Subgroups — #24984495

Order 11008.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19132806	C₂	1	2	yes	maximal
2	C₄×C₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₄₃⋊C₆₄	—	2	2	no	—
4	C₂×C₃₂×C₄₃	C₄	1	1	yes	characteristic
5	C₂×C₃₂×C₄₃	C₂²	1	1	yes	characteristic
6	C₄×C₁₆×C₄₃	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₄₃	C₈	1	1	yes	characteristic
8	C₂×C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
9	C₄×C₈×C₄₃	C₈	1	1	yes	characteristic
10	C₃₂×C₄₃	—	2	1	no	—
11	C₃₂×C₄₃	D₄	1	1	yes	characteristic
12	C₃₂×C₄₃	Q₈	1	1	yes	characteristic
13	C₂×C₈×C₄₃	C₁₆	1	1	yes	characteristic
14	C₂×C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
15	C₄²×C₄₃	C₁₆	1	1	yes	characteristic
16	C₁₆×C₄₃	—	2	1	no	—
17	C₁₆×C₄₃	C₄⋊C₄	1	1	yes	characteristic
18	C₁₆×C₄₃	M₁₆	1	1	yes	characteristic
19	C₂×C₄×C₄₃	—	2	1	no	—
20	C₂×C₄×C₄₃	C₂×C₁₆	1	1	yes	characteristic
21	C₈×C₄₃	C₃₂	1	2	yes	—
22	C₈×C₄₃	C₄⋊C₈	1	1	yes	characteristic
23	C₈×C₄₃	M₃₂	1	1	yes	characteristic
24	#7544	—	43	1	no	maximal, Sylow
25	C₂²×C₄₃	M₆₄	1	1	yes	characteristic
26	C₄×C₄₃	—	2	2	no	—
27	C₄×C₄₃	C₄⋊C₁₆	1	1	yes	characteristic
28	C₄×C₄₃	C₂×C₃₂	1	1	yes	characteristic
29	M₁₂₈	—	43	2	no	—
30	C₄×C₃₂	D₄₃	1	1	yes	characteristic
31	C₂×C₄₃	—	2	1	no	—
32	C₂×C₄₃	C₄⋊C₃₂	1	1	yes	characteristic
33	C₂×C₃₂	Dic₄₃	1	1	yes	characteristic
34	C₂×C₃₂	C₂×D₄₃	1	1	yes	characteristic
35	C₄×C₁₆	Dic₄₃	1	1	yes	characteristic
36	C₆₄	—	86	2	no	—
37	C₄₃	#7544	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₁₆	C₄₃⋊C₈	1	1	yes	characteristic
39	C₂×C₁₆	C₂×Dic₄₃	1	1	yes	characteristic
40	C₄×C₈	C₄₃⋊C₈	1	1	yes	characteristic
41	C₃₂	—	2	1	no	—
42	C₃₂	Dic₈₆	1	1	yes	characteristic
43	C₃₂	D₁₇₂	1	1	yes	characteristic
44	C₂×C₈	C₄₃⋊C₁₆	1	1	yes	characteristic
45	C₂×C₈	C₂×C₄₃⋊C₈	1	1	yes	characteristic
46	C₄²	C₄₃⋊C₁₆	1	1	yes	characteristic
47	C₁₆	—	2	1	no	—
48	C₁₆	#10621877	1	1	yes	characteristic
49	C₁₆	C₄⋊Dic₄₃	1	1	yes	characteristic
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	C₂×C₄₃⋊C₁₆	1	1	yes	characteristic
52	C₈	C₄₃⋊C₃₂	1	2	yes	—
53	C₈	C₄⋊(C₄₃⋊C₈)	1	1	yes	characteristic
54	C₈	#13063265	1	1	yes	characteristic
55	C₂²	#14582733	1	1	yes	characteristic
56	C₄	—	2	2	no	—
57	C₄	C₄⋊(C₄₃⋊C₁₆)	1	1	yes	characteristic
58	C₄	C₂×C₄₃⋊C₃₂	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	C₄⋊(C₄₃⋊C₃₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₃₂	D₁₇₂
commutator	C₄×C₄₃	C₂×C₃₂
Frattini	C₂×C₃₂	C₂×D₄₃
Fitting	C₄×C₃₂×C₄₃	C₂
socle	C₂×C₄₃	C₄⋊C₃₂
prime radical	C₂²×C₄₃	M₆₄
cosocle	C₂×C₃₂×C₄₃	C₂²
hypercenter	C₄×C₃₂	D₄₃
hypocenter	C₄₃	#7544
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃₂ ◁ C₂×C₃₂ ◁ C₄×C₃₂

Complements

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

N	H ≅ G/N	type
37. 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
C₄×C₃₂×C₄₃	2
#7544	43