Subgroups — #10619580

Order 648.

71 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×SL(2,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
2	Q₈×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
3	#6204	C₃	1	2	yes	maximal, complemented
4	C₂×AΣL(1,𝔽₂₇)	—	4	1	no	maximal
5	C₄×H(3,𝔽₃)	—	3	1	no	—
6	AΣL(1,𝔽₂₇)	—	4	1	no	Sylow
7	C₃²×Q₈	—	3	1	no	—
8	C₃²×Q₈	C₃²	1	1	yes	characteristic
9	C₃×SL(2,𝔽₃)	—	3	1	no	—
10	C₃×SL(2,𝔽₃)	—	3	3	no	—
11	Q₈⋊C₉	—	3	2	no	—
12	C₂×C₃³	—	4	1	no	—
13	C₂×3₋¹⁺²	—	4	2	no	—
14	C₂×H(3,𝔽₃)	A₄	1	1	yes	characteristic
15	C₃²×C₄	—	3	3	no	—
16	C₃²×C₄	—	3	1	no	—
17	C₃³	—	4	1	no	—
18	3₋¹⁺²	—	4	2	no	—
19	H(3,𝔽₃)	SL(2,𝔽₃)	1	1	yes	characteristic, complemented
20	C₃×Q₈	—	3	1	no	—
21	C₃×Q₈	—	9	1	no	—
22	C₃×Q₈	H(3,𝔽₃)	1	1	yes	characteristic
23	SL(2,𝔽₃)	—	3	3	no	—
24	C₂×C₃²	—	3	1	no	—
25	C₂×C₃²	—	12	3	no	—
26	C₂×C₃²	—	12	1	no	—
27	C₂×C₃²	C₃×A₄	1	1	yes	characteristic
28	C₂×C₉	—	12	2	no	—
29	C₃×C₄	—	3	1	no	—
30	C₃×C₄	—	9	1	no	—
31	C₃×C₄	—	9	3	no	—
32	C₃²	—	3	1	no	—
33	C₃²	—	12	3	no	—
34	C₃²	—	12	1	no	—
35	C₃²	C₃×SL(2,𝔽₃)	1	1	yes	characteristic
36	C₉	—	12	2	no	—
37	Q₈	AΣL(1,𝔽₂₇)	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₃	—	3	1	no	—
39	C₂×C₃	—	9	1	no	—
40	C₂×C₃	—	12	3	no	—
41	C₂×C₃	C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic
42	C₄	—	3	1	no	—
43	C₃	—	3	1	no	—
44	C₃	—	9	1	no	—
45	C₃	—	12	3	no	—
46	C₃	Q₈⋊H(3,𝔽₃)	1	1	yes	characteristic
47	C₂	#66363	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.