Subgroups — C₇₃×C₃⋊AGL(1,𝔽₇) #22604131

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	AGL(1,𝔽₇)×C₇₃	—	3	1	no	maximal
3	D₂₁×C₇₃	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×D₃×C₇₃	—	7	1	no	maximal, Hall
8	D₇×C₇₃	—	3	1	no	Hall
9	C₃²×C₇₃	—	7	1	no	Hall
10	C₇×C₇₃	C₃×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×C₇₃	—	21	1	no	—
12	D₃×C₇₃	—	7	1	no	—
13	C₃×C₇₃	—	7	1	no	—
14	C₃×C₇₃	—	14	1	no	—
15	C₃×C₇₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
16	C₂×C₇₃	—	21	1	no	Hall
17	C₃⋊AGL(1,𝔽₇)	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₇₃	C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×ΓL(1,𝔽₈)	C₂×C₇₃	1	1	yes	characteristic, complemented, Hall
20	D₂₁	C₃×C₇₃	1	1	yes	characteristic, complemented
21	AGL(1,𝔽₇)	—	3	1	no	—
22	C₃×C₇	C₂×C₃×C₇₃	1	1	yes	characteristic, complemented
23	ΓL(1,𝔽₈)	—	2	1	no	—
24	ΓL(1,𝔽₈)	D₃×C₇₃	1	1	yes	characteristic, complemented
25	C₃×D₃	—	7	1	no	Hall
26	D₇	—	3	1	no	Hall
27	C₃²	—	7	1	no	Sylow
28	C₇	C₃×D₃×C₇₃	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	21	1	no	—
30	D₃	—	7	1	no	—
31	C₃	—	7	1	no	—
32	C₃	—	14	1	no	—
33	C₃	AGL(1,𝔽₇)×C₇₃	1	1	yes	characteristic, complemented
34	C₂	—	21	1	no	Sylow

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