Subgroups — C₂³×C₂²⋊D₃₇ #14558354

Order 2368.

1362 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂²⋊D₃₇	C₂	1	28	yes	maximal, direct product factor
3	C₂³×Dic₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁵×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁴×C₃₇	—	2	8	no	—
6	C₂⁴×C₃₇	C₂²	1	1	yes	characteristic
7	C₂⁴×C₃₇	C₂²	1	14	yes	complemented
8	C₂³×D₃₇	—	2	8	no	—
9	C₂³×D₃₇	C₂²	1	14	yes	complemented
10	C₂×C₂²⋊D₃₇	C₂²	1	112	yes	direct product factor
11	C₂²×Dic₃₇	C₂²	1	14	yes	complemented
12	C₂³×C₃₇	—	2	56	no	—
13	C₂³×C₃₇	D₄	1	8	yes	complemented
14	C₂³×C₃₇	C₂³	1	7	yes	—
15	C₂³×C₃₇	C₂³	1	28	yes	complemented
16	C₂²×D₃₇	—	2	56	no	—
17	C₂²×D₃₇	C₂³	1	28	yes	complemented
18	C₂²⋊D₃₇	C₂³	1	64	yes	direct product factor
19	C₂×Dic₃₇	C₂³	1	28	yes	complemented
20	C₂²×C₃₇	—	2	56	no	—
21	C₂²×C₃₇	C₂×D₄	1	28	yes	complemented
22	C₂²×C₃₇	C₂⁴	1	7	yes	—
23	C₂²×C₃₇	C₂⁴	1	8	yes	complemented
24	C₂×D₃₇	—	2	56	no	—
25	C₂×D₃₇	C₂⁴	1	8	yes	complemented
26	Dic₃₇	C₂⁴	1	8	yes	complemented
27	C₂×C₃₇	—	2	8	no	—
28	C₂×C₃₇	C₂²×D₄	1	14	yes	complemented
29	C₂×C₃₇	C₂⁵	1	1	yes	characteristic
30	D₃₇	—	2	8	no	—
31	C₂³×D₄	—	37	1	no	maximal, Sylow
32	C₃₇	C₂³×D₄	1	1	yes	characteristic, complemented, Sylow
33	C₂⁵	—	37	1	no	—
34	C₂⁵	D₃₇	1	1	yes	characteristic, complemented
35	C₂²×D₄	—	37	28	no	—
36	C₂³×C₄	—	37	1	no	—
37	C₂⁴	—	2	8	no	—
38	C₂⁴	—	37	14	no	—
39	C₂⁴	—	74	8	no	—
40	C₂⁴	C₂×D₃₇	1	1	yes	characteristic
41	C₂⁴	C₂×D₃₇	1	14	yes	complemented
42	C₂×D₄	—	37	112	no	—
43	C₂²×C₄	—	37	14	no	—
44	C₂³	—	2	56	no	—
45	C₂³	—	37	28	no	—
46	C₂³	—	74	56	no	—
47	C₂³	C₂²⋊D₃₇	1	8	yes	direct product factor
48	C₂³	C₂²×D₃₇	1	7	yes	—
49	C₂³	C₂²×D₃₇	1	28	yes	complemented
50	D₄	—	37	64	no	—
51	C₂×C₄	—	37	28	no	—
52	C₂²	—	2	56	no	—
53	C₂²	—	37	8	no	—
54	C₂²	—	74	56	no	—
55	C₂²	C₂×C₂²⋊D₃₇	1	28	yes	direct product factor
56	C₂²	C₂³×D₃₇	1	7	yes	—
57	C₂²	C₂³×D₃₇	1	8	yes	complemented
58	C₄	—	37	8	no	—
59	C₂	—	2	8	no	—
60	C₂	—	74	8	no	—
61	C₂	C₂²×C₂²⋊D₃₇	1	14	yes	direct product factor
62	C₂	C₂⁴×D₃₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₃₇
commutator, cosocle	C₂×C₃₇	C₂⁵
Frattini	C₂	C₂⁴×D₃₇
Fitting	C₂⁵×C₃₇	C₂
socle	C₂⁴×C₃₇	C₂²
hypercenter	C₂⁵	D₃₇
hypocenter	C₃₇	C₂³×D₄
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂⁴ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
1. C₂⁴×D₃₇	C₂	semidirect
2. C₂²×C₂²⋊D₃₇	C₂	direct (N × H)
3. C₂³×Dic₃₇	C₂	semidirect
4. C₂⁵×C₃₇	C₂	semidirect
7. C₂⁴×C₃₇	C₂²	semidirect
9. C₂³×D₃₇	C₂²	semidirect
10. C₂×C₂²⋊D₃₇	C₂²	direct (N × H)
11. C₂²×Dic₃₇	C₂²	semidirect
13. C₂³×C₃₇	D₄	semidirect
15. C₂³×C₃₇	C₂³	semidirect
17. C₂²×D₃₇	C₂³	semidirect
18. C₂²⋊D₃₇	C₂³	direct (N × H)
19. C₂×Dic₃₇	C₂³	semidirect
21. C₂²×C₃₇	C₂×D₄	semidirect
23. C₂²×C₃₇	C₂⁴	semidirect
25. C₂×D₃₇	C₂⁴	semidirect
26. Dic₃₇	C₂⁴	semidirect
28. C₂×C₃₇	C₂²×D₄	semidirect
32. C₃₇	C₂³×D₄	semidirect
34. C₂⁵	D₃₇	semidirect
41. C₂⁴	C₂×D₃₇	semidirect
47. C₂³	C₂²⋊D₃₇	direct (N × H)
49. C₂³	C₂²×D₃₇	semidirect
55. C₂²	C₂×C₂²⋊D₃₇	direct (N × H)
57. C₂²	C₂³×D₃₇	semidirect
61. C₂	C₂²×C₂²⋊D₃₇	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×D₃₇	2
C₂²×C₂²⋊D₃₇	2
C₂³×Dic₃₇	2
C₂⁵×C₃₇	2
C₂³×D₄	37

Subgroups — C23×C22⋊D37 #14558354

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₂²⋊D₃₇ #14558354