Subgroups — C₃₁×#21302 #21478061

Order 7936.

1170 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#533	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1985	C₂	1	4	yes	maximal, complemented
5	C₃₁×#1984	C₂	1	4	yes	maximal, complemented
6	C₃₁×#1729	C₂	1	4	yes	maximal
7	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
8	C₂³×C₈×C₃₁	C₂²	1	2	yes	—
9	C₃₁×#533	—	2	4	no	—
10	C₃₁×#533	—	2	4	no	—
11	C₂×C₃₁×C₄⋊Q₈	C₄	1	1	yes	characteristic
12	C₂×C₃₁×C₄⋊Q₈	C₄	1	1	yes	characteristic
13	C₂×C₃₁×#125	C₄	1	2	yes	—
14	C₂×C₃₁×C₂²⋊Q₈	C₄	1	2	yes	—
15	C₂×C₃₁×C₂²⋊Q₈	C₄	1	2	yes	—
16	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
17	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
18	C₂×C₃₁×#117	C₂²	1	2	yes	—
19	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×C₄⋊C₈	—	2	4	no	—
21	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
23	C₄×M₁₆×C₃₁	—	2	4	no	—
24	C₂×C₃₁×#97	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
26	C₃₁×#336	C₂²	1	16	yes	—
27	C₂²×Q₈×C₃₁	C₂×C₄	1	2	yes	—
28	C₂²×Q₈×C₃₁	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
32	C₂×M₁₆×C₃₁	—	2	4	no	—
33	C₂×M₁₆×C₃₁	—	2	4	no	—
34	C₂×M₁₆×C₃₁	Q₈	1	8	yes	complemented
35	C₂²×C₈×C₃₁	—	2	4	no	—
36	C₂²×C₈×C₃₁	—	2	8	no	—
37	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
38	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
39	C₃₁×C₄⋊Q₈	—	2	4	no	—
40	C₃₁×C₄⋊Q₈	—	2	4	no	—
41	C₃₁×#125	—	2	8	no	—
42	C₃₁×C₂²⋊Q₈	—	2	8	no	—
43	C₃₁×C₂²⋊Q₈	—	2	8	no	—
44	C₄×Q₈×C₃₁	—	2	4	no	—
45	C₄×Q₈×C₃₁	—	2	4	no	—
46	C₄×Q₈×C₃₁	—	2	4	no	—
47	C₄×Q₈×C₃₁	—	2	4	no	—
48	C₃₁×#117	—	2	4	no	—
49	C₃₁×#117	—	2	4	no	—
50	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
53	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
54	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
56	C₂×C₂²⋊C₄×C₃₁	C₂×C₄	1	4	yes	—
57	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₃₁	D₄	1	4	yes	—
60	C₂×C₄²×C₃₁	D₄	1	4	yes	—
61	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
62	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
64	C₃₁×C₄⋊C₈	—	2	4	no	—
65	C₃₁×C₄⋊C₈	—	2	4	no	—
66	C₃₁×#97	—	2	4	no	—
67	C₄×C₈×C₃₁	—	2	4	no	—
68	C₂⁴×C₃₁	C₂²×C₄	1	1	yes	characteristic
69	C₂×Q₈×C₃₁	—	2	4	no	—
70	C₂×Q₈×C₃₁	—	2	4	no	—
71	C₂×Q₈×C₃₁	—	2	8	no	—
72	C₂×Q₈×C₃₁	—	4	4	no	—
73	C₂²×C₄×C₃₁	—	2	4	no	—
74	C₂²×C₄×C₃₁	—	4	2	no	—
75	C₂²×C₄×C₃₁	C₂²⋊C₄	1	4	yes	—
76	C₂²×C₄×C₃₁	C₂²⋊C₄	1	4	yes	—
77	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
78	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
79	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₃₁	C₂×Q₈	1	4	yes	—
87	C₂²×C₄×C₃₁	#41	1	4	yes	—
88	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
89	M₁₆×C₃₁	—	2	16	no	—
90	C₂×C₈×C₃₁	—	2	4	no	—
91	C₂×C₈×C₃₁	—	2	4	no	—
92	C₂×C₈×C₃₁	—	2	4	no	—
93	C₂×C₈×C₃₁	—	2	8	no	—
94	C₂×C₈×C₃₁	—	4	8	no	—
95	C₂×C₈×C₃₁	C₂×Q₈	1	8	yes	—
96	C₄⋊C₄×C₃₁	—	2	4	no	—
97	C₄⋊C₄×C₃₁	—	2	4	no	—
98	C₄⋊C₄×C₃₁	—	2	8	no	—
99	C₄⋊C₄×C₃₁	—	2	8	no	—
100	C₄⋊C₄×C₃₁	—	2	4	no	—
101	C₄⋊C₄×C₃₁	—	2	4	no	—
102	C₂²⋊C₄×C₃₁	—	2	8	no	—
103	C₄²×C₃₁	—	2	4	no	—
104	C₄²×C₃₁	—	2	4	no	—
105	C₄²×C₃₁	C₂²⋊C₄	1	4	yes	—
106	C₄²×C₃₁	C₂²⋊C₄	1	4	yes	—
107	C₄²×C₃₁	C₂×D₄	1	2	yes	—
108	C₄²×C₃₁	C₂×D₄	1	2	yes	—
109	C₄²×C₃₁	C₂×D₄	1	2	yes	—
110	C₄²×C₃₁	C₂×D₄	1	2	yes	—
111	#21302	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂³×C₃₁	—	2	2	no	—
113	C₂³×C₃₁	—	2	2	no	—
114	C₂³×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
115	C₂³×C₃₁	C₄×Q₈	1	4	yes	—
116	C₂³×C₃₁	C₂³×C₄	1	1	yes	characteristic
117	Q₈×C₃₁	—	4	8	no	—
118	Q₈×C₃₁	—	4	8	no	—
119	C₂×C₄×C₃₁	—	2	2	no	—
120	C₂×C₄×C₃₁	—	2	2	no	—
121	C₂×C₄×C₃₁	—	2	2	no	—
122	C₂×C₄×C₃₁	—	2	8	no	—
123	C₂×C₄×C₃₁	—	2	4	no	—
124	C₂×C₄×C₃₁	—	2	4	no	—
125	C₂×C₄×C₃₁	—	2	8	no	—
126	C₂×C₄×C₃₁	—	2	8	no	—
127	C₂×C₄×C₃₁	—	4	4	no	—
128	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
129	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
130	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
131	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
132	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
133	C₂×C₄×C₃₁	C₄×Q₈	1	4	yes	—
134	C₂×C₄×C₃₁	C₂²⋊Q₈	1	8	yes	—
135	C₂×C₄×C₃₁	#124	1	4	yes	—
136	C₂×C₄×C₃₁	C₄⋊Q₈	1	4	yes	—
137	C₂×C₄×C₃₁	#131	1	4	yes	—
138	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
139	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
140	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
141	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
142	C₈×C₃₁	—	2	8	no	—
143	C₈×C₃₁	—	4	4	no	—
144	C₂×#533	C₂×C₃₁	1	1	yes	characteristic
145	C₂²×C₄⋊C₈	C₂×C₃₁	1	1	yes	characteristic
146	C₂×C₄×M₁₆	C₂×C₃₁	1	1	yes	characteristic
147	#1985	C₂×C₃₁	1	4	yes	complemented
148	#1984	C₂×C₃₁	1	4	yes	complemented
149	#1729	C₂×C₃₁	1	4	yes	—
150	C₂²×C₃₁	—	2	2	no	—
151	C₂²×C₃₁	—	2	2	no	—
152	C₂²×C₃₁	—	2	8	no	—
153	C₂²×C₃₁	#391	1	4	yes	—
154	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₃₁	C₂×C₄×Q₈	1	2	yes	—
156	C₂²×C₃₁	C₂×#131	1	2	yes	—
157	C₂²×C₃₁	#568	1	2	yes	—
158	C₄×C₃₁	—	2	2	no	—
159	C₄×C₃₁	—	2	2	no	—
160	C₄×C₃₁	—	2	2	no	—
161	C₄×C₃₁	—	4	4	no	—
162	C₄×C₃₁	—	4	4	no	—
163	C₄×C₃₁	#391	1	4	yes	—
164	C₄×C₃₁	#408	1	4	yes	—
165	C₄×C₃₁	C₂×C₂²⋊Q₈	1	2	yes	—
166	C₄×C₃₁	C₂×#124	1	1	yes	characteristic
167	C₄×C₃₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
168	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
169	C₂³×C₈	C₂²×C₃₁	1	2	yes	—
170	#533	—	2	4	no	—
171	#533	—	2	4	no	—
172	C₂×C₄⋊Q₈	C₄×C₃₁	1	1	yes	characteristic
173	C₂×C₄⋊Q₈	C₄×C₃₁	1	1	yes	characteristic
174	C₂×#125	C₄×C₃₁	1	2	yes	—
175	C₂×C₂²⋊Q₈	C₄×C₃₁	1	2	yes	—
176	C₂×C₂²⋊Q₈	C₄×C₃₁	1	2	yes	—
177	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
178	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
179	C₂×#117	C₂²×C₃₁	1	2	yes	—
180	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
181	C₂×C₄⋊C₈	—	2	4	no	—
182	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
183	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
184	C₄×M₁₆	—	2	4	no	—
185	C₂×#97	C₂²×C₃₁	1	2	yes	—
186	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
187	#336	C₂²×C₃₁	1	16	yes	—
188	C₂×C₃₁	—	2	4	no	—
189	C₂×C₃₁	C₂×#391	1	1	yes	characteristic
190	C₂×C₃₁	C₂×#408	1	1	yes	characteristic
191	C₂×C₃₁	#2879	1	1	yes	characteristic
192	C₂×C₃₁	#2962	1	4	yes	—
193	C₂²×Q₈	C₂×C₄×C₃₁	1	2	yes	—
194	C₂²×Q₈	C₂×C₄×C₃₁	1	2	yes	—
195	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
196	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
197	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
198	C₂×M₁₆	—	2	4	no	—
199	C₂×M₁₆	—	2	4	no	—
200	C₂×M₁₆	Q₈×C₃₁	1	8	yes	complemented
201	C₂²×C₈	—	2	4	no	—
202	C₂²×C₈	—	2	8	no	—
203	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
204	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
205	C₄⋊Q₈	—	2	4	no	—
206	C₄⋊Q₈	—	2	4	no	—
207	#125	—	2	8	no	—
208	C₂²⋊Q₈	—	2	8	no	—
209	C₂²⋊Q₈	—	2	8	no	—
210	C₄×Q₈	—	2	4	no	—
211	C₄×Q₈	—	2	4	no	—
212	C₄×Q₈	—	2	4	no	—
213	C₄×Q₈	—	2	4	no	—
214	#117	—	2	4	no	—
215	#117	—	2	4	no	—
216	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
217	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
218	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
219	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
220	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
221	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
222	C₂×C₂²⋊C₄	C₂×C₄×C₃₁	1	4	yes	—
223	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
224	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
225	C₂×C₄²	D₄×C₃₁	1	4	yes	—
226	C₂×C₄²	D₄×C₃₁	1	4	yes	—
227	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
228	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
229	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
230	C₄⋊C₈	—	2	4	no	—
231	C₄⋊C₈	—	2	4	no	—
232	#97	—	2	4	no	—
233	C₄×C₈	—	2	4	no	—
234	C₃₁	#21302	1	1	yes	characteristic, direct product factor, Sylow
235	C₂⁴	C₂²×C₄×C₃₁	1	1	yes	characteristic
236	C₂×Q₈	—	2	4	no	—
237	C₂×Q₈	—	2	4	no	—
238	C₂×Q₈	—	2	8	no	—
239	C₂×Q₈	—	4	4	no	—
240	C₂²×C₄	—	2	4	no	—
241	C₂²×C₄	—	4	2	no	—
242	C₂²×C₄	C₂²⋊C₄×C₃₁	1	4	yes	—
243	C₂²×C₄	C₂²⋊C₄×C₃₁	1	4	yes	—
244	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
245	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
246	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
247	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
248	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
249	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
250	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
251	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
252	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
253	C₂²×C₄	C₂×Q₈×C₃₁	1	4	yes	—
254	C₂²×C₄	#41×C₃₁	1	4	yes	—
255	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
256	M₁₆	—	2	16	no	—
257	C₂×C₈	—	2	4	no	—
258	C₂×C₈	—	2	4	no	—
259	C₂×C₈	—	2	4	no	—
260	C₂×C₈	—	2	8	no	—
261	C₂×C₈	—	4	8	no	—
262	C₂×C₈	C₂×Q₈×C₃₁	1	8	yes	—
263	C₄⋊C₄	—	2	4	no	—
264	C₄⋊C₄	—	2	4	no	—
265	C₄⋊C₄	—	2	8	no	—
266	C₄⋊C₄	—	2	8	no	—
267	C₄⋊C₄	—	2	4	no	—
268	C₄⋊C₄	—	2	4	no	—
269	C₂²⋊C₄	—	2	8	no	—
270	C₄²	—	2	4	no	—
271	C₄²	—	2	4	no	—
272	C₄²	C₂²⋊C₄×C₃₁	1	4	yes	—
273	C₄²	C₂²⋊C₄×C₃₁	1	4	yes	—
274	C₄²	C₂×D₄×C₃₁	1	2	yes	—
275	C₄²	C₂×D₄×C₃₁	1	2	yes	—
276	C₄²	C₂×D₄×C₃₁	1	2	yes	—
277	C₄²	C₂×D₄×C₃₁	1	2	yes	—
278	C₂³	—	2	2	no	—
279	C₂³	—	2	2	no	—
280	C₂³	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
281	C₂³	C₄×Q₈×C₃₁	1	4	yes	—
282	C₂³	C₂³×C₄×C₃₁	1	1	yes	characteristic
283	Q₈	—	4	8	no	—
284	Q₈	—	4	8	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	8	no	—
289	C₂×C₄	—	2	4	no	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	2	8	no	—
292	C₂×C₄	—	2	8	no	—
293	C₂×C₄	—	4	4	no	—
294	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
295	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
296	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
297	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
298	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
299	C₂×C₄	C₄×Q₈×C₃₁	1	4	yes	—
300	C₂×C₄	C₃₁×C₂²⋊Q₈	1	8	yes	—
301	C₂×C₄	C₃₁×#124	1	4	yes	—
302	C₂×C₄	C₃₁×C₄⋊Q₈	1	4	yes	—
303	C₂×C₄	C₃₁×#131	1	4	yes	—
304	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
305	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
306	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
307	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
308	C₈	—	2	8	no	—
309	C₈	—	4	4	no	—
310	C₂²	—	2	2	no	—
311	C₂²	—	2	2	no	—
312	C₂²	—	2	8	no	—
313	C₂²	C₃₁×#391	1	4	yes	—
314	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
315	C₂²	C₂×C₄×Q₈×C₃₁	1	2	yes	—
316	C₂²	C₂×C₃₁×#131	1	2	yes	—
317	C₂²	C₃₁×#568	1	2	yes	—
318	C₄	—	2	2	no	—
319	C₄	—	2	2	no	—
320	C₄	—	2	2	no	—
321	C₄	—	4	4	no	—
322	C₄	—	4	4	no	—
323	C₄	C₃₁×#391	1	4	yes	—
324	C₄	C₃₁×#408	1	4	yes	—
325	C₄	C₂×C₃₁×C₂²⋊Q₈	1	2	yes	—
326	C₄	C₂×C₃₁×#124	1	1	yes	characteristic
327	C₄	C₂×C₃₁×C₄⋊Q₈	1	1	yes	characteristic
328	C₂	—	2	4	no	—
329	C₂	C₂×C₃₁×#391	1	1	yes	characteristic
330	C₂	C₂×C₃₁×#408	1	1	yes	characteristic
331	C₂	C₃₁×#2879	1	1	yes	characteristic
332	C₂	C₃₁×#2962	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₃₁×#1985	C₂	semidirect
5. C₃₁×#1984	C₂	semidirect
34. C₂×M₁₆×C₃₁	Q₈	semidirect
111. #21302	C₃₁	direct (N × H)
147. #1985	C₂×C₃₁	semidirect
148. #1984	C₂×C₃₁	semidirect
200. C₂×M₁₆	Q₈×C₃₁	semidirect
234. C₃₁	#21302	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#533	2
C₂²×C₃₁×C₄⋊C₈	2
C₂×C₄×M₁₆×C₃₁	2
C₃₁×#1985	2
C₃₁×#1984	2
C₃₁×#1729	2
#21302	31

Subgroups — C31×#21302 #21478061

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#21302 #21478061