Subgroups — #11928363

Order 1248.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₃⋊#261)	C₂	1	2	yes	maximal
2	C₃×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
3	#88101	—	3	1	no	maximal, Hall
4	C₂×C₃⋊#261	—	2	2	no	—
5	C₃×C₄×D₁₃	C₂²	1	1	yes	characteristic
6	C₃×C₈×C₁₃	C₄	1	1	yes	characteristic, complemented
7	C₃×#1055	C₄	1	1	yes	characteristic, complemented
8	C₄⋊#261	—	3	2	no	—
9	C₈×D₁₃	D₃	1	1	yes	characteristic
10	C₂×C₃×D₁₃	D₄	1	1	yes	characteristic
11	C₃⋊#261	—	4	2	no	—
12	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₃×Dic₁₃	Q₈	1	1	yes	characteristic
14	C₂×#261	—	6	2	no	—
15	C₄×D₁₃	C₂×D₃	1	1	yes	characteristic
16	C₈×C₁₃	Dic₃	1	1	yes	characteristic, complemented
17	#1055	Dic₃	1	1	yes	characteristic, complemented
18	#817	—	13	1	no	maximal, Hall
19	C₂×C₃×C₁₃	C₄⋊C₄	1	1	yes	characteristic
20	C₃×D₁₃	SD₁₆	1	2	yes	—
21	C₂×D₁₃	D₁₂	1	1	yes	characteristic
22	#261	—	12	2	no	—
23	C₄×C₁₃	C₂×Dic₃	1	1	yes	characteristic
24	Dic₁₃	Dic₆	1	1	yes	characteristic
25	C₂×C₃×C₈	—	13	1	no	—
26	C₄⋊Dic₃	—	13	2	no	—
27	C₃×C₁₃	#106	1	1	yes	characteristic, complemented, Hall
28	#106	—	39	1	no	Sylow
29	C₂×C₁₃	C₄⋊Dic₃	1	1	yes	characteristic
30	D₁₃	#204	1	2	yes	—
31	C₂×C₃×C₄	—	13	1	no	—
32	C₂×Dic₃	—	26	2	no	—
33	C₃×C₈	—	13	1	no	—
34	C₃×C₈	#261	1	1	yes	characteristic, complemented
35	C₂×C₈	—	13	1	no	—
36	C₄⋊C₄	—	39	2	no	—
37	C₁₃	#817	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₃	—	13	1	no	—
39	C₃×C₄	—	13	1	no	—
40	C₃×C₄	C₂×#261	1	1	yes	characteristic
41	Dic₃	—	52	2	no	—
42	C₂×C₄	—	13	1	no	—
43	C₂×C₄	—	78	2	no	—
44	C₈	—	13	1	no	—
45	C₈	C₃⋊#261	1	1	yes	characteristic, complemented
46	C₂×C₃	—	13	2	no	—
47	C₂×C₃	C₄⋊#261	1	1	yes	characteristic
48	C₂²	—	13	1	no	—
49	C₄	—	13	1	no	—
50	C₄	—	156	2	no	—
51	C₄	C₂×C₃⋊#261	1	1	yes	characteristic
52	C₃	#88101	1	1	yes	characteristic, complemented, Sylow
53	C₂	—	13	2	no	—
54	C₂	C₄⋊(C₃⋊#261)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₄⋊(C₃⋊#261)
commutator	C₃×C₄×C₁₃	C₂×C₄
Frattini	C₄	C₂×C₃⋊#261
Fitting	C₃×C₈×C₁₃	C₄
socle	C₂×C₃×C₁₃	C₄⋊C₄
prime radical	C₂×C₃×D₁₃	D₄
cosocle	C₃×C₄×D₁₃	C₂²
hypercenter	C₈	C₃⋊#261
hypocenter	C₃×C₁₃	#106
LCS	G ▷ C₃×C₄×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
6. C₃×C₈×C₁₃	C₄	semidirect
7. C₃×#1055	C₄	semidirect
16. C₈×C₁₃	Dic₃	semidirect
17. #1055	Dic₃	semidirect
27. C₃×C₁₃	#106	semidirect
34. C₃×C₈	#261	semidirect
37. C₁₃	#817	semidirect
45. C₈	C₃⋊#261	semidirect
52. C₃	#88101	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊(C₃⋊#261)	2
C₃×C₈×D₁₃	2
#88101	3
#817	13