Subgroups — C₂×M₁₆×C₇₅₁ #37562329

Order 24032.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₇₅₁	C₂	1	1	yes	maximal, characteristic
2	M₁₆×C₇₅₁	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×C₇₅₁	C₂	1	2	yes	maximal, complemented
4	C₂³×C₇₅₁	C₄	1	1	yes	characteristic
5	C₂×C₄×C₇₅₁	C₄	1	1	yes	characteristic
6	C₂×C₄×C₇₅₁	C₄	1	2	yes	—
7	C₂×C₄×C₇₅₁	C₂²	1	2	yes	—
8	C₂×C₄×C₇₅₁	C₂²	1	1	yes	characteristic
9	C₈×C₇₅₁	C₂²	1	4	yes	complemented
10	C₂²×C₇₅₁	—	2	2	no	—
11	C₂²×C₇₅₁	C₂×C₄	1	2	yes	—
12	C₂²×C₇₅₁	C₂×C₄	1	1	yes	characteristic
13	C₄×C₇₅₁	C₂×C₄	1	2	yes	—
14	C₄×C₇₅₁	C₂×C₄	1	1	yes	characteristic
15	C₄×C₇₅₁	C₂³	1	1	yes	characteristic
16	C₂×C₇₅₁	—	2	2	no	—
17	C₂×C₇₅₁	M₁₆	1	2	yes	direct product factor
18	C₂×C₇₅₁	C₂²×C₄	1	1	yes	characteristic
19	C₇₅₁	C₂×M₁₆	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×M₁₆	C₇₅₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂²×C₄	C₂×C₇₅₁	1	1	yes	characteristic
22	M₁₆	C₂×C₇₅₁	1	4	yes	direct product factor
23	C₂×C₈	C₂×C₇₅₁	1	2	yes	complemented
24	C₂³	C₄×C₇₅₁	1	1	yes	characteristic
25	C₂×C₄	C₄×C₇₅₁	1	2	yes	—
26	C₂×C₄	C₄×C₇₅₁	1	1	yes	characteristic
27	C₂×C₄	C₂²×C₇₅₁	1	1	yes	characteristic
28	C₂×C₄	C₂²×C₇₅₁	1	2	yes	—
29	C₈	C₂²×C₇₅₁	1	4	yes	complemented
30	C₂²	—	2	2	no	—
31	C₂²	C₂×C₄×C₇₅₁	1	2	yes	—
32	C₂²	C₂×C₄×C₇₅₁	1	1	yes	characteristic
33	C₄	C₂×C₄×C₇₅₁	1	1	yes	characteristic
34	C₄	C₂×C₄×C₇₅₁	1	2	yes	—
35	C₄	C₂³×C₇₅₁	1	1	yes	characteristic
36	C₂	—	2	2	no	—
37	C₂	M₁₆×C₇₅₁	1	2	yes	direct product factor
38	C₂	C₂²×C₄×C₇₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇₅₁	C₂²
commutator	C₂	C₂²×C₄×C₇₅₁
Frattini, cosocle	C₄	C₂³×C₇₅₁
socle	C₂²×C₇₅₁	C₂×C₄
prime radical	C₂³×C₇₅₁	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇₅₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. M₁₆×C₇₅₁	C₂	direct (N × H)
3. C₂×C₈×C₇₅₁	C₂	semidirect
9. C₈×C₇₅₁	C₂²	semidirect
17. C₂×C₇₅₁	M₁₆	direct (N × H)
19. C₇₅₁	C₂×M₁₆	direct (N × H)
20. C₂×M₁₆	C₇₅₁	direct (N × H)
22. M₁₆	C₂×C₇₅₁	direct (N × H)
23. C₂×C₈	C₂×C₇₅₁	semidirect
29. C₈	C₂²×C₇₅₁	semidirect
37. C₂	M₁₆×C₇₅₁	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×C₄×C₇₅₁	2
M₁₆×C₇₅₁	2
C₂×C₈×C₇₅₁	2
C₂×M₁₆	751

Subgroups — C2×M16×C751 #37562329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×M₁₆×C₇₅₁ #37562329