Subgroups — #14521454

Order 1984.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11758446	C₂	1	2	yes	maximal
2	C₄×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic
3	#11758406	C₂	1	4	yes	maximal
4	C₂×Dic₆₂	—	2	2	no	—
5	C₂×C₈×C₃₁	C₂²	1	2	yes	—
6	C₄²×C₃₁	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₃₁	—	2	2	no	—
8	C₄⋊Dic₃₁	C₂²	1	4	yes	—
9	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
10	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
11	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
12	C₂×Dic₃₁	—	2	4	no	—
13	Dic₆₂	—	4	4	no	—
14	C₈×C₃₁	Q₈	1	4	yes	complemented
15	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
16	C₄×C₃₁	D₈	1	2	yes	—
17	C₄×C₃₁	Q₁₆	1	2	yes	—
18	C₄×C₃₁	C₂×Q₈	1	2	yes	—
19	Dic₃₁	—	4	4	no	—
20	#500	—	31	1	no	maximal, Sylow
21	C₂×C₃₁	C₄⋊Q₈	1	1	yes	characteristic
22	C₂×C₃₁	C₂×D₈	1	1	yes	characteristic
23	C₂×C₃₁	C₂×Q₁₆	1	1	yes	characteristic
24	C₄⋊Q₈	—	31	2	no	—
25	#107	—	31	4	no	—
26	C₄×C₈	D₃₁	1	1	yes	characteristic
27	C₃₁	#500	1	1	yes	characteristic, complemented, Sylow
28	C₂×Q₈	—	62	2	no	—
29	C₂×C₈	C₂×D₃₁	1	2	yes	—
30	C₄⋊C₄	—	31	4	no	—
31	C₄⋊C₄	—	62	2	no	—
32	C₄²	C₂×D₃₁	1	1	yes	characteristic
33	Q₈	—	124	4	no	—
34	C₂×C₄	—	62	4	no	—
35	C₂×C₄	D₁₂₄	1	1	yes	characteristic
36	C₂×C₄	D₁₂₄	1	1	yes	characteristic
37	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
38	C₈	Dic₆₂	1	4	yes	complemented
39	C₂²	C₂×D₁₂₄	1	1	yes	characteristic
40	C₄	—	124	4	no	—
41	C₄	D₂₄₈	1	2	yes	—
42	C₄	Dic₁₂₄	1	2	yes	—
43	C₄	C₂×Dic₆₂	1	2	yes	—
44	C₂	#11758446	1	1	yes	characteristic
45	C₂	C₂×D₂₄₈	1	1	yes	characteristic
46	C₂	C₂×Dic₁₂₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₂₄
commutator, cosocle	C₂×C₄×C₃₁	C₂³
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₄×C₈×C₃₁	C₂
socle, prime radical	C₂²×C₃₁	C₂×D₄
hypercenter	C₄×C₈	D₃₁
hypocenter	C₃₁	#500
LCS	G ▷ C₂×C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
14. C₈×C₃₁	Q₈	semidirect
27. C₃₁	#500	semidirect
38. C₈	Dic₆₂	semidirect

Maximal subgroups

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

subgroup	index
#11758446	2
C₄×C₈×C₃₁	2
#11758406	2
#500	31