Subgroups — #88432

Order 432.

85 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊((C₃⋊D₃)⋊C₃)	C₂	1	2	yes	maximal, complemented
2	#6180	C₂	1	1	yes	maximal, characteristic, complemented
3	#3714	—	3	2	no	maximal
4	C₂×(C₃⋊D₃)⋊C₃	—	2	2	no	—
5	C₄×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
6	C₄⋊(C₃⋊D₃)	D₃	1	2	yes	complemented
7	C₃×D₁₂	—	3	2	no	—
8	C₃×C₃⋊C₈	—	3	2	no	—
9	C₃×C₃⋊C₈	—	6	1	no	—
10	C₂×H(3,𝔽₃)	D₄	1	1	yes	characteristic
11	(C₃⋊D₃)⋊C₃	—	4	2	no	—
12	#213	—	9	2	no	—
13	D₂₄	—	9	1	no	—
14	C₂×C₃⋊D₃	—	2	2	no	—
15	C₂×C₃×D₃	—	6	2	no	—
16	C₃²×C₄	—	2	1	no	—
17	C₃²×C₄	C₂×D₃	1	2	yes	—
18	H(3,𝔽₃)	D₈	1	1	yes	characteristic, complemented, Sylow
19	C₃×D₄	—	9	2	no	—
20	D₁₂	—	3	2	no	—
21	D₁₂	—	18	2	no	—
22	C₃×C₈	—	9	1	no	—
23	C₃⋊C₈	—	3	2	no	—
24	C₃⋊C₈	—	6	1	no	—
25	C₂×C₃²	—	2	1	no	—
26	C₂×C₃²	#67	1	2	yes	—
27	C₃⋊D₃	—	4	2	no	—
28	C₃×D₃	—	12	2	no	—
29	D₈	—	27	1	no	Sylow
30	C₂²×C₃	—	18	2	no	—
31	C₂×D₃	—	6	2	no	—
32	C₂×D₃	—	18	2	no	—
33	C₃×C₄	—	6	2	no	—
34	C₃×C₄	—	6	1	no	—
35	C₃×C₄	D₃²	1	1	yes	characteristic
36	C₃²	—	2	1	no	—
37	C₃²	#213	1	2	yes	complemented
38	D₄	—	9	2	no	—
39	C₈	—	9	1	no	—
40	C₂×C₃	—	6	2	no	—
41	C₂×C₃	—	6	1	no	—
42	C₂×C₃	—	36	2	no	—
43	C₂×C₃	#625	1	1	yes	characteristic
44	D₃	—	12	2	no	—
45	D₃	—	36	2	no	—
46	C₂²	—	18	2	no	—
47	C₄	((C₃⋊D₃)⋊C₃)⋊C₂	1	1	yes	characteristic
48	C₃	—	6	2	no	—
49	C₃	—	6	1	no	—
50	C₃	#3713	1	1	yes	characteristic
51	C₂	—	36	2	no	—
52	C₂	#6198	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.