Subgroups — C₈×C₇⋊C₂₇ #13094105

Order 1512.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇⋊C₂₇	C₂	1	1	yes	maximal, characteristic
2	C₇×C₈×C₉	C₃	1	1	yes	maximal, characteristic
3	C₂×C₇⋊C₂₇	C₄	1	1	yes	characteristic
4	C₄×C₇×C₉	C₂×C₃	1	1	yes	characteristic
5	C₈×C₂₇	—	7	1	no	maximal, Hall
6	C₇⋊C₂₇	C₈	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₇×C₈	C₉	1	1	yes	characteristic
8	C₂×C₇×C₉	C₃×C₄	1	1	yes	characteristic
9	C₄×C₂₇	—	7	1	no	—
10	C₃×C₄×C₇	C₂×C₉	1	1	yes	characteristic
11	C₈×C₉	ΓL(1,𝔽₈)	1	1	yes	characteristic
12	C₇×C₉	C₃×C₈	1	1	yes	characteristic
13	C₇×C₈	C₂₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₂₇	—	7	1	no	—
15	C₂×C₃×C₇	C₄×C₉	1	1	yes	characteristic
16	C₄×C₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
17	C₄×C₇	C₂×C₂₇	1	1	yes	characteristic
18	C₂₇	—	7	1	no	Sylow
19	C₃×C₈	C₇⋊C₉	1	1	yes	characteristic
20	C₃×C₇	C₈×C₉	1	1	yes	characteristic
21	C₂×C₉	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic
22	C₂×C₇	C₄×C₂₇	1	1	yes	characteristic
23	C₃×C₄	C₂×C₇⋊C₉	1	1	yes	characteristic
24	C₉	C₈×ΓL(1,𝔽₈)	1	1	yes	characteristic
25	C₈	C₇⋊C₂₇	1	1	yes	characteristic, direct product factor, Sylow
26	C₇	C₈×C₂₇	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	C₄×C₇⋊C₉	1	1	yes	characteristic
28	C₄	C₂×C₇⋊C₂₇	1	1	yes	characteristic
29	C₃	C₈×C₇⋊C₉	1	1	yes	characteristic
30	C₂	C₄×C₇⋊C₂₇	1	1	yes	characteristic

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.