Subgroups — C₂×#6308 #89073

Order 432.

532 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊(C₃⋊Dic₃)	C₂	1	2	yes	maximal
3	#6308	C₂	1	4	yes	maximal, direct product factor
4	C₂×#634	—	3	13	no	maximal
5	C₂²×C₃³	C₂²	1	1	yes	characteristic
6	C₃³×C₄	C₂²	1	2	yes	—
7	C₃⋊(C₃⋊Dic₃)	C₂²	1	4	yes	—
8	C₂×C₃²×C₄	D₃	1	13	yes	—
9	C₂×C₃⋊Dic₃	—	3	26	no	—
10	#634	—	3	52	no	—
11	C₂×C₃³	Q₈	1	2	yes	complemented
12	C₂×C₃³	C₂³	1	1	yes	characteristic
13	C₂×Dic₆	—	9	13	no	—
14	C₂²×C₃²	C₂×D₃	1	13	yes	—
15	C₃²×C₄	C₂×D₃	1	26	yes	—
16	C₃⋊Dic₃	—	3	52	no	—
17	C₃³	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃×C₄	C₃⋊D₃	1	13	yes	—
19	C₂×Dic₃	—	9	26	no	—
20	Dic₆	—	9	52	no	—
21	C₂×C₃²	Dic₆	1	26	yes	complemented
22	C₂×C₃²	C₂²×D₃	1	13	yes	—
23	C₂×Q₈	—	27	1	no	Sylow
24	C₂²×C₃	C₂×C₃⋊D₃	1	13	yes	—
25	C₃×C₄	C₂×C₃⋊D₃	1	26	yes	—
26	Dic₃	—	9	52	no	—
27	C₃²	C₂×Dic₆	1	13	yes	complemented
28	Q₈	—	27	4	no	—
29	C₂×C₄	—	27	2	no	—
30	C₂×C₄	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
31	C₂×C₃	#634	1	26	yes	complemented
32	C₂×C₃	C₂²×C₃⋊D₃	1	13	yes	—
33	C₂²	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
34	C₄	—	27	4	no	—
35	C₄	C₂×C₃⋊(C₃⋊D₃)	1	2	yes	—
36	C₃	C₂×#634	1	13	yes	complemented
37	C₂	#6308	1	2	yes	direct product factor
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.