Subgroups — C₂²×#1088 #88896

Order 432.

145 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#272	C₂	1	1	yes	maximal, characteristic
2	C₂×#1088	C₂	1	6	yes	maximal, direct product factor
3	C₂²×H(3,𝔽₃)	C₄	1	1	yes	characteristic, complemented
4	C₂×#272	C₄	1	3	yes	complemented
5	C₂×#272	C₂²	1	3	yes	—
6	#1088	C₂²	1	4	yes	direct product factor
7	C₂²×C₃×D₃	—	6	2	no	—
8	C₂×H(3,𝔽₃)	C₂×C₄	1	3	yes	complemented
9	#272	C₂×C₄	1	3	yes	complemented
10	#272	C₂³	1	1	yes	characteristic
11	C₂²×C₃×C₄	—	9	1	no	maximal
12	C₂²×C₃²	—	2	2	no	—
13	C₂×C₃×D₃	—	6	6	no	—
14	C₂×C₃×D₃	—	6	6	no	—
15	H(3,𝔽₃)	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
16	C₂³×C₃	—	9	1	no	—
17	C₂²×D₃	—	6	2	no	—
18	C₂×C₃×C₄	—	9	6	no	—
19	C₂×C₃²	—	2	6	no	—
20	C₃×D₃	—	6	6	no	—
21	C₃×D₃	—	6	2	no	—
22	C₂²×C₄	—	9	1	no	Sylow
23	C₂²×C₃	—	6	2	no	—
24	C₂²×C₃	—	9	3	no	—
25	C₂²×C₃	—	9	3	no	—
26	C₂²×C₃	#157	1	1	yes	characteristic
27	C₂×D₃	—	6	6	no	—
28	C₂×D₃	—	6	6	no	—
29	C₃×C₄	—	9	4	no	—
30	C₃²	—	2	2	no	—
31	C₂³	—	9	1	no	—
32	C₂×C₄	—	9	6	no	—
33	C₂×C₃	—	6	6	no	—
34	C₂×C₃	—	9	1	no	—
35	C₂×C₃	—	9	3	no	—
36	C₂×C₃	C₂×#157	1	3	yes	—
37	D₃	—	6	2	no	—
38	D₃	—	6	6	no	—
39	C₂²	—	9	3	no	—
40	C₂²	—	9	3	no	—
41	C₂²	#1088	1	1	yes	characteristic, direct product factor
42	C₄	—	9	4	no	—
43	C₃	—	6	2	no	—
44	C₃	C₂²×#157	1	1	yes	characteristic
45	C₂	—	9	1	no	—
46	C₂	—	9	3	no	—
47	C₂	C₂×#1088	1	3	yes	direct product factor

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.