Subgroups — #11928134

Order 1248.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
2	#10597662	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃⋊#1055	C₂	1	1	yes	maximal, characteristic
4	#88062	—	3	1	no	maximal, Hall
5	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
6	C₃×C₈×C₁₃	—	2	1	no	—
7	C₃⋊#1055	—	2	1	no	—
8	C₃⋊#1055	C₄	1	2	yes	—
9	C₁₃×M₁₆	D₃	1	1	yes	characteristic
10	#6099	—	3	1	no	—
11	C₂×#1055	—	3	1	no	—
12	C₂²×C₃×C₁₃	Q₈	1	1	yes	characteristic
13	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
15	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
16	C₈×C₁₃	—	2	1	no	—
17	#1055	—	3	2	no	—
18	#1055	—	6	1	no	—
19	#822	—	13	1	no	maximal, Hall
20	C₂×C₃×C₁₃	—	2	1	no	—
21	C₂×C₃×C₁₃	C₄⋊C₄	1	1	yes	characteristic
22	C₂²×C₁₃	Dic₆	1	1	yes	characteristic
23	C₄×C₁₃	C₄×D₃	1	1	yes	characteristic
24	C₄×C₁₃	#67	1	1	yes	characteristic
25	C₃×M₁₆	D₁₃	1	1	yes	characteristic
26	#208	—	13	1	no	—
27	C₂×C₃⋊C₈	—	13	1	no	—
28	C₃×C₁₃	#108	1	1	yes	characteristic, complemented, Hall
29	#108	—	39	1	no	Sylow
30	C₂×C₁₃	—	2	1	no	—
31	C₂×C₁₃	Dic₃⋊C₄	1	1	yes	characteristic
32	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
33	C₃×C₈	—	2	1	no	—
34	C₃⋊C₈	—	13	2	no	—
35	C₃⋊C₈	—	26	1	no	—
36	M₁₆	—	39	1	no	—
37	M₁₆	D₃₉	1	1	yes	characteristic
38	C₂×C₈	—	39	1	no	—
39	C₁₃	#822	1	1	yes	characteristic, complemented, Sylow
40	C₂²×C₃	Dic₂₆	1	1	yes	characteristic
41	C₃×C₄	C₄×D₁₃	1	1	yes	characteristic
42	C₃×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
43	C₂×C₄	C₂×D₃₉	1	1	yes	characteristic
44	C₈	—	2	1	no	—
45	C₈	—	39	2	no	—
46	C₈	—	78	1	no	—
47	C₂×C₃	—	2	1	no	—
48	C₂×C₃	#6101	1	1	yes	characteristic
49	C₂²	Dic₇₈	1	1	yes	characteristic
50	C₄	C₄×D₃₉	1	1	yes	characteristic
51	C₄	#64625	1	1	yes	characteristic
52	C₃	#88062	1	1	yes	characteristic, complemented, Sylow
53	C₂	—	2	1	no	—
54	C₂	#10597664	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#64625
commutator	C₃×C₄×C₁₃	C₂×C₄
Frattini	C₂×C₄	C₂×D₃₉
Fitting	C₃×C₁₃×M₁₆	C₂
socle	C₂×C₃×C₁₃	C₄⋊C₄
prime radical	C₂²×C₃×C₁₃	Q₈
cosocle	C₂×C₃×C₄×C₁₃	C₂²
hypercenter	M₁₆	D₃₉
hypocenter	C₃×C₁₃	#108
LCS	G ▷ C₃×C₄×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
28. C₃×C₁₃	#108	semidirect
39. C₁₃	#822	semidirect
52. C₃	#88062	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₃×M₁₆	2
#10597662	2
C₂×C₃⋊#1055	2
#88062	3
#822	13