Subgroups — #19132671

Order 5504.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14582720	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
3	#13063265	—	2	2	no	—
4	C₂×C₁₆×C₄₃	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₄₃	C₄	1	1	yes	characteristic
6	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
8	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
9	C₄²×C₄₃	Q₈	1	1	yes	characteristic
10	C₁₆×C₄₃	—	2	1	no	—
11	C₁₆×C₄₃	C₈	1	2	yes	—
12	C₄₃⋊C₁₆	—	4	2	no	—
13	C₂×C₄×C₄₃	—	2	1	no	—
14	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
15	C₈×C₄₃	C₂×C₈	1	1	yes	characteristic
16	C₈×C₄₃	M₁₆	1	1	yes	characteristic
17	C₈×C₄₃	D₈	1	1	yes	characteristic
18	C₈×C₄₃	Q₁₆	1	1	yes	characteristic
19	C₂²×C₄₃	#108	1	1	yes	characteristic
20	C₄×C₄₃	—	2	2	no	—
21	C₄×C₄₃	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₄₃	#107	1	1	yes	characteristic
23	#1373	—	43	1	no	maximal, Sylow
24	C₂×C₄₃	—	2	1	no	—
25	C₂×C₄₃	#335	1	1	yes	characteristic
26	#364	—	43	2	no	—
27	C₄×C₁₆	D₄₃	1	1	yes	characteristic
28	C₄₃	#1373	1	1	yes	characteristic, complemented, Sylow
29	M₃₂	—	86	2	no	—
30	C₂×C₁₆	Dic₄₃	1	1	yes	characteristic
31	C₂×C₁₆	Dic₄₃	1	1	yes	characteristic
32	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
33	C₂×C₈	D₁₇₂	1	1	yes	characteristic
34	C₂×C₈	C₂×Dic₄₃	1	1	yes	characteristic
35	C₄²	Dic₈₆	1	1	yes	characteristic
36	C₁₆	—	2	1	no	—
37	C₁₆	—	172	2	no	—
38	C₁₆	C₄₃⋊C₈	1	2	yes	—
39	C₂×C₄	—	2	1	no	—
40	C₂×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
41	C₈	D₃₄₄	1	1	yes	characteristic
42	C₈	Dic₁₇₂	1	1	yes	characteristic
43	C₈	C₂×C₄₃⋊C₈	1	1	yes	characteristic
44	C₈	#10621877	1	1	yes	characteristic
45	C₂²	#13063261	1	1	yes	characteristic
46	C₄	—	2	2	no	—
47	C₄	C₄⋊(C₄₃⋊C₈)	1	1	yes	characteristic
48	C₄	#13063259	1	1	yes	characteristic
49	C₂	—	2	1	no	—
50	C₂	#14582652	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₃₄₄
commutator	C₈×C₄₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₄₃
Fitting	C₄×C₁₆×C₄₃	C₂
socle	C₂×C₄₃	#335
hypercenter	C₄×C₁₆	D₄₃
hypocenter	C₄₃	#1373
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
28. C₄₃	#1373	semidirect