Subgroups — C₃₁×#7547 #21464306

Order 7936.

60 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×#1425	C₂	1	2	yes	maximal
3	C₂×C₃₁×C₃₂	C₂²	1	1	yes	characteristic
4	C₃₁×#368	—	2	2	no	—
5	C₃₁×C₆₄	C₄	1	2	yes	—
6	C₂×C₁₆×C₃₁	D₄	1	1	yes	characteristic
7	C₃₁×#108	—	4	2	no	—
8	C₃₁×C₃₂	C₂×C₄	1	1	yes	characteristic
9	C₃₁×C₃₂	Q₈	1	1	yes	characteristic
10	M₁₆×C₃₁	—	8	2	no	—
11	C₂×C₈×C₃₁	D₈	1	1	yes	characteristic
12	C₁₆×C₃₁	C₄⋊C₄	1	1	yes	characteristic
13	C₁₆×C₃₁	Q₁₆	1	1	yes	characteristic
14	#7547	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂×C₄×C₃₁	D₁₆	1	1	yes	characteristic
16	C₈×C₃₁	—	16	2	no	—
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	#1425	C₂×C₃₁	1	2	yes	—
21	C₂²×C₃₁	Q₆₄	1	1	yes	characteristic
22	C₄×C₃₁	#366	1	1	yes	characteristic
23	C₄×C₃₁	D₃₂	1	1	yes	characteristic
24	C₂×C₃₂	C₂²×C₃₁	1	1	yes	characteristic
25	#368	—	2	2	no	—
26	C₆₄	C₄×C₃₁	1	2	yes	—
27	C₂×C₃₁	—	2	1	no	—
28	C₂×C₃₁	#1423	1	1	yes	characteristic
29	C₂×C₁₆	D₄×C₃₁	1	1	yes	characteristic
30	#108	—	4	2	no	—
31	C₃₂	C₂×C₄×C₃₁	1	1	yes	characteristic
32	C₃₂	Q₈×C₃₁	1	1	yes	characteristic
33	C₃₁	#7547	1	1	yes	characteristic, direct product factor, Sylow
34	M₁₆	—	8	2	no	—
35	C₂×C₈	D₈×C₃₁	1	1	yes	characteristic
36	C₁₆	C₄⋊C₄×C₃₁	1	1	yes	characteristic
37	C₁₆	Q₁₆×C₃₁	1	1	yes	characteristic
38	C₂×C₄	C₃₁×D₁₆	1	1	yes	characteristic
39	C₈	—	16	2	no	—
40	C₈	C₃₁×#107	1	1	yes	characteristic
41	C₈	C₃₁×Q₃₂	1	1	yes	characteristic
42	C₂²	C₃₁×Q₆₄	1	1	yes	characteristic
43	C₄	C₃₁×#366	1	1	yes	characteristic
44	C₄	C₃₁×D₃₂	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	C₃₁×#1423	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₃₁	D₃₂
commutator	C₃₂	C₂×C₄×C₃₁
Frattini, cosocle	C₂×C₃₂	C₂²×C₃₁
socle	C₂×C₃₁	#1423
prime radical	C₂²×C₃₁	Q₆₄
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×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
14. #7547	C₃₁	direct (N × H)
33. C₃₁	#7547	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×#1425	2
#7547	31

Subgroups — C31×#7547 #21464306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#7547 #21464306