Subgroups — C₂²×(C₂²⋊D₁₃)⋊C₃ #11929144

Order 1248.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×(C₂²⋊D₁₃)⋊C₃	C₂	1	12	yes	maximal, direct product factor
4	C₂²×Dic₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₂²⋊D₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂³×C₁₃⋊C₃	—	2	4	no	—
7	C₂³×C₁₃⋊C₃	C₂²	1	1	yes	characteristic
8	C₂³×C₁₃⋊C₃	C₂²	1	6	yes	complemented
9	C₂²×D₁₃⋊C₃	—	2	4	no	—
10	C₂²×D₁₃⋊C₃	C₂²	1	6	yes	complemented
11	(C₂²⋊D₁₃)⋊C₃	C₂²	1	16	yes	direct product factor
12	C₂×Dic₁₃⋊C₃	C₂²	1	6	yes	complemented
13	C₂⁴×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂³×D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂×C₂²⋊D₁₃	C₂×C₃	1	12	yes	complemented
16	C₂²×Dic₁₃	C₂×C₃	1	1	yes	characteristic, complemented
17	C₂²×C₁₃⋊C₃	—	2	12	no	—
18	C₂²×C₁₃⋊C₃	D₄	1	4	yes	complemented
19	C₂²×C₁₃⋊C₃	C₂³	1	3	yes	—
20	C₂²×C₁₃⋊C₃	C₂³	1	4	yes	complemented
21	C₂×D₁₃⋊C₃	—	2	12	no	—
22	C₂×D₁₃⋊C₃	C₂³	1	4	yes	complemented
23	Dic₁₃⋊C₃	C₂³	1	4	yes	complemented
24	C₂³×C₁₃	—	2	4	no	—
25	C₂³×C₁₃	C₂²×C₃	1	1	yes	characteristic
26	C₂³×C₁₃	C₂²×C₃	1	6	yes	complemented
27	C₂²×D₁₃	—	2	4	no	—
28	C₂²×D₁₃	C₂²×C₃	1	6	yes	complemented
29	C₂²⋊D₁₃	C₂²×C₃	1	16	yes	complemented
30	C₂×Dic₁₃	C₂²×C₃	1	6	yes	complemented
31	C₂²×C₃×D₄	—	13	1	no	maximal, Hall
32	C₂×C₁₃⋊C₃	—	2	4	no	—
33	C₂×C₁₃⋊C₃	C₂×D₄	1	6	yes	complemented
34	C₂×C₁₃⋊C₃	C₂⁴	1	1	yes	characteristic
35	D₁₃⋊C₃	—	2	4	no	—
36	C₂²×C₁₃	—	2	12	no	—
37	C₂²×C₁₃	C₃×D₄	1	4	yes	complemented
38	C₂²×C₁₃	C₂³×C₃	1	3	yes	—
39	C₂²×C₁₃	C₂³×C₃	1	4	yes	complemented
40	C₂×D₁₃	—	2	12	no	—
41	C₂×D₁₃	C₂³×C₃	1	4	yes	complemented
42	Dic₁₃	C₂³×C₃	1	4	yes	complemented
43	C₂⁴×C₃	—	13	1	no	—
44	C₂⁴×C₃	—	13	1	no	—
45	C₂×C₃×D₄	—	13	12	no	—
46	C₂²×C₃×C₄	—	13	1	no	—
47	C₁₃⋊C₃	C₂²×D₄	1	1	yes	characteristic, complemented, Hall
48	C₂²×D₄	—	13	1	no	Sylow
49	C₂×C₁₃	—	2	4	no	—
50	C₂×C₁₃	C₂×C₃×D₄	1	6	yes	complemented
51	C₂×C₁₃	C₂⁴×C₃	1	1	yes	characteristic
52	D₁₃	—	2	4	no	—
53	C₂³×C₃	—	13	6	no	—
54	C₂³×C₃	—	13	1	no	—
55	C₂³×C₃	—	13	6	no	—
56	C₂³×C₃	—	26	4	no	—
57	C₂³×C₃	—	26	4	no	—
58	C₃×D₄	—	13	16	no	—
59	C₂×C₃×C₄	—	13	6	no	—
60	C₂⁴	—	13	1	no	—
61	C₂⁴	D₁₃⋊C₃	1	1	yes	characteristic, complemented
62	C₂×D₄	—	13	12	no	—
63	C₂²×C₄	—	13	1	no	—
64	C₁₃	C₂²×C₃×D₄	1	1	yes	characteristic, complemented, Sylow
65	C₂²×C₃	—	13	4	no	—
66	C₂²×C₃	—	13	4	no	—
67	C₂²×C₃	—	13	3	no	—
68	C₂²×C₃	—	13	4	no	—
69	C₂²×C₃	—	26	12	no	—
70	C₂²×C₃	—	26	12	no	—
71	C₃×C₄	—	13	4	no	—
72	C₂³	—	2	4	no	—
73	C₂³	—	13	6	no	—
74	C₂³	—	26	4	no	—
75	C₂³	C₂×D₁₃⋊C₃	1	1	yes	characteristic
76	C₂³	C₂×D₁₃⋊C₃	1	6	yes	complemented
77	D₄	—	13	16	no	—
78	C₂×C₄	—	13	6	no	—
79	C₂×C₃	—	13	6	no	—
80	C₂×C₃	—	13	1	no	—
81	C₂×C₃	—	26	4	no	—
82	C₂×C₃	—	26	4	no	—
83	C₂²	—	2	12	no	—
84	C₂²	—	13	4	no	—
85	C₂²	—	26	12	no	—
86	C₂²	(C₂²⋊D₁₃)⋊C₃	1	4	yes	direct product factor
87	C₂²	C₂²×D₁₃⋊C₃	1	3	yes	—
88	C₂²	C₂²×D₁₃⋊C₃	1	4	yes	complemented
89	C₄	—	13	4	no	—
90	C₃	—	13	1	no	Sylow
91	C₂	—	2	4	no	—
92	C₂	—	26	4	no	—
93	C₂	C₂×(C₂²⋊D₁₃)⋊C₃	1	6	yes	direct product factor
94	C₂	C₂³×D₁₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₁₃⋊C₃
commutator, cosocle	C₂×C₁₃	C₂⁴×C₃
Frattini	C₂	C₂³×D₁₃⋊C₃
Fitting	C₂⁴×C₁₃	C₂×C₃
socle	C₂³×C₁₃	C₂²×C₃
hypercenter	C₂⁴	D₁₃⋊C₃
hypocenter	C₁₃	C₂²×C₃×D₄
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₁₃⋊C₃	C₂	semidirect
2. C₂³×D₁₃⋊C₃	C₂	semidirect
3. C₂×(C₂²⋊D₁₃)⋊C₃	C₂	direct (N × H)
4. C₂²×Dic₁₃⋊C₃	C₂	semidirect
5. C₂²×C₂²⋊D₁₃	C₃	semidirect
8. C₂³×C₁₃⋊C₃	C₂²	semidirect
10. C₂²×D₁₃⋊C₃	C₂²	semidirect
11. (C₂²⋊D₁₃)⋊C₃	C₂²	direct (N × H)
12. C₂×Dic₁₃⋊C₃	C₂²	semidirect
13. C₂⁴×C₁₃	C₂×C₃	semidirect
14. C₂³×D₁₃	C₂×C₃	semidirect
15. C₂×C₂²⋊D₁₃	C₂×C₃	semidirect
16. C₂²×Dic₁₃	C₂×C₃	semidirect
18. C₂²×C₁₃⋊C₃	D₄	semidirect
20. C₂²×C₁₃⋊C₃	C₂³	semidirect
22. C₂×D₁₃⋊C₃	C₂³	semidirect
23. Dic₁₃⋊C₃	C₂³	semidirect
26. C₂³×C₁₃	C₂²×C₃	semidirect
28. C₂²×D₁₃	C₂²×C₃	semidirect
29. C₂²⋊D₁₃	C₂²×C₃	semidirect
30. C₂×Dic₁₃	C₂²×C₃	semidirect
33. C₂×C₁₃⋊C₃	C₂×D₄	semidirect
37. C₂²×C₁₃	C₃×D₄	semidirect
39. C₂²×C₁₃	C₂³×C₃	semidirect
41. C₂×D₁₃	C₂³×C₃	semidirect
42. Dic₁₃	C₂³×C₃	semidirect
47. C₁₃⋊C₃	C₂²×D₄	semidirect
50. C₂×C₁₃	C₂×C₃×D₄	semidirect
61. C₂⁴	D₁₃⋊C₃	semidirect
64. C₁₃	C₂²×C₃×D₄	semidirect
76. C₂³	C₂×D₁₃⋊C₃	semidirect
86. C₂²	(C₂²⋊D₁₃)⋊C₃	direct (N × H)
88. C₂²	C₂²×D₁₃⋊C₃	semidirect
93. C₂	C₂×(C₂²⋊D₁₃)⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₁₃⋊C₃	2
C₂³×D₁₃⋊C₃	2
C₂×(C₂²⋊D₁₃)⋊C₃	2
C₂²×Dic₁₃⋊C₃	2
C₂²×C₂²⋊D₁₃	3
C₂²×C₃×D₄	13

Subgroups — C22×(C22⋊D13)⋊C3 #11929144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×(C₂²⋊D₁₃)⋊C₃ #11929144