Subgroups — #14520804

Order 1984.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃₁⋊C₈	C₂	1	2	yes	maximal
3	C₂²×C₄×C₃₁	C₄	1	2	yes	—
4	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
5	C₄²×C₃₁	—	2	2	no	—
6	C₂×C₃₁⋊C₈	—	2	2	no	—
7	C₂×C₃₁⋊C₈	—	2	2	no	—
8	C₂×C₃₁⋊C₈	C₄	1	4	yes	complemented
9	C₂³×C₃₁	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₃₁	—	2	2	no	—
11	C₂×C₄×C₃₁	—	2	2	no	—
12	C₂×C₄×C₃₁	C₈	1	4	yes	complemented
13	C₂×C₄×C₃₁	C₂×C₄	1	2	yes	—
14	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
15	C₂×C₄×C₃₁	D₄	1	2	yes	—
16	C₂×C₄×C₃₁	Q₈	1	1	yes	characteristic
17	C₃₁⋊C₈	—	2	4	no	—
18	C₂²×C₃₁	C₄²	1	1	yes	characteristic
19	C₂²×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
20	C₂²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
21	C₂²×C₃₁	C₂×C₈	1	2	yes	—
22	C₂²×C₃₁	M₁₆	1	2	yes	—
23	C₄×C₃₁	—	2	4	no	—
24	C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
25	C₄×C₃₁	C₄⋊C₄	1	2	yes	—
26	#336	—	31	1	no	maximal, Sylow
27	C₂×C₃₁	#95	1	1	yes	characteristic
28	C₂×C₃₁	C₄×C₈	1	1	yes	characteristic
29	C₂×C₃₁	#97	1	1	yes	characteristic
30	C₂×C₃₁	C₂²⋊C₈	1	2	yes	—
31	C₂×C₃₁	C₄⋊C₈	1	2	yes	—
32	C₂²×C₈	—	31	2	no	—
33	C₂×C₄²	D₃₁	1	1	yes	characteristic
34	C₃₁	#336	1	1	yes	characteristic, complemented, Sylow
35	C₂²×C₄	Dic₃₁	1	2	yes	—
36	C₂²×C₄	C₂×D₃₁	1	1	yes	characteristic
37	C₂×C₈	—	31	4	no	—
38	C₂×C₈	—	62	2	no	—
39	C₂×C₈	—	62	2	no	—
40	C₄²	—	2	2	no	—
41	C₂³	C₂×Dic₃₁	1	1	yes	characteristic
42	C₂×C₄	—	2	2	no	—
43	C₂×C₄	—	2	2	no	—
44	C₂×C₄	C₃₁⋊C₈	1	4	yes	complemented
45	C₂×C₄	Dic₆₂	1	1	yes	characteristic
46	C₂×C₄	C₄×D₃₁	1	2	yes	—
47	C₂×C₄	D₁₂₄	1	1	yes	characteristic
48	C₂×C₄	C₂²⋊D₃₁	1	2	yes	—
49	C₈	—	62	4	no	—
50	C₂²	C₂×C₃₁⋊C₈	1	2	yes	—
51	C₂²	#92474	1	2	yes	—
52	C₂²	C₄×Dic₃₁	1	1	yes	characteristic
53	C₂²	C₄⋊Dic₃₁	1	1	yes	characteristic
54	C₂²	C₂²⋊Dic₃₁	1	1	yes	characteristic
55	C₄	—	2	4	no	—
56	C₄	Dic₃₁⋊C₄	1	2	yes	—
57	C₄	(C₂×D₃₁)⋊C₄	1	2	yes	—
58	C₂	C₄×C₃₁⋊C₈	1	1	yes	characteristic
59	C₂	#11758391	1	1	yes	characteristic
60	C₂	C₄⋊(C₃₁⋊C₈)	1	2	yes	—
61	C₂	C₂²⋊(C₃₁⋊C₈)	1	2	yes	—
62	C₂	C₃₁⋊#95	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂×D₃₁
commutator	C₂×C₃₁	C₄×C₈
Fitting	C₂×C₄²×C₃₁	C₂
socle, prime radical	C₂³×C₃₁	C₂×C₄
cosocle	C₂²×C₄×C₃₁	C₂²
hypercenter	C₂×C₄²	D₃₁
hypocenter	C₃₁	#336
LCS	G ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
8. C₂×C₃₁⋊C₈	C₄	semidirect
12. C₂×C₄×C₃₁	C₈	semidirect
34. C₃₁	#336	semidirect
44. C₂×C₄	C₃₁⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄²×C₃₁	2
C₂²×C₃₁⋊C₈	2
#336	31