Subgroups — #19132513

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	2	yes	maximal
2	C₈²×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃⋊C₁₆	C₄	1	4	yes	—
4	C₄×C₈×C₄₃	C₄	1	1	yes	characteristic
5	C₄×C₈×C₄₃	C₄	1	1	yes	characteristic
6	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₄₃	C₈	1	2	yes	—
8	C₂×C₈×C₄₃	C₈	1	2	yes	—
9	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
10	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
11	C₄₃⋊C₁₆	—	2	4	no	—
12	C₂×C₄×C₄₃	C₄²	1	1	yes	characteristic
13	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
14	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
15	C₈×C₄₃	—	2	2	no	—
16	C₈×C₄₃	C₁₆	1	4	yes	complemented
17	C₈×C₄₃	M₁₆	1	4	yes	—
18	C₂²×C₄₃	C₄×C₈	1	1	yes	characteristic
19	C₄×C₄₃	#97	1	2	yes	—
20	C₄×C₄₃	C₂×C₁₆	1	2	yes	—
21	C₄×C₄₃	M₃₂	1	2	yes	—
22	#1312	—	43	1	no	maximal, Sylow
23	C₂×C₄₃	#322	1	1	yes	characteristic
24	C₂×C₄₃	C₄×C₁₆	1	1	yes	characteristic
25	C₂×C₄₃	#346	1	1	yes	characteristic
26	C₄×C₁₆	—	43	2	no	—
27	C₈²	D₄₃	1	1	yes	characteristic
28	C₄₃	#1312	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₁₆	—	43	4	no	—
30	C₄×C₈	Dic₄₃	1	1	yes	characteristic
31	C₄×C₈	Dic₄₃	1	1	yes	characteristic
32	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
33	C₂×C₈	C₄₃⋊C₈	1	2	yes	—
34	C₂×C₈	C₄₃⋊C₈	1	2	yes	—
35	C₂×C₈	C₄×D₄₃	1	2	yes	—
36	C₄²	C₂×Dic₄₃	1	1	yes	characteristic
37	C₁₆	—	86	4	no	—
38	C₂×C₄	C₂×C₄₃⋊C₈	1	1	yes	characteristic
39	C₂×C₄	C₂×C₄₃⋊C₈	1	1	yes	characteristic
40	C₂×C₄	C₄×Dic₄₃	1	1	yes	characteristic
41	C₈	—	2	2	no	—
42	C₈	C₄₃⋊C₁₆	1	4	yes	complemented
43	C₈	#10621872	1	4	yes	—
44	C₂²	C₄×C₄₃⋊C₈	1	1	yes	characteristic
45	C₄	#13063235	1	2	yes	—
46	C₄	C₂×C₄₃⋊C₁₆	1	2	yes	—
47	C₄	#13063265	1	2	yes	—
48	C₂	#14582620	1	1	yes	characteristic
49	C₂	C₄×C₄₃⋊C₁₆	1	1	yes	characteristic
50	C₂	#14582675	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄×C₈	C₂×D₄₃
commutator	C₂×C₄₃	C₄×C₁₆
Fitting	C₈²×C₄₃	C₂
socle	C₂²×C₄₃	C₄×C₈
hypercenter	C₈²	D₄₃
hypocenter	C₄₃	#1312
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄×C₈ ◁ C₈²

Complements

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

N	H ≅ G/N	type
16. C₈×C₄₃	C₁₆	semidirect
28. C₄₃	#1312	semidirect
42. C₈	C₄₃⋊C₁₆	semidirect