Subgroups — #1010⋊C₃ #64278

Order 288.

97 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#41⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×SL(2,𝔽₃)	C₂	1	2	yes	maximal, complemented
3	#1010	C₃	1	1	yes	maximal, characteristic, complemented
4	2₋¹⁺⁴⋊C₃	—	3	1	no	maximal
5	C₃×D₁₂	—	4	1	no	maximal
6	C₃×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic
7	C₃×#41	C₂×C₃	1	1	yes	characteristic, complemented
8	D₃×Q₈	C₂×C₃	1	2	yes	complemented
9	#237	—	3	2	no	—
10	#235	—	3	1	no	—
11	C₂×Dic₆	—	3	1	no	—
12	#41⋊C₃	—	2	1	no	—
13	#41⋊C₃	D₃	1	1	yes	characteristic, complemented
14	C₂×SL(2,𝔽₃)	—	3	2	no	—
15	C₂×C₃×D₃	—	4	2	no	—
16	C₃²×C₄	—	4	1	no	—
17	2₋¹⁺⁴	—	3	1	no	Sylow
18	C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
19	C₃×D₄	—	3	1	no	—
20	C₃×D₄	—	12	1	no	—
21	C₂×C₃×C₄	—	3	1	no	—
22	#67	—	3	2	no	—
23	C₂×Dic₃	—	3	2	no	—
24	D₁₂	A₄	1	1	yes	characteristic
25	C₄×D₃	—	3	2	no	—
26	Dic₆	—	3	1	no	—
27	Dic₆	—	3	2	no	—
28	SL(2,𝔽₃)	—	2	1	no	—
29	SL(2,𝔽₃)	C₂×D₃	1	1	yes	characteristic
30	C₂×C₃²	—	4	1	no	—
31	C₃×D₃	—	8	2	no	—
32	#41	—	9	1	no	—
33	#41	—	9	2	no	—
34	#41	C₃×D₃	1	1	yes	characteristic, complemented
35	C₂×Q₈	—	3	2	no	—
36	C₂×Q₈	—	9	1	no	—
37	C₂²×C₃	—	3	1	no	—
38	C₂²×C₃	—	12	2	no	—
39	C₂×D₃	C₂×A₄	1	2	yes	—
40	C₃×C₄	—	3	1	no	—
41	C₃×C₄	—	4	1	no	—
42	C₃×C₄	—	8	1	no	—
43	C₃×C₄	C₂×A₄	1	1	yes	characteristic
44	Dic₃	—	3	2	no	—
45	C₃²	—	4	1	no	Sylow
46	Q₈	—	9	2	no	—
47	Q₈	—	9	1	no	—
48	Q₈	C₂×C₃×D₃	1	1	yes	characteristic
49	D₄	—	3	1	no	—
50	D₄	—	3	1	no	—
51	D₄	—	9	2	no	—
52	C₂×C₄	—	3	1	no	—
53	C₂×C₄	—	9	2	no	—
54	C₂×C₄	—	9	2	no	—
55	C₂×C₃	—	4	1	no	—
56	C₂×C₃	—	6	1	no	—
57	C₂×C₃	—	8	1	no	—
58	C₂×C₃	—	24	2	no	—
59	C₂×C₃	C₂²×A₄	1	1	yes	characteristic
60	D₃	—	2	2	no	—
61	C₂²	—	3	1	no	—
62	C₂²	—	3	2	no	—
63	C₄	—	3	1	no	—
64	C₄	—	9	2	no	—
65	C₄	D₃×A₄	1	1	yes	characteristic
66	C₃	—	4	1	no	—
67	C₃	—	8	1	no	—
68	C₃	2₋¹⁺⁴⋊C₃	1	1	yes	characteristic, complemented
69	C₂	—	6	2	no	—
70	C₂	—	6	1	no	—
71	C₂	C₂×D₃×A₄	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×D₃×A₄
commutator, cosocle, hypocenter	C₃×Q₈	C₂²×C₃
Fitting	C₃×#41	C₂×C₃
socle	C₂×C₃	C₂²×A₄
hypercenter	C₄	D₃×A₄
LCS	G ▷ C₃×Q₈
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
1. C₃×#41⋊C₃	C₂	semidirect
2. D₃×SL(2,𝔽₃)	C₂	semidirect
3. #1010	C₃	semidirect
7. C₃×#41	C₂×C₃	semidirect
8. D₃×Q₈	C₂×C₃	semidirect
13. #41⋊C₃	D₃	semidirect
34. #41	C₃×D₃	semidirect
68. C₃	2₋¹⁺⁴⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×#41⋊C₃	2
D₃×SL(2,𝔽₃)	2
#1010	3
2₋¹⁺⁴⋊C₃	3
C₃×D₁₂	4

Subgroups — #1010⋊C3 #64278

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1010⋊C₃ #64278