Subgroups — #49093506

Order 35968.

50 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	#31823293	C₂	1	1	yes	maximal, characteristic
3	#368×C₂₈₁	C₂	1	1	yes	maximal, characteristic
4	#22582815	—	2	1	no	—
5	#22582785	C₄	1	2	yes	—
6	C₂×C₁₆×C₂₈₁	C₂²	1	1	yes	characteristic
7	#108×C₂₈₁	—	2	1	no	—
8	#17985122	—	4	1	no	—
9	M₁₆×C₂₈₁	—	4	1	no	—
10	C₂×C₈×C₂₈₁	D₄	1	1	yes	characteristic
11	C₁₆×C₂₈₁	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₂₈₁	Q₈	1	1	yes	characteristic
13	#14555886	—	8	1	no	—
14	C₂×C₄×C₂₈₁	D₈	1	1	yes	characteristic
15	C₈×C₂₈₁	—	8	1	no	—
16	C₈×C₂₈₁	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₂₈₁	Q₁₆	1	1	yes	characteristic
18	C₂²×C₂₈₁	Q₃₂	1	1	yes	characteristic
19	C₄×C₂₈₁	#107	1	1	yes	characteristic
20	C₄×C₂₈₁	D₁₆	1	1	yes	characteristic
21	C₂×C₂₈₁	—	2	1	no	—
22	C₂×C₂₈₁	#366	1	1	yes	characteristic
23	C₂₈₁	#1425	1	1	yes	characteristic, complemented, Sylow
24	#1425	—	281	1	no	maximal, Sylow
25	C₂×C₃₂	—	281	1	no	—
26	#368	—	281	1	no	—
27	#368	D₂₈₁	1	1	yes	characteristic
28	C₂×C₁₆	C₂×D₂₈₁	1	1	yes	characteristic
29	#108	—	2	1	no	—
30	#108	—	562	1	no	—
31	C₃₂	—	281	2	no	—
32	M₁₆	—	4	1	no	—
33	M₁₆	—	1124	1	no	—
34	C₂×C₈	C₂²⋊D₂₈₁	1	1	yes	characteristic
35	C₁₆	C₄×D₂₈₁	1	1	yes	characteristic
36	C₁₆	Dic₅₆₂	1	1	yes	characteristic
37	C₂×C₄	#17985123	1	1	yes	characteristic
38	C₈	—	8	1	no	—
39	C₈	—	2248	1	no	—
40	C₈	#17985117	1	1	yes	characteristic
41	C₈	#17985128	1	1	yes	characteristic
42	C₂²	#22582825	1	1	yes	characteristic
43	C₄	#22582812	1	1	yes	characteristic
44	C₄	#22582820	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#31823288	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#22582820
commutator	C₁₆×C₂₈₁	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₈₁
Fitting	#368×C₂₈₁	C₂
socle	C₂×C₂₈₁	#366
prime radical	C₂²×C₂₈₁	Q₃₂
cosocle	C₂×C₁₆×C₂₈₁	C₂²
hypercenter	#368	D₂₈₁
hypocenter	C₂₈₁	#1425
LCS	G ▷ C₁₆×C₂₈₁ ▷ C₈×C₂₈₁ ▷ C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
23. C₂₈₁	#1425	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
#31823293	2
#368×C₂₈₁	2
#1425	281