Subgroups — ΓL(1,𝔽₈)×C₃⋊(C₃⋊D₃) #11765812

Order 1134.

380 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₃⋊(C₃⋊D₃)	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃⋊D₃×ΓL(1,𝔽₈)	—	3	13	no	maximal
4	C₃³×C₇	C₂×C₃	1	1	yes	characteristic, complemented
5	C₃²×ΓL(1,𝔽₈)	—	2	13	no	—
6	C₃²×ΓL(1,𝔽₈)	D₃	1	13	yes	complemented
7	C₃×C₃⋊(C₃⋊D₃)	—	7	1	no	maximal, Hall
8	C₇×C₃⋊D₃	—	3	13	no	—
9	D₃×ΓL(1,𝔽₈)	—	9	13	no	—
10	C₃⁴	—	7	1	no	Sylow
11	C₃²×C₇	C₃×D₃	1	13	yes	complemented
12	C₃×ΓL(1,𝔽₈)	—	2	52	no	—
13	C₃×ΓL(1,𝔽₈)	C₃⋊D₃	1	13	yes	complemented
14	C₃⋊(C₃⋊D₃)	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
15	C₃×C₃⋊D₃	—	21	13	no	—
16	D₃×C₇	—	9	13	no	—
17	C₂×ΓL(1,𝔽₈)	—	27	1	no	—
18	C₃³	—	7	13	no	—
19	C₃³	—	14	13	no	—
20	C₃³	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
21	C₃×C₇	C₃×C₃⋊D₃	1	13	yes	complemented
22	ΓL(1,𝔽₈)	—	2	13	no	—
23	ΓL(1,𝔽₈)	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, direct product factor
24	C₃⋊D₃	—	3	13	no	—
25	C₃×D₃	—	63	13	no	—
26	C₂×C₇	—	27	1	no	Hall
27	C₃²	—	7	13	no	—
28	C₃²	—	14	52	no	—
29	C₃²	D₃×ΓL(1,𝔽₈)	1	13	yes	complemented
30	C₇	C₃×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	189	1	no	—
32	D₃	—	9	13	no	—
33	C₃	—	7	1	no	—
34	C₃	—	14	13	no	—
35	C₃	C₃⋊D₃×ΓL(1,𝔽₈)	1	13	yes	complemented
36	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃³×C₇	C₂×C₃
LCS	G ▷ C₃³×C₇
UCS	C₁

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.