Subgroups — C₂×C₃⋊#226 #64262

Order 288.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#226	C₂	1	2	yes	maximal, direct product factor
3	C₂×#226	—	3	3	no	maximal
4	C₂×#216	—	3	1	no	maximal
5	C₂×C₃⋊Dic₃	—	4	1	no	maximal
6	C₃×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic
7	C₂×C₃×Q₈	D₃	1	1	yes	characteristic
8	C₂×Dic₆	—	3	1	no	—
9	C₂×SL(2,𝔽₃)	D₃	1	3	yes	—
10	#226	—	3	6	no	—
11	#216	—	3	2	no	—
12	#216	—	3	2	no	—
13	C₂×C₃⋊C₈	—	3	1	no	—
14	C₂²×C₃²	—	4	1	no	—
15	C₃⋊Dic₃	—	4	2	no	—
16	C₂×Q₁₆	—	9	1	no	Sylow
17	C₃×Q₈	—	3	1	no	—
18	C₃×Q₈	C₂×D₃	1	1	yes	characteristic
19	C₂×C₃×C₄	—	3	1	no	—
20	C₂×Dic₃	—	6	1	no	—
21	C₂×Dic₃	—	12	3	no	—
22	Dic₆	—	3	2	no	—
23	Dic₆	—	6	1	no	—
24	SL(2,𝔽₃)	C₂×D₃	1	3	yes	—
25	C₃⋊C₈	—	3	2	no	—
26	C₂×C₃²	—	4	2	no	—
27	C₂×C₃²	—	4	1	no	—
28	C₂×Q₈	—	9	1	no	—
29	C₂×Q₈	C₃⋊D₃	1	1	yes	characteristic
30	Q₁₆	—	9	2	no	—
31	Q₁₆	—	9	2	no	—
32	C₂×C₈	—	9	1	no	—
33	C₂²×C₃	—	4	3	no	—
34	C₂²×C₃	S₄	1	1	yes	characteristic
35	C₃×C₄	—	3	1	no	—
36	C₃×C₄	—	3	1	no	—
37	Dic₃	—	6	2	no	—
38	Dic₃	—	12	6	no	—
39	C₃²	—	4	1	no	Sylow
40	Q₈	—	3	1	no	—
41	Q₈	—	9	2	no	—
42	Q₈	—	18	1	no	—
43	Q₈	C₂×C₃⋊D₃	1	1	yes	characteristic
44	C₂×C₄	—	3	1	no	—
45	C₂×C₄	—	18	1	no	—
46	C₈	—	9	2	no	—
47	C₂×C₃	—	4	3	no	—
48	C₂×C₃	—	4	6	no	—
49	C₂×C₃	#226	1	2	yes	complemented
50	C₂×C₃	C₂×S₄	1	1	yes	characteristic
51	C₂²	C₃⋊S₄	1	1	yes	characteristic
52	C₄	—	3	1	no	—
53	C₄	—	3	1	no	—
54	C₄	—	18	2	no	—
55	C₃	—	4	3	no	—
56	C₃	C₂×#226	1	1	yes	characteristic, complemented
57	C₂	C₃⋊#226	1	2	yes	direct product factor
58	C₂	C₂×C₃⋊S₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	C₃⋊S₄
commutator, cosocle, hypocenter	C₃×SL(2,𝔽₃)	C₂²
Frattini	C₂	C₂×C₃⋊S₄
Fitting	C₂×C₃×Q₈	D₃
socle	C₂²×C₃	S₄
prime radical	C₂×C₃×SL(2,𝔽₃)	C₂
LCS	G ▷ C₃×SL(2,𝔽₃)
UCS	C₁ ◁ C₂²

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₃⋊#226	C₂	direct (N × H)
49. C₂×C₃	#226	semidirect
56. C₃	C₂×#226	semidirect
57. C₂	C₃⋊#226	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×SL(2,𝔽₃)	2
C₃⋊#226	2
C₂×#226	3
C₂×#216	3
C₂×C₃⋊Dic₃	4

Subgroups — C2×C3⋊#226 #64262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊#226 #64262