Subgroups — #19136504

Order 5504.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₄₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₄₃⋊C₁₆)	C₂	1	2	yes	maximal
3	#14582675	C₂	1	2	yes	maximal
4	C₄×C₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₈×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₄₃⋊C₁₆	C₂²	1	2	yes	—
8	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
9	C₄×Q₈×C₄₃	C₄	1	1	yes	characteristic
10	C₄⋊C₈×C₄₃	C₄	1	2	yes	—
11	C₄⋊C₈×C₄₃	C₄	1	1	yes	characteristic
12	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₄₃	C₂²	1	2	yes	—
14	C₂×Q₈×C₄₃	C₈	1	1	yes	characteristic
15	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
18	C₄⋊C₄×C₄₃	C₈	1	2	yes	—
19	C₄⋊C₄×C₄₃	C₈	1	1	yes	characteristic
20	C₄²×C₄₃	C₂×C₄	1	2	yes	—
21	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
22	C₄₃⋊C₁₆	—	2	1	no	—
23	C₄₃⋊C₁₆	—	2	2	no	—
24	C₄₃⋊C₁₆	Q₈	1	2	yes	complemented
25	Q₈×C₄₃	—	2	2	no	—
26	C₂×C₄×C₄₃	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₄₃	C₂×C₈	1	2	yes	—
29	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
31	C₈×C₄₃	—	2	1	no	—
32	C₈×C₄₃	—	2	2	no	—
33	C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
34	C₈×C₄₃	#41	1	1	yes	characteristic
35	C₂²×C₄₃	C₂²×C₈	1	1	yes	characteristic
36	C₄×C₄₃	—	2	2	no	—
37	C₄×C₄₃	—	2	2	no	—
38	C₄×C₄₃	—	2	1	no	—
39	C₄×C₄₃	M₃₂	1	2	yes	—
40	C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
41	C₄×C₄₃	#131	1	1	yes	characteristic
42	#2183	—	43	1	no	maximal, Sylow
43	C₂×C₄₃	C₈×Q₈	1	1	yes	characteristic
44	C₂×C₄₃	C₂×M₃₂	1	1	yes	characteristic
45	C₂×C₄₃	#504	1	1	yes	characteristic
46	C₈×Q₈	D₄₃	1	1	yes	characteristic
47	C₄⋊C₁₆	—	43	1	no	—
48	C₄⋊C₁₆	—	43	2	no	—
49	#346	—	43	2	no	—
50	C₄×C₁₆	—	43	1	no	—
51	C₄₃	#2183	1	1	yes	characteristic, complemented, Sylow
52	C₄×Q₈	Dic₄₃	1	1	yes	characteristic
53	C₂×C₁₆	—	43	1	no	—
54	C₂×C₁₆	—	43	1	no	—
55	C₂×C₁₆	—	43	2	no	—
56	C₄⋊C₈	Dic₄₃	1	2	yes	—
57	C₄⋊C₈	Dic₄₃	1	1	yes	characteristic
58	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
59	C₄×C₈	C₂×D₄₃	1	2	yes	—
60	C₂×Q₈	C₄₃⋊C₈	1	1	yes	characteristic
61	C₂×C₈	C₂×Dic₄₃	1	1	yes	characteristic
62	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
63	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
64	C₄⋊C₄	C₄₃⋊C₈	1	2	yes	—
65	C₄⋊C₄	C₄₃⋊C₈	1	1	yes	characteristic
66	C₄²	C₂×Dic₄₃	1	2	yes	—
67	C₄²	C₂×Dic₄₃	1	1	yes	characteristic
68	C₁₆	—	43	2	no	—
69	C₁₆	—	86	1	no	—
70	C₁₆	—	86	2	no	—
71	Q₈	—	2	2	no	—
72	C₂×C₄	C₂×C₄₃⋊C₈	1	2	yes	—
73	C₂×C₄	C₂×C₄₃⋊C₈	1	1	yes	characteristic
74	C₂×C₄	C₂×C₄₃⋊C₈	1	2	yes	—
75	C₂×C₄	C₂×C₄₃⋊C₈	1	1	yes	characteristic
76	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	2	2	no	—
79	C₈	Q₈×D₄₃	1	1	yes	characteristic
80	C₈	#10621902	1	1	yes	characteristic
81	C₂²	C₂²×C₄₃⋊C₈	1	1	yes	characteristic
82	C₄	—	2	2	no	—
83	C₄	—	2	2	no	—
84	C₄	—	2	1	no	—
85	C₄	#13063265	1	2	yes	—
86	C₄	Q₈×Dic₄₃	1	1	yes	characteristic
87	C₄	#13063332	1	1	yes	characteristic
88	C₂	Q₈×C₄₃⋊C₈	1	1	yes	characteristic
89	C₂	C₂×#13063265	1	1	yes	characteristic
90	C₂	#14583316	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₄₃
commutator, socle	C₂²×C₄₃	C₂²×C₈
Fitting	C₈×Q₈×C₄₃	C₂
hypercenter	C₈×Q₈	D₄₃
hypocenter	C₄₃	#2183
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₈×Q₈

Complements

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

N	H ≅ G/N	type
24. C₄₃⋊C₁₆	Q₈	semidirect
51. C₄₃	#2183	semidirect