Subgroups — #14520845

Order 1984.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758524	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#101	C₂	1	1	yes	maximal, characteristic, complemented
3	#11758424	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Q₈×C₃₁	C₂²	1	1	yes	characteristic
5	C₂×D₁₂₄	C₄	1	1	yes	characteristic
6	M₁₆×C₃₁	—	2	1	no	—
7	(C₂×D₃₁)⋊C₄	—	2	1	no	—
8	(C₂×D₃₁)⋊C₄	—	2	1	no	—
9	C₄×Dic₃₁	C₄	1	1	yes	characteristic
10	#92474	—	2	1	no	—
11	C₂²×D₃₁	—	2	1	no	—
12	Q₈×C₃₁	—	4	1	no	—
13	C₂×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
15	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
16	C₂×Dic₃₁	—	2	1	no	—
17	D₁₂₄	—	4	1	no	—
18	C₈×C₃₁	—	4	1	no	—
19	C₃₁⋊C₈	—	4	1	no	—
20	C₂²×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×D₃₁	—	4	2	no	—
22	C₂×D₃₁	—	4	1	no	—
23	C₄×C₃₁	—	2	1	no	—
24	C₄×C₃₁	—	2	1	no	—
25	C₄×C₃₁	—	2	1	no	—
26	Dic₃₁	—	4	1	no	—
27	#355	—	31	1	no	maximal, Sylow
28	C₂×C₃₁	—	2	1	no	—
29	C₂×C₃₁	#99	1	1	yes	characteristic
30	D₃₁	—	8	1	no	—
31	#124	—	31	1	no	—
32	#101	—	31	1	no	—
33	#101	D₃₁	1	1	yes	characteristic, complemented
34	C₃₁	#355	1	1	yes	characteristic, complemented, Sylow
35	C₂×Q₈	C₂×D₃₁	1	1	yes	characteristic
36	C₂×D₄	—	31	1	no	—
37	M₁₆	—	2	1	no	—
38	M₁₆	—	62	1	no	—
39	C₂²⋊C₄	—	62	1	no	—
40	C₂²⋊C₄	—	62	1	no	—
41	C₄²	—	31	1	no	—
42	C₂³	—	62	1	no	—
43	Q₈	—	4	1	no	—
44	D₄	—	124	1	no	—
45	C₂×C₄	—	62	1	no	—
46	C₂×C₄	C₄×D₃₁	1	1	yes	characteristic
47	C₂×C₄	D₁₂₄	1	1	yes	characteristic
48	C₂×C₄	C₂²⋊D₃₁	1	1	yes	characteristic
49	C₈	—	4	1	no	—
50	C₈	—	124	1	no	—
51	C₂²	—	124	2	no	—
52	C₂²	—	124	1	no	—
53	C₂²	(C₂×D₃₁)⋊C₄	1	1	yes	characteristic
54	C₄	—	2	1	no	—
55	C₄	—	2	1	no	—
56	C₄	—	2	1	no	—
57	C₄	—	124	1	no	—
58	C₂	—	2	1	no	—
59	C₂	—	248	1	no	—
60	C₂	#11758394	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11758394
commutator	C₂×C₄×C₃₁	C₂×C₄
Frattini	C₂×Q₈	C₂×D₃₁
Fitting	C₃₁×#101	C₂
socle	C₂×C₃₁	#99
prime radical	C₂×D₁₂₄	C₄
cosocle	C₂×Q₈×C₃₁	C₂²
hypercenter	#101	D₃₁
hypocenter	C₃₁	#355
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂²×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×Q₈ ◁ #101

Complements

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

N	H ≅ G/N	type
2. C₃₁×#101	C₂	semidirect
3. #11758424	C₂	semidirect
33. #101	D₃₁	semidirect
34. C₃₁	#355	semidirect

Maximal subgroups

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

subgroup	index
#11758524	2
C₃₁×#101	2
#11758424	2
#355	31