Subgroups — C₃×C₇₉×C₇⋊D₇ #37551174

Order 23226.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇²×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇₉×C₇⋊D₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₇²×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₇×C₇₉	—	7	8	no	maximal
5	C₃×C₇×C₇₉	D₇	1	8	yes	complemented
6	D₇×C₇₉	—	7	8	no	—
7	C₇×C₇₉	C₃×D₇	1	8	yes	complemented
8	C₂×C₃×C₇₉	—	49	1	no	Hall
9	C₃×C₇⋊D₇	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃×C₇₉	C₇⋊D₇	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₇₉	—	49	1	no	Hall
12	C₃×C₇²	C₂×C₇₉	1	1	yes	characteristic, complemented, Hall
13	C₇⋊D₇	C₃×C₇₉	1	1	yes	characteristic, direct product factor, Hall
14	C₇₉	C₃×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
15	C₇²	C₂×C₃×C₇₉	1	1	yes	characteristic, complemented, Sylow
16	C₃×D₇	—	7	8	no	—
17	C₃×C₇	D₇×C₇₉	1	8	yes	complemented
18	D₇	—	7	8	no	—
19	C₇	C₃×D₇×C₇₉	1	8	yes	complemented
20	C₂×C₃	—	49	1	no	Hall
21	C₃	C₇₉×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₇₉	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂×C₃×C₇₉
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₇₉	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃×C₇₉

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.