Subgroups — C₁₂₇×#6856 #44524849

Order 30861.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×H(3,𝔽₃)×C₁₂₇	C₃	1	2	yes	maximal, complemented
2	C₃²⋊C₉×C₁₂₇	C₃	1	2	yes	maximal, complemented
3	C₃³×C₁₂₇	—	3	2	no	—
4	C₃³×C₁₂₇	C₃²	1	1	yes	characteristic
5	H(3,𝔽₃)×C₁₂₇	—	3	6	no	—
6	C₃×C₉×C₁₂₇	—	3	2	no	—
7	C₃²×C₁₂₇	—	3	2	no	—
8	C₃²×C₁₂₇	—	3	6	no	—
9	C₃²×C₁₂₇	—	3	2	no	—
10	C₃²×C₁₂₇	—	9	2	no	—
11	C₃²×C₁₂₇	—	9	4	no	—
12	C₃²×C₁₂₇	H(3,𝔽₃)	1	1	yes	characteristic
13	C₉×C₁₂₇	—	9	2	no	—
14	C₃×C₁₂₇	—	9	1	no	—
15	C₃×C₁₂₇	—	9	6	no	—
16	C₃×C₁₂₇	AΣL(1,𝔽₂₇)	1	2	yes	—
17	C₃×C₁₂₇	#732	1	2	yes	—
18	#6856	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₁₂₇	#6856	1	1	yes	characteristic, direct product factor, Sylow
20	C₃×H(3,𝔽₃)	C₃×C₁₂₇	1	2	yes	complemented
21	C₃²⋊C₉	C₃×C₁₂₇	1	2	yes	complemented
22	C₃³	—	3	2	no	—
23	C₃³	C₃²×C₁₂₇	1	1	yes	characteristic
24	H(3,𝔽₃)	—	3	6	no	—
25	C₃×C₉	—	3	2	no	—
26	C₃²	—	3	2	no	—
27	C₃²	—	3	6	no	—
28	C₃²	—	3	2	no	—
29	C₃²	—	9	2	no	—
30	C₃²	—	9	4	no	—
31	C₃²	H(3,𝔽₃)×C₁₂₇	1	1	yes	characteristic
32	C₉	—	9	2	no	—
33	C₃	—	9	1	no	—
34	C₃	—	9	6	no	—
35	C₃	AΣL(1,𝔽₂₇)×C₁₂₇	1	2	yes	—
36	C₃	#732×C₁₂₇	1	2	yes	—

	subgroup	G/H
center, socle	C₃²×C₁₂₇	H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃²×C₁₂₇
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₁₂₇ ◁ C₃³×C₁₂₇ ◁ G

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.