Subgroups — ΓL(1,𝔽₈)×D₃₀₁ #27162441

Order 12642.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×ΓL(1,𝔽₈)×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₃₀₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇²×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₃₀₁	—	7	1	no	maximal
5	ΓL(1,𝔽₈)×D₄₃	—	7	1	no	maximal
6	C₃×C₇×C₄₃	—	7	1	no	—
7	ΓL(1,𝔽₈)×C₄₃	D₇	1	1	yes	characteristic, complemented
8	D₃₀₁	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
9	C₇×D₄₃	—	7	1	no	—
10	C₇×C₄₃	—	6	1	no	—
11	C₇×C₄₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
12	C₇×C₄₃	C₃×D₇	1	1	yes	characteristic, complemented
13	D₇×ΓL(1,𝔽₈)	—	43	1	no	maximal, Hall
14	C₃×D₄₃	—	49	1	no	Hall
15	C₇×ΓL(1,𝔽₈)	D₄₃	1	1	yes	characteristic, complemented, Hall
16	C₃×C₄₃	—	7	1	no	Hall
17	C₇×D₇	—	43	1	no	Hall
18	D₄₃	—	7	1	no	Hall
19	C₇²	C₃×D₄₃	1	1	yes	characteristic, complemented, Sylow
20	C₄₃	D₇×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
21	C₃×D₇	—	301	1	no	—
22	C₂×ΓL(1,𝔽₈)	—	301	1	no	—
23	C₃×C₇	—	7	1	no	—
24	ΓL(1,𝔽₈)	D₃₀₁	1	1	yes	characteristic, direct product factor
25	C₂×C₇	—	301	1	no	—
26	D₇	—	43	1	no	—
27	C₇	—	6	1	no	—
28	C₇	ΓL(1,𝔽₈)×D₄₃	1	1	yes	characteristic, complemented
29	C₇	C₃×D₃₀₁	1	1	yes	characteristic, complemented
30	C₂×C₃	—	2107	1	no	Hall
31	C₃	—	7	1	no	Sylow
32	C₂	—	301	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₄₃	C₂×C₃
LCS	G ▷ C₇²×C₄₃
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.