Subgroups — C₃×#23755282 #44446113

Order 29718.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#19097153	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#23755282	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₁₃×D₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₃×C₁₂₇	C₂×C₃	1	1	yes	characteristic, complemented
5	#19097153	C₂×C₃	1	3	yes	complemented
6	C₁₃×D₁₂₇	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×D₁₂₇⋊C₃	—	13	1	no	maximal, Hall
8	C₁₃×C₁₂₇	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₁₂₇⋊C₃	—	13	1	no	Hall
10	C₃×D₁₂₇	C₁₃⋊C₃	1	1	yes	characteristic, complemented
11	D₁₂₇⋊C₃	—	13	3	no	—
12	C₃×C₁₂₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
13	C₁₂₇⋊C₃	—	13	3	no	—
14	D₁₂₇	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₁₃⋊C₃	—	127	1	no	maximal, Hall
16	C₁₂₇	C₂×C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₁₃⋊C₃	—	127	1	no	Hall
18	C₂×C₃×C₁₃	—	381	1	no	—
19	C₂×C₁₃⋊C₃	—	127	3	no	—
20	C₃×C₁₃	D₁₂₇⋊C₃	1	1	yes	characteristic, complemented
21	C₁₃⋊C₃	—	127	3	no	—
22	C₂×C₁₃	—	381	1	no	Hall
23	C₂×C₃²	—	1651	1	no	Hall
24	C₁₃	C₃×D₁₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
25	C₃²	—	1651	1	no	Sylow
26	C₂×C₃	—	1651	3	no	—
27	C₂×C₃	—	381	1	no	—
28	C₃	—	1651	3	no	—
29	C₃	#23755282	1	1	yes	characteristic, direct product factor
30	C₂	—	381	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#23755282
commutator, cosocle, hypocenter	C₁₃×C₁₂₇	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₁₂₇	C₂×C₃
LCS	G ▷ C₁₃×C₁₂₇
UCS	C₁ ◁ C₃

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.