Subgroups — C₃×#88123 #11928759

Order 1248.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Dic₂₆	C₂	1	2	yes	maximal
2	C₃×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄⋊Dic₁₃	C₂	1	4	yes	maximal
4	#88123	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄×C₁₃	C₂²	1	2	yes	—
7	C₂×C₃×Dic₁₃	C₂²	1	4	yes	—
8	C₃×Dic₂₆	—	2	4	no	—
9	C₂×Dic₂₆	C₂×C₃	1	2	yes	—
10	C₄²×C₁₃	C₂×C₃	1	1	yes	characteristic
11	C₄⋊Dic₁₃	C₂×C₃	1	4	yes	—
12	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
13	C₃×C₄×C₁₃	D₄	1	2	yes	—
14	C₃×C₄×C₁₃	Q₈	1	4	yes	complemented
15	C₃×Dic₁₃	—	2	4	no	—
16	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
17	C₂×C₄×C₁₃	C₂²×C₃	1	2	yes	—
18	C₂×Dic₁₃	C₂²×C₃	1	4	yes	—
19	Dic₂₆	—	2	4	no	—
20	C₃×C₄⋊Q₈	—	13	1	no	maximal, Hall
21	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
22	C₂×C₃×C₁₃	C₂×Q₈	1	2	yes	—
23	C₂²×C₁₃	C₂³×C₃	1	1	yes	characteristic
24	C₄×C₁₃	C₃×D₄	1	2	yes	—
25	C₄×C₁₃	C₃×Q₈	1	4	yes	complemented
26	Dic₁₃	—	2	4	no	—
27	C₂×C₃×Q₈	—	13	2	no	—
28	C₃×C₄⋊C₄	—	13	4	no	—
29	C₃×C₄²	D₁₃	1	1	yes	characteristic
30	C₃×C₁₃	C₄⋊Q₈	1	1	yes	characteristic, complemented, Hall
31	C₄⋊Q₈	—	13	1	no	Sylow
32	C₂×C₁₃	C₂×C₃×D₄	1	1	yes	characteristic
33	C₂×C₁₃	C₂×C₃×Q₈	1	2	yes	—
34	C₃×Q₈	—	26	4	no	—
35	C₂×C₃×C₄	—	13	4	no	—
36	C₂×C₃×C₄	C₂×D₁₃	1	2	yes	—
37	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
38	C₂×Q₈	—	13	2	no	—
39	C₄⋊C₄	—	13	4	no	—
40	C₄²	C₃×D₁₃	1	1	yes	characteristic
41	C₁₃	C₃×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
42	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
43	C₃×C₄	—	26	4	no	—
44	C₃×C₄	Dic₂₆	1	4	yes	complemented
45	C₃×C₄	D₅₂	1	2	yes	—
46	Q₈	—	26	4	no	—
47	C₂×C₄	—	13	4	no	—
48	C₂×C₄	C₂×C₃×D₁₃	1	2	yes	—
49	C₂×C₄	C₂×C₃×D₁₃	1	1	yes	characteristic
50	C₂×C₃	C₂×Dic₂₆	1	2	yes	—
51	C₂×C₃	C₂×D₅₂	1	1	yes	characteristic
52	C₂²	C₂²×C₃×D₁₃	1	1	yes	characteristic
53	C₄	—	26	4	no	—
54	C₄	C₃×Dic₂₆	1	4	yes	complemented
55	C₄	C₃×D₅₂	1	2	yes	—
56	C₃	#88123	1	1	yes	characteristic, direct product factor, Sylow
57	C₂	C₂×C₃×Dic₂₆	1	2	yes	—
58	C₂	C₂×C₃×D₅₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂³×C₃
Frattini	C₂²	C₂²×C₃×D₁₃
Fitting	C₃×C₄²×C₁₃	C₂
socle, prime radical	C₂²×C₃×C₁₃	C₂³
hypercenter	C₃×C₄²	D₁₃
hypocenter	C₁₃	C₃×C₄⋊Q₈
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄²

Complements

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

N	H ≅ G/N	type
4. #88123	C₃	direct (N × H)
14. C₃×C₄×C₁₃	Q₈	semidirect
25. C₄×C₁₃	C₃×Q₈	semidirect
30. C₃×C₁₃	C₄⋊Q₈	semidirect
41. C₁₃	C₃×C₄⋊Q₈	semidirect
44. C₃×C₄	Dic₂₆	semidirect
54. C₄	C₃×Dic₂₆	semidirect
56. C₃	#88123	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×Dic₂₆	2
C₃×C₄²×C₁₃	2
C₃×C₄⋊Dic₁₃	2
#88123	3
C₃×C₄⋊Q₈	13

Subgroups — C3×#88123 #11928759

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#88123 #11928759