Subgroups — #19134749

Order 5504.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊(C₄₃⋊C₈)	C₂	1	6	yes	maximal
2	C₄₃×#376	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄₃⋊C₈	C₂²	1	4	yes	—
4	C₄⋊(C₄₃⋊C₈)	—	2	12	no	—
5	C₂×C₄²×C₄₃	C₂²	1	3	yes	—
6	#95×C₄₃	C₄	1	4	yes	—
7	C₂²×C₄×C₄₃	C₂×C₄	1	6	yes	—
8	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
9	C₄²×C₄₃	D₄	1	6	yes	—
10	C₄²×C₄₃	Q₈	1	6	yes	—
11	C₂×C₄₃⋊C₈	—	2	12	no	—
12	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
13	C₂×C₄×C₄₃	—	2	12	no	—
14	C₂×C₄×C₄₃	C₄⋊C₄	1	12	yes	—
15	C₂×C₄×C₄₃	C₂×D₄	1	3	yes	—
16	C₂×C₄×C₄₃	C₂×Q₈	1	3	yes	—
17	C₄₃⋊C₈	—	4	4	no	—
18	C₂²×C₄₃	C₂×C₄⋊C₄	1	3	yes	—
19	C₂²×C₄₃	#131	1	4	yes	—
20	C₄×C₄₃	—	2	12	no	—
21	C₄×C₄₃	#127	1	1	yes	characteristic
22	C₄×C₄₃	C₄⋊Q₈	1	3	yes	—
23	#1843	—	43	1	no	maximal, Sylow
24	C₂×C₄₃	#384	1	1	yes	characteristic
25	C₂×C₄₃	#424	1	6	yes	—
26	C₂×C₄⋊C₈	—	43	6	no	—
27	#376	D₄₃	1	1	yes	characteristic
28	C₄₃	#1843	1	1	yes	characteristic, complemented, Sylow
29	C₂²×C₈	—	43	4	no	—
30	C₂×C₄²	C₂×D₄₃	1	3	yes	—
31	C₄⋊C₈	—	86	12	no	—
32	#95	Dic₄₃	1	4	yes	—
33	C₂²×C₄	C₂×Dic₄₃	1	6	yes	—
34	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
35	C₂×C₈	—	86	12	no	—
36	C₄²	Dic₈₆	1	6	yes	—
37	C₄²	D₁₇₂	1	6	yes	—
38	C₂³	C₂²×Dic₄₃	1	1	yes	characteristic
39	C₂×C₄	—	2	12	no	—
40	C₂×C₄	C₄⋊Dic₄₃	1	12	yes	—
41	C₂×C₄	C₂×Dic₈₆	1	3	yes	—
42	C₂×C₄	C₂×D₁₇₂	1	3	yes	—
43	C₈	—	172	4	no	—
44	C₂²	C₂×C₄⋊Dic₄₃	1	3	yes	—
45	C₂²	#13063332	1	4	yes	—
46	C₄	—	2	12	no	—
47	C₄	#13063322	1	1	yes	characteristic
48	C₄	#13063325	1	3	yes	—
49	C₂	#14582769	1	1	yes	characteristic
50	C₂	#14582926	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₄₃
commutator, socle	C₂³×C₄₃	C₂²×C₄
Fitting	C₄₃×#376	C₂
hypercenter	#376	D₄₃
hypocenter	C₄₃	#1843
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
28. C₄₃	#1843	semidirect