Subgroups — C₂²×#64601 #11929237

Order 1248.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₃×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#64601	C₂	1	12	yes	maximal, direct product factor
5	C₂²×C₄×D₁₃	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×D₃₉	C₄	1	8	yes	complemented
8	C₂²×D₃₉	C₂²	1	6	yes	—
9	C₂×Dic₃×C₁₃	C₂²	1	6	yes	complemented
10	C₂×C₃×Dic₁₃	C₂²	1	6	yes	complemented
11	#64601	C₂²	1	16	yes	direct product factor
12	C₂³×D₁₃	—	3	1	no	—
13	C₂²×C₄×C₁₃	—	3	1	no	—
14	C₂²×Dic₁₃	D₃	1	1	yes	characteristic, complemented
15	C₂×C₄×D₁₃	—	3	12	no	—
16	C₂²×C₃×C₁₃	C₂×C₄	1	4	yes	complemented
17	C₂²×C₃×C₁₃	C₂³	1	3	yes	—
18	C₂×D₃₉	C₂×C₄	1	24	yes	complemented
19	C₂×D₃₉	C₂³	1	4	yes	—
20	C₃×Dic₁₃	C₂³	1	4	yes	complemented
21	Dic₃×C₁₃	C₂³	1	4	yes	complemented
22	C₂³×C₁₃	C₂×D₃	1	1	yes	characteristic
23	C₂²×D₁₃	—	3	8	no	—
24	C₂²×D₁₃	—	3	6	no	—
25	C₂×C₄×C₁₃	—	3	6	no	—
26	C₂×Dic₁₃	C₂×D₃	1	6	yes	complemented
27	C₄×D₁₃	—	3	16	no	—
28	C₂²×C₄×D₃	—	13	1	no	maximal, Hall
29	C₂×C₃×C₁₃	C₂²×C₄	1	6	yes	complemented
30	C₂×C₃×C₁₃	C₂⁴	1	1	yes	characteristic
31	D₃₉	C₂²×C₄	1	8	yes	complemented
32	C₂²×C₁₃	C₄×D₃	1	4	yes	complemented
33	C₂²×C₁₃	C₂²×D₃	1	3	yes	—
34	C₂×D₁₃	—	3	24	no	—
35	C₂×D₁₃	—	3	4	no	—
36	C₄×C₁₃	—	3	4	no	—
37	Dic₁₃	C₂²×D₃	1	4	yes	complemented
38	C₂³×D₃	—	13	1	no	—
39	C₂²×C₃×C₄	—	13	1	no	—
40	C₂²×Dic₃	D₁₃	1	1	yes	characteristic, complemented
41	C₂×C₄×D₃	—	13	12	no	—
42	C₃×C₁₃	C₂³×C₄	1	1	yes	characteristic, complemented, Hall
43	C₂³×C₄	—	39	1	no	Sylow
44	C₂×C₁₃	C₂×C₄×D₃	1	6	yes	complemented
45	C₂×C₁₃	C₂³×D₃	1	1	yes	characteristic
46	D₁₃	—	3	8	no	—
47	C₂³×C₃	C₂×D₁₃	1	1	yes	characteristic
48	C₂²×D₃	—	13	8	no	—
49	C₂²×D₃	—	13	6	no	—
50	C₂×C₃×C₄	—	13	6	no	—
51	C₂×Dic₃	C₂×D₁₃	1	6	yes	complemented
52	C₄×D₃	—	13	16	no	—
53	C₂⁴	—	39	1	no	—
54	C₂²×C₄	—	3	1	no	—
55	C₂²×C₄	—	13	1	no	—
56	C₂²×C₄	—	39	12	no	—
57	C₁₃	C₂²×C₄×D₃	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₃	C₄×D₁₃	1	4	yes	complemented
59	C₂²×C₃	C₂²×D₁₃	1	3	yes	—
60	C₂×D₃	—	13	24	no	—
61	C₂×D₃	—	13	4	no	—
62	C₃×C₄	—	13	4	no	—
63	Dic₃	C₂²×D₁₃	1	4	yes	complemented
64	C₂³	—	39	8	no	—
65	C₂³	—	39	6	no	—
66	C₂³	D₃×D₁₃	1	1	yes	characteristic
67	C₂×C₄	—	3	6	no	—
68	C₂×C₄	—	13	6	no	—
69	C₂×C₄	—	39	16	no	—
70	C₂×C₃	C₂×C₄×D₁₃	1	6	yes	complemented
71	C₂×C₃	C₂³×D₁₃	1	1	yes	characteristic
72	D₃	—	13	8	no	—
73	C₂²	—	39	24	no	—
74	C₂²	—	39	4	no	—
75	C₂²	#64601	1	4	yes	direct product factor
76	C₂²	C₂×D₃×D₁₃	1	3	yes	—
77	C₄	—	3	4	no	—
78	C₄	—	13	4	no	—
79	C₃	C₂²×C₄×D₁₃	1	1	yes	characteristic, complemented, Sylow
80	C₂	—	39	8	no	—
81	C₂	C₂×#64601	1	6	yes	direct product factor
82	C₂	C₂²×D₃×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³	D₃×D₁₃
commutator, hypocenter	C₃×C₁₃	C₂³×C₄
Frattini	C₂	C₂²×D₃×D₁₃
Fitting, socle	C₂³×C₃×C₁₃	C₂²
prime radical	C₂³×D₃₉	C₂
cosocle	C₂×C₃×C₁₃	C₂⁴
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₂³

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₃×C₁₃	C₂	semidirect
3. C₂²×C₃×Dic₁₃	C₂	semidirect
4. C₂×#64601	C₂	direct (N × H)
7. C₂²×D₃₉	C₄	semidirect
9. C₂×Dic₃×C₁₃	C₂²	semidirect
10. C₂×C₃×Dic₁₃	C₂²	semidirect
11. #64601	C₂²	direct (N × H)
14. C₂²×Dic₁₃	D₃	semidirect
16. C₂²×C₃×C₁₃	C₂×C₄	semidirect
18. C₂×D₃₉	C₂×C₄	semidirect
20. C₃×Dic₁₃	C₂³	semidirect
21. Dic₃×C₁₃	C₂³	semidirect
26. C₂×Dic₁₃	C₂×D₃	semidirect
29. C₂×C₃×C₁₃	C₂²×C₄	semidirect
31. D₃₉	C₂²×C₄	semidirect
32. C₂²×C₁₃	C₄×D₃	semidirect
37. Dic₁₃	C₂²×D₃	semidirect
40. C₂²×Dic₃	D₁₃	semidirect
42. C₃×C₁₃	C₂³×C₄	semidirect
44. C₂×C₁₃	C₂×C₄×D₃	semidirect
51. C₂×Dic₃	C₂×D₁₃	semidirect
57. C₁₃	C₂²×C₄×D₃	semidirect
58. C₂²×C₃	C₄×D₁₃	semidirect
63. Dic₃	C₂²×D₁₃	semidirect
70. C₂×C₃	C₂×C₄×D₁₃	semidirect
75. C₂²	#64601	direct (N × H)
79. C₃	C₂²×C₄×D₁₃	semidirect
81. C₂	C₂×#64601	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₃₉	2
C₂²×Dic₃×C₁₃	2
C₂²×C₃×Dic₁₃	2
C₂×#64601	2
C₂²×C₄×D₁₃	3
C₂²×C₄×D₃	13

Subgroups — C22×#64601 #11929237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#64601 #11929237