Subgroups — C₂×C₁₃×Dic₃⋊C₄ #11928899

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×Dic₃×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×Dic₃×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₁₃×Dic₃⋊C₄	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₁₃×C₄⋊C₄	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₄×C₁₃	—	2	2	no	—
8	C₂×C₃×C₄×C₁₃	C₂²	1	2	yes	—
9	C₂×Dic₃×C₁₃	—	2	2	no	—
10	C₂×Dic₃×C₁₃	C₄	1	4	yes	complemented
11	C₂×Dic₃×C₁₃	C₂²	1	2	yes	—
12	C₂×Dic₃×C₁₃	C₂²	1	2	yes	—
13	C₂²×C₄×C₁₃	—	3	1	no	—
14	C₂²×C₄×C₁₃	—	3	1	no	—
15	C₂²×C₄×C₁₃	D₃	1	1	yes	characteristic
16	C₁₃×C₄⋊C₄	—	3	4	no	—
17	C₂²×C₃×C₁₃	C₂×C₄	1	2	yes	—
18	C₂²×C₃×C₁₃	D₄	1	2	yes	—
19	C₂²×C₃×C₁₃	Q₈	1	2	yes	—
20	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
21	C₃×C₄×C₁₃	—	2	2	no	—
22	Dic₃×C₁₃	—	2	2	no	—
23	Dic₃×C₁₃	C₂×C₄	1	4	yes	complemented
24	C₂³×C₁₃	C₂×D₃	1	1	yes	characteristic
25	C₂×C₄×C₁₃	—	2	2	no	—
26	C₂×C₄×C₁₃	—	3	4	no	—
27	C₂×C₄×C₁₃	—	3	2	no	—
28	C₂×C₄×C₁₃	—	3	2	no	—
29	C₂×C₄×C₁₃	—	6	2	no	—
30	C₂×C₄×C₁₃	C₂×D₃	1	2	yes	—
31	C₂×Dic₃⋊C₄	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₃×C₁₃	C₄⋊C₄	1	4	yes	complemented
33	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
35	C₂×C₃×C₁₃	C₂×Q₈	1	1	yes	characteristic
36	C₂²×C₁₃	Dic₆	1	2	yes	—
37	C₂²×C₁₃	C₄×D₃	1	2	yes	—
38	C₂²×C₁₃	#67	1	2	yes	—
39	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
40	C₄×C₁₃	—	2	2	no	—
41	C₄×C₁₃	—	3	4	no	—
42	C₄×C₁₃	—	6	2	no	—
43	C₂²×C₃×C₄	C₂×C₁₃	1	1	yes	characteristic
44	C₂²×Dic₃	C₂×C₁₃	1	1	yes	characteristic
45	C₂²×Dic₃	C₂×C₁₃	1	1	yes	characteristic
46	Dic₃⋊C₄	C₂×C₁₃	1	4	yes	direct product factor
47	C₃×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Hall
48	C₂×C₄⋊C₄	—	3	1	no	Sylow
49	C₂×C₁₃	Dic₃⋊C₄	1	4	yes	direct product factor
50	C₂×C₁₃	C₂×Dic₆	1	1	yes	characteristic
51	C₂×C₁₃	C₂×C₄×D₃	1	1	yes	characteristic
52	C₂×C₁₃	C₂×#67	1	1	yes	characteristic
53	C₂³×C₃	C₂²×C₁₃	1	1	yes	characteristic
54	C₂×C₃×C₄	—	2	2	no	—
55	C₂×C₃×C₄	C₂²×C₁₃	1	2	yes	—
56	C₂×Dic₃	—	2	2	no	—
57	C₂×Dic₃	C₄×C₁₃	1	4	yes	complemented
58	C₂×Dic₃	C₂²×C₁₃	1	2	yes	—
59	C₂×Dic₃	C₂²×C₁₃	1	2	yes	—
60	C₂²×C₄	—	3	1	no	—
61	C₂²×C₄	—	3	1	no	—
62	C₂²×C₄	D₃×C₁₃	1	1	yes	characteristic
63	C₄⋊C₄	—	3	4	no	—
64	C₁₃	C₂×Dic₃⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
65	C₂²×C₃	C₂×C₄×C₁₃	1	2	yes	—
66	C₂²×C₃	D₄×C₁₃	1	2	yes	—
67	C₂²×C₃	Q₈×C₁₃	1	2	yes	—
68	C₂²×C₃	C₂³×C₁₃	1	1	yes	characteristic
69	C₃×C₄	—	2	2	no	—
70	Dic₃	—	2	2	no	—
71	Dic₃	C₂×C₄×C₁₃	1	4	yes	complemented
72	C₂³	C₂×D₃×C₁₃	1	1	yes	characteristic
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	3	4	no	—
75	C₂×C₄	—	3	2	no	—
76	C₂×C₄	—	3	2	no	—
77	C₂×C₄	—	6	2	no	—
78	C₂×C₄	C₂×D₃×C₁₃	1	2	yes	—
79	C₂×C₃	C₁₃×C₄⋊C₄	1	4	yes	complemented
80	C₂×C₃	C₂²×C₄×C₁₃	1	1	yes	characteristic
81	C₂×C₃	C₂×D₄×C₁₃	1	1	yes	characteristic
82	C₂×C₃	C₂×Q₈×C₁₃	1	1	yes	characteristic
83	C₂²	C₁₃×Dic₆	1	2	yes	—
84	C₂²	C₄×D₃×C₁₃	1	2	yes	—
85	C₂²	C₁₃×#67	1	2	yes	—
86	C₂²	C₂²×D₃×C₁₃	1	1	yes	characteristic
87	C₄	—	2	2	no	—
88	C₄	—	3	4	no	—
89	C₄	—	6	2	no	—
90	C₃	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
91	C₂	C₁₃×Dic₃⋊C₄	1	4	yes	direct product factor
92	C₂	C₂×C₁₃×Dic₆	1	1	yes	characteristic
93	C₂	C₂×C₄×D₃×C₁₃	1	1	yes	characteristic
94	C₂	C₂×C₁₃×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₁₃	C₂×D₃
commutator	C₂×C₃	C₂²×C₄×C₁₃
Frattini	C₂²	C₂²×D₃×C₁₃
Fitting	C₂²×C₃×C₄×C₁₃	C₂
socle, prime radical	C₂³×C₃×C₁₃	C₂²
cosocle	C₂²×C₃	C₂³×C₁₃
hypercenter	C₂²×C₄×C₁₃	D₃
hypocenter	C₃	C₂×C₁₃×C₄⋊C₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄×C₁₃

Complements

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

N	H ≅ G/N	type
4. C₁₃×Dic₃⋊C₄	C₂	direct (N × H)
10. C₂×Dic₃×C₁₃	C₄	semidirect
23. Dic₃×C₁₃	C₂×C₄	semidirect
31. C₂×Dic₃⋊C₄	C₁₃	direct (N × H)
32. C₂×C₃×C₁₃	C₄⋊C₄	semidirect
46. Dic₃⋊C₄	C₂×C₁₃	direct (N × H)
47. C₃×C₁₃	C₂×C₄⋊C₄	semidirect
49. C₂×C₁₃	Dic₃⋊C₄	direct (N × H)
57. C₂×Dic₃	C₄×C₁₃	semidirect
64. C₁₃	C₂×Dic₃⋊C₄	direct (N × H)
71. Dic₃	C₂×C₄×C₁₃	semidirect
79. C₂×C₃	C₁₃×C₄⋊C₄	semidirect
90. C₃	C₂×C₁₃×C₄⋊C₄	semidirect
91. C₂	C₁₃×Dic₃⋊C₄	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×Dic₃×C₁₃	2
C₁₃×Dic₃⋊C₄	2
C₂×C₁₃×C₄⋊C₄	3
C₂×Dic₃⋊C₄	13

Subgroups — C2×C13×Dic3⋊C4 #11928899

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×Dic₃⋊C₄ #11928899