Subgroups — C₃×#88112 #11928349

Order 1248.

76 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	#88112	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	—	2	2	no	—
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	—	2	1	no	—
12	C₃×Dic₁₃	C₈	1	2	yes	complemented
13	C₃×Dic₁₃	D₄	1	1	yes	characteristic
14	C₃×Dic₁₃	Q₈	1	1	yes	characteristic
15	C₂×C₄×C₁₃	C₃×C₄	1	1	yes	characteristic
16	C₂×Dic₁₃	C₃×C₄	1	1	yes	characteristic
17	C₂×Dic₁₃	C₂²×C₃	1	1	yes	characteristic
18	#1057	—	2	2	no	—
19	C₃×C₄⋊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×C₃×C₄	1	1	yes	characteristic
24	C₄×C₁₃	—	2	1	no	—
25	Dic₁₃	C₃×C₈	1	2	yes	complemented
26	Dic₁₃	C₃×D₄	1	1	yes	characteristic
27	Dic₁₃	C₃×Q₈	1	1	yes	characteristic
28	C₂×C₃×C₈	—	13	2	no	—
29	C₃×C₄²	—	13	1	no	—
30	C₃×C₁₃	C₄⋊C₈	1	1	yes	characteristic, complemented, Hall
31	C₄⋊C₈	—	13	1	no	Sylow
32	C₂×C₁₃	C₃×C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₁₃	C₂×C₃×C₈	1	1	yes	characteristic
34	C₂×C₁₃	C₃×M₁₆	1	1	yes	characteristic
35	C₂×C₃×C₄	—	13	1	no	—
36	C₂×C₃×C₄	—	13	1	no	—
37	C₂×C₃×C₄	#261	1	1	yes	characteristic
38	C₃×C₈	—	26	2	no	—
39	C₂×C₈	—	13	2	no	—
40	C₄²	—	13	1	no	—
41	C₁₃	C₃×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
42	C₂²×C₃	C₂×#261	1	1	yes	characteristic
43	C₃×C₄	—	2	1	no	—
44	C₃×C₄	—	13	2	no	—
45	C₃×C₄	—	13	1	no	—
46	C₃×C₄	—	13	1	no	—
47	C₂×C₄	—	13	1	no	—
48	C₂×C₄	—	13	1	no	—
49	C₂×C₄	C₃×#261	1	1	yes	characteristic
50	C₈	—	26	2	no	—
51	C₂×C₃	D₁₃⋊C₈	1	1	yes	characteristic
52	C₂×C₃	C₄⋊#261	1	1	yes	characteristic
53	C₂×C₃	#6122	1	1	yes	characteristic
54	C₂²	C₂×C₃×#261	1	1	yes	characteristic
55	C₄	—	2	1	no	—
56	C₄	—	13	2	no	—
57	C₄	—	13	1	no	—
58	C₄	—	13	1	no	—
59	C₃	#88112	1	1	yes	characteristic, direct product factor, Sylow
60	C₂	C₃×D₁₃⋊C₈	1	1	yes	characteristic
61	C₂	C₃×C₄⋊#261	1	1	yes	characteristic
62	C₂	C₃×#6122	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×#261
commutator	C₂×C₁₃	C₂×C₃×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
hypercenter	C₂×C₃×C₄	#261
hypocenter	C₁₃	C₃×C₄⋊C₈
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄

Complements

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

N	H ≅ G/N	type
3. #88112	C₃	direct (N × H)
12. C₃×Dic₁₃	C₈	semidirect
25. Dic₁₃	C₃×C₈	semidirect
30. C₃×C₁₃	C₄⋊C₈	semidirect
41. C₁₃	C₃×C₄⋊C₈	semidirect
59. C₃	#88112	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
#88112	3
C₃×C₄⋊C₈	13

Subgroups — C3×#88112 #11928349

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#88112 #11928349