Subgroups — #11928938

Order 1248.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#10597666	C₂	1	3	yes	maximal
3	#10597664	C₂	1	3	yes	maximal, complemented
4	#88130	—	3	1	no	maximal, Hall
5	C₂²×D₃₉	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄×C₁₃	C₂²	1	3	yes	—
7	C₂×Dic₃₉	C₂²	1	3	yes	—
8	C₄²×C₁₃	D₃	1	1	yes	characteristic, complemented
9	#6103	—	3	3	no	—
10	#6101	—	3	3	no	—
11	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
12	C₂×D₃₉	—	2	3	no	—
13	C₃×C₄×C₁₃	—	2	3	no	—
14	Dic₃₉	—	2	3	no	—
15	C₂²×D₁₃	—	3	1	no	—
16	C₂×C₄×C₁₃	C₂×D₃	1	3	yes	—
17	C₂×Dic₁₃	—	3	3	no	—
18	#876	—	13	1	no	maximal, Hall
19	C₂×C₃×C₁₃	#41	1	3	yes	—
20	D₃₉	—	4	1	no	—
21	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
22	C₂×D₁₃	—	6	3	no	—
23	C₄×C₁₃	—	2	3	no	—
24	Dic₁₃	—	6	3	no	—
25	C₃×C₄²	D₁₃	1	1	yes	characteristic, complemented
26	(C₂×D₃)⋊C₄	—	13	3	no	—
27	Dic₃⋊C₄	—	13	3	no	—
28	C₃×C₁₃	#126	1	1	yes	characteristic, complemented, Hall
29	#126	—	39	1	no	Sylow
30	C₂×C₁₃	#235	1	3	yes	—
31	D₁₃	—	12	1	no	—
32	C₂²×D₃	—	13	1	no	—
33	C₂×C₃×C₄	C₂×D₁₃	1	3	yes	—
34	C₂×Dic₃	—	13	3	no	—
35	C₄⋊C₄	—	39	3	no	—
36	C₂²⋊C₄	—	39	3	no	—
37	C₄²	D₃₉	1	1	yes	characteristic, complemented
38	C₁₃	#876	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
40	C₂×D₃	—	26	3	no	—
41	C₃×C₄	—	2	3	no	—
42	Dic₃	—	26	3	no	—
43	C₂³	—	39	1	no	—
44	C₂×C₄	—	39	3	no	—
45	C₂×C₄	C₂×D₃₉	1	3	yes	—
46	C₂×C₃	#6127	1	3	yes	—
47	D₃	—	52	1	no	—
48	C₂²	—	78	3	no	—
49	C₂²	C₂²×D₃₉	1	1	yes	characteristic
50	C₄	—	2	3	no	—
51	C₄	—	78	3	no	—
52	C₃	#88130	1	1	yes	characteristic, complemented, Sylow
53	C₂	—	156	1	no	—
54	C₂	#10597790	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃₉
commutator, socle, cosocle	C₂²×C₃×C₁₃	C₂³
Fitting	C₃×C₄²×C₁₃	C₂
prime radical	C₂²×D₃₉	C₂²
hypercenter	C₄²	D₃₉
hypocenter	C₃×C₁₃	#126
LCS	G ▷ C₂²×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂² ◁ C₄²

Complements

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

N	H ≅ G/N	type
1. C₃×C₄²×C₁₃	C₂	semidirect
3. #10597664	C₂	semidirect
8. C₄²×C₁₃	D₃	semidirect
25. C₃×C₄²	D₁₃	semidirect
28. C₃×C₁₃	#126	semidirect
37. C₄²	D₃₉	semidirect
38. C₁₃	#876	semidirect
52. C₃	#88130	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄²×C₁₃	2
#10597666	2
#10597664	2
#88130	3
#876	13