Subgroups — #49093504

Order 35968.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22582785	C₂	1	1	yes	maximal, characteristic
2	#31823289	C₂	1	1	yes	maximal, characteristic
3	#366×C₂₈₁	C₂	1	1	yes	maximal, characteristic
4	#22582813	—	2	1	no	—
5	#22582785	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₂₈₁	C₂²	1	1	yes	characteristic
7	#107×C₂₈₁	—	2	1	no	—
8	C₄⋊Dic₂₈₁	—	4	1	no	—
9	C₂×C₈×C₂₈₁	D₄	1	1	yes	characteristic
10	C₄⋊C₄×C₂₈₁	—	4	1	no	—
11	C₁₆×C₂₈₁	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₂₈₁	Q₈	1	1	yes	characteristic
13	C₂×Dic₂₈₁	—	8	1	no	—
14	C₂×C₄×C₂₈₁	—	8	1	no	—
15	C₂×C₄×C₂₈₁	D₈	1	1	yes	characteristic
16	C₈×C₂₈₁	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₂₈₁	Q₁₆	1	1	yes	characteristic
18	C₂²×C₂₈₁	D₁₆	1	1	yes	characteristic
19	C₄×C₂₈₁	—	16	1	no	—
20	C₄×C₂₈₁	#107	1	1	yes	characteristic
21	C₄×C₂₈₁	Q₃₂	1	1	yes	characteristic
22	Dic₂₈₁	—	16	1	no	—
23	C₂×C₂₈₁	#366	1	1	yes	characteristic
24	C₂×C₂₈₁	SD₆₄	1	1	yes	characteristic
25	C₂×C₂₈₁	SD₆₄	1	1	yes	characteristic
26	C₂₈₁	#1424	1	1	yes	characteristic, complemented, Sylow
27	#1424	—	281	1	no	maximal, Sylow
28	C₂×C₃₂	—	281	1	no	—
29	#366	—	281	1	no	—
30	#366	D₂₈₁	1	1	yes	characteristic
31	C₂×C₁₆	C₂×D₂₈₁	1	1	yes	characteristic
32	#107	—	2	1	no	—
33	#107	—	562	1	no	—
34	C₃₂	—	281	2	no	—
35	C₂×C₈	C₂²⋊D₂₈₁	1	1	yes	characteristic
36	C₄⋊C₄	—	4	1	no	—
37	C₄⋊C₄	—	1124	1	no	—
38	C₁₆	C₄×D₂₈₁	1	1	yes	characteristic
39	C₁₆	Dic₅₆₂	1	1	yes	characteristic
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	2248	1	no	—
42	C₂×C₄	#17985123	1	1	yes	characteristic
43	C₈	#17985117	1	1	yes	characteristic
44	C₈	#17985128	1	1	yes	characteristic
45	C₂²	#22582820	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	4496	1	no	—
48	C₄	#22582812	1	1	yes	characteristic
49	C₄	#22582825	1	1	yes	characteristic
50	C₂	#31823288	1	1	yes	characteristic
51	C₂	#31823300	1	1	yes	characteristic
52	C₂	#31823301	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#22582820
commutator	C₁₆×C₂₈₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₈₁
Fitting	#366×C₂₈₁	C₂
socle, prime radical	C₂²×C₂₈₁	D₁₆
cosocle	C₂×C₁₆×C₂₈₁	C₂²
hypercenter	#366	D₂₈₁
hypocenter	C₂₈₁	#1424
LCS	G ▷ C₁₆×C₂₈₁ ▷ C₈×C₂₈₁ ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
5. #22582785	C₄	semidirect
26. C₂₈₁	#1424	semidirect

Maximal subgroups

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

subgroup	index
C₂×#22582785	2
#31823289	2
#366×C₂₈₁	2
#1424	281