Subgroups — #23780924

Order 10404.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₃⋊D₅₁	C₂	1	2	yes	maximal, complemented
2	C₃²×C₁₇⋊D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₅₁⋊D₁₇	—	3	4	no	maximal
4	C₃²×C₁₇²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₁₇⋊D₁₇	D₃	1	4	yes	complemented
6	C₁₇×D₅₁	—	3	8	no	—
7	D₁₇²	—	9	1	no	Hall
8	C₃×C₁₇²	C₂×D₃	1	4	yes	complemented
9	C₃⋊D₃×D₁₇	—	17	2	no	maximal
10	C₁₇⋊D₁₇	C₃⋊D₃	1	1	yes	characteristic, complemented
11	C₁₇×D₁₇	—	9	2	no	—
12	C₃⋊D₅₁	D₁₇	1	2	yes	complemented
13	C₁₇×C₃⋊D₃	—	17	2	no	—
14	C₃²×D₁₇	—	17	2	no	—
15	C₃²×D₁₇	—	34	8	no	—
16	C₁₇²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
17	D₃×D₁₇	—	51	8	no	—
18	C₃²×C₁₇	—	2	8	no	—
19	C₃²×C₁₇	C₂×D₁₇	1	2	yes	complemented
20	D₅₁	—	3	8	no	—
21	C₃×D₁₇	—	17	8	no	—
22	C₃×D₁₇	—	34	32	no	—
23	D₃×C₁₇	—	51	8	no	—
24	C₂×D₁₇	—	153	2	no	—
25	C₃×C₁₇	—	2	32	no	—
26	C₃×C₁₇	D₃×D₁₇	1	8	yes	complemented
27	C₂×C₃⋊D₃	—	289	1	no	Hall
28	C₂×C₁₇	—	153	2	no	—
29	D₁₇	—	9	2	no	—
30	D₁₇	—	17	2	no	—
31	D₁₇	—	34	8	no	—
32	C₂×C₃²	—	289	1	no	—
33	C₃⋊D₃	—	17	2	no	—
34	C₁₇	—	2	8	no	—
35	C₁₇	C₃⋊D₃×D₁₇	1	2	yes	complemented
36	C₂×D₃	—	867	4	no	—
37	C₃²	D₁₇²	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₃	—	289	4	no	—
39	D₃	—	51	8	no	—
40	C₂²	—	2601	1	no	Sylow
41	C₃	D₅₁⋊D₁₇	1	4	yes	complemented
42	C₂	—	289	1	no	—
43	C₂	—	153	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₇²	C₂²
LCS	G ▷ C₃²×C₁₇²
UCS	C₁

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