Subgroups — C₃×C₄×Dic₂₆ #11928758

Order 1248.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Dic₂₆	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	C₃×#6101	C₂	1	2	yes	maximal
5	C₃×C₄×Dic₁₃	C₂	1	2	yes	maximal
6	C₄×Dic₂₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₃×Dic₁₃	C₂²	1	2	yes	—
11	C₂×C₃×Dic₁₃	C₂²	1	2	yes	—
12	C₃×Dic₂₆	C₄	1	4	yes	direct product factor
13	C₂×Dic₂₆	C₂×C₃	1	1	yes	characteristic
14	C₄²×C₁₃	C₂×C₃	1	1	yes	characteristic
15	C₄⋊Dic₁₃	C₂×C₃	1	1	yes	characteristic
16	#6101	C₂×C₃	1	2	yes	—
17	C₄×Dic₁₃	C₂×C₃	1	2	yes	—
18	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
19	C₃×C₄×C₁₃	—	2	1	no	—
20	C₃×C₄×C₁₃	C₂×C₄	1	2	yes	—
21	C₃×C₄×C₁₃	Q₈	1	2	yes	complemented
22	C₃×Dic₁₃	—	2	2	no	—
23	C₃×Dic₁₃	C₂×C₄	1	4	yes	—
24	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
25	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
26	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
27	C₂×Dic₁₃	C₂²×C₃	1	2	yes	—
28	C₂×Dic₁₃	C₂²×C₃	1	2	yes	—
29	Dic₂₆	C₃×C₄	1	4	yes	direct product factor
30	C₃×C₄×Q₈	—	13	1	no	maximal, Hall
31	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₃×C₁₃	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₃×C₁₃	#41	1	1	yes	characteristic
34	C₂²×C₁₃	C₂³×C₃	1	1	yes	characteristic
35	C₄×C₁₃	—	2	1	no	—
36	C₄×C₁₃	C₂×C₃×C₄	1	2	yes	—
37	C₄×C₁₃	C₃×Q₈	1	2	yes	complemented
38	Dic₁₃	—	2	2	no	—
39	Dic₁₃	C₂×C₃×C₄	1	4	yes	—
40	C₂×C₃×Q₈	—	13	1	no	—
41	C₃×C₄⋊C₄	—	13	2	no	—
42	C₃×C₄⋊C₄	—	13	1	no	—
43	C₃×C₄²	—	13	2	no	—
44	C₃×C₄²	D₁₃	1	1	yes	characteristic
45	C₃×C₁₃	C₄×Q₈	1	1	yes	characteristic, complemented, Hall
46	C₄×Q₈	—	13	1	no	Sylow
47	C₂×C₁₃	C₂²×C₃×C₄	1	1	yes	characteristic
48	C₂×C₁₃	C₂×C₃×Q₈	1	1	yes	characteristic
49	C₂×C₁₃	C₃×#41	1	1	yes	characteristic
50	C₃×Q₈	—	13	4	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	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
55	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
56	C₂×Q₈	—	13	1	no	—
57	C₄⋊C₄	—	13	2	no	—
58	C₄⋊C₄	—	13	1	no	—
59	C₄²	—	13	2	no	—
60	C₄²	C₃×D₁₃	1	1	yes	characteristic
61	C₁₃	C₃×C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
63	C₃×C₄	—	2	1	no	—
64	C₃×C₄	—	13	4	no	—
65	C₃×C₄	—	26	2	no	—
66	C₃×C₄	Dic₂₆	1	2	yes	direct product factor
67	C₃×C₄	C₄×D₁₃	1	2	yes	—
68	Q₈	—	13	4	no	—
69	C₂×C₄	—	13	2	no	—
70	C₂×C₄	—	13	2	no	—
71	C₂×C₄	C₂×C₃×D₁₃	1	1	yes	characteristic
72	C₂×C₄	C₂×C₃×D₁₃	1	1	yes	characteristic
73	C₂×C₄	C₂×C₃×D₁₃	1	1	yes	characteristic
74	C₂×C₃	C₂×Dic₂₆	1	1	yes	characteristic
75	C₂×C₃	C₂×C₄×D₁₃	1	1	yes	characteristic
76	C₂×C₃	#6127	1	1	yes	characteristic
77	C₂²	C₂²×C₃×D₁₃	1	1	yes	characteristic
78	C₄	—	2	1	no	—
79	C₄	—	13	4	no	—
80	C₄	—	26	2	no	—
81	C₄	C₃×Dic₂₆	1	2	yes	direct product factor
82	C₄	C₃×C₄×D₁₃	1	2	yes	—
83	C₃	C₄×Dic₂₆	1	1	yes	characteristic, direct product factor, Sylow
84	C₂	C₂×C₃×Dic₂₆	1	1	yes	characteristic
85	C₂	C₂×C₃×C₄×D₁₃	1	1	yes	characteristic
86	C₂	C₃×#6127	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
6. C₄×Dic₂₆	C₃	direct (N × H)
12. C₃×Dic₂₆	C₄	direct (N × H)
21. C₃×C₄×C₁₃	Q₈	semidirect
29. Dic₂₆	C₃×C₄	direct (N × H)
37. C₄×C₁₃	C₃×Q₈	semidirect
45. C₃×C₁₃	C₄×Q₈	semidirect
61. C₁₃	C₃×C₄×Q₈	semidirect
66. C₃×C₄	Dic₂₆	direct (N × H)
81. C₄	C₃×Dic₂₆	direct (N × H)
83. C₃	C₄×Dic₂₆	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
C₃×#6101	2
C₃×C₄×Dic₁₃	2
C₄×Dic₂₆	3
C₃×C₄×Q₈	13

Subgroups — C3×C4×Dic26 #11928758

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×Dic₂₆ #11928758