Subgroups — C₃⋊(C₇⋊D₇₆₃) #44545273

Order 32046.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇²×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇⋊D₇₆₃	—	3	1	no	maximal, Hall
3	C₇²×C₁₀₉	D₃	1	1	yes	characteristic, complemented, Hall
4	D₂₂₈₉	—	7	8	no	maximal
5	C₃×C₇×C₁₀₉	D₇	1	8	yes	complemented
6	D₇₆₃	—	21	8	no	—
7	C₇×C₁₀₉	D₂₁	1	8	yes	complemented
8	D₃₂₇	—	49	1	no	Hall
9	C₃×C₁₀₉	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
10	C₃⋊(C₇⋊D₇)	—	109	1	no	maximal, Hall
11	D₁₀₉	—	147	1	no	Hall
12	C₃×C₇²	D₁₀₉	1	1	yes	characteristic, complemented, Hall
13	C₁₀₉	C₃⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented, Sylow
14	C₇⋊D₇	—	327	1	no	Hall
15	C₇²	D₃₂₇	1	1	yes	characteristic, complemented, Sylow
16	D₂₁	—	763	8	no	—
17	C₃×C₇	D₇₆₃	1	8	yes	complemented
18	D₇	—	2289	8	no	—
19	C₇	D₂₂₈₉	1	8	yes	complemented
20	D₃	—	5341	1	no	Hall
21	C₃	C₇⋊D₇₆₃	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	16023	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇²×C₁₀₉	C₂
LCS	G ▷ C₃×C₇²×C₁₀₉
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.