Subgroups — Dic₃×C₁₁₃⋊C₇ #23748770

Order 9492.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₁₃⋊C₇	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₁₃⋊C₇	—	3	1	no	maximal, Hall
3	C₃×C₁₁₃⋊C₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁₃⋊C₇	D₃	1	1	yes	characteristic
5	Dic₃×C₁₁₃	C₇	1	1	yes	maximal, characteristic, complemented, Hall
6	C₁₁₃⋊C₇	Dic₃	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃×C₁₁₃	C₂×C₇	1	1	yes	characteristic
8	C₄×C₁₁₃	—	3	1	no	Hall
9	C₃×C₁₁₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₁₃	D₃×C₇	1	1	yes	characteristic
11	C₁₁₃	C₇×Dic₃	1	1	yes	characteristic, complemented, Sylow
12	C₇×Dic₃	—	113	1	no	maximal, Hall
13	C₂×C₃×C₇	—	113	1	no	—
14	C₄×C₇	—	339	1	no	Hall
15	C₃×C₇	—	113	1	no	Hall
16	C₂×C₇	—	113	1	no	—
17	Dic₃	C₁₁₃⋊C₇	1	1	yes	characteristic, direct product factor, Hall
18	C₇	—	113	1	no	Sylow
19	C₂×C₃	C₂×C₁₁₃⋊C₇	1	1	yes	characteristic
20	C₄	—	3	1	no	Sylow
21	C₃	C₄×C₁₁₃⋊C₇	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₃×C₁₁₃⋊C₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×C₁₁₃⋊C₇
commutator, hypocenter	C₃×C₁₁₃	C₄×C₇
Fitting, socle, cosocle	C₂×C₃×C₁₁₃	C₂×C₇
prime radical	C₂×C₃×C₁₁₃⋊C₇	C₂
LCS	G ▷ C₃×C₁₁₃
UCS	C₁ ◁ C₂

Splittings G = N ⋊ H with N normal; H ≅ G/N.