Subgroups — AGL(1,𝔽₁₂₈) #30653545

Order 16256.

234 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁷	C₁₂₇	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₁₂₇	—	128	1	no	maximal, Sylow
3	C₂⁶	—	127	1	no	—
4	C₂⁵	—	127	7	no	—
5	C₂⁵	—	127	7	no	—
6	C₂⁵	—	127	7	no	—
7	C₂⁴	—	127	7	no	—
8	C₂⁴	—	127	7	no	—
9	C₂⁴	—	127	7	no	—
10	C₂⁴	—	127	1	no	—
11	C₂⁴	—	127	1	no	—
12	C₂⁴	—	127	7	no	—
13	C₂⁴	—	127	7	no	—
14	C₂⁴	—	127	7	no	—
15	C₂⁴	—	127	7	no	—
16	C₂⁴	—	127	7	no	—
17	C₂⁴	—	127	7	no	—
18	C₂⁴	—	127	7	no	—
19	C₂⁴	—	127	7	no	—
20	C₂⁴	—	127	7	no	—
21	C₂⁴	—	127	7	no	—
22	C₂³	—	127	7	no	—
23	C₂³	—	127	7	no	—
24	C₂³	—	127	7	no	—
25	C₂³	—	127	1	no	—
26	C₂³	—	127	1	no	—
27	C₂³	—	127	7	no	—
28	C₂³	—	127	7	no	—
29	C₂³	—	127	7	no	—
30	C₂³	—	127	7	no	—
31	C₂³	—	127	7	no	—
32	C₂³	—	127	7	no	—
33	C₂³	—	127	7	no	—
34	C₂³	—	127	7	no	—
35	C₂³	—	127	7	no	—
36	C₂³	—	127	7	no	—
37	C₂²	—	127	7	no	—
38	C₂²	—	127	7	no	—
39	C₂²	—	127	7	no	—
40	C₂	—	127	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂⁷	C₁₂₇
LCS	G ▷ C₂⁷
UCS	C₁

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

N	H ≅ G/N	type
1. C₂⁷	C₁₂₇	semidirect

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

subgroup	index
C₂⁷	127
C₁₂₇	128