Subgroups — C₃⋊(ΓL(1,𝔽₈)⋊D₁₅₇) #34089978

Order 19782.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×ΓL(1,𝔽₈)×C₁₅₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	ΓL(1,𝔽₈)⋊D₁₅₇	—	3	1	no	maximal
3	D₃₂₉₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₇×C₁₅₇	C₂×C₃	1	1	yes	characteristic, complemented
5	ΓL(1,𝔽₈)×C₁₅₇	—	2	1	no	—
6	ΓL(1,𝔽₈)×C₁₅₇	D₃	1	1	yes	characteristic, complemented
7	C₃×D₄₇₁	—	7	1	no	maximal, Hall
8	D₁₀₉₉	—	3	1	no	Hall
9	C₃²×C₁₅₇	—	14	1	no	Hall
10	C₇×C₁₅₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
11	D₄₇₁	—	7	1	no	—
12	C₃×D₁₅₇	—	21	1	no	—
13	C₃×C₁₅₇	—	14	1	no	—
14	C₃×C₁₅₇	—	14	1	no	—
15	C₃×C₁₅₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
16	D₁₅₇	—	21	1	no	Hall
17	C₁₅₇	C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
18	C₃⋊AGL(1,𝔽₇)	—	157	1	no	maximal, Hall
19	C₃×ΓL(1,𝔽₈)	D₁₅₇	1	1	yes	characteristic, complemented, Hall
20	D₂₁	—	157	1	no	—
21	AGL(1,𝔽₇)	—	471	1	no	—
22	C₃×C₇	C₃×D₁₅₇	1	1	yes	characteristic, complemented
23	ΓL(1,𝔽₈)	—	2	1	no	—
24	ΓL(1,𝔽₈)	D₄₇₁	1	1	yes	characteristic, complemented
25	C₃×D₃	—	1099	1	no	Hall
26	D₇	—	471	1	no	Hall
27	C₃²	—	14	1	no	Sylow
28	C₇	C₃×D₄₇₁	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	3297	1	no	—
30	D₃	—	1099	1	no	—
31	C₃	—	7	1	no	—
32	C₃	—	14	1	no	—
33	C₃	ΓL(1,𝔽₈)⋊D₁₅₇	1	1	yes	characteristic, complemented
34	C₂	—	3297	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₅₇	C₂×C₃
LCS	G ▷ C₃×C₇×C₁₅₇
UCS	C₁

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

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