Subgroups — C₁₂₇×#6880 #44524873

Order 30861.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#733×C₁₂₇	C₃	1	3	yes	maximal
2	C₉²×C₁₂₇	C₃	1	1	yes	maximal, characteristic
3	3₋¹⁺²×C₁₂₇	—	3	3	no	—
4	C₃×C₉×C₁₂₇	—	3	1	no	—
5	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
6	C₃²×C₁₂₇	H(3,𝔽₃)	1	1	yes	characteristic
7	C₉×C₁₂₇	—	3	3	no	—
8	C₉×C₁₂₇	—	3	1	no	—
9	C₉×C₁₂₇	—	9	3	no	—
10	C₃×C₁₂₇	—	3	1	no	—
11	C₃×C₁₂₇	#732	1	1	yes	characteristic
12	#6880	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₁₂₇	#6880	1	1	yes	characteristic, direct product factor, Sylow
14	#733	C₃×C₁₂₇	1	3	yes	—
15	C₉²	C₃×C₁₂₇	1	1	yes	characteristic
16	3₋¹⁺²	—	3	3	no	—
17	C₃×C₉	—	3	1	no	—
18	C₃×C₉	C₃²×C₁₂₇	1	1	yes	characteristic
19	C₃²	H(3,𝔽₃)×C₁₂₇	1	1	yes	characteristic
20	C₉	—	3	3	no	—
21	C₉	—	3	1	no	—
22	C₉	—	9	3	no	—
23	C₃	—	3	1	no	—
24	C₃	#732×C₁₂₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₁₂₇	#732
commutator, Frattini, cosocle	C₃×C₉	C₃²×C₁₂₇
prime radical	C₃²×C₁₂₇	H(3,𝔽₃)
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₂₇ ◁ C₃²×C₁₂₇ ◁ C₃×C₉×C₁₂₇ ◁ G

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
12. #6880	C₁₂₇	direct (N × H)
13. C₁₂₇	#6880	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.