Subgroups — C₃₇⋊C₃×#1181 #27166149

Order 12876.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₉×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃₇×#1181	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂₉×C₃₇⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃₇×D₂₉	C₂×C₃	1	1	yes	characteristic
5	C₂₉×C₃₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₄×C₃₇⋊C₃	—	29	1	no	maximal, Hall
7	C₃×#1181	—	37	1	no	maximal, Hall
8	C₂×C₃₇⋊C₃	—	29	1	no	—
9	C₃×D₂₉	—	37	1	no	—
10	C₄×C₃₇	—	29	1	no	Hall
11	#1181	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
12	C₃₇⋊C₃	#1181	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₂₉	—	37	1	no	Hall
14	C₂×C₃₇	—	29	1	no	—
15	D₂₉	C₂×C₃₇⋊C₃	1	1	yes	characteristic
16	C₃₇	C₃×#1181	1	1	yes	characteristic, complemented, Sylow
17	C₂₉	C₄×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	1073	1	no	Hall
19	C₂×C₃	—	1073	1	no	—
20	C₄	—	29	1	no	Sylow
21	C₃	—	37	1	no	Sylow
22	C₂	—	29	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₂₉×C₃₇	C₃×C₄
prime radical	D₂₉×C₃₇⋊C₃	C₂
cosocle	C₃₇×D₂₉	C₂×C₃
LCS	G ▷ C₂₉×C₃₇
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.