Subgroups — #64078

Order 288.

204 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#634	C₂	1	2	yes	maximal
2	C₃²×C₄²	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₃⋊Dic₃)	C₂	1	4	yes	maximal
4	#869	—	3	4	no	maximal
5	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
6	C₂×C₃²×C₄	C₂²	1	2	yes	—
7	C₂×C₃⋊Dic₃	C₂²	1	4	yes	—
8	#634	—	2	4	no	—
9	C₂×Dic₆	—	3	8	no	—
10	C₃×C₄²	D₃	1	4	yes	—
11	C₄⋊Dic₃	—	3	16	no	—
12	C₂²×C₃²	C₂³	1	1	yes	characteristic
13	C₃²×C₄	D₄	1	2	yes	—
14	C₃²×C₄	Q₈	1	4	yes	complemented
15	C₃⋊Dic₃	—	2	4	no	—
16	C₄⋊Q₈	—	9	1	no	Sylow
17	C₂×C₃×C₄	C₂×D₃	1	8	yes	—
18	C₂×C₃×C₄	C₂×D₃	1	4	yes	—
19	C₂×Dic₃	—	3	16	no	—
20	Dic₆	—	6	16	no	—
21	C₂×C₃²	C₂×D₄	1	1	yes	characteristic
22	C₂×C₃²	C₂×Q₈	1	2	yes	—
23	C₂×Q₈	—	9	2	no	—
24	C₄⋊C₄	—	9	4	no	—
25	C₄²	C₃⋊D₃	1	1	yes	characteristic
26	C₂²×C₃	C₂²×D₃	1	4	yes	—
27	C₃×C₄	Dic₆	1	16	yes	complemented
28	C₃×C₄	D₁₂	1	8	yes	—
29	Dic₃	—	6	16	no	—
30	C₃²	C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
31	Q₈	—	18	4	no	—
32	C₂×C₄	—	9	4	no	—
33	C₂×C₄	C₂×C₃⋊D₃	1	2	yes	—
34	C₂×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
35	C₂×C₃	C₂×Dic₆	1	8	yes	—
36	C₂×C₃	C₂×D₁₂	1	4	yes	—
37	C₂²	C₂²×C₃⋊D₃	1	1	yes	characteristic
38	C₄	—	18	4	no	—
39	C₄	#634	1	4	yes	complemented
40	C₄	C₄⋊(C₃⋊D₃)	1	2	yes	—
41	C₃	#869	1	4	yes	complemented
42	C₂	C₂×#634	1	2	yes	—
43	C₂	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×C₃⋊D₃
commutator, socle, prime radical, cosocle	C₂²×C₃²	C₂³
Fitting	C₃²×C₄²	C₂
hypercenter	C₄²	C₃⋊D₃
hypocenter	C₃²	C₄⋊Q₈
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₄²

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.