Subgroups — #24984500

Order 11008.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃⋊C₆₄	C₂	1	1	yes	maximal, characteristic
2	#19132799	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1425	C₂	1	1	yes	maximal, characteristic
4	#14582729	—	2	1	no	—
5	C₄₃⋊C₆₄	C₄	1	2	yes	—
6	C₂×C₃₂×C₄₃	C₂²	1	1	yes	characteristic
7	C₄₃×#368	—	2	1	no	—
8	#13063261	—	4	1	no	—
9	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
10	#108×C₄₃	—	4	1	no	—
11	C₃₂×C₄₃	C₂×C₄	1	1	yes	characteristic
12	C₃₂×C₄₃	Q₈	1	1	yes	characteristic
13	M₁₆×C₄₃	—	8	1	no	—
14	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
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	C₈×C₄₃	—	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	#7547	—	43	1	no	maximal, Sylow
24	C₂²×C₄₃	Q₆₄	1	1	yes	characteristic
25	C₄×C₄₃	#366	1	1	yes	characteristic
26	C₄×C₄₃	D₃₂	1	1	yes	characteristic
27	C₂×C₆₄	—	43	1	no	—
28	#1425	—	43	1	no	—
29	#1425	D₄₃	1	1	yes	characteristic
30	C₂×C₄₃	—	2	1	no	—
31	C₂×C₄₃	#1423	1	1	yes	characteristic
32	C₂×C₃₂	C₂×D₄₃	1	1	yes	characteristic
33	#368	—	2	1	no	—
34	#368	—	86	1	no	—
35	C₆₄	—	43	2	no	—
36	C₄₃	#7547	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
38	#108	—	4	1	no	—
39	#108	—	172	1	no	—
40	C₃₂	Dic₈₆	1	1	yes	characteristic
41	C₃₂	C₄×D₄₃	1	1	yes	characteristic
42	M₁₆	—	8	1	no	—
43	M₁₆	—	344	1	no	—
44	C₂×C₈	#10621882	1	1	yes	characteristic
45	C₁₆	Dic₄₃⋊C₄	1	1	yes	characteristic
46	C₁₆	#10621885	1	1	yes	characteristic
47	C₂×C₄	#13063266	1	1	yes	characteristic
48	C₈	—	16	1	no	—
49	C₈	—	688	1	no	—
50	C₈	#13063258	1	1	yes	characteristic
51	C₈	#13063271	1	1	yes	characteristic
52	C₂²	#14582739	1	1	yes	characteristic
53	C₄	#14582724	1	1	yes	characteristic
54	C₄	#14582734	1	1	yes	characteristic
55	C₂	—	2	1	no	—
56	C₂	#19132794	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14582734
commutator	C₃₂×C₄₃	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₄₃
Fitting	C₄₃×#1425	C₂
socle	C₂×C₄₃	#1423
prime radical	C₂²×C₄₃	Q₆₄
cosocle	C₂×C₃₂×C₄₃	C₂²
hypercenter	#1425	D₄₃
hypocenter	C₄₃	#7547
LCS	G ▷ C₃₂×C₄₃ ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #1425

Complements

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

N	H ≅ G/N	type
36. C₄₃	#7547	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃⋊C₆₄	2
#19132799	2
C₄₃×#1425	2
#7547	43