Subgroups — #31823879

Order 17984.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582885	C₂	1	1	yes	maximal, characteristic
2	#22582819	C₂	1	1	yes	maximal, characteristic, complemented
3	#22582818	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₂₈₁	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₆×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#17985138	C₄	1	1	yes	characteristic
7	#17985122	C₄	1	1	yes	characteristic
8	#17985121	C₄	1	2	yes	—
9	C₈×D₂₈₁	C₂²	1	2	yes	—
10	#17985113	C₂²	1	2	yes	—
11	C₂×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
12	C₁₆×C₂₈₁	C₂²	1	1	yes	characteristic
13	C₁₆×C₂₈₁	C₂²	1	1	yes	characteristic
14	Dic₅₆₂	C₈	1	1	yes	characteristic
15	D₁₁₂₄	C₈	1	1	yes	characteristic
16	C₂²⋊D₂₈₁	C₈	1	2	yes	—
17	C₄×D₂₈₁	C₂×C₄	1	2	yes	—
18	#14555886	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₂₈₁	C₂×C₄	1	1	yes	characteristic
20	C₈×C₂₈₁	C₂×C₄	1	1	yes	characteristic
21	C₈×C₂₈₁	C₂³	1	1	yes	characteristic
22	C₂²×C₂₈₁	C₂×C₈	1	1	yes	characteristic
23	C₂×D₂₈₁	C₂×C₈	1	2	yes	—
24	C₄×C₂₈₁	C₂×C₈	1	1	yes	characteristic
25	C₄×C₂₈₁	C₂²×C₄	1	1	yes	characteristic
26	Dic₂₈₁	C₂×C₈	1	2	yes	—
27	C₂×C₂₈₁	—	2	1	no	—
28	C₂×C₂₈₁	C₂²×C₈	1	1	yes	characteristic
29	D₂₈₁	—	2	2	no	—
30	C₂₈₁	#504	1	1	yes	characteristic, complemented, Sylow
31	#504	—	281	1	no	maximal, Sylow
32	#131	—	281	1	no	—
33	M₃₂	—	281	1	no	—
34	M₃₂	—	281	2	no	—
35	C₂×C₁₆	—	281	2	no	—
36	C₂×C₁₆	D₂₈₁	1	1	yes	characteristic, complemented
37	#41	—	281	1	no	—
38	M₁₆	—	281	1	no	—
39	M₁₆	—	281	2	no	—
40	C₂×C₈	—	281	2	no	—
41	C₂×C₈	C₂×D₂₈₁	1	1	yes	characteristic
42	C₁₆	—	281	2	no	—
43	C₁₆	C₂×D₂₈₁	1	1	yes	characteristic
44	C₁₆	C₂×D₂₈₁	1	1	yes	characteristic
45	Q₈	—	281	1	no	—
46	D₄	—	281	2	no	—
47	D₄	—	281	1	no	—
48	C₂×C₄	—	281	2	no	—
49	C₂×C₄	C₄×D₂₈₁	1	1	yes	characteristic
50	C₈	—	281	2	no	—
51	C₈	C₄×D₂₈₁	1	1	yes	characteristic
52	C₈	C₂²×D₂₈₁	1	1	yes	characteristic
53	C₂²	—	281	2	no	—
54	C₂²	C₈×D₂₈₁	1	1	yes	characteristic
55	C₄	—	281	2	no	—
56	C₄	C₈×D₂₈₁	1	1	yes	characteristic
57	C₄	C₂×C₄×D₂₈₁	1	1	yes	characteristic
58	C₂	—	2	1	no	—
59	C₂	—	562	2	no	—
60	C₂	C₂×C₈×D₂₈₁	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂×D₂₈₁
commutator, socle	C₂×C₂₈₁	C₂²×C₈
Frattini	C₈	C₂²×D₂₈₁
Fitting	C₂×C₁₆×C₂₈₁	C₂
prime radical	#17985138	C₄
cosocle	C₈×C₂₈₁	C₂³
hypercenter	C₂×C₁₆	D₂₈₁
hypocenter	C₂₈₁	#504
LCS	G ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. #22582819	C₂	semidirect
3. #22582818	C₂	semidirect
4. C₁₆×D₂₈₁	C₂	semidirect
5. C₂×C₁₆×C₂₈₁	C₂	semidirect
30. C₂₈₁	#504	semidirect
36. 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
#22582885	2
#22582819	2
#22582818	2
C₁₆×D₂₈₁	2
C₂×C₁₆×C₂₈₁	2
#504	281