Subgroups — C₃₁×#12899 #21469658

Order 7936.

370 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×C₄⋊C₁₆	C₂	1	6	yes	maximal
2	C₃₁×#1726	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₆×C₃₁	C₂²	1	4	yes	—
4	C₂×C₃₁×#97	C₄	1	3	yes	—
5	C₂×C₄×C₈×C₃₁	C₂²	1	3	yes	—
6	C₃₁×#376	C₄	1	1	yes	characteristic
7	C₃₁×C₄⋊C₁₆	—	2	12	no	—
8	C₂²×C₈×C₃₁	C₂×C₄	1	3	yes	—
9	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
10	C₂×C₄²×C₃₁	C₂×C₄	1	3	yes	—
11	C₂×C₁₆×C₃₁	—	2	12	no	—
12	C₃₁×#97	—	2	6	no	—
13	C₄×C₈×C₃₁	D₄	1	6	yes	—
14	C₄×C₈×C₃₁	Q₈	1	6	yes	—
15	C₃₁×#95	C₈	1	4	yes	—
16	C₂²×C₄×C₃₁	C₂×C₈	1	6	yes	—
17	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₈×C₃₁	—	2	6	no	—
19	C₂×C₈×C₃₁	C₄⋊C₄	1	6	yes	—
20	C₂×C₈×C₃₁	C₂×D₄	1	3	yes	—
21	C₂×C₈×C₃₁	C₂×Q₈	1	3	yes	—
22	C₄²×C₃₁	C₄⋊C₄	1	6	yes	—
23	C₄²×C₃₁	M₁₆	1	6	yes	—
24	C₁₆×C₃₁	—	4	4	no	—
25	#12899	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
26	C₂³×C₃₁	C₂²×C₈	1	1	yes	characteristic
27	C₂×C₄×C₃₁	—	2	12	no	—
28	C₂×C₄×C₃₁	C₄⋊C₈	1	12	yes	—
29	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	3	yes	—
30	C₂×C₄×C₃₁	C₂×M₁₆	1	3	yes	—
31	C₈×C₃₁	—	2	6	no	—
32	C₈×C₃₁	#127	1	1	yes	characteristic
33	C₈×C₃₁	C₄⋊Q₈	1	3	yes	—
34	C₂×C₄⋊C₁₆	C₂×C₃₁	1	6	yes	—
35	#1726	C₂×C₃₁	1	1	yes	characteristic
36	C₂²×C₃₁	C₂×C₄⋊C₈	1	3	yes	—
37	C₂²×C₃₁	#504	1	4	yes	—
38	C₄×C₃₁	—	2	12	no	—
39	C₄×C₃₁	#384	1	1	yes	characteristic
40	C₄×C₃₁	#423	1	3	yes	—
41	C₂²×C₁₆	C₂²×C₃₁	1	4	yes	—
42	C₂×#97	C₄×C₃₁	1	3	yes	—
43	C₂×C₄×C₈	C₂²×C₃₁	1	3	yes	—
44	#376	C₄×C₃₁	1	1	yes	characteristic
45	C₄⋊C₁₆	—	2	12	no	—
46	C₂×C₃₁	#1842	1	1	yes	characteristic
47	C₂×C₃₁	#2151	1	6	yes	—
48	C₂²×C₈	C₂×C₄×C₃₁	1	3	yes	—
49	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
50	C₂×C₄²	C₂×C₄×C₃₁	1	3	yes	—
51	C₂×C₁₆	—	2	12	no	—
52	#97	—	2	6	no	—
53	C₄×C₈	D₄×C₃₁	1	6	yes	—
54	C₄×C₈	Q₈×C₃₁	1	6	yes	—
55	#95	C₈×C₃₁	1	4	yes	—
56	C₃₁	#12899	1	1	yes	characteristic, direct product factor, Sylow
57	C₂²×C₄	C₂×C₈×C₃₁	1	6	yes	—
58	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
59	C₂×C₈	—	2	6	no	—
60	C₂×C₈	C₄⋊C₄×C₃₁	1	6	yes	—
61	C₂×C₈	C₂×D₄×C₃₁	1	3	yes	—
62	C₂×C₈	C₂×Q₈×C₃₁	1	3	yes	—
63	C₄²	C₄⋊C₄×C₃₁	1	6	yes	—
64	C₄²	M₁₆×C₃₁	1	6	yes	—
65	C₁₆	—	4	4	no	—
66	C₂³	C₂²×C₈×C₃₁	1	1	yes	characteristic
67	C₂×C₄	—	2	12	no	—
68	C₂×C₄	C₃₁×C₄⋊C₈	1	12	yes	—
69	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	3	yes	—
70	C₂×C₄	C₂×M₁₆×C₃₁	1	3	yes	—
71	C₈	—	2	6	no	—
72	C₈	C₃₁×#127	1	1	yes	characteristic
73	C₈	C₃₁×C₄⋊Q₈	1	3	yes	—
74	C₂²	C₂×C₃₁×C₄⋊C₈	1	3	yes	—
75	C₂²	C₃₁×#504	1	4	yes	—
76	C₄	—	2	12	no	—
77	C₄	C₃₁×#384	1	1	yes	characteristic
78	C₄	C₃₁×#423	1	3	yes	—
79	C₂	C₃₁×#1842	1	1	yes	characteristic
80	C₂	C₃₁×#2151	1	6	yes	—

	subgroup	G/H
center	C₂²×C₈×C₃₁	C₂³
commutator	C₂³	C₂²×C₈×C₃₁
Frattini, cosocle	C₂²×C₈	C₂³×C₃₁
socle, prime radical	C₂³×C₃₁	C₂²×C₈
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
25. #12899	C₃₁	direct (N × H)
56. C₃₁	#12899	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×C₄⋊C₁₆	2
C₃₁×#1726	2
#12899	31

Subgroups — C31×#12899 #21469658

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#12899 #21469658