Subgroups — #44540372

Order 31712.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₉₆₄	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₉₉₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×C₉₉₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₉₉₁	—	2	1	no	—
5	D₃₉₆₄	—	2	1	no	—
6	D₃₉₆₄	C₄	1	2	yes	complemented
7	C₂×Dic₉₉₁	—	2	1	no	—
8	C₂×C₄×C₉₉₁	C₂²	1	1	yes	characteristic
9	C₈×C₉₉₁	—	2	1	no	—
10	C₂²×C₉₉₁	D₄	1	1	yes	characteristic
11	C₂×D₉₉₁	—	2	2	no	—
12	C₂×D₉₉₁	—	4	1	no	—
13	C₂×D₉₉₁	—	4	1	no	—
14	C₄×C₉₉₁	C₂×C₄	1	1	yes	characteristic
15	C₄×C₉₉₁	D₄	1	1	yes	characteristic
16	Dic₉₉₁	—	4	1	no	—
17	C₂×C₉₉₁	C₂²⋊C₄	1	1	yes	characteristic
18	C₂×C₉₉₁	D₈	1	1	yes	characteristic
19	C₂×C₉₉₁	SD₁₆	1	1	yes	characteristic
20	D₉₉₁	—	4	2	no	—
21	C₉₉₁	#102	1	1	yes	characteristic, complemented, Sylow
22	#102	—	991	1	no	maximal, Sylow
23	C₂×D₄	—	991	1	no	—
24	C₂×C₈	D₉₉₁	1	1	yes	characteristic, complemented
25	C₄⋊C₄	—	991	1	no	—
26	C₂³	—	1982	1	no	—
27	D₄	—	1982	1	no	—
28	D₄	—	991	2	no	—
29	C₂×C₄	—	1982	1	no	—
30	C₂×C₄	C₂×D₉₉₁	1	1	yes	characteristic
31	C₈	—	2	1	no	—
32	C₂²	—	3964	1	no	—
33	C₂²	—	3964	1	no	—
34	C₂²	—	1982	2	no	—
35	C₂²	D₃₉₆₄	1	1	yes	characteristic
36	C₄	—	3964	1	no	—
37	C₄	C₄×D₉₉₁	1	1	yes	characteristic
38	C₄	C₂²⋊D₉₉₁	1	1	yes	characteristic
39	C₂	—	3964	2	no	—
40	C₂	(C₂×D₉₉₁)⋊C₄	1	1	yes	characteristic
41	C₂	D₇₉₂₈	1	1	yes	characteristic
42	C₂	#30629381	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃₉₆₄
commutator	C₄×C₉₉₁	C₂×C₄
Frattini	C₂×C₄	C₂×D₉₉₁
Fitting	C₂×C₈×C₉₉₁	C₂
socle	C₂²×C₉₉₁	D₄
prime radical	C₂×D₃₉₆₄	C₂
cosocle	C₂×C₄×C₉₉₁	C₂²
hypercenter	C₂×C₈	D₉₉₁
hypocenter	C₉₉₁	#102
LCS	G ▷ C₄×C₉₉₁ ▷ C₂×C₉₉₁ ▷ C₉₉₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₄⋊Dic₉₉₁	C₂	semidirect
3. C₂×C₈×C₉₉₁	C₂	semidirect
6. D₃₉₆₄	C₄	semidirect
21. C₉₉₁	#102	semidirect
24. C₂×C₈	D₉₉₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃₉₆₄	2
C₄⋊Dic₉₉₁	2
C₂×C₈×C₉₉₁	2
#102	991