Subgroups — C₃₁×#36583 #21493342

Order 7936.

2522 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#550	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2858	C₂	1	3	yes	maximal, complemented
4	C₃₁×#2548	C₂	1	3	yes	maximal, complemented
5	C₃₁×#2547	C₂	1	3	yes	maximal, complemented
6	C₃₁×#2490	C₂	1	12	yes	maximal, complemented
7	C₃₁×#2341	C₂	1	4	yes	maximal, complemented
8	C₄×C₃₁×#124	C₂	1	3	yes	maximal, complemented
9	C₄²×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₃₁	C₂²	1	2	yes	—
11	C₃₁×#557	—	2	8	no	—
12	C₃₁×#550	—	2	8	no	—
13	C₂×C₃₁×C₄⋊Q₈	C₂²	1	3	yes	—
14	C₂×C₃₁×#127	C₂²	1	3	yes	—
15	C₂×C₃₁×#125	C₂²	1	6	yes	—
16	C₂×C₃₁×#124	C₂²	1	3	yes	—
17	C₂×C₃₁×#124	C₂²	1	6	yes	—
18	C₂×C₃₁×#121	C₂²	1	6	yes	—
19	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₃₁	C₂²	1	3	yes	—
22	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₃₁	C₂²	1	3	yes	—
24	C₃₁×#397	C₂²	1	12	yes	—
25	C₃₁×#394	C₂²	1	12	yes	—
26	C₃₁×#391	C₂²	1	3	yes	—
27	C₃₁×#390	C₂²	1	12	yes	—
28	C₃₁×#390	C₂²	1	12	yes	—
29	C₃₁×#390	C₂²	1	12	yes	—
30	C₃₁×#390	C₂²	1	3	yes	—
31	C₃₁×#388	C₂²	1	12	yes	—
32	C₃₁×#382	C₂²	1	1	yes	characteristic
33	C₃₁×#380	C₂²	1	12	yes	—
34	C₄×C₄⋊C₄×C₃₁	C₂²	1	6	yes	—
35	C₄×C₄⋊C₄×C₃₁	C₂²	1	3	yes	—
36	C₄×C₂²⋊C₄×C₃₁	C₂²	1	12	yes	—
37	C₄³×C₃₁	C₂²	1	3	yes	—
38	C₂×#41×C₃₁	—	2	8	no	—
39	C₂×#41×C₃₁	—	2	16	no	—
40	C₂²×Q₈×C₃₁	C₂³	1	3	yes	—
41	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₃₁	C₂³	1	3	yes	—
43	C₂²×D₄×C₃₁	C₂³	1	6	yes	—
44	C₂²×D₄×C₃₁	C₂³	1	6	yes	—
45	C₂³×C₄×C₃₁	C₂³	1	6	yes	—
46	C₃₁×C₄⋊Q₈	—	2	12	no	—
47	C₃₁×#127	—	2	12	no	—
48	C₃₁×#125	—	2	24	no	—
49	C₃₁×#124	—	2	12	no	—
50	C₃₁×#124	—	4	12	no	—
51	C₃₁×#121	—	2	24	no	—
52	C₄×Q₈×C₃₁	—	2	8	no	—
53	C₄×Q₈×C₃₁	—	2	8	no	—
54	C₄×Q₈×C₃₁	—	2	12	no	—
55	C₄×Q₈×C₃₁	D₄	1	8	yes	—
56	C₄×D₄×C₃₁	—	2	12	no	—
57	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	—
58	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	—
61	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	—
62	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	—
63	C₂×C₄⋊C₄×C₃₁	C₂³	1	3	yes	—
64	C₂×C₂²⋊C₄×C₃₁	C₂³	1	6	yes	—
65	C₂×C₂²⋊C₄×C₃₁	C₂³	1	12	yes	—
66	C₂×C₂²⋊C₄×C₃₁	C₂³	1	24	yes	—
67	C₂×C₂²⋊C₄×C₃₁	C₂³	1	12	yes	—
68	C₂×C₄²×C₃₁	C₂³	1	6	yes	—
69	C₂×C₄²×C₃₁	C₂³	1	6	yes	—
70	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
71	C₂×C₄²×C₃₁	C₂³	1	6	yes	—
72	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
73	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
74	C₃₁×#95	C₂³	1	12	yes	—
75	C₃₁×#95	C₂³	1	6	yes	—
76	C₃₁×#95	C₂³	1	4	yes	—
77	C₂⁴×C₃₁	C₂⁴	1	6	yes	—
78	#41×C₃₁	—	4	32	no	—
79	C₂×Q₈×C₃₁	—	2	6	no	—
80	C₂×Q₈×C₃₁	—	2	6	no	—
81	C₂×Q₈×C₃₁	—	2	6	no	—
82	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	—
83	C₂×Q₈×C₃₁	#41	1	8	yes	—
84	C₂×D₄×C₃₁	—	2	6	no	—
85	C₂×D₄×C₃₁	—	2	12	no	—
86	C₂×D₄×C₃₁	—	2	12	no	—
87	C₂×D₄×C₃₁	—	2	6	no	—
88	C₂×D₄×C₃₁	—	2	24	no	—
89	C₂×D₄×C₃₁	—	2	6	no	—
90	C₂×D₄×C₃₁	—	4	12	no	—
91	C₂²×C₄×C₃₁	—	2	12	no	—
92	C₂²×C₄×C₃₁	—	2	24	no	—
93	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
94	C₂²×C₄×C₃₁	C₂⁴	1	6	yes	—
95	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
96	C₂²×C₄×C₃₁	C₂⁴	1	6	yes	—
97	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
98	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
99	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
100	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
101	C₄⋊C₄×C₃₁	—	2	2	no	—
102	C₄⋊C₄×C₃₁	—	2	2	no	—
103	C₄⋊C₄×C₃₁	—	2	12	no	—
104	C₄⋊C₄×C₃₁	—	2	12	no	—
105	C₄⋊C₄×C₃₁	—	2	12	no	—
106	C₄⋊C₄×C₃₁	—	2	12	no	—
107	C₄⋊C₄×C₃₁	C₂×D₄	1	12	yes	—
108	C₂²⋊C₄×C₃₁	—	2	12	no	—
109	C₂²⋊C₄×C₃₁	—	2	24	no	—
110	C₂²⋊C₄×C₃₁	—	4	12	no	—
111	C₂²⋊C₄×C₃₁	—	4	24	no	—
112	C₄²×C₃₁	—	2	12	no	—
113	C₄²×C₃₁	—	2	12	no	—
114	C₄²×C₃₁	—	2	6	no	—
115	C₄²×C₃₁	—	4	6	no	—
116	C₄²×C₃₁	C₂×D₄	1	12	yes	—
117	C₄²×C₃₁	#41	1	4	yes	complemented
118	#36583	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂³×C₃₁	—	2	6	no	—
120	C₂³×C₃₁	—	2	6	no	—
121	C₂³×C₃₁	—	2	12	no	—
122	C₂³×C₃₁	—	2	6	no	—
123	C₂³×C₃₁	—	2	12	no	—
124	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
125	Q₈×C₃₁	—	4	12	no	—
126	Q₈×C₃₁	#124	1	16	yes	complemented
127	D₄×C₃₁	—	4	24	no	—
128	D₄×C₃₁	—	4	12	no	—
129	D₄×C₃₁	—	8	12	no	—
130	C₂×C₄×C₃₁	—	2	2	no	—
131	C₂×C₄×C₃₁	—	2	2	no	—
132	C₂×C₄×C₃₁	—	2	6	no	—
133	C₂×C₄×C₃₁	—	2	2	no	—
134	C₂×C₄×C₃₁	—	2	6	no	—
135	C₂×C₄×C₃₁	—	2	2	no	—
136	C₂×C₄×C₃₁	—	2	6	no	—
137	C₂×C₄×C₃₁	—	2	6	no	—
138	C₂×C₄×C₃₁	—	2	4	no	—
139	C₂×C₄×C₃₁	—	2	6	no	—
140	C₂×C₄×C₃₁	—	2	6	no	—
141	C₂×C₄×C₃₁	—	2	6	no	—
142	C₂×C₄×C₃₁	—	2	4	no	—
143	C₂×C₄×C₃₁	—	4	24	no	—
144	C₂×C₄×C₃₁	C₂²×D₄	1	6	yes	—
145	C₂×C₄×C₃₁	C₂²×D₄	1	6	yes	—
146	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
147	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
148	C₂×C₄×C₃₁	C₂×#41	1	12	yes	—
149	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
150	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
151	C₂×#557	C₂×C₃₁	1	1	yes	characteristic, complemented
152	C₂×#550	C₂×C₃₁	1	1	yes	characteristic
153	#2858	C₂×C₃₁	1	3	yes	complemented
154	#2548	C₂×C₃₁	1	3	yes	complemented
155	#2547	C₂×C₃₁	1	3	yes	complemented
156	#2490	C₂×C₃₁	1	12	yes	complemented
157	#2341	C₂×C₃₁	1	4	yes	complemented
158	C₄×#124	C₂×C₃₁	1	3	yes	complemented
159	C₄²×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
160	C₂²×C₃₁	—	4	6	no	—
161	C₂²×C₃₁	—	4	6	no	—
162	C₂²×C₃₁	—	4	12	no	—
163	C₂²×C₃₁	—	4	6	no	—
164	C₂²×C₃₁	—	4	12	no	—
165	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
166	C₂²×C₃₁	C₂²×#41	1	2	yes	—
167	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
168	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
169	C₂²×C₃₁	#585	1	2	yes	—
170	C₄×C₃₁	—	2	4	no	—
171	C₄×C₃₁	—	2	6	no	—
172	C₄×C₃₁	—	4	2	no	—
173	C₄×C₃₁	—	4	6	no	—
174	C₄×C₃₁	—	4	2	no	—
175	C₄×C₃₁	—	4	6	no	—
176	C₄×C₃₁	C₂×#124	1	12	yes	—
177	C₄×C₃₁	#550	1	4	yes	—
178	C₂²×#41	C₂²×C₃₁	1	2	yes	—
179	#557	—	2	8	no	—
180	#550	—	2	8	no	—
181	C₂×C₄⋊Q₈	C₂²×C₃₁	1	3	yes	—
182	C₂×#127	C₂²×C₃₁	1	3	yes	—
183	C₂×#125	C₂²×C₃₁	1	6	yes	—
184	C₂×#124	C₂²×C₃₁	1	3	yes	—
185	C₂×#124	C₂²×C₃₁	1	6	yes	—
186	C₂×#121	C₂²×C₃₁	1	6	yes	—
187	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
188	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
189	C₂×C₄×Q₈	C₂²×C₃₁	1	3	yes	—
190	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
191	C₂×C₄×D₄	C₂²×C₃₁	1	3	yes	—
192	#397	C₂²×C₃₁	1	12	yes	—
193	#394	C₂²×C₃₁	1	12	yes	—
194	#391	C₂²×C₃₁	1	3	yes	—
195	#390	C₂²×C₃₁	1	12	yes	—
196	#390	C₂²×C₃₁	1	12	yes	—
197	#390	C₂²×C₃₁	1	12	yes	—
198	#390	C₂²×C₃₁	1	3	yes	—
199	#388	C₂²×C₃₁	1	12	yes	—
200	#382	C₂²×C₃₁	1	1	yes	characteristic
201	#380	C₂²×C₃₁	1	12	yes	—
202	C₄×C₄⋊C₄	C₂²×C₃₁	1	6	yes	—
203	C₄×C₄⋊C₄	C₂²×C₃₁	1	3	yes	—
204	C₄×C₂²⋊C₄	C₂²×C₃₁	1	12	yes	—
205	C₄³	C₂²×C₃₁	1	3	yes	—
206	C₂×C₃₁	—	8	6	no	—
207	C₂×C₃₁	C₂²×#124	1	1	yes	characteristic
208	C₂×C₃₁	C₂×#550	1	1	yes	characteristic
209	C₂×C₃₁	#3480	1	2	yes	—
210	C₂×C₃₁	#3500	1	1	yes	characteristic
211	C₂×C₃₁	#3517	1	2	yes	—
212	C₂×#41	—	2	8	no	—
213	C₂×#41	—	2	16	no	—
214	C₂²×Q₈	C₂³×C₃₁	1	3	yes	—
215	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
216	C₂²×D₄	C₂³×C₃₁	1	3	yes	—
217	C₂²×D₄	C₂³×C₃₁	1	6	yes	—
218	C₂²×D₄	C₂³×C₃₁	1	6	yes	—
219	C₂³×C₄	C₂³×C₃₁	1	6	yes	—
220	C₄⋊Q₈	—	2	12	no	—
221	#127	—	2	12	no	—
222	#125	—	2	24	no	—
223	#124	—	2	12	no	—
224	#124	—	4	12	no	—
225	#121	—	2	24	no	—
226	C₄×Q₈	—	2	8	no	—
227	C₄×Q₈	—	2	8	no	—
228	C₄×Q₈	—	2	12	no	—
229	C₄×Q₈	D₄×C₃₁	1	8	yes	—
230	C₄×D₄	—	2	12	no	—
231	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	—
234	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	—
235	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	—
236	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	—
237	C₂×C₄⋊C₄	C₂³×C₃₁	1	3	yes	—
238	C₂×C₂²⋊C₄	C₂³×C₃₁	1	6	yes	—
239	C₂×C₂²⋊C₄	C₂³×C₃₁	1	12	yes	—
240	C₂×C₂²⋊C₄	C₂³×C₃₁	1	24	yes	—
241	C₂×C₂²⋊C₄	C₂³×C₃₁	1	12	yes	—
242	C₂×C₄²	C₂³×C₃₁	1	6	yes	—
243	C₂×C₄²	C₂³×C₃₁	1	6	yes	—
244	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
245	C₂×C₄²	C₂³×C₃₁	1	6	yes	—
246	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
247	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
248	#95	C₂³×C₃₁	1	4	yes	—
249	#95	C₂³×C₃₁	1	12	yes	—
250	#95	C₂³×C₃₁	1	6	yes	—
251	C₃₁	#36583	1	1	yes	characteristic, direct product factor, Sylow
252	C₂⁴	C₂⁴×C₃₁	1	6	yes	—
253	#41	—	4	32	no	—
254	C₂×Q₈	—	2	6	no	—
255	C₂×Q₈	—	2	6	no	—
256	C₂×Q₈	—	2	6	no	—
257	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	—
258	C₂×Q₈	#41×C₃₁	1	8	yes	—
259	C₂×D₄	—	2	6	no	—
260	C₂×D₄	—	2	12	no	—
261	C₂×D₄	—	2	12	no	—
262	C₂×D₄	—	2	6	no	—
263	C₂×D₄	—	2	24	no	—
264	C₂×D₄	—	2	6	no	—
265	C₂×D₄	—	4	12	no	—
266	C₂²×C₄	—	2	12	no	—
267	C₂²×C₄	—	2	24	no	—
268	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
269	C₂²×C₄	C₂⁴×C₃₁	1	6	yes	—
270	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
271	C₂²×C₄	C₂⁴×C₃₁	1	6	yes	—
272	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
273	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
274	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
275	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	2	2	no	—
278	C₄⋊C₄	—	2	12	no	—
279	C₄⋊C₄	—	2	12	no	—
280	C₄⋊C₄	—	2	12	no	—
281	C₄⋊C₄	—	2	12	no	—
282	C₄⋊C₄	C₂×D₄×C₃₁	1	12	yes	—
283	C₂²⋊C₄	—	2	12	no	—
284	C₂²⋊C₄	—	2	24	no	—
285	C₂²⋊C₄	—	4	12	no	—
286	C₂²⋊C₄	—	4	24	no	—
287	C₄²	—	2	12	no	—
288	C₄²	—	2	12	no	—
289	C₄²	—	2	6	no	—
290	C₄²	—	4	6	no	—
291	C₄²	C₂×D₄×C₃₁	1	12	yes	—
292	C₄²	#41×C₃₁	1	4	yes	complemented
293	C₂³	—	2	6	no	—
294	C₂³	—	2	6	no	—
295	C₂³	—	2	12	no	—
296	C₂³	—	2	6	no	—
297	C₂³	—	2	12	no	—
298	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
299	Q₈	—	4	12	no	—
300	Q₈	C₃₁×#124	1	16	yes	complemented
301	D₄	—	4	24	no	—
302	D₄	—	4	12	no	—
303	D₄	—	8	12	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	6	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	6	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	6	no	—
311	C₂×C₄	—	2	6	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	6	no	—
314	C₂×C₄	—	2	6	no	—
315	C₂×C₄	—	2	6	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	4	24	no	—
318	C₂×C₄	C₂²×D₄×C₃₁	1	6	yes	—
319	C₂×C₄	C₂²×D₄×C₃₁	1	6	yes	—
320	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
321	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
322	C₂×C₄	C₂×#41×C₃₁	1	12	yes	—
323	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
324	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
325	C₂²	—	4	6	no	—
326	C₂²	—	4	6	no	—
327	C₂²	—	4	12	no	—
328	C₂²	—	4	6	no	—
329	C₂²	—	4	12	no	—
330	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
331	C₂²	C₂²×#41×C₃₁	1	2	yes	—
332	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
333	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
334	C₂²	C₃₁×#585	1	2	yes	—
335	C₄	—	2	4	no	—
336	C₄	—	2	6	no	—
337	C₄	—	4	2	no	—
338	C₄	—	4	6	no	—
339	C₄	—	4	2	no	—
340	C₄	—	4	6	no	—
341	C₄	C₂×C₃₁×#124	1	12	yes	—
342	C₄	C₃₁×#550	1	4	yes	—
343	C₂	—	8	6	no	—
344	C₂	C₂²×C₃₁×#124	1	1	yes	characteristic
345	C₂	C₂×C₃₁×#550	1	1	yes	characteristic
346	C₂	C₃₁×#3480	1	2	yes	—
347	C₂	C₃₁×#3500	1	1	yes	characteristic
348	C₂	C₃₁×#3517	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#550	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#557	C₂	semidirect
3. C₃₁×#2858	C₂	semidirect
4. C₃₁×#2548	C₂	semidirect
5. C₃₁×#2547	C₂	semidirect
6. C₃₁×#2490	C₂	semidirect
7. C₃₁×#2341	C₂	semidirect
8. C₄×C₃₁×#124	C₂	semidirect
9. C₄²×Q₈×C₃₁	C₂	semidirect
117. C₄²×C₃₁	#41	semidirect
118. #36583	C₃₁	direct (N × H)
126. Q₈×C₃₁	#124	semidirect
151. C₂×#557	C₂×C₃₁	semidirect
153. #2858	C₂×C₃₁	semidirect
154. #2548	C₂×C₃₁	semidirect
155. #2547	C₂×C₃₁	semidirect
156. #2490	C₂×C₃₁	semidirect
157. #2341	C₂×C₃₁	semidirect
158. C₄×#124	C₂×C₃₁	semidirect
159. C₄²×Q₈	C₂×C₃₁	semidirect
251. C₃₁	#36583	direct (N × H)
292. C₄²	#41×C₃₁	semidirect
300. Q₈	C₃₁×#124	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#557	2
C₂×C₃₁×#550	2
C₃₁×#2858	2
C₃₁×#2548	2
C₃₁×#2547	2
C₃₁×#2490	2
C₃₁×#2341	2
C₄×C₃₁×#124	2
C₄²×Q₈×C₃₁	2
#36583	31

Subgroups — C31×#36583 #21493342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#36583 #21493342