Subgroups — (#11765917⋊C₂)⋊C₇ #30630673

Order 16002.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11765917⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₂₇⋊C₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₂₇⋊C₇	C₂×C₃	1	1	yes	characteristic
4	#11765917⋊C₂	C₇	1	1	yes	maximal, characteristic, complemented, Hall
5	D₁₂₇⋊C₇	C₉	1	1	yes	characteristic, complemented, Hall
6	#11765917	C₂×C₇	1	1	yes	characteristic, complemented, Hall
7	C₁₂₇⋊C₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×D₁₂₇	C₃×C₇	1	1	yes	characteristic
9	C₃×C₁₂₇	C₂×C₃×C₇	1	1	yes	characteristic
10	D₁₂₇	C₇×C₉	1	1	yes	characteristic, complemented, Hall
11	C₁₂₇	C₂×C₇×C₉	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₇×C₉	—	127	1	no	maximal, Hall
13	C₇×C₉	—	127	1	no	Hall
14	C₂×C₃×C₇	—	127	1	no	—
15	C₃×C₇	—	127	1	no	—
16	C₂×C₉	—	127	1	no	Hall
17	C₂×C₇	—	127	1	no	Hall
18	C₉	—	127	1	no	Sylow
19	C₇	—	127	1	no	Sylow
20	C₂×C₃	—	127	1	no	—
21	C₃	(D₁₂₇⋊C₃)⋊C₇	1	1	yes	characteristic
22	C₂	—	127	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	(D₁₂₇⋊C₃)⋊C₇
commutator, hypocenter	C₁₂₇	C₂×C₇×C₉
Fitting, socle, cosocle	C₃×C₁₂₇	C₂×C₃×C₇
prime radical	C₃×D₁₂₇⋊C₇	C₃
LCS	G ▷ C₁₂₇
UCS	C₁ ◁ C₃

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.