Subgroups — C₇⋊(C₁₁⋊D₂₀₉) #44565693

Order 32186.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₁²×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁⋊D₂₀₉	—	7	1	no	maximal, Hall
3	D₁₄₆₃	—	11	12	no	maximal
4	C₁₁²×C₁₉	D₇	1	1	yes	characteristic, complemented, Hall
5	C₇⋊(C₁₁⋊D₁₁)	—	19	1	no	maximal, Hall
6	C₇×C₁₁×C₁₉	D₁₁	1	12	yes	complemented
7	C₇×C₁₁²	D₁₉	1	1	yes	characteristic, complemented, Hall
8	D₂₀₉	—	77	12	no	—
9	D₁₃₃	—	121	1	no	Hall
10	C₁₁⋊D₁₁	—	133	1	no	Hall
11	C₁₁×C₁₉	D₇₇	1	12	yes	complemented
12	D₇₇	—	209	12	no	—
13	C₇×C₁₉	C₁₁⋊D₁₁	1	1	yes	characteristic, complemented, Hall
14	C₁₁²	D₁₃₃	1	1	yes	characteristic, complemented, Sylow
15	C₇×C₁₁	D₂₀₉	1	12	yes	complemented
16	D₁₉	—	847	1	no	Hall
17	D₁₁	—	1463	12	no	—
18	C₁₉	C₇⋊(C₁₁⋊D₁₁)	1	1	yes	characteristic, complemented, Sylow
19	D₇	—	2299	1	no	Hall
20	C₁₁	D₁₄₆₃	1	12	yes	complemented
21	C₇	C₁₁⋊D₂₀₉	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	16093	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₁²×C₁₉	C₂
LCS	G ▷ C₇×C₁₁²×C₁₉
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.