Subgroups — C₂²×C₃⋊#1057 #11929190

Order 1248.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×Dic₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊#1057	C₂	1	6	yes	maximal, direct product factor
3	C₂²×#1057	—	3	1	no	maximal, Hall
4	C₂³×C₃×C₁₃	C₄	1	1	yes	characteristic
5	C₂×C₃×Dic₁₃	C₄	1	3	yes	—
6	C₂×C₃×Dic₁₃	C₂²	1	3	yes	—
7	C₃⋊#1057	C₂²	1	4	yes	direct product factor
8	C₂²×Dic₁₃	D₃	1	1	yes	characteristic
9	C₂×#1057	—	3	6	no	—
10	C₂²×C₃×C₁₃	C₈	1	4	yes	complemented
11	C₂²×C₃×C₁₃	C₂×C₄	1	3	yes	—
12	C₃×Dic₁₃	C₂×C₄	1	3	yes	—
13	C₃×Dic₁₃	C₂³	1	1	yes	characteristic
14	C₂³×C₁₃	Dic₃	1	1	yes	characteristic
15	C₂×Dic₁₃	Dic₃	1	3	yes	—
16	C₂×Dic₁₃	C₂×D₃	1	3	yes	—
17	#1057	—	3	4	no	—
18	C₂²×C₃⋊C₈	—	13	1	no	maximal, Hall
19	C₂×C₃×C₁₃	C₂×C₈	1	6	yes	complemented
20	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
21	C₂²×C₁₃	C₃⋊C₈	1	4	yes	complemented
22	C₂²×C₁₃	C₂×Dic₃	1	3	yes	—
23	Dic₁₃	C₂×Dic₃	1	3	yes	—
24	Dic₁₃	C₂²×D₃	1	1	yes	characteristic
25	C₂²×C₃×C₄	—	13	1	no	—
26	C₂×C₃⋊C₈	—	13	6	no	—
27	C₃×C₁₃	C₂²×C₈	1	1	yes	characteristic, complemented, Hall
28	C₂²×C₈	—	39	1	no	Sylow
29	C₂×C₁₃	C₂×C₃⋊C₈	1	6	yes	complemented
30	C₂×C₁₃	C₂²×Dic₃	1	1	yes	characteristic
31	C₂³×C₃	#261	1	1	yes	characteristic
32	C₂×C₃×C₄	—	13	3	no	—
33	C₂×C₃×C₄	—	13	3	no	—
34	C₃⋊C₈	—	13	4	no	—
35	C₂²×C₄	—	13	1	no	—
36	C₂×C₈	—	39	6	no	—
37	C₁₃	C₂²×C₃⋊C₈	1	1	yes	characteristic, complemented, Sylow
38	C₂²×C₃	#1057	1	4	yes	complemented
39	C₂²×C₃	C₂×#261	1	3	yes	—
40	C₃×C₄	—	13	1	no	—
41	C₃×C₄	—	13	3	no	—
42	C₂³	C₃⋊#261	1	1	yes	characteristic
43	C₂×C₄	—	13	3	no	—
44	C₂×C₄	—	13	3	no	—
45	C₈	—	39	4	no	—
46	C₂×C₃	C₂×#1057	1	6	yes	complemented
47	C₂×C₃	C₂²×#261	1	1	yes	characteristic
48	C₂²	C₃⋊#1057	1	4	yes	direct product factor
49	C₂²	C₂×C₃⋊#261	1	3	yes	—
50	C₄	—	13	3	no	—
51	C₄	—	13	1	no	—
52	C₃	C₂²×#1057	1	1	yes	characteristic, complemented, Sylow
53	C₂	C₂×C₃⋊#1057	1	6	yes	direct product factor
54	C₂	C₂²×C₃⋊#261	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³	C₃⋊#261
commutator, hypocenter	C₃×C₁₃	C₂²×C₈
Frattini	C₂	C₂²×C₃⋊#261
Fitting, socle, prime radical	C₂³×C₃×C₁₃	C₄
cosocle	C₃×Dic₁₃	C₂³
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₂³

Complements

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

N	H ≅ G/N	type
2. C₂×C₃⋊#1057	C₂	direct (N × H)
7. C₃⋊#1057	C₂²	direct (N × H)
10. C₂²×C₃×C₁₃	C₈	semidirect
19. C₂×C₃×C₁₃	C₂×C₈	semidirect
21. C₂²×C₁₃	C₃⋊C₈	semidirect
27. C₃×C₁₃	C₂²×C₈	semidirect
29. C₂×C₁₃	C₂×C₃⋊C₈	semidirect
37. C₁₃	C₂²×C₃⋊C₈	semidirect
38. C₂²×C₃	#1057	semidirect
46. C₂×C₃	C₂×#1057	semidirect
48. C₂²	C₃⋊#1057	direct (N × H)
52. C₃	C₂²×#1057	semidirect
53. C₂	C₂×C₃⋊#1057	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×Dic₁₃	2
C₂×C₃⋊#1057	2
C₂²×#1057	3
C₂²×C₃⋊C₈	13

Subgroups — C22×C3⋊#1057 #11929190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃⋊#1057 #11929190