Subgroups — C₂⁶×ΓL(1,𝔽₈) #13062421

Order 1344.

11300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×ΓL(1,𝔽₈)	C₂	1	63	yes	maximal, direct product factor
2	C₂⁶×C₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂⁴×ΓL(1,𝔽₈)	C₂²	1	651	yes	direct product factor
4	C₂⁵×C₇	C₂×C₃	1	63	yes	complemented
5	C₂⁶×C₃	—	7	1	no	maximal, Hall
6	C₂³×ΓL(1,𝔽₈)	C₂³	1	1395	yes	direct product factor
7	C₂⁴×C₇	C₂²×C₃	1	651	yes	complemented
8	C₂⁵×C₃	—	7	63	no	—
9	C₂²×ΓL(1,𝔽₈)	C₂⁴	1	651	yes	direct product factor
10	C₂⁶	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Sylow
11	C₂³×C₇	C₂³×C₃	1	1395	yes	complemented
12	C₂⁴×C₃	—	7	651	no	—
13	C₂×ΓL(1,𝔽₈)	C₂⁵	1	63	yes	direct product factor
14	C₂⁵	C₂×ΓL(1,𝔽₈)	1	63	yes	direct product factor
15	C₂²×C₇	C₂⁴×C₃	1	651	yes	complemented
16	C₂³×C₃	—	7	1395	no	—
17	ΓL(1,𝔽₈)	C₂⁶	1	1	yes	characteristic, direct product factor, Hall
18	C₂⁴	C₂²×ΓL(1,𝔽₈)	1	651	yes	direct product factor
19	C₂×C₇	C₂⁵×C₃	1	63	yes	complemented
20	C₂²×C₃	—	7	651	no	—
21	C₂³	C₂³×ΓL(1,𝔽₈)	1	1395	yes	direct product factor
22	C₇	C₂⁶×C₃	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₃	—	7	63	no	—
24	C₂²	C₂⁴×ΓL(1,𝔽₈)	1	651	yes	direct product factor
25	C₃	—	7	1	no	Sylow
26	C₂	C₂⁵×ΓL(1,𝔽₈)	1	63	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁶	ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₇	C₂⁶×C₃
Frattini	C₁	G
Fitting, socle	C₂⁶×C₇	C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₂⁶

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.