Subgroups — C₇×(C₇₉⋊C₃)⋊D₇ #37551131

Order 23226.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₇₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₅₅₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇²×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	(C₇₉⋊C₃)⋊D₇	C₇	1	1	yes	maximal, characteristic, direct product factor
5	C₇×D₇₉⋊C₃	—	7	1	no	maximal
6	C₇×C₇₉⋊C₃	—	2	3	no	—
7	C₇×C₇₉⋊C₃	D₇	1	1	yes	characteristic, complemented
8	C₇×C₇₉⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented
9	D₅₅₃	C₃×C₇	1	1	yes	characteristic, complemented
10	C₇×D₇₉	—	7	1	no	—
11	C₇×C₇₉	—	2	3	no	—
12	C₇×C₇₉	C₃×D₇	1	1	yes	characteristic, complemented
13	C₇×C₇₉	C₂×C₃×C₇	1	1	yes	characteristic, complemented
14	D₇₉⋊C₃	—	7	1	no	Hall
15	C₃×C₇×D₇	—	79	1	no	maximal, Hall
16	C₇₉⋊C₃	C₇×D₇	1	1	yes	characteristic, complemented, Hall
17	D₇₉	—	7	1	no	Hall
18	C₃×C₇²	—	79	1	no	Hall
19	C₇×D₇	—	237	1	no	Hall
20	C₇₉	C₃×C₇×D₇	1	1	yes	characteristic, complemented, Sylow
21	C₇²	D₇₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃×C₇	—	553	1	no	—
23	C₃×D₇	—	79	1	no	—
24	C₃×C₇	—	79	1	no	—
25	C₃×C₇	—	79	1	no	—
26	C₃×C₇	—	158	3	no	—
27	C₂×C₇	—	1659	1	no	—
28	D₇	—	237	1	no	—
29	C₇	—	2	3	no	—
30	C₇	C₇×D₇₉⋊C₃	1	1	yes	characteristic, complemented
31	C₇	(C₇₉⋊C₃)⋊D₇	1	1	yes	characteristic, direct product factor
32	C₂×C₃	—	553	1	no	Hall
33	C₃	—	79	1	no	Sylow
34	C₂	—	1659	1	no	Sylow

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

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.