Subgroups — C₃₂×Dic₄₃ #19132726

Order 5504.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₆×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₃⋊C₁₆	C₄	1	1	yes	characteristic
5	C₈×Dic₄₃	C₄	1	1	yes	characteristic
6	C₄₃⋊C₃₂	C₄	1	2	yes	complemented
7	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
8	C₃₂×C₄₃	C₄	1	2	yes	complemented
9	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
10	C₄×Dic₄₃	C₈	1	1	yes	characteristic
11	C₂×C₄₃⋊C₈	C₈	1	1	yes	characteristic
12	C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
13	C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
14	C₄₃⋊C₁₆	C₈	1	2	yes	—
15	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
16	C₂×Dic₄₃	C₁₆	1	2	yes	—
17	C₈×C₄₃	C₄²	1	1	yes	characteristic
18	C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
19	C₄₃⋊C₈	C₁₆	1	2	yes	—
20	C₂²×C₄₃	C₂×C₁₆	1	1	yes	characteristic
21	C₄×C₄₃	C₄×C₈	1	1	yes	characteristic
22	C₄×C₄₃	C₂×C₁₆	1	1	yes	characteristic
23	Dic₄₃	C₃₂	1	4	yes	direct product factor
24	C₄×C₃₂	—	43	1	no	maximal, Sylow
25	C₂×C₄₃	C₄×C₁₆	1	1	yes	characteristic
26	C₂×C₄₃	C₂×C₃₂	1	2	yes	—
27	C₂×C₃₂	—	43	1	no	—
28	C₂×C₃₂	D₄₃	1	1	yes	characteristic
29	C₄×C₁₆	—	43	1	no	—
30	C₄₃	C₄×C₃₂	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₁₆	—	43	1	no	—
32	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
33	C₄×C₈	—	43	1	no	—
34	C₃₂	—	43	2	no	—
35	C₃₂	Dic₄₃	1	2	yes	direct product factor
36	C₂×C₈	—	43	1	no	—
37	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
38	C₄²	—	43	1	no	—
39	C₁₆	—	43	2	no	—
40	C₁₆	C₄×D₄₃	1	1	yes	characteristic
41	C₁₆	C₂×Dic₄₃	1	1	yes	characteristic
42	C₂×C₄	—	43	2	no	—
43	C₂×C₄	C₈×D₄₃	1	1	yes	characteristic
44	C₈	—	43	2	no	—
45	C₈	C₈×D₄₃	1	1	yes	characteristic
46	C₈	C₄×Dic₄₃	1	1	yes	characteristic
47	C₂²	C₁₆×D₄₃	1	1	yes	characteristic
48	C₄	—	43	4	no	—
49	C₄	C₈×Dic₄₃	1	1	yes	characteristic
50	C₄	C₁₆×D₄₃	1	1	yes	characteristic
51	C₂	C₁₆×Dic₄₃	1	1	yes	characteristic
52	C₂	C₃₂×D₄₃	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₃₂	D₄₃
commutator, hypocenter	C₄₃	C₄×C₃₂
Frattini	C₂×C₁₆	C₂×D₄₃
Fitting	C₂×C₃₂×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₁₆
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
6. C₄₃⋊C₃₂	C₄	semidirect
8. C₃₂×C₄₃	C₄	semidirect
23. Dic₄₃	C₃₂	direct (N × H)
30. C₄₃	C₄×C₃₂	semidirect
35. C₃₂	Dic₄₃	direct (N × H)

Subgroups — C32×Dic43 #19132726

Conjugacy classes of subgroups

Complements

Subgroups — C₃₂×Dic₄₃ #19132726