Subgroups — C₃₁×#2864 #16842797

Order 3968.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#389	C₂	1	4	yes	maximal
2	C₃₁×#387	C₂	1	8	yes	maximal
3	C₃₁×#382	C₂	1	2	yes	maximal
4	C₄³×C₃₁	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
6	C₂×C₄⋊C₄×C₃₁	C₂²	1	8	yes	—
7	C₂×C₄²×C₃₁	C₂²	1	4	yes	—
8	C₂×C₄²×C₃₁	C₂²	1	2	yes	—
9	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
10	C₃₁×#95	C₂²	1	8	yes	—
11	C₃₁×#95	C₂²	1	8	yes	—
12	C₂²×C₄×C₃₁	C₂³	1	8	yes	—
13	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
14	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
15	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
16	C₄⋊C₄×C₃₁	—	2	16	no	—
17	C₄⋊C₄×C₃₁	—	2	8	no	—
18	C₄²×C₃₁	—	2	8	no	—
19	C₄²×C₃₁	—	2	4	no	—
20	C₄²×C₃₁	Q₈	1	4	yes	—
21	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
22	C₂×C₄×C₃₁	—	2	4	no	—
23	C₂×C₄×C₃₁	—	2	4	no	—
24	C₂×C₄×C₃₁	—	2	4	no	—
25	C₂×C₄×C₃₁	—	2	8	no	—
26	C₂×C₄×C₃₁	—	2	16	no	—
27	C₂×C₄×C₃₁	C₂×Q₈	1	4	yes	—
28	C₂×C₄×C₃₁	C₂×Q₈	1	2	yes	—
29	C₂×C₄×C₃₁	#41	1	8	yes	—
30	C₂×C₄×C₃₁	#41	1	4	yes	—
31	#2864	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂²×C₃₁	C₂²×Q₈	1	1	yes	characteristic
33	C₂²×C₃₁	C₂×#41	1	2	yes	—
34	C₂²×C₃₁	C₂×#41	1	4	yes	—
35	C₄×C₃₁	—	2	8	no	—
36	C₄×C₃₁	—	2	4	no	—
37	C₄×C₃₁	—	4	8	no	—
38	C₄×C₃₁	#125	1	4	yes	—
39	#389	C₂×C₃₁	1	4	yes	—
40	#387	C₂×C₃₁	1	8	yes	—
41	#382	C₂×C₃₁	1	2	yes	—
42	C₄³	C₂×C₃₁	1	1	yes	characteristic
43	C₂×C₃₁	C₂×#125	1	1	yes	characteristic
44	C₂×C₃₁	#529	1	4	yes	—
45	C₂×C₃₁	#533	1	2	yes	—
46	C₂×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
47	C₂×C₄⋊C₄	C₂²×C₃₁	1	8	yes	—
48	C₂×C₄²	C₂²×C₃₁	1	4	yes	—
49	C₂×C₄²	C₂²×C₃₁	1	2	yes	—
50	C₂×C₄²	C₂²×C₃₁	1	1	yes	characteristic
51	#95	C₂²×C₃₁	1	8	yes	—
52	#95	C₂²×C₃₁	1	8	yes	—
53	C₃₁	#2864	1	1	yes	characteristic, direct product factor, Sylow
54	C₂²×C₄	C₂³×C₃₁	1	8	yes	—
55	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
56	C₂²×C₄	C₂³×C₃₁	1	4	yes	—
57	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
58	C₄⋊C₄	—	2	16	no	—
59	C₄⋊C₄	—	2	8	no	—
60	C₄²	—	2	8	no	—
61	C₄²	—	2	4	no	—
62	C₄²	Q₈×C₃₁	1	4	yes	—
63	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	2	4	no	—
66	C₂×C₄	—	2	4	no	—
67	C₂×C₄	—	2	8	no	—
68	C₂×C₄	—	2	16	no	—
69	C₂×C₄	C₂×Q₈×C₃₁	1	4	yes	—
70	C₂×C₄	C₂×Q₈×C₃₁	1	2	yes	—
71	C₂×C₄	#41×C₃₁	1	8	yes	—
72	C₂×C₄	#41×C₃₁	1	4	yes	—
73	C₂²	C₂²×Q₈×C₃₁	1	1	yes	characteristic
74	C₂²	C₂×#41×C₃₁	1	2	yes	—
75	C₂²	C₂×#41×C₃₁	1	4	yes	—
76	C₄	—	2	8	no	—
77	C₄	—	2	4	no	—
78	C₄	—	4	8	no	—
79	C₄	C₃₁×#125	1	4	yes	—
80	C₂	C₂×C₃₁×#125	1	1	yes	characteristic
81	C₂	C₃₁×#529	1	4	yes	—
82	C₂	C₃₁×#533	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃₁
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
31. #2864	C₃₁	direct (N × H)
53. C₃₁	#2864	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#389	2
C₃₁×#387	2
C₃₁×#382	2
C₄³×C₃₁	2
#2864	31

Subgroups — C31×#2864 #16842797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#2864 #16842797