Subgroups — (C₃⋊D₃)⋊D₁₇₃ #20262012

Order 6228.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₅₁₉	C₂	1	2	yes	maximal, complemented
3	D₃×D₁₇₃	—	3	2	no	maximal
4	C₃²×C₁₇₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₅₁₉	D₃	1	2	yes	complemented
6	C₃×D₁₇₃	—	3	2	no	—
7	D₃×C₁₇₃	—	3	2	no	—
8	D₃×C₁₇₃	—	6	1	no	—
9	C₂×D₁₇₃	—	9	1	no	Hall
10	C₃×C₁₇₃	—	2	1	no	—
11	C₃×C₁₇₃	C₂×D₃	1	2	yes	complemented
12	C₂×C₁₇₃	—	9	1	no	—
13	D₁₇₃	—	3	2	no	—
14	C₁₇₃	D₃²	1	1	yes	characteristic, complemented, Sylow
15	D₃²	—	173	1	no	maximal, Hall
16	C₃⋊D₃	D₁₇₃	1	1	yes	characteristic, complemented
17	C₃×D₃	—	173	2	no	—
18	C₂×D₃	—	519	2	no	—
19	C₃²	C₂×D₁₇₃	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃	—	519	2	no	—
21	D₃	—	3	2	no	—
22	D₃	—	6	1	no	—
23	D₃	—	173	2	no	—
24	C₂²	—	1557	1	no	Sylow
25	C₃	—	2	1	no	—
26	C₃	D₃×D₁₇₃	1	2	yes	complemented
27	C₂	—	519	2	no	—
28	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₇₃	C₂²
LCS	G ▷ C₃²×C₁₇₃
UCS	C₁

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