Subgroups — C₂²×C₃×C₁₁₃⋊C₇ #23748786

Order 9492.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₁₃⋊C₇	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₁₁₃⋊C₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₁₃⋊C₇	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₁₁₃⋊C₇	C₂×C₃	1	3	yes	direct product factor
5	C₂²×C₃×C₁₁₃	C₇	1	1	yes	maximal, characteristic, complemented, Hall
6	C₁₁₃⋊C₇	C₂²×C₃	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃×C₁₁₃	C₂×C₇	1	3	yes	complemented
8	C₂²×C₁₁₃	C₃×C₇	1	1	yes	characteristic, complemented, Hall
9	C₃×C₁₁₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₁₃	C₂×C₃×C₇	1	3	yes	complemented
11	C₁₁₃	C₂²×C₃×C₇	1	1	yes	characteristic, complemented, Sylow
12	C₂²×C₃×C₇	—	113	1	no	maximal, Hall
13	C₂×C₃×C₇	—	113	3	no	—
14	C₂²×C₇	—	113	1	no	Hall
15	C₃×C₇	—	113	1	no	Hall
16	C₂×C₇	—	113	3	no	—
17	C₂²×C₃	C₁₁₃⋊C₇	1	1	yes	characteristic, direct product factor, Hall
18	C₇	—	113	1	no	Sylow
19	C₂×C₃	C₂×C₁₁₃⋊C₇	1	3	yes	direct product factor
20	C₂²	C₃×C₁₁₃⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	C₂²×C₁₁₃⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₃×C₁₁₃⋊C₇	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃	C₁₁₃⋊C₇
commutator, cosocle, hypocenter	C₁₁₃	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₁₃	C₇
LCS	G ▷ C₁₁₃
UCS	C₁ ◁ C₂²×C₃

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