Subgroups — C₃×C₈×#261 #11928336

Order 1248.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×#261	C₂	1	1	yes	maximal, characteristic
2	C₃×D₁₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
4	C₈×#261	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×#261	C₄	1	2	yes	—
6	C₃×C₄×D₁₃	C₂²	1	1	yes	characteristic
7	C₃×#1057	C₄	1	2	yes	complemented
8	C₃×C₈×C₁₃	C₄	1	1	yes	characteristic, complemented
9	C₃×#1055	C₄	1	1	yes	characteristic, complemented
10	C₄×#261	C₂×C₃	1	1	yes	characteristic
11	D₁₃⋊C₈	C₂×C₃	1	1	yes	characteristic
12	C₈×D₁₃	C₂×C₃	1	1	yes	characteristic
13	C₂×C₃×D₁₃	C₂×C₄	1	1	yes	characteristic
14	C₃×#261	C₈	1	4	yes	direct product factor
15	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₃×Dic₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×#261	C₃×C₄	1	2	yes	—
18	C₄×D₁₃	C₂²×C₃	1	1	yes	characteristic
19	#1057	C₃×C₄	1	2	yes	complemented
20	C₈×C₁₃	C₃×C₄	1	1	yes	characteristic, complemented
21	#1055	C₃×C₄	1	1	yes	characteristic, complemented
22	C₃×C₄×C₈	—	13	1	no	maximal, Hall
23	C₂×C₃×C₁₃	C₄²	1	1	yes	characteristic
24	C₃×D₁₃	C₂×C₈	1	2	yes	—
25	C₂×D₁₃	C₂×C₃×C₄	1	1	yes	characteristic
26	#261	C₃×C₈	1	4	yes	direct product factor
27	C₄×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic
28	Dic₁₃	C₂×C₃×C₄	1	1	yes	characteristic
29	C₂×C₃×C₈	—	13	1	no	—
30	C₂×C₃×C₈	—	13	1	no	—
31	C₃×C₄²	—	13	1	no	—
32	C₃×C₁₃	C₄×C₈	1	1	yes	characteristic, complemented, Hall
33	C₄×C₈	—	13	1	no	Sylow
34	C₂×C₁₃	C₃×C₄²	1	1	yes	characteristic
35	D₁₃	C₂×C₃×C₈	1	2	yes	—
36	C₂×C₃×C₄	—	13	2	no	—
37	C₂×C₃×C₄	—	13	1	no	—
38	C₃×C₈	—	13	2	no	—
39	C₃×C₈	—	13	1	no	—
40	C₃×C₈	#261	1	1	yes	characteristic, direct product factor
41	C₂×C₈	—	13	1	no	—
42	C₂×C₈	—	13	1	no	—
43	C₄²	—	13	1	no	—
44	C₁₃	C₃×C₄×C₈	1	1	yes	characteristic, complemented, Sylow
45	C₂²×C₃	—	13	1	no	—
46	C₃×C₄	—	13	4	no	—
47	C₃×C₄	—	13	1	no	—
48	C₃×C₄	C₂×#261	1	1	yes	characteristic
49	C₂×C₄	—	13	2	no	—
50	C₂×C₄	—	13	1	no	—
51	C₈	—	13	2	no	—
52	C₈	—	13	1	no	—
53	C₈	C₃×#261	1	1	yes	characteristic, direct product factor
54	C₂×C₃	—	13	2	no	—
55	C₂×C₃	C₄×#261	1	1	yes	characteristic
56	C₂²	—	13	1	no	—
57	C₄	—	13	4	no	—
58	C₄	—	13	1	no	—
59	C₄	C₂×C₃×#261	1	1	yes	characteristic
60	C₃	C₈×#261	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	—	13	2	no	—
62	C₂	C₃×C₄×#261	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₈	#261
commutator, hypocenter	C₁₃	C₃×C₄×C₈
Frattini	C₄	C₂×C₃×#261
Fitting	C₃×C₈×C₁₃	C₄
socle	C₂×C₃×C₁₃	C₄²
prime radical	C₂×C₃×D₁₃	C₂×C₄
cosocle	C₄×D₁₃	C₂²×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₈

Complements

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

N	H ≅ G/N	type
4. C₈×#261	C₃	direct (N × H)
7. C₃×#1057	C₄	semidirect
8. C₃×C₈×C₁₃	C₄	semidirect
9. C₃×#1055	C₄	semidirect
14. C₃×#261	C₈	direct (N × H)
19. #1057	C₃×C₄	semidirect
20. C₈×C₁₃	C₃×C₄	semidirect
21. #1055	C₃×C₄	semidirect
26. #261	C₃×C₈	direct (N × H)
32. C₃×C₁₃	C₄×C₈	semidirect
40. C₃×C₈	#261	direct (N × H)
44. C₁₃	C₃×C₄×C₈	semidirect
53. C₈	C₃×#261	direct (N × H)
60. C₃	C₈×#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
C₃×C₄×#261	2
C₃×D₁₃⋊C₈	2
C₃×C₈×D₁₃	2
C₈×#261	3
C₃×C₄×C₈	13

Subgroups — C3×C8×#261 #11928336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₈×#261 #11928336