Subgroups — #49093602

Order 35968.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31823514	C₂	1	3	yes	maximal
2	#31823185	C₂	1	3	yes	maximal, complemented
3	C₈²×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄²×D₂₈₁	C₂²	1	1	yes	characteristic
5	#22582808	C₄	1	6	yes	—
6	#22582791	C₄	1	6	yes	—
7	C₄×#14555886	C₂²	1	3	yes	—
8	C₄×C₈×C₂₈₁	C₂²	1	3	yes	—
9	C₂×C₄×D₂₈₁	C₂×C₄	1	3	yes	—
10	C₂×#14555886	C₂×C₄	1	6	yes	—
11	C₄×Dic₂₈₁	C₂×C₄	1	3	yes	—
12	C₂×C₈×C₂₈₁	C₂×C₄	1	6	yes	—
13	C₄²×C₂₈₁	C₂³	1	1	yes	characteristic
14	C₂²×D₂₈₁	C₄²	1	1	yes	characteristic
15	C₂×Dic₂₈₁	C₄²	1	3	yes	—
16	C₄×D₂₈₁	—	2	6	no	—
17	#14555886	—	2	6	no	—
18	C₂×C₄×C₂₈₁	C₂²×C₄	1	3	yes	—
19	C₈×C₂₈₁	—	2	6	no	—
20	C₂²×C₂₈₁	C₂×C₄²	1	1	yes	characteristic
21	C₂×D₂₈₁	—	2	3	no	—
22	C₄×C₂₈₁	#131	1	6	yes	—
23	Dic₂₈₁	—	2	3	no	—
24	C₂×C₂₈₁	#405	1	3	yes	—
25	D₂₈₁	—	4	1	no	—
26	C₂₈₁	#1454	1	1	yes	characteristic, complemented, Sylow
27	#1454	—	281	1	no	maximal, Sylow
28	#431	—	281	3	no	—
29	#322	—	281	3	no	—
30	C₈²	D₂₈₁	1	1	yes	characteristic, complemented
31	C₂×C₄²	—	281	1	no	—
32	C₄⋊C₈	—	281	6	no	—
33	C₂²⋊C₈	—	281	6	no	—
34	C₄×C₈	—	281	3	no	—
35	C₄×C₈	C₂×D₂₈₁	1	3	yes	—
36	C₂²×C₄	—	281	3	no	—
37	C₂×C₈	—	281	6	no	—
38	C₂×C₈	C₄×D₂₈₁	1	6	yes	—
39	C₄²	—	281	3	no	—
40	C₄²	C₂²×D₂₈₁	1	1	yes	characteristic
41	C₂³	—	281	1	no	—
42	C₂×C₄	—	281	3	no	—
43	C₂×C₄	—	562	6	no	—
44	C₂×C₄	C₂×C₄×D₂₈₁	1	3	yes	—
45	C₈	—	2	6	no	—
46	C₈	—	562	6	no	—
47	C₂²	—	562	3	no	—
48	C₂²	C₄²×D₂₈₁	1	1	yes	characteristic
49	C₄	—	562	3	no	—
50	C₄	#22582885	1	6	yes	—
51	C₂	—	1124	1	no	—
52	C₂	#31823417	1	3	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₂₈₁
commutator, socle	C₂²×C₂₈₁	C₂×C₄²
Fitting	C₈²×C₂₈₁	C₂
prime radical	C₂²×D₂₈₁	C₄²
cosocle	C₄²×C₂₈₁	C₂³
hypercenter	C₈²	D₂₈₁
hypocenter	C₂₈₁	#1454
LCS	G ▷ C₂²×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
2. #31823185	C₂	semidirect
3. C₈²×C₂₈₁	C₂	semidirect
26. C₂₈₁	#1454	semidirect
30. C₈²	D₂₈₁	semidirect

Maximal subgroups

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

subgroup	index
#31823514	2
#31823185	2
C₈²×C₂₈₁	2
#1454	281