Subgroups — C₃⋊#16814887 #26012913

Order 11100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×D₃₇	C₂	1	1	yes	maximal, characteristic
2	#16814887	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊#10625194	—	5	6	no	maximal
5	C₅²×D₃₇	D₃	1	1	yes	characteristic
6	C₃×C₅×D₃₇	D₅	1	6	yes	—
7	C₅²×C₃₇	Dic₃	1	1	yes	characteristic, complemented, Hall
8	#10625194	—	15	6	no	—
9	C₃×C₅×C₃₇	Dic₅	1	6	yes	complemented
10	C₃⋊#3866	—	25	1	no	Hall
11	C₅×D₃₇	D₁₅	1	6	yes	—
12	C₃⋊#1039	—	37	1	no	maximal, Hall
13	C₃×D₃₇	C₅⋊D₅	1	1	yes	characteristic
14	C₅×C₃₇	Dic₁₅	1	6	yes	complemented
15	C₂×C₃×C₅²	—	37	1	no	—
16	#3866	—	75	1	no	Hall
17	C₃×C₃₇	#1039	1	1	yes	characteristic, complemented, Hall
18	#1039	—	111	1	no	Hall
19	C₃×C₅²	#3866	1	1	yes	characteristic, complemented, Hall
20	D₃₇	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
21	Dic₁₅	—	185	6	no	—
22	C₂×C₅²	—	37	1	no	—
23	C₃₇	C₃⋊#1039	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃×C₅	—	37	6	no	—
25	C₅²	C₃⋊#3866	1	1	yes	characteristic, complemented, Sylow
26	Dic₅	—	555	6	no	—
27	C₃×C₅	#10625194	1	6	yes	complemented
28	Dic₃	—	925	1	no	Hall
29	C₂×C₅	—	37	6	no	—
30	C₂×C₃	—	37	1	no	—
31	C₅	C₃⋊#10625194	1	6	yes	complemented
32	C₄	—	2775	1	no	Sylow
33	C₃	#16814887	1	1	yes	characteristic, complemented, Sylow
34	C₂	—	37	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅²×C₃₇	C₄
prime radical, cosocle	C₃×C₅²×D₃₇	C₂
LCS	G ▷ C₃×C₅²×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.