Subgroups — PΣL(2,𝔽₂₇) #72224464

Order 29484.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	PSL(2,𝔽₂₇)	C₃	1	1	yes	maximal, characteristic, complemented
2	(C₃³⋊C₁₃)⋊C₃	—	28	1	no	maximal, Hall
3	C₃³⋊C₁₃	—	28	1	no	—
4	C₂×AGL(1,𝔽₇)	—	351	1	no	maximal
5	AΣL(1,𝔽₂₇)	—	364	1	no	Sylow
6	D₁₃⋊C₃	—	378	1	no	maximal
7	C₂×ΓL(1,𝔽₈)	—	351	1	no	—
8	AGL(1,𝔽₇)	—	351	2	no	—
9	C₁₃⋊C₃	—	378	1	no	—
10	C₃×A₄	—	819	1	no	maximal
11	C₂×D₇	—	351	1	no	Hall
12	C₃³	—	28	1	no	—
13	3₋¹⁺²	—	364	2	no	—
14	H(3,𝔽₃)	—	364	1	no	—
15	D₁₃	—	378	1	no	—
16	ΓL(1,𝔽₈)	—	351	1	no	—
17	C₂×C₇	—	351	1	no	—
18	D₇	—	351	2	no	—
19	C₁₃	—	378	1	no	Sylow
20	C₂²×C₃	—	819	1	no	—
21	A₄	—	819	2	no	—
22	A₄	—	819	1	no	—
23	C₃²	—	1092	1	no	—
24	C₃²	—	364	1	no	—
25	C₉	—	1092	2	no	—
26	C₇	—	351	1	no	Sylow
27	C₂×C₃	—	2457	1	no	—
28	C₂²	—	819	1	no	Sylow
29	C₃	—	819	1	no	—
30	C₃	—	364	1	no	—
31	C₂	—	351	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, socle, cosocle, hypocenter	PSL(2,𝔽₂₇)	C₃
LCS	G ▷ PSL(2,𝔽₂₇)
UCS	C₁

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

N	H ≅ G/N	type
1. PSL(2,𝔽₂₇)	C₃	semidirect

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