Subgroups — Q₈×C₃⋊(C₃⋊D₃) #89079

Order 432.

532 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₃⋊(C₃⋊D₃)	C₂	1	3	yes	maximal
3	#6308	C₂	1	3	yes	maximal, complemented
4	Q₈×C₃⋊D₃	—	3	13	no	maximal
5	C₂×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
6	C₃³×C₄	C₂²	1	3	yes	—
7	C₃⋊(C₃⋊Dic₃)	C₂²	1	3	yes	—
8	C₃²×Q₈	D₃	1	13	yes	complemented
9	C₄×C₃⋊D₃	—	3	39	no	—
10	#634	—	3	39	no	—
11	C₂×C₃³	C₂³	1	1	yes	characteristic
12	C₃⋊(C₃⋊D₃)	Q₈	1	2	yes	direct product factor
13	D₃×Q₈	—	9	13	no	—
14	C₂×C₃⋊D₃	—	3	13	no	—
15	C₃²×C₄	C₂×D₃	1	39	yes	—
16	C₃⋊Dic₃	—	3	39	no	—
17	C₃³	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
18	C₃×Q₈	C₃⋊D₃	1	13	yes	complemented
19	C₄×D₃	—	9	39	no	—
20	Dic₆	—	9	39	no	—
21	C₂×C₃²	C₂²×D₃	1	13	yes	—
22	C₃⋊D₃	—	3	26	no	—
23	C₂×Q₈	—	27	1	no	Sylow
24	C₂×D₃	—	9	13	no	—
25	C₃×C₄	C₂×C₃⋊D₃	1	39	yes	—
26	Dic₃	—	9	39	no	—
27	C₃²	D₃×Q₈	1	13	yes	complemented
28	Q₈	—	27	3	no	—
29	Q₈	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, direct product factor
30	C₂×C₄	—	27	3	no	—
31	C₂×C₃	C₂²×C₃⋊D₃	1	13	yes	—
32	D₃	—	9	26	no	—
33	C₂²	—	27	1	no	—
34	C₄	—	27	3	no	—
35	C₄	C₂×C₃⋊(C₃⋊D₃)	1	3	yes	—
36	C₃	Q₈×C₃⋊D₃	1	13	yes	complemented
37	C₂	—	27	2	no	—
38	C₂	C₂²×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.