Subgroups — C₃²×D₁₃₈₇ #38735802

Order 24966.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₉×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₃₈₇	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₁₉×C₇₃	C₂×C₃	1	4	yes	complemented
4	D₁₃₈₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
5	C₁₉×C₇₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
6	C₃²×D₇₃	—	19	1	no	maximal, Hall
7	C₃²×C₇₃	D₁₉	1	1	yes	characteristic, complemented, Hall
8	C₃×D₇₃	—	19	4	no	—
9	C₃²×D₁₉	—	73	1	no	maximal, Hall
10	C₃×C₇₃	C₃×D₁₉	1	4	yes	complemented
11	C₃²×C₁₉	D₇₃	1	1	yes	characteristic, complemented, Hall
12	D₇₃	—	19	1	no	Hall
13	C₃×D₁₉	—	73	4	no	—
14	C₇₃	C₃²×D₁₉	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₁₉	C₃×D₇₃	1	4	yes	complemented
16	D₁₉	—	73	1	no	Hall
17	C₁₉	C₃²×D₇₃	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃²	—	1387	1	no	Hall
19	C₃²	D₁₃₈₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	—	1387	4	no	—
21	C₃	C₃×D₁₃₈₇	1	4	yes	direct product factor
22	C₂	—	1387	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²	D₁₃₈₇
commutator, cosocle, hypocenter	C₁₉×C₇₃	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₁₉×C₇₃	C₂
LCS	G ▷ C₁₉×C₇₃
UCS	C₁ ◁ C₃²

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.