Subgroups — C₁₂₇×#6881 #44524874

Order 30861.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#733×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
2	#732×C₁₂₇	C₃	1	2	yes	maximal, complemented
3	C₉⋊C₉×C₁₂₇	C₃	1	1	yes	maximal, characteristic, complemented
4	3₋¹⁺²×C₁₂₇	—	3	1	no	—
5	H(3,𝔽₃)×C₁₂₇	—	3	2	no	—
6	C₃×C₉×C₁₂₇	—	3	1	no	—
7	C₃×C₉×C₁₂₇	C₃²	1	1	yes	characteristic
8	C₃²×C₁₂₇	—	9	2	no	—
9	C₃²×C₁₂₇	H(3,𝔽₃)	1	1	yes	characteristic
10	C₉×C₁₂₇	—	3	1	no	—
11	C₉×C₁₂₇	—	9	1	no	—
12	C₉×C₁₂₇	—	9	1	no	—
13	C₃×C₁₂₇	—	3	1	no	—
14	C₃×C₁₂₇	—	27	2	no	—
15	C₃×C₁₂₇	#732	1	1	yes	characteristic
16	#6881	C₁₂₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₁₂₇	#6881	1	1	yes	characteristic, direct product factor, Sylow
18	#733	C₃×C₁₂₇	1	1	yes	characteristic, complemented
19	#732	C₃×C₁₂₇	1	2	yes	complemented
20	C₉⋊C₉	C₃×C₁₂₇	1	1	yes	characteristic, complemented
21	3₋¹⁺²	—	3	1	no	—
22	H(3,𝔽₃)	—	3	2	no	—
23	C₃×C₉	—	3	1	no	—
24	C₃×C₉	C₃²×C₁₂₇	1	1	yes	characteristic
25	C₃²	—	9	2	no	—
26	C₃²	H(3,𝔽₃)×C₁₂₇	1	1	yes	characteristic
27	C₉	—	3	1	no	—
28	C₉	—	9	1	no	—
29	C₉	—	9	1	no	—
30	C₃	—	3	1	no	—
31	C₃	—	27	2	no	—
32	C₃	#732×C₁₂₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₁₂₇	#732
commutator, Frattini, cosocle	C₃×C₉	C₃²×C₁₂₇
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.

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