Subgroups — D₂₁×C₁₃₉⋊C₃ #31776144

Order 17514.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₃₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₇×C₁₃₉⋊C₃	—	3	1	no	maximal
3	D₂₁×C₁₃₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₇×C₁₃₉	C₂×C₃	1	1	yes	characteristic, complemented
5	C₇×C₁₃₉⋊C₃	—	2	1	no	—
6	C₇×C₁₃₉⋊C₃	D₃	1	1	yes	characteristic, complemented
7	D₃×C₁₃₉⋊C₃	—	7	1	no	maximal, Hall
8	D₇×C₁₃₉	—	3	1	no	Hall
9	C₃×C₁₃₉⋊C₃	D₇	1	1	yes	characteristic, complemented, Hall
10	C₇×C₁₃₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
11	D₃×C₁₃₉	—	7	1	no	—
12	C₂×C₁₃₉⋊C₃	—	21	1	no	—
13	C₃×C₁₃₉	C₃×D₇	1	1	yes	characteristic, complemented
14	C₁₃₉⋊C₃	—	2	1	no	—
15	C₁₃₉⋊C₃	D₂₁	1	1	yes	characteristic, direct product factor
16	C₂×C₁₃₉	—	21	1	no	Hall
17	C₁₃₉	C₃×D₂₁	1	1	yes	characteristic, complemented, Sylow
18	C₃×D₂₁	—	139	1	no	maximal, Hall
19	C₃²×C₇	—	139	1	no	Hall
20	D₂₁	C₁₃₉⋊C₃	1	1	yes	characteristic, direct product factor
21	C₃×D₇	—	417	1	no	—
22	C₃×C₇	—	278	1	no	—
23	C₃×C₇	—	139	1	no	—
24	C₃×C₇	C₂×C₁₃₉⋊C₃	1	1	yes	characteristic, complemented
25	C₃×D₃	—	973	1	no	Hall
26	D₇	—	3	1	no	Hall
27	C₃²	—	139	1	no	Sylow
28	C₇	D₃×C₁₃₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	2919	1	no	—
30	D₃	—	7	1	no	—
31	C₃	—	278	1	no	—
32	C₃	—	139	1	no	—
33	C₃	D₇×C₁₃₉⋊C₃	1	1	yes	characteristic, complemented
34	C₂	—	21	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₃₉	C₂×C₃
LCS	G ▷ C₃×C₇×C₁₃₉
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.