Subgroups — C₃×C₂²⋊(C₁₇²⋊C₃) #23780939

Order 10404.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊(C₁₇²⋊C₃)	C₃	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₁₇²	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₇²⋊C₃	—	4	1	no	maximal, Hall
4	C₂×C₃×C₁₇²	—	3	1	no	—
5	C₂²×C₁₇²	C₃²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₇²	A₄	1	1	yes	characteristic, complemented
7	C₁₇²⋊C₃	—	4	3	no	—
8	C₂×C₁₇²	—	3	1	no	—
9	C₁₇²	C₃×A₄	1	1	yes	characteristic, complemented, Sylow
10	C₂²×C₃×C₁₇	—	3	6	no	—
11	C₂×C₃×C₁₇	—	3	18	no	—
12	C₂²×C₁₇	—	3	6	no	—
13	C₃×C₁₇	—	3	6	no	—
14	C₃×A₄	—	289	1	no	maximal, Hall
15	C₂×C₁₇	—	3	18	no	—
16	C₁₇	—	3	6	no	—
17	C₂²×C₃	C₁₇²⋊C₃	1	1	yes	characteristic, complemented
18	A₄	—	289	3	no	—
19	C₃²	—	1156	1	no	Sylow
20	C₂×C₃	—	3	1	no	—
21	C₂²	C₃×C₁₇²⋊C₃	1	1	yes	characteristic, complemented, Sylow
22	C₃	—	1156	3	no	—
23	C₃	C₂²⋊(C₁₇²⋊C₃)	1	1	yes	characteristic, direct product factor
24	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₂²⋊(C₁₇²⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₁₇²	C₃²
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₇²	C₃
LCS	G ▷ C₂²×C₁₇²
UCS	C₁ ◁ C₃

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