Subgroups — #11928368

Order 1248.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#1055	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#6092	C₂	1	2	yes	maximal, complemented
3	#88106	—	3	1	no	maximal, Hall
4	C₂×C₃×C₄×C₁₃	C₄	1	1	yes	characteristic
5	C₃×#1055	C₄	1	1	yes	characteristic
6	C₃×#1055	C₂²	1	1	yes	characteristic
7	C₂×#1055	D₃	1	1	yes	characteristic
8	#6092	—	3	2	no	—
9	C₂²×C₃×C₁₃	C₈	1	1	yes	characteristic
10	C₃×C₄×C₁₃	C₈	1	1	yes	characteristic
11	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₃	Dic₃	1	1	yes	characteristic
13	#1055	Dic₃	1	1	yes	characteristic
14	#1055	C₂×D₃	1	1	yes	characteristic
15	#812	—	13	1	no	maximal, Hall
16	C₂×C₃×C₁₃	—	2	1	no	—
17	C₂×C₃×C₁₃	C₂×C₈	1	1	yes	characteristic
18	C₂²×C₁₃	C₃⋊C₈	1	1	yes	characteristic
19	C₄×C₁₃	C₃⋊C₈	1	1	yes	characteristic
20	C₄×C₁₃	C₂×Dic₃	1	1	yes	characteristic
21	C₂×C₃×C₈	—	13	1	no	—
22	C₃⋊C₁₆	—	13	2	no	—
23	C₃×C₁₃	M₃₂	1	1	yes	characteristic, complemented, Hall
24	M₃₂	—	39	1	no	Sylow
25	C₂×C₁₃	—	2	1	no	—
26	C₂×C₁₃	C₂×C₃⋊C₈	1	1	yes	characteristic
27	C₂×C₃×C₄	#261	1	1	yes	characteristic
28	C₃×C₈	—	13	1	no	—
29	C₃×C₈	—	13	1	no	—
30	C₂×C₈	—	13	1	no	—
31	C₁₆	—	39	2	no	—
32	C₁₃	#812	1	1	yes	characteristic, complemented, Sylow
33	C₂²×C₃	#1057	1	1	yes	characteristic
34	C₃×C₄	#1057	1	1	yes	characteristic
35	C₃×C₄	C₂×#261	1	1	yes	characteristic
36	C₂×C₄	C₃⋊#261	1	1	yes	characteristic
37	C₈	—	13	1	no	—
38	C₈	—	13	1	no	—
39	C₂×C₃	—	2	1	no	—
40	C₂×C₃	C₂×#1057	1	1	yes	characteristic
41	C₂²	C₃⋊#1057	1	1	yes	characteristic
42	C₄	C₃⋊#1057	1	1	yes	characteristic
43	C₄	C₂×C₃⋊#261	1	1	yes	characteristic
44	C₃	#88106	1	1	yes	characteristic, complemented, Sylow
45	C₂	—	2	1	no	—
46	C₂	C₂×C₃⋊#1057	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂×C₃⋊#261
commutator, socle	C₂×C₃×C₁₃	C₂×C₈
Fitting	C₂×C₃×C₄×C₁₃	C₄
prime radical	C₂²×C₃×C₁₃	C₈
cosocle	C₃×#1055	C₂²
hypercenter	C₂×C₄	C₃⋊#261
hypocenter	C₃×C₁₃	M₃₂
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. C₃⋊#6092	C₂	semidirect
23. C₃×C₁₃	M₃₂	semidirect
32. C₁₃	#812	semidirect
44. C₃	#88106	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#1055	2
C₃⋊#6092	2
#88106	3
#812	13