Subgroups — C₂²×C₃×C₁₇²⋊C₃ #23780941

Order 10404.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

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