Subgroups — C₃×A₄×C₁₇² #23780940

Order 10404.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₄×C₁₇²	C₃	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₁₇²	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₁₇²	—	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	—	4	3	no	—
7	C₃×C₁₇²	A₄	1	1	yes	characteristic, direct product factor
8	C₃×A₄×C₁₇	C₁₇	1	18	yes	maximal, direct product factor
9	C₂×C₁₇²	—	3	1	no	—
10	C₁₇²	C₃×A₄	1	1	yes	characteristic, direct product factor, Sylow
11	C₂²×C₃×C₁₇	C₃×C₁₇	1	18	yes	complemented
12	A₄×C₁₇	C₃×C₁₇	1	54	yes	direct product factor
13	C₃²×C₁₇	—	4	18	no	—
14	C₂×C₃×C₁₇	—	3	18	no	—
15	C₂²×C₁₇	C₃²×C₁₇	1	18	yes	complemented
16	C₃×C₁₇	—	4	54	no	—
17	C₃×C₁₇	A₄×C₁₇	1	18	yes	direct product factor
18	C₃×A₄	C₁₇²	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₁₇	—	3	18	no	—
20	C₁₇	C₃×A₄×C₁₇	1	18	yes	direct product factor
21	C₂²×C₃	C₃×C₁₇²	1	1	yes	characteristic, complemented
22	A₄	C₃×C₁₇²	1	3	yes	direct product factor
23	C₃²	—	4	1	no	Sylow
24	C₂×C₃	—	3	1	no	—
25	C₂²	C₃²×C₁₇²	1	1	yes	characteristic, complemented, Sylow
26	C₃	—	4	3	no	—
27	C₃	A₄×C₁₇²	1	1	yes	characteristic, direct product factor
28	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₁₇²	A₄
commutator, cosocle, hypocenter	C₂²	C₃²×C₁₇²
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₇²	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃×C₁₇²

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