Subgroups — #24984494

Order 11008.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19132806	C₂	1	1	yes	maximal, characteristic
2	C₃₂×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	C₄₃×M₁₂₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₃⋊C₃₂	C₄	1	1	yes	characteristic
5	C₁₆×Dic₄₃	C₄	1	1	yes	characteristic
6	C₄₃⋊C₆₄	—	2	1	no	—
7	C₂×C₃₂×C₄₃	C₂²	1	1	yes	characteristic
8	C₄₃×C₆₄	—	2	1	no	—
9	C₂×C₄₃⋊C₁₆	C₈	1	1	yes	characteristic
10	C₈×Dic₄₃	C₈	1	1	yes	characteristic
11	C₄₃⋊C₃₂	—	2	1	no	—
12	C₂×C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
13	C₃₂×C₄₃	D₄	1	1	yes	characteristic
14	C₃₂×C₄₃	Q₈	1	1	yes	characteristic
15	C₂×C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
16	C₄×Dic₄₃	C₁₆	1	1	yes	characteristic
17	C₂×C₄₃⋊C₈	C₁₆	1	1	yes	characteristic
18	C₁₆×C₄₃	C₄⋊C₄	1	1	yes	characteristic
19	C₁₆×C₄₃	M₁₆	1	1	yes	characteristic
20	C₄₃⋊C₁₆	—	2	1	no	—
21	C₂×C₄×C₄₃	C₂×C₁₆	1	1	yes	characteristic
22	C₂×Dic₄₃	—	2	1	no	—
23	C₈×C₄₃	C₄⋊C₈	1	1	yes	characteristic
24	C₈×C₄₃	M₃₂	1	1	yes	characteristic
25	C₄₃⋊C₈	C₃₂	1	2	yes	—
26	#7544	—	43	1	no	maximal, Sylow
27	C₂²×C₄₃	M₆₄	1	1	yes	characteristic
28	C₄×C₄₃	C₄⋊C₁₆	1	1	yes	characteristic
29	C₄×C₄₃	C₂×C₃₂	1	1	yes	characteristic
30	Dic₄₃	—	2	2	no	—
31	M₁₂₈	—	43	1	no	—
32	M₁₂₈	D₄₃	1	1	yes	characteristic
33	C₄×C₃₂	—	43	1	no	—
34	C₂×C₄₃	—	2	1	no	—
35	C₂×C₄₃	C₄⋊C₃₂	1	1	yes	characteristic
36	C₂×C₃₂	—	43	1	no	—
37	C₂×C₃₂	C₂×D₄₃	1	1	yes	characteristic
38	C₄×C₁₆	—	43	1	no	—
39	C₆₄	—	2	1	no	—
40	C₆₄	—	86	1	no	—
41	C₄₃	#7544	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₁₆	—	43	1	no	—
43	C₂×C₁₆	C₄×D₄₃	1	1	yes	characteristic
44	C₄×C₈	—	43	1	no	—
45	C₃₂	—	86	1	no	—
46	C₃₂	Dic₈₆	1	1	yes	characteristic
47	C₃₂	C₂²⋊D₄₃	1	1	yes	characteristic
48	C₂×C₈	—	43	1	no	—
49	C₂×C₈	C₈×D₄₃	1	1	yes	characteristic
50	C₄²	—	43	1	no	—
51	C₁₆	—	86	1	no	—
52	C₁₆	#10621872	1	1	yes	characteristic
53	C₁₆	Dic₄₃⋊C₄	1	1	yes	characteristic
54	C₂×C₄	—	86	1	no	—
55	C₂×C₄	C₁₆×D₄₃	1	1	yes	characteristic
56	C₈	—	43	2	no	—
57	C₈	Dic₄₃⋊C₈	1	1	yes	characteristic
58	C₈	#13063264	1	1	yes	characteristic
59	C₂²	#14582732	1	1	yes	characteristic
60	C₄	—	86	2	no	—
61	C₄	Dic₄₃⋊C₁₆	1	1	yes	characteristic
62	C₄	C₃₂×D₄₃	1	1	yes	characteristic
63	C₂	—	2	1	no	—
64	C₂	Dic₄₃⋊C₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₃₂	C₂²⋊D₄₃
commutator	C₄×C₄₃	C₂×C₃₂
Frattini	C₂×C₃₂	C₂×D₄₃
Fitting	C₄₃×M₁₂₈	C₂
socle	C₂×C₄₃	C₄⋊C₃₂
prime radical	C₂²×C₄₃	M₆₄
cosocle	C₂×C₃₂×C₄₃	C₂²
hypercenter	M₁₂₈	D₄₃
hypocenter	C₄₃	#7544
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃₂ ◁ C₂×C₃₂ ◁ M₁₂₈

Complements

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

N	H ≅ G/N	type
41. C₄₃	#7544	semidirect

Maximal subgroups

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

subgroup	index
#19132806	2
C₃₂×Dic₄₃	2
C₄₃×M₁₂₈	2
#7544	43