Subgroups — C₃⋊(C₃⋊(C₇⋊D₁₁₉)) #28418428

Order 14994.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊(C₇⋊D₁₁₉)	—	3	4	no	maximal
3	C₃×C₇²×C₁₇	D₃	1	4	yes	complemented
4	C₃⋊D₃₅₇	—	7	8	no	maximal
5	C₇⋊D₁₁₉	—	9	1	no	Hall
6	C₃²×C₇×C₁₇	D₇	1	8	yes	complemented
7	C₃⋊(C₃⋊(C₇⋊D₇))	—	17	1	no	maximal, Hall
8	C₇²×C₁₇	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
9	D₃₅₇	—	21	32	no	—
10	C₃²×C₇²	D₁₇	1	1	yes	characteristic, complemented, Hall
11	C₃×C₇×C₁₇	D₂₁	1	32	yes	complemented
12	C₃⋊D₅₁	—	49	1	no	Hall
13	C₃⋊(C₇⋊D₇)	—	51	4	no	—
14	D₁₁₉	—	63	8	no	—
15	C₃²×C₁₇	C₇⋊D₇	1	1	yes	characteristic, complemented, Hall
16	C₃×C₇²	D₅₁	1	4	yes	complemented
17	C₃⋊D₂₁	—	119	8	no	—
18	C₇×C₁₇	C₃⋊D₂₁	1	8	yes	complemented
19	D₅₁	—	147	4	no	—
20	C₇⋊D₇	—	153	1	no	Hall
21	C₃²×C₇	D₁₁₉	1	8	yes	complemented
22	C₃×C₁₇	C₃⋊(C₇⋊D₇)	1	4	yes	complemented
23	C₇²	C₃⋊D₅₁	1	1	yes	characteristic, complemented, Sylow
24	D₂₁	—	357	32	no	—
25	D₁₇	—	441	1	no	Hall
26	C₃×C₇	D₃₅₇	1	32	yes	complemented
27	C₃⋊D₃	—	833	1	no	Hall
28	C₁₇	C₃⋊(C₃⋊(C₇⋊D₇))	1	1	yes	characteristic, complemented, Sylow
29	D₇	—	1071	8	no	—
30	C₃²	C₇⋊D₁₁₉	1	1	yes	characteristic, complemented, Sylow
31	C₇	C₃⋊D₃₅₇	1	8	yes	complemented
32	D₃	—	2499	4	no	—
33	C₃	C₃⋊(C₇⋊D₁₁₉)	1	4	yes	complemented
34	C₂	—	7497	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₇²×C₁₇	C₂
LCS	G ▷ C₃²×C₇²×C₁₇
UCS	C₁

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.