Subgroups — C₄₇×#20628 #26060326

Order 12032.

1582 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#117×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#424	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₇×#407	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₂²⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#1798	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1797	C₂	1	4	yes	maximal, complemented
7	C₄₇×#1729	C₂	1	2	yes	maximal, complemented
8	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
10	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
11	C₂×#117×C₄₇	—	2	8	no	—
12	C₂×#117×C₄₇	C₄	1	2	yes	—
13	C₂×#117×C₄₇	C₄	1	2	yes	—
14	C₂×#117×C₄₇	C₂²	1	2	yes	—
15	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₄₇	C₄	1	2	yes	—
19	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
20	C₄₇×#424	—	2	8	no	—
21	C₂×C₄⋊C₈×C₄₇	C₂²	1	8	yes	complemented
22	C₄₇×#407	—	2	4	no	—
23	C₂×C₂²⋊C₈×C₄₇	—	2	4	no	—
24	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
28	C₄₇×#336	C₂²	1	8	yes	complemented
29	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₄₇	—	2	4	no	—
31	C₂³×C₄×C₄₇	—	2	4	no	—
32	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
33	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₄₇	D₄	1	4	yes	—
37	C₂³×C₄×C₄₇	Q₈	1	4	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	C₂×M₁₆×C₄₇	—	2	4	no	—
42	C₂×M₁₆×C₄₇	—	2	4	no	—
43	C₂×M₁₆×C₄₇	—	2	4	no	—
44	C₂²×C₈×C₄₇	—	2	4	no	—
45	C₂²×C₈×C₄₇	—	2	4	no	—
46	C₂²×C₈×C₄₇	—	2	4	no	—
47	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
48	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
49	#117×C₄₇	—	2	4	no	—
50	#117×C₄₇	—	2	8	no	—
51	#117×C₄₇	—	2	8	no	—
52	#117×C₄₇	—	2	8	no	—
53	#117×C₄₇	D₄	1	8	yes	—
54	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
55	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
57	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
58	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
59	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
61	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
62	C₂×C₄²×C₄₇	—	2	8	no	—
63	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
64	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
65	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
66	C₄⋊C₈×C₄₇	—	2	16	no	—
67	C₂²⋊C₈×C₄₇	—	2	4	no	—
68	C₂²⋊C₈×C₄₇	—	2	4	no	—
69	C₂²⋊C₈×C₄₇	—	2	4	no	—
70	C₂²⋊C₈×C₄₇	—	2	4	no	—
71	C₂⁴×C₄₇	—	2	2	no	—
72	C₂⁴×C₄₇	—	2	2	no	—
73	C₂⁴×C₄₇	—	2	4	no	—
74	C₂⁴×C₄₇	—	4	2	no	—
75	C₂⁴×C₄₇	C₄⋊C₄	1	4	yes	—
76	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
77	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
78	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
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	2	no	—
83	C₂²×C₄×C₄₇	—	2	2	no	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	—	2	16	no	—
86	C₂²×C₄×C₄₇	—	2	16	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	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	2	8	no	—
92	C₂²×C₄×C₄₇	—	2	8	no	—
93	C₂²×C₄×C₄₇	—	4	4	no	—
94	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
95	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
96	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
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	4	yes	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₄₇	#41	1	4	yes	—
110	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
111	M₁₆×C₄₇	—	4	8	no	—
112	C₂×C₈×C₄₇	—	2	4	no	—
113	C₂×C₈×C₄₇	—	2	4	no	—
114	C₂×C₈×C₄₇	—	2	4	no	—
115	C₂×C₈×C₄₇	—	2	4	no	—
116	C₂×C₈×C₄₇	—	2	4	no	—
117	C₂×C₈×C₄₇	—	2	4	no	—
118	C₂×C₈×C₄₇	—	4	8	no	—
119	C₄⋊C₄×C₄₇	—	2	8	no	—
120	C₄⋊C₄×C₄₇	—	2	4	no	—
121	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
122	C₂²⋊C₄×C₄₇	—	2	4	no	—
123	C₂²⋊C₄×C₄₇	—	2	8	no	—
124	C₂²⋊C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
125	C₄²×C₄₇	—	2	8	no	—
126	C₄²×C₄₇	—	2	4	no	—
127	C₄²×C₄₇	C₂×D₄	1	8	yes	—
128	C₂³×C₄₇	—	2	1	no	—
129	C₂³×C₄₇	—	2	1	no	—
130	C₂³×C₄₇	—	2	2	no	—
131	C₂³×C₄₇	—	2	2	no	—
132	C₂³×C₄₇	—	2	2	no	—
133	C₂³×C₄₇	—	2	1	no	—
134	C₂³×C₄₇	—	2	1	no	—
135	C₂³×C₄₇	—	2	2	no	—
136	C₂³×C₄₇	—	2	2	no	—
137	C₂³×C₄₇	—	2	8	no	—
138	C₂³×C₄₇	—	2	8	no	—
139	C₂³×C₄₇	—	4	4	no	—
140	C₂³×C₄₇	—	4	8	no	—
141	C₂³×C₄₇	—	4	8	no	—
142	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
143	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
144	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
145	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
146	C₂³×C₄₇	#117	1	2	yes	—
147	C₂³×C₄₇	#131	1	4	yes	—
148	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	—	2	1	no	—
150	C₂×C₄×C₄₇	—	2	1	no	—
151	C₂×C₄×C₄₇	—	2	1	no	—
152	C₂×C₄×C₄₇	—	2	1	no	—
153	C₂×C₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	2	4	no	—
155	C₂×C₄×C₄₇	—	2	8	no	—
156	C₂×C₄×C₄₇	—	2	4	no	—
157	C₂×C₄×C₄₇	—	2	4	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	2	4	no	—
160	C₂×C₄×C₄₇	—	2	8	no	—
161	C₂×C₄×C₄₇	—	2	8	no	—
162	C₂×C₄×C₄₇	—	2	4	no	—
163	C₂×C₄×C₄₇	—	2	4	no	—
164	C₂×C₄×C₄₇	—	2	4	no	—
165	C₂×C₄×C₄₇	—	4	16	no	—
166	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
167	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
169	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
170	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
171	C₂×C₄×C₄₇	#117	1	2	yes	—
172	C₂×C₄×C₄₇	#121	1	8	yes	—
173	C₂×C₄×C₄₇	C₂²⋊Q₈	1	8	yes	—
174	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
176	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
178	C₈×C₄₇	—	4	4	no	—
179	C₈×C₄₇	—	4	4	no	—
180	#20628	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂²×C₄₇	—	2	4	no	—
182	C₂²×C₄₇	—	2	4	no	—
183	C₂²×C₄₇	—	2	2	no	—
184	C₂²×C₄₇	—	2	2	no	—
185	C₂²×C₄₇	—	2	2	no	—
186	C₂²×C₄₇	—	2	4	no	—
187	C₂²×C₄₇	—	2	4	no	—
188	C₂²×C₄₇	—	2	2	no	—
189	C₂²×C₄₇	—	2	2	no	—
190	C₂²×C₄₇	—	2	2	no	—
191	C₂²×C₄₇	—	2	2	no	—
192	C₂²×C₄₇	—	4	16	no	—
193	C₂²×C₄₇	—	4	2	no	—
194	C₂²×C₄₇	—	4	2	no	—
195	C₂²×C₄₇	#380	1	4	yes	—
196	C₂²×C₄₇	#424	1	4	yes	complemented
197	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
198	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
199	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
200	C₂²×C₄₇	C₂×#131	1	2	yes	—
201	C₂²×C₄₇	#568	1	2	yes	—
202	C₄×C₄₇	—	2	8	no	—
203	C₄×C₄₇	—	2	2	no	—
204	C₄×C₄₇	—	2	2	no	—
205	C₄×C₄₇	—	4	4	no	—
206	C₄×C₄₇	#380	1	4	yes	—
207	C₄×C₄₇	C₂×#121	1	2	yes	—
208	C₄×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
209	C₂²×#117	C₂×C₄₇	1	1	yes	characteristic
210	C₂×#424	C₂×C₄₇	1	2	yes	complemented
211	C₂×#407	C₂×C₄₇	1	1	yes	characteristic
212	C₂²×C₂²⋊C₈	C₂×C₄₇	1	1	yes	characteristic
213	#1798	C₂×C₄₇	1	4	yes	complemented
214	#1797	C₂×C₄₇	1	4	yes	complemented
215	#1729	C₂×C₄₇	1	2	yes	complemented
216	C₂×C₄₇	—	2	4	no	—
217	C₂×C₄₇	—	2	4	no	—
218	C₂×C₄₇	—	4	2	no	—
219	C₂×C₄₇	C₂×#380	1	1	yes	characteristic
220	C₂×C₄₇	#2880	1	2	yes	—
221	C₂×C₄₇	C₂×#424	1	1	yes	characteristic
222	C₂×C₄₇	#2905	1	1	yes	characteristic
223	C₂×C₄₇	#2924	1	2	yes	—
224	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
225	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
226	C₂³×C₈	C₂²×C₄₇	1	2	yes	—
227	C₂×#117	—	2	8	no	—
228	C₂×#117	C₄×C₄₇	1	2	yes	—
229	C₂×#117	C₄×C₄₇	1	2	yes	—
230	C₂×#117	C₂²×C₄₇	1	2	yes	—
231	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
232	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
233	C₂²×C₄⋊C₄	C₄×C₄₇	1	2	yes	—
234	C₂²×C₂²⋊C₄	C₄×C₄₇	1	2	yes	—
235	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
236	#424	—	2	8	no	—
237	C₂×C₄⋊C₈	C₂²×C₄₇	1	8	yes	complemented
238	#407	—	2	4	no	—
239	C₂×C₂²⋊C₈	—	2	4	no	—
240	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
241	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
242	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
243	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
244	#336	C₂²×C₄₇	1	8	yes	complemented
245	C₄₇	#20628	1	1	yes	characteristic, direct product factor, Sylow
246	C₂⁵	C₂×C₄×C₄₇	1	1	yes	characteristic
247	C₂³×C₄	—	2	4	no	—
248	C₂³×C₄	—	2	4	no	—
249	C₂³×C₄	C₂×C₄×C₄₇	1	4	yes	—
250	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
251	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
252	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
253	C₂³×C₄	D₄×C₄₇	1	4	yes	—
254	C₂³×C₄	Q₈×C₄₇	1	4	yes	—
255	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
256	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
257	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
258	C₂×M₁₆	—	2	4	no	—
259	C₂×M₁₆	—	2	4	no	—
260	C₂×M₁₆	—	2	4	no	—
261	C₂²×C₈	—	2	4	no	—
262	C₂²×C₈	—	2	4	no	—
263	C₂²×C₈	—	2	4	no	—
264	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
265	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
266	#117	—	2	4	no	—
267	#117	—	2	8	no	—
268	#117	—	2	8	no	—
269	#117	—	2	8	no	—
270	#117	D₄×C₄₇	1	8	yes	—
271	C₂×C₄⋊C₄	—	2	8	no	—
272	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
273	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
274	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
275	C₂×C₂²⋊C₄	—	2	8	no	—
276	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
277	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
278	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
279	C₂×C₄²	—	2	8	no	—
280	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
281	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
282	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
283	C₄⋊C₈	—	2	16	no	—
284	C₂²⋊C₈	—	2	4	no	—
285	C₂²⋊C₈	—	2	4	no	—
286	C₂²⋊C₈	—	2	4	no	—
287	C₂²⋊C₈	—	2	4	no	—
288	C₂⁴	—	2	2	no	—
289	C₂⁴	—	2	2	no	—
290	C₂⁴	—	2	4	no	—
291	C₂⁴	—	4	2	no	—
292	C₂⁴	C₄⋊C₄×C₄₇	1	4	yes	—
293	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
294	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
295	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	16	no	—
303	C₂²×C₄	—	2	16	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	8	no	—
309	C₂²×C₄	—	2	8	no	—
310	C₂²×C₄	—	4	4	no	—
311	C₂²×C₄	C₄⋊C₄×C₄₇	1	4	yes	—
312	C₂²×C₄	C₄⋊C₄×C₄₇	1	4	yes	—
313	C₂²×C₄	C₄⋊C₄×C₄₇	1	4	yes	—
314	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
315	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
316	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
317	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
318	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
321	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
322	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
323	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
324	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
325	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
326	C₂²×C₄	#41×C₄₇	1	4	yes	—
327	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
328	M₁₆	—	4	8	no	—
329	C₂×C₈	—	2	4	no	—
330	C₂×C₈	—	2	4	no	—
331	C₂×C₈	—	2	4	no	—
332	C₂×C₈	—	2	4	no	—
333	C₂×C₈	—	2	4	no	—
334	C₂×C₈	—	2	4	no	—
335	C₂×C₈	—	4	8	no	—
336	C₄⋊C₄	—	2	8	no	—
337	C₄⋊C₄	—	2	4	no	—
338	C₄⋊C₄	C₂²⋊C₄×C₄₇	1	8	yes	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	2	8	no	—
341	C₂²⋊C₄	C₂²⋊C₄×C₄₇	1	8	yes	—
342	C₄²	—	2	8	no	—
343	C₄²	—	2	4	no	—
344	C₄²	C₂×D₄×C₄₇	1	8	yes	—
345	C₂³	—	2	1	no	—
346	C₂³	—	2	1	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	8	no	—
355	C₂³	—	2	8	no	—
356	C₂³	—	4	4	no	—
357	C₂³	—	4	8	no	—
358	C₂³	—	4	8	no	—
359	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
360	C₂³	C₂×C₄⋊C₄×C₄₇	1	2	yes	—
361	C₂³	C₂×C₄⋊C₄×C₄₇	1	2	yes	—
362	C₂³	C₂×C₄⋊C₄×C₄₇	1	2	yes	—
363	C₂³	#117×C₄₇	1	2	yes	—
364	C₂³	#131×C₄₇	1	4	yes	—
365	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	8	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	8	no	—
378	C₂×C₄	—	2	8	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	4	16	no	—
383	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	8	yes	—
384	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
385	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	2	yes	—
386	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	2	yes	—
387	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	2	yes	—
388	C₂×C₄	#117×C₄₇	1	2	yes	—
389	C₂×C₄	#121×C₄₇	1	8	yes	—
390	C₂×C₄	C₂²⋊Q₈×C₄₇	1	8	yes	—
391	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
392	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
393	C₂×C₄	C₂²×Q₈×C₄₇	1	1	yes	characteristic
394	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
395	C₈	—	4	4	no	—
396	C₈	—	4	4	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	2	4	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	4	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	4	16	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	C₄₇×#380	1	4	yes	—
412	C₂²	C₄₇×#424	1	4	yes	complemented
413	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
414	C₂²	C₂²×C₄⋊C₄×C₄₇	1	1	yes	characteristic
415	C₂²	C₂×#117×C₄₇	1	1	yes	characteristic
416	C₂²	C₂×#131×C₄₇	1	2	yes	—
417	C₂²	C₄₇×#568	1	2	yes	—
418	C₄	—	2	2	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	8	no	—
421	C₄	—	4	4	no	—
422	C₄	C₄₇×#380	1	4	yes	—
423	C₄	C₂×#121×C₄₇	1	2	yes	—
424	C₄	C₂×C₂²⋊Q₈×C₄₇	1	2	yes	—
425	C₂	—	2	4	no	—
426	C₂	—	2	4	no	—
427	C₂	—	4	2	no	—
428	C₂	C₂×C₄₇×#380	1	1	yes	characteristic
429	C₂	C₄₇×#2880	1	2	yes	—
430	C₂	C₂×C₄₇×#424	1	1	yes	characteristic
431	C₂	C₄₇×#2905	1	1	yes	characteristic
432	C₂	C₄₇×#2924	1	2	yes	—

	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	C₂⁵×C₄₇	C₂×C₄
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
5. C₄₇×#1798	C₂	semidirect
6. C₄₇×#1797	C₂	semidirect
7. C₄₇×#1729	C₂	semidirect
21. C₂×C₄⋊C₈×C₄₇	C₂²	semidirect
28. C₄₇×#336	C₂²	semidirect
180. #20628	C₄₇	direct (N × H)
196. C₂²×C₄₇	#424	semidirect
210. C₂×#424	C₂×C₄₇	semidirect
213. #1798	C₂×C₄₇	semidirect
214. #1797	C₂×C₄₇	semidirect
215. #1729	C₂×C₄₇	semidirect
237. C₂×C₄⋊C₈	C₂²×C₄₇	semidirect
244. #336	C₂²×C₄₇	semidirect
245. C₄₇	#20628	direct (N × H)
412. C₂²	C₄₇×#424	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#117×C₄₇	2
C₂×C₄₇×#424	2
C₂×C₄₇×#407	2
C₂²×C₂²⋊C₈×C₄₇	2
C₄₇×#1798	2
C₄₇×#1797	2
C₄₇×#1729	2
#20628	47

Subgroups — C47×#20628 #26060326

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#20628 #26060326