Subgroups — #24984266

Order 11008.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19132731	C₂	1	1	yes	maximal, characteristic
2	#19132663	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1368	C₂	1	1	yes	maximal, characteristic
4	#14582733	C₄	1	1	yes	characteristic
5	#14582733	C₄	1	1	yes	characteristic
6	#14582720	—	2	1	no	—
7	C₄₃×#346	C₂²	1	1	yes	characteristic
8	C₄₃×#334	—	2	1	no	—
9	#13063265	—	4	1	no	—
10	C₄₃⋊C₃₂	—	2	1	no	—
11	C₄₃⋊C₃₂	C₈	1	2	yes	complemented
12	C₂×C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₁₆×C₄₃	Q₈	1	1	yes	characteristic
14	C₄⋊C₈×C₄₃	—	4	1	no	—
15	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
16	C₂×C₈×C₄₃	—	8	1	no	—
17	C₂×C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₈×C₄₃	SD₁₆	1	1	yes	characteristic
19	C₄²×C₄₃	SD₁₆	1	1	yes	characteristic
20	C₁₆×C₄₃	—	2	1	no	—
21	C₁₆×C₄₃	C₂×C₈	1	1	yes	characteristic
22	C₁₆×C₄₃	M₁₆	1	1	yes	characteristic
23	C₄₃⋊C₁₆	—	8	1	no	—
24	C₂×C₄×C₄₃	—	2	1	no	—
25	C₂×C₄×C₄₃	#106	1	1	yes	characteristic
26	C₈×C₄₃	—	2	1	no	—
27	C₈×C₄₃	—	16	1	no	—
28	C₈×C₄₃	C₄⋊C₈	1	1	yes	characteristic
29	C₈×C₄₃	#108	1	1	yes	characteristic
30	#7457	—	43	1	no	maximal, Sylow
31	C₂²×C₄₃	#365	1	1	yes	characteristic
32	C₄×C₄₃	—	4	1	no	—
33	C₄×C₄₃	#334	1	1	yes	characteristic
34	C₄×C₄₃	#365	1	1	yes	characteristic
35	#1398	—	43	1	no	—
36	#1369	—	43	1	no	—
37	#1368	D₄₃	1	1	yes	characteristic
38	C₂×C₄₃	—	2	1	no	—
39	C₂×C₄₃	#1368	1	1	yes	characteristic
40	M₆₄	—	43	1	no	—
41	M₆₄	—	43	1	no	—
42	#364	—	86	1	no	—
43	#346	C₂×D₄₃	1	1	yes	characteristic
44	#334	—	2	1	no	—
45	C₄₃	#7457	1	1	yes	characteristic, complemented, Sylow
46	M₃₂	—	172	1	no	—
47	C₂×C₁₆	Dic₈₆	1	1	yes	characteristic
48	C₂×C₁₆	C₄×D₄₃	1	1	yes	characteristic
49	C₄⋊C₈	—	4	1	no	—
50	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
51	C₃₂	—	43	2	no	—
52	C₃₂	—	86	1	no	—
53	C₂×C₈	—	8	1	no	—
54	C₂×C₈	Dic₄₃⋊C₄	1	1	yes	characteristic
55	C₂×C₈	#10621884	1	1	yes	characteristic
56	C₄²	#10621883	1	1	yes	characteristic
57	C₁₆	—	2	1	no	—
58	C₁₆	—	344	1	no	—
59	C₁₆	C₈×D₄₃	1	1	yes	characteristic
60	C₁₆	#10621872	1	1	yes	characteristic
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	#13063256	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	16	1	no	—
65	C₈	Dic₄₃⋊C₈	1	1	yes	characteristic
66	C₈	#13063260	1	1	yes	characteristic
67	C₂²	#14582721	1	1	yes	characteristic
68	C₄	—	4	1	no	—
69	C₄	#14582649	1	1	yes	characteristic
70	C₄	#14582723	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#19132660	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19132660
commutator	C₁₆×C₄₃	C₂×C₈
Frattini	#346	C₂×D₄₃
Fitting	C₄₃×#1368	C₂
socle	C₂×C₄₃	#1368
prime radical	C₂²×C₄₃	#365
cosocle	C₄₃×#346	C₂²
hypercenter	#1368	D₄₃
hypocenter	C₄₃	#7457
LCS	G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #346 ◁ #1368

Complements

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

N	H ≅ G/N	type
11. C₄₃⋊C₃₂	C₈	semidirect
45. C₄₃	#7457	semidirect

Maximal subgroups

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

subgroup	index
#19132731	2
#19132663	2
C₄₃×#1368	2
#7457	43