Subgroups — #11928366

Order 1248.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10597724	C₂	1	2	yes	maximal
2	C₃×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
3	#88104	—	3	1	no	maximal, Hall
4	C₃×C₄×D₁₃	C₂²	1	1	yes	characteristic
5	C₃⋊#1057	—	2	2	no	—
6	C₃×C₈×C₁₃	C₄	1	1	yes	characteristic
7	C₃×#1055	C₄	1	1	yes	characteristic
8	#6118	—	3	2	no	—
9	C₈×D₁₃	D₃	1	1	yes	characteristic
10	C₂×C₃×D₁₃	Q₈	1	1	yes	characteristic
11	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₃×Dic₁₃	D₄	1	1	yes	characteristic
13	C₄×D₁₃	C₂×D₃	1	1	yes	characteristic
14	#1057	—	6	2	no	—
15	C₈×C₁₃	Dic₃	1	1	yes	characteristic
16	#1055	Dic₃	1	1	yes	characteristic
17	#819	—	13	1	no	maximal, Hall
18	C₂×C₃×C₁₃	C₄⋊C₄	1	1	yes	characteristic
19	C₃×D₁₃	—	2	1	no	—
20	C₂×D₁₃	Dic₆	1	1	yes	characteristic
21	C₄×C₁₃	C₂×Dic₃	1	1	yes	characteristic
22	Dic₁₃	D₁₂	1	1	yes	characteristic
23	C₂×C₃×C₈	—	13	1	no	—
24	#208	—	13	2	no	—
25	C₃×C₁₃	#108	1	1	yes	characteristic, complemented, Hall
26	#108	—	39	1	no	Sylow
27	C₂×C₁₃	C₄⋊Dic₃	1	1	yes	characteristic
28	D₁₃	—	2	1	no	—
29	C₂×C₃×C₄	—	13	1	no	—
30	C₃×C₈	—	13	1	no	—
31	C₃×C₈	#261	1	1	yes	characteristic
32	C₃⋊C₈	—	26	2	no	—
33	M₁₆	—	39	2	no	—
34	C₂×C₈	—	13	1	no	—
35	C₁₃	#819	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₃	—	13	1	no	—
37	C₃×C₄	—	13	1	no	—
38	C₃×C₄	C₂×#261	1	1	yes	characteristic
39	C₂×C₄	—	13	1	no	—
40	C₈	—	13	1	no	—
41	C₈	—	78	2	no	—
42	C₈	C₃⋊#261	1	1	yes	characteristic
43	C₂×C₃	—	26	1	no	—
44	C₂×C₃	C₄⋊#261	1	1	yes	characteristic
45	C₂²	—	13	1	no	—
46	C₄	—	13	1	no	—
47	C₄	C₂×C₃⋊#261	1	1	yes	characteristic
48	C₃	#88104	1	1	yes	characteristic, complemented, Sylow
49	C₂	—	26	1	no	—
50	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	Q₈
cosocle	C₃×C₄×D₁₃	C₂²
hypercenter	C₈	C₃⋊#261
hypocenter	C₃×C₁₃	#108
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
25. C₃×C₁₃	#108	semidirect
35. C₁₃	#819	semidirect
48. C₃	#88104	semidirect

Maximal subgroups

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

subgroup	index
#10597724	2
C₃×C₈×D₁₃	2
#88104	3
#819	13