Subgroups — C₃×#88207 #11928843

Order 1248.

260 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₂²⋊D₁₃	C₂	1	3	yes	maximal, complemented
3	C₃×C₂²⋊Dic₁₃	C₂	1	3	yes	maximal, complemented
4	#88207	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂³×C₃×C₁₃	—	2	6	no	—
6	C₂³×C₃×C₁₃	C₂²	1	3	yes	—
7	C₂²×C₃×D₁₃	C₂²	1	1	yes	characteristic, complemented
8	C₃×C₂²⋊D₁₃	—	2	6	no	—
9	C₂×C₃×Dic₁₃	C₂²	1	3	yes	complemented
10	C₂⁴×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₂²⋊D₁₃	C₂×C₃	1	3	yes	complemented
12	C₂²⋊Dic₁₃	C₂×C₃	1	3	yes	complemented
13	C₂²×C₃×C₁₃	—	2	8	no	—
14	C₂²×C₃×C₁₃	—	2	6	no	—
15	C₂²×C₃×C₁₃	D₄	1	6	yes	complemented
16	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
17	C₂×C₃×D₁₃	—	2	3	no	—
18	C₃×Dic₁₃	—	2	3	no	—
19	C₂³×C₁₃	—	2	6	no	—
20	C₂³×C₁₃	C₂²×C₃	1	3	yes	—
21	C₂²×D₁₃	C₂²×C₃	1	1	yes	characteristic, complemented
22	C₂²⋊D₁₃	—	2	6	no	—
23	C₂×Dic₁₃	C₂²×C₃	1	3	yes	complemented
24	C₃×#120	—	13	1	no	maximal, Hall
25	C₂×C₃×C₁₃	—	2	6	no	—
26	C₂×C₃×C₁₃	C₂×D₄	1	3	yes	—
27	C₃×D₁₃	—	4	1	no	—
28	C₂²×C₁₃	—	2	8	no	—
29	C₂²×C₁₃	—	2	6	no	—
30	C₂²×C₁₃	C₃×D₄	1	6	yes	complemented
31	C₂²×C₁₃	C₂³×C₃	1	1	yes	characteristic
32	C₂×D₁₃	—	2	3	no	—
33	Dic₁₃	—	2	3	no	—
34	C₂⁴×C₃	D₁₃	1	1	yes	characteristic, complemented
35	C₂×C₃×D₄	—	13	3	no	—
36	C₃×C₂²⋊C₄	—	13	3	no	—
37	C₃×C₁₃	#120	1	1	yes	characteristic, complemented, Hall
38	#120	—	13	1	no	Sylow
39	C₂×C₁₃	—	2	6	no	—
40	C₂×C₁₃	C₂×C₃×D₄	1	3	yes	—
41	D₁₃	—	4	1	no	—
42	C₂³×C₃	—	2	6	no	—
43	C₂³×C₃	—	13	1	no	—
44	C₂³×C₃	C₂×D₁₃	1	3	yes	—
45	C₃×D₄	—	26	6	no	—
46	C₂×C₃×C₄	—	13	3	no	—
47	C₂⁴	C₃×D₁₃	1	1	yes	characteristic, complemented
48	C₂×D₄	—	13	3	no	—
49	C₂²⋊C₄	—	13	3	no	—
50	C₁₃	C₃×#120	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₃	—	2	8	no	—
52	C₂²×C₃	—	2	6	no	—
53	C₂²×C₃	—	26	3	no	—
54	C₂²×C₃	C₂²⋊D₁₃	1	6	yes	complemented
55	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
56	C₃×C₄	—	26	3	no	—
57	C₂³	—	2	6	no	—
58	C₂³	—	13	1	no	—
59	C₂³	C₂×C₃×D₁₃	1	3	yes	—
60	D₄	—	26	6	no	—
61	C₂×C₄	—	13	3	no	—
62	C₂×C₃	—	2	6	no	—
63	C₂×C₃	—	52	1	no	—
64	C₂×C₃	C₂×C₂²⋊D₁₃	1	3	yes	—
65	C₂²	—	2	8	no	—
66	C₂²	—	2	6	no	—
67	C₂²	—	26	3	no	—
68	C₂²	C₃×C₂²⋊D₁₃	1	6	yes	complemented
69	C₂²	C₂²×C₃×D₁₃	1	1	yes	characteristic
70	C₄	—	26	3	no	—
71	C₃	#88207	1	1	yes	characteristic, direct product factor, Sylow
72	C₂	—	2	6	no	—
73	C₂	—	52	1	no	—
74	C₂	C₂×C₃×C₂²⋊D₁₃	1	3	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂²×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂³×C₃
Frattini	C₂²	C₂²×C₃×D₁₃
Fitting	C₂⁴×C₃×C₁₃	C₂
socle	C₂²×C₃×C₁₃	C₂³
hypercenter	C₂⁴×C₃	D₁₃
hypocenter	C₁₃	C₃×#120
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂⁴×C₃

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃×C₁₃	C₂	semidirect
2. C₂×C₃×C₂²⋊D₁₃	C₂	semidirect
3. C₃×C₂²⋊Dic₁₃	C₂	semidirect
4. #88207	C₃	direct (N × H)
7. C₂²×C₃×D₁₃	C₂²	semidirect
9. C₂×C₃×Dic₁₃	C₂²	semidirect
10. C₂⁴×C₁₃	C₂×C₃	semidirect
11. C₂×C₂²⋊D₁₃	C₂×C₃	semidirect
12. C₂²⋊Dic₁₃	C₂×C₃	semidirect
15. C₂²×C₃×C₁₃	D₄	semidirect
21. C₂²×D₁₃	C₂²×C₃	semidirect
23. C₂×Dic₁₃	C₂²×C₃	semidirect
30. C₂²×C₁₃	C₃×D₄	semidirect
34. C₂⁴×C₃	D₁₃	semidirect
37. C₃×C₁₃	#120	semidirect
47. C₂⁴	C₃×D₁₃	semidirect
50. C₁₃	C₃×#120	semidirect
54. C₂²×C₃	C₂²⋊D₁₃	semidirect
68. C₂²	C₃×C₂²⋊D₁₃	semidirect
71. C₃	#88207	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃×C₁₃	2
C₂×C₃×C₂²⋊D₁₃	2
C₃×C₂²⋊Dic₁₃	2
#88207	3
C₃×#120	13

Subgroups — C3×#88207 #11928843

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#88207 #11928843