Subgroups — C₂×C₃⋊D₁₀₄₇ #27160284

Order 12564.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂	C₃⋊D₁₀₄₇
commutator, cosocle, hypocenter	C₃²×C₃₄₉	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₃₄₉	C₂
LCS	G ▷ C₃²×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.