Subgroups — #14583341

Order 2752.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063348	C₂	1	1	yes	maximal, characteristic
2	Q₁₆×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#13063271	C₂	1	1	yes	maximal, characteristic, complemented
4	#13063270	C₂	1	1	yes	maximal, characteristic, complemented
5	#13063268	C₂	1	1	yes	maximal, characteristic, complemented
6	#13063264	C₂	1	1	yes	maximal, characteristic, complemented
7	Q₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#10621902	—	2	1	no	—
9	Q₈×D₄₃	—	2	1	no	—
10	Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
11	Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
12	#10621885	—	2	1	no	—
13	#10621884	—	2	1	no	—
14	Dic₁₇₂	C₂²	1	1	yes	characteristic
15	D₃₄₄	C₂²	1	1	yes	characteristic
16	C₈×D₄₃	C₂²	1	1	yes	characteristic
17	C₁₆×C₄₃	C₂²	1	1	yes	characteristic
18	C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
19	Q₈×C₄₃	—	2	1	no	—
20	Q₈×C₄₃	—	2	1	no	—
21	D₁₇₂	—	2	1	no	—
22	D₁₇₂	—	4	1	no	—
23	C₄×D₄₃	—	4	1	no	—
24	C₄×D₄₃	—	4	1	no	—
25	C₄×D₄₃	D₄	1	1	yes	characteristic
26	Dic₈₆	—	2	1	no	—
27	Dic₈₆	—	4	1	no	—
28	C₈×C₄₃	C₂³	1	1	yes	characteristic
29	C₄₃⋊C₈	D₄	1	1	yes	characteristic
30	C₂×D₄₃	—	4	1	no	—
31	C₂×D₄₃	D₈	1	1	yes	characteristic
32	C₄×C₄₃	—	4	1	no	—
33	C₄×C₄₃	—	4	1	no	—
34	C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
35	Dic₄₃	—	4	1	no	—
36	Dic₄₃	D₈	1	1	yes	characteristic
37	C₂×C₄₃	C₂×D₈	1	1	yes	characteristic
38	D₄₃	—	2	1	no	—
39	D₄₃	—	8	1	no	—
40	#510	—	43	1	no	maximal, Sylow
41	C₄₃	#510	1	1	yes	characteristic, complemented, Sylow
42	#135	—	43	1	no	—
43	C₂×Q₁₆	—	43	1	no	—
44	Q₃₂	—	43	1	no	—
45	Q₃₂	D₄₃	1	1	yes	characteristic, complemented
46	SD₃₂	—	43	1	no	—
47	SD₃₂	—	43	1	no	—
48	M₃₂	—	43	1	no	—
49	#41	—	86	1	no	—
50	C₂×Q₈	—	86	1	no	—
51	Q₁₆	—	43	1	no	—
52	Q₁₆	—	86	1	no	—
53	Q₁₆	C₂×D₄₃	1	1	yes	characteristic
54	Q₁₆	C₂×D₄₃	1	1	yes	characteristic
55	SD₁₆	—	86	1	no	—
56	D₈	—	43	1	no	—
57	C₂×C₈	—	43	1	no	—
58	C₁₆	—	43	1	no	—
59	C₁₆	C₂×D₄₃	1	1	yes	characteristic
60	Q₈	—	2	1	no	—
61	Q₈	—	2	1	no	—
62	Q₈	—	86	1	no	—
63	Q₈	—	172	1	no	—
64	D₄	—	86	1	no	—
65	D₄	—	172	1	no	—
66	C₂×C₄	—	43	1	no	—
67	C₂×C₄	—	172	1	no	—
68	C₂×C₄	—	172	1	no	—
69	C₈	—	43	1	no	—
70	C₈	C₂²×D₄₃	1	1	yes	characteristic
71	C₂²	—	43	1	no	—
72	C₂²	—	172	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	4	1	no	—
75	C₄	—	43	1	no	—
76	C₄	—	172	1	no	—
77	C₄	D₄×D₄₃	1	1	yes	characteristic
78	C₂	—	86	1	no	—
79	C₂	—	344	1	no	—
80	C₂	D₈×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₄₃
commutator, cosocle	C₈×C₄₃	C₂³
Frattini	C₈	C₂²×D₄₃
Fitting	Q₃₂×C₄₃	C₂
socle	C₂×C₄₃	C₂×D₈
prime radical	#13063348	C₂
hypercenter	Q₃₂	D₄₃
hypocenter	C₄₃	#510
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
2. Q₁₆×D₄₃	C₂	semidirect
3. #13063271	C₂	semidirect
4. #13063270	C₂	semidirect
5. #13063268	C₂	semidirect
6. #13063264	C₂	semidirect
7. Q₃₂×C₄₃	C₂	semidirect
41. C₄₃	#510	semidirect
45. Q₃₂	D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#13063348	2
Q₁₆×D₄₃	2
#13063271	2
#13063270	2
#13063268	2
#13063264	2
Q₃₂×C₄₃	2
#510	43