Subgroups — #31773722

Order 17344.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₇₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#22576094	C₂	1	1	yes	maximal, characteristic
3	#107×C₂₇₁	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Dic₂₇₁	—	2	1	no	—
5	C₂₇₁⋊C₁₆	C₄	1	2	yes	complemented
6	C₂×C₈×C₂₇₁	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₂₇₁	—	2	1	no	—
8	C₂×Dic₂₇₁	—	4	1	no	—
9	C₂×C₄×C₂₇₁	—	4	1	no	—
10	C₂×C₄×C₂₇₁	D₄	1	1	yes	characteristic
11	C₈×C₂₇₁	C₂×C₄	1	1	yes	characteristic
12	C₈×C₂₇₁	Q₈	1	1	yes	characteristic
13	C₂²×C₂₇₁	D₈	1	1	yes	characteristic
14	C₄×C₂₇₁	—	8	1	no	—
15	C₄×C₂₇₁	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₂₇₁	Q₁₆	1	1	yes	characteristic
17	Dic₂₇₁	—	8	1	no	—
18	C₂×C₂₇₁	#107	1	1	yes	characteristic
19	C₂×C₂₇₁	D₁₆	1	1	yes	characteristic
20	C₂×C₂₇₁	Q₃₂	1	1	yes	characteristic
21	C₂₇₁	#366	1	1	yes	characteristic, complemented, Sylow
22	#366	—	271	1	no	maximal, Sylow
23	C₂×C₁₆	—	271	1	no	—
24	#107	—	271	1	no	—
25	#107	D₂₇₁	1	1	yes	characteristic
26	C₂×C₈	C₂×D₂₇₁	1	1	yes	characteristic
27	C₄⋊C₄	—	2	1	no	—
28	C₄⋊C₄	—	542	1	no	—
29	C₁₆	—	271	2	no	—
30	C₂×C₄	—	4	1	no	—
31	C₂×C₄	—	1084	1	no	—
32	C₂×C₄	C₂²⋊D₂₇₁	1	1	yes	characteristic
33	C₈	C₄×D₂₇₁	1	1	yes	characteristic
34	C₈	Dic₅₄₂	1	1	yes	characteristic
35	C₂²	#16864639	1	1	yes	characteristic
36	C₄	—	8	1	no	—
37	C₄	—	2168	1	no	—
38	C₄	Dic₂₇₁⋊C₄	1	1	yes	characteristic
39	C₄	#16864644	1	1	yes	characteristic
40	C₂	#22576093	1	1	yes	characteristic
41	C₂	#22576101	1	1	yes	characteristic
42	C₂	#22576106	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16864639
commutator	C₈×C₂₇₁	C₂×C₄
Frattini	C₂×C₈	C₂×D₂₇₁
Fitting	#107×C₂₇₁	C₂
socle, prime radical	C₂²×C₂₇₁	D₈
cosocle	C₂×C₈×C₂₇₁	C₂²
hypercenter	#107	D₂₇₁
hypocenter	C₂₇₁	#366
LCS	G ▷ C₈×C₂₇₁ ▷ C₄×C₂₇₁ ▷ C₂×C₂₇₁ ▷ C₂₇₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
5. C₂₇₁⋊C₁₆	C₄	semidirect
21. C₂₇₁	#366	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₇₁⋊C₁₆	2
#22576094	2
#107×C₂₇₁	2
#366	271