Subgroups — C₈₃×C₃⋊(C₇⋊D₇) #37567403

Order 24402.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇²×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₈₃×C₇⋊D₇	—	3	1	no	maximal, Hall
3	C₇²×C₈₃	D₃	1	1	yes	characteristic, complemented, Hall
4	D₂₁×C₈₃	—	7	8	no	maximal
5	C₃×C₇×C₈₃	D₇	1	8	yes	complemented
6	D₇×C₈₃	—	21	8	no	—
7	C₇×C₈₃	D₂₁	1	8	yes	complemented
8	D₃×C₈₃	—	49	1	no	Hall
9	C₃⋊(C₇⋊D₇)	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₈₃	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
11	C₂×C₈₃	—	147	1	no	Hall
12	C₃×C₇²	C₂×C₈₃	1	1	yes	characteristic, complemented, Hall
13	C₇⋊D₇	—	3	1	no	Hall
14	C₈₃	C₃⋊(C₇⋊D₇)	1	1	yes	characteristic, direct product factor, Sylow
15	C₇²	D₃×C₈₃	1	1	yes	characteristic, complemented, Sylow
16	D₂₁	—	7	8	no	—
17	C₃×C₇	D₇×C₈₃	1	8	yes	complemented
18	D₇	—	21	8	no	—
19	C₇	D₂₁×C₈₃	1	8	yes	complemented
20	D₃	—	49	1	no	Hall
21	C₃	C₈₃×C₇⋊D₇	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	147	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₈₃	C₃⋊(C₇⋊D₇)
commutator, cosocle, hypocenter	C₃×C₇²	C₂×C₈₃
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₈₃	C₂
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₈₃

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.