Subgroups — #14521467

Order 1984.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758478	C₂	1	1	yes	maximal, characteristic
2	C₃₁×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#11758386	C₂	1	2	yes	maximal, complemented
5	C₁₆×D₃₁	C₂	1	2	yes	maximal, complemented
6	#92495	C₄	1	1	yes	characteristic
7	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
8	#92474	C₄	1	1	yes	characteristic
9	#92469	C₄	1	2	yes	—
10	C₈×D₃₁	C₂²	1	2	yes	—
11	C₁₆×C₃₁	C₂²	1	2	yes	—
12	C₃₁⋊C₁₆	C₂²	1	1	yes	characteristic
13	C₃₁⋊C₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
15	C₂²⋊D₃₁	C₈	1	2	yes	—
16	D₁₂₄	C₈	1	1	yes	characteristic
17	C₄×D₃₁	C₂×C₄	1	2	yes	—
18	Dic₆₂	C₈	1	1	yes	characteristic
19	C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
20	C₈×C₃₁	C₂³	1	1	yes	characteristic
21	C₃₁⋊C₈	C₂×C₄	1	2	yes	—
22	C₂²×C₃₁	C₂×C₈	1	1	yes	characteristic
23	C₂×D₃₁	C₂×C₈	1	2	yes	—
24	C₄×C₃₁	C₂×C₈	1	1	yes	characteristic
25	C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
26	Dic₃₁	C₂×C₈	1	2	yes	—
27	#504	—	31	1	no	maximal, Sylow
28	C₂×C₃₁	—	2	1	no	—
29	C₂×C₃₁	C₂²×C₈	1	1	yes	characteristic
30	D₃₁	—	2	2	no	—
31	#131	—	31	1	no	—
32	M₃₂	—	31	2	no	—
33	M₃₂	D₃₁	1	1	yes	characteristic, complemented
34	C₂×C₁₆	—	31	1	no	—
35	C₂×C₁₆	—	31	2	no	—
36	C₃₁	#504	1	1	yes	characteristic, complemented, Sylow
37	#41	—	31	1	no	—
38	M₁₆	—	31	1	no	—
39	M₁₆	—	31	2	no	—
40	C₂×C₈	—	31	2	no	—
41	C₂×C₈	C₂×D₃₁	1	1	yes	characteristic
42	C₁₆	—	31	1	no	—
43	C₁₆	—	31	1	no	—
44	C₁₆	C₂×D₃₁	1	2	yes	—
45	Q₈	—	31	1	no	—
46	D₄	—	31	2	no	—
47	D₄	—	31	1	no	—
48	C₂×C₄	—	31	2	no	—
49	C₂×C₄	C₄×D₃₁	1	1	yes	characteristic
50	C₈	—	31	2	no	—
51	C₈	C₄×D₃₁	1	1	yes	characteristic
52	C₈	C₂²×D₃₁	1	1	yes	characteristic
53	C₂²	—	31	2	no	—
54	C₂²	C₈×D₃₁	1	1	yes	characteristic
55	C₄	—	31	2	no	—
56	C₄	C₈×D₃₁	1	1	yes	characteristic
57	C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
58	C₂	—	2	1	no	—
59	C₂	—	62	2	no	—
60	C₂	C₂×C₈×D₃₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×D₃₁
commutator, socle	C₂×C₃₁	C₂²×C₈
Fitting	C₃₁×M₃₂	C₂
prime radical	#92495	C₄
cosocle	C₈×C₃₁	C₂³
hypercenter	M₃₂	D₃₁
hypocenter	C₃₁	#504
LCS	G ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. C₃₁×M₃₂	C₂	semidirect
3. C₂×C₃₁⋊C₁₆	C₂	semidirect
4. #11758386	C₂	semidirect
5. C₁₆×D₃₁	C₂	semidirect
33. M₃₂	D₃₁	semidirect
36. C₃₁	#504	semidirect

Maximal subgroups

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

subgroup	index
#11758478	2
C₃₁×M₃₂	2
C₂×C₃₁⋊C₁₆	2
#11758386	2
C₁₆×D₃₁	2
#504	31