Subgroups — C₃₁×#10848 #21467607

Order 7936.

802 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#423	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2285	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃₁×#344	C₂	1	4	yes	maximal
5	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
6	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
7	C₂×C₃₁×#117	C₂²	1	2	yes	—
8	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
9	C₃₁×#423	—	2	1	no	—
10	C₃₁×#423	—	2	1	no	—
11	C₃₁×#423	C₄	1	4	yes	complemented
12	C₂×C₃₁×C₄⋊C₈	—	2	2	no	—
13	C₄×M₁₆×C₃₁	—	2	2	no	—
14	C₄×M₁₆×C₃₁	—	2	2	no	—
15	C₂×C₃₁×#97	C₄	1	2	yes	complemented
16	C₂×C₄×C₈×C₃₁	C₄	1	2	yes	complemented
17	C₃₁×#384	—	2	1	no	—
18	C₃₁×#382	—	2	1	no	—
19	C₃₁×#380	C₄	1	4	yes	—
20	C₄×C₄⋊C₄×C₃₁	—	2	2	no	—
21	C₃₁×#344	—	2	8	no	—
22	C₂³×C₄×C₃₁	C₂×C₄	1	2	yes	—
23	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
24	C₂×M₁₆×C₃₁	—	2	2	no	—
25	C₂×M₁₆×C₃₁	—	2	2	no	—
26	C₂×M₁₆×C₃₁	—	2	2	no	—
27	C₂×M₁₆×C₃₁	—	2	2	no	—
28	C₂×M₁₆×C₃₁	—	2	2	no	—
29	C₂×M₁₆×C₃₁	—	2	4	no	—
30	C₂×M₁₆×C₃₁	—	2	4	no	—
31	C₂×M₁₆×C₃₁	C₂×C₄	1	4	yes	—
32	C₂×M₁₆×C₃₁	D₄	1	4	yes	—
33	C₂×M₁₆×C₃₁	Q₈	1	4	yes	—
34	C₂²×C₈×C₃₁	—	2	2	no	—
35	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
36	C₃₁×#117	—	2	4	no	—
37	C₃₁×#117	—	2	4	no	—
38	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
39	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
40	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
41	C₂×C₄²×C₃₁	—	2	2	no	—
42	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₃₁	D₄	1	2	yes	—
46	C₂×C₄²×C₃₁	D₄	1	2	yes	—
47	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₃₁	Q₈	1	1	yes	characteristic
50	C₂×C₄²×C₃₁	Q₈	1	1	yes	characteristic
51	C₃₁×C₄⋊C₈	—	2	4	no	—
52	C₃₁×C₄⋊C₈	—	2	4	no	—
53	C₃₁×#97	—	2	4	no	—
54	C₄×C₈×C₃₁	—	2	4	no	—
55	C₃₁×#95	—	2	4	no	—
56	C₂⁴×C₃₁	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₃₁	—	2	4	no	—
58	C₂²×C₄×C₃₁	—	4	4	no	—
59	C₂²×C₄×C₃₁	C₄²	1	2	yes	—
60	C₂²×C₄×C₃₁	C₄²	1	2	yes	—
61	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
62	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
63	C₂²×C₄×C₃₁	C₄⋊C₄	1	2	yes	—
64	C₂²×C₄×C₃₁	C₄⋊C₄	1	2	yes	—
65	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
71	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
72	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
73	C₂²×C₄×C₃₁	#41	1	2	yes	—
74	C₂²×C₄×C₃₁	#41	1	2	yes	—
75	M₁₆×C₃₁	—	2	4	no	—
76	M₁₆×C₃₁	—	2	4	no	—
77	M₁₆×C₃₁	—	2	4	no	—
78	M₁₆×C₃₁	—	2	4	no	—
79	M₁₆×C₃₁	—	2	8	no	—
80	M₁₆×C₃₁	—	4	2	no	—
81	M₁₆×C₃₁	—	4	2	no	—
82	C₂×C₈×C₃₁	—	2	4	no	—
83	C₂×C₈×C₃₁	—	2	4	no	—
84	C₂×C₈×C₃₁	—	2	4	no	—
85	C₂×C₈×C₃₁	—	4	4	no	—
86	C₂×C₈×C₃₁	C₄⋊C₄	1	8	yes	complemented
87	C₄⋊C₄×C₃₁	—	4	8	no	—
88	C₄⋊C₄×C₃₁	—	4	2	no	—
89	C₄⋊C₄×C₃₁	—	4	2	no	—
90	C₂²⋊C₄×C₃₁	—	2	8	no	—
91	C₄²×C₃₁	—	4	4	no	—
92	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
93	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
94	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
95	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
96	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
97	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
98	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₃₁	C₄⋊C₄	1	2	yes	—
100	C₄²×C₃₁	C₄⋊C₄	1	2	yes	—
101	C₄²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
102	#10848	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₂³×C₃₁	—	4	2	no	—
104	C₂³×C₃₁	C₂×C₄²	1	1	yes	characteristic
105	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
106	C₂³×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
107	C₂³×C₃₁	C₄×D₄	1	2	yes	—
108	C₂³×C₃₁	C₄×Q₈	1	2	yes	—
109	C₂×C₄×C₃₁	—	2	4	no	—
110	C₂×C₄×C₃₁	—	2	4	no	—
111	C₂×C₄×C₃₁	—	2	4	no	—
112	C₂×C₄×C₃₁	—	4	2	no	—
113	C₂×C₄×C₃₁	—	4	2	no	—
114	C₂×C₄×C₃₁	—	4	2	no	—
115	C₂×C₄×C₃₁	—	4	8	no	—
116	C₂×C₄×C₃₁	—	4	4	no	—
117	C₂×C₄×C₃₁	#95	1	2	yes	—
118	C₂×C₄×C₃₁	#95	1	2	yes	—
119	C₂×C₄×C₃₁	#95	1	2	yes	—
120	C₂×C₄×C₃₁	#95	1	2	yes	—
121	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
123	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
124	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
125	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
126	C₂×C₄×C₃₁	#117	1	2	yes	—
127	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
128	C₂×C₄×C₃₁	C₄×Q₈	1	2	yes	—
129	C₂×C₄×C₃₁	#121	1	2	yes	—
130	C₂×C₄×C₃₁	#121	1	2	yes	—
131	C₂×C₄×C₃₁	C₂²⋊Q₈	1	2	yes	—
132	C₂×C₄×C₃₁	C₂²⋊Q₈	1	2	yes	—
133	C₂×C₄×C₃₁	#124	1	1	yes	characteristic
134	C₂×C₄×C₃₁	#124	1	1	yes	characteristic
135	C₂×C₄×C₃₁	#125	1	2	yes	—
136	C₂×C₄×C₃₁	#127	1	1	yes	characteristic
137	C₂×C₄×C₃₁	C₄⋊Q₈	1	2	yes	—
138	C₂×C₄×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
139	C₈×C₃₁	—	2	8	no	—
140	C₈×C₃₁	—	4	4	no	—
141	C₂×#423	C₂×C₃₁	1	1	yes	characteristic
142	C₂×C₄×M₁₆	C₂×C₃₁	1	1	yes	characteristic
143	#2285	C₂×C₃₁	1	1	yes	characteristic
144	C₂×#344	C₂×C₃₁	1	4	yes	—
145	C₂²×C₃₁	—	2	2	no	—
146	C₂²×C₃₁	—	2	2	no	—
147	C₂²×C₃₁	—	2	2	no	—
148	C₂²×C₃₁	—	4	2	no	—
149	C₂²×C₃₁	—	4	2	no	—
150	C₂²×C₃₁	C₂×#95	1	1	yes	characteristic
151	C₂²×C₃₁	C₄×C₄⋊C₄	1	2	yes	—
152	C₂²×C₃₁	#389	1	2	yes	—
153	C₂²×C₃₁	#390	1	1	yes	characteristic
154	C₂²×C₃₁	#391	1	1	yes	characteristic
155	C₄×C₃₁	—	2	2	no	—
156	C₄×C₃₁	—	2	2	no	—
157	C₄×C₃₁	—	2	2	no	—
158	C₄×C₃₁	—	8	4	no	—
159	C₄×C₃₁	#344	1	4	yes	complemented
160	C₄×C₃₁	#380	1	2	yes	—
161	C₄×C₃₁	#382	1	1	yes	characteristic
162	C₄×C₃₁	#384	1	1	yes	characteristic
163	C₄×C₃₁	#389	1	2	yes	—
164	C₄×C₃₁	#390	1	1	yes	characteristic
165	C₄×C₃₁	#391	1	1	yes	characteristic
166	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
167	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
168	C₂×#117	C₂²×C₃₁	1	2	yes	—
169	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
170	#423	—	2	1	no	—
171	#423	—	2	1	no	—
172	#423	C₄×C₃₁	1	4	yes	complemented
173	C₂×C₄⋊C₈	—	2	2	no	—
174	C₄×M₁₆	—	2	2	no	—
175	C₄×M₁₆	—	2	2	no	—
176	C₂×#97	C₄×C₃₁	1	2	yes	complemented
177	C₂×C₄×C₈	C₄×C₃₁	1	2	yes	complemented
178	#384	—	2	1	no	—
179	#382	—	2	1	no	—
180	#380	C₄×C₃₁	1	4	yes	—
181	C₄×C₄⋊C₄	—	2	2	no	—
182	#344	—	2	8	no	—
183	C₂×C₃₁	—	2	1	no	—
184	C₂×C₃₁	—	2	2	no	—
185	C₂×C₃₁	—	2	2	no	—
186	C₂×C₃₁	—	2	1	no	—
187	C₂×C₃₁	C₄⋊#95	1	1	yes	characteristic
188	C₂×C₃₁	C₂×#344	1	2	yes	—
189	C₂³×C₄	C₂×C₄×C₃₁	1	2	yes	—
190	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
191	C₂×M₁₆	—	2	2	no	—
192	C₂×M₁₆	—	2	2	no	—
193	C₂×M₁₆	—	2	2	no	—
194	C₂×M₁₆	—	2	2	no	—
195	C₂×M₁₆	—	2	2	no	—
196	C₂×M₁₆	—	2	4	no	—
197	C₂×M₁₆	—	2	4	no	—
198	C₂×M₁₆	C₂×C₄×C₃₁	1	4	yes	—
199	C₂×M₁₆	D₄×C₃₁	1	4	yes	—
200	C₂×M₁₆	Q₈×C₃₁	1	4	yes	—
201	C₂²×C₈	—	2	2	no	—
202	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
203	#117	—	2	4	no	—
204	#117	—	2	4	no	—
205	C₂×C₄⋊C₄	—	2	4	no	—
206	C₂×C₄⋊C₄	—	2	2	no	—
207	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
208	C₂×C₄²	—	2	2	no	—
209	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
210	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
211	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
212	C₂×C₄²	D₄×C₃₁	1	2	yes	—
213	C₂×C₄²	D₄×C₃₁	1	2	yes	—
214	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
215	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
216	C₂×C₄²	Q₈×C₃₁	1	1	yes	characteristic
217	C₂×C₄²	Q₈×C₃₁	1	1	yes	characteristic
218	C₄⋊C₈	—	2	4	no	—
219	C₄⋊C₈	—	2	4	no	—
220	#97	—	2	4	no	—
221	C₄×C₈	—	2	4	no	—
222	#95	—	2	4	no	—
223	C₃₁	#10848	1	1	yes	characteristic, direct product factor, Sylow
224	C₂⁴	C₂²×C₄×C₃₁	1	1	yes	characteristic
225	C₂²×C₄	—	2	4	no	—
226	C₂²×C₄	—	4	4	no	—
227	C₂²×C₄	C₄²×C₃₁	1	2	yes	—
228	C₂²×C₄	C₄²×C₃₁	1	2	yes	—
229	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
230	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
231	C₂²×C₄	C₄⋊C₄×C₃₁	1	2	yes	—
232	C₂²×C₄	C₄⋊C₄×C₃₁	1	2	yes	—
233	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
234	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
235	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
236	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
237	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
238	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
239	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
240	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
241	C₂²×C₄	#41×C₃₁	1	2	yes	—
242	C₂²×C₄	#41×C₃₁	1	2	yes	—
243	M₁₆	—	2	4	no	—
244	M₁₆	—	2	4	no	—
245	M₁₆	—	2	4	no	—
246	M₁₆	—	2	4	no	—
247	M₁₆	—	2	8	no	—
248	M₁₆	—	4	2	no	—
249	M₁₆	—	4	2	no	—
250	C₂×C₈	—	2	4	no	—
251	C₂×C₈	—	2	4	no	—
252	C₂×C₈	—	2	4	no	—
253	C₂×C₈	—	4	4	no	—
254	C₂×C₈	C₄⋊C₄×C₃₁	1	8	yes	complemented
255	C₄⋊C₄	—	4	8	no	—
256	C₄⋊C₄	—	4	2	no	—
257	C₄⋊C₄	—	4	2	no	—
258	C₂²⋊C₄	—	2	8	no	—
259	C₄²	—	4	4	no	—
260	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
261	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
262	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
263	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
264	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
265	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
266	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
267	C₄²	C₄⋊C₄×C₃₁	1	2	yes	—
268	C₄²	C₄⋊C₄×C₃₁	1	2	yes	—
269	C₄²	C₄⋊C₄×C₃₁	1	1	yes	characteristic
270	C₂³	—	4	2	no	—
271	C₂³	C₂×C₄²×C₃₁	1	1	yes	characteristic
272	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
273	C₂³	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
274	C₂³	C₄×D₄×C₃₁	1	2	yes	—
275	C₂³	C₄×Q₈×C₃₁	1	2	yes	—
276	C₂×C₄	—	2	4	no	—
277	C₂×C₄	—	2	4	no	—
278	C₂×C₄	—	2	4	no	—
279	C₂×C₄	—	4	2	no	—
280	C₂×C₄	—	4	2	no	—
281	C₂×C₄	—	4	2	no	—
282	C₂×C₄	—	4	8	no	—
283	C₂×C₄	—	4	4	no	—
284	C₂×C₄	C₃₁×#95	1	2	yes	—
285	C₂×C₄	C₃₁×#95	1	2	yes	—
286	C₂×C₄	C₃₁×#95	1	2	yes	—
287	C₂×C₄	C₃₁×#95	1	2	yes	—
288	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
289	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
290	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
291	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
292	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
293	C₂×C₄	C₃₁×#117	1	2	yes	—
294	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
295	C₂×C₄	C₄×Q₈×C₃₁	1	2	yes	—
296	C₂×C₄	C₃₁×#121	1	2	yes	—
297	C₂×C₄	C₃₁×#121	1	2	yes	—
298	C₂×C₄	C₃₁×C₂²⋊Q₈	1	2	yes	—
299	C₂×C₄	C₃₁×C₂²⋊Q₈	1	2	yes	—
300	C₂×C₄	C₃₁×#124	1	1	yes	characteristic
301	C₂×C₄	C₃₁×#124	1	1	yes	characteristic
302	C₂×C₄	C₃₁×#125	1	2	yes	—
303	C₂×C₄	C₃₁×#127	1	1	yes	characteristic
304	C₂×C₄	C₃₁×C₄⋊Q₈	1	2	yes	—
305	C₂×C₄	C₃₁×C₄⋊Q₈	1	1	yes	characteristic
306	C₈	—	2	8	no	—
307	C₈	—	4	4	no	—
308	C₂²	—	2	2	no	—
309	C₂²	—	2	2	no	—
310	C₂²	—	2	2	no	—
311	C₂²	—	4	2	no	—
312	C₂²	—	4	2	no	—
313	C₂²	C₂×C₃₁×#95	1	1	yes	characteristic
314	C₂²	C₄×C₄⋊C₄×C₃₁	1	2	yes	—
315	C₂²	C₃₁×#389	1	2	yes	—
316	C₂²	C₃₁×#390	1	1	yes	characteristic
317	C₂²	C₃₁×#391	1	1	yes	characteristic
318	C₄	—	2	2	no	—
319	C₄	—	2	2	no	—
320	C₄	—	2	2	no	—
321	C₄	—	8	4	no	—
322	C₄	C₃₁×#344	1	4	yes	complemented
323	C₄	C₃₁×#380	1	2	yes	—
324	C₄	C₃₁×#382	1	1	yes	characteristic
325	C₄	C₃₁×#384	1	1	yes	characteristic
326	C₄	C₃₁×#389	1	2	yes	—
327	C₄	C₃₁×#390	1	1	yes	characteristic
328	C₄	C₃₁×#391	1	1	yes	characteristic
329	C₂	—	2	1	no	—
330	C₂	—	2	2	no	—
331	C₂	—	2	2	no	—
332	C₂	—	2	1	no	—
333	C₂	C₃₁×C₄⋊#95	1	1	yes	characteristic
334	C₂	C₂×C₃₁×#344	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂×C₂²⋊C₄
commutator	C₂³	C₂×C₄²×C₃₁
Frattini, cosocle	C₂³×C₄	C₂³×C₃₁
socle	C₂²×C₃₁	C₂×#95
prime radical	C₂⁴×C₃₁	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
11. C₃₁×#423	C₄	semidirect
15. C₂×C₃₁×#97	C₄	semidirect
16. C₂×C₄×C₈×C₃₁	C₄	semidirect
86. C₂×C₈×C₃₁	C₄⋊C₄	semidirect
102. #10848	C₃₁	direct (N × H)
159. C₄×C₃₁	#344	semidirect
172. #423	C₄×C₃₁	semidirect
176. C₂×#97	C₄×C₃₁	semidirect
177. C₂×C₄×C₈	C₄×C₃₁	semidirect
223. C₃₁	#10848	direct (N × H)
254. C₂×C₈	C₄⋊C₄×C₃₁	semidirect
322. C₄	C₃₁×#344	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#423	2
C₂×C₄×M₁₆×C₃₁	2
C₃₁×#2285	2
C₂×C₃₁×#344	2
#10848	31

Subgroups — C31×#10848 #21467607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#10848 #21467607