Subgroups — ΓL(1,𝔽₈)⋊D₁₃₃ #19150310

Order 5586.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₉×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇⋊D₁₃₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₁₃₃	—	7	1	no	maximal
5	ΓL(1,𝔽₈)⋊D₁₉	—	7	1	no	maximal
6	C₃×C₇×C₁₉	—	7	1	no	—
7	C₁₉×ΓL(1,𝔽₈)	D₇	1	1	yes	characteristic, complemented
8	ΓL(1,𝔽₈)⋊D₇	—	19	1	no	maximal, Hall
9	D₁₃₃	—	7	1	no	—
10	D₁₃₃	—	7	1	no	—
11	D₁₃₃	—	21	2	no	—
12	C₇×ΓL(1,𝔽₈)	D₁₉	1	1	yes	characteristic, complemented, Hall
13	C₇×C₁₉	—	3	2	no	—
14	C₇×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
15	C₇×C₁₉	C₃×D₇	1	1	yes	characteristic, complemented
16	C₃×D₁₉	—	49	1	no	Hall
17	C₇⋊D₇	—	19	1	no	Hall
18	C₃×C₁₉	—	7	1	no	Hall
19	C₇²	C₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
20	C₃×D₇	—	133	1	no	—
21	AGL(1,𝔽₇)	—	133	1	no	—
22	D₁₉	—	49	1	no	Hall
23	C₃×C₇	—	7	1	no	—
24	ΓL(1,𝔽₈)	D₁₃₃	1	1	yes	characteristic, complemented
25	C₁₉	ΓL(1,𝔽₈)⋊D₇	1	1	yes	characteristic, complemented, Sylow
26	D₇	—	133	1	no	—
27	D₇	—	133	1	no	—
28	D₇	—	399	2	no	—
29	C₇	—	3	2	no	—
30	C₇	ΓL(1,𝔽₈)⋊D₁₉	1	1	yes	characteristic, complemented
31	C₇	C₃×D₁₃₃	1	1	yes	characteristic, complemented
32	C₂×C₃	—	931	1	no	Hall
33	C₃	—	7	1	no	Sylow
34	C₂	—	931	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁

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