Subgroups — C₉×GL(2,𝔽₃) #88594

Order 432.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×GL(2,𝔽₃)	C₃	1	1	yes	maximal, characteristic
3	C₉×SD₁₆	—	3	1	no	maximal
4	C₂×D₃×C₉	—	4	1	no	maximal
5	C₃×SL(2,𝔽₃)	C₂×C₃	1	1	yes	characteristic
6	Q₈×C₉	D₃	1	1	yes	characteristic, complemented
7	D₄×C₉	—	3	1	no	—
8	Q₈⋊C₉	—	2	1	no	—
9	C₈×C₉	—	3	1	no	—
10	C₂×C₃×C₉	—	4	1	no	—
11	D₃×C₉	—	4	2	no	—
12	GL(2,𝔽₃)	C₉	1	1	yes	characteristic, direct product factor
13	C₃×SD₁₆	—	3	1	no	—
14	C₂×C₃×D₃	—	4	1	no	—
15	C₂²×C₉	—	6	1	no	—
16	C₄×C₉	—	3	1	no	—
17	C₃×C₉	—	4	1	no	Sylow
18	C₃×Q₈	C₃×D₃	1	1	yes	characteristic
19	C₃×D₄	—	3	1	no	—
20	SL(2,𝔽₃)	—	2	1	no	—
21	SL(2,𝔽₃)	C₂×C₉	1	1	yes	characteristic, complemented
22	C₃×C₈	—	3	1	no	—
23	C₂×C₃²	—	4	1	no	—
24	C₃×D₃	—	4	2	no	—
25	C₂×C₉	—	8	1	no	—
26	C₂×C₉	—	12	1	no	—
27	C₂×C₉	S₄	1	1	yes	characteristic
28	SD₁₆	—	3	1	no	Sylow
29	C₂²×C₃	—	6	1	no	—
30	C₂×D₃	—	4	1	no	—
31	C₃×C₄	—	3	1	no	—
32	C₃²	—	4	1	no	—
33	C₉	—	8	1	no	—
34	C₉	GL(2,𝔽₃)	1	1	yes	characteristic, direct product factor
35	Q₈	D₃×C₉	1	1	yes	characteristic, complemented
36	D₄	—	3	1	no	—
37	C₈	—	3	1	no	—
38	C₂×C₃	—	4	1	no	—
39	C₂×C₃	—	8	1	no	—
40	C₂×C₃	—	12	1	no	—
41	C₂×C₃	C₃×S₄	1	1	yes	characteristic
42	D₃	—	4	2	no	—
43	C₂²	—	6	1	no	—
44	C₄	—	3	1	no	—
45	C₃	—	4	1	no	—
46	C₃	—	8	1	no	—
47	C₃	C₃×GL(2,𝔽₃)	1	1	yes	characteristic
48	C₂	—	12	1	no	—
49	C₂	C₉×S₄	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.