Subgroups — #31823188

Order 17984.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17985117	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊#14555886	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊C₈×C₂₈₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₂₈₁	C₄	1	1	yes	characteristic
5	C₂²×Dic₂₈₁	C₄	1	1	yes	characteristic
6	C₂×#14555886	—	2	1	no	—
7	#17985117	—	2	1	no	—
8	#17985117	—	2	1	no	—
9	C₂²×C₄×C₂₈₁	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₂₈₁	—	2	1	no	—
11	C₂×Dic₂₈₁	—	2	1	no	—
12	C₂×Dic₂₈₁	—	2	1	no	—
13	C₂×Dic₂₈₁	—	2	1	no	—
14	C₂×Dic₂₈₁	—	4	1	no	—
15	C₂×Dic₂₈₁	C₈	1	2	yes	complemented
16	#14555886	—	4	1	no	—
17	C₂³×C₂₈₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₂₈₁	—	4	1	no	—
19	C₂×C₄×C₂₈₁	D₄	1	1	yes	characteristic
20	C₂×C₄×C₂₈₁	D₄	1	1	yes	characteristic
21	C₈×C₂₈₁	—	4	1	no	—
22	C₂²×C₂₈₁	—	2	1	no	—
23	C₂²×C₂₈₁	—	2	1	no	—
24	C₂²×C₂₈₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂²×C₂₈₁	C₂×C₈	1	1	yes	characteristic
26	C₂²×C₂₈₁	M₁₆	1	1	yes	characteristic
27	C₄×C₂₈₁	—	2	1	no	—
28	C₄×C₂₈₁	—	2	1	no	—
29	Dic₂₈₁	—	2	2	no	—
30	Dic₂₈₁	—	4	1	no	—
31	C₂×C₂₈₁	—	2	1	no	—
32	C₂×C₂₈₁	—	2	1	no	—
33	C₂×C₂₈₁	C₂²⋊C₈	1	1	yes	characteristic
34	C₂×C₂₈₁	#99	1	1	yes	characteristic
35	C₂×C₂₈₁	#101	1	1	yes	characteristic
36	C₂₈₁	#324	1	1	yes	characteristic, complemented, Sylow
37	#324	—	281	1	no	maximal, Sylow
38	C₂×C₄⋊C₄	—	281	1	no	—
39	C₂²⋊C₈	—	281	1	no	—
40	C₂²⋊C₈	D₂₈₁	1	1	yes	characteristic
41	C₂²×C₄	—	281	1	no	—
42	C₂²×C₄	—	281	1	no	—
43	C₂²×C₄	C₂×D₂₈₁	1	1	yes	characteristic
44	C₂×C₈	—	2	1	no	—
45	C₂×C₈	—	562	1	no	—
46	C₄⋊C₄	—	562	1	no	—
47	C₄⋊C₄	—	562	1	no	—
48	C₂³	C₄×D₂₈₁	1	1	yes	characteristic
49	C₂×C₄	—	4	1	no	—
50	C₂×C₄	—	281	2	no	—
51	C₂×C₄	—	562	1	no	—
52	C₂×C₄	—	562	1	no	—
53	C₂×C₄	—	562	1	no	—
54	C₂×C₄	—	1124	1	no	—
55	C₂×C₄	C₂²⋊D₂₈₁	1	1	yes	characteristic
56	C₂×C₄	D₁₁₂₄	1	1	yes	characteristic
57	C₈	—	4	1	no	—
58	C₈	—	1124	1	no	—
59	C₂²	—	2	1	no	—
60	C₂²	—	2	1	no	—
61	C₂²	#17985115	1	1	yes	characteristic
62	C₂²	C₈×D₂₈₁	1	1	yes	characteristic
63	C₂²	#17985121	1	1	yes	characteristic
64	C₄	—	2	1	no	—
65	C₄	—	2	1	no	—
66	C₄	—	562	2	no	—
67	C₄	—	1124	1	no	—
68	C₂	—	2	1	no	—
69	C₂	—	2	1	no	—
70	C₂	#22582791	1	1	yes	characteristic
71	C₂	#22582793	1	1	yes	characteristic
72	C₂	#22582797	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#17985115
commutator	C₂²×C₂₈₁	C₂×C₈
Frattini	C₂²×C₄	C₂×D₂₈₁
Fitting	C₂²⋊C₈×C₂₈₁	C₂
socle	C₂²×C₂₈₁	C₂²⋊C₄
prime radical	C₂³×C₂₈₁	C₂×C₄
cosocle	C₂²×C₄×C₂₈₁	C₂²
hypercenter	C₂²⋊C₈	D₂₈₁
hypocenter	C₂₈₁	#324
LCS	G ▷ C₂²×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
15. C₂×Dic₂₈₁	C₈	semidirect
36. C₂₈₁	#324	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17985117	2
C₂²⋊#14555886	2
C₂²⋊C₈×C₂₈₁	2
#324	281