Subgroups — C₃×(C₁₂₇⋊C₃)⋊D₇ #30630713

Order 16002.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₂₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	(C₁₂₇⋊C₃)⋊D₇	C₃	1	3	yes	maximal, direct product factor
3	C₃×D₈₈₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₇×C₁₂₇	C₂×C₃	1	1	yes	characteristic, complemented
5	C₇×C₁₂₇⋊C₃	C₂×C₃	1	3	yes	complemented
6	C₃×D₁₂₇⋊C₃	—	7	1	no	maximal, Hall
7	D₈₈₉	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₂₇⋊C₃	D₇	1	1	yes	characteristic, complemented, Hall
9	C₇×C₁₂₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
10	C₃×D₁₂₇	—	7	1	no	—
11	D₁₂₇⋊C₃	—	7	3	no	—
12	C₃×C₁₂₇	C₃×D₇	1	1	yes	characteristic, complemented
13	C₁₂₇⋊C₃	C₃×D₇	1	3	yes	complemented
14	D₁₂₇	—	7	1	no	Hall
15	C₁₂₇	C₃²×D₇	1	1	yes	characteristic, complemented, Sylow
16	C₃²×D₇	—	127	1	no	maximal, Hall
17	C₃²×C₇	—	127	1	no	Hall
18	C₃×D₇	—	127	3	no	—
19	C₃×D₇	—	127	1	no	—
20	C₃×C₇	—	127	3	no	—
21	C₃×C₇	D₁₂₇⋊C₃	1	1	yes	characteristic, complemented
22	C₂×C₃²	—	889	1	no	Hall
23	D₇	—	127	1	no	Hall
24	C₃²	—	127	1	no	Sylow
25	C₇	C₃×D₁₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₃	—	889	3	no	—
27	C₂×C₃	—	889	1	no	—
28	C₃	—	127	3	no	—
29	C₃	(C₁₂₇⋊C₃)⋊D₇	1	1	yes	characteristic, direct product factor
30	C₂	—	889	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	(C₁₂₇⋊C₃)⋊D₇
commutator, cosocle, hypocenter	C₇×C₁₂₇	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₂₇	C₂×C₃
LCS	G ▷ C₇×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.