Subgroups — C₁₁⋊AGL(1,𝔽₂₉) #22582002

Order 8932.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₂₉⋊C₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁⋊#1181	C₇	1	1	yes	maximal, characteristic, complemented, Hall
4	AGL(1,𝔽₂₉)	—	11	1	no	maximal, Hall
5	C₁₁×D₂₉	C₂×C₇	1	1	yes	characteristic
6	D₂₉⋊C₇	D₁₁	1	1	yes	characteristic
7	C₁₁×C₂₉	C₄×C₇	1	1	yes	characteristic, complemented, Hall
8	C₇×Dic₁₁	—	29	1	no	maximal, Hall
9	C₂₉⋊C₇	Dic₁₁	1	1	yes	characteristic, complemented, Hall
10	C₂×C₇×C₁₁	—	29	1	no	—
11	#1181	—	11	1	no	Hall
12	C₇×C₁₁	—	29	1	no	Hall
13	D₂₉	C₇×D₁₁	1	1	yes	characteristic
14	Dic₁₁	—	29	1	no	Hall
15	C₂₉	C₇×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
16	C₄×C₇	—	319	1	no	Hall
17	C₂×C₁₁	—	29	1	no	—
18	C₂×C₇	—	29	1	no	—
19	C₁₁	AGL(1,𝔽₂₉)	1	1	yes	characteristic, complemented, Sylow
20	C₇	—	29	1	no	Sylow
21	C₄	—	319	1	no	Sylow
22	C₂	—	29	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₁×C₂₉	C₄×C₇
LCS	G ▷ C₁₁×C₂₉
UCS	C₁

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