Subgroups — C₂×C₃×#6106 #11928833

Order 1248.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₅₂	C₂	1	1	yes	maximal, characteristic
3	C₃×#6106	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃×#1055	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#6106	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₃×D₁₃	—	2	1	no	—
7	C₃×Q₈×C₁₃	—	2	1	no	—
8	C₃×Q₈×C₁₃	C₂²	1	2	yes	complemented
9	C₂×C₃×C₄×C₁₃	—	2	1	no	—
10	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₃×D₅₂	—	2	1	no	—
12	C₃×D₅₂	C₂²	1	2	yes	—
13	C₃×#1055	C₂²	1	2	yes	complemented
14	C₂×Q₈×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂×D₅₂	C₂×C₃	1	1	yes	characteristic
16	#6106	C₂×C₃	1	4	yes	direct product factor
17	C₂×#1055	C₂×C₃	1	1	yes	characteristic, complemented
18	C₂²×C₃×C₁₃	D₄	1	1	yes	characteristic
19	C₂×C₃×D₁₃	—	2	2	no	—
20	C₂×C₃×D₁₃	—	4	2	no	—
21	C₃×C₄×C₁₃	—	2	2	no	—
22	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
23	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
24	C₂²×D₁₃	—	2	1	no	—
25	Q₈×C₁₃	—	2	1	no	—
26	Q₈×C₁₃	C₂²×C₃	1	2	yes	complemented
27	C₂×C₄×C₁₃	—	2	1	no	—
28	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
29	D₅₂	—	2	1	no	—
30	D₅₂	C₂²×C₃	1	2	yes	—
31	#1055	C₂²×C₃	1	2	yes	complemented
32	C₂×C₃×SD₁₆	—	13	1	no	maximal, Hall
33	C₂×C₃×C₁₃	SD₁₆	1	2	yes	complemented
34	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
35	C₃×D₁₃	—	4	2	no	—
36	C₂²×C₁₃	C₃×D₄	1	1	yes	characteristic
37	C₂×D₁₃	—	2	2	no	—
38	C₂×D₁₃	—	4	2	no	—
39	C₄×C₁₃	—	2	2	no	—
40	C₄×C₁₃	C₃×D₄	1	1	yes	characteristic
41	C₄×C₁₃	C₂³×C₃	1	1	yes	characteristic
42	C₂×C₃×Q₈	D₁₃	1	1	yes	characteristic, complemented
43	C₂×C₃×D₄	—	13	1	no	—
44	C₃×SD₁₆	—	13	4	no	—
45	C₂×C₃×C₈	—	13	1	no	—
46	C₃×C₁₃	C₂×SD₁₆	1	1	yes	characteristic, complemented, Hall
47	C₂×SD₁₆	—	13	1	no	Sylow
48	C₂×C₁₃	C₃×SD₁₆	1	2	yes	complemented
49	C₂×C₁₃	C₂×C₃×D₄	1	1	yes	characteristic
50	D₁₃	—	4	2	no	—
51	C₂³×C₃	—	26	1	no	—
52	C₃×Q₈	—	2	1	no	—
53	C₃×Q₈	C₂×D₁₃	1	2	yes	complemented
54	C₃×D₄	—	13	2	no	—
55	C₃×D₄	—	26	1	no	—
56	C₂×C₃×C₄	—	2	1	no	—
57	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
58	C₃×C₈	—	13	2	no	—
59	C₂×Q₈	C₃×D₁₃	1	1	yes	characteristic, complemented
60	C₂×D₄	—	13	1	no	—
61	SD₁₆	—	13	4	no	—
62	C₂×C₈	—	13	1	no	—
63	C₁₃	C₂×C₃×SD₁₆	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₃	—	26	2	no	—
65	C₂²×C₃	—	52	2	no	—
66	C₂²×C₃	C₂²⋊D₁₃	1	1	yes	characteristic
67	C₃×C₄	—	2	2	no	—
68	C₃×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
69	C₃×C₄	C₂²×D₁₃	1	1	yes	characteristic
70	C₂³	—	26	1	no	—
71	Q₈	—	2	1	no	—
72	Q₈	C₂×C₃×D₁₃	1	2	yes	complemented
73	D₄	—	13	2	no	—
74	D₄	—	26	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	C₂×C₃×D₁₃	1	1	yes	characteristic
77	C₈	—	13	2	no	—
78	C₂×C₃	—	52	2	no	—
79	C₂×C₃	#6106	1	2	yes	direct product factor
80	C₂×C₃	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
81	C₂²	—	26	2	no	—
82	C₂²	—	52	2	no	—
83	C₂²	C₃×C₂²⋊D₁₃	1	1	yes	characteristic
84	C₄	—	2	2	no	—
85	C₄	C₃×C₂²⋊D₁₃	1	1	yes	characteristic
86	C₄	C₂²×C₃×D₁₃	1	1	yes	characteristic
87	C₃	C₂×#6106	1	1	yes	characteristic, direct product factor, Sylow
88	C₂	—	52	2	no	—
89	C₂	C₃×#6106	1	2	yes	direct product factor
90	C₂	C₂×C₃×C₂²⋊D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²⋊D₁₃
commutator, cosocle	C₄×C₁₃	C₂³×C₃
Frattini	C₄	C₂²×C₃×D₁₃
Fitting	C₂×C₃×Q₈×C₁₃	C₂
socle	C₂²×C₃×C₁₃	D₄
prime radical	C₂×C₃×D₅₂	C₂
hypercenter	C₂×C₃×Q₈	D₁₃
hypocenter	C₁₃	C₂×C₃×SD₁₆
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×Q₈×C₁₃	C₂	semidirect
3. C₃×#6106	C₂	direct (N × H)
4. C₂×C₃×#1055	C₂	semidirect
5. C₂×#6106	C₃	direct (N × H)
8. C₃×Q₈×C₁₃	C₂²	semidirect
13. C₃×#1055	C₂²	semidirect
14. C₂×Q₈×C₁₃	C₂×C₃	semidirect
16. #6106	C₂×C₃	direct (N × H)
17. C₂×#1055	C₂×C₃	semidirect
26. Q₈×C₁₃	C₂²×C₃	semidirect
31. #1055	C₂²×C₃	semidirect
33. C₂×C₃×C₁₃	SD₁₆	semidirect
42. C₂×C₃×Q₈	D₁₃	semidirect
46. C₃×C₁₃	C₂×SD₁₆	semidirect
48. C₂×C₁₃	C₃×SD₁₆	semidirect
53. C₃×Q₈	C₂×D₁₃	semidirect
59. C₂×Q₈	C₃×D₁₃	semidirect
63. C₁₃	C₂×C₃×SD₁₆	semidirect
72. Q₈	C₂×C₃×D₁₃	semidirect
79. C₂×C₃	#6106	direct (N × H)
87. C₃	C₂×#6106	direct (N × H)
89. C₂	C₃×#6106	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×Q₈×C₁₃	2
C₂×C₃×D₅₂	2
C₃×#6106	2
C₂×C₃×#1055	2
C₂×#6106	3
C₂×C₃×SD₁₆	13

Subgroups — C2×C3×#6106 #11928833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#6106 #11928833