Subgroups — #19132648

Order 5504.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583301	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₄₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#334	C₂	1	1	yes	maximal, characteristic
4	#13063317	—	2	1	no	—
5	C₂×C₄₃⋊C₁₆	—	2	1	no	—
6	#13063259	C₄	1	1	yes	characteristic
7	#13063259	C₄	1	1	yes	characteristic
8	#13063257	—	2	1	no	—
9	C₄⋊C₈×C₄₃	—	2	1	no	—
10	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₄₃	—	4	1	no	—
12	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
14	C₄²×C₄₃	D₄	1	1	yes	characteristic
15	C₄⋊Dic₄₃	—	2	1	no	—
16	C₄⋊Dic₄₃	—	2	1	no	—
17	Dic₄₃⋊C₄	—	4	1	no	—
18	Dic₄₃⋊C₄	—	4	1	no	—
19	C₄₃⋊C₁₆	—	4	1	no	—
20	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
22	C₂×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
23	C₂×Dic₄₃	—	4	1	no	—
24	C₂×Dic₄₃	—	4	1	no	—
25	C₈×C₄₃	—	2	1	no	—
26	C₈×C₄₃	—	8	1	no	—
27	C₈×C₄₃	SD₁₆	1	1	yes	characteristic
28	C₈×C₄₃	Q₁₆	1	1	yes	characteristic
29	C₂²×C₄₃	#102	1	1	yes	characteristic
30	C₄×C₄₃	—	2	1	no	—
31	C₄×C₄₃	—	2	1	no	—
32	C₄×C₄₃	#101	1	1	yes	characteristic
33	C₄×C₄₃	#103	1	1	yes	characteristic
34	Dic₄₃	—	8	1	no	—
35	Dic₄₃	—	8	1	no	—
36	#1363	—	43	1	no	maximal, Sylow
37	C₂×C₄₃	#332	1	1	yes	characteristic
38	C₂×C₄₃	#359	1	1	yes	characteristic
39	C₂×C₄₃	#360	1	1	yes	characteristic
40	#499	—	43	1	no	—
41	C₄⋊C₁₆	—	43	1	no	—
42	#334	D₄₃	1	1	yes	characteristic
43	C₄₃	#1363	1	1	yes	characteristic, complemented, Sylow
44	#125	—	86	1	no	—
45	C₂×C₁₆	—	86	1	no	—
46	#107	—	43	1	no	—
47	#107	—	43	1	no	—
48	#106	—	86	1	no	—
49	C₄⋊C₈	—	2	1	no	—
50	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
51	C₂×C₈	—	4	1	no	—
52	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
53	C₂×C₈	D₁₇₂	1	1	yes	characteristic
54	C₄⋊C₄	—	86	1	no	—
55	C₄⋊C₄	—	86	1	no	—
56	C₄⋊C₄	—	172	1	no	—
57	C₄⋊C₄	—	172	1	no	—
58	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
59	C₁₆	—	172	1	no	—
60	C₂×C₄	—	172	1	no	—
61	C₂×C₄	—	172	1	no	—
62	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
63	C₂×C₄	#10621882	1	1	yes	characteristic
64	C₂×C₄	#10621884	1	1	yes	characteristic
65	C₈	—	2	1	no	—
66	C₈	—	8	1	no	—
67	C₈	#10621873	1	1	yes	characteristic
68	C₈	Dic₁₇₂	1	1	yes	characteristic
69	C₂²	#13063245	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	2	1	no	—
72	C₄	—	344	1	no	—
73	C₄	—	344	1	no	—
74	C₄	#13063243	1	1	yes	characteristic
75	C₄	#13063250	1	1	yes	characteristic
76	C₂	#14582646	1	1	yes	characteristic
77	C₂	#14582705	1	1	yes	characteristic
78	C₂	#14582708	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13063245
commutator	C₂×C₈×C₄₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₄₃
Fitting	C₄₃×#334	C₂
socle	C₂²×C₄₃	#102
hypercenter	#334	D₄₃
hypocenter	C₄₃	#1363
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #334

Complements

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

N	H ≅ G/N	type
43. C₄₃	#1363	semidirect