Subgroups — C₄⋊(C₃⋊#1055) #11928116

Order 1248.

76 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
2	C₂×C₃⋊#1055	C₂	1	2	yes	maximal
3	C₄⋊#1055	—	3	1	no	maximal, Hall
4	C₂×C₃×C₄×C₁₃	C₄	1	1	yes	characteristic
5	C₂×C₃×C₄×C₁₃	C₄	1	1	yes	characteristic
6	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
7	C₃⋊#1055	—	2	2	no	—
8	C₄²×C₁₃	D₃	1	1	yes	characteristic
9	C₂×#1055	—	3	2	no	—
10	C₂²×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
11	C₃×C₄×C₁₃	—	2	1	no	—
12	C₃×C₄×C₁₃	C₈	1	2	yes	complemented
13	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
14	C₃×C₄×C₁₃	Q₈	1	1	yes	characteristic
15	C₂×C₄×C₁₃	Dic₃	1	1	yes	characteristic
16	C₂×C₄×C₁₃	Dic₃	1	1	yes	characteristic
17	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
18	#1055	—	6	2	no	—
19	C₄⋊(C₃⋊C₈)	—	13	1	no	maximal, Hall
20	C₂×C₃×C₁₃	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₃×C₁₃	C₂×C₈	1	1	yes	characteristic
22	C₂×C₃×C₁₃	M₁₆	1	1	yes	characteristic
23	C₂²×C₁₃	C₂×Dic₃	1	1	yes	characteristic
24	C₄×C₁₃	—	2	1	no	—
25	C₄×C₁₃	C₃⋊C₈	1	2	yes	complemented
26	C₄×C₁₃	Dic₆	1	1	yes	characteristic
27	C₄×C₁₃	D₁₂	1	1	yes	characteristic
28	C₃×C₄²	D₁₃	1	1	yes	characteristic
29	C₂×C₃⋊C₈	—	13	2	no	—
30	C₃×C₁₃	C₄⋊C₈	1	1	yes	characteristic, complemented, Hall
31	C₄⋊C₈	—	39	1	no	Sylow
32	C₂×C₁₃	C₂×C₃⋊C₈	1	1	yes	characteristic
33	C₂×C₁₃	#208	1	1	yes	characteristic
34	C₂×C₁₃	C₄⋊Dic₃	1	1	yes	characteristic
35	C₂×C₃×C₄	Dic₁₃	1	1	yes	characteristic
36	C₂×C₃×C₄	Dic₁₃	1	1	yes	characteristic
37	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
38	C₃⋊C₈	—	26	2	no	—
39	C₂×C₈	—	39	2	no	—
40	C₄²	D₃₉	1	1	yes	characteristic
41	C₁₃	C₄⋊(C₃⋊C₈)	1	1	yes	characteristic, complemented, Sylow
42	C₂²×C₃	C₂×Dic₁₃	1	1	yes	characteristic
43	C₃×C₄	—	2	1	no	—
44	C₃×C₄	#1055	1	2	yes	complemented
45	C₃×C₄	Dic₂₆	1	1	yes	characteristic
46	C₃×C₄	D₅₂	1	1	yes	characteristic
47	C₂×C₄	Dic₃₉	1	1	yes	characteristic
48	C₂×C₄	Dic₃₉	1	1	yes	characteristic
49	C₂×C₄	C₂×D₃₉	1	1	yes	characteristic
50	C₈	—	78	2	no	—
51	C₂×C₃	C₂×#1055	1	1	yes	characteristic
52	C₂×C₃	#6099	1	1	yes	characteristic
53	C₂×C₃	C₄⋊Dic₁₃	1	1	yes	characteristic
54	C₂²	C₂×Dic₃₉	1	1	yes	characteristic
55	C₄	—	2	1	no	—
56	C₄	C₃⋊#1055	1	2	yes	complemented
57	C₄	Dic₇₈	1	1	yes	characteristic
58	C₄	D₁₅₆	1	1	yes	characteristic
59	C₃	C₄⋊#1055	1	1	yes	characteristic, complemented, Sylow
60	C₂	C₂×C₃⋊#1055	1	1	yes	characteristic
61	C₂	#10597662	1	1	yes	characteristic
62	C₂	C₄⋊Dic₃₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
12. C₃×C₄×C₁₃	C₈	semidirect
25. C₄×C₁₃	C₃⋊C₈	semidirect
30. C₃×C₁₃	C₄⋊C₈	semidirect
41. C₁₃	C₄⋊(C₃⋊C₈)	semidirect
44. C₃×C₄	#1055	semidirect
56. C₄	C₃⋊#1055	semidirect
59. C₃	C₄⋊#1055	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
C₂×C₃⋊#1055	2
C₄⋊#1055	3
C₄⋊(C₃⋊C₈)	13

Subgroups — C4⋊(C3⋊#1055) #11928116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊(C₃⋊#1055) #11928116