Subgroups — #11928127

Order 1248.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃⋊#1055	C₂	1	1	yes	maximal, characteristic
4	#88055	—	3	1	no	maximal, Hall
5	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×Dic₃₉	C₄	1	2	yes	—
7	C₃×C₈×C₁₃	C₄	1	2	yes	complemented
8	C₃⋊#1055	C₄	1	2	yes	complemented
9	C₂×C₈×C₁₃	D₃	1	1	yes	characteristic
10	C₄×Dic₁₃	—	3	1	no	—
11	C₂×#1055	—	3	1	no	—
12	C₂²×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
15	Dic₃₉	—	2	2	no	—
16	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
17	C₂×Dic₁₃	—	3	2	no	—
18	C₈×C₁₃	Dic₃	1	2	yes	complemented
19	#1055	—	3	2	no	—
20	#815	—	13	1	no	maximal, Hall
21	C₂×C₃×C₁₃	C₄²	1	1	yes	characteristic
22	C₂×C₃×C₁₃	M₁₆	1	2	yes	—
23	C₂²×C₁₃	C₄×D₃	1	1	yes	characteristic
24	C₄×C₁₃	C₄×D₃	1	1	yes	characteristic
25	C₄×C₁₃	C₂×Dic₃	1	1	yes	characteristic
26	Dic₁₃	—	6	2	no	—
27	C₂×C₃×C₈	D₁₃	1	1	yes	characteristic
28	C₄×Dic₃	—	13	1	no	—
29	C₂×C₃⋊C₈	—	13	1	no	—
30	C₃×C₁₃	#97	1	1	yes	characteristic, complemented, Hall
31	#97	—	39	1	no	Sylow
32	C₂×C₁₃	ΓL(1,𝔽₂₅)	1	2	yes	—
33	C₂×C₁₃	C₄×Dic₃	1	1	yes	characteristic
34	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
35	C₂×Dic₃	—	13	2	no	—
36	C₃×C₈	Dic₁₃	1	2	yes	complemented
37	C₃⋊C₈	—	13	2	no	—
38	C₂×C₈	—	39	1	no	—
39	C₂×C₈	D₃₉	1	1	yes	characteristic
40	C₄²	—	39	1	no	—
41	C₁₃	#815	1	1	yes	characteristic, complemented, Sylow
42	C₂²×C₃	C₄×D₁₃	1	1	yes	characteristic
43	C₃×C₄	C₄×D₁₃	1	1	yes	characteristic
44	C₃×C₄	C₂×Dic₁₃	1	1	yes	characteristic
45	Dic₃	—	26	2	no	—
46	C₂×C₄	—	39	2	no	—
47	C₂×C₄	C₂×D₃₉	1	1	yes	characteristic
48	C₈	—	39	2	no	—
49	C₈	Dic₃₉	1	2	yes	complemented
50	C₂×C₃	#6094	1	2	yes	—
51	C₂×C₃	C₄×Dic₁₃	1	1	yes	characteristic
52	C₂²	C₄×D₃₉	1	1	yes	characteristic
53	C₄	—	78	2	no	—
54	C₄	C₄×D₃₉	1	1	yes	characteristic
55	C₄	C₂×Dic₃₉	1	1	yes	characteristic
56	C₃	#88055	1	1	yes	characteristic, complemented, Sylow
57	C₂	#10597657	1	2	yes	—
58	C₂	C₄×Dic₃₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×D₃₉
commutator	C₂×C₃×C₁₃	C₄²
Fitting	C₂×C₃×C₈×C₁₃	C₂
socle, prime radical	C₂²×C₃×C₁₃	C₂×C₄
cosocle	C₂×C₃×C₄×C₁₃	C₂²
hypercenter	C₂×C₈	D₃₉
hypocenter	C₃×C₁₃	#97
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
7. C₃×C₈×C₁₃	C₄	semidirect
8. C₃⋊#1055	C₄	semidirect
18. C₈×C₁₃	Dic₃	semidirect
30. C₃×C₁₃	#97	semidirect
36. C₃×C₈	Dic₁₃	semidirect
41. C₁₃	#815	semidirect
49. C₈	Dic₃₉	semidirect
56. C₃	#88055	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₈×C₁₃	2
C₄×Dic₃₉	2
C₂×C₃⋊#1055	2
#88055	3
#815	13