Subgroups — C₂×C₃×C₄⋊Dic₁₃ #11928815

Order 1248.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×Dic₁₃	C₂	1	2	yes	maximal
3	C₃×C₄⋊Dic₁₃	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄⋊Dic₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂³×C₃×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄×C₁₃	C₄	1	4	yes	complemented
7	C₂×C₃×C₄×C₁₃	C₂²	1	2	yes	—
8	C₂×C₃×Dic₁₃	—	2	4	no	—
9	C₂×C₃×Dic₁₃	C₂²	1	4	yes	—
10	C₂²×C₄×C₁₃	C₂×C₃	1	1	yes	characteristic
11	C₂²×Dic₁₃	C₂×C₃	1	2	yes	—
12	C₄⋊Dic₁₃	C₂×C₃	1	4	yes	direct product factor
13	C₂²×C₃×C₁₃	C₂×C₄	1	2	yes	—
14	C₂²×C₃×C₁₃	D₄	1	2	yes	—
15	C₂²×C₃×C₁₃	Q₈	1	2	yes	—
16	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
17	C₃×C₄×C₁₃	C₂×C₄	1	4	yes	complemented
18	C₃×Dic₁₃	—	2	4	no	—
19	C₂³×C₁₃	C₂²×C₃	1	1	yes	characteristic
20	C₂×C₄×C₁₃	C₃×C₄	1	4	yes	complemented
21	C₂×C₄×C₁₃	C₂²×C₃	1	2	yes	—
22	C₂×Dic₁₃	—	2	4	no	—
23	C₂×Dic₁₃	C₂²×C₃	1	4	yes	—
24	C₂×C₃×C₄⋊C₄	—	13	1	no	maximal, Hall
25	C₂×C₃×C₁₃	C₄⋊C₄	1	4	yes	complemented
26	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
28	C₂×C₃×C₁₃	C₂×Q₈	1	1	yes	characteristic
29	C₂²×C₁₃	C₂×C₃×C₄	1	2	yes	—
30	C₂²×C₁₃	C₃×D₄	1	2	yes	—
31	C₂²×C₁₃	C₃×Q₈	1	2	yes	—
32	C₂²×C₁₃	C₂³×C₃	1	1	yes	characteristic
33	C₄×C₁₃	C₂×C₃×C₄	1	4	yes	complemented
34	Dic₁₃	—	2	4	no	—
35	C₂²×C₃×C₄	—	13	2	no	—
36	C₂²×C₃×C₄	D₁₃	1	1	yes	characteristic
37	C₃×C₄⋊C₄	—	13	4	no	—
38	C₃×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
39	C₂×C₄⋊C₄	—	13	1	no	Sylow
40	C₂×C₁₃	C₃×C₄⋊C₄	1	4	yes	complemented
41	C₂×C₁₃	C₂²×C₃×C₄	1	1	yes	characteristic
42	C₂×C₁₃	C₂×C₃×D₄	1	1	yes	characteristic
43	C₂×C₁₃	C₂×C₃×Q₈	1	1	yes	characteristic
44	C₂³×C₃	C₂×D₁₃	1	1	yes	characteristic
45	C₂×C₃×C₄	—	13	4	no	—
46	C₂×C₃×C₄	—	26	4	no	—
47	C₂×C₃×C₄	Dic₁₃	1	4	yes	complemented
48	C₂×C₃×C₄	C₂×D₁₃	1	2	yes	—
49	C₂²×C₄	—	13	2	no	—
50	C₂²×C₄	C₃×D₁₃	1	1	yes	characteristic
51	C₄⋊C₄	—	13	4	no	—
52	C₁₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₃	Dic₂₆	1	2	yes	—
54	C₂²×C₃	D₅₂	1	2	yes	—
55	C₂²×C₃	C₂×Dic₁₃	1	2	yes	—
56	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
57	C₃×C₄	—	26	4	no	—
58	C₃×C₄	C₂×Dic₁₃	1	4	yes	complemented
59	C₂³	C₂×C₃×D₁₃	1	1	yes	characteristic
60	C₂×C₄	—	13	4	no	—
61	C₂×C₄	—	26	4	no	—
62	C₂×C₄	C₃×Dic₁₃	1	4	yes	complemented
63	C₂×C₄	C₂×C₃×D₁₃	1	2	yes	—
64	C₂×C₃	C₄⋊Dic₁₃	1	4	yes	direct product factor
65	C₂×C₃	C₂×Dic₂₆	1	1	yes	characteristic
66	C₂×C₃	C₂×D₅₂	1	1	yes	characteristic
67	C₂×C₃	C₂²×Dic₁₃	1	1	yes	characteristic
68	C₂²	C₃×Dic₂₆	1	2	yes	—
69	C₂²	C₃×D₅₂	1	2	yes	—
70	C₂²	C₂×C₃×Dic₁₃	1	2	yes	—
71	C₂²	C₂²×C₃×D₁₃	1	1	yes	characteristic
72	C₄	—	26	4	no	—
73	C₄	C₂×C₃×Dic₁₃	1	4	yes	complemented
74	C₃	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic, direct product factor, Sylow
75	C₂	C₃×C₄⋊Dic₁₃	1	4	yes	direct product factor
76	C₂	C₂×C₃×Dic₂₆	1	1	yes	characteristic
77	C₂	C₂×C₃×D₅₂	1	1	yes	characteristic
78	C₂	C₂²×C₃×Dic₁₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₃×C₄⋊Dic₁₃	C₂	direct (N × H)
4. C₂×C₄⋊Dic₁₃	C₃	direct (N × H)
6. C₂×C₃×C₄×C₁₃	C₄	semidirect
12. C₄⋊Dic₁₃	C₂×C₃	direct (N × H)
17. C₃×C₄×C₁₃	C₂×C₄	semidirect
20. C₂×C₄×C₁₃	C₃×C₄	semidirect
25. C₂×C₃×C₁₃	C₄⋊C₄	semidirect
33. C₄×C₁₃	C₂×C₃×C₄	semidirect
38. C₃×C₁₃	C₂×C₄⋊C₄	semidirect
40. C₂×C₁₃	C₃×C₄⋊C₄	semidirect
47. C₂×C₃×C₄	Dic₁₃	semidirect
52. C₁₃	C₂×C₃×C₄⋊C₄	semidirect
58. C₃×C₄	C₂×Dic₁₃	semidirect
62. C₂×C₄	C₃×Dic₁₃	semidirect
64. C₂×C₃	C₄⋊Dic₁₃	direct (N × H)
73. C₄	C₂×C₃×Dic₁₃	semidirect
74. C₃	C₂×C₄⋊Dic₁₃	direct (N × H)
75. C₂	C₃×C₄⋊Dic₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄×C₁₃	2
C₂²×C₃×Dic₁₃	2
C₃×C₄⋊Dic₁₃	2
C₂×C₄⋊Dic₁₃	3
C₂×C₃×C₄⋊C₄	13

Subgroups — C2×C3×C4⋊Dic13 #11928815

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₄⋊Dic₁₃ #11928815