—
140	C₂×C₄×C₄₇	—	4	8	no	—
141	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
142	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
143	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
144	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
145	C₂×C₄×C₄₇	#117	1	2	yes	—
146	C₂×C₄×C₄₇	#121	1	8	yes	—
147	C₂×C₄×C₄₇	C₂²⋊Q₈	1	8	yes	—
148	C₂×C₄×C₄₇	#131	1	4	yes	—
149	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
151	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
153	C₈×C₄₇	—	4	4	no	—
154	C₈×C₄₇	—	4	4	no	—
155	#20630	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂²×C₄₇	—	2	4	no	—
157	C₂²×C₄₇	—	2	4	no	—
158	C₂²×C₄₇	—	2	2	no	—
159	C₂²×C₄₇	—	2	2	no	—
160	C₂²×C₄₇	—	2	8	no	—
161	C₂²×C₄₇	—	2	4	no	—
162	C₂²×C₄₇	—	4	4	no	—
163	C₂²×C₄₇	—	4	2	no	—
164	C₂²×C₄₇	—	4	2	no	—
165	C₂²×C₄₇	#380	1	4	yes	—
166	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
168	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
169	C₂²×C₄₇	C₂×#131	1	2	yes	—
170	C₂²×C₄₇	#568	1	2	yes	—
171	C₄×C₄₇	—	2	4	no	—
172	C₄×C₄₇	—	2	8	no	—
173	C₄×C₄₇	—	2	4	no	—
174	C₄×C₄₇	—	4	2	no	—
175	C₄×C₄₇	#380	1	4	yes	—
176	C₄×C₄₇	C₂×#121	1	2	yes	—
177	C₄×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
178	C₂×C₄×#41	C₂×C₄₇	1	1	yes	characteristic
179	C₂×#424	C₂×C₄₇	1	2	yes	complemented
180	C₂×#408	C₂×C₄₇	1	2	yes	—
181	#1798	C₂×C₄₇	1	4	yes	complemented
182	#1797	C₂×C₄₇	1	4	yes	complemented
183	#1728	C₂×C₄₇	1	1	yes	characteristic, complemented
184	C₂×#336	C₂×C₄₇	1	1	yes	characteristic, complemented
185	C₂×C₄₇	—	2	4	no	—
186	C₂×C₄₇	—	4	4	no	—
187	C₂×C₄₇	C₂×#380	1	1	yes	characteristic
188	C₂×C₄₇	#2880	1	2	yes	—
189	C₂×C₄₇	#2906	1	2	yes	—
190	C₂×C₄₇	#2922	1	1	yes	characteristic
191	C₂×C₄₇	#2923	1	1	yes	characteristic
192	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
193	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
194	C₂³×C₈	C₂²×C₄₇	1	2	yes	—
195	C₄×#41	—	2	8	no	—
196	C₂×C₄×Q₈	C₄×C₄₇	1	2	yes	—
197	C₂×C₄×D₄	C₄×C₄₇	1	2	yes	—
198	C₂×C₄×D₄	C₄×C₄₇	1	4	yes	—
199	C₂×#117	C₂²×C₄₇	1	2	yes	—
200	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
201	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
202	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
203	#424	—	2	8	no	—
204	C₂×C₄⋊C₈	C₂²×C₄₇	1	8	yes	—
205	#408	—	2	8	no	—
206	C₂×C₂²⋊C₈	C₂²×C₄₇	1	8	yes	—
207	#336	C₂²×C₄₇	1	2	yes	—
208	#336	C₂²×C₄₇	1	2	yes	—
209	#336	C₂²×C₄₇	1	2	yes	—
210	#336	C₂²×C₄₇	1	2	yes	—
211	C₄₇	#20630	1	1	yes	characteristic, direct product factor, Sylow
212	C₂×#41	—	2	4	no	—
213	C₂×#41	—	2	4	no	—
214	C₂×#41	D₄×C₄₇	1	4	yes	—
215	C₂×#41	Q₈×C₄₇	1	4	yes	—
216	C₂²×Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
217	C₂²×D₄	C₂×C₄×C₄₇	1	2	yes	—
218	C₂²×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic
219	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
220	C₂³×C₄	C₂×C₄×C₄₇	1	4	yes	—
221	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
222	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
223	C₂×M₁₆	—	2	4	no	—
224	C₂×M₁₆	—	2	4	no	—
225	C₂×M₁₆	—	2	4	no	—
226	C₂²×C₈	—	2	4	no	—
227	C₂²×C₈	—	2	4	no	—
228	C₂²×C₈	—	2	4	no	—
229	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
230	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
231	C₄×Q₈	—	2	8	no	—
232	C₄×D₄	—	2	8	no	—
233	C₄×D₄	—	2	16	no	—
234	#117	—	2	8	no	—
235	#117	D₄×C₄₇	1	8	yes	—
236	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
237	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
238	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
239	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
240	C₂×C₄²	—	2	4	no	—
241	C₂×C₄²	—	2	8	no	—
242	C₂×C₄²	C₂×C₄×C₄₇	1	2	yes	—
243	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
244	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
245	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
246	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
247	C₄⋊C₈	—	2	16	no	—
248	C₂²⋊C₈	—	2	16	no	—
249	C₂⁴	C₂²×C₄×C₄₇	1	2	yes	—
250	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
251	#41	—	2	16	no	—
252	#41	—	2	16	no	—
253	C₂×Q₈	—	2	2	no	—
254	C₂×Q₈	—	2	2	no	—
255	C₂×Q₈	C₄⋊C₄×C₄₇	1	4	yes	—
256	C₂×D₄	—	2	4	no	—
257	C₂×D₄	—	2	4	no	—
258	C₂×D₄	—	2	2	no	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	C₄⋊C₄×C₄₇	1	8	yes	—
261	C₂×D₄	C₄⋊C₄×C₄₇	1	4	yes	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	8	no	—
266	C₂²×C₄	—	2	8	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	4	4	no	—
269	C₂²×C₄	—	4	2	no	—
270	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
271	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
272	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
273	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
274	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
276	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
277	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
278	C₂²×C₄	C₂×Q₈×C₄₇	1	4	yes	—
279	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
280	C₂²×C₄	#41×C₄₇	1	4	yes	—
281	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
282	M₁₆	—	4	8	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	—	2	4	no	—
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	4	8	no	—
290	C₄⋊C₄	—	2	8	no	—
291	C₄⋊C₄	C₂²⋊C₄×C₄₇	1	8	yes	—
292	C₂²⋊C₄	—	2	8	no	—
293	C₂²⋊C₄	C₂²⋊C₄×C₄₇	1	8	yes	—
294	C₄²	—	2	8	no	—
295	C₄²	—	2	4	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	2	no	—
298	C₄²	C₂×D₄×C₄₇	1	8	yes	—
299	C₂³	—	2	2	no	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	2	no	—
302	C₂³	—	2	2	no	—
303	C₂³	—	2	4	no	—
304	C₂³	—	2	4	no	—
305	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
306	C₂³	C₂×C₄⋊C₄×C₄₇	1	4	yes	—
307	C₂³	C₂×C₄⋊C₄×C₄₇	1	2	yes	—
308	C₂³	#117×C₄₇	1	2	yes	—
309	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
310	Q₈	—	2	8	no	—
311	D₄	—	2	16	no	—
312	D₄	—	2	8	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	8	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	4	16	no	—
325	C₂×C₄	—	4	8	no	—
326	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	8	yes	—
327	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
328	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	4	yes	—
329	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	2	yes	—
330	C₂×C₄	#117×C₄₇	1	2	yes	—
331	C₂×C₄	#121×C₄₇	1	8	yes	—
332	C₂×C₄	C₂²⋊Q₈×C₄₇	1	8	yes	—
333	C₂×C₄	#131×C₄₇	1	4	yes	—
334	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
335	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
336	C₂×C₄	C₂²×Q₈×C₄₇	1	1	yes	characteristic
337	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
338	C₈	—	4	4	no	—
339	C₈	—	4	4	no	—
340	C₂²	—	2	4	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	8	no	—
346	C₂²	—	4	4	no	—
347	C₂²	—	4	2	no	—
348	C₂²	—	4	2	no	—
349	C₂²	C₄₇×#380	1	4	yes	—
350	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
351	C₂²	C₂²×C₄⋊C₄×C₄₇	1	1	yes	characteristic
352	C₂²	C₂×#117×C₄₇	1	1	yes	characteristic
353	C₂²	C₂×#131×C₄₇	1	2	yes	—
354	C₂²	C₄₇×#568	1	2	yes	—
355	C₄	—	2	4	no	—
356	C₄	—	2	4	no	—
357	C₄	—	2	8	no	—
358	C₄	—	4	2	no	—
359	C₄	C₄₇×#380	1	4	yes	—
360	C₄	C₂×#121×C₄₇	1	2	yes	—
361	C₄	C₂×C₂²⋊Q₈×C₄₇	1	2	yes	—
362	C₂	—	2	4	no	—
363	C₂	—	4	4	no	—
364	C₂	C₂×C₄₇×#380	1	1	yes	characteristic
365	C₂	C₄₇×#2880	1	2	yes	—
366	C₂	C₄₇×#2906	1	2	yes	—
367	C₂	C₄₇×#2922	1	1	yes	characteristic
368	C₂	C₄₇×#2923	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₄₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×#41×C₄₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#424	C₂	semidirect
4. C₄₇×#1798	C₂	semidirect
5. C₄₇×#1797	C₂	semidirect
6. C₄₇×#1728	C₂	semidirect
7. C₂×C₄₇×#336	C₂	semidirect
155. #20630	C₄₇	direct (N × H)
179. C₂×#424	C₂×C₄₇	semidirect
181. #1798	C₂×C₄₇	semidirect
182. #1797	C₂×C₄₇	semidirect
183. #1728	C₂×C₄₇	semidirect
184. C₂×#336	C₂×C₄₇	semidirect
211. C₄₇	#20630	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₄₇	2
C₂×C₄₇×#424	2
C₂×C₄₇×#408	2
C₄₇×#1798	2
C₄₇×#1797	2
C₄₇×#1728	2
C₂×C₄₇×#336	2
#20630	47

Subgroups — C47×#20630 #26060328

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#20630 #26060328