Subgroups — #63642

Order 288.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	#815	—	3	4	no	maximal
5	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
6	C₂×C₃⋊Dic₃	C₄	1	2	yes	—
7	C₃²×C₈	C₄	1	2	yes	complemented
8	C₃⋊(C₃⋊C₈)	C₄	1	2	yes	complemented
9	C₂×C₃×C₈	D₃	1	4	yes	—
10	C₄×Dic₃	—	3	4	no	—
11	C₂×C₃⋊C₈	—	3	4	no	—
12	C₂²×C₃²	C₂×C₄	1	1	yes	characteristic
13	C₃²×C₄	C₂×C₄	1	1	yes	characteristic
14	C₃²×C₄	C₂×C₄	1	1	yes	characteristic
15	C₃⋊Dic₃	—	2	2	no	—
16	#97	—	9	1	no	Sylow
17	C₂×C₃×C₄	C₂×D₃	1	4	yes	—
18	C₂×Dic₃	—	3	8	no	—
19	C₃×C₈	Dic₃	1	8	yes	complemented
20	C₃⋊C₈	—	3	8	no	—
21	C₂×C₃²	C₄²	1	1	yes	characteristic
22	C₂×C₃²	M₁₆	1	2	yes	—
23	C₂×C₈	—	9	1	no	—
24	C₂×C₈	C₃⋊D₃	1	1	yes	characteristic
25	C₄²	—	9	1	no	—
26	C₂²×C₃	C₄×D₃	1	4	yes	—
27	C₃×C₄	C₄×D₃	1	4	yes	—
28	C₃×C₄	C₂×Dic₃	1	4	yes	—
29	Dic₃	—	6	8	no	—
30	C₃²	#97	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₄	—	9	2	no	—
32	C₂×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
33	C₈	—	9	2	no	—
34	C₈	C₃⋊Dic₃	1	2	yes	complemented
35	C₂×C₃	ΓL(1,𝔽₂₅)	1	8	yes	—
36	C₂×C₃	C₄×Dic₃	1	4	yes	—
37	C₂²	C₄×C₃⋊D₃	1	1	yes	characteristic
38	C₄	—	18	2	no	—
39	C₄	C₄×C₃⋊D₃	1	1	yes	characteristic
40	C₄	C₂×C₃⋊Dic₃	1	1	yes	characteristic
41	C₃	#815	1	4	yes	complemented
42	C₂	#3743	1	2	yes	—
43	C₂	C₄×C₃⋊Dic₃	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.