Subgroups — ΓL(1,𝔽₈)×D₂₁₉ #22604142

Order 9198.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×ΓL(1,𝔽₈)×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	ΓL(1,𝔽₈)×D₇₃	—	3	1	no	maximal
3	C₇×D₂₁₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₇×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented
5	ΓL(1,𝔽₈)×C₇₃	—	2	1	no	—
6	ΓL(1,𝔽₈)×C₇₃	D₃	1	1	yes	characteristic, complemented
7	C₃×D₂₁₉	—	7	1	no	maximal, Hall
8	C₇×D₇₃	—	3	1	no	Hall
9	C₃²×C₇₃	—	7	1	no	Hall
10	C₇×C₇₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
11	D₂₁₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
12	C₃×D₇₃	—	21	1	no	—
13	C₃×C₇₃	—	7	1	no	—
14	C₃×C₇₃	—	14	1	no	—
15	C₃×C₇₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
16	D₇₃	—	3	1	no	Hall
17	D₃×ΓL(1,𝔽₈)	—	73	1	no	maximal, Hall
18	C₇₃	D₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
19	C₃×ΓL(1,𝔽₈)	D₇₃	1	1	yes	characteristic, complemented, Hall
20	D₃×C₇	—	73	1	no	—
21	C₂×ΓL(1,𝔽₈)	—	219	1	no	—
22	C₃×C₇	C₃×D₇₃	1	1	yes	characteristic, complemented
23	ΓL(1,𝔽₈)	—	2	1	no	—
24	ΓL(1,𝔽₈)	D₂₁₉	1	1	yes	characteristic, direct product factor
25	C₃×D₃	—	511	1	no	Hall
26	C₂×C₇	—	219	1	no	Hall
27	C₃²	—	7	1	no	Sylow
28	C₇	C₃×D₂₁₉	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	1533	1	no	—
30	D₃	—	73	1	no	—
31	C₃	—	7	1	no	—
32	C₃	—	14	1	no	—
33	C₃	ΓL(1,𝔽₈)×D₇₃	1	1	yes	characteristic, complemented
34	C₂	—	219	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₇×C₇₃	C₂×C₃
LCS	G ▷ C₃×C₇×C₇₃
UCS	C₁

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