Subgroups — C₃⋊D₃×D₂₉₃ #24902144

Order 10548.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₈₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊D₃×C₂₉₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₂₉₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₂₉₃	—	3	4	no	maximal
5	C₃²×C₂₉₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₈₇₉	—	3	4	no	—
7	C₃×D₂₉₃	D₃	1	4	yes	complemented
8	D₃×C₂₉₃	—	3	4	no	—
9	C₂×D₂₉₃	—	9	1	no	Hall
10	C₃×C₂₉₃	C₂×D₃	1	4	yes	complemented
11	C₂×C₂₉₃	—	9	1	no	—
12	D₂₉₃	—	9	1	no	—
13	D₂₉₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor
14	C₂₉₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₃⋊D₃	—	293	1	no	maximal, Hall
16	C₂×C₃²	—	293	1	no	—
17	C₃⋊D₃	—	293	1	no	—
18	C₃⋊D₃	D₂₉₃	1	1	yes	characteristic, direct product factor
19	C₂×D₃	—	879	4	no	—
20	C₃²	C₂×D₂₉₃	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃	—	293	4	no	—
22	D₃	—	3	4	no	—
23	D₃	—	879	4	no	—
24	C₂²	—	2637	1	no	Sylow
25	C₃	D₃×D₂₉₃	1	4	yes	complemented
26	C₂	—	9	1	no	—
27	C₂	—	293	1	no	—
28	C₂	—	2637	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₂₉₃	C₂²
LCS	G ▷ C₃²×C₂₉₃
UCS	C₁

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