Subgroups — (C₃⋊D₃)⋊D₃₄₉ #27160277

Order 12564.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×C₃₄₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₀₄₇	C₂	1	2	yes	maximal, complemented
3	D₃×D₃₄₉	—	3	2	no	maximal
4	C₃²×C₃₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₀₄₇	D₃	1	2	yes	complemented
6	C₃×D₃₄₉	—	3	2	no	—
7	D₃×C₃₄₉	—	3	2	no	—
8	D₃×C₃₄₉	—	6	1	no	—
9	C₂×D₃₄₉	—	9	1	no	Hall
10	C₃×C₃₄₉	—	2	1	no	—
11	C₃×C₃₄₉	C₂×D₃	1	2	yes	complemented
12	C₂×C₃₄₉	—	9	1	no	—
13	D₃₄₉	—	3	2	no	—
14	C₃₄₉	D₃²	1	1	yes	characteristic, complemented, Sylow
15	D₃²	—	349	1	no	maximal, Hall
16	C₃⋊D₃	D₃₄₉	1	1	yes	characteristic, complemented
17	C₃×D₃	—	349	2	no	—
18	C₂×D₃	—	1047	2	no	—
19	C₃²	C₂×D₃₄₉	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃	—	1047	2	no	—
21	D₃	—	3	2	no	—
22	D₃	—	6	1	no	—
23	D₃	—	349	2	no	—
24	C₂²	—	3141	1	no	Sylow
25	C₃	—	2	1	no	—
26	C₃	D₃×D₃₄₉	1	2	yes	complemented
27	C₂	—	9	1	no	—
28	C₂	—	1047	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₃₄₉	C₂²
LCS	G ▷ C₃²×C₃₄₉
UCS	C₁

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.