Subgroups — #19132687

Order 5504.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063259	C₂	1	2	yes	maximal
2	C₂²×C₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊Dic₄₃	—	2	2	no	—
4	#13063259	—	2	2	no	—
5	#13063259	C₄	1	4	yes	complemented
6	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₄₃	—	2	2	no	—
8	C₂×C₁₆×C₄₃	C₄	1	2	yes	complemented
9	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
10	C₂²×Dic₄₃	—	4	2	no	—
11	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₄₃	D₄	1	2	yes	—
14	C₂×C₈×C₄₃	Q₈	1	1	yes	characteristic
15	C₄⋊Dic₄₃	—	2	4	no	—
16	C₄⋊Dic₄₃	—	4	2	no	—
17	C₁₆×C₄₃	—	2	2	no	—
18	C₂³×C₄₃	D₈	1	1	yes	characteristic
19	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₄₃	SD₁₆	1	2	yes	—
22	C₂×C₄×C₄₃	Q₁₆	1	1	yes	characteristic
23	C₂×Dic₄₃	—	4	4	no	—
24	C₂×Dic₄₃	—	8	2	no	—
25	C₂×Dic₄₃	—	8	2	no	—
26	C₈×C₄₃	C₄²	1	1	yes	characteristic
27	C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₈×C₄₃	C₄⋊C₄	1	2	yes	—
29	C₂²×C₄₃	#102	1	2	yes	—
30	C₂²×C₄₃	#107	1	1	yes	characteristic
31	C₂²×C₄₃	D₁₆	1	1	yes	characteristic
32	C₂²×C₄₃	SD₃₂	1	2	yes	—
33	C₂²×C₄₃	Q₃₂	1	1	yes	characteristic
34	C₄×C₄₃	#95	1	1	yes	characteristic
35	C₄×C₄₃	#103	1	2	yes	—
36	C₄×C₄₃	#106	1	1	yes	characteristic
37	Dic₄₃	—	8	4	no	—
38	#1380	—	43	1	no	maximal, Sylow
39	C₂×C₄₃	#340	1	1	yes	characteristic
40	C₂×C₄₃	#357	1	2	yes	—
41	C₂×C₄₃	#358	1	2	yes	—
42	C₂×C₄₃	#366	1	1	yes	characteristic
43	C₂×C₄₃	#367	1	1	yes	characteristic
44	C₂²×C₁₆	D₄₃	1	1	yes	characteristic
45	C₂×#107	—	43	2	no	—
46	C₄₃	#1380	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
48	C₂×C₄⋊C₄	—	86	2	no	—
49	C₂×C₁₆	—	2	2	no	—
50	C₂×C₁₆	Dic₄₃	1	2	yes	complemented
51	#107	—	43	4	no	—
52	#107	—	86	2	no	—
53	C₂²×C₄	—	172	2	no	—
54	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
55	C₂×C₈	Dic₈₆	1	1	yes	characteristic
56	C₂×C₈	C₄×D₄₃	1	2	yes	—
57	C₂×C₈	C₂×Dic₄₃	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₄₃	1	2	yes	—
59	C₄⋊C₄	—	86	4	no	—
60	C₄⋊C₄	—	172	2	no	—
61	C₁₆	—	2	2	no	—
62	C₂³	D₃₄₄	1	1	yes	characteristic
63	C₂×C₄	—	344	2	no	—
64	C₂×C₄	—	344	2	no	—
65	C₂×C₄	—	172	4	no	—
66	C₂×C₄	#10621873	1	2	yes	—
67	C₂×C₄	Dic₁₇₂	1	1	yes	characteristic
68	C₂×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
69	C₂×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
70	C₈	C₄×Dic₄₃	1	1	yes	characteristic
71	C₈	Dic₄₃⋊C₄	1	2	yes	—
72	C₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
73	C₂²	#13063247	1	2	yes	—
74	C₂²	#13063259	1	1	yes	characteristic
75	C₂²	D₆₈₈	1	1	yes	characteristic
76	C₂²	#13063270	1	2	yes	—
77	C₂²	Dic₃₄₄	1	1	yes	characteristic
78	C₄	—	344	4	no	—
79	C₄	C₄₃⋊#95	1	1	yes	characteristic
80	C₄	#13063250	1	2	yes	—
81	C₄	#13063257	1	1	yes	characteristic
82	C₂	#14582662	1	1	yes	characteristic
83	C₂	#14582701	1	2	yes	—
84	C₂	#14582704	1	2	yes	—
85	C₂	#14582725	1	1	yes	characteristic
86	C₂	#14582727	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₃₄₄
commutator	C₈×C₄₃	C₄²
Frattini	C₂²×C₈	C₂×D₄₃
Fitting	C₂²×C₁₆×C₄₃	C₂
socle	C₂³×C₄₃	D₈
hypercenter	C₂²×C₁₆	D₄₃
hypocenter	C₄₃	#1380
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
5. #13063259	C₄	semidirect
8. C₂×C₁₆×C₄₃	C₄	semidirect
46. C₄₃	#1380	semidirect
50. C₂×C₁₆	Dic₄₃	semidirect