Subgroups — C₃⋊(Dic₃₄₉⋊C₃) #27160254

Order 12564.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₃₄₉⋊C₃	C₂	1	1	yes	maximal, characteristic
2	Dic₁₀₄₇	C₃	1	1	yes	maximal, characteristic, complemented
3	Dic₃₄₉⋊C₃	—	3	1	no	maximal
4	C₃×C₃₄₉⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₃₄₉	C₂×C₃	1	1	yes	characteristic
6	C₂×C₃₄₉⋊C₃	—	2	1	no	—
7	C₂×C₃₄₉⋊C₃	D₃	1	1	yes	characteristic
8	Dic₃₄₉	—	3	1	no	Hall
9	C₃×C₃₄₉	C₃×C₄	1	1	yes	characteristic, complemented
10	C₃₄₉⋊C₃	—	2	1	no	—
11	C₃₄₉⋊C₃	Dic₃	1	1	yes	characteristic, complemented
12	C₂×C₃₄₉	C₃×D₃	1	1	yes	characteristic
13	C₃₄₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Sylow
14	C₃×Dic₃	—	349	1	no	maximal, Hall
15	C₂×C₃²	—	349	1	no	—
16	C₃×C₄	—	1047	1	no	—
17	Dic₃	—	349	1	no	—
18	C₃²	—	349	1	no	Sylow
19	C₂×C₃	—	349	1	no	—
20	C₂×C₃	—	698	1	no	—
21	C₂×C₃	D₃₄₉⋊C₃	1	1	yes	characteristic
22	C₄	—	1047	1	no	Sylow
23	C₃	—	349	1	no	—
24	C₃	—	698	1	no	—
25	C₃	Dic₃₄₉⋊C₃	1	1	yes	characteristic, complemented
26	C₂	C₃⋊(D₃₄₉⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊(D₃₄₉⋊C₃)
commutator, hypocenter	C₃×C₃₄₉	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₃₄₉	C₂×C₃
prime radical	C₂×C₃×C₃₄₉⋊C₃	C₂
LCS	G ▷ C₃×C₃₄₉
UCS	C₁ ◁ C₂

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.