Subgroups — C₃×ΓL(1,𝔽₈)⋊D₁₅₇ #34089965

Order 19782.

48 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	C₃	1	3	yes	maximal, direct product factor
3	C₃×D₁₀₉₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₇×C₁₅₇	C₂×C₃	1	1	yes	characteristic, complemented
5	ΓL(1,𝔽₈)×C₁₅₇	C₂×C₃	1	3	yes	complemented
6	C₃²×D₁₅₇	—	7	1	no	maximal, Hall
7	D₁₀₉₉	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃²×C₁₅₇	—	7	1	no	Hall
9	C₇×C₁₅₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
10	C₃×D₁₅₇	—	7	3	no	—
11	C₃×D₁₅₇	—	21	1	no	—
12	C₃×C₁₅₇	—	7	3	no	—
13	C₃×C₁₅₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
14	D₁₅₇	—	21	1	no	Hall
15	C₁₅₇	C₃×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
16	C₃×AGL(1,𝔽₇)	—	157	1	no	maximal, Hall
17	C₃×ΓL(1,𝔽₈)	D₁₅₇	1	1	yes	characteristic, complemented, Hall
18	C₃×D₇	—	157	1	no	—
19	AGL(1,𝔽₇)	—	157	3	no	—
20	C₃×C₇	C₃×D₁₅₇	1	1	yes	characteristic, complemented
21	ΓL(1,𝔽₈)	C₃×D₁₅₇	1	3	yes	complemented
22	C₂×C₃²	—	1099	1	no	Hall
23	D₇	—	157	1	no	Hall
24	C₃²	—	7	1	no	Sylow
25	C₇	C₃²×D₁₅₇	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃	—	1099	3	no	—
27	C₂×C₃	—	1099	1	no	—
28	C₃	—	7	3	no	—
29	C₃	ΓL(1,𝔽₈)⋊D₁₅₇	1	1	yes	characteristic, direct product factor
30	C₂	—	1099	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	ΓL(1,𝔽₈)⋊D₁₅₇
commutator, cosocle, hypocenter	C₇×C₁₅₇	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₅₇	C₂×C₃
LCS	G ▷ C₇×C₁₅₇
UCS	C₁ ◁ C₃

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.