Subgroups — #14583333

Order 2752.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063344	C₂	1	1	yes	maximal, characteristic, complemented
2	D₈×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#13063270	C₂	1	1	yes	maximal, characteristic, complemented
4	#13063269	C₂	1	1	yes	maximal, characteristic, complemented
5	#13063266	C₂	1	1	yes	maximal, characteristic, complemented
6	#13063264	C₂	1	1	yes	maximal, characteristic, complemented
7	D₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#10621900	—	2	1	no	—
9	D₄×D₄₃	—	2	1	no	—
10	D₈×C₄₃	C₂²	1	1	yes	characteristic
11	D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
12	#10621883	—	2	1	no	—
13	#10621882	—	2	1	no	—
14	Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
15	D₃₄₄	C₂²	1	1	yes	characteristic
16	C₈×D₄₃	C₂²	1	1	yes	characteristic
17	C₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
18	C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₄₃	—	4	1	no	—
20	D₄×C₄₃	—	2	1	no	—
21	D₄×C₄₃	—	2	1	no	—
22	C₂²⋊D₄₃	—	4	1	no	—
23	C₂²⋊D₄₃	—	4	1	no	—
24	C₂×Dic₄₃	—	4	1	no	—
25	D₁₇₂	—	2	1	no	—
26	C₄×D₄₃	D₄	1	1	yes	characteristic
27	Dic₈₆	—	2	1	no	—
28	C₈×C₄₃	C₂³	1	1	yes	characteristic
29	C₄₃⋊C₈	D₄	1	1	yes	characteristic
30	C₂²×C₄₃	—	4	1	no	—
31	C₂²×C₄₃	—	4	1	no	—
32	C₂×D₄₃	—	4	1	no	—
33	C₂×D₄₃	—	8	2	no	—
34	C₂×D₄₃	D₈	1	1	yes	characteristic
35	C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
36	Dic₄₃	—	4	1	no	—
37	Dic₄₃	D₈	1	1	yes	characteristic
38	C₂×C₄₃	—	8	1	no	—
39	C₂×C₄₃	—	8	1	no	—
40	C₂×C₄₃	C₂×D₈	1	1	yes	characteristic
41	D₄₃	—	2	1	no	—
42	D₄₃	—	8	1	no	—
43	#509	—	43	1	no	maximal, Sylow
44	C₄₃	#509	1	1	yes	characteristic, complemented, Sylow
45	#135	—	43	1	no	—
46	C₂×D₈	—	43	1	no	—
47	SD₃₂	—	43	1	no	—
48	SD₃₂	—	43	1	no	—
49	D₁₆	—	43	1	no	—
50	D₁₆	D₄₃	1	1	yes	characteristic, complemented
51	M₃₂	—	43	1	no	—
52	#41	—	86	1	no	—
53	C₂×D₄	—	86	1	no	—
54	Q₁₆	—	43	1	no	—
55	SD₁₆	—	86	1	no	—
56	D₈	—	43	1	no	—
57	D₈	—	86	1	no	—
58	D₈	C₂×D₄₃	1	1	yes	characteristic
59	D₈	C₂×D₄₃	1	1	yes	characteristic, complemented
60	C₂×C₈	—	43	1	no	—
61	C₁₆	—	43	1	no	—
62	C₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
63	C₂³	—	172	1	no	—
64	Q₈	—	86	1	no	—
65	D₄	—	2	1	no	—
66	D₄	—	2	1	no	—
67	D₄	—	86	1	no	—
68	D₄	—	172	1	no	—
69	D₄	—	172	1	no	—
70	C₂×C₄	—	43	1	no	—
71	C₂×C₄	—	172	1	no	—
72	C₈	—	43	1	no	—
73	C₈	C₂²×D₄₃	1	1	yes	characteristic
74	C₂²	—	4	1	no	—
75	C₂²	—	4	1	no	—
76	C₂²	—	43	1	no	—
77	C₂²	—	344	2	no	—
78	C₂²	—	172	1	no	—
79	C₄	—	43	1	no	—
80	C₄	—	172	1	no	—
81	C₄	D₄×D₄₃	1	1	yes	characteristic
82	C₂	—	8	1	no	—
83	C₂	—	8	1	no	—
84	C₂	—	86	1	no	—
85	C₂	—	344	1	no	—
86	C₂	D₈×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₄₃
commutator, cosocle	C₈×C₄₃	C₂³
Frattini	C₈	C₂²×D₄₃
Fitting	D₁₆×C₄₃	C₂
socle	C₂×C₄₃	C₂×D₈
hypercenter	D₁₆	D₄₃
hypocenter	C₄₃	#509
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. #13063344	C₂	semidirect
2. D₈×D₄₃	C₂	semidirect
3. #13063270	C₂	semidirect
4. #13063269	C₂	semidirect
5. #13063266	C₂	semidirect
6. #13063264	C₂	semidirect
7. D₁₆×C₄₃	C₂	semidirect
11. D₈×C₄₃	C₂²	semidirect
14. Dic₁₇₂	C₂²	semidirect
17. C₁₆×C₄₃	C₂²	semidirect
18. C₄₃⋊C₁₆	C₂²	semidirect
44. C₄₃	#509	semidirect
50. D₁₆	D₄₃	semidirect
59. D₈	C₂×D₄₃	semidirect
62. C₁₆	C₂×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#13063344	2
D₈×D₄₃	2
#13063270	2
#13063269	2
#13063266	2
#13063264	2
D₁₆×C₄₃	2
#509	43