Subgroups — #19132514

Order 5504.

92 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	C₈×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₃⋊C₁₆	C₄	1	2	yes	—
5	C₄×C₄₃⋊C₈	C₄	1	1	yes	characteristic
6	C₄×C₄₃⋊C₈	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₄₃	C₄	1	2	yes	—
8	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
10	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
11	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄₃⋊C₈	C₈	1	2	yes	—
13	C₂×C₄₃⋊C₈	C₈	1	2	yes	—
14	C₁₆×C₄₃	—	2	2	no	—
15	C₄₃⋊C₁₆	—	2	2	no	—
16	C₂×C₄×C₄₃	C₄²	1	1	yes	characteristic
17	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
18	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
19	C₈×C₄₃	M₁₆	1	2	yes	—
20	C₈×C₄₃	M₁₆	1	2	yes	—
21	C₄₃⋊C₈	—	2	2	no	—
22	C₄₃⋊C₈	C₁₆	1	4	yes	complemented
23	C₂²×C₄₃	C₄×C₈	1	1	yes	characteristic
24	C₄×C₄₃	#97	1	1	yes	characteristic
25	C₄×C₄₃	#97	1	1	yes	characteristic
26	C₄×C₄₃	C₂×C₁₆	1	2	yes	—
27	C₄×C₄₃	M₃₂	1	2	yes	—
28	#1312	—	43	1	no	maximal, Sylow
29	C₂×C₄₃	#322	1	1	yes	characteristic
30	C₂×C₄₃	C₄×C₁₆	1	1	yes	characteristic
31	C₂×C₄₃	#346	1	1	yes	characteristic
32	C₄×C₁₆	—	43	1	no	—
33	C₄×C₁₆	D₄₃	1	1	yes	characteristic
34	C₈²	—	43	1	no	—
35	C₄₃	#1312	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₁₆	—	43	2	no	—
37	C₂×C₁₆	Dic₄₃	1	2	yes	—
38	C₄×C₈	—	43	1	no	—
39	C₄×C₈	—	43	1	no	—
40	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
41	C₂×C₈	—	43	2	no	—
42	C₂×C₈	—	43	2	no	—
43	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
44	C₂×C₈	C₂×Dic₄₃	1	1	yes	characteristic
45	C₄²	C₄×D₄₃	1	1	yes	characteristic
46	C₁₆	—	2	2	no	—
47	C₁₆	—	86	2	no	—
48	C₂×C₄	C₈×D₄₃	1	1	yes	characteristic
49	C₂×C₄	C₈×D₄₃	1	1	yes	characteristic
50	C₂×C₄	C₄×Dic₄₃	1	1	yes	characteristic
51	C₈	—	43	4	no	—
52	C₈	—	86	2	no	—
53	C₈	#10621872	1	2	yes	—
54	C₈	#10621877	1	2	yes	—
55	C₂²	C₈×Dic₄₃	1	1	yes	characteristic
56	C₄	#13063235	1	1	yes	characteristic
57	C₄	#13063236	1	1	yes	characteristic
58	C₄	C₁₆×D₄₃	1	2	yes	—
59	C₄	#13063264	1	2	yes	—
60	C₂	#14582621	1	1	yes	characteristic
61	C₂	C₁₆×Dic₄₃	1	1	yes	characteristic
62	C₂	#14582674	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄×C₈	C₂×D₄₃
commutator	C₂×C₄₃	C₄×C₁₆
Fitting	C₄×C₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₄×C₈
hypercenter	C₄×C₁₆	D₄₃
hypocenter	C₄₃	#1312
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
22. C₄₃⋊C₈	C₁₆	semidirect
35. C₄₃	#1312	semidirect