Subgroups — C₃×C₄×#1057 #11928345

Order 1248.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
3. C₄×#1057	C₃	direct (N × H)
7. C₃×#1057	C₄	direct (N × H)
11. C₃×C₄×C₁₃	C₈	semidirect
12. C₃×Dic₁₃	C₈	semidirect
17. #1057	C₃×C₄	direct (N × H)
23. C₄×C₁₃	C₃×C₈	semidirect
24. Dic₁₃	C₃×C₈	semidirect
28. C₃×C₁₃	C₄×C₈	semidirect
39. C₁₃	C₃×C₄×C₈	semidirect
43. C₃×C₄	#1057	direct (N × H)
54. C₄	C₃×#1057	direct (N × H)
55. C₃	C₄×#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
C₂×C₃×#1057	2
C₃×C₄×Dic₁₃	2
C₄×#1057	3
C₃×C₄×C₈	13

Subgroups — C3×C4×#1057 #11928345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#1057 #11928345