Subgroups — C₄₇×#60427 #26100125

Order 12032.

2678 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#575	C₂	1	1	yes	maximal, characteristic
2	C₂²×#137×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#536	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#3428	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#3046	C₂	1	8	yes	maximal, complemented
6	C₄₇×#3044	C₂	1	4	yes	maximal, complemented
7	C₄₇×#3042	C₂	1	4	yes	maximal, complemented
8	C₄₇×#3040	C₂	1	4	yes	maximal, complemented
9	C₄₇×#3039	C₂	1	4	yes	maximal, complemented
10	C₄₇×#2905	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2896	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄₇×#419	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
14	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
15	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₄₇×#575	—	2	8	no	—
17	C₂×#137×C₄₇	—	2	8	no	—
18	C₂×#137×C₄₇	C₂²	1	2	yes	—
19	C₂×#137×C₄₇	C₂²	1	4	yes	—
20	C₂×#137×C₄₇	C₂²	1	2	yes	—
21	C₂×#137×C₄₇	C₂²	1	4	yes	complemented
22	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	2	yes	—
23	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	2	yes	—
24	C₂×#135×C₄₇	C₂²	1	4	yes	—
25	C₂²×Q₁₆×C₄₇	C₂²	1	2	yes	complemented
26	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	complemented
27	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
28	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
29	C₄₇×#536	—	2	2	no	—
30	C₄₇×#536	—	2	2	no	—
31	C₄₇×#536	C₂²	1	4	yes	—
32	C₄₇×#536	C₂²	1	4	yes	complemented
33	C₂×C₄⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
34	C₂×#124×C₄₇	C₂²	1	2	yes	complemented
35	C₂×#123×C₄₇	—	2	2	no	—
36	C₂×C₂²⋊Q₈×C₄₇	—	2	2	no	—
37	C₄₇×#520	—	2	2	no	—
38	C₄₇×#520	C₂²	1	4	yes	complemented
39	C₄₇×#519	C₂²	1	2	yes	complemented
40	C₄₇×#518	—	2	2	no	—
41	C₄₇×#518	C₂²	1	2	yes	complemented
42	C₄×#41×C₄₇	—	2	2	no	—
43	C₄×#41×C₄₇	C₂²	1	4	yes	—
44	C₂×#117×C₄₇	—	2	2	no	—
45	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
46	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
47	C₄₇×#464	C₂²	1	16	yes	complemented
48	C₄₇×#463	C₂²	1	16	yes	complemented
49	C₄₇×#462	C₂²	1	16	yes	complemented
50	C₄₇×#461	C₂²	1	16	yes	complemented
51	C₄₇×#424	C₂²	1	4	yes	complemented
52	C₄₇×#424	C₂²	1	4	yes	complemented
53	C₄₇×#423	C₂²	1	4	yes	complemented
54	C₄₇×#419	C₂²	1	2	yes	complemented
55	C₄₇×#419	C₂²	1	4	yes	complemented
56	C₄₇×#419	C₂²	1	4	yes	complemented
57	C₄₇×#418	C₂²	1	2	yes	complemented
58	C₄₇×#417	C₂²	1	4	yes	complemented
59	C₄₇×#416	C₂²	1	4	yes	—
60	C₂×#103×C₄₇	C₂²	1	4	yes	complemented
61	C₂×#41×C₄₇	—	2	1	no	—
62	C₂×#41×C₄₇	—	2	1	no	—
63	C₂×#41×C₄₇	—	2	1	no	—
64	C₂×#41×C₄₇	—	2	1	no	—
65	C₂×#41×C₄₇	—	2	4	no	—
66	C₂×#41×C₄₇	—	2	4	no	—
67	C₂×#41×C₄₇	—	2	4	no	—
68	C₂×#41×C₄₇	D₄	1	8	yes	—
69	C₂×#41×C₄₇	C₂³	1	2	yes	—
70	C₂×#41×C₄₇	C₂³	1	2	yes	—
71	C₂×#41×C₄₇	C₂³	1	2	yes	—
72	C₂×#41×C₄₇	C₂³	1	2	yes	—
73	C₂²×Q₈×C₄₇	—	2	1	no	—
74	C₂²×Q₈×C₄₇	—	2	1	no	—
75	C₂²×Q₈×C₄₇	—	2	1	no	—
76	C₂²×Q₈×C₄₇	—	2	4	no	—
77	C₂²×Q₈×C₄₇	—	2	4	no	—
78	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
79	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
81	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
82	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₄₇	—	2	1	no	—
84	C₂²×D₄×C₄₇	—	2	1	no	—
85	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₄₇	—	2	1	no	—
88	C₂³×C₄×C₄₇	—	2	1	no	—
89	C₂³×C₄×C₄₇	—	2	1	no	—
90	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
91	#137×C₄₇	—	2	16	no	—
92	#137×C₄₇	—	2	16	no	—
93	#137×C₄₇	—	2	8	no	—
94	#137×C₄₇	—	2	8	no	—
95	AGL(1,ℤ/8)×C₄₇	—	2	8	no	—
96	AGL(1,ℤ/8)×C₄₇	—	2	8	no	—
97	#135×C₄₇	—	2	16	no	—
98	C₂×Q₁₆×C₄₇	—	2	8	no	—
99	C₂×Q₁₆×C₄₇	C₂³	1	4	yes	—
100	C₂×Q₁₆×C₄₇	C₂³	1	8	yes	—
101	C₂×SD₁₆×C₄₇	—	2	8	no	—
102	C₂×SD₁₆×C₄₇	C₂³	1	4	yes	—
103	C₂×SD₁₆×C₄₇	C₂³	1	8	yes	—
104	C₂×SD₁₆×C₄₇	C₂³	1	4	yes	—
105	C₂×D₈×C₄₇	C₂³	1	4	yes	—
106	C₂×M₁₆×C₄₇	—	2	4	no	—
107	C₂×M₁₆×C₄₇	—	2	4	no	—
108	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
109	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
110	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
111	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
112	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
113	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
114	C₄⋊Q₈×C₄₇	—	2	4	no	—
115	C₄⋊Q₈×C₄₇	C₂³	1	8	yes	—
116	#124×C₄₇	—	2	4	no	—
117	#124×C₄₇	C₂³	1	8	yes	—
118	#123×C₄₇	—	2	8	no	—
119	#123×C₄₇	—	2	8	no	—
120	C₂²⋊Q₈×C₄₇	—	2	8	no	—
121	C₂²⋊Q₈×C₄₇	—	2	8	no	—
122	C₄×Q₈×C₄₇	—	2	4	no	—
123	C₄×Q₈×C₄₇	C₂³	1	8	yes	—
124	C₄×D₄×C₄₇	—	2	8	no	—
125	C₄×D₄×C₄₇	—	2	4	no	—
126	C₄×D₄×C₄₇	—	2	8	no	—
127	C₄×D₄×C₄₇	C₂³	1	8	yes	—
128	#117×C₄₇	—	2	1	no	—
129	#117×C₄₇	—	2	1	no	—
130	#117×C₄₇	—	2	4	no	—
131	#117×C₄₇	—	2	4	no	—
132	#117×C₄₇	—	2	4	no	—
133	#117×C₄₇	D₄	1	2	yes	—
134	#117×C₄₇	D₄	1	2	yes	—
135	#117×C₄₇	C₂³	1	2	yes	—
136	#117×C₄₇	C₂³	1	2	yes	—
137	#117×C₄₇	C₂³	1	2	yes	—
138	#117×C₄₇	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
140	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
141	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
142	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
144	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
145	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
146	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
147	C₂×C₄²×C₄₇	—	2	1	no	—
148	C₂×C₄²×C₄₇	—	2	4	no	—
149	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
150	C₄⋊C₈×C₄₇	C₂³	1	16	yes	—
151	#103×C₄₇	C₂³	1	8	yes	—
152	#103×C₄₇	C₂³	1	16	yes	—
153	#102×C₄₇	C₂³	1	8	yes	—
154	C₂⁴×C₄₇	—	2	1	no	—
155	C₂⁴×C₄₇	—	2	1	no	—
156	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
157	#41×C₄₇	—	2	8	no	—
158	#41×C₄₇	—	2	8	no	—
159	#41×C₄₇	—	2	4	no	—
160	#41×C₄₇	—	2	4	no	—
161	#41×C₄₇	—	2	4	no	—
162	#41×C₄₇	—	2	4	no	—
163	#41×C₄₇	—	2	4	no	—
164	#41×C₄₇	—	2	4	no	—
165	#41×C₄₇	—	4	4	no	—
166	#41×C₄₇	—	4	4	no	—
167	#41×C₄₇	C₂×D₄	1	8	yes	—
168	#41×C₄₇	C₂×D₄	1	8	yes	—
169	C₂×Q₈×C₄₇	—	2	1	no	—
170	C₂×Q₈×C₄₇	—	2	2	no	—
171	C₂×Q₈×C₄₇	—	2	2	no	—
172	C₂×Q₈×C₄₇	—	2	2	no	—
173	C₂×Q₈×C₄₇	—	2	1	no	—
174	C₂×Q₈×C₄₇	—	2	2	no	—
175	C₂×Q₈×C₄₇	—	2	4	no	—
176	C₂×Q₈×C₄₇	—	2	4	no	—
177	C₂×Q₈×C₄₇	—	2	4	no	—
178	C₂×Q₈×C₄₇	—	2	2	no	—
179	C₂×Q₈×C₄₇	—	2	4	no	—
180	C₂×Q₈×C₄₇	—	2	4	no	—
181	C₂×Q₈×C₄₇	—	2	4	no	—
182	C₂×Q₈×C₄₇	—	2	2	no	—
183	C₂×Q₈×C₄₇	—	4	4	no	—
184	C₂×Q₈×C₄₇	—	4	4	no	—
185	C₂×Q₈×C₄₇	—	4	4	no	—
186	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
187	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
188	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
189	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
190	C₂×D₄×C₄₇	—	2	8	no	—
191	C₂×D₄×C₄₇	—	2	2	no	—
192	C₂×D₄×C₄₇	—	2	2	no	—
193	C₂×D₄×C₄₇	—	2	2	no	—
194	C₂×D₄×C₄₇	—	2	2	no	—
195	C₂×D₄×C₄₇	—	2	1	no	—
196	C₂×D₄×C₄₇	—	2	2	no	—
197	C₂×D₄×C₄₇	—	2	1	no	—
198	C₂×D₄×C₄₇	—	2	2	no	—
199	C₂×D₄×C₄₇	—	2	2	no	—
200	C₂×D₄×C₄₇	—	4	4	no	—
201	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
202	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
203	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₄₇	—	2	1	no	—
205	C₂²×C₄×C₄₇	—	2	8	no	—
206	C₂²×C₄×C₄₇	—	2	2	no	—
207	C₂²×C₄×C₄₇	—	2	2	no	—
208	C₂²×C₄×C₄₇	—	2	2	no	—
209	C₂²×C₄×C₄₇	—	2	1	no	—
210	C₂²×C₄×C₄₇	—	2	2	no	—
211	C₂²×C₄×C₄₇	—	2	2	no	—
212	C₂²×C₄×C₄₇	—	2	2	no	—
213	C₂²×C₄×C₄₇	—	2	2	no	—
214	C₂²×C₄×C₄₇	—	2	2	no	—
215	C₂²×C₄×C₄₇	—	2	8	no	—
216	C₂²×C₄×C₄₇	—	4	4	no	—
217	C₂²×C₄×C₄₇	—	4	4	no	—
218	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
219	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
223	C₂²×C₄×C₄₇	#41	1	4	yes	—
224	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
227	Q₁₆×C₄₇	—	2	16	no	—
228	Q₁₆×C₄₇	—	2	8	no	—
229	SD₁₆×C₄₇	—	2	8	no	—
230	SD₁₆×C₄₇	—	2	16	no	—
231	SD₁₆×C₄₇	—	2	8	no	—
232	D₈×C₄₇	—	2	8	no	—
233	M₁₆×C₄₇	—	2	4	no	—
234	M₁₆×C₄₇	—	2	4	no	—
235	M₁₆×C₄₇	—	2	4	no	—
236	M₁₆×C₄₇	—	2	4	no	—
237	C₂×C₈×C₄₇	—	2	4	no	—
238	C₂×C₈×C₄₇	—	2	4	no	—
239	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
240	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
241	C₄⋊C₄×C₄₇	—	2	2	no	—
242	C₄⋊C₄×C₄₇	—	2	8	no	—
243	C₄⋊C₄×C₄₇	—	2	16	no	—
244	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
245	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
246	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
247	C₂²⋊C₄×C₄₇	—	2	2	no	—
248	C₂²⋊C₄×C₄₇	—	2	2	no	—
249	C₂²⋊C₄×C₄₇	—	2	8	no	—
250	C₂²⋊C₄×C₄₇	—	2	16	no	—
251	C₂²⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
252	C₂²⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
253	C₄²×C₄₇	—	2	2	no	—
254	C₄²×C₄₇	—	2	8	no	—
255	C₄²×C₄₇	—	2	2	no	—
256	C₄²×C₄₇	C₂×D₄	1	4	yes	—
257	C₄²×C₄₇	C₂⁴	1	4	yes	—
258	C₂³×C₄₇	—	2	2	no	—
259	C₂³×C₄₇	—	2	4	no	—
260	C₂³×C₄₇	—	2	2	no	—
261	C₂³×C₄₇	—	4	2	no	—
262	C₂³×C₄₇	—	4	4	no	—
263	C₂³×C₄₇	—	4	2	no	—
264	C₂³×C₄₇	—	8	2	no	—
265	C₂³×C₄₇	#121	1	4	yes	—
266	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
267	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
268	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
269	Q₈×C₄₇	—	2	4	no	—
270	Q₈×C₄₇	—	2	2	no	—
271	Q₈×C₄₇	—	2	4	no	—
272	Q₈×C₄₇	—	2	2	no	—
273	Q₈×C₄₇	—	2	4	no	—
274	Q₈×C₄₇	—	2	2	no	—
275	Q₈×C₄₇	—	4	4	no	—
276	Q₈×C₄₇	—	4	4	no	—
277	Q₈×C₄₇	—	4	4	no	—
278	Q₈×C₄₇	—	4	2	no	—
279	Q₈×C₄₇	C₂²×D₄	1	4	yes	—
280	D₄×C₄₇	—	2	8	no	—
281	D₄×C₄₇	—	2	8	no	—
282	D₄×C₄₇	—	2	4	no	—
283	D₄×C₄₇	—	2	2	no	—
284	D₄×C₄₇	—	2	2	no	—
285	D₄×C₄₇	—	2	2	no	—
286	D₄×C₄₇	—	4	4	no	—
287	D₄×C₄₇	—	4	4	no	—
288	D₄×C₄₇	—	4	2	no	—
289	D₄×C₄₇	C₂²×D₄	1	4	yes	—
290	C₂×C₄×C₄₇	—	2	4	no	—
291	C₂×C₄×C₄₇	—	2	2	no	—
292	C₂×C₄×C₄₇	—	2	8	no	—
293	C₂×C₄×C₄₇	—	2	8	no	—
294	C₂×C₄×C₄₇	—	2	4	no	—
295	C₂×C₄×C₄₇	—	2	4	no	—
296	C₂×C₄×C₄₇	—	2	2	no	—
297	C₂×C₄×C₄₇	—	4	4	no	—
298	C₂×C₄×C₄₇	—	4	2	no	—
299	C₂×C₄×C₄₇	—	4	4	no	—
300	C₂×C₄×C₄₇	—	4	4	no	—
301	C₂×C₄×C₄₇	—	4	4	no	—
302	C₂×C₄×C₄₇	—	4	4	no	—
303	C₂×C₄×C₄₇	—	4	4	no	—
304	C₂×C₄×C₄₇	—	8	8	no	—
305	C₂×C₄×C₄₇	—	8	2	no	—
306	C₂×C₄×C₄₇	#121	1	4	yes	—
307	C₂×C₄×C₄₇	#121	1	4	yes	—
308	C₂×C₄×C₄₇	#121	1	4	yes	—
309	C₂×C₄×C₄₇	C₂²×D₄	1	8	yes	—
310	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
312	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
314	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
315	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
316	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
317	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
318	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
319	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
320	C₈×C₄₇	—	2	4	no	—
321	C₈×C₄₇	—	2	4	no	—
322	#60427	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
323	C₂²×C₄₇	—	2	2	no	—
324	C₂²×C₄₇	—	2	2	no	—
325	C₂²×C₄₇	—	2	2	no	—
326	C₂²×C₄₇	—	2	4	no	—
327	C₂²×C₄₇	—	4	4	no	—
328	C₂²×C₄₇	—	4	4	no	—
329	C₂²×C₄₇	—	4	4	no	—
330	C₂²×C₄₇	—	4	2	no	—
331	C₂²×C₄₇	—	8	4	no	—
332	C₂²×C₄₇	—	8	4	no	—
333	C₂²×C₄₇	C₂×#121	1	2	yes	—
334	C₂²×C₄₇	C₂×#121	1	2	yes	—
335	C₂²×C₄₇	C₂×#121	1	2	yes	—
336	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
337	C₄×C₄₇	—	2	8	no	—
338	C₄×C₄₇	—	2	4	no	—
339	C₄×C₄₇	—	4	4	no	—
340	C₄×C₄₇	—	4	2	no	—
341	C₄×C₄₇	—	4	4	no	—
342	C₄×C₄₇	C₂×#121	1	2	yes	—
343	C₄×C₄₇	C₂×#121	1	2	yes	—
344	C₄×C₄₇	C₂×#121	1	2	yes	—
345	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
346	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
347	C₂×#575	C₂×C₄₇	1	1	yes	characteristic
348	C₂²×#137	C₂×C₄₇	1	1	yes	characteristic, complemented
349	C₂×#536	C₂×C₄₇	1	1	yes	characteristic, complemented
350	#3428	C₂×C₄₇	1	1	yes	characteristic, complemented
351	#3046	C₂×C₄₇	1	8	yes	complemented
352	#3044	C₂×C₄₇	1	4	yes	complemented
353	#3042	C₂×C₄₇	1	4	yes	complemented
354	#3040	C₂×C₄₇	1	4	yes	complemented
355	#3039	C₂×C₄₇	1	4	yes	complemented
356	#2905	C₂×C₄₇	1	1	yes	characteristic, complemented
357	#2896	C₂×C₄₇	1	1	yes	characteristic, complemented
358	C₂×#419	C₂×C₄₇	1	1	yes	characteristic, complemented
359	C₂×C₄₇	—	2	2	no	—
360	C₂×C₄₇	—	2	2	no	—
361	C₂×C₄₇	—	2	2	no	—
362	C₂×C₄₇	—	4	4	no	—
363	C₂×C₄₇	—	8	2	no	—
364	C₂×C₄₇	C₂²×#121	1	1	yes	characteristic
365	C₂×C₄₇	#3586	1	2	yes	—
366	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
367	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
368	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
369	#575	—	2	8	no	—
370	C₂×#137	—	2	8	no	—
371	C₂×#137	C₂²×C₄₇	1	2	yes	—
372	C₂×#137	C₂²×C₄₇	1	4	yes	—
373	C₂×#137	C₂²×C₄₇	1	2	yes	—
374	C₂×#137	C₂²×C₄₇	1	4	yes	complemented
375	C₂×AGL(1,ℤ/8)	C₂²×C₄₇	1	2	yes	—
376	C₂×AGL(1,ℤ/8)	C₂²×C₄₇	1	2	yes	—
377	C₂×#135	C₂²×C₄₇	1	4	yes	—
378	C₂²×Q₁₆	C₂²×C₄₇	1	2	yes	complemented
379	C₂²×SD₁₆	C₂²×C₄₇	1	2	yes	complemented
380	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
381	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
382	#536	—	2	2	no	—
383	#536	—	2	2	no	—
384	#536	C₂²×C₄₇	1	4	yes	—
385	#536	C₂²×C₄₇	1	4	yes	complemented
386	C₂×C₄⋊Q₈	C₂²×C₄₇	1	2	yes	complemented
387	C₂×#124	C₂²×C₄₇	1	2	yes	complemented
388	C₂×#123	—	2	2	no	—
389	C₂×C₂²⋊Q₈	—	2	2	no	—
390	#520	—	2	2	no	—
391	#520	C₂²×C₄₇	1	4	yes	complemented
392	#519	C₂²×C₄₇	1	2	yes	complemented
393	#518	—	2	2	no	—
394	#518	C₂²×C₄₇	1	2	yes	complemented
395	C₄×#41	—	2	2	no	—
396	C₄×#41	C₂²×C₄₇	1	4	yes	—
397	C₂×#117	—	2	2	no	—
398	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
399	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
400	#464	C₂²×C₄₇	1	16	yes	complemented
401	#463	C₂²×C₄₇	1	16	yes	complemented
402	#462	C₂²×C₄₇	1	16	yes	complemented
403	#461	C₂²×C₄₇	1	16	yes	complemented
404	#424	C₂²×C₄₇	1	4	yes	complemented
405	#424	C₂²×C₄₇	1	4	yes	complemented
406	#423	C₂²×C₄₇	1	4	yes	complemented
407	#419	C₂²×C₄₇	1	4	yes	complemented
408	#419	C₂²×C₄₇	1	4	yes	complemented
409	#419	C₂²×C₄₇	1	2	yes	complemented
410	#418	C₂²×C₄₇	1	2	yes	complemented
411	#417	C₂²×C₄₇	1	4	yes	complemented
412	#416	C₂²×C₄₇	1	4	yes	—
413	C₂×#103	C₂²×C₄₇	1	4	yes	complemented
414	C₄₇	#60427	1	1	yes	characteristic, direct product factor, Sylow
415	C₂×#41	—	2	1	no	—
416	C₂×#41	—	2	1	no	—
417	C₂×#41	—	2	1	no	—
418	C₂×#41	—	2	1	no	—
419	C₂×#41	—	2	4	no	—
420	C₂×#41	—	2	4	no	—
421	C₂×#41	—	2	4	no	—
422	C₂×#41	D₄×C₄₇	1	8	yes	—
423	C₂×#41	C₂³×C₄₇	1	2	yes	—
424	C₂×#41	C₂³×C₄₇	1	2	yes	—
425	C₂×#41	C₂³×C₄₇	1	2	yes	—
426	C₂×#41	C₂³×C₄₇	1	2	yes	—
427	C₂²×Q₈	—	2	1	no	—
428	C₂²×Q₈	—	2	1	no	—
429	C₂²×Q₈	—	2	1	no	—
430	C₂²×Q₈	—	2	4	no	—
431	C₂²×Q₈	—	2	4	no	—
432	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
433	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
434	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
435	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
436	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
437	C₂²×D₄	—	2	1	no	—
438	C₂²×D₄	—	2	1	no	—
439	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
440	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
441	C₂³×C₄	—	2	1	no	—
442	C₂³×C₄	—	2	1	no	—
443	C₂³×C₄	—	2	1	no	—
444	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
445	#137	—	2	16	no	—
446	#137	—	2	16	no	—
447	#137	—	2	8	no	—
448	#137	—	2	8	no	—
449	AGL(1,ℤ/8)	—	2	8	no	—
450	AGL(1,ℤ/8)	—	2	8	no	—
451	#135	—	2	16	no	—
452	C₂×Q₁₆	—	2	8	no	—
453	C₂×Q₁₆	C₂³×C₄₇	1	8	yes	—
454	C₂×Q₁₆	C₂³×C₄₇	1	4	yes	—
455	C₂×SD₁₆	—	2	8	no	—
456	C₂×SD₁₆	C₂³×C₄₇	1	8	yes	—
457	C₂×SD₁₆	C₂³×C₄₇	1	4	yes	—
458	C₂×SD₁₆	C₂³×C₄₇	1	4	yes	—
459	C₂×D₈	C₂³×C₄₇	1	4	yes	—
460	C₂×M₁₆	—	2	4	no	—
461	C₂×M₁₆	—	2	4	no	—
462	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
463	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
464	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
465	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
466	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
467	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
468	C₄⋊Q₈	—	2	4	no	—
469	C₄⋊Q₈	C₂³×C₄₇	1	8	yes	—
470	#124	—	2	4	no	—
471	#124	C₂³×C₄₇	1	8	yes	—
472	#123	—	2	8	no	—
473	#123	—	2	8	no	—
474	C₂²⋊Q₈	—	2	8	no	—
475	C₂²⋊Q₈	—	2	8	no	—
476	C₄×Q₈	—	2	4	no	—
477	C₄×Q₈	C₂³×C₄₇	1	8	yes	—
478	C₄×D₄	—	2	8	no	—
479	C₄×D₄	—	2	4	no	—
480	C₄×D₄	—	2	8	no	—
481	C₄×D₄	C₂³×C₄₇	1	8	yes	—
482	#117	—	2	1	no	—
483	#117	—	2	1	no	—
484	#117	—	2	4	no	—
485	#117	—	2	4	no	—
486	#117	—	2	4	no	—
487	#117	D₄×C₄₇	1	2	yes	—
488	#117	D₄×C₄₇	1	2	yes	—
489	#117	C₂³×C₄₇	1	2	yes	—
490	#117	C₂³×C₄₇	1	2	yes	—
491	#117	C₂³×C₄₇	1	2	yes	—
492	#117	C₂³×C₄₇	1	2	yes	—
493	C₂×C₄⋊C₄	—	2	4	no	—
494	C₂×C₄⋊C₄	—	2	4	no	—
495	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
497	C₂×C₂²⋊C₄	—	2	1	no	—
498	C₂×C₂²⋊C₄	—	2	4	no	—
499	C₂×C₂²⋊C₄	—	2	4	no	—
500	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
501	C₂×C₄²	—	2	1	no	—
502	C₂×C₄²	—	2	4	no	—
503	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
504	C₄⋊C₈	C₂³×C₄₇	1	16	yes	—
505	#103	C₂³×C₄₇	1	16	yes	—
506	#103	C₂³×C₄₇	1	8	yes	—
507	#102	C₂³×C₄₇	1	8	yes	—
508	C₂⁴	—	2	1	no	—
509	C₂⁴	—	2	1	no	—
510	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
511	#41	—	2	8	no	—
512	#41	—	2	8	no	—
513	#41	—	2	4	no	—
514	#41	—	2	4	no	—
515	#41	—	2	4	no	—
516	#41	—	2	4	no	—
517	#41	—	2	4	no	—
518	#41	—	2	4	no	—
519	#41	—	4	4	no	—
520	#41	—	4	4	no	—
521	#41	C₂×D₄×C₄₇	1	8	yes	—
522	#41	C₂×D₄×C₄₇	1	8	yes	—
523	C₂×Q₈	—	2	1	no	—
524	C₂×Q₈	—	2	2	no	—
525	C₂×Q₈	—	2	2	no	—
526	C₂×Q₈	—	2	2	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	—	2	2	no	—
529	C₂×Q₈	—	2	4	no	—
530	C₂×Q₈	—	2	4	no	—
531	C₂×Q₈	—	2	4	no	—
532	C₂×Q₈	—	2	2	no	—
533	C₂×Q₈	—	2	4	no	—
534	C₂×Q₈	—	2	4	no	—
535	C₂×Q₈	—	2	4	no	—
536	C₂×Q₈	—	2	2	no	—
537	C₂×Q₈	—	4	4	no	—
538	C₂×Q₈	—	4	4	no	—
539	C₂×Q₈	—	4	4	no	—
540	C₂×Q₈	C₂×D₄×C₄₇	1	4	yes	—
541	C₂×Q₈	C₂⁴×C₄₇	1	4	yes	—
542	C₂×Q₈	C₂⁴×C₄₇	1	2	yes	—
543	C₂×Q₈	C₂⁴×C₄₇	1	2	yes	—
544	C₂×D₄	—	2	8	no	—
545	C₂×D₄	—	2	2	no	—
546	C₂×D₄	—	2	2	no	—
547	C₂×D₄	—	2	2	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	4	4	no	—
555	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
556	C₂×D₄	C₂⁴×C₄₇	1	2	yes	—
557	C₂×D₄	C₂⁴×C₄₇	1	2	yes	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	8	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	8	no	—
570	C₂²×C₄	—	4	4	no	—
571	C₂²×C₄	—	4	4	no	—
572	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
573	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
574	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
575	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
576	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
577	C₂²×C₄	#41×C₄₇	1	4	yes	—
578	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
579	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
580	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
581	Q₁₆	—	2	16	no	—
582	Q₁₆	—	2	8	no	—
583	SD₁₆	—	2	8	no	—
584	SD₁₆	—	2	16	no	—
585	SD₁₆	—	2	8	no	—
586	D₈	—	2	8	no	—
587	M₁₆	—	2	4	no	—
588	M₁₆	—	2	4	no	—
589	M₁₆	—	2	4	no	—
590	M₁₆	—	2	4	no	—
591	C₂×C₈	—	2	4	no	—
592	C₂×C₈	—	2	4	no	—
593	C₂×C₈	C₂⁴×C₄₇	1	4	yes	—
594	C₂×C₈	C₂⁴×C₄₇	1	4	yes	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	8	no	—
597	C₄⋊C₄	—	2	16	no	—
598	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
599	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
600	C₄⋊C₄	C₂⁴×C₄₇	1	4	yes	—
601	C₂²⋊C₄	—	2	2	no	—
602	C₂²⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	2	8	no	—
604	C₂²⋊C₄	—	2	16	no	—
605	C₂²⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
606	C₂²⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
607	C₄²	—	2	2	no	—
608	C₄²	—	2	8	no	—
609	C₄²	—	2	2	no	—
610	C₄²	C₂×D₄×C₄₇	1	4	yes	—
611	C₄²	C₂⁴×C₄₇	1	4	yes	—
612	C₂³	—	2	2	no	—
613	C₂³	—	2	4	no	—
614	C₂³	—	2	2	no	—
615	C₂³	—	4	2	no	—
616	C₂³	—	4	4	no	—
617	C₂³	—	4	2	no	—
618	C₂³	—	8	2	no	—
619	C₂³	#121×C₄₇	1	4	yes	—
620	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
621	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
622	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
623	Q₈	—	2	4	no	—
624	Q₈	—	2	2	no	—
625	Q₈	—	2	4	no	—
626	Q₈	—	2	2	no	—
627	Q₈	—	2	4	no	—
628	Q₈	—	2	2	no	—
629	Q₈	—	4	4	no	—
630	Q₈	—	4	4	no	—
631	Q₈	—	4	4	no	—
632	Q₈	—	4	2	no	—
633	Q₈	C₂²×D₄×C₄₇	1	4	yes	—
634	D₄	—	2	8	no	—
635	D₄	—	2	8	no	—
636	D₄	—	2	4	no	—
637	D₄	—	2	2	no	—
638	D₄	—	2	2	no	—
639	D₄	—	2	2	no	—
640	D₄	—	4	4	no	—
641	D₄	—	4	4	no	—
642	D₄	—	4	2	no	—
643	D₄	C₂²×D₄×C₄₇	1	4	yes	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	8	no	—
647	C₂×C₄	—	2	8	no	—
648	C₂×C₄	—	2	4	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	4	4	no	—
652	C₂×C₄	—	4	2	no	—
653	C₂×C₄	—	4	4	no	—
654	C₂×C₄	—	4	4	no	—
655	C₂×C₄	—	4	4	no	—
656	C₂×C₄	—	4	4	no	—
657	C₂×C₄	—	4	4	no	—
658	C₂×C₄	—	8	8	no	—
659	C₂×C₄	—	8	2	no	—
660	C₂×C₄	#121×C₄₇	1	4	yes	—
661	C₂×C₄	#121×C₄₇	1	4	yes	—
662	C₂×C₄	#121×C₄₇	1	4	yes	—
663	C₂×C₄	C₂²×D₄×C₄₇	1	8	yes	—
664	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
665	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
666	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
667	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
668	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
669	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
670	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
671	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
672	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
673	C₂×C₄	C₂⁵×C₄₇	1	1	yes	characteristic
674	C₈	—	2	4	no	—
675	C₈	—	2	4	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	4	no	—
680	C₂²	—	4	4	no	—
681	C₂²	—	4	4	no	—
682	C₂²	—	4	4	no	—
683	C₂²	—	4	2	no	—
684	C₂²	—	8	4	no	—
685	C₂²	—	8	4	no	—
686	C₂²	C₂×#121×C₄₇	1	2	yes	—
687	C₂²	C₂×#121×C₄₇	1	2	yes	—
688	C₂²	C₂×#121×C₄₇	1	2	yes	—
689	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
690	C₄	—	2	8	no	—
691	C₄	—	2	4	no	—
692	C₄	—	4	4	no	—
693	C₄	—	4	2	no	—
694	C₄	—	4	4	no	—
695	C₄	C₂×#121×C₄₇	1	2	yes	—
696	C₄	C₂×#121×C₄₇	1	2	yes	—
697	C₄	C₂×#121×C₄₇	1	2	yes	—
698	C₄	C₂³×D₄×C₄₇	1	1	yes	characteristic
699	C₄	C₂²×#41×C₄₇	1	1	yes	characteristic
700	C₂	—	2	2	no	—
701	C₂	—	2	2	no	—
702	C₂	—	2	2	no	—
703	C₂	—	4	4	no	—
704	C₂	—	8	2	no	—
705	C₂	C₂²×#121×C₄₇	1	1	yes	characteristic
706	C₂	C₄₇×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₇
prime radical	C₂×C₄₇×#575	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂×#117×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#137×C₄₇	C₂	semidirect
3. C₂×C₄₇×#536	C₂	semidirect
4. C₄₇×#3428	C₂	semidirect
5. C₄₇×#3046	C₂	semidirect
6. C₄₇×#3044	C₂	semidirect
7. C₄₇×#3042	C₂	semidirect
8. C₄₇×#3040	C₂	semidirect
9. C₄₇×#3039	C₂	semidirect
10. C₄₇×#2905	C₂	semidirect
11. C₄₇×#2896	C₂	semidirect
12. C₂×C₄₇×#419	C₂	semidirect
21. C₂×#137×C₄₇	C₂²	semidirect
25. C₂²×Q₁₆×C₄₇	C₂²	semidirect
26. C₂²×SD₁₆×C₄₇	C₂²	semidirect
32. C₄₇×#536	C₂²	semidirect
33. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
34. C₂×#124×C₄₇	C₂²	semidirect
38. C₄₇×#520	C₂²	semidirect
39. C₄₇×#519	C₂²	semidirect
41. C₄₇×#518	C₂²	semidirect
47. C₄₇×#464	C₂²	semidirect
48. C₄₇×#463	C₂²	semidirect
49. C₄₇×#462	C₂²	semidirect
50. C₄₇×#461	C₂²	semidirect
51. C₄₇×#424	C₂²	semidirect
52. C₄₇×#424	C₂²	semidirect
53. C₄₇×#423	C₂²	semidirect
54. C₄₇×#419	C₂²	semidirect
55. C₄₇×#419	C₂²	semidirect
56. C₄₇×#419	C₂²	semidirect
57. C₄₇×#418	C₂²	semidirect
58. C₄₇×#417	C₂²	semidirect
60. C₂×#103×C₄₇	C₂²	semidirect
322. #60427	C₄₇	direct (N × H)
348. C₂²×#137	C₂×C₄₇	semidirect
349. C₂×#536	C₂×C₄₇	semidirect
350. #3428	C₂×C₄₇	semidirect
351. #3046	C₂×C₄₇	semidirect
352. #3044	C₂×C₄₇	semidirect
353. #3042	C₂×C₄₇	semidirect
354. #3040	C₂×C₄₇	semidirect
355. #3039	C₂×C₄₇	semidirect
356. #2905	C₂×C₄₇	semidirect
357. #2896	C₂×C₄₇	semidirect
358. C₂×#419	C₂×C₄₇	semidirect
374. C₂×#137	C₂²×C₄₇	semidirect
378. C₂²×Q₁₆	C₂²×C₄₇	semidirect
379. C₂²×SD₁₆	C₂²×C₄₇	semidirect
385. #536	C₂²×C₄₇	semidirect
386. C₂×C₄⋊Q₈	C₂²×C₄₇	semidirect
387. C₂×#124	C₂²×C₄₇	semidirect
391. #520	C₂²×C₄₇	semidirect
392. #519	C₂²×C₄₇	semidirect
394. #518	C₂²×C₄₇	semidirect
400. #464	C₂²×C₄₇	semidirect
401. #463	C₂²×C₄₇	semidirect
402. #462	C₂²×C₄₇	semidirect
403. #461	C₂²×C₄₇	semidirect
404. #424	C₂²×C₄₇	semidirect
405. #424	C₂²×C₄₇	semidirect
406. #423	C₂²×C₄₇	semidirect
407. #419	C₂²×C₄₇	semidirect
408. #419	C₂²×C₄₇	semidirect
409. #419	C₂²×C₄₇	semidirect
410. #418	C₂²×C₄₇	semidirect
411. #417	C₂²×C₄₇	semidirect
413. C₂×#103	C₂²×C₄₇	semidirect
414. C₄₇	#60427	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×C₄₇×#575	2
C₂²×#137×C₄₇	2
C₂×C₄₇×#536	2
C₄₇×#3428	2
C₄₇×#3046	2
C₄₇×#3044	2
C₄₇×#3042	2
C₄₇×#3040	2
C₄₇×#3039	2
C₄₇×#2905	2
C₄₇×#2896	2
C₂×C₄₇×#419	2
#60427	47

Subgroups — C47×#60427 #26100125

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#60427 #26100125