Subgroups — #14520813

Order 1984.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#92474	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃₁⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
5	M₁₆×C₃₁	—	2	1	no	—
6	M₁₆×C₃₁	C₄	1	2	yes	—
7	C₂×C₈×C₃₁	—	2	1	no	—
8	#92474	—	2	1	no	—
9	#92474	C₄	1	2	yes	—
10	C₂×C₃₁⋊C₈	—	2	1	no	—
11	C₂×C₃₁⋊C₈	—	2	1	no	—
12	C₂×C₃₁⋊C₈	—	2	1	no	—
13	C₂×C₃₁⋊C₈	C₄	1	2	yes	—
14	C₂³×C₃₁	Q₈	1	1	yes	characteristic
15	C₂×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
19	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
20	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
21	C₈×C₃₁	—	2	2	no	—
22	C₃₁⋊C₈	—	2	2	no	—
23	C₃₁⋊C₈	—	2	2	no	—
24	C₂²×C₃₁	—	2	2	no	—
25	C₂²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
26	C₂²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
27	C₂²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
28	C₄×C₃₁	C₄²	1	1	yes	characteristic
29	C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
30	C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
31	C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
32	#341	—	31	1	no	maximal, Sylow
33	C₂×C₃₁	—	2	1	no	—
34	C₂×C₃₁	—	2	1	no	—
35	C₂×C₃₁	#95	1	1	yes	characteristic
36	C₂×C₃₁	#108	1	2	yes	—
37	C₂×M₁₆	—	31	1	no	—
38	C₂×M₁₆	D₃₁	1	1	yes	characteristic
39	C₂²×C₈	—	31	1	no	—
40	C₃₁	#341	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₄	C₂×D₃₁	1	1	yes	characteristic
42	M₁₆	—	2	1	no	—
43	M₁₆	—	31	2	no	—
44	M₁₆	—	62	1	no	—
45	M₁₆	Dic₃₁	1	2	yes	—
46	C₂×C₈	—	2	1	no	—
47	C₂×C₈	—	31	2	no	—
48	C₂×C₈	—	62	1	no	—
49	C₂×C₈	—	62	1	no	—
50	C₂×C₈	—	62	1	no	—
51	C₂³	Dic₆₂	1	1	yes	characteristic
52	C₂×C₄	C₄×D₃₁	1	1	yes	characteristic
53	C₂×C₄	C₄×D₃₁	1	1	yes	characteristic
54	C₂×C₄	D₁₂₄	1	1	yes	characteristic
55	C₂×C₄	C₂×Dic₃₁	1	1	yes	characteristic
56	C₂×C₄	C₂²⋊D₃₁	1	1	yes	characteristic
57	C₂×C₄	C₂²⋊D₃₁	1	1	yes	characteristic
58	C₈	—	2	2	no	—
59	C₈	—	62	2	no	—
60	C₈	—	62	2	no	—
61	C₂²	—	2	2	no	—
62	C₂²	Dic₃₁⋊C₄	1	1	yes	characteristic
63	C₂²	Dic₃₁⋊C₄	1	1	yes	characteristic
64	C₂²	C₄⋊Dic₃₁	1	1	yes	characteristic
65	C₄	C₄×Dic₃₁	1	1	yes	characteristic
66	C₄	(C₂×D₃₁)⋊C₄	1	1	yes	characteristic
67	C₄	(C₂×D₃₁)⋊C₄	1	1	yes	characteristic
68	C₄	C₂²⋊Dic₃₁	1	1	yes	characteristic
69	C₂	—	2	1	no	—
70	C₂	—	2	1	no	—
71	C₂	#11758410	1	2	yes	—
72	C₂	C₃₁⋊#95	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₃₁
commutator	C₄×C₃₁	C₄²
Frattini	C₂²×C₄	C₂×D₃₁
Fitting	C₂×M₁₆×C₃₁	C₂
socle	C₂²×C₃₁	C₄⋊C₄
prime radical	C₂³×C₃₁	Q₈
cosocle	C₂²×C₄×C₃₁	C₂²
hypercenter	C₂×M₁₆	D₃₁
hypocenter	C₃₁	#341
LCS	G ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
40. C₃₁	#341	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×C₃₁	2
C₂×#92474	2
C₂²×C₃₁⋊C₈	2
#341	31