Subgroups — #11929010

Order 1248.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
2	#10597662	C₂	1	3	yes	maximal, complemented
3	C₂×C₃⋊#1055	C₂	1	3	yes	maximal, complemented
4	#88202	—	3	1	no	maximal, Hall
5	C₃×Q₈×C₁₃	C₄	1	1	yes	characteristic
6	C₃×D₄×C₁₃	C₄	1	3	yes	—
7	C₂×C₃×C₄×C₁₃	C₂²	1	3	yes	—
8	C₃⋊#1055	C₂²	1	1	yes	characteristic
9	C₃⋊#1055	C₂²	1	3	yes	—
10	C₁₃×#41	D₃	1	1	yes	characteristic
11	#6099	—	3	3	no	—
12	C₂×#1055	—	3	3	no	—
13	C₂²×C₃×C₁₃	C₂×C₄	1	3	yes	—
14	C₃×C₄×C₁₃	C₂×C₄	1	3	yes	—
15	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
16	Q₈×C₁₃	Dic₃	1	1	yes	characteristic
17	D₄×C₁₃	Dic₃	1	3	yes	—
18	C₂×C₄×C₁₃	C₂×D₃	1	3	yes	—
19	#1055	—	3	1	no	—
20	#1055	—	3	3	no	—
21	#948	—	13	1	no	maximal, Hall
22	C₂×C₃×C₁₃	—	2	3	no	—
23	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
24	C₂²×C₁₃	C₂×Dic₃	1	3	yes	—
25	C₄×C₁₃	C₂×Dic₃	1	3	yes	—
26	C₄×C₁₃	C₂²×D₃	1	1	yes	characteristic
27	C₃×#41	D₁₃	1	1	yes	characteristic
28	#208	—	13	3	no	—
29	C₂×C₃⋊C₈	—	13	3	no	—
30	C₃×C₁₃	#131	1	1	yes	characteristic, complemented, Hall
31	#131	—	39	1	no	Sylow
32	C₂×C₁₃	—	2	3	no	—
33	C₂×C₁₃	C₂²×Dic₃	1	1	yes	characteristic
34	C₃×Q₈	Dic₁₃	1	1	yes	characteristic
35	C₃×D₄	Dic₁₃	1	3	yes	—
36	C₂×C₃×C₄	C₂×D₁₃	1	3	yes	—
37	C₃⋊C₈	—	13	1	no	—
38	C₃⋊C₈	—	13	3	no	—
39	#41	D₃₉	1	1	yes	characteristic
40	M₁₆	—	39	3	no	—
41	C₂×C₈	—	39	3	no	—
42	C₁₃	#948	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₃	C₂×Dic₁₃	1	3	yes	—
44	C₃×C₄	C₂×Dic₁₃	1	3	yes	—
45	C₃×C₄	C₂²×D₁₃	1	1	yes	characteristic
46	Q₈	Dic₃₉	1	1	yes	characteristic
47	D₄	Dic₃₉	1	3	yes	—
48	C₂×C₄	C₂×D₃₉	1	3	yes	—
49	C₈	—	39	1	no	—
50	C₈	—	39	3	no	—
51	C₂×C₃	—	2	3	no	—
52	C₂×C₃	C₂²×Dic₁₃	1	1	yes	characteristic
53	C₂²	C₂×Dic₃₉	1	3	yes	—
54	C₄	C₂×Dic₃₉	1	3	yes	—
55	C₄	C₂²×D₃₉	1	1	yes	characteristic
56	C₃	#88202	1	1	yes	characteristic, complemented, Sylow
57	C₂	—	2	3	no	—
58	C₂	C₂²×Dic₃₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×D₃₉
commutator, socle	C₂×C₃×C₁₃	C₂²×C₄
Fitting, prime radical	C₃×C₁₃×#41	C₂
cosocle	C₃×C₄×C₁₃	C₂³
hypercenter	#41	D₃₉
hypocenter	C₃×C₁₃	#131
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
2. #10597662	C₂	semidirect
3. C₂×C₃⋊#1055	C₂	semidirect
30. C₃×C₁₃	#131	semidirect
42. C₁₃	#948	semidirect
56. C₃	#88202	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₁₃×#41	2
#10597662	2
C₂×C₃⋊#1055	2
#88202	3
#948	13