Subgroups — C₂×C₃×#6094 #11928790

Order 1248.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#1055	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#6094	C₂	1	4	yes	maximal, direct product factor
5	C₂×#6094	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₃×D₁₃	C₄	1	1	yes	characteristic
7	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₃×Dic₁₃	C₄	1	1	yes	characteristic
9	C₃×C₄×D₁₃	C₄	1	2	yes	—
10	C₃×C₄×D₁₃	C₂²	1	2	yes	—
11	C₃×C₈×C₁₃	C₂²	1	2	yes	complemented
12	C₃×#1055	C₂²	1	2	yes	complemented
13	C₂×C₄×D₁₃	C₂×C₃	1	1	yes	characteristic
14	C₂×C₈×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂×#1055	C₂×C₃	1	1	yes	characteristic, complemented
16	#6094	C₂×C₃	1	4	yes	direct product factor
17	C₂²×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₃×D₁₃	—	2	2	no	—
19	C₂×C₃×D₁₃	C₂×C₄	1	2	yes	—
20	C₃×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
22	C₃×Dic₁₃	C₂×C₄	1	2	yes	—
23	C₂²×D₁₃	C₃×C₄	1	1	yes	characteristic
24	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
25	C₂×Dic₁₃	C₃×C₄	1	1	yes	characteristic
26	C₄×D₁₃	C₃×C₄	1	2	yes	—
27	C₄×D₁₃	C₂²×C₃	1	2	yes	—
28	C₈×C₁₃	C₂²×C₃	1	2	yes	complemented
29	#1055	C₂²×C₃	1	2	yes	complemented
30	C₂×C₃×M₁₆	—	13	1	no	maximal, Hall
31	C₂×C₃×C₁₃	M₁₆	1	2	yes	complemented
32	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
33	C₃×D₁₃	—	2	2	no	—
34	C₂²×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic
35	C₂×D₁₃	—	2	2	no	—
36	C₂×D₁₃	C₂×C₃×C₄	1	2	yes	—
37	C₄×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic
38	C₄×C₁₃	C₂³×C₃	1	1	yes	characteristic
39	Dic₁₃	C₂×C₃×C₄	1	2	yes	—
40	C₂²×C₃×C₄	—	13	1	no	—
41	C₃×M₁₆	—	13	4	no	—
42	C₂×C₃×C₈	—	13	1	no	—
43	C₂×C₃×C₈	D₁₃	1	1	yes	characteristic, complemented
44	C₃×C₁₃	C₂×M₁₆	1	1	yes	characteristic, complemented, Hall
45	C₂×M₁₆	—	13	1	no	Sylow
46	C₂×C₁₃	C₃×M₁₆	1	2	yes	complemented
47	C₂×C₁₃	C₂²×C₃×C₄	1	1	yes	characteristic
48	D₁₃	—	2	2	no	—
49	C₂³×C₃	—	13	1	no	—
50	C₂×C₃×C₄	—	13	1	no	—
51	C₂×C₃×C₄	—	13	2	no	—
52	C₂×C₃×C₄	—	13	2	no	—
53	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
54	C₃×C₈	—	13	2	no	—
55	C₃×C₈	C₂×D₁₃	1	2	yes	complemented
56	C₂²×C₄	—	13	1	no	—
57	M₁₆	—	13	4	no	—
58	C₂×C₈	—	13	1	no	—
59	C₂×C₈	C₃×D₁₃	1	1	yes	characteristic, complemented
60	C₁₃	C₂×C₃×M₁₆	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₃	—	13	2	no	—
62	C₂²×C₃	—	26	2	no	—
63	C₂²×C₃	C₄×D₁₃	1	1	yes	characteristic
64	C₃×C₄	—	13	2	no	—
65	C₃×C₄	C₄×D₁₃	1	1	yes	characteristic
66	C₃×C₄	C₂²×D₁₃	1	1	yes	characteristic
67	C₂³	—	13	1	no	—
68	C₂×C₄	—	13	1	no	—
69	C₂×C₄	—	13	2	no	—
70	C₂×C₄	—	13	2	no	—
71	C₂×C₄	C₂×C₃×D₁₃	1	1	yes	characteristic
72	C₈	—	13	2	no	—
73	C₈	C₂×C₃×D₁₃	1	2	yes	complemented
74	C₂×C₃	—	26	2	no	—
75	C₂×C₃	#6094	1	2	yes	direct product factor
76	C₂×C₃	C₂×C₄×D₁₃	1	1	yes	characteristic
77	C₂²	—	13	2	no	—
78	C₂²	—	26	2	no	—
79	C₂²	C₃×C₄×D₁₃	1	1	yes	characteristic
80	C₄	—	13	2	no	—
81	C₄	C₃×C₄×D₁₃	1	1	yes	characteristic
82	C₄	C₂²×C₃×D₁₃	1	1	yes	characteristic
83	C₃	C₂×#6094	1	1	yes	characteristic, direct product factor, Sylow
84	C₂	—	26	2	no	—
85	C₂	C₃×#6094	1	2	yes	direct product factor
86	C₂	C₂×C₃×C₄×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₁₃
commutator	C₂×C₁₃	C₂²×C₃×C₄
Frattini	C₄	C₂²×C₃×D₁₃
Fitting	C₂×C₃×C₈×C₁₃	C₂
socle	C₂²×C₃×C₁₃	C₂×C₄
prime radical	C₂²×C₃×D₁₃	C₄
cosocle	C₄×C₁₃	C₂³×C₃
hypercenter	C₂×C₃×C₈	D₁₃
hypocenter	C₁₃	C₂×C₃×M₁₆
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₈×C₁₃	C₂	semidirect
3. C₂×C₃×#1055	C₂	semidirect
4. C₃×#6094	C₂	direct (N × H)
5. C₂×#6094	C₃	direct (N × H)
11. C₃×C₈×C₁₃	C₂²	semidirect
12. C₃×#1055	C₂²	semidirect
14. C₂×C₈×C₁₃	C₂×C₃	semidirect
15. C₂×#1055	C₂×C₃	semidirect
16. #6094	C₂×C₃	direct (N × H)
28. C₈×C₁₃	C₂²×C₃	semidirect
29. #1055	C₂²×C₃	semidirect
31. C₂×C₃×C₁₃	M₁₆	semidirect
43. C₂×C₃×C₈	D₁₃	semidirect
44. C₃×C₁₃	C₂×M₁₆	semidirect
46. C₂×C₁₃	C₃×M₁₆	semidirect
55. C₃×C₈	C₂×D₁₃	semidirect
59. C₂×C₈	C₃×D₁₃	semidirect
60. C₁₃	C₂×C₃×M₁₆	semidirect
73. C₈	C₂×C₃×D₁₃	semidirect
75. C₂×C₃	#6094	direct (N × H)
83. C₃	C₂×#6094	direct (N × H)
85. C₂	C₃×#6094	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×C₄×D₁₃	2
C₂×C₃×C₈×C₁₃	2
C₂×C₃×#1055	2
C₃×#6094	2
C₂×#6094	3
C₂×C₃×M₁₆	13

Subgroups — C2×C3×#6094 #11928790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#6094 #11928790