Subgroups — #14521110

Order 1984.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#117	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊(C₃₁⋊C₈)	C₂	1	2	yes	maximal
3	C₄⋊(C₃₁⋊C₈)	C₂	1	2	yes	maximal, complemented
4	#11758391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₃₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₃₁	C₄	1	2	yes	—
8	C₂²⋊C₄×C₃₁	C₄	1	2	yes	—
9	C₄²×C₃₁	C₂²	1	1	yes	characteristic
10	C₄²×C₃₁	C₂²	1	1	yes	characteristic
11	C₂×C₃₁⋊C₈	C₂²	1	2	yes	—
12	C₂×C₃₁⋊C₈	C₂²	1	2	yes	—
13	C₂³×C₃₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₃₁	—	2	2	no	—
15	C₂×C₄×C₃₁	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₃₁	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
19	C₃₁⋊C₈	—	2	2	no	—
20	C₃₁⋊C₈	—	2	2	no	—
21	C₂²×C₃₁	—	2	1	no	—
22	C₂²×C₃₁	—	2	2	no	—
23	C₂²×C₃₁	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₃₁	—	2	1	no	—
25	C₄×C₃₁	—	2	2	no	—
26	C₄×C₃₁	—	2	2	no	—
27	C₄×C₃₁	#41	1	2	yes	—
28	#433	—	31	1	no	maximal, Sylow
29	C₂×C₃₁	—	4	1	no	—
30	C₂×C₃₁	#117	1	1	yes	characteristic
31	C₂×C₃₁	#131	1	2	yes	—
32	#117	D₃₁	1	1	yes	characteristic
33	C₄⋊C₈	—	31	2	no	—
34	C₂²⋊C₈	—	31	2	no	—
35	#97	—	31	1	no	—
36	C₄×C₈	—	31	1	no	—
37	C₃₁	#433	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₄	C₂×D₃₁	1	1	yes	characteristic
39	C₂×C₈	—	31	2	no	—
40	C₂×C₈	—	31	2	no	—
41	C₄⋊C₄	Dic₃₁	1	2	yes	—
42	C₂²⋊C₄	Dic₃₁	1	2	yes	—
43	C₄²	C₂×D₃₁	1	1	yes	characteristic
44	C₄²	C₂×D₃₁	1	1	yes	characteristic
45	C₂³	C₂×Dic₃₁	1	1	yes	characteristic
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	C₂×Dic₃₁	1	2	yes	—
48	C₂×C₄	C₂×Dic₃₁	1	2	yes	—
49	C₂×C₄	C₂×Dic₃₁	1	1	yes	characteristic
50	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
51	C₈	—	62	2	no	—
52	C₈	—	62	2	no	—
53	C₂²	—	2	1	no	—
54	C₂²	—	2	2	no	—
55	C₂²	C₂²×Dic₃₁	1	1	yes	characteristic
56	C₄	—	2	1	no	—
57	C₄	—	2	2	no	—
58	C₄	—	2	2	no	—
59	C₄	#92495	1	2	yes	—
60	C₂	—	4	1	no	—
61	C₂	#11758503	1	1	yes	characteristic
62	C₂	#11758525	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃₁
commutator, socle	C₂²×C₃₁	C₂²×C₄
Fitting	C₃₁×#117	C₂
prime radical	C₂³×C₃₁	C₂×C₄
cosocle	C₂×C₄×C₃₁	C₂³
hypercenter	#117	D₃₁
hypocenter	C₃₁	#433
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
3. C₄⋊(C₃₁⋊C₈)	C₂	semidirect
4. #11758391	C₂	semidirect
5. C₄×C₃₁⋊C₈	C₂	semidirect
37. C₃₁	#433	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#117	2
C₂²⋊(C₃₁⋊C₈)	2
C₄⋊(C₃₁⋊C₈)	2
#11758391	2
C₄×C₃₁⋊C₈	2
#433	31