Subgroups — A₄×C₁₇²⋊C₃ #23780898

Order 10404.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊(C₁₇²⋊C₃)	C₃	1	2	yes	maximal, complemented
2	A₄×C₁₇²	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₇²⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₇²⋊C₃	—	4	1	no	maximal, Hall
5	C₂×C₁₇²⋊C₃	—	3	1	no	—
6	C₂²×C₁₇²	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₇²	—	4	1	no	—
8	C₁₇²⋊C₃	—	4	2	no	—
9	C₁₇²⋊C₃	A₄	1	1	yes	characteristic, direct product factor
10	C₂×C₁₇²	—	3	1	no	—
11	C₁₇²	C₃×A₄	1	1	yes	characteristic, complemented, Sylow
12	A₄×C₁₇	—	3	6	no	—
13	C₂²×C₁₇	—	3	6	no	—
14	C₃×C₁₇	—	12	6	no	—
15	C₃×A₄	—	289	1	no	maximal, Hall
16	C₂×C₁₇	—	9	6	no	—
17	C₁₇	—	3	6	no	—
18	C₂²×C₃	—	289	1	no	—
19	A₄	—	289	2	no	—
20	A₄	C₁₇²⋊C₃	1	1	yes	characteristic, direct product factor
21	C₃²	—	1156	1	no	Sylow
22	C₂×C₃	—	867	1	no	—
23	C₂²	C₃×C₁₇²⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₃	—	4	1	no	—
25	C₃	—	289	1	no	—
26	C₃	—	1156	2	no	—
27	C₂	—	3	1	no	—

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

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