Subgroups — #31823271

Order 17984.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582901	C₂	1	1	yes	maximal, characteristic
2	#22582815	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₆×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#17985138	—	2	1	no	—
5	Dic₁₁₂₄	C₄	1	1	yes	characteristic
6	#17985127	—	2	1	no	—
7	D₂₂₄₈	C₄	1	1	yes	characteristic
8	#17985122	—	2	1	no	—
9	C₂×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
10	C₁₆×C₂₈₁	—	2	1	no	—
11	Dic₅₆₂	—	2	1	no	—
12	D₁₁₂₄	—	2	1	no	—
13	C₂²⋊D₂₈₁	—	4	1	no	—
14	C₄×D₂₈₁	—	4	1	no	—
15	#14555886	—	4	1	no	—
16	C₂×C₄×C₂₈₁	D₄	1	1	yes	characteristic
17	C₈×C₂₈₁	C₂×C₄	1	1	yes	characteristic
18	C₈×C₂₈₁	D₄	1	1	yes	characteristic
19	C₂²×C₂₈₁	SD₁₆	1	1	yes	characteristic
20	C₂×D₂₈₁	—	4	1	no	—
21	C₄×C₂₈₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₂₈₁	D₈	1	1	yes	characteristic
23	Dic₂₈₁	—	4	1	no	—
24	C₂×C₂₈₁	—	2	1	no	—
25	C₂×C₂₈₁	#102	1	1	yes	characteristic
26	D₂₈₁	—	8	1	no	—
27	C₂₈₁	#359	1	1	yes	characteristic, complemented, Sylow
28	#359	—	281	1	no	maximal, Sylow
29	#135	—	281	1	no	—
30	C₂×C₁₆	D₂₈₁	1	1	yes	characteristic, complemented
31	#108	—	281	1	no	—
32	#41	—	562	1	no	—
33	Q₁₆	—	281	1	no	—
34	SD₁₆	—	562	1	no	—
35	D₈	—	281	1	no	—
36	M₁₆	—	562	1	no	—
37	C₂×C₈	C₂×D₂₈₁	1	1	yes	characteristic
38	C₁₆	—	2	1	no	—
39	Q₈	—	562	1	no	—
40	D₄	—	562	1	no	—
41	D₄	—	1124	1	no	—
42	C₂×C₄	—	1124	1	no	—
43	C₂×C₄	D₁₁₂₄	1	1	yes	characteristic
44	C₈	—	1124	1	no	—
45	C₈	C₄×D₂₈₁	1	1	yes	characteristic
46	C₈	C₂²⋊D₂₈₁	1	1	yes	characteristic
47	C₂²	—	1124	1	no	—
48	C₂²	#17985127	1	1	yes	characteristic
49	C₄	—	1124	1	no	—
50	C₄	#17985115	1	1	yes	characteristic
51	C₄	D₂₂₄₈	1	1	yes	characteristic
52	C₂	—	2	1	no	—
53	C₂	—	2248	1	no	—
54	C₂	#22582801	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₂₂₄₈
commutator	C₈×C₂₈₁	C₂×C₄
Frattini	C₂×C₈	C₂×D₂₈₁
Fitting	C₂×C₁₆×C₂₈₁	C₂
socle	C₂×C₂₈₁	#102
prime radical	#22582901	C₂
cosocle	C₂×C₈×C₂₈₁	C₂²
hypercenter	C₂×C₁₆	D₂₈₁
hypocenter	C₂₈₁	#359
LCS	G ▷ C₈×C₂₈₁ ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. #22582815	C₂	semidirect
3. C₂×C₁₆×C₂₈₁	C₂	semidirect
27. C₂₈₁	#359	semidirect
30. C₂×C₁₆	D₂₈₁	semidirect

Maximal subgroups

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

subgroup	index
#22582901	2
#22582815	2
C₂×C₁₆×C₂₈₁	2
#359	281