Subgroups — C₄×#1084 #88539

Order 432.

165 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic
2	C₂×#1084	C₂	1	2	yes	maximal
3	C₃×C₄×Dic₃	—	3	4	no	maximal
4	C₂²×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
5	C₄×H(3,𝔽₃)	C₄	1	2	yes	complemented
6	#1084	C₄	1	4	yes	direct product factor
7	C₂×C₃²×C₄	D₃	1	4	yes	—
8	C₂×C₃×Dic₃	—	3	8	no	—
9	C₂×H(3,𝔽₃)	C₂×C₄	1	2	yes	—
10	C₂×H(3,𝔽₃)	C₂×C₄	1	1	yes	characteristic
11	C₃×C₄²	—	9	1	no	—
12	C₄×Dic₃	—	3	4	no	—
13	C₂²×C₃²	C₂×D₃	1	4	yes	—
14	C₃²×C₄	Dic₃	1	8	yes	complemented
15	C₃×Dic₃	—	3	16	no	—
16	H(3,𝔽₃)	C₄²	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃×C₄	—	3	4	no	—
18	C₂×C₃×C₄	—	9	2	no	—
19	C₂×C₃×C₄	C₃⋊D₃	1	1	yes	characteristic
20	C₂×Dic₃	—	3	8	no	—
21	C₂×C₃²	C₄×D₃	1	8	yes	—
22	C₂×C₃²	C₂×Dic₃	1	4	yes	—
23	C₄²	—	9	1	no	Sylow
24	C₂²×C₃	—	3	4	no	—
25	C₂²×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
26	C₃×C₄	—	3	8	no	—
27	C₃×C₄	—	9	4	no	—
28	C₃×C₄	C₃⋊Dic₃	1	2	yes	—
29	Dic₃	—	3	16	no	—
30	C₃²	C₄×Dic₃	1	4	yes	complemented
31	C₂×C₄	—	9	2	no	—
32	C₂×C₄	#272	1	1	yes	characteristic
33	C₂×C₃	—	3	8	no	—
34	C₂×C₃	—	3	4	no	—
35	C₂×C₃	C₄×C₃⋊D₃	1	2	yes	—
36	C₂×C₃	C₂×C₃⋊Dic₃	1	1	yes	characteristic
37	C₂²	C₂×#272	1	1	yes	characteristic
38	C₄	—	9	4	no	—
39	C₄	#1084	1	2	yes	direct product factor
40	C₃	—	3	4	no	—
41	C₃	C₄×C₃⋊Dic₃	1	1	yes	characteristic
42	C₂	C₄×#272	1	2	yes	—
43	C₂	C₂×#1084	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.