Subgroups — C₃₁×#19114 #21475873

Order 7936.

714 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3147	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#3103	C₂	1	2	yes	maximal, complemented
3	C₂×C₈×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#1670	C₂	1	2	yes	maximal, complemented
5	C₃₁×#1668	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1666	C₂	1	4	yes	maximal, complemented
7	C₃₁×#1564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#1540	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₁×#135	—	2	1	no	—
10	C₂×C₃₁×#135	—	2	1	no	—
11	C₃₁×#532	C₂²	1	2	yes	—
12	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
13	C₃₁×#495	—	2	1	no	—
14	C₃₁×#495	—	2	1	no	—
15	C₃₁×#494	C₂²	1	1	yes	characteristic
16	C₃₁×#493	C₂²	1	1	yes	characteristic
17	C₃₁×#492	C₂²	1	2	yes	—
18	C₃₁×#481	—	2	2	no	—
19	C₃₁×#475	C₂²	1	4	yes	—
20	C₃₁×#460	C₂²	1	4	yes	—
21	C₃₁×#448	—	2	2	no	—
22	C₈×Q₈×C₃₁	—	2	1	no	—
23	C₈×Q₈×C₃₁	—	2	1	no	—
24	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
25	C₈×Q₈×C₃₁	C₂²	1	2	yes	—
26	C₄×SD₁₆×C₃₁	—	2	4	no	—
27	C₃₁×#431	C₂²	1	2	yes	—
28	C₂×C₃₁×C₄⋊C₈	—	2	1	no	—
29	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₃₁	—	2	1	no	—
31	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
32	C₃₁×#335	C₂²	1	2	yes	—
33	C₃₁×#334	C₂²	1	2	yes	—
34	C₃₁×#332	C₂²	1	4	yes	—
35	C₃₁×#331	C₂²	1	4	yes	—
36	C₂×#41×C₃₁	—	2	2	no	—
37	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
38	C₃₁×#135	—	4	4	no	—
39	C₃₁×#135	—	4	4	no	—
40	C₂×Q₁₆×C₃₁	—	2	1	no	—
41	C₂×Q₁₆×C₃₁	—	2	1	no	—
42	C₂×SD₁₆×C₃₁	—	2	4	no	—
43	C₂×SD₁₆×C₃₁	—	2	2	no	—
44	C₂×SD₁₆×C₃₁	—	2	2	no	—
45	C₂×D₈×C₃₁	—	2	1	no	—
46	C₂×D₈×C₃₁	—	2	1	no	—
47	C₂²×C₈×C₃₁	—	2	1	no	—
48	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
49	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
50	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
51	C₃₁×#127	C₂³	1	2	yes	—
52	C₃₁×#124	—	2	2	no	—
53	C₃₁×#121	—	2	2	no	—
54	C₃₁×#121	—	2	2	no	—
55	C₄×Q₈×C₃₁	—	2	1	no	—
56	C₄×Q₈×C₃₁	—	2	1	no	—
57	C₄×Q₈×C₃₁	D₄	1	2	yes	—
58	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
59	C₄×D₄×C₃₁	—	2	2	no	—
60	C₄×D₄×C₃₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₃₁	—	2	1	no	—
64	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
65	C₃₁×#106	—	2	4	no	—
66	C₃₁×C₄⋊C₈	—	2	2	no	—
67	C₃₁×C₄⋊C₈	—	2	2	no	—
68	C₃₁×C₄⋊C₈	—	2	1	no	—
69	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
70	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
71	C₃₁×#103	—	2	4	no	—
72	C₃₁×#102	—	2	4	no	—
73	C₃₁×C₂²⋊C₈	—	2	2	no	—
74	C₄×C₈×C₃₁	—	2	2	no	—
75	C₄×C₈×C₃₁	—	2	2	no	—
76	C₄×C₈×C₃₁	—	2	2	no	—
77	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
78	C₄×C₈×C₃₁	D₄	1	1	yes	characteristic
79	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
80	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
81	#41×C₃₁	—	4	4	no	—
82	#41×C₃₁	—	4	4	no	—
83	C₂×Q₈×C₃₁	—	2	4	no	—
84	C₂×Q₈×C₃₁	—	2	1	no	—
85	C₂×Q₈×C₃₁	—	2	2	no	—
86	C₂×Q₈×C₃₁	C₂×D₄	1	2	yes	—
87	C₂×D₄×C₃₁	—	2	2	no	—
88	C₂×D₄×C₃₁	—	2	2	no	—
89	C₂×D₄×C₃₁	—	2	2	no	—
90	C₂×D₄×C₃₁	—	4	2	no	—
91	C₂²×C₄×C₃₁	—	2	1	no	—
92	C₂²×C₄×C₃₁	—	2	1	no	—
93	C₂²×C₄×C₃₁	—	4	2	no	—
94	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
97	Q₁₆×C₃₁	—	4	2	no	—
98	Q₁₆×C₃₁	—	4	2	no	—
99	SD₁₆×C₃₁	—	4	4	no	—
100	SD₁₆×C₃₁	—	4	8	no	—
101	SD₁₆×C₃₁	—	4	4	no	—
102	D₈×C₃₁	—	4	2	no	—
103	D₈×C₃₁	—	4	2	no	—
104	C₂×C₈×C₃₁	—	2	2	no	—
105	C₂×C₈×C₃₁	—	2	2	no	—
106	C₂×C₈×C₃₁	—	2	4	no	—
107	C₂×C₈×C₃₁	—	4	2	no	—
108	C₂×C₈×C₃₁	SD₁₆	1	4	yes	complemented
109	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
113	C₄⋊C₄×C₃₁	—	2	2	no	—
114	C₄⋊C₄×C₃₁	—	2	1	no	—
115	C₄⋊C₄×C₃₁	—	2	2	no	—
116	C₄⋊C₄×C₃₁	—	2	2	no	—
117	C₄⋊C₄×C₃₁	—	2	2	no	—
118	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
119	C₂²⋊C₄×C₃₁	—	4	2	no	—
120	C₂²⋊C₄×C₃₁	—	4	2	no	—
121	C₄²×C₃₁	—	2	2	no	—
122	C₄²×C₃₁	—	2	2	no	—
123	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₃₁	#41	1	1	yes	characteristic
126	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
127	#19114	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂³×C₃₁	—	4	2	no	—
129	C₂³×C₃₁	#121	1	1	yes	characteristic
130	Q₈×C₃₁	—	2	4	no	—
131	Q₈×C₃₁	—	2	2	no	—
132	Q₈×C₃₁	—	4	2	no	—
133	Q₈×C₃₁	—	4	2	no	—
134	Q₈×C₃₁	#135	1	4	yes	complemented
135	D₄×C₃₁	—	4	2	no	—
136	D₄×C₃₁	—	4	4	no	—
137	D₄×C₃₁	—	4	2	no	—
138	D₄×C₃₁	—	8	2	no	—
139	D₄×C₃₁	—	8	4	no	—
140	C₂×C₄×C₃₁	—	2	4	no	—
141	C₂×C₄×C₃₁	—	2	2	no	—
142	C₂×C₄×C₃₁	—	2	2	no	—
143	C₂×C₄×C₃₁	—	2	2	no	—
144	C₂×C₄×C₃₁	—	4	1	no	—
145	C₂×C₄×C₃₁	—	4	2	no	—
146	C₂×C₄×C₃₁	—	4	2	no	—
147	C₂×C₄×C₃₁	—	8	4	no	—
148	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
149	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
150	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
151	C₂×C₄×C₃₁	C₂×SD₁₆	1	2	yes	—
152	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
153	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
156	C₈×C₃₁	—	2	1	no	—
157	C₈×C₃₁	—	2	1	no	—
158	C₈×C₃₁	—	4	4	no	—
159	C₈×C₃₁	—	4	2	no	—
160	C₈×C₃₁	C₂×SD₁₆	1	2	yes	—
161	C₈×C₃₁	C₂×SD₁₆	1	2	yes	—
162	#3147	C₂×C₃₁	1	1	yes	characteristic
163	#3103	C₂×C₃₁	1	2	yes	complemented
164	C₂×C₈×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
165	#1670	C₂×C₃₁	1	2	yes	complemented
166	#1668	C₂×C₃₁	1	2	yes	complemented
167	#1666	C₂×C₃₁	1	4	yes	complemented
168	#1564	C₂×C₃₁	1	1	yes	characteristic, complemented
169	#1540	C₂×C₃₁	1	2	yes	complemented
170	C₂²×C₃₁	—	2	1	no	—
171	C₂²×C₃₁	—	2	1	no	—
172	C₂²×C₃₁	—	8	2	no	—
173	C₂²×C₃₁	—	8	2	no	—
174	C₂²×C₃₁	—	8	2	no	—
175	C₂²×C₃₁	#460	1	2	yes	—
176	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
177	C₄×C₃₁	—	2	4	no	—
178	C₄×C₃₁	—	2	1	no	—
179	C₄×C₃₁	—	2	1	no	—
180	C₄×C₃₁	—	2	1	no	—
181	C₄×C₃₁	—	4	2	no	—
182	C₄×C₃₁	—	8	2	no	—
183	C₄×C₃₁	#460	1	2	yes	—
184	C₄×C₃₁	C₂²×SD₁₆	1	1	yes	characteristic
185	C₄×C₃₁	C₂×#135	1	2	yes	—
186	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂×#135	—	2	1	no	—
188	C₂×#135	—	2	1	no	—
189	#532	C₂²×C₃₁	1	2	yes	—
190	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
191	#495	—	2	1	no	—
192	#495	—	2	1	no	—
193	#494	C₂²×C₃₁	1	1	yes	characteristic
194	#493	C₂²×C₃₁	1	1	yes	characteristic
195	#492	C₂²×C₃₁	1	2	yes	—
196	#481	—	2	2	no	—
197	#475	C₂²×C₃₁	1	4	yes	—
198	#460	C₂²×C₃₁	1	4	yes	—
199	#448	—	2	2	no	—
200	C₈×Q₈	—	2	1	no	—
201	C₈×Q₈	—	2	1	no	—
202	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
203	C₈×Q₈	C₂²×C₃₁	1	2	yes	—
204	C₄×SD₁₆	—	2	4	no	—
205	#431	C₂²×C₃₁	1	2	yes	—
206	C₂×C₄⋊C₈	—	2	1	no	—
207	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
208	C₂×C₄×C₈	—	2	1	no	—
209	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
210	#335	C₂²×C₃₁	1	2	yes	—
211	#334	C₂²×C₃₁	1	2	yes	—
212	#332	C₂²×C₃₁	1	4	yes	—
213	#331	C₂²×C₃₁	1	4	yes	—
214	C₂×C₃₁	—	2	2	no	—
215	C₂×C₃₁	—	16	2	no	—
216	C₂×C₃₁	C₂×#460	1	1	yes	characteristic
217	C₂×C₃₁	#3050	1	1	yes	characteristic
218	C₂×C₃₁	#3067	1	1	yes	characteristic
219	C₂×#41	—	2	2	no	—
220	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
221	#135	—	4	4	no	—
222	#135	—	4	4	no	—
223	C₂×Q₁₆	—	2	1	no	—
224	C₂×Q₁₆	—	2	1	no	—
225	C₂×SD₁₆	—	2	4	no	—
226	C₂×SD₁₆	—	2	2	no	—
227	C₂×SD₁₆	—	2	2	no	—
228	C₂×D₈	—	2	1	no	—
229	C₂×D₈	—	2	1	no	—
230	C₂²×C₈	—	2	1	no	—
231	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
232	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
233	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
234	#127	C₂³×C₃₁	1	2	yes	—
235	#124	—	2	2	no	—
236	#121	—	2	2	no	—
237	#121	—	2	2	no	—
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×Q₈	D₄×C₃₁	1	2	yes	—
241	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
242	C₄×D₄	—	2	2	no	—
243	C₄×D₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
246	C₂×C₄²	—	2	1	no	—
247	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
248	#106	—	2	4	no	—
249	C₄⋊C₈	—	2	2	no	—
250	C₄⋊C₈	—	2	2	no	—
251	C₄⋊C₈	—	2	1	no	—
252	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
253	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
254	#103	—	2	4	no	—
255	#102	—	2	4	no	—
256	C₂²⋊C₈	—	2	2	no	—
257	C₄×C₈	—	2	2	no	—
258	C₄×C₈	—	2	2	no	—
259	C₄×C₈	—	2	2	no	—
260	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
261	C₄×C₈	D₄×C₃₁	1	1	yes	characteristic
262	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
263	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
264	C₃₁	#19114	1	1	yes	characteristic, direct product factor, Sylow
265	#41	—	4	4	no	—
266	#41	—	4	4	no	—
267	C₂×Q₈	—	2	4	no	—
268	C₂×Q₈	—	2	1	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	C₂×D₄×C₃₁	1	2	yes	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	4	2	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
279	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
280	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
281	Q₁₆	—	4	2	no	—
282	Q₁₆	—	4	2	no	—
283	SD₁₆	—	4	4	no	—
284	SD₁₆	—	4	8	no	—
285	SD₁₆	—	4	4	no	—
286	D₈	—	4	2	no	—
287	D₈	—	4	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	—	4	2	no	—
292	C₂×C₈	SD₁₆×C₃₁	1	4	yes	complemented
293	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
294	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
295	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
296	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
303	C₂²⋊C₄	—	4	2	no	—
304	C₂²⋊C₄	—	4	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
308	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
309	C₄²	#41×C₃₁	1	1	yes	characteristic
310	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
311	C₂³	—	4	2	no	—
312	C₂³	C₃₁×#121	1	1	yes	characteristic
313	Q₈	—	2	4	no	—
314	Q₈	—	2	2	no	—
315	Q₈	—	4	2	no	—
316	Q₈	—	4	2	no	—
317	Q₈	C₃₁×#135	1	4	yes	complemented
318	D₄	—	4	2	no	—
319	D₄	—	4	4	no	—
320	D₄	—	4	2	no	—
321	D₄	—	8	2	no	—
322	D₄	—	8	4	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	8	4	no	—
331	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
332	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
333	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
334	C₂×C₄	C₂×SD₁₆×C₃₁	1	2	yes	—
335	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
336	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
337	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
338	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
339	C₈	—	2	1	no	—
340	C₈	—	2	1	no	—
341	C₈	—	4	4	no	—
342	C₈	—	4	2	no	—
343	C₈	C₂×SD₁₆×C₃₁	1	2	yes	—
344	C₈	C₂×SD₁₆×C₃₁	1	2	yes	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	8	2	no	—
348	C₂²	—	8	2	no	—
349	C₂²	—	8	2	no	—
350	C₂²	C₃₁×#460	1	2	yes	—
351	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
352	C₄	—	2	4	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	4	2	no	—
357	C₄	—	8	2	no	—
358	C₄	C₃₁×#460	1	2	yes	—
359	C₄	C₂²×SD₁₆×C₃₁	1	1	yes	characteristic
360	C₄	C₂×C₃₁×#135	1	2	yes	—
361	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
362	C₂	—	2	2	no	—
363	C₂	—	16	2	no	—
364	C₂	C₂×C₃₁×#460	1	1	yes	characteristic
365	C₂	C₃₁×#3050	1	1	yes	characteristic
366	C₂	C₃₁×#3067	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂×#121
prime radical	C₃₁×#3147	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#3103	C₂	semidirect
3. C₂×C₈×Q₈×C₃₁	C₂	semidirect
4. C₃₁×#1670	C₂	semidirect
5. C₃₁×#1668	C₂	semidirect
6. C₃₁×#1666	C₂	semidirect
7. C₃₁×#1564	C₂	semidirect
8. C₃₁×#1540	C₂	semidirect
108. C₂×C₈×C₃₁	SD₁₆	semidirect
127. #19114	C₃₁	direct (N × H)
134. Q₈×C₃₁	#135	semidirect
163. #3103	C₂×C₃₁	semidirect
164. C₂×C₈×Q₈	C₂×C₃₁	semidirect
165. #1670	C₂×C₃₁	semidirect
166. #1668	C₂×C₃₁	semidirect
167. #1666	C₂×C₃₁	semidirect
168. #1564	C₂×C₃₁	semidirect
169. #1540	C₂×C₃₁	semidirect
264. C₃₁	#19114	direct (N × H)
292. C₂×C₈	SD₁₆×C₃₁	semidirect
317. Q₈	C₃₁×#135	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#3147	2
C₃₁×#3103	2
C₂×C₈×Q₈×C₃₁	2
C₃₁×#1670	2
C₃₁×#1668	2
C₃₁×#1666	2
C₃₁×#1564	2
C₃₁×#1540	2
#19114	31

Subgroups — C31×#19114 #21475873

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#19114 #21475873