Subgroups — C₃₁×#7546 #21464305

Order 7936.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×C₆₄	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#1423	C₂	1	2	yes	maximal
3	C₂×C₃₁×C₃₂	C₂²	1	1	yes	characteristic
4	C₃₁×#366	—	2	2	no	—
5	C₃₁×C₆₄	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₃₁	D₄	1	1	yes	characteristic
7	C₃₁×#107	—	4	2	no	—
8	C₃₁×C₃₂	C₂×C₄	1	1	yes	characteristic
9	C₃₁×C₃₂	Q₈	1	1	yes	characteristic
10	C₂×C₈×C₃₁	D₈	1	1	yes	characteristic
11	C₄⋊C₄×C₃₁	—	8	2	no	—
12	C₁₆×C₃₁	C₄⋊C₄	1	1	yes	characteristic
13	C₁₆×C₃₁	Q₁₆	1	1	yes	characteristic
14	#7546	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂×C₄×C₃₁	—	16	2	no	—
16	C₂×C₄×C₃₁	D₁₆	1	1	yes	characteristic
17	C₈×C₃₁	#107	1	1	yes	characteristic
18	C₈×C₃₁	Q₃₂	1	1	yes	characteristic
19	C₂×C₆₄	C₂×C₃₁	1	1	yes	characteristic
20	#1423	C₂×C₃₁	1	2	yes	—
21	C₂²×C₃₁	D₃₂	1	1	yes	characteristic
22	C₄×C₃₁	—	32	2	no	—
23	C₄×C₃₁	#366	1	1	yes	characteristic
24	C₄×C₃₁	Q₆₄	1	1	yes	characteristic
25	C₂×C₃₂	C₂²×C₃₁	1	1	yes	characteristic
26	#366	—	2	2	no	—
27	C₆₄	C₄×C₃₁	1	2	yes	complemented
28	C₂×C₃₁	#1423	1	1	yes	characteristic
29	C₂×C₃₁	SD₁₂₈	1	2	yes	—
30	C₂×C₁₆	D₄×C₃₁	1	1	yes	characteristic
31	#107	—	4	2	no	—
32	C₃₂	C₂×C₄×C₃₁	1	1	yes	characteristic
33	C₃₂	Q₈×C₃₁	1	1	yes	characteristic
34	C₃₁	#7546	1	1	yes	characteristic, direct product factor, Sylow
35	C₂×C₈	D₈×C₃₁	1	1	yes	characteristic
36	C₄⋊C₄	—	8	2	no	—
37	C₁₆	C₄⋊C₄×C₃₁	1	1	yes	characteristic
38	C₁₆	Q₁₆×C₃₁	1	1	yes	characteristic
39	C₂×C₄	—	16	2	no	—
40	C₂×C₄	C₃₁×D₁₆	1	1	yes	characteristic
41	C₈	C₃₁×#107	1	1	yes	characteristic
42	C₈	C₃₁×Q₃₂	1	1	yes	characteristic
43	C₂²	C₃₁×D₃₂	1	1	yes	characteristic
44	C₄	—	32	2	no	—
45	C₄	C₃₁×#366	1	1	yes	characteristic
46	C₄	C₃₁×Q₆₄	1	1	yes	characteristic
47	C₂	C₃₁×#1423	1	1	yes	characteristic
48	C₂	C₃₁×SD₁₂₈	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₃₁	D₃₂
commutator	C₃₂	C₂×C₄×C₃₁
Frattini, cosocle	C₂×C₃₂	C₂²×C₃₁
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄×C₃₁ ◁ C₂×C₈×C₃₁ ◁ C₂×C₁₆×C₃₁ ◁ C₂×C₃₁×C₃₂ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₃₁×C₆₄	C₄	semidirect
14. #7546	C₃₁	direct (N × H)
27. C₆₄	C₄×C₃₁	semidirect
34. C₃₁	#7546	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×C₆₄	2
C₃₁×#1423	2
#7546	31

Subgroups — C31×#7546 #21464305

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#7546 #21464305