Subgroups — #24984481

Order 11008.

88 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, complemented
2	#19132799	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2262	C₂	1	1	yes	maximal, characteristic
4	#14582729	—	2	1	no	—
5	C₄₃⋊C₆₄	—	2	1	no	—
6	C₄₃×#508	—	2	1	no	—
7	C₄₃×Q₆₄	C₄	1	1	yes	characteristic
8	C₄₃×SD₆₄	—	2	1	no	—
9	C₄₃×D₃₂	C₄	1	1	yes	characteristic
10	C₂×C₃₂×C₄₃	C₂²	1	1	yes	characteristic
11	#13063261	—	4	1	no	—
12	#135×C₄₃	—	4	1	no	—
13	Q₃₂×C₄₃	—	2	1	no	—
14	SD₃₂×C₄₃	—	4	1	no	—
15	D₁₆×C₄₃	—	2	1	no	—
16	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
17	C₃₂×C₄₃	C₂×C₄	1	1	yes	characteristic
18	C₃₂×C₄₃	D₄	1	1	yes	characteristic
19	#41×C₄₃	—	8	1	no	—
20	Q₁₆×C₄₃	—	4	1	no	—
21	SD₁₆×C₄₃	—	8	1	no	—
22	D₈×C₄₃	—	4	1	no	—
23	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
24	#10621877	—	8	1	no	—
25	C₁₆×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₁₆×C₄₃	SD₁₆	1	1	yes	characteristic
27	Q₈×C₄₃	—	8	1	no	—
28	D₄×C₄₃	—	8	1	no	—
29	D₄×C₄₃	—	16	1	no	—
30	C₂×C₄×C₄₃	—	16	1	no	—
31	C₂×C₄×C₄₃	D₁₆	1	1	yes	characteristic
32	C₈×C₄₃	#102	1	1	yes	characteristic
33	C₈×C₄₃	SD₃₂	1	1	yes	characteristic
34	C₄₃⋊C₈	—	16	1	no	—
35	#7539	—	43	1	no	maximal, Sylow
36	C₂²×C₄₃	—	16	1	no	—
37	C₂²×C₄₃	SD₆₄	1	1	yes	characteristic
38	C₄×C₄₃	—	16	1	no	—
39	C₄×C₄₃	#357	1	1	yes	characteristic
40	C₄×C₄₃	D₃₂	1	1	yes	characteristic
41	#2262	D₄₃	1	1	yes	characteristic
42	C₂×C₆₄	—	43	1	no	—
43	#1425	—	43	1	no	—
44	C₂×C₄₃	—	2	1	no	—
45	C₂×C₄₃	—	32	1	no	—
46	C₂×C₄₃	#1415	1	1	yes	characteristic
47	#508	—	2	1	no	—
48	Q₆₄	Dic₄₃	1	1	yes	characteristic
49	SD₆₄	—	2	1	no	—
50	D₃₂	Dic₄₃	1	1	yes	characteristic
51	C₂×C₃₂	C₂×D₄₃	1	1	yes	characteristic
52	#368	—	86	1	no	—
53	C₆₄	—	86	1	no	—
54	C₄₃	#7539	1	1	yes	characteristic, complemented, Sylow
55	#135	—	4	1	no	—
56	Q₃₂	—	2	1	no	—
57	SD₃₂	—	4	1	no	—
58	D₁₆	—	2	1	no	—
59	C₂×C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
60	#108	—	172	1	no	—
61	C₃₂	C₂×Dic₄₃	1	1	yes	characteristic
62	C₃₂	C₂²⋊D₄₃	1	1	yes	characteristic
63	#41	—	8	1	no	—
64	Q₁₆	—	4	1	no	—
65	SD₁₆	—	8	1	no	—
66	D₈	—	4	1	no	—
67	M₁₆	—	344	1	no	—
68	C₂×C₈	#10621882	1	1	yes	characteristic
69	C₁₆	#10621883	1	1	yes	characteristic
70	C₁₆	C₂²⋊Dic₄₃	1	1	yes	characteristic
71	Q₈	—	8	1	no	—
72	D₄	—	8	1	no	—
73	D₄	—	16	1	no	—
74	C₂×C₄	—	16	1	no	—
75	C₂×C₄	#13063266	1	1	yes	characteristic
76	C₈	—	688	1	no	—
77	C₈	#13063246	1	1	yes	characteristic
78	C₈	#13063269	1	1	yes	characteristic
79	C₂²	—	16	1	no	—
80	C₂²	#14582737	1	1	yes	characteristic
81	C₄	—	16	1	no	—
82	C₄	#14582700	1	1	yes	characteristic
83	C₄	#14582734	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	32	1	no	—
86	C₂	#19132773	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14582734
commutator	C₃₂×C₄₃	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₄₃
Fitting, prime radical	C₄₃×#2262	C₂
socle	C₂×C₄₃	#1415
cosocle	C₂×C₃₂×C₄₃	C₂²
hypercenter	#2262	D₄₃
hypocenter	C₄₃	#7539
LCS	G ▷ C₃₂×C₄₃ ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #2262

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃⋊C₆₄	C₂	semidirect
2. #19132799	C₂	semidirect
54. C₄₃	#7539	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×#2262	2
#7539	43