Subgroups — #31823213

Order 17984.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14555886	C₂	1	1	yes	maximal, characteristic
2	C₄×#14555886	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₈×C₂₈₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#14555886	—	2	1	no	—
5	C₂×#14555886	C₄	1	1	yes	characteristic
6	C₂×#14555886	C₄	1	1	yes	characteristic
7	C₂×C₈×C₂₈₁	—	2	1	no	—
8	C₄²×C₂₈₁	C₂²	1	1	yes	characteristic
9	#14555886	—	2	1	no	—
10	#14555886	—	4	1	no	—
11	#14555886	C₈	1	2	yes	complemented
12	C₂×C₄×C₂₈₁	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₂₈₁	D₄	1	1	yes	characteristic
14	C₂×C₄×C₂₈₁	Q₈	1	1	yes	characteristic
15	C₈×C₂₈₁	—	4	1	no	—
16	C₂²×C₂₈₁	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₂₈₁	—	2	1	no	—
18	C₄×C₂₈₁	C₂×C₈	1	1	yes	characteristic
19	C₄×C₂₈₁	M₁₆	1	1	yes	characteristic
20	C₄×C₂₈₁	SD₁₆	1	1	yes	characteristic
21	C₄×C₂₈₁	SD₁₆	1	1	yes	characteristic
22	C₂×C₂₈₁	C₄⋊C₈	1	1	yes	characteristic
23	C₂×C₂₈₁	#106	1	1	yes	characteristic
24	C₂×C₂₈₁	#108	1	1	yes	characteristic
25	C₂₈₁	#334	1	1	yes	characteristic, complemented, Sylow
26	#334	—	281	1	no	maximal, Sylow
27	C₄⋊C₈	—	281	1	no	—
28	C₄⋊C₈	D₂₈₁	1	1	yes	characteristic
29	C₄×C₈	—	281	1	no	—
30	C₂×C₈	—	2	1	no	—
31	C₂×C₈	—	281	1	no	—
32	C₂×C₈	—	281	1	no	—
33	C₂×C₈	—	562	1	no	—
34	C₄²	C₂×D₂₈₁	1	1	yes	characteristic
35	C₂×C₄	C₄×D₂₈₁	1	1	yes	characteristic
36	C₂×C₄	C₂²⋊D₂₈₁	1	1	yes	characteristic
37	C₂×C₄	Dic₅₆₂	1	1	yes	characteristic
38	C₈	—	4	1	no	—
39	C₈	—	281	2	no	—
40	C₈	—	562	1	no	—
41	C₈	—	1124	1	no	—
42	C₂²	#17985117	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	C₈×D₂₈₁	1	1	yes	characteristic
45	C₄	#17985121	1	1	yes	characteristic
46	C₄	#17985125	1	1	yes	characteristic
47	C₄	#17985126	1	1	yes	characteristic
48	C₂	#22582808	1	1	yes	characteristic
49	C₂	#22582810	1	1	yes	characteristic
50	C₂	#22582814	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₂₈₁
commutator	C₄×C₂₈₁	C₂×C₈
Frattini	C₄²	C₂×D₂₈₁
Fitting	C₄⋊C₈×C₂₈₁	C₂
socle, prime radical	C₂²×C₂₈₁	C₄⋊C₄
cosocle	C₄²×C₂₈₁	C₂²
hypercenter	C₄⋊C₈	D₂₈₁
hypocenter	C₂₈₁	#334
LCS	G ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
11. #14555886	C₈	semidirect
25. C₂₈₁	#334	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#14555886	2
C₄×#14555886	2
C₄⋊C₈×C₂₈₁	2
#334	281