Subgroups — C₈×C₃⋊(C₃⋊D₃) #88849

Order 432.

308 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic
2	C₃³×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₃⋊(C₃⋊C₈))	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×C₃⋊D₃	—	3	13	no	maximal
5	C₂×C₃⋊(C₃⋊D₃)	C₄	1	1	yes	characteristic
6	C₃³×C₄	C₂²	1	1	yes	characteristic
7	C₃⋊(C₃⋊Dic₃)	C₄	1	1	yes	characteristic
8	C₄×C₃⋊D₃	—	3	13	no	—
9	C₃²×C₈	D₃	1	13	yes	complemented
10	C₃⋊(C₃⋊C₈)	—	3	13	no	—
11	C₂×C₃³	C₂×C₄	1	1	yes	characteristic
12	C₃⋊(C₃⋊D₃)	C₈	1	2	yes	direct product factor
13	D₃×C₈	—	9	13	no	—
14	C₂×C₃⋊D₃	—	3	13	no	—
15	C₃²×C₄	C₂×D₃	1	13	yes	—
16	C₃⋊Dic₃	—	3	13	no	—
17	C₃³	C₂×C₈	1	1	yes	characteristic, complemented, Sylow
18	C₄×D₃	—	9	13	no	—
19	C₃×C₈	C₃⋊D₃	1	13	yes	complemented
20	C₃⋊C₈	—	9	13	no	—
21	C₂×C₃²	C₄×D₃	1	13	yes	—
22	C₃⋊D₃	—	3	26	no	—
23	C₂×C₈	—	27	1	no	Sylow
24	C₂×D₃	—	9	13	no	—
25	C₃×C₄	C₂×C₃⋊D₃	1	13	yes	—
26	Dic₃	—	9	13	no	—
27	C₃²	D₃×C₈	1	13	yes	complemented
28	C₂×C₄	—	27	1	no	—
29	C₈	—	27	1	no	—
30	C₈	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, direct product factor
31	C₂×C₃	C₄×C₃⋊D₃	1	13	yes	—
32	D₃	—	9	26	no	—
33	C₂²	—	27	1	no	—
34	C₄	—	27	1	no	—
35	C₄	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
36	C₃	C₈×C₃⋊D₃	1	13	yes	complemented
37	C₂	—	27	2	no	—
38	C₂	C₄×C₃⋊(C₃⋊D₃)	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.