Subgroups — #88691

Order 432.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6204	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×#41	C₃	1	1	yes	maximal, characteristic
3	#41⋊C₉	C₃	1	3	yes	maximal, complemented
4	C₄×3₋¹⁺²	—	4	1	no	maximal
5	C₃²×Q₈	C₂×C₃	1	1	yes	characteristic
6	C₃²×D₄	—	3	1	no	—
7	C₂×C₃²×C₄	—	3	1	no	—
8	Q₈⋊C₉	C₂×C₃	1	3	yes	complemented
9	C₂×3₋¹⁺²	—	4	1	no	—
10	C₃×#41	—	3	1	no	—
11	C₃×#41	C₃²	1	1	yes	characteristic
12	C₂²×C₃²	—	3	1	no	—
13	C₃²×C₄	—	3	1	no	—
14	C₃²×C₄	A₄	1	1	yes	characteristic
15	C₄×C₉	—	4	3	no	—
16	3₋¹⁺²	—	4	1	no	Sylow
17	C₃×Q₈	—	3	1	no	—
18	C₃×Q₈	C₂×C₃²	1	1	yes	characteristic
19	C₃×D₄	—	3	1	no	—
20	C₃×D₄	—	3	3	no	—
21	C₂×C₃×C₄	—	3	3	no	—
22	C₂×C₃×C₄	—	3	1	no	—
23	C₂×C₃²	—	6	1	no	—
24	C₂×C₃²	C₂×A₄	1	1	yes	characteristic
25	C₂×C₉	—	4	3	no	—
26	#41	3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
27	C₂²×C₃	—	3	3	no	—
28	C₂²×C₃	—	3	1	no	—
29	C₃×C₄	—	3	3	no	—
30	C₃×C₄	—	3	1	no	—
31	C₃×C₄	—	3	1	no	—
32	C₃×C₄	C₃×A₄	1	1	yes	characteristic
33	C₃²	#41⋊C₃	1	1	yes	characteristic
34	C₉	—	4	3	no	—
35	Q₈	C₂×3₋¹⁺²	1	1	yes	characteristic
36	D₄	—	3	1	no	—
37	C₂×C₄	—	3	1	no	—
38	C₂×C₃	—	3	1	no	—
39	C₂×C₃	—	6	3	no	—
40	C₂×C₃	—	6	1	no	—
41	C₂×C₃	C₂×C₃×A₄	1	1	yes	characteristic
42	C₂²	—	3	1	no	—
43	C₄	—	3	1	no	—
44	C₄	#1094	1	1	yes	characteristic
45	C₃	—	3	1	no	—
46	C₃	C₃×#41⋊C₃	1	1	yes	characteristic
47	C₂	—	6	1	no	—
48	C₂	C₂×#1094	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.