Subgroups — #31823510

Order 17984.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17985121	C₂	1	1	yes	maximal, characteristic
2	M₁₆×D₂₈₁	C₂	1	2	yes	maximal
3	#22582815	C₂	1	1	yes	maximal, characteristic, complemented
4	#22582814	C₂	1	2	yes	maximal, complemented
5	#108×C₂₈₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₂₈₁	C₂²	1	1	yes	characteristic
7	#17985122	C₂²	1	2	yes	—
8	#17985121	—	2	2	no	—
9	#17985121	C₄	1	4	yes	—
10	C₂×#14555886	C₂²	1	1	yes	characteristic
11	C₈×D₂₈₁	—	2	2	no	—
12	M₁₆×C₂₈₁	C₂²	1	2	yes	—
13	C₂×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
14	C₂²×D₂₈₁	Q₈	1	1	yes	characteristic
15	C₂×Dic₂₈₁	Q₈	1	1	yes	characteristic
16	C₄×D₂₈₁	C₂×C₄	1	2	yes	—
17	C₄×D₂₈₁	D₄	1	2	yes	—
18	#14555886	—	2	2	no	—
19	#14555886	C₂×C₄	1	2	yes	—
20	C₂×C₄×C₂₈₁	C₂³	1	1	yes	characteristic
21	C₈×C₂₈₁	—	2	2	no	—
22	C₈×C₂₈₁	C₂×C₄	1	2	yes	—
23	C₂²×C₂₈₁	C₂×Q₈	1	1	yes	characteristic
24	C₂×D₂₈₁	—	4	1	no	—
25	C₂×D₂₈₁	C₄⋊C₄	1	2	yes	—
26	C₄×C₂₈₁	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
28	Dic₂₈₁	C₄⋊C₄	1	2	yes	—
29	C₂×C₂₈₁	—	2	1	no	—
30	C₂×C₂₈₁	C₂×C₄⋊C₄	1	1	yes	characteristic
31	D₂₈₁	—	2	2	no	—
32	C₂₈₁	#430	1	1	yes	characteristic, complemented, Sylow
33	#430	—	281	1	no	maximal, Sylow
34	C₂×M₁₆	—	281	1	no	—
35	C₂×M₁₆	—	281	2	no	—
36	#108	—	281	2	no	—
37	#108	—	281	1	no	—
38	#108	D₂₈₁	1	1	yes	characteristic, complemented
39	C₂²×C₄	—	281	1	no	—
40	M₁₆	—	281	4	no	—
41	M₁₆	—	281	2	no	—
42	M₁₆	—	562	2	no	—
43	M₁₆	C₂×D₂₈₁	1	2	yes	—
44	C₂×C₈	—	281	1	no	—
45	C₂×C₈	—	562	2	no	—
46	C₂×C₈	C₂×D₂₈₁	1	1	yes	characteristic
47	C₂³	—	281	1	no	—
48	C₂×C₄	—	281	1	no	—
49	C₂×C₄	—	281	2	no	—
50	C₂×C₄	—	281	2	no	—
51	C₂×C₄	C₂²×D₂₈₁	1	1	yes	characteristic
52	C₈	—	2	2	no	—
53	C₈	—	281	2	no	—
54	C₈	—	562	2	no	—
55	C₈	C₄×D₂₈₁	1	2	yes	—
56	C₂²	—	281	2	no	—
57	C₂²	—	1124	1	no	—
58	C₂²	Q₈×D₂₈₁	1	1	yes	characteristic
59	C₄	—	281	2	no	—
60	C₄	C₂×C₄×D₂₈₁	1	1	yes	characteristic
61	C₄	D₄×D₂₈₁	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	562	2	no	—
64	C₂	C₄⋊C₄×D₂₈₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₂₈₁
commutator	C₄×C₂₈₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₂₈₁
Fitting	#108×C₂₈₁	C₂
socle	C₂×C₂₈₁	C₂×C₄⋊C₄
prime radical	C₂²×D₂₈₁	Q₈
cosocle	C₂×C₄×C₂₈₁	C₂³
hypercenter	#108	D₂₈₁
hypocenter	C₂₈₁	#430
LCS	G ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
3. #22582815	C₂	semidirect
4. #22582814	C₂	semidirect
5. #108×C₂₈₁	C₂	semidirect
32. C₂₈₁	#430	semidirect
38. #108	D₂₈₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17985121	2
M₁₆×D₂₈₁	2
#22582815	2
#22582814	2
#108×C₂₈₁	2
#430	281