Subgroups — C₃₁×#33703 #21490462

Order 7936.

570 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3164	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#3156	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2245	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2243	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2242	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2241	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2141	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#2139	C₂	1	1	yes	maximal, characteristic
9	C₃₁×#2138	C₂	1	1	yes	maximal, characteristic
10	C₂×C₃₁×#358	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#2108	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#137	—	2	1	no	—
13	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
15	C₃₁×#544	—	2	1	no	—
16	C₃₁×#536	—	2	1	no	—
17	C₂×C₃₁×M₃₂	C₂²	1	1	yes	characteristic
18	C₂²×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
19	C₃₁×#501	—	2	2	no	—
20	C₃₁×#500	C₂²	1	2	yes	—
21	C₃₁×#499	C₂²	1	2	yes	—
22	C₃₁×#497	—	2	2	no	—
23	C₃₁×#495	C₂²	1	2	yes	—
24	C₃₁×#494	C₂²	1	2	yes	—
25	C₃₁×#428	—	2	1	no	—
26	C₃₁×#427	C₂²	1	1	yes	characteristic
27	C₂×C₃₁×#107	C₂²	1	1	yes	characteristic
28	C₃₁×#405	C₂²	1	1	yes	characteristic
29	C₃₁×#358	C₂²	1	2	yes	—
30	C₃₁×#358	C₂²	1	2	yes	—
31	C₃₁×#358	C₂²	1	1	yes	characteristic
32	C₃₁×#358	C₂²	1	1	yes	characteristic
33	C₃₁×#358	C₂²	1	2	yes	—
34	C₃₁×#358	C₂²	1	2	yes	—
35	C₃₁×#358	C₂²	1	2	yes	—
36	C₃₁×#357	C₂²	1	1	yes	characteristic
37	C₃₁×#357	C₂²	1	1	yes	characteristic
38	C₃₁×#357	C₂²	1	2	yes	—
39	C₃₁×#346	C₂²	1	2	yes	—
40	C₄×C₁₆×C₃₁	C₂²	1	2	yes	—
41	C₂×#41×C₃₁	—	2	1	no	—
42	C₂²×Q₈×C₃₁	—	2	1	no	—
43	C₃₁×#137	—	4	4	no	—
44	C₃₁×#135	—	2	2	no	—
45	C₃₁×#135	—	2	2	no	—
46	C₂×Q₁₆×C₃₁	—	2	2	no	—
47	C₂×Q₁₆×C₃₁	—	2	1	no	—
48	C₂×Q₁₆×C₃₁	—	2	2	no	—
49	C₂×Q₁₆×C₃₁	—	2	2	no	—
50	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
51	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
52	C₂×SD₁₆×C₃₁	—	2	2	no	—
53	C₂×SD₁₆×C₃₁	—	2	1	no	—
54	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
55	C₂×M₁₆×C₃₁	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
57	C₃₁×C₄⋊Q₈	—	2	2	no	—
58	C₃₁×C₄⋊Q₈	—	2	2	no	—
59	C₃₁×C₄⋊Q₈	—	4	1	no	—
60	C₃₁×#125	—	2	2	no	—
61	C₃₁×#125	—	4	1	no	—
62	C₃₁×#124	—	2	2	no	—
63	C₃₁×#123	—	4	2	no	—
64	C₃₁×C₂²⋊Q₈	—	4	1	no	—
65	C₃₁×C₂²⋊Q₈	—	4	1	no	—
66	C₃₁×C₂²⋊Q₈	—	4	2	no	—
67	C₃₁×#117	—	2	1	no	—
68	C₃₁×#117	D₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
70	C₃₁×M₃₂	—	2	2	no	—
71	C₂×C₁₆×C₃₁	—	2	2	no	—
72	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
73	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
74	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
75	C₃₁×#107	—	2	1	no	—
76	C₃₁×#107	—	2	2	no	—
77	C₃₁×#107	C₂³	1	2	yes	—
78	C₃₁×#107	C₂³	1	1	yes	characteristic
79	C₃₁×#107	C₂³	1	1	yes	characteristic
80	C₃₁×#106	—	2	1	no	—
81	C₃₁×#106	—	2	2	no	—
82	C₃₁×#97	D₄	1	2	yes	—
83	C₄×C₈×C₃₁	C₂³	1	2	yes	—
84	#41×C₃₁	—	4	2	no	—
85	#41×C₃₁	—	4	2	no	—
86	C₂×Q₈×C₃₁	—	2	2	no	—
87	C₂×Q₈×C₃₁	—	2	1	no	—
88	C₂×Q₈×C₃₁	—	4	1	no	—
89	C₂×Q₈×C₃₁	—	4	2	no	—
90	C₂×Q₈×C₃₁	—	4	2	no	—
91	C₂×Q₈×C₃₁	—	4	2	no	—
92	C₂×D₄×C₃₁	—	2	1	no	—
93	C₂×D₄×C₃₁	—	4	1	no	—
94	C₂²×C₄×C₃₁	—	4	1	no	—
95	C₂²×C₄×C₃₁	—	4	1	no	—
96	C₂²×C₄×C₃₁	—	4	1	no	—
97	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
98	Q₁₆×C₃₁	—	2	2	no	—
99	Q₁₆×C₃₁	—	2	2	no	—
100	Q₁₆×C₃₁	—	2	1	no	—
101	Q₁₆×C₃₁	—	2	1	no	—
102	Q₁₆×C₃₁	—	4	2	no	—
103	Q₁₆×C₃₁	—	4	4	no	—
104	SD₁₆×C₃₁	—	4	2	no	—
105	SD₁₆×C₃₁	—	4	4	no	—
106	D₈×C₃₁	—	2	1	no	—
107	D₈×C₃₁	—	2	1	no	—
108	M₁₆×C₃₁	SD₁₆	1	4	yes	—
109	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₃₁	#41	1	2	yes	—
112	C₂×C₈×C₃₁	#41	1	2	yes	—
113	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
114	C₄⋊C₄×C₃₁	—	2	1	no	—
115	C₄⋊C₄×C₃₁	—	2	2	no	—
116	C₄⋊C₄×C₃₁	—	2	1	no	—
117	C₄⋊C₄×C₃₁	—	4	1	no	—
118	C₄⋊C₄×C₃₁	—	4	2	no	—
119	C₄⋊C₄×C₃₁	—	4	2	no	—
120	C₄⋊C₄×C₃₁	—	4	2	no	—
121	C₄⋊C₄×C₃₁	—	4	2	no	—
122	C₄⋊C₄×C₃₁	—	4	2	no	—
123	C₄⋊C₄×C₃₁	D₈	1	1	yes	characteristic
124	C₄⋊C₄×C₃₁	D₈	1	1	yes	characteristic
125	C₂²⋊C₄×C₃₁	—	4	1	no	—
126	C₂²⋊C₄×C₃₁	—	4	2	no	—
127	C₂²⋊C₄×C₃₁	—	4	2	no	—
128	C₂²⋊C₄×C₃₁	D₈	1	2	yes	—
129	C₄²×C₃₁	—	4	1	no	—
130	C₄²×C₃₁	C₂×D₄	1	2	yes	—
131	C₁₆×C₃₁	—	2	1	no	—
132	C₁₆×C₃₁	—	2	1	no	—
133	C₁₆×C₃₁	—	2	2	no	—
134	#33703	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
135	C₂³×C₃₁	—	4	1	no	—
136	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
137	Q₈×C₃₁	—	4	1	no	—
138	Q₈×C₃₁	—	4	2	no	—
139	Q₈×C₃₁	—	4	2	no	—
140	Q₈×C₃₁	—	4	1	no	—
141	Q₈×C₃₁	—	8	2	no	—
142	Q₈×C₃₁	—	16	2	no	—
143	D₄×C₃₁	—	4	1	no	—
144	D₄×C₃₁	—	4	1	no	—
145	D₄×C₃₁	—	8	2	no	—
146	C₂×C₄×C₃₁	—	4	1	no	—
147	C₂×C₄×C₃₁	—	4	1	no	—
148	C₂×C₄×C₃₁	—	4	2	no	—
149	C₂×C₄×C₃₁	—	4	2	no	—
150	C₂×C₄×C₃₁	—	4	1	no	—
151	C₂×C₄×C₃₁	—	8	2	no	—
152	C₂×C₄×C₃₁	—	8	2	no	—
153	C₂×C₄×C₃₁	—	16	1	no	—
154	C₂×C₄×C₃₁	#124	1	2	yes	—
155	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
156	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
157	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
158	C₂×C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
159	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
160	C₈×C₃₁	#124	1	2	yes	—
161	C₈×C₃₁	C₂×SD₁₆	1	4	yes	—
162	C₈×C₃₁	C₂×#41	1	1	yes	characteristic
163	C₈×C₃₁	C₂×#41	1	1	yes	characteristic
164	#3164	C₂×C₃₁	1	1	yes	characteristic, complemented
165	#3156	C₂×C₃₁	1	1	yes	characteristic
166	#2245	C₂×C₃₁	1	2	yes	complemented
167	#2243	C₂×C₃₁	1	2	yes	complemented
168	#2242	C₂×C₃₁	1	2	yes	complemented
169	#2241	C₂×C₃₁	1	2	yes	complemented
170	#2141	C₂×C₃₁	1	1	yes	characteristic, complemented
171	#2139	C₂×C₃₁	1	1	yes	characteristic
172	#2138	C₂×C₃₁	1	1	yes	characteristic
173	C₂×#358	C₂×C₃₁	1	1	yes	characteristic, complemented
174	#2108	C₂×C₃₁	1	1	yes	characteristic, complemented
175	C₂²×C₃₁	—	2	1	no	—
176	C₂²×C₃₁	—	2	1	no	—
177	C₂²×C₃₁	—	8	1	no	—
178	C₂²×C₃₁	—	8	1	no	—
179	C₂²×C₃₁	—	8	1	no	—
180	C₂²×C₃₁	#486	1	2	yes	—
181	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
182	C₄×C₃₁	—	2	2	no	—
183	C₄×C₃₁	—	2	2	no	—
184	C₄×C₃₁	—	8	1	no	—
185	C₄×C₃₁	—	8	2	no	—
186	C₄×C₃₁	—	8	2	no	—
187	C₄×C₃₁	—	8	1	no	—
188	C₄×C₃₁	—	8	1	no	—
189	C₄×C₃₁	#486	1	2	yes	—
190	C₄×C₃₁	C₂×#124	1	1	yes	characteristic
191	C₄×C₃₁	C₂²×SD₁₆	1	1	yes	characteristic
192	C₂×#137	—	2	1	no	—
193	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
194	C₂²×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
195	#544	—	2	1	no	—
196	#536	—	2	1	no	—
197	C₂×M₃₂	C₂²×C₃₁	1	1	yes	characteristic
198	C₂²×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
199	#501	—	2	2	no	—
200	#500	C₂²×C₃₁	1	2	yes	—
201	#499	C₂²×C₃₁	1	2	yes	—
202	#497	—	2	2	no	—
203	#495	C₂²×C₃₁	1	2	yes	—
204	#494	C₂²×C₃₁	1	2	yes	—
205	#428	—	2	1	no	—
206	#427	C₂²×C₃₁	1	1	yes	characteristic
207	C₂×#107	C₂²×C₃₁	1	1	yes	characteristic
208	#405	C₂²×C₃₁	1	1	yes	characteristic
209	#358	C₂²×C₃₁	1	2	yes	—
210	#358	C₂²×C₃₁	1	2	yes	—
211	#358	C₂²×C₃₁	1	1	yes	characteristic
212	#358	C₂²×C₃₁	1	1	yes	characteristic
213	#358	C₂²×C₃₁	1	2	yes	—
214	#358	C₂²×C₃₁	1	2	yes	—
215	#358	C₂²×C₃₁	1	2	yes	—
216	#357	C₂²×C₃₁	1	1	yes	characteristic
217	#357	C₂²×C₃₁	1	1	yes	characteristic
218	#357	C₂²×C₃₁	1	2	yes	—
219	#346	C₂²×C₃₁	1	2	yes	—
220	C₄×C₁₆	C₂²×C₃₁	1	2	yes	—
221	C₂×C₃₁	—	2	2	no	—
222	C₂×C₃₁	—	16	1	no	—
223	C₂×C₃₁	C₂×#486	1	1	yes	characteristic
224	C₂×C₃₁	#3416	1	1	yes	characteristic
225	C₂×C₃₁	#3417	1	1	yes	characteristic
226	C₂×#41	—	2	1	no	—
227	C₂²×Q₈	—	2	1	no	—
228	#137	—	4	4	no	—
229	#135	—	2	2	no	—
230	#135	—	2	2	no	—
231	C₂×Q₁₆	—	2	1	no	—
232	C₂×Q₁₆	—	2	2	no	—
233	C₂×Q₁₆	—	2	2	no	—
234	C₂×Q₁₆	—	2	2	no	—
235	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
236	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
237	C₂×SD₁₆	—	2	1	no	—
238	C₂×SD₁₆	—	2	2	no	—
239	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
240	C₂×M₁₆	D₄×C₃₁	1	1	yes	characteristic
241	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
242	C₄⋊Q₈	—	2	2	no	—
243	C₄⋊Q₈	—	2	2	no	—
244	C₄⋊Q₈	—	4	1	no	—
245	#125	—	2	2	no	—
246	#125	—	4	1	no	—
247	#124	—	2	2	no	—
248	#123	—	4	2	no	—
249	C₂²⋊Q₈	—	4	1	no	—
250	C₂²⋊Q₈	—	4	1	no	—
251	C₂²⋊Q₈	—	4	2	no	—
252	#117	—	2	1	no	—
253	#117	D₄×C₃₁	1	1	yes	characteristic
254	C₂×C₄⋊C₄	—	2	1	no	—
255	M₃₂	—	2	2	no	—
256	C₂×C₁₆	—	2	2	no	—
257	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
258	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
259	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
260	#107	—	2	1	no	—
261	#107	—	2	2	no	—
262	#107	C₂³×C₃₁	1	2	yes	—
263	#107	C₂³×C₃₁	1	1	yes	characteristic
264	#107	C₂³×C₃₁	1	1	yes	characteristic
265	#106	—	2	1	no	—
266	#106	—	2	2	no	—
267	#97	D₄×C₃₁	1	2	yes	—
268	C₄×C₈	C₂³×C₃₁	1	2	yes	—
269	C₃₁	#33703	1	1	yes	characteristic, direct product factor, Sylow
270	#41	—	4	2	no	—
271	#41	—	4	2	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	—	2	1	no	—
274	C₂×Q₈	—	4	1	no	—
275	C₂×Q₈	—	4	2	no	—
276	C₂×Q₈	—	4	2	no	—
277	C₂×Q₈	—	4	2	no	—
278	C₂×D₄	—	2	1	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂²×C₄	—	4	1	no	—
281	C₂²×C₄	—	4	1	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
284	Q₁₆	—	2	2	no	—
285	Q₁₆	—	2	2	no	—
286	Q₁₆	—	2	1	no	—
287	Q₁₆	—	2	1	no	—
288	Q₁₆	—	4	2	no	—
289	Q₁₆	—	4	4	no	—
290	SD₁₆	—	4	2	no	—
291	SD₁₆	—	4	4	no	—
292	D₈	—	2	1	no	—
293	D₈	—	2	1	no	—
294	M₁₆	SD₁₆×C₃₁	1	4	yes	—
295	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
296	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
297	C₂×C₈	#41×C₃₁	1	2	yes	—
298	C₂×C₈	#41×C₃₁	1	2	yes	—
299	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	1	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	2	no	—
305	C₄⋊C₄	—	4	2	no	—
306	C₄⋊C₄	—	4	2	no	—
307	C₄⋊C₄	—	4	2	no	—
308	C₄⋊C₄	—	4	2	no	—
309	C₄⋊C₄	D₈×C₃₁	1	1	yes	characteristic
310	C₄⋊C₄	D₈×C₃₁	1	1	yes	characteristic
311	C₂²⋊C₄	—	4	1	no	—
312	C₂²⋊C₄	—	4	2	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	D₈×C₃₁	1	2	yes	—
315	C₄²	—	4	1	no	—
316	C₄²	C₂×D₄×C₃₁	1	2	yes	—
317	C₁₆	—	2	1	no	—
318	C₁₆	—	2	1	no	—
319	C₁₆	—	2	2	no	—
320	C₂³	—	4	1	no	—
321	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
322	Q₈	—	4	1	no	—
323	Q₈	—	4	2	no	—
324	Q₈	—	4	2	no	—
325	Q₈	—	4	1	no	—
326	Q₈	—	8	2	no	—
327	Q₈	—	16	2	no	—
328	D₄	—	4	1	no	—
329	D₄	—	4	1	no	—
330	D₄	—	8	2	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	8	2	no	—
337	C₂×C₄	—	8	2	no	—
338	C₂×C₄	—	16	1	no	—
339	C₂×C₄	C₃₁×#124	1	2	yes	—
340	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
341	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
342	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
343	C₂×C₄	C₂×SD₁₆×C₃₁	1	2	yes	—
344	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
345	C₈	C₃₁×#124	1	2	yes	—
346	C₈	C₂×SD₁₆×C₃₁	1	4	yes	—
347	C₈	C₂×#41×C₃₁	1	1	yes	characteristic
348	C₈	C₂×#41×C₃₁	1	1	yes	characteristic
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	8	1	no	—
352	C₂²	—	8	1	no	—
353	C₂²	—	8	1	no	—
354	C₂²	C₃₁×#486	1	2	yes	—
355	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
356	C₄	—	2	2	no	—
357	C₄	—	2	2	no	—
358	C₄	—	8	1	no	—
359	C₄	—	8	2	no	—
360	C₄	—	8	2	no	—
361	C₄	—	8	1	no	—
362	C₄	—	8	1	no	—
363	C₄	C₃₁×#486	1	2	yes	—
364	C₄	C₂×C₃₁×#124	1	1	yes	characteristic
365	C₄	C₂²×SD₁₆×C₃₁	1	1	yes	characteristic
366	C₂	—	2	2	no	—
367	C₂	—	16	1	no	—
368	C₂	C₂×C₃₁×#486	1	1	yes	characteristic
369	C₂	C₃₁×#3416	1	1	yes	characteristic
370	C₂	C₃₁×#3417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
prime radical	C₂×C₃₁×#135	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₃₁×#117 ◁ C₃₁×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3164	C₂	semidirect
3. C₃₁×#2245	C₂	semidirect
4. C₃₁×#2243	C₂	semidirect
5. C₃₁×#2242	C₂	semidirect
6. C₃₁×#2241	C₂	semidirect
7. C₃₁×#2141	C₂	semidirect
10. C₂×C₃₁×#358	C₂	semidirect
11. C₃₁×#2108	C₂	semidirect
134. #33703	C₃₁	direct (N × H)
164. #3164	C₂×C₃₁	semidirect
166. #2245	C₂×C₃₁	semidirect
167. #2243	C₂×C₃₁	semidirect
168. #2242	C₂×C₃₁	semidirect
169. #2241	C₂×C₃₁	semidirect
170. #2141	C₂×C₃₁	semidirect
173. C₂×#358	C₂×C₃₁	semidirect
174. #2108	C₂×C₃₁	semidirect
269. C₃₁	#33703	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×#3164	2
C₃₁×#3156	2
C₃₁×#2245	2
C₃₁×#2243	2
C₃₁×#2242	2
C₃₁×#2241	2
C₃₁×#2141	2
C₃₁×#2139	2
C₃₁×#2138	2
C₂×C₃₁×#358	2
C₃₁×#2108	2
#33703	31

Subgroups — C31×#33703 #21490462

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33703 #21490462