Subgroups — C₃₁×#358 #14520539

Order 1984.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#107	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₃₁	—	2	1	no	—
5	Q₁₆×C₃₁	—	2	1	no	—
6	Q₁₆×C₃₁	C₄	1	2	yes	complemented
7	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
8	C₄⋊C₄×C₃₁	—	2	1	no	—
9	C₁₆×C₃₁	—	2	1	no	—
10	Q₈×C₃₁	—	2	2	no	—
11	Q₈×C₃₁	—	4	1	no	—
12	C₂×C₄×C₃₁	—	4	1	no	—
13	C₂×C₄×C₃₁	—	4	1	no	—
14	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
15	C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
16	C₈×C₃₁	D₄	1	1	yes	characteristic
17	C₂²×C₃₁	D₈	1	1	yes	characteristic
18	C₄×C₃₁	—	4	2	no	—
19	C₄×C₃₁	—	8	1	no	—
20	C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₃₁	SD₁₆	1	1	yes	characteristic
22	#358	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₂×C₃₁	#102	1	1	yes	characteristic
24	C₂×C₃₁	SD₃₂	1	1	yes	characteristic
25	C₂×C₃₁	Q₃₂	1	1	yes	characteristic
26	C₂×Q₁₆	C₂×C₃₁	1	1	yes	characteristic
27	C₂×C₁₆	C₂×C₃₁	1	1	yes	characteristic
28	#107	C₂×C₃₁	1	1	yes	characteristic
29	C₃₁	#358	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×Q₈	—	2	1	no	—
31	Q₁₆	—	2	1	no	—
32	Q₁₆	C₄×C₃₁	1	2	yes	complemented
33	C₂×C₈	C₂²×C₃₁	1	1	yes	characteristic
34	C₄⋊C₄	—	2	1	no	—
35	C₁₆	—	2	1	no	—
36	Q₈	—	2	2	no	—
37	Q₈	—	4	1	no	—
38	C₂×C₄	—	4	1	no	—
39	C₂×C₄	—	4	1	no	—
40	C₂×C₄	D₄×C₃₁	1	1	yes	characteristic
41	C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
42	C₈	D₄×C₃₁	1	1	yes	characteristic
43	C₂²	D₈×C₃₁	1	1	yes	characteristic
44	C₄	—	4	2	no	—
45	C₄	—	8	1	no	—
46	C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
47	C₄	SD₁₆×C₃₁	1	1	yes	characteristic
48	C₂	C₃₁×#102	1	1	yes	characteristic
49	C₂	C₃₁×SD₃₂	1	1	yes	characteristic
50	C₂	C₃₁×Q₃₂	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₃₁	D₈
commutator	C₈	C₂×C₄×C₃₁
Frattini, cosocle	C₂×C₈	C₂²×C₃₁
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄×C₃₁ ◁ C₂×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. Q₁₆×C₃₁	C₄	semidirect
22. #358	C₃₁	direct (N × H)
29. C₃₁	#358	direct (N × H)
32. Q₁₆	C₄×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×C₃₁	2
C₂×C₁₆×C₃₁	2
C₃₁×#107	2
#358	31

Subgroups — C31×#358 #14520539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#358 #14520539