Subgroups — C₂×C₉×ΓL(1,𝔽₈) #67370

Order 378.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×ΓL(1,𝔽₈)	C₃	1	1	yes	maximal, characteristic
3	C₂×C₇×C₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇⋊C₉	C₃	1	2	yes	maximal, complemented
5	C₃×ΓL(1,𝔽₈)	C₂×C₃	1	1	yes	characteristic
6	C₇×C₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇⋊C₉	C₂×C₃	1	2	yes	complemented
8	C₂×C₃×C₉	—	7	1	no	maximal, Hall
9	C₂×C₃×C₇	C₃²	1	1	yes	characteristic
10	C₂×ΓL(1,𝔽₈)	C₉	1	3	yes	direct product factor
11	C₃×C₉	—	7	1	no	Sylow
12	C₃×C₇	C₂×C₃²	1	1	yes	characteristic
13	ΓL(1,𝔽₈)	C₂×C₉	1	3	yes	direct product factor
14	C₂×C₃²	—	7	1	no	—
15	C₂×C₉	—	7	2	no	—
16	C₂×C₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
17	C₂×C₇	C₃×C₉	1	1	yes	characteristic, complemented, Hall
18	C₃²	—	7	1	no	—
19	C₉	—	7	2	no	—
20	C₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
21	C₇	C₂×C₃×C₉	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₃	—	7	3	no	—
23	C₂×C₃	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
24	C₃	—	7	3	no	—
25	C₃	C₂×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
26	C₂	C₉×ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Sylow

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.