Subgroups — #19136905

Order 5504.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583332	C₂	1	2	yes	maximal, complemented
2	#14582736	C₂	1	2	yes	maximal, complemented
3	D₁₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₂×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	#13063348	—	2	2	no	—
7	#13063268	—	2	2	no	—
8	D₆₈₈	C₂²	1	2	yes	—
9	C₁₆×D₄₃	C₂²	1	1	yes	characteristic
10	C₄₃⋊C₃₂	C₂²	1	1	yes	characteristic
11	Q₃₂×C₄₃	C₂²	1	2	yes	—
12	C₃₂×C₄₃	C₂²	1	1	yes	characteristic
13	#10621902	—	4	2	no	—
14	Q₁₆×C₄₃	—	2	2	no	—
15	#10621884	—	4	2	no	—
16	D₃₄₄	—	2	2	no	—
17	C₈×D₄₃	D₄	1	1	yes	characteristic
18	C₁₆×C₄₃	C₂³	1	1	yes	characteristic
19	C₄₃⋊C₁₆	D₄	1	1	yes	characteristic
20	Q₈×C₄₃	—	4	2	no	—
21	D₁₇₂	—	4	2	no	—
22	D₁₇₂	—	8	2	no	—
23	C₄×D₄₃	—	8	2	no	—
24	C₄×D₄₃	D₈	1	1	yes	characteristic
25	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
26	C₄₃⋊C₈	D₈	1	1	yes	characteristic
27	C₂×D₄₃	—	8	2	no	—
28	C₂×D₄₃	D₁₆	1	1	yes	characteristic
29	C₄×C₄₃	—	8	2	no	—
30	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
31	Dic₄₃	D₁₆	1	1	yes	characteristic
32	#2262	—	43	1	no	maximal, Sylow
33	C₂×C₄₃	C₂×D₁₆	1	1	yes	characteristic
34	D₄₃	—	2	1	no	—
35	D₄₃	—	16	2	no	—
36	#508	—	43	2	no	—
37	Q₆₄	D₄₃	1	1	yes	characteristic, complemented
38	SD₆₄	—	43	2	no	—
39	D₃₂	—	43	1	no	—
40	C₂×C₃₂	—	43	1	no	—
41	C₄₃	#2262	1	1	yes	characteristic, complemented, Sylow
42	#135	—	86	2	no	—
43	Q₃₂	C₂×D₄₃	1	2	yes	—
44	SD₃₂	—	86	2	no	—
45	D₁₆	—	43	2	no	—
46	C₂×C₁₆	—	43	1	no	—
47	C₃₂	—	43	1	no	—
48	C₃₂	C₂×D₄₃	1	1	yes	characteristic
49	#41	—	172	2	no	—
50	Q₁₆	—	2	2	no	—
51	SD₁₆	—	172	2	no	—
52	D₈	—	86	2	no	—
53	C₂×C₈	—	43	1	no	—
54	C₁₆	—	43	1	no	—
55	C₁₆	C₂²×D₄₃	1	1	yes	characteristic
56	Q₈	—	4	2	no	—
57	D₄	—	344	2	no	—
58	D₄	—	172	2	no	—
59	C₂×C₄	—	43	1	no	—
60	C₂×C₄	—	344	2	no	—
61	C₈	—	43	1	no	—
62	C₈	D₄×D₄₃	1	1	yes	characteristic
63	C₂²	—	43	1	no	—
64	C₂²	—	344	2	no	—
65	C₄	—	8	2	no	—
66	C₄	—	43	1	no	—
67	C₄	D₈×D₄₃	1	1	yes	characteristic
68	C₂	—	86	1	no	—
69	C₂	—	688	2	no	—
70	C₂	D₁₆×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₄₃
commutator	C₁₆×C₄₃	C₂³
Frattini	C₁₆	C₂²×D₄₃
Fitting	C₄₃×Q₆₄	C₂
socle	C₂×C₄₃	C₂×D₁₆
hypercenter	Q₆₄	D₄₃
hypocenter	C₄₃	#2262
LCS	G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₆₄

Complements

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

N	H ≅ G/N	type
1. #14583332	C₂	semidirect
2. #14582736	C₂	semidirect
3. D₁₃₇₆	C₂	semidirect
4. C₃₂×D₄₃	C₂	semidirect
5. C₄₃×Q₆₄	C₂	semidirect
37. Q₆₄	D₄₃	semidirect
41. C₄₃	#2262	semidirect