Subgroups — #49097597

Order 35968.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31823297	C₂	1	3	yes	maximal, complemented
2	C₂×#22582785	C₂	1	3	yes	maximal, complemented
3	#504×C₂₈₁	C₂	1	1	yes	maximal, characteristic
4	#22582785	C₂²	1	1	yes	characteristic
5	#22582785	C₂²	1	3	yes	—
6	#131×C₂₈₁	C₄	1	1	yes	characteristic
7	M₃₂×C₂₈₁	C₄	1	3	yes	—
8	C₂×C₁₆×C₂₈₁	C₂²	1	3	yes	—
9	#41×C₂₈₁	C₈	1	1	yes	characteristic
10	M₁₆×C₂₈₁	C₈	1	3	yes	—
11	C₂×C₈×C₂₈₁	C₂×C₄	1	3	yes	—
12	C₁₆×C₂₈₁	C₂×C₄	1	3	yes	—
13	C₁₆×C₂₈₁	C₂³	1	1	yes	characteristic
14	Q₈×C₂₈₁	C₁₆	1	1	yes	characteristic
15	D₄×C₂₈₁	C₁₆	1	3	yes	—
16	C₂×C₄×C₂₈₁	C₂×C₈	1	3	yes	—
17	C₈×C₂₈₁	C₂×C₈	1	3	yes	—
18	C₈×C₂₈₁	C₂²×C₄	1	1	yes	characteristic
19	C₂²×C₂₈₁	C₂×C₁₆	1	3	yes	—
20	C₄×C₂₈₁	C₂×C₁₆	1	3	yes	—
21	C₄×C₂₈₁	C₂²×C₈	1	1	yes	characteristic
22	C₂×C₂₈₁	—	2	3	no	—
23	C₂×C₂₈₁	C₂²×C₁₆	1	1	yes	characteristic
24	C₂₈₁	#2258	1	1	yes	characteristic, complemented, Sylow
25	#2258	—	281	1	no	maximal, Sylow
26	#504	D₂₈₁	1	1	yes	characteristic
27	M₆₄	—	281	3	no	—
28	C₂×C₃₂	—	281	3	no	—
29	#131	Dic₂₈₁	1	1	yes	characteristic
30	M₃₂	Dic₂₈₁	1	3	yes	—
31	C₂×C₁₆	C₂×D₂₈₁	1	3	yes	—
32	C₃₂	—	281	1	no	—
33	C₃₂	—	281	3	no	—
34	#41	#14555886	1	1	yes	characteristic
35	M₁₆	#14555886	1	3	yes	—
36	C₂×C₈	C₂×Dic₂₈₁	1	3	yes	—
37	C₁₆	C₂×Dic₂₈₁	1	3	yes	—
38	C₁₆	C₂²×D₂₈₁	1	1	yes	characteristic
39	Q₈	#17985113	1	1	yes	characteristic
40	D₄	#17985113	1	3	yes	—
41	C₂×C₄	C₂×#14555886	1	3	yes	—
42	C₈	C₂×#14555886	1	3	yes	—
43	C₈	C₂²×Dic₂₈₁	1	1	yes	characteristic
44	C₂²	C₂×#17985113	1	3	yes	—
45	C₄	C₂×#17985113	1	3	yes	—
46	C₄	C₂²×#14555886	1	1	yes	characteristic
47	C₂	—	2	3	no	—
48	C₂	C₂²×#17985113	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₁₆	C₂²×D₂₈₁
commutator, socle	C₂×C₂₈₁	C₂²×C₁₆
Fitting	#504×C₂₈₁	C₂
prime radical	#41×C₂₈₁	C₈
cosocle	C₁₆×C₂₈₁	C₂³
hypercenter	#504	D₂₈₁
hypocenter	C₂₈₁	#2258
LCS	G ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₁₆ ◁ #504

Complements

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

N	H ≅ G/N	type
1. #31823297	C₂	semidirect
2. C₂×#22582785	C₂	semidirect
24. C₂₈₁	#2258	semidirect

Maximal subgroups

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

subgroup	index
#31823297	2
C₂×#22582785	2
#504×C₂₈₁	2
#2258	281