Subgroups — C₂²×C₃×#1055 #11928810

Order 1248.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#1055	C₂	1	6	yes	maximal, direct product factor
3	C₂²×#1055	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂³×C₃×C₁₃	C₄	1	1	yes	characteristic
5	C₂×C₃×C₄×C₁₃	C₄	1	3	yes	—
6	C₂×C₃×C₄×C₁₃	C₂²	1	3	yes	—
7	C₃×#1055	C₂²	1	4	yes	direct product factor
8	C₂²×C₄×C₁₃	C₂×C₃	1	1	yes	characteristic
9	C₂×#1055	C₂×C₃	1	6	yes	direct product factor
10	C₂²×C₃×C₁₃	C₈	1	4	yes	complemented
11	C₂²×C₃×C₁₃	C₂×C₄	1	3	yes	—
12	C₃×C₄×C₁₃	C₂×C₄	1	3	yes	—
13	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
14	C₂³×C₁₃	C₃×C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₃	C₃×C₄	1	3	yes	—
16	C₂×C₄×C₁₃	C₂²×C₃	1	3	yes	—
17	#1055	C₂²×C₃	1	4	yes	direct product factor
18	C₂²×C₃×C₈	—	13	1	no	maximal, Hall
19	C₂×C₃×C₁₃	C₂×C₈	1	6	yes	complemented
20	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
21	C₂²×C₁₃	C₃×C₈	1	4	yes	complemented
22	C₂²×C₁₃	C₂×C₃×C₄	1	3	yes	—
23	C₄×C₁₃	C₂×C₃×C₄	1	3	yes	—
24	C₄×C₁₃	C₂³×C₃	1	1	yes	characteristic
25	C₂²×C₃×C₄	D₁₃	1	1	yes	characteristic
26	C₂×C₃×C₈	—	13	6	no	—
27	C₃×C₁₃	C₂²×C₈	1	1	yes	characteristic, complemented, Hall
28	C₂²×C₈	—	13	1	no	Sylow
29	C₂×C₁₃	C₂×C₃×C₈	1	6	yes	complemented
30	C₂×C₁₃	C₂²×C₃×C₄	1	1	yes	characteristic
31	C₂³×C₃	Dic₁₃	1	1	yes	characteristic
32	C₂×C₃×C₄	Dic₁₃	1	3	yes	—
33	C₂×C₃×C₄	C₂×D₁₃	1	3	yes	—
34	C₃×C₈	—	13	4	no	—
35	C₂²×C₄	C₃×D₁₃	1	1	yes	characteristic
36	C₂×C₈	—	13	6	no	—
37	C₁₃	C₂²×C₃×C₈	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₃	#1055	1	4	yes	direct product factor
39	C₂²×C₃	C₂×Dic₁₃	1	3	yes	—
40	C₃×C₄	C₂×Dic₁₃	1	3	yes	—
41	C₃×C₄	C₂²×D₁₃	1	1	yes	characteristic
42	C₂³	C₃×Dic₁₃	1	1	yes	characteristic
43	C₂×C₄	C₃×Dic₁₃	1	3	yes	—
44	C₂×C₄	C₂×C₃×D₁₃	1	3	yes	—
45	C₈	—	13	4	no	—
46	C₂×C₃	C₂×#1055	1	6	yes	direct product factor
47	C₂×C₃	C₂²×Dic₁₃	1	1	yes	characteristic
48	C₂²	C₃×#1055	1	4	yes	direct product factor
49	C₂²	C₂×C₃×Dic₁₃	1	3	yes	—
50	C₄	C₂×C₃×Dic₁₃	1	3	yes	—
51	C₄	C₂²×C₃×D₁₃	1	1	yes	characteristic
52	C₃	C₂²×#1055	1	1	yes	characteristic, direct product factor, Sylow
53	C₂	C₂×C₃×#1055	1	6	yes	direct product factor
54	C₂	C₂²×C₃×Dic₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₃×C₄	D₁₃
commutator, hypocenter	C₁₃	C₂²×C₃×C₈
Frattini	C₄	C₂²×C₃×D₁₃
Fitting	C₂²×C₃×C₄×C₁₃	C₂
socle, prime radical	C₂³×C₃×C₁₃	C₄
cosocle	C₄×C₁₃	C₂³×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂²×C₃×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#1055	C₂	direct (N × H)
3. C₂²×#1055	C₃	direct (N × H)
7. C₃×#1055	C₂²	direct (N × H)
9. C₂×#1055	C₂×C₃	direct (N × H)
10. C₂²×C₃×C₁₃	C₈	semidirect
17. #1055	C₂²×C₃	direct (N × H)
19. C₂×C₃×C₁₃	C₂×C₈	semidirect
21. C₂²×C₁₃	C₃×C₈	semidirect
27. C₃×C₁₃	C₂²×C₈	semidirect
29. C₂×C₁₃	C₂×C₃×C₈	semidirect
37. C₁₃	C₂²×C₃×C₈	semidirect
38. C₂²×C₃	#1055	direct (N × H)
46. C₂×C₃	C₂×#1055	direct (N × H)
48. C₂²	C₃×#1055	direct (N × H)
52. C₃	C₂²×#1055	direct (N × H)
53. C₂	C₂×C₃×#1055	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄×C₁₃	2
C₂×C₃×#1055	2
C₂²×#1055	3
C₂²×C₃×C₈	13

Subgroups — C22×C3×#1055 #11928810

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#1055 #11928810