Subgroups — C₃×C₃₇×C₇⋊D₇ #24926005

Order 10878.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇²×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₇×C₇⋊D₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇²×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₇×C₃₇	—	7	8	no	maximal
5	C₃×C₇×C₃₇	D₇	1	8	yes	complemented
6	D₇×C₃₇	—	7	8	no	—
7	C₃×C₇⋊D₇	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₃₇	C₃×D₇	1	8	yes	complemented
9	C₂×C₃×C₃₇	—	49	1	no	Hall
10	C₃×C₇²	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
11	C₃×C₃₇	C₇⋊D₇	1	1	yes	characteristic, direct product factor, Hall
12	C₇⋊D₇	C₃×C₃₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃₇	—	49	1	no	Hall
14	C₇²	C₂×C₃×C₃₇	1	1	yes	characteristic, complemented, Sylow
15	C₃×D₇	—	7	8	no	—
16	C₃₇	C₃×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
17	C₃×C₇	D₇×C₃₇	1	8	yes	complemented
18	D₇	—	7	8	no	—
19	C₇	C₃×D₇×C₃₇	1	8	yes	complemented
20	C₂×C₃	—	49	1	no	Hall
21	C₃	C₃₇×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₃₇	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂×C₃×C₃₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₃₇	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃×C₃₇

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.