Subgroups — C₁₁×C₂₉×C₇⋊D₇ #44530513

Order 31262.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₁₁×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₇×C₂₉	—	7	8	no	maximal
3	C₂₉×C₇⋊D₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₁₁×C₂₉	D₇	1	8	yes	complemented
5	C₇²×C₂₉	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
6	C₁₁×C₇⋊D₇	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₁₁×C₂₉	—	49	1	no	Hall
8	C₇²×C₁₁	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
9	D₇×C₂₉	—	7	8	no	—
10	C₁₁×C₂₉	C₇⋊D₇	1	1	yes	characteristic, direct product factor, Hall
11	C₇×C₂₉	C₁₁×D₇	1	8	yes	complemented
12	C₁₁×D₇	—	7	8	no	—
13	C₇⋊D₇	C₁₁×C₂₉	1	1	yes	characteristic, direct product factor, Hall
14	C₇×C₁₁	D₇×C₂₉	1	8	yes	complemented
15	C₂×C₂₉	—	49	1	no	Hall
16	C₇²	C₂×C₁₁×C₂₉	1	1	yes	characteristic, complemented, Sylow
17	C₂₉	C₁₁×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₁₁	—	49	1	no	Hall
19	D₇	—	7	8	no	—
20	C₁₁	C₂₉×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₇	C₁₁×D₇×C₂₉	1	8	yes	complemented
22	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₂₉	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂×C₁₁×C₂₉
Frattini	C₁	G
Fitting, socle	C₇²×C₁₁×C₂₉	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₁₁×C₂₉

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.