Subgroups — C₃₁×#21962 #21478721

Order 7936.

862 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2285	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2283	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1949	C₂	1	4	yes	maximal, complemented
5	C₃₁×#1948	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1947	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1808	C₂	1	2	yes	maximal
8	C₃₁×#1807	C₂	1	2	yes	maximal
9	C₂³×C₈×C₃₁	C₂²	1	2	yes	—
10	C₂×C₃₁×#117	—	2	1	no	—
11	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₃₁×#107	C₂²	1	4	yes	—
13	C₂×C₃₁×#106	C₂²	1	4	yes	—
14	C₂×C₃₁×C₄⋊C₈	C₄	1	8	yes	complemented
15	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
18	C₃₁×#384	C₂²	1	2	yes	—
19	C₃₁×#383	—	2	1	no	—
20	C₃₁×#382	—	2	1	no	—
21	C₃₁×#382	C₂²	1	2	yes	—
22	C₃₁×#381	—	2	1	no	—
23	C₃₁×#380	—	2	1	no	—
24	C₃₁×#380	C₂²	1	1	yes	characteristic
25	C₃₁×#380	C₂²	1	2	yes	—
26	C₃₁×#380	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₃₁	—	2	1	no	—
28	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
30	C₄×C₂²⋊C₄×C₃₁	—	2	1	no	—
31	C₃₁×#376	—	2	1	no	—
32	C₃₁×#340	C₂²	1	4	yes	—
33	C₃₁×#340	C₂²	1	4	yes	—
34	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₃₁	—	4	4	no	—
38	C₂²×C₈×C₃₁	C₂×C₄	1	8	yes	—
39	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
40	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
41	C₃₁×#117	—	4	4	no	—
42	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
43	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
44	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
45	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
46	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
47	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
49	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
50	C₂×C₄²×C₃₁	—	2	2	no	—
51	C₂×C₄²×C₃₁	—	2	2	no	—
52	C₂×C₄²×C₃₁	C₂×C₄	1	4	yes	—
53	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₃₁	Q₈	1	4	yes	—
56	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
58	C₃₁×#107	—	4	4	no	—
59	C₃₁×#106	—	4	4	no	—
60	C₃₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
61	C₃₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
62	C₃₁×C₄⋊C₈	C₂×C₄	1	8	yes	—
63	C₃₁×#95	—	2	1	no	—
64	C₃₁×#95	—	2	1	no	—
65	C₃₁×#95	—	2	2	no	—
66	C₃₁×#95	—	2	2	no	—
67	C₃₁×#95	—	2	2	no	—
68	C₃₁×#95	—	2	2	no	—
69	C₃₁×#95	—	2	2	no	—
70	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₃₁	—	2	2	no	—
72	C₂²×C₄×C₃₁	—	2	2	no	—
73	C₂²×C₄×C₃₁	—	2	4	no	—
74	C₂²×C₄×C₃₁	—	2	2	no	—
75	C₂²×C₄×C₃₁	—	2	2	no	—
76	C₂²×C₄×C₃₁	—	2	2	no	—
77	C₂²×C₄×C₃₁	—	2	2	no	—
78	C₂²×C₄×C₃₁	—	2	4	no	—
79	C₂²×C₄×C₃₁	C₄⋊C₄	1	4	yes	—
80	C₂²×C₄×C₃₁	C₄⋊C₄	1	4	yes	—
81	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
88	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
89	C₂×C₈×C₃₁	—	2	4	no	—
90	C₂×C₈×C₃₁	—	2	4	no	—
91	C₂×C₈×C₃₁	—	4	8	no	—
92	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
93	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
94	C₄⋊C₄×C₃₁	—	2	2	no	—
95	C₄⋊C₄×C₃₁	—	2	4	no	—
96	C₄⋊C₄×C₃₁	—	2	2	no	—
97	C₄⋊C₄×C₃₁	—	2	2	no	—
98	C₄⋊C₄×C₃₁	—	2	4	no	—
99	C₄⋊C₄×C₃₁	—	2	2	no	—
100	C₄⋊C₄×C₃₁	—	4	4	no	—
101	C₄⋊C₄×C₃₁	—	4	4	no	—
102	C₂²⋊C₄×C₃₁	—	4	2	no	—
103	C₂²⋊C₄×C₃₁	—	4	4	no	—
104	C₂²⋊C₄×C₃₁	—	4	2	no	—
105	C₄²×C₃₁	—	4	4	no	—
106	C₄²×C₃₁	—	4	4	no	—
107	C₄²×C₃₁	C₄⋊C₄	1	4	yes	—
108	C₄²×C₃₁	C₄⋊C₄	1	4	yes	—
109	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
110	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
111	C₄²×C₃₁	C₂×Q₈	1	2	yes	—
112	C₄²×C₃₁	C₂×Q₈	1	2	yes	—
113	#21962	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂³×C₃₁	—	2	2	no	—
115	C₂³×C₃₁	—	2	2	no	—
116	C₂³×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
117	C₂³×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
118	C₂³×C₃₁	#137	1	2	yes	—
119	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
120	C₂×C₄×C₃₁	—	2	2	no	—
121	C₂×C₄×C₃₁	—	2	2	no	—
122	C₂×C₄×C₃₁	—	2	1	no	—
123	C₂×C₄×C₃₁	—	2	1	no	—
124	C₂×C₄×C₃₁	—	2	1	no	—
125	C₂×C₄×C₃₁	—	2	1	no	—
126	C₂×C₄×C₃₁	—	2	8	no	—
127	C₂×C₄×C₃₁	—	2	2	no	—
128	C₂×C₄×C₃₁	—	2	2	no	—
129	C₂×C₄×C₃₁	—	2	4	no	—
130	C₂×C₄×C₃₁	—	2	8	no	—
131	C₂×C₄×C₃₁	—	4	4	no	—
132	C₂×C₄×C₃₁	—	4	2	no	—
133	C₂×C₄×C₃₁	—	4	2	no	—
134	C₂×C₄×C₃₁	—	4	2	no	—
135	C₂×C₄×C₃₁	—	4	2	no	—
136	C₂×C₄×C₃₁	—	4	4	no	—
137	C₂×C₄×C₃₁	—	4	4	no	—
138	C₂×C₄×C₃₁	—	4	2	no	—
139	C₂×C₄×C₃₁	—	4	2	no	—
140	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
141	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
142	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
143	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
144	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
145	C₂×C₄×C₃₁	#135	1	4	yes	—
146	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
149	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
150	C₈×C₃₁	—	2	4	no	—
151	C₈×C₃₁	—	2	4	no	—
152	C₂²×C₄⋊C₈	C₂×C₃₁	1	1	yes	characteristic
153	#2285	C₂×C₃₁	1	1	yes	characteristic
154	#2283	C₂×C₃₁	1	1	yes	characteristic
155	#1949	C₂×C₃₁	1	4	yes	complemented
156	#1948	C₂×C₃₁	1	2	yes	complemented
157	#1947	C₂×C₃₁	1	2	yes	complemented
158	#1808	C₂×C₃₁	1	2	yes	—
159	#1807	C₂×C₃₁	1	2	yes	—
160	C₂²×C₃₁	—	2	2	no	—
161	C₂²×C₃₁	—	2	2	no	—
162	C₂²×C₃₁	—	2	4	no	—
163	C₂²×C₃₁	—	2	4	no	—
164	C₂²×C₃₁	#428	1	4	yes	—
165	C₂²×C₃₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
166	C₂²×C₃₁	#537	1	2	yes	—
167	C₂²×C₃₁	C₂×#135	1	2	yes	—
168	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
169	C₂²×C₃₁	C₂×#137	1	1	yes	characteristic
170	C₄×C₃₁	—	2	2	no	—
171	C₄×C₃₁	—	2	2	no	—
172	C₄×C₃₁	—	2	2	no	—
173	C₄×C₃₁	—	2	2	no	—
174	C₄×C₃₁	—	8	2	no	—
175	C₄×C₃₁	—	8	4	no	—
176	C₄×C₃₁	—	8	2	no	—
177	C₄×C₃₁	#427	1	4	yes	—
178	C₄×C₃₁	#518	1	1	yes	characteristic
179	C₄×C₃₁	#519	1	1	yes	characteristic
180	C₄×C₃₁	#544	1	2	yes	—
181	C₂³×C₈	C₂²×C₃₁	1	2	yes	—
182	C₂×#117	—	2	1	no	—
183	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
184	C₂×#107	C₂²×C₃₁	1	4	yes	—
185	C₂×#106	C₂²×C₃₁	1	4	yes	—
186	C₂×C₄⋊C₈	C₄×C₃₁	1	8	yes	complemented
187	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
188	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
189	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
190	#384	C₂²×C₃₁	1	2	yes	—
191	#383	—	2	1	no	—
192	#382	—	2	1	no	—
193	#382	C₂²×C₃₁	1	2	yes	—
194	#381	—	2	1	no	—
195	#380	—	2	1	no	—
196	#380	C₂²×C₃₁	1	1	yes	characteristic
197	#380	C₂²×C₃₁	1	2	yes	—
198	#380	C₂²×C₃₁	1	1	yes	characteristic
199	C₄×C₄⋊C₄	—	2	1	no	—
200	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
201	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
202	C₄×C₂²⋊C₄	—	2	1	no	—
203	#376	—	2	1	no	—
204	#340	C₂²×C₃₁	1	4	yes	—
205	#340	C₂²×C₃₁	1	4	yes	—
206	C₂×C₃₁	—	2	4	no	—
207	C₂×C₃₁	#2316	1	1	yes	characteristic
208	C₂×C₃₁	C₂×#427	1	1	yes	characteristic
209	C₂×C₃₁	C₂×#428	1	1	yes	characteristic
210	C₂×C₃₁	#3247	1	2	yes	—
211	C₂×C₃₁	#3248	1	2	yes	—
212	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
213	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
214	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
215	C₂²×C₈	—	4	4	no	—
216	C₂²×C₈	C₂×C₄×C₃₁	1	8	yes	—
217	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
218	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
219	#117	—	4	4	no	—
220	C₂×C₄⋊C₄	—	2	2	no	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
223	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
224	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
225	C₂×C₂²⋊C₄	—	2	2	no	—
226	C₂×C₂²⋊C₄	—	2	1	no	—
227	C₂×C₂²⋊C₄	—	2	1	no	—
228	C₂×C₄²	—	2	2	no	—
229	C₂×C₄²	—	2	2	no	—
230	C₂×C₄²	C₂×C₄×C₃₁	1	4	yes	—
231	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
232	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
233	C₂×C₄²	Q₈×C₃₁	1	4	yes	—
234	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
235	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
236	#107	—	4	4	no	—
237	#106	—	4	4	no	—
238	C₄⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
239	C₄⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
240	C₄⋊C₈	C₂×C₄×C₃₁	1	8	yes	—
241	#95	—	2	1	no	—
242	#95	—	2	1	no	—
243	#95	—	2	2	no	—
244	#95	—	2	2	no	—
245	#95	—	2	2	no	—
246	#95	—	2	2	no	—
247	#95	—	2	2	no	—
248	C₃₁	#21962	1	1	yes	characteristic, direct product factor, Sylow
249	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	C₄⋊C₄×C₃₁	1	4	yes	—
259	C₂²×C₄	C₄⋊C₄×C₃₁	1	4	yes	—
260	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
261	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
262	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
264	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
266	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
267	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
268	C₂×C₈	—	2	4	no	—
269	C₂×C₈	—	2	4	no	—
270	C₂×C₈	—	4	8	no	—
271	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
272	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	—	2	4	no	—
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	2	2	no	—
278	C₄⋊C₄	—	2	4	no	—
279	C₄⋊C₄	—	4	4	no	—
280	C₄⋊C₄	—	4	4	no	—
281	C₂²⋊C₄	—	4	2	no	—
282	C₂²⋊C₄	—	4	4	no	—
283	C₂²⋊C₄	—	4	2	no	—
284	C₄²	—	4	4	no	—
285	C₄²	—	4	4	no	—
286	C₄²	C₄⋊C₄×C₃₁	1	4	yes	—
287	C₄²	C₄⋊C₄×C₃₁	1	4	yes	—
288	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
289	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
290	C₄²	C₂×Q₈×C₃₁	1	2	yes	—
291	C₄²	C₂×Q₈×C₃₁	1	2	yes	—
292	C₂³	—	2	2	no	—
293	C₂³	—	2	2	no	—
294	C₂³	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
295	C₂³	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
296	C₂³	C₃₁×#137	1	2	yes	—
297	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
298	C₂×C₄	—	2	8	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	8	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	4	4	no	—
310	C₂×C₄	—	4	2	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	4	no	—
315	C₂×C₄	—	4	4	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
319	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
320	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
321	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
322	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
323	C₂×C₄	C₃₁×#135	1	4	yes	—
324	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
325	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
326	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
327	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
328	C₈	—	2	4	no	—
329	C₈	—	2	4	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	2	2	no	—
332	C₂²	—	2	4	no	—
333	C₂²	—	2	4	no	—
334	C₂²	C₃₁×#428	1	4	yes	—
335	C₂²	C₂²×C₄⋊C₄×C₃₁	1	1	yes	characteristic
336	C₂²	C₃₁×#537	1	2	yes	—
337	C₂²	C₂×C₃₁×#135	1	2	yes	—
338	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
339	C₂²	C₂×C₃₁×#137	1	1	yes	characteristic
340	C₄	—	2	2	no	—
341	C₄	—	2	2	no	—
342	C₄	—	2	2	no	—
343	C₄	—	2	2	no	—
344	C₄	—	8	2	no	—
345	C₄	—	8	4	no	—
346	C₄	—	8	2	no	—
347	C₄	C₃₁×#427	1	4	yes	—
348	C₄	C₃₁×#518	1	1	yes	characteristic
349	C₄	C₃₁×#519	1	1	yes	characteristic
350	C₄	C₃₁×#544	1	2	yes	—
351	C₂	—	2	4	no	—
352	C₂	C₃₁×#2316	1	1	yes	characteristic
353	C₂	C₂×C₃₁×#427	1	1	yes	characteristic
354	C₂	C₂×C₃₁×#428	1	1	yes	characteristic
355	C₂	C₃₁×#3247	1	2	yes	—
356	C₂	C₃₁×#3248	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂⁴×C₃₁	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₃₁×#1949	C₂	semidirect
5. C₃₁×#1948	C₂	semidirect
6. C₃₁×#1947	C₂	semidirect
14. C₂×C₃₁×C₄⋊C₈	C₄	semidirect
113. #21962	C₃₁	direct (N × H)
155. #1949	C₂×C₃₁	semidirect
156. #1948	C₂×C₃₁	semidirect
157. #1947	C₂×C₃₁	semidirect
186. C₂×C₄⋊C₈	C₄×C₃₁	semidirect
248. C₃₁	#21962	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×C₄⋊C₈	2
C₃₁×#2285	2
C₃₁×#2283	2
C₃₁×#1949	2
C₃₁×#1948	2
C₃₁×#1947	2
C₃₁×#1808	2
C₃₁×#1807	2
#21962	31

Subgroups — C31×#21962 #21478721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#21962 #21478721