Subgroups — C₂³×C₃⋊#261 #11929338

Order 1248.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃⋊#261	C₂	1	14	yes	maximal, direct product factor
3	C₂³×#261	—	3	1	no	maximal, Hall
4	C₂³×C₃×C₁₃	C₄	1	1	yes	characteristic, complemented
5	C₂²×C₃×D₁₃	C₄	1	7	yes	complemented
6	C₂²×C₃×D₁₃	C₂²	1	7	yes	—
7	C₂×C₃⋊#261	C₂²	1	28	yes	direct product factor
8	C₂³×D₁₃	D₃	1	1	yes	characteristic
9	C₂²×#261	—	3	14	no	—
10	C₂²×C₃×C₁₃	C₂×C₄	1	7	yes	complemented
11	C₂×C₃×D₁₃	C₂×C₄	1	21	yes	complemented
12	C₂×C₃×D₁₃	C₂³	1	7	yes	—
13	C₃⋊#261	C₂³	1	8	yes	direct product factor
14	C₂³×C₁₃	Dic₃	1	1	yes	characteristic, complemented
15	C₂²×D₁₃	Dic₃	1	7	yes	complemented
16	C₂²×D₁₃	C₂×D₃	1	7	yes	—
17	C₂×#261	—	3	28	no	—
18	C₂³×Dic₃	—	13	1	no	maximal, Hall
19	C₂×C₃×C₁₃	C₂²×C₄	1	7	yes	complemented
20	C₃×D₁₃	C₂²×C₄	1	7	yes	complemented
21	C₃×D₁₃	C₂⁴	1	1	yes	characteristic
22	C₂²×C₁₃	C₂×Dic₃	1	7	yes	complemented
23	C₂×D₁₃	C₂×Dic₃	1	21	yes	complemented
24	C₂×D₁₃	C₂²×D₃	1	7	yes	—
25	#261	—	3	8	no	—
26	C₂⁴×C₃	—	13	1	no	—
27	C₂²×Dic₃	—	13	14	no	—
28	C₃×C₁₃	C₂³×C₄	1	1	yes	characteristic, complemented, Hall
29	C₂³×C₄	—	39	1	no	Sylow
30	C₂×C₁₃	C₂²×Dic₃	1	7	yes	complemented
31	D₁₃	C₂²×Dic₃	1	7	yes	complemented
32	D₁₃	C₂³×D₃	1	1	yes	characteristic
33	C₂³×C₃	—	13	7	no	—
34	C₂³×C₃	—	13	7	no	—
35	C₂³×C₃	#261	1	1	yes	characteristic, complemented
36	C₂×Dic₃	—	13	28	no	—
37	C₂⁴	—	13	1	no	—
38	C₂²×C₄	—	39	14	no	—
39	C₁₃	C₂³×Dic₃	1	1	yes	characteristic, complemented, Sylow
40	C₂²×C₃	—	13	7	no	—
41	C₂²×C₃	—	13	21	no	—
42	C₂²×C₃	C₂×#261	1	7	yes	complemented
43	Dic₃	—	13	8	no	—
44	C₂³	—	13	7	no	—
45	C₂³	—	13	7	no	—
46	C₂³	C₃⋊#261	1	1	yes	characteristic, direct product factor
47	C₂×C₄	—	39	28	no	—
48	C₂×C₃	—	13	1	no	—
49	C₂×C₃	—	13	7	no	—
50	C₂×C₃	C₂²×#261	1	7	yes	complemented
51	C₂²	—	13	21	no	—
52	C₂²	—	13	7	no	—
53	C₂²	C₂×C₃⋊#261	1	7	yes	direct product factor
54	C₄	—	39	8	no	—
55	C₃	C₂³×#261	1	1	yes	characteristic, complemented, Sylow
56	C₂	—	13	1	no	—
57	C₂	—	13	7	no	—
58	C₂	C₂²×C₃⋊#261	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³	C₃⋊#261
commutator, hypocenter	C₃×C₁₃	C₂³×C₄
Frattini	C₁	G
Fitting, socle	C₂³×C₃×C₁₃	C₄
prime radical	C₂³×C₃×D₁₃	C₂
cosocle	C₃×D₁₃	C₂⁴
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₂³

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃⋊#261	C₂	direct (N × H)
4. C₂³×C₃×C₁₃	C₄	semidirect
5. C₂²×C₃×D₁₃	C₄	semidirect
7. C₂×C₃⋊#261	C₂²	direct (N × H)
10. C₂²×C₃×C₁₃	C₂×C₄	semidirect
11. C₂×C₃×D₁₃	C₂×C₄	semidirect
13. C₃⋊#261	C₂³	direct (N × H)
14. C₂³×C₁₃	Dic₃	semidirect
15. C₂²×D₁₃	Dic₃	semidirect
19. C₂×C₃×C₁₃	C₂²×C₄	semidirect
20. C₃×D₁₃	C₂²×C₄	semidirect
22. C₂²×C₁₃	C₂×Dic₃	semidirect
23. C₂×D₁₃	C₂×Dic₃	semidirect
28. C₃×C₁₃	C₂³×C₄	semidirect
30. C₂×C₁₃	C₂²×Dic₃	semidirect
31. D₁₃	C₂²×Dic₃	semidirect
35. C₂³×C₃	#261	semidirect
39. C₁₃	C₂³×Dic₃	semidirect
42. C₂²×C₃	C₂×#261	semidirect
46. C₂³	C₃⋊#261	direct (N × H)
50. C₂×C₃	C₂²×#261	semidirect
53. C₂²	C₂×C₃⋊#261	direct (N × H)
55. C₃	C₂³×#261	semidirect
58. C₂	C₂²×C₃⋊#261	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×D₁₃	2
C₂²×C₃⋊#261	2
C₂³×#261	3
C₂³×Dic₃	13

Subgroups — C23×C3⋊#261 #11929338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₃⋊#261 #11929338