Subgroups — #88538

Order 432.

110 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	#6180	C₂	1	2	yes	maximal, complemented
3	C₃×#208	—	3	4	no	maximal
4	C₂²×H(3,𝔽₃)	C₄	1	1	yes	characteristic
5	C₄×H(3,𝔽₃)	C₄	1	1	yes	characteristic
6	C₄×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
7	C₂×C₃²×C₄	D₃	1	4	yes	—
8	C₃×C₃⋊C₈	—	3	8	no	—
9	C₂×H(3,𝔽₃)	—	2	1	no	—
10	C₂×H(3,𝔽₃)	C₂×C₄	1	1	yes	characteristic
11	C₃×M₁₆	—	9	1	no	—
12	#208	—	3	4	no	—
13	C₂²×C₃²	Dic₃	1	4	yes	—
14	C₃²×C₄	Dic₃	1	4	yes	—
15	C₃²×C₄	C₂×D₃	1	4	yes	—
16	H(3,𝔽₃)	M₁₆	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃×C₄	—	3	4	no	—
18	C₂×C₃×C₄	C₃⋊D₃	1	1	yes	characteristic
19	C₃×C₈	—	9	2	no	—
20	C₃⋊C₈	—	3	8	no	—
21	C₂×C₃²	—	2	4	no	—
22	C₂×C₃²	C₂×Dic₃	1	4	yes	—
23	M₁₆	—	9	1	no	Sylow
24	C₂²×C₃	—	3	4	no	—
25	C₂²×C₃	C₃⋊Dic₃	1	1	yes	characteristic
26	C₃×C₄	—	3	4	no	—
27	C₃×C₄	—	3	4	no	—
28	C₃×C₄	C₃⋊Dic₃	1	1	yes	characteristic
29	C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
30	C₃²	#208	1	4	yes	complemented
31	C₂×C₄	#272	1	1	yes	characteristic
32	C₈	—	9	2	no	—
33	C₂×C₃	—	2	1	no	—
34	C₂×C₃	—	3	4	no	—
35	C₂×C₃	—	6	4	no	—
36	C₂×C₃	C₂×C₃⋊Dic₃	1	1	yes	characteristic
37	C₂²	#1084	1	1	yes	characteristic
38	C₄	#1084	1	1	yes	characteristic
39	C₄	C₂×#272	1	1	yes	characteristic
40	C₃	—	3	4	no	—
41	C₃	#3748	1	1	yes	characteristic
42	C₂	—	2	1	no	—
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.