Subgroups — C₃×#994 #64336

Order 288.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41⋊C₃	C₂	1	3	yes	maximal, complemented
2	C₃×H(5,𝔽₂)	C₃	1	1	yes	maximal, characteristic, complemented
3	#994	C₃	1	3	yes	maximal, direct product factor
4	C₃²×Q₈	—	4	1	no	maximal
5	C₃×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic, complemented
6	C₃×#41	—	3	1	no	—
7	C₃×#41	C₂×C₃	1	3	yes	—
8	C₂×C₃×D₄	—	3	3	no	—
9	#41⋊C₃	C₂×C₃	1	9	yes	complemented
10	C₃²×C₄	—	4	3	no	—
11	H(5,𝔽₂)	C₃²	1	1	yes	characteristic, complemented, Sylow
12	C₂³×C₃	—	3	2	no	—
13	C₃×Q₈	—	4	3	no	—
14	C₃×Q₈	A₄	1	1	yes	characteristic
15	C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
16	C₃×D₄	—	3	3	no	—
17	C₃×D₄	—	3	3	no	—
18	C₂×C₃×C₄	—	3	3	no	—
19	SL(2,𝔽₃)	C₂²×C₃	1	3	yes	complemented
20	C₂×C₃²	—	4	1	no	—
21	#41	—	3	1	no	—
22	#41	C₂×C₃²	1	3	yes	—
23	C₂×D₄	—	3	3	no	—
24	C₂²×C₃	—	3	3	no	—
25	C₂²×C₃	—	12	2	no	—
26	C₃×C₄	—	3	1	no	—
27	C₃×C₄	—	4	9	no	—
28	C₃×C₄	C₂×A₄	1	3	yes	—
29	C₃²	—	4	1	no	Sylow
30	C₂³	—	3	2	no	—
31	Q₈	C₃×A₄	1	1	yes	characteristic
32	Q₈	C₂²×C₃²	1	1	yes	characteristic
33	D₄	—	3	3	no	—
34	D₄	—	3	3	no	—
35	C₂×C₄	—	3	3	no	—
36	C₂×C₃	—	4	3	no	—
37	C₂×C₃	—	6	3	no	—
38	C₂×C₃	C₂²×A₄	1	1	yes	characteristic
39	C₂²	—	3	3	no	—
40	C₂²	—	12	2	no	—
41	C₄	—	3	1	no	—
42	C₄	C₂×C₃×A₄	1	3	yes	—
43	C₃	—	4	3	no	—
44	C₃	#994	1	1	yes	characteristic, direct product factor
45	C₂	—	6	3	no	—
46	C₂	C₂²×C₃×A₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	C₂²×A₄
commutator, cosocle, hypocenter	Q₈	C₂²×C₃²
Frattini	C₂	C₂²×C₃×A₄
Fitting	C₃×H(5,𝔽₂)	C₃
hypercenter	C₃×Q₈	A₄
LCS	G ▷ Q₈
UCS	C₁ ◁ C₂×C₃ ◁ C₃×Q₈

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.