Subgroups — C₃×#88103 #11928340

Order 1248.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6118	C₂	1	2	yes	maximal
2	C₃×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
3	#88103	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₄×D₁₃	C₂²	1	1	yes	characteristic
5	C₃×#1057	—	2	2	no	—
6	C₃×C₈×C₁₃	C₄	1	1	yes	characteristic
7	C₃×#1055	C₄	1	1	yes	characteristic
8	#6118	C₂×C₃	1	2	yes	—
9	C₈×D₁₃	C₂×C₃	1	1	yes	characteristic
10	C₂×C₃×D₁₃	Q₈	1	1	yes	characteristic
11	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₃×Dic₁₃	D₄	1	1	yes	characteristic
13	C₄×D₁₃	C₂²×C₃	1	1	yes	characteristic
14	#1057	—	2	2	no	—
15	C₈×C₁₃	C₃×C₄	1	1	yes	characteristic
16	#1055	C₃×C₄	1	1	yes	characteristic
17	C₃×#108	—	13	1	no	maximal, Hall
18	C₂×C₃×C₁₃	C₄⋊C₄	1	1	yes	characteristic
19	C₃×D₁₃	—	2	1	no	—
20	C₂×D₁₃	C₃×Q₈	1	1	yes	characteristic
21	C₄×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic
22	Dic₁₃	C₃×D₄	1	1	yes	characteristic
23	C₃×M₁₆	—	13	2	no	—
24	C₂×C₃×C₈	—	13	1	no	—
25	C₃×C₁₃	#108	1	1	yes	characteristic, complemented, Hall
26	#108	—	13	1	no	Sylow
27	C₂×C₁₃	C₃×C₄⋊C₄	1	1	yes	characteristic
28	D₁₃	—	2	1	no	—
29	C₂×C₃×C₄	—	13	1	no	—
30	C₃×C₈	—	13	1	no	—
31	C₃×C₈	—	26	2	no	—
32	C₃×C₈	#261	1	1	yes	characteristic
33	M₁₆	—	13	2	no	—
34	C₂×C₈	—	13	1	no	—
35	C₁₃	C₃×#108	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₃	—	13	1	no	—
37	C₃×C₄	—	13	1	no	—
38	C₃×C₄	C₂×#261	1	1	yes	characteristic
39	C₂×C₄	—	13	1	no	—
40	C₈	—	13	1	no	—
41	C₈	—	26	2	no	—
42	C₈	C₃×#261	1	1	yes	characteristic
43	C₂×C₃	—	26	1	no	—
44	C₂×C₃	C₄⋊#261	1	1	yes	characteristic
45	C₂²	—	13	1	no	—
46	C₄	—	13	1	no	—
47	C₄	C₂×C₃×#261	1	1	yes	characteristic
48	C₃	#88103	1	1	yes	characteristic, direct product factor, Sylow
49	C₂	—	26	1	no	—
50	C₂	C₃×C₄⋊#261	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₄⋊#261
commutator	C₄×C₁₃	C₂×C₃×C₄
Frattini	C₄	C₂×C₃×#261
Fitting	C₃×C₈×C₁₃	C₄
socle	C₂×C₃×C₁₃	C₄⋊C₄
prime radical	C₂×C₃×D₁₃	Q₈
cosocle	C₄×D₁₃	C₂²×C₃
hypercenter	C₃×C₈	#261
hypocenter	C₁₃	C₃×#108
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈

Complements

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

N	H ≅ G/N	type
3. #88103	C₃	direct (N × H)
25. C₃×C₁₃	#108	semidirect
35. C₁₃	C₃×#108	semidirect
48. C₃	#88103	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#6118	2
C₃×C₈×D₁₃	2
#88103	3
C₃×#108	13

Subgroups — C3×#88103 #11928340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#88103 #11928340