Subgroups — C₃×#803 #63589

Order 288.

95 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₃⋊C₈	C₂	1	2	yes	maximal
3	C₃×#97	—	3	1	no	maximal
4	#803	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₃²×C₄	C₄	1	2	yes	—
6	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
7	C₃×C₃⋊C₈	C₄	1	4	yes	complemented
8	C₂×C₃×C₈	—	3	2	no	—
9	C₃×C₄²	—	2	1	no	—
10	C₃×C₄²	D₃	1	1	yes	characteristic
11	C₃×C₄²	C₂×C₃	1	1	yes	characteristic
12	C₂×C₃⋊C₈	C₂×C₃	1	2	yes	—
13	C₂²×C₃²	C₂×C₄	1	1	yes	characteristic
14	C₃²×C₄	—	2	2	no	—
15	C₃²×C₄	C₂×C₄	1	2	yes	—
16	#97	—	3	1	no	Sylow
17	C₂×C₃×C₄	—	2	2	no	—
18	C₂×C₃×C₄	—	2	1	no	—
19	C₂×C₃×C₄	Dic₃	1	2	yes	—
20	C₂×C₃×C₄	C₃×C₄	1	2	yes	—
21	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
22	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
23	C₃×C₈	—	3	4	no	—
24	C₃⋊C₈	C₃×C₄	1	4	yes	complemented
25	C₂×C₃²	C₄²	1	1	yes	characteristic
26	C₂×C₃²	M₁₆	1	2	yes	—
27	C₂×C₈	—	3	2	no	—
28	C₄²	C₃×D₃	1	1	yes	characteristic
29	C₂²×C₃	—	2	1	no	—
30	C₂²×C₃	C₂×Dic₃	1	1	yes	characteristic
31	C₂²×C₃	C₂×C₃×C₄	1	1	yes	characteristic
32	C₃×C₄	—	2	4	no	—
33	C₃×C₄	—	2	2	no	—
34	C₃×C₄	—	2	2	no	—
35	C₃×C₄	—	2	2	no	—
36	C₃×C₄	C₄×D₃	1	2	yes	—
37	C₃×C₄	C₂×C₃×C₄	1	2	yes	—
38	C₃²	#97	1	1	yes	characteristic, complemented, Sylow
39	C₂×C₄	C₃×Dic₃	1	2	yes	—
40	C₂×C₄	C₂×C₃×D₃	1	1	yes	characteristic
41	C₈	—	3	4	no	—
42	C₂×C₃	—	2	2	no	—
43	C₂×C₃	—	2	1	no	—
44	C₂×C₃	#208	1	2	yes	—
45	C₂×C₃	C₄×Dic₃	1	1	yes	characteristic
46	C₂×C₃	C₃×C₄²	1	1	yes	characteristic
47	C₂×C₃	C₃×M₁₆	1	2	yes	—
48	C₂²	C₂×C₃×Dic₃	1	1	yes	characteristic
49	C₄	—	2	2	no	—
50	C₄	C₃×C₄×D₃	1	2	yes	—
51	C₃	—	2	1	no	—
52	C₃	#803	1	1	yes	characteristic, direct product factor
53	C₃	C₃×#97	1	1	yes	characteristic, complemented
54	C₂	C₃×#208	1	2	yes	—
55	C₂	C₃×C₄×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₃
commutator	C₂×C₃	C₃×C₄²
Frattini	C₂×C₄	C₂×C₃×D₃
Fitting	C₃²×C₄²	C₂
socle, prime radical	C₂²×C₃²	C₂×C₄
cosocle	C₂×C₃×C₄	C₂²×C₃
hypercenter	C₃×C₄²	D₃
hypocenter	C₃	C₃×#97
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄²

Complements

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

N	H ≅ G/N	type
4. #803	C₃	direct (N × H)
7. C₃×C₃⋊C₈	C₄	semidirect
24. C₃⋊C₈	C₃×C₄	semidirect
38. C₃²	#97	semidirect
52. C₃	#803	direct (N × H)
53. C₃	C₃×#97	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₄²	2
C₂×C₃×C₃⋊C₈	2
C₃×#97	3
#803	3

Subgroups — C3×#803 #63589

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#803 #63589