Subgroups — C₂×ΓL(1,𝔽₈)×D₁₁ #11745113

Order 924.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented
2	ΓL(1,𝔽₈)×D₁₁	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇×D₁₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₁×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×C₁₁	C₂×C₃	1	1	yes	characteristic, complemented
6	C₇×D₁₁	C₂×C₃	1	2	yes	complemented
7	C₂×C₃×D₁₁	—	7	1	no	maximal, Hall
8	C₂²×ΓL(1,𝔽₈)	—	11	1	no	maximal, Hall
9	C₇×C₁₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₁₁	—	7	1	no	—
11	C₃×D₁₁	—	7	2	no	—
12	C₂×D₁₁	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Hall
13	C₂×ΓL(1,𝔽₈)	—	11	2	no	—
14	C₂×ΓL(1,𝔽₈)	D₁₁	1	1	yes	characteristic, direct product factor
15	C₃×C₁₁	—	7	1	no	Hall
16	C₂²×C₇	—	11	1	no	Hall
17	C₂×C₁₁	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
18	D₁₁	C₂×ΓL(1,𝔽₈)	1	2	yes	direct product factor
19	ΓL(1,𝔽₈)	C₂×D₁₁	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₇	—	11	2	no	—
21	C₂×C₇	C₃×D₁₁	1	1	yes	characteristic, complemented
22	C₂²×C₃	—	77	1	no	Hall
23	C₁₁	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
24	C₇	C₂×C₃×D₁₁	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃	—	7	1	no	—
26	C₂×C₃	—	77	2	no	—
27	C₂²	—	11	1	no	Sylow
28	C₃	—	7	1	no	Sylow
29	C₂	—	11	2	no	—
30	C₂	ΓL(1,𝔽₈)×D₁₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	ΓL(1,𝔽₈)×D₁₁
commutator, cosocle, hypocenter	C₇×C₁₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₁	C₂×C₃
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₂

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.