Subgroups — C₂⁴×C₁₆×C₃₇ #22683873

Order 9472.

2590 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₈×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₁₆×C₃₇	C₂	1	30	yes	maximal, direct product factor
3	C₂⁴×C₄×C₃₇	C₄	1	1	yes	characteristic
4	C₂³×C₈×C₃₇	C₄	1	15	yes	—
5	C₂³×C₈×C₃₇	C₂²	1	15	yes	—
6	C₂²×C₁₆×C₃₇	C₂²	1	140	yes	direct product factor
7	C₂⁵×C₃₇	C₈	1	1	yes	characteristic
8	C₂³×C₄×C₃₇	C₈	1	15	yes	—
9	C₂³×C₄×C₃₇	C₂×C₄	1	15	yes	—
10	C₂²×C₈×C₃₇	C₂×C₄	1	105	yes	—
11	C₂²×C₈×C₃₇	C₂³	1	35	yes	—
12	C₂×C₁₆×C₃₇	C₂³	1	120	yes	direct product factor
13	C₂⁴×C₃₇	C₁₆	1	16	yes	direct product factor
14	C₂⁴×C₃₇	C₂×C₈	1	15	yes	—
15	C₂²×C₄×C₃₇	C₂×C₈	1	105	yes	—
16	C₂²×C₄×C₃₇	C₂²×C₄	1	35	yes	—
17	C₂×C₈×C₃₇	C₂²×C₄	1	105	yes	—
18	C₂×C₈×C₃₇	C₂⁴	1	15	yes	—
19	C₁₆×C₃₇	C₂⁴	1	16	yes	direct product factor
20	C₂³×C₃₇	C₂×C₁₆	1	120	yes	direct product factor
21	C₂³×C₃₇	C₂²×C₈	1	35	yes	—
22	C₂×C₄×C₃₇	C₂²×C₈	1	105	yes	—
23	C₂×C₄×C₃₇	C₂³×C₄	1	15	yes	—
24	C₈×C₃₇	C₂³×C₄	1	15	yes	—
25	C₈×C₃₇	C₂⁵	1	1	yes	characteristic
26	C₂⁴×C₁₆	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂²×C₃₇	C₂²×C₁₆	1	140	yes	direct product factor
28	C₂²×C₃₇	C₂³×C₈	1	15	yes	—
29	C₄×C₃₇	C₂³×C₈	1	15	yes	—
30	C₄×C₃₇	C₂⁴×C₄	1	1	yes	characteristic
31	C₂⁴×C₈	C₂×C₃₇	1	1	yes	characteristic
32	C₂³×C₁₆	C₂×C₃₇	1	30	yes	direct product factor
33	C₂×C₃₇	C₂³×C₁₆	1	30	yes	direct product factor
34	C₂×C₃₇	C₂⁴×C₈	1	1	yes	characteristic
35	C₂⁴×C₄	C₄×C₃₇	1	1	yes	characteristic
36	C₂³×C₈	C₄×C₃₇	1	15	yes	—
37	C₂³×C₈	C₂²×C₃₇	1	15	yes	—
38	C₂²×C₁₆	C₂²×C₃₇	1	140	yes	direct product factor
39	C₃₇	C₂⁴×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
40	C₂⁵	C₈×C₃₇	1	1	yes	characteristic
41	C₂³×C₄	C₈×C₃₇	1	15	yes	—
42	C₂³×C₄	C₂×C₄×C₃₇	1	15	yes	—
43	C₂²×C₈	C₂×C₄×C₃₇	1	105	yes	—
44	C₂²×C₈	C₂³×C₃₇	1	35	yes	—
45	C₂×C₁₆	C₂³×C₃₇	1	120	yes	direct product factor
46	C₂⁴	C₁₆×C₃₇	1	16	yes	direct product factor
47	C₂⁴	C₂×C₈×C₃₇	1	15	yes	—
48	C₂²×C₄	C₂×C₈×C₃₇	1	105	yes	—
49	C₂²×C₄	C₂²×C₄×C₃₇	1	35	yes	—
50	C₂×C₈	C₂²×C₄×C₃₇	1	105	yes	—
51	C₂×C₈	C₂⁴×C₃₇	1	15	yes	—
52	C₁₆	C₂⁴×C₃₇	1	16	yes	direct product factor
53	C₂³	C₂×C₁₆×C₃₇	1	120	yes	direct product factor
54	C₂³	C₂²×C₈×C₃₇	1	35	yes	—
55	C₂×C₄	C₂²×C₈×C₃₇	1	105	yes	—
56	C₂×C₄	C₂³×C₄×C₃₇	1	15	yes	—
57	C₈	C₂³×C₄×C₃₇	1	15	yes	—
58	C₈	C₂⁵×C₃₇	1	1	yes	characteristic
59	C₂²	C₂²×C₁₆×C₃₇	1	140	yes	direct product factor
60	C₂²	C₂³×C₈×C₃₇	1	15	yes	—
61	C₄	C₂³×C₈×C₃₇	1	15	yes	—
62	C₄	C₂⁴×C₄×C₃₇	1	1	yes	characteristic
63	C₂	C₂³×C₁₆×C₃₇	1	30	yes	direct product factor
64	C₂	C₂⁴×C₈×C₃₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini	C₈	C₂⁵×C₃₇
socle	C₂⁵×C₃₇	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₁₆×C₃₇	C₂	direct (N × H)
6. C₂²×C₁₆×C₃₇	C₂²	direct (N × H)
12. C₂×C₁₆×C₃₇	C₂³	direct (N × H)
13. C₂⁴×C₃₇	C₁₆	direct (N × H)
19. C₁₆×C₃₇	C₂⁴	direct (N × H)
20. C₂³×C₃₇	C₂×C₁₆	direct (N × H)
26. C₂⁴×C₁₆	C₃₇	direct (N × H)
27. C₂²×C₃₇	C₂²×C₁₆	direct (N × H)
32. C₂³×C₁₆	C₂×C₃₇	direct (N × H)
33. C₂×C₃₇	C₂³×C₁₆	direct (N × H)
38. C₂²×C₁₆	C₂²×C₃₇	direct (N × H)
39. C₃₇	C₂⁴×C₁₆	direct (N × H)
45. C₂×C₁₆	C₂³×C₃₇	direct (N × H)
46. C₂⁴	C₁₆×C₃₇	direct (N × H)
52. C₁₆	C₂⁴×C₃₇	direct (N × H)
53. C₂³	C₂×C₁₆×C₃₇	direct (N × H)
59. C₂²	C₂²×C₁₆×C₃₇	direct (N × H)
63. C₂	C₂³×C₁₆×C₃₇	direct (N × H)

Subgroups — C24×C16×C37 #22683873

Conjugacy classes of subgroups

Complements

Subgroups — C₂⁴×C₁₆×C₃₇ #22683873