Subgroups — C₂₇⋊SL(2,𝔽₃) #10619568

Order 648.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×SL(2,𝔽₃)	C₃	1	1	yes	maximal, characteristic
2	Q₈×C₂₇	C₃	1	1	yes	maximal, characteristic, complemented
3	Q₈⋊C₂₇	C₃	1	2	yes	maximal, complemented
4	C₂×C₂₇⋊C₃	—	4	1	no	maximal
5	C₄×C₂₇	—	3	1	no	—
6	C₂₇⋊C₃	—	4	1	no	Sylow
7	C₃×SL(2,𝔽₃)	C₉	1	1	yes	characteristic
8	Q₈×C₉	C₃²	1	1	yes	characteristic
9	Q₈⋊C₉	C₉	1	2	yes	—
10	C₂×C₃×C₉	—	4	1	no	—
11	C₂×C₂₇	—	4	2	no	—
12	C₂×C₂₇	A₄	1	1	yes	characteristic
13	C₄×C₉	—	3	1	no	—
14	C₃×C₉	—	4	1	no	—
15	C₂₇	—	4	2	no	—
16	C₂₇	SL(2,𝔽₃)	1	1	yes	characteristic, complemented
17	C₃×Q₈	C₃×C₉	1	1	yes	characteristic
18	SL(2,𝔽₃)	—	3	1	no	—
19	C₂×C₃²	—	4	1	no	—
20	C₂×C₉	—	4	2	no	—
21	C₂×C₉	C₃×A₄	1	1	yes	characteristic
22	C₃×C₄	—	3	1	no	—
23	C₃²	—	4	1	no	—
24	C₉	—	4	2	no	—
25	C₉	C₃×SL(2,𝔽₃)	1	1	yes	characteristic
26	Q₈	C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	12	1	no	—
28	C₂×C₃	C₉×A₄	1	1	yes	characteristic
29	C₄	—	3	1	no	—
30	C₃	—	12	1	no	—
31	C₃	C₉×SL(2,𝔽₃)	1	1	yes	characteristic
32	C₂	C₂₇⋊A₄	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.