Subgroups — C₃₁×#33481 #21490240

Order 7936.

508 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2966	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2183	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2169	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2168	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2168	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2164	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2163	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2108	C₂	1	2	yes	maximal, complemented
9	C₄×C₃₁×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#529	C₄	1	1	yes	characteristic
11	C₂×C₃₁×M₃₂	C₂²	1	2	yes	—
12	C₂×C₃₁×M₃₂	C₂²	1	2	yes	—
13	C₂²×C₁₆×C₃₁	C₂²	1	2	yes	—
14	C₃₁×#446	C₄	1	1	yes	characteristic
15	C₈×Q₈×C₃₁	C₂²	1	1	yes	characteristic
16	C₃₁×#436	C₄	1	1	yes	characteristic
17	C₃₁×#435	C₄	1	2	yes	—
18	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
19	C₈×D₄×C₃₁	C₂²	1	2	yes	—
20	C₃₁×#433	C₄	1	2	yes	—
21	C₃₁×#432	C₄	1	1	yes	characteristic
22	C₃₁×#405	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
24	C₃₁×C₄⋊C₁₆	C₂²	1	2	yes	—
25	C₃₁×C₄⋊C₁₆	C₂²	1	2	yes	—
26	C₃₁×C₄⋊C₁₆	C₂²	1	2	yes	—
27	C₃₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
28	C₃₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
29	C₃₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
30	C₃₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
31	C₃₁×#346	C₂²	1	2	yes	—
32	C₃₁×#346	C₂²	1	2	yes	—
33	C₃₁×#346	C₂²	1	2	yes	—
34	C₄×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
35	C₄×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
36	C₄×C₁₆×C₃₁	C₂²	1	2	yes	—
37	C₂×M₁₆×C₃₁	C₂×C₄	1	2	yes	—
38	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
41	C₃₁×#126	C₈	1	2	yes	—
42	C₃₁×#125	C₈	1	1	yes	characteristic
43	C₃₁×#124	C₈	1	1	yes	characteristic
44	C₃₁×#123	C₈	1	2	yes	—
45	C₃₁×C₂²⋊Q₈	C₈	1	1	yes	characteristic
46	C₃₁×#121	C₈	1	1	yes	characteristic
47	C₄×Q₈×C₃₁	C₂×C₄	1	1	yes	characteristic
48	C₄×D₄×C₃₁	C₂×C₄	1	2	yes	—
49	C₄×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
50	C₃₁×#117	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
52	C₃₁×M₃₂	—	2	4	no	—
53	C₃₁×M₃₂	—	2	4	no	—
54	C₂×C₁₆×C₃₁	—	2	4	no	—
55	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
56	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
57	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
58	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
59	C₃₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
60	C₃₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
61	C₃₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
62	C₃₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
63	C₃₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
64	C₃₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
65	C₃₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
66	C₃₁×#97	C₂×C₄	1	2	yes	—
67	C₃₁×#97	C₂×C₄	1	2	yes	—
68	C₄×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
69	C₄×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
70	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
71	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
72	C₄×C₈×C₃₁	C₂³	1	2	yes	—
73	C₂×Q₈×C₃₁	C₂×C₈	1	1	yes	characteristic
74	C₂×D₄×C₃₁	C₂×C₈	1	2	yes	—
75	C₂×D₄×C₃₁	C₂×C₈	1	1	yes	characteristic
76	C₂²×C₄×C₃₁	C₂×C₈	1	1	yes	characteristic
77	C₂²×C₄×C₃₁	C₂×C₈	1	1	yes	characteristic
78	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
80	M₁₆×C₃₁	—	2	4	no	—
81	C₂×C₈×C₃₁	—	2	2	no	—
82	C₂×C₈×C₃₁	—	2	2	no	—
83	C₂×C₈×C₃₁	—	2	2	no	—
84	C₂×C₈×C₃₁	—	2	2	no	—
85	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
86	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
88	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
89	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
91	C₄⋊C₄×C₃₁	C₂×C₈	1	2	yes	—
92	C₄⋊C₄×C₃₁	C₂×C₈	1	2	yes	—
93	C₄⋊C₄×C₃₁	C₂×C₈	1	1	yes	characteristic
94	C₄⋊C₄×C₃₁	C₂×C₈	1	2	yes	—
95	C₄⋊C₄×C₃₁	C₂×C₈	1	1	yes	characteristic
96	C₄⋊C₄×C₃₁	C₂×C₈	1	2	yes	—
97	C₂²⋊C₄×C₃₁	C₂×C₈	1	2	yes	—
98	C₂²⋊C₄×C₃₁	C₂×C₈	1	2	yes	—
99	C₂²⋊C₄×C₃₁	C₂×C₈	1	2	yes	—
100	C₂²⋊C₄×C₃₁	C₂×C₈	1	2	yes	—
101	C₂²⋊C₄×C₃₁	C₂×C₈	1	2	yes	—
102	C₄²×C₃₁	C₂×C₈	1	1	yes	characteristic
103	C₄²×C₃₁	C₂×C₈	1	1	yes	characteristic
104	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
106	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
107	C₁₆×C₃₁	—	2	2	no	—
108	C₁₆×C₃₁	—	2	2	no	—
109	C₁₆×C₃₁	—	2	2	no	—
110	C₁₆×C₃₁	#41	1	4	yes	—
111	#33481	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂³×C₃₁	C₂²×C₈	1	2	yes	—
113	C₂³×C₃₁	C₂²×C₈	1	1	yes	characteristic
114	Q₈×C₃₁	—	4	1	no	—
115	D₄×C₃₁	—	4	1	no	—
116	D₄×C₃₁	—	4	2	no	—
117	C₂×C₄×C₃₁	—	2	2	no	—
118	C₂×C₄×C₃₁	—	2	1	no	—
119	C₂×C₄×C₃₁	—	2	1	no	—
120	C₂×C₄×C₃₁	—	2	2	no	—
121	C₂×C₄×C₃₁	—	4	1	no	—
122	C₂×C₄×C₃₁	—	4	1	no	—
123	C₂×C₄×C₃₁	C₂²×C₈	1	1	yes	characteristic
124	C₂×C₄×C₃₁	C₂²×C₈	1	1	yes	characteristic
125	C₂×C₄×C₃₁	C₂²×C₈	1	1	yes	characteristic
126	C₂×C₄×C₃₁	C₂²×C₈	1	1	yes	characteristic
127	C₂×C₄×C₃₁	C₂²×C₈	1	1	yes	characteristic
128	C₂×C₄×C₃₁	C₂²×C₈	1	2	yes	—
129	C₂×C₄×C₃₁	C₂²×C₈	1	2	yes	—
130	C₂×C₄×C₃₁	C₂²×C₈	1	2	yes	—
131	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
132	C₈×C₃₁	—	2	2	no	—
133	C₈×C₃₁	—	2	1	no	—
134	C₈×C₃₁	—	2	1	no	—
135	C₈×C₃₁	—	2	2	no	—
136	C₈×C₃₁	#131	1	2	yes	—
137	C₈×C₃₁	C₂×#41	1	2	yes	—
138	#2966	C₂×C₃₁	1	1	yes	characteristic
139	#2183	C₂×C₃₁	1	2	yes	complemented
140	#2169	C₂×C₃₁	1	2	yes	complemented
141	#2168	C₂×C₃₁	1	2	yes	complemented
142	#2168	C₂×C₃₁	1	2	yes	complemented
143	#2164	C₂×C₃₁	1	2	yes	complemented
144	#2163	C₂×C₃₁	1	1	yes	characteristic, complemented
145	#2108	C₂×C₃₁	1	2	yes	complemented
146	C₄×M₃₂	C₂×C₃₁	1	1	yes	characteristic, complemented
147	C₂²×C₃₁	—	2	1	no	—
148	C₂²×C₃₁	—	2	1	no	—
149	C₂²×C₃₁	—	2	2	no	—
150	C₂²×C₃₁	—	2	2	no	—
151	C₂²×C₃₁	—	2	1	no	—
152	C₂²×C₃₁	—	2	2	no	—
153	C₂²×C₃₁	C₂³×C₈	1	1	yes	characteristic
154	C₄×C₃₁	—	2	1	no	—
155	C₄×C₃₁	—	2	1	no	—
156	C₄×C₃₁	—	2	1	no	—
157	C₄×C₃₁	—	2	1	no	—
158	C₄×C₃₁	—	2	2	no	—
159	C₄×C₃₁	—	2	2	no	—
160	C₄×C₃₁	—	2	1	no	—
161	C₄×C₃₁	—	2	2	no	—
162	C₄×C₃₁	C₄×#41	1	1	yes	characteristic
163	C₄×C₃₁	C₂×#131	1	1	yes	characteristic
164	#529	C₄×C₃₁	1	1	yes	characteristic
165	C₂×M₃₂	C₂²×C₃₁	1	2	yes	—
166	C₂×M₃₂	C₂²×C₃₁	1	2	yes	—
167	C₂²×C₁₆	C₂²×C₃₁	1	2	yes	—
168	#446	C₄×C₃₁	1	1	yes	characteristic
169	C₈×Q₈	C₂²×C₃₁	1	1	yes	characteristic
170	#436	C₄×C₃₁	1	1	yes	characteristic
171	#435	C₄×C₃₁	1	2	yes	—
172	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
173	C₈×D₄	C₂²×C₃₁	1	2	yes	—
174	#433	C₄×C₃₁	1	2	yes	—
175	#432	C₄×C₃₁	1	1	yes	characteristic
176	#405	C₂²×C₃₁	1	2	yes	—
177	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
178	C₄⋊C₁₆	C₂²×C₃₁	1	2	yes	—
179	C₄⋊C₁₆	C₂²×C₃₁	1	2	yes	—
180	C₄⋊C₁₆	C₂²×C₃₁	1	2	yes	—
181	C₂²⋊C₁₆	C₂²×C₃₁	1	1	yes	characteristic
182	C₂²⋊C₁₆	C₂²×C₃₁	1	1	yes	characteristic
183	C₂²⋊C₁₆	C₂²×C₃₁	1	2	yes	—
184	C₂²⋊C₁₆	C₂²×C₃₁	1	2	yes	—
185	#346	C₂²×C₃₁	1	2	yes	—
186	#346	C₂²×C₃₁	1	2	yes	—
187	#346	C₂²×C₃₁	1	2	yes	—
188	C₄×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
189	C₄×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
190	C₄×C₁₆	C₂²×C₃₁	1	2	yes	—
191	C₂×C₃₁	—	4	1	no	—
192	C₂×C₃₁	—	4	2	no	—
193	C₂×C₃₁	C₈×#41	1	1	yes	characteristic
194	C₂×C₃₁	#3407	1	1	yes	characteristic
195	C₂×C₃₁	#3407	1	1	yes	characteristic
196	C₂×M₁₆	C₂×C₄×C₃₁	1	2	yes	—
197	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
198	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
199	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
200	#126	C₈×C₃₁	1	2	yes	—
201	#125	C₈×C₃₁	1	1	yes	characteristic
202	#124	C₈×C₃₁	1	1	yes	characteristic
203	#123	C₈×C₃₁	1	2	yes	—
204	C₂²⋊Q₈	C₈×C₃₁	1	1	yes	characteristic
205	#121	C₈×C₃₁	1	1	yes	characteristic
206	C₄×Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic
207	C₄×D₄	C₂×C₄×C₃₁	1	2	yes	—
208	C₄×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
209	#117	C₂×C₄×C₃₁	1	2	yes	—
210	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
211	M₃₂	—	2	4	no	—
212	M₃₂	—	2	4	no	—
213	C₂×C₁₆	—	2	4	no	—
214	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
215	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
216	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
217	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
218	C₄⋊C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
219	C₄⋊C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
220	C₄⋊C₈	C₂×C₄×C₃₁	1	2	yes	—
221	C₄⋊C₈	C₂×C₄×C₃₁	1	2	yes	—
222	C₂²⋊C₈	C₂×C₄×C₃₁	1	2	yes	—
223	C₂²⋊C₈	C₂×C₄×C₃₁	1	2	yes	—
224	C₂²⋊C₈	C₂×C₄×C₃₁	1	2	yes	—
225	#97	C₂×C₄×C₃₁	1	2	yes	—
226	#97	C₂×C₄×C₃₁	1	2	yes	—
227	C₄×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
228	C₄×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
229	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
230	C₄×C₈	C₂³×C₃₁	1	2	yes	—
231	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
232	C₃₁	#33481	1	1	yes	characteristic, direct product factor, Sylow
233	C₂×Q₈	C₂×C₈×C₃₁	1	1	yes	characteristic
234	C₂×D₄	C₂×C₈×C₃₁	1	2	yes	—
235	C₂×D₄	C₂×C₈×C₃₁	1	1	yes	characteristic
236	C₂²×C₄	C₂×C₈×C₃₁	1	1	yes	characteristic
237	C₂²×C₄	C₂×C₈×C₃₁	1	1	yes	characteristic
238	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
239	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
240	M₁₆	—	2	4	no	—
241	C₂×C₈	—	2	2	no	—
242	C₂×C₈	—	2	2	no	—
243	C₂×C₈	—	2	2	no	—
244	C₂×C₈	—	2	2	no	—
245	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
246	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
247	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
248	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
249	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
250	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
251	C₄⋊C₄	C₂×C₈×C₃₁	1	2	yes	—
252	C₄⋊C₄	C₂×C₈×C₃₁	1	2	yes	—
253	C₄⋊C₄	C₂×C₈×C₃₁	1	1	yes	characteristic
254	C₄⋊C₄	C₂×C₈×C₃₁	1	2	yes	—
255	C₄⋊C₄	C₂×C₈×C₃₁	1	1	yes	characteristic
256	C₄⋊C₄	C₂×C₈×C₃₁	1	2	yes	—
257	C₂²⋊C₄	C₂×C₈×C₃₁	1	2	yes	—
258	C₂²⋊C₄	C₂×C₈×C₃₁	1	2	yes	—
259	C₂²⋊C₄	C₂×C₈×C₃₁	1	2	yes	—
260	C₂²⋊C₄	C₂×C₈×C₃₁	1	2	yes	—
261	C₂²⋊C₄	C₂×C₈×C₃₁	1	2	yes	—
262	C₄²	C₂×C₈×C₃₁	1	1	yes	characteristic
263	C₄²	C₂×C₈×C₃₁	1	1	yes	characteristic
264	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
265	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
266	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
267	C₁₆	—	2	2	no	—
268	C₁₆	—	2	2	no	—
269	C₁₆	—	2	2	no	—
270	C₁₆	#41×C₃₁	1	4	yes	—
271	C₂³	C₂²×C₈×C₃₁	1	2	yes	—
272	C₂³	C₂²×C₈×C₃₁	1	1	yes	characteristic
273	Q₈	—	4	1	no	—
274	D₄	—	4	1	no	—
275	D₄	—	4	2	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	1	no	—
278	C₂×C₄	—	2	1	no	—
279	C₂×C₄	—	2	2	no	—
280	C₂×C₄	—	4	1	no	—
281	C₂×C₄	—	4	1	no	—
282	C₂×C₄	C₂²×C₈×C₃₁	1	1	yes	characteristic
283	C₂×C₄	C₂²×C₈×C₃₁	1	1	yes	characteristic
284	C₂×C₄	C₂²×C₈×C₃₁	1	1	yes	characteristic
285	C₂×C₄	C₂²×C₈×C₃₁	1	1	yes	characteristic
286	C₂×C₄	C₂²×C₈×C₃₁	1	1	yes	characteristic
287	C₂×C₄	C₂²×C₈×C₃₁	1	2	yes	—
288	C₂×C₄	C₂²×C₈×C₃₁	1	2	yes	—
289	C₂×C₄	C₂²×C₈×C₃₁	1	2	yes	—
290	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
291	C₈	—	2	2	no	—
292	C₈	—	2	1	no	—
293	C₈	—	2	1	no	—
294	C₈	—	2	2	no	—
295	C₈	C₃₁×#131	1	2	yes	—
296	C₈	C₂×#41×C₃₁	1	2	yes	—
297	C₂²	—	2	1	no	—
298	C₂²	—	2	1	no	—
299	C₂²	—	2	2	no	—
300	C₂²	—	2	2	no	—
301	C₂²	—	2	1	no	—
302	C₂²	—	2	2	no	—
303	C₂²	C₂³×C₈×C₃₁	1	1	yes	characteristic
304	C₄	—	2	1	no	—
305	C₄	—	2	1	no	—
306	C₄	—	2	1	no	—
307	C₄	—	2	1	no	—
308	C₄	—	2	2	no	—
309	C₄	—	2	2	no	—
310	C₄	—	2	1	no	—
311	C₄	—	2	2	no	—
312	C₄	C₄×#41×C₃₁	1	1	yes	characteristic
313	C₄	C₂×C₃₁×#131	1	1	yes	characteristic
314	C₂	—	4	1	no	—
315	C₂	—	4	2	no	—
316	C₂	C₈×#41×C₃₁	1	1	yes	characteristic
317	C₂	C₃₁×#3407	1	1	yes	characteristic
318	C₂	C₃₁×#3407	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₃₁	C₂⁴
commutator	C₂²	C₂³×C₈×C₃₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂³×C₈
prime radical	C₃₁×#121	C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2183	C₂	semidirect
3. C₃₁×#2169	C₂	semidirect
4. C₃₁×#2168	C₂	semidirect
5. C₃₁×#2168	C₂	semidirect
6. C₃₁×#2164	C₂	semidirect
7. C₃₁×#2163	C₂	semidirect
8. C₃₁×#2108	C₂	semidirect
9. C₄×C₃₁×M₃₂	C₂	semidirect
111. #33481	C₃₁	direct (N × H)
139. #2183	C₂×C₃₁	semidirect
140. #2169	C₂×C₃₁	semidirect
141. #2168	C₂×C₃₁	semidirect
142. #2168	C₂×C₃₁	semidirect
143. #2164	C₂×C₃₁	semidirect
144. #2163	C₂×C₃₁	semidirect
145. #2108	C₂×C₃₁	semidirect
146. C₄×M₃₂	C₂×C₃₁	semidirect
232. C₃₁	#33481	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#2966	2
C₃₁×#2183	2
C₃₁×#2169	2
C₃₁×#2168	2
C₃₁×#2164	2
C₃₁×#2163	2
C₃₁×#2108	2
C₄×C₃₁×M₃₂	2
#33481	31

Subgroups — C31×#33481 #21490240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33481 #21490240