Subgroups — C₇⋊D₂₂₃₃ #44530516

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	D₂₂₃₃	—	7	8	no	maximal
3	C₇⋊D₂₀₃	—	11	1	no	maximal, Hall
4	C₇×C₁₁×C₂₉	D₇	1	8	yes	complemented
5	C₇²×C₂₉	D₁₁	1	1	yes	characteristic, complemented, Hall
6	C₇⋊D₇₇	—	29	1	no	maximal, Hall
7	D₃₁₉	—	49	1	no	Hall
8	C₇²×C₁₁	D₂₉	1	1	yes	characteristic, complemented, Hall
9	D₂₀₃	—	77	8	no	—
10	C₁₁×C₂₉	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
11	C₇×C₂₉	D₇₇	1	8	yes	complemented
12	D₇₇	—	203	8	no	—
13	C₇⋊D₇	—	319	1	no	Hall
14	C₇×C₁₁	D₂₀₃	1	8	yes	complemented
15	D₂₉	—	539	1	no	Hall
16	C₇²	D₃₁₉	1	1	yes	characteristic, complemented, Sylow
17	C₂₉	C₇⋊D₇₇	1	1	yes	characteristic, complemented, Sylow
18	D₁₁	—	1421	1	no	Hall
19	D₇	—	2233	8	no	—
20	C₁₁	C₇⋊D₂₀₃	1	1	yes	characteristic, complemented, Sylow
21	C₇	D₂₂₃₃	1	8	yes	complemented
22	C₂	—	15631	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₁₁×C₂₉	C₂
LCS	G ▷ C₇²×C₁₁×C₂₉
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.