Subgroups — #31823242

Order 17984.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₂₈₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#17985113	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₆×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₂₈₁	C₄	1	1	yes	characteristic
5	C₂×#14555886	C₄	1	1	yes	characteristic
6	C₈×D₂₈₁	—	2	1	no	—
7	C₈×D₂₈₁	—	2	1	no	—
8	#17985113	—	2	1	no	—
9	C₂×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
10	C₁₆×C₂₈₁	—	2	1	no	—
11	C₂²×D₂₈₁	C₈	1	1	yes	characteristic
12	C₂×Dic₂₈₁	C₈	1	1	yes	characteristic
13	C₄×D₂₈₁	—	2	1	no	—
14	C₄×D₂₈₁	—	2	1	no	—
15	#14555886	—	2	1	no	—
16	C₂×C₄×C₂₈₁	C₂×C₄	1	1	yes	characteristic
17	C₈×C₂₈₁	D₄	1	1	yes	characteristic
18	C₈×C₂₈₁	D₄	1	1	yes	characteristic
19	C₂²×C₂₈₁	C₂×C₈	1	1	yes	characteristic
20	C₂×D₂₈₁	—	2	1	no	—
21	C₂×D₂₈₁	—	2	1	no	—
22	C₂×D₂₈₁	C₁₆	1	2	yes	complemented
23	C₄×C₂₈₁	C₂²⋊C₄	1	1	yes	characteristic
24	C₄×C₂₈₁	M₁₆	1	1	yes	characteristic
25	Dic₂₈₁	—	2	1	no	—
26	C₂×C₂₈₁	C₂²⋊C₈	1	1	yes	characteristic
27	C₂×C₂₈₁	C₂×C₁₆	1	1	yes	characteristic
28	C₂×C₂₈₁	M₃₂	1	1	yes	characteristic
29	D₂₈₁	—	2	2	no	—
30	C₂₈₁	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
31	C₂²⋊C₁₆	—	281	1	no	maximal, Sylow
32	C₂²×C₈	—	281	1	no	—
33	C₂×C₁₆	—	281	1	no	—
34	C₂×C₁₆	D₂₈₁	1	1	yes	characteristic, complemented
35	C₂²×C₄	—	281	1	no	—
36	C₂×C₈	—	281	1	no	—
37	C₂×C₈	—	562	1	no	—
38	C₂×C₈	—	562	1	no	—
39	C₂×C₈	C₂×D₂₈₁	1	1	yes	characteristic
40	C₁₆	—	2	1	no	—
41	C₁₆	—	562	1	no	—
42	C₂³	—	281	1	no	—
43	C₂×C₄	—	281	1	no	—
44	C₂×C₄	—	562	1	no	—
45	C₂×C₄	—	562	1	no	—
46	C₂×C₄	C₄×D₂₈₁	1	1	yes	characteristic
47	C₈	—	562	1	no	—
48	C₈	C₂²⋊D₂₈₁	1	1	yes	characteristic
49	C₈	D₁₁₂₄	1	1	yes	characteristic
50	C₂²	—	281	2	no	—
51	C₂²	—	562	1	no	—
52	C₂²	—	562	1	no	—
53	C₂²	C₈×D₂₈₁	1	1	yes	characteristic
54	C₄	—	562	1	no	—
55	C₄	#17985115	1	1	yes	characteristic
56	C₄	#17985121	1	1	yes	characteristic
57	C₂	—	562	2	no	—
58	C₂	#22582791	1	1	yes	characteristic
59	C₂	C₁₆×D₂₈₁	1	1	yes	characteristic
60	C₂	#22582818	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₂₈₁
commutator	C₂×C₂₈₁	C₂×C₁₆
Fitting	C₂×C₁₆×C₂₈₁	C₂
socle	C₂²×C₂₈₁	C₂×C₈
prime radical	C₂²×D₂₈₁	C₈
cosocle	C₂×C₈×C₂₈₁	C₂²
hypercenter	C₂×C₁₆	D₂₈₁
hypocenter	C₂₈₁	C₂²⋊C₁₆
LCS	G ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×#17985113	C₂	semidirect
3. C₂×C₁₆×C₂₈₁	C₂	semidirect
22. C₂×D₂₈₁	C₁₆	semidirect
30. C₂₈₁	C₂²⋊C₁₆	semidirect
34. 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
C₂×C₈×D₂₈₁	2
C₂×#17985113	2
C₂×C₁₆×C₂₈₁	2
C₂²⋊C₁₆	281