Subgroups — #31823498

Order 17984.

114 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	#22582837	C₂	1	2	yes	maximal
3	#22582812	C₂	1	2	yes	maximal, complemented
4	#22582811	C₂	1	1	yes	maximal, characteristic, complemented
5	#106×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₂₈₁	C₂²	1	1	yes	characteristic
7	C₂×#14555886	C₂²	1	1	yes	characteristic
8	C₈×D₂₈₁	C₄	1	4	yes	complemented
9	C₄⋊Dic₂₈₁	C₂²	1	2	yes	—
10	#17985115	—	2	2	no	—
11	C₄×Dic₂₈₁	—	2	2	no	—
12	C₂×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₂₈₁	C₂²	1	2	yes	—
14	C₂²×D₂₈₁	D₄	1	1	yes	characteristic
15	C₂×Dic₂₈₁	—	2	2	no	—
16	C₂×Dic₂₈₁	D₄	1	1	yes	characteristic
17	C₄×D₂₈₁	C₂×C₄	1	2	yes	—
18	C₄×D₂₈₁	Q₈	1	2	yes	—
19	#14555886	C₂×C₄	1	2	yes	—
20	C₂×C₄×C₂₈₁	—	2	2	no	—
21	C₂×C₄×C₂₈₁	C₂³	1	1	yes	characteristic
22	C₈×C₂₈₁	C₂×C₄	1	2	yes	—
23	C₂²×C₂₈₁	C₂×D₄	1	1	yes	characteristic
24	C₂×D₂₈₁	—	2	2	no	—
25	C₂×D₂₈₁	C₄⋊C₄	1	2	yes	—
26	C₄×C₂₈₁	—	4	2	no	—
27	C₄×C₂₈₁	C₂²×C₄	1	1	yes	characteristic
28	C₄×C₂₈₁	C₂×Q₈	1	1	yes	characteristic
29	Dic₂₈₁	—	4	2	no	—
30	Dic₂₈₁	C₄⋊C₄	1	2	yes	—
31	C₂×C₂₈₁	C₂×C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₂₈₁	#135	1	2	yes	—
33	D₂₈₁	—	2	2	no	—
34	C₂₈₁	#427	1	1	yes	characteristic, complemented, Sylow
35	#427	—	281	1	no	maximal, Sylow
36	C₂²×C₈	—	281	1	no	—
37	#117	—	281	2	no	—
38	#107	—	281	2	no	—
39	#106	—	281	1	no	—
40	#106	D₂₈₁	1	1	yes	characteristic, complemented
41	C₂²×C₄	—	281	1	no	—
42	C₂×C₈	—	281	1	no	—
43	C₂×C₈	—	281	4	no	—
44	C₂×C₈	C₂×D₂₈₁	1	1	yes	characteristic
45	C₄⋊C₄	—	281	2	no	—
46	C₄⋊C₄	C₂×D₂₈₁	1	2	yes	—
47	C₂²⋊C₄	—	562	2	no	—
48	C₄²	—	562	2	no	—
49	C₂³	—	281	1	no	—
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	—	281	1	no	—
52	C₂×C₄	—	281	2	no	—
53	C₂×C₄	—	281	2	no	—
54	C₂×C₄	—	562	2	no	—
55	C₂×C₄	C₂²×D₂₈₁	1	1	yes	characteristic
56	C₈	—	281	2	no	—
57	C₈	C₄×D₂₈₁	1	2	yes	—
58	C₂²	—	281	2	no	—
59	C₂²	—	562	2	no	—
60	C₂²	D₄×D₂₈₁	1	1	yes	characteristic
61	C₄	—	4	2	no	—
62	C₄	—	281	2	no	—
63	C₄	—	1124	2	no	—
64	C₄	C₂×C₄×D₂₈₁	1	1	yes	characteristic
65	C₄	Q₈×D₂₈₁	1	1	yes	characteristic
66	C₂	—	562	2	no	—
67	C₂	C₄⋊C₄×D₂₈₁	1	1	yes	characteristic
68	C₂	#22582900	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₂₈₁
commutator	C₄×C₂₈₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₈₁
Fitting	#106×C₂₈₁	C₂
socle	C₂²×C₂₈₁	C₂×D₄
prime radical	C₂²×D₂₈₁	D₄
cosocle	C₂×C₄×C₂₈₁	C₂³
hypercenter	#106	D₂₈₁
hypocenter	C₂₈₁	#427
LCS	G ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
3. #22582812	C₂	semidirect
4. #22582811	C₂	semidirect
5. #106×C₂₈₁	C₂	semidirect
8. C₈×D₂₈₁	C₄	semidirect
34. C₂₈₁	#427	semidirect
40. #106	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
#22582837	2
#22582812	2
#22582811	2
#106×C₂₈₁	2
#427	281