Subgroups — #19132770

Order 5504.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14582696	C₂	1	1	yes	maximal, characteristic
2	#14582694	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#488	C₂	1	1	yes	maximal, characteristic
4	#13063244	—	2	1	no	—
5	#13063240	—	2	1	no	—
6	#125×C₄₃	C₄	1	1	yes	characteristic, complemented
7	#124×C₄₃	C₂²	1	1	yes	characteristic
8	#103×C₄₃	—	2	1	no	—
9	#102×C₄₃	—	2	1	no	—
10	C₄×C₈×C₄₃	C₄	1	1	yes	characteristic, complemented
11	C₂×Q₈×C₄₃	D₄	1	1	yes	characteristic
12	C₂×D₄×C₄₃	D₄	1	1	yes	characteristic
13	C₂×C₈×C₄₃	—	2	1	no	—
14	C₄⋊C₄×C₄₃	—	2	1	no	—
15	C₄⋊C₄×C₄₃	—	4	1	no	—
16	C₂²⋊C₄×C₄₃	—	4	1	no	—
17	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂²⋊Dic₄₃	—	4	1	no	—
19	#10621877	—	4	1	no	—
20	C₂³×C₄₃	—	2	1	no	—
21	Q₈×C₄₃	—	4	1	no	—
22	D₄×C₄₃	—	4	1	no	—
23	C₂×C₄×C₄₃	—	2	1	no	—
24	C₂×C₄×C₄₃	—	2	1	no	—
25	C₂×C₄×C₄₃	—	4	1	no	—
26	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×Dic₄₃	—	8	1	no	—
28	C₈×C₄₃	—	4	1	no	—
29	C₄₃⋊C₈	—	8	1	no	—
30	C₂²×C₄₃	—	4	1	no	—
31	C₂²×C₄₃	—	8	1	no	—
32	C₂²×C₄₃	#99	1	1	yes	characteristic
33	C₄×C₄₃	—	2	1	no	—
34	C₄×C₄₃	—	4	1	no	—
35	C₄×C₄₃	—	4	1	no	—
36	C₄×C₄₃	—	8	1	no	—
37	Dic₄₃	—	16	1	no	—
38	#1414	—	43	1	no	maximal, Sylow
39	C₂×C₄₃	—	2	1	no	—
40	C₂×C₄₃	—	8	1	no	—
41	C₂×C₄₃	#354	1	1	yes	characteristic
42	#488	D₄₃	1	1	yes	characteristic
43	#355	—	43	1	no	—
44	#354	—	43	1	no	—
45	C₄₃	#1414	1	1	yes	characteristic, complemented, Sylow
46	#125	Dic₄₃	1	1	yes	characteristic, complemented
47	#124	C₂×D₄₃	1	1	yes	characteristic
48	#103	—	2	1	no	—
49	#102	—	2	1	no	—
50	#101	—	86	1	no	—
51	#99	—	86	1	no	—
52	C₄×C₈	Dic₄₃	1	1	yes	characteristic, complemented
53	C₂×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
54	C₂×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
55	M₁₆	—	172	1	no	—
56	C₂×C₈	—	2	1	no	—
57	C₄⋊C₄	—	2	1	no	—
58	C₄⋊C₄	—	4	1	no	—
59	C₂²⋊C₄	—	4	1	no	—
60	C₂²⋊C₄	—	172	1	no	—
61	C₄²	C₂×Dic₄₃	1	1	yes	characteristic
62	C₂³	—	2	1	no	—
63	Q₈	—	4	1	no	—
64	D₄	—	4	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	4	1	no	—
68	C₂×C₄	—	344	1	no	—
69	C₂×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
70	C₈	—	4	1	no	—
71	C₈	—	344	1	no	—
72	C₂²	—	4	1	no	—
73	C₂²	—	8	1	no	—
74	C₂²	#13063240	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	4	1	no	—
78	C₄	—	8	1	no	—
79	C₄	—	688	1	no	—
80	C₂	—	2	1	no	—
81	C₂	—	8	1	no	—
82	C₂	#14582694	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14582694
commutator	C₄²×C₄₃	C₂×C₄
Frattini	#124	C₂×D₄₃
Fitting	C₄₃×#488	C₂
socle	C₂×C₄₃	#354
hypercenter	#488	D₄₃
hypocenter	C₄₃	#1414
LCS	G ▷ C₄²×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #488

Complements

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

N	H ≅ G/N	type
6. #125×C₄₃	C₄	semidirect
10. C₄×C₈×C₄₃	C₄	semidirect
45. C₄₃	#1414	semidirect
46. #125	Dic₄₃	semidirect
52. C₄×C₈	Dic₄₃	semidirect