Subgroups — #24984503

Order 11008.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19132799	C₂	1	1	yes	maximal, characteristic
2	#19132797	C₂	1	1	yes	maximal, characteristic
3	C₄₃×M₁₂₈	C₂	1	1	yes	maximal, characteristic
4	#14582729	—	2	1	no	—
5	#14582725	—	2	1	no	—
6	C₂×C₃₂×C₄₃	C₂²	1	1	yes	characteristic
7	C₄₃×C₆₄	C₄	1	2	yes	complemented
8	#13063261	—	4	1	no	—
9	#13063259	—	4	1	no	—
10	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
11	C₃₂×C₄₃	C₂×C₄	1	1	yes	characteristic
12	C₃₂×C₄₃	Q₈	1	1	yes	characteristic
13	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
14	C₄⋊Dic₄₃	—	8	1	no	—
15	#10621877	—	8	1	no	—
16	C₁₆×C₄₃	C₄⋊C₄	1	1	yes	characteristic
17	C₁₆×C₄₃	Q₁₆	1	1	yes	characteristic
18	C₂×C₄×C₄₃	D₁₆	1	1	yes	characteristic
19	C₂×Dic₄₃	—	16	1	no	—
20	C₈×C₄₃	#107	1	1	yes	characteristic
21	C₈×C₄₃	Q₃₂	1	1	yes	characteristic
22	C₄₃⋊C₈	—	16	1	no	—
23	#7548	—	43	1	no	maximal, Sylow
24	C₂²×C₄₃	SD₆₄	1	1	yes	characteristic
25	C₄×C₄₃	#366	1	1	yes	characteristic
26	C₄×C₄₃	SD₆₄	1	1	yes	characteristic
27	Dic₄₃	—	32	1	no	—
28	M₁₂₈	D₄₃	1	1	yes	characteristic
29	#1425	—	43	1	no	—
30	#1424	—	43	1	no	—
31	C₂×C₄₃	—	2	1	no	—
32	C₂×C₄₃	#1424	1	1	yes	characteristic
33	C₂×C₃₂	C₂×D₄₃	1	1	yes	characteristic
34	#368	—	86	1	no	—
35	#366	—	86	1	no	—
36	C₆₄	Dic₄₃	1	2	yes	complemented
37	C₄₃	#7548	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₁₆	D₁₇₂	1	1	yes	characteristic
39	#108	—	172	1	no	—
40	#107	—	172	1	no	—
41	C₃₂	Dic₈₆	1	1	yes	characteristic
42	C₃₂	C₂×Dic₄₃	1	1	yes	characteristic
43	M₁₆	—	344	1	no	—
44	C₂×C₈	D₃₄₄	1	1	yes	characteristic
45	C₄⋊C₄	—	344	1	no	—
46	C₁₆	Dic₁₇₂	1	1	yes	characteristic
47	C₁₆	C₄⋊Dic₄₃	1	1	yes	characteristic
48	C₂×C₄	—	688	1	no	—
49	C₂×C₄	D₆₈₈	1	1	yes	characteristic
50	C₈	—	688	1	no	—
51	C₈	#13063259	1	1	yes	characteristic
52	C₈	Dic₃₄₄	1	1	yes	characteristic
53	C₂²	#14582738	1	1	yes	characteristic
54	C₄	—	1376	1	no	—
55	C₄	#14582725	1	1	yes	characteristic
56	C₄	#14582738	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	#19132797	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19132797
commutator	C₃₂×C₄₃	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₄₃
Fitting	C₄₃×M₁₂₈	C₂
socle	C₂×C₄₃	#1424
prime radical	C₂²×C₄₃	SD₆₄
cosocle	C₂×C₃₂×C₄₃	C₂²
hypercenter	M₁₂₈	D₄₃
hypocenter	C₄₃	#7548
LCS	G ▷ C₃₂×C₄₃ ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ M₁₂₈

Complements

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

N	H ≅ G/N	type
7. C₄₃×C₆₄	C₄	semidirect
36. C₆₄	Dic₄₃	semidirect
37. C₄₃	#7548	semidirect

Maximal subgroups

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

subgroup	index
#19132799	2
#19132797	2
C₄₃×M₁₂₈	2
#7548	43