Subgroups — C₇²×C₃⋊D₅₁ #28418432

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	C₇²×D₅₁	—	3	4	no	maximal
3	C₃×C₇²×C₁₇	D₃	1	4	yes	complemented
4	C₇×C₃⋊D₅₁	C₇	1	8	yes	maximal, direct product factor
5	C₇²×D₁₇	—	9	1	no	Hall
6	C₃²×C₇×C₁₇	C₂×C₇	1	8	yes	complemented
7	C₇²×C₃⋊D₃	—	17	1	no	maximal, Hall
8	C₇²×C₁₇	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
9	C₇×D₅₁	—	3	32	no	—
10	C₃²×C₇²	D₁₇	1	1	yes	characteristic, complemented, Hall
11	C₃×C₇×C₁₇	D₃×C₇	1	32	yes	complemented
12	C₃⋊D₅₁	C₇²	1	1	yes	characteristic, direct product factor, Hall
13	D₃×C₇²	—	51	4	no	—
14	C₇×D₁₇	—	9	8	no	—
15	C₃²×C₁₇	C₂×C₇²	1	1	yes	characteristic, complemented, Hall
16	C₃×C₇²	D₅₁	1	4	yes	complemented
17	C₇×C₃⋊D₃	—	17	8	no	—
18	C₇×C₁₇	C₇×C₃⋊D₃	1	8	yes	complemented
19	D₅₁	—	3	4	no	—
20	C₂×C₇²	—	153	1	no	Hall
21	C₃²×C₇	C₇×D₁₇	1	8	yes	complemented
22	C₃×C₁₇	D₃×C₇²	1	4	yes	complemented
23	C₇²	C₃⋊D₅₁	1	1	yes	characteristic, direct product factor, Sylow
24	D₃×C₇	—	51	32	no	—
25	D₁₇	—	9	1	no	Hall
26	C₃×C₇	C₇×D₅₁	1	32	yes	complemented
27	C₃⋊D₃	—	17	1	no	Hall
28	C₁₇	C₇²×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₇	—	153	8	no	—
30	C₃²	C₇²×D₁₇	1	1	yes	characteristic, complemented, Sylow
31	C₇	C₇×C₃⋊D₅₁	1	8	yes	direct product factor
32	D₃	—	51	4	no	—
33	C₃	C₇²×D₅₁	1	4	yes	complemented
34	C₂	—	153	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇²	C₃⋊D₅₁
commutator, cosocle, hypocenter	C₃²×C₁₇	C₂×C₇²
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₇	C₂
LCS	G ▷ C₃²×C₁₇
UCS	C₁ ◁ C₇²

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.