Subgroups — #19132794

Order 5504.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	#14582725	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#366	C₂	1	1	yes	maximal, characteristic
4	#13063259	—	2	1	no	—
5	C₄₃⋊C₃₂	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
7	#107×C₄₃	—	2	1	no	—
8	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
9	C₄⋊C₄×C₄₃	—	4	1	no	—
10	C₄⋊Dic₄₃	—	4	1	no	—
11	C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₄₃	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₄₃	—	8	1	no	—
14	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
15	C₂×Dic₄₃	—	8	1	no	—
16	C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₄₃	Q₁₆	1	1	yes	characteristic
18	C₂²×C₄₃	D₁₆	1	1	yes	characteristic
19	C₄×C₄₃	—	16	1	no	—
20	C₄×C₄₃	#107	1	1	yes	characteristic
21	C₄×C₄₃	Q₃₂	1	1	yes	characteristic
22	Dic₄₃	—	16	1	no	—
23	#1423	—	43	1	no	maximal, Sylow
24	C₂×C₄₃	#366	1	1	yes	characteristic
25	C₂×C₄₃	D₃₂	1	1	yes	characteristic
26	C₂×C₄₃	Q₆₄	1	1	yes	characteristic
27	C₂×C₃₂	—	43	1	no	—
28	#366	—	43	1	no	—
29	#366	D₄₃	1	1	yes	characteristic
30	C₄₃	#1423	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
32	#107	—	2	1	no	—
33	#107	—	86	1	no	—
34	C₃₂	—	43	2	no	—
35	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
36	C₄⋊C₄	—	4	1	no	—
37	C₄⋊C₄	—	172	1	no	—
38	C₁₆	Dic₈₆	1	1	yes	characteristic
39	C₁₆	C₄×D₄₃	1	1	yes	characteristic
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	344	1	no	—
42	C₂×C₄	#10621882	1	1	yes	characteristic
43	C₈	Dic₄₃⋊C₄	1	1	yes	characteristic
44	C₈	#10621885	1	1	yes	characteristic
45	C₂²	#13063266	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	688	1	no	—
48	C₄	#13063258	1	1	yes	characteristic
49	C₄	#13063271	1	1	yes	characteristic
50	C₂	#14582724	1	1	yes	characteristic
51	C₂	#14582734	1	1	yes	characteristic
52	C₂	#14582739	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13063266
commutator	C₁₆×C₄₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₄₃
Fitting	C₄₃×#366	C₂
socle	C₂²×C₄₃	D₁₆
hypercenter	#366	D₄₃
hypocenter	C₄₃	#1423
LCS	G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
5. C₄₃⋊C₃₂	C₄	semidirect
30. C₄₃	#1423	semidirect