Subgroups — #11928362

Order 1248.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₃⋊#261	C₂	1	1	yes	maximal, characteristic
2	D₁₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₃×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
4	#88100	—	3	1	no	maximal, Hall
5	C₂×C₃⋊#261	C₄	1	2	yes	—
6	C₃×C₄×D₁₃	C₂²	1	1	yes	characteristic
7	C₃⋊#1057	C₄	1	2	yes	complemented
8	C₃×C₈×C₁₃	C₄	1	1	yes	characteristic, complemented
9	C₃×#1055	C₄	1	1	yes	characteristic, complemented
10	C₄×#261	—	3	1	no	—
11	D₁₃⋊C₈	—	3	1	no	—
12	C₈×D₁₃	D₃	1	1	yes	characteristic
13	C₂×C₃×D₁₃	C₂×C₄	1	1	yes	characteristic
14	C₃⋊#261	—	2	2	no	—
15	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₃×Dic₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×#261	—	3	2	no	—
18	C₄×D₁₃	C₂×D₃	1	1	yes	characteristic
19	#1057	—	3	2	no	—
20	C₈×C₁₃	Dic₃	1	1	yes	characteristic, complemented
21	#1055	Dic₃	1	1	yes	characteristic, complemented
22	#815	—	13	1	no	maximal, Hall
23	C₂×C₃×C₁₃	C₄²	1	1	yes	characteristic
24	C₃×D₁₃	M₁₆	1	2	yes	—
25	C₂×D₁₃	C₄×D₃	1	1	yes	characteristic
26	#261	—	6	2	no	—
27	C₄×C₁₃	C₂×Dic₃	1	1	yes	characteristic
28	Dic₁₃	C₄×D₃	1	1	yes	characteristic
29	C₂×C₃×C₈	—	13	1	no	—
30	C₄×Dic₃	—	13	1	no	—
31	C₂×C₃⋊C₈	—	13	1	no	—
32	C₃×C₁₃	#97	1	1	yes	characteristic, complemented, Hall
33	#97	—	39	1	no	Sylow
34	C₂×C₁₃	C₄×Dic₃	1	1	yes	characteristic
35	D₁₃	ΓL(1,𝔽₂₅)	1	2	yes	—
36	C₂×C₃×C₄	—	13	1	no	—
37	C₂×Dic₃	—	13	2	no	—
38	C₃×C₈	—	13	1	no	—
39	C₃×C₈	#261	1	1	yes	characteristic, complemented
40	C₃⋊C₈	—	13	2	no	—
41	C₂×C₈	—	13	1	no	—
42	C₂×C₈	—	39	1	no	—
43	C₄²	—	39	1	no	—
44	C₁₃	#815	1	1	yes	characteristic, complemented, Sylow
45	C₂²×C₃	—	13	1	no	—
46	C₃×C₄	—	13	1	no	—
47	C₃×C₄	C₂×#261	1	1	yes	characteristic
48	Dic₃	—	26	2	no	—
49	C₂×C₄	—	13	1	no	—
50	C₂×C₄	—	39	2	no	—
51	C₈	—	13	1	no	—
52	C₈	—	39	2	no	—
53	C₈	C₃⋊#261	1	1	yes	characteristic, complemented
54	C₂×C₃	—	13	2	no	—
55	C₂×C₃	C₄×#261	1	1	yes	characteristic
56	C₂²	—	13	1	no	—
57	C₄	—	13	1	no	—
58	C₄	—	78	2	no	—
59	C₄	C₂×C₃⋊#261	1	1	yes	characteristic
60	C₃	#88100	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	13	2	no	—
62	C₂	C₄×C₃⋊#261	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂×C₃⋊#261
commutator, socle	C₂×C₃×C₁₃	C₄²
Fitting	C₃×C₈×C₁₃	C₄
prime radical	C₂×C₃×D₁₃	C₂×C₄
cosocle	C₃×C₄×D₁₃	C₂²
hypercenter	C₈	C₃⋊#261
hypocenter	C₃×C₁₃	#97
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
7. C₃⋊#1057	C₄	semidirect
8. C₃×C₈×C₁₃	C₄	semidirect
9. C₃×#1055	C₄	semidirect
20. C₈×C₁₃	Dic₃	semidirect
21. #1055	Dic₃	semidirect
32. C₃×C₁₃	#97	semidirect
39. C₃×C₈	#261	semidirect
44. C₁₃	#815	semidirect
53. C₈	C₃⋊#261	semidirect
60. C₃	#88100	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₃⋊#261	2
D₁₃⋊(C₃⋊C₈)	2
C₃×C₈×D₁₃	2
#88100	3
#815	13