Subgroups — #19133897

Order 5504.

182 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583265	C₂	1	3	yes	maximal
2	#14582641	C₂	1	3	yes	maximal, complemented
3	C₄₃×#564	C₂	1	1	yes	maximal, characteristic, complemented
4	#13063322	C₂²	1	1	yes	characteristic
5	#13063245	—	2	6	no	—
6	#13063236	C₂²	1	3	yes	—
7	#125×C₄₃	—	2	6	no	—
8	#125×C₄₃	C₂²	1	3	yes	—
9	C₂×D₁₇₂	—	2	3	no	—
10	C₄⋊C₄×C₄₃	—	2	6	no	—
11	C₄⋊C₄×C₄₃	—	2	6	no	—
12	C₄⋊C₄×C₄₃	D₄	1	6	yes	—
13	C₄²×C₄₃	—	2	2	no	—
14	C₄²×C₄₃	C₂³	1	1	yes	characteristic
15	C₂×C₄₃⋊C₈	—	2	3	no	—
16	C₂²×D₄₃	—	4	1	no	—
17	C₂×C₄×C₄₃	—	2	6	no	—
18	C₂×C₄×C₄₃	C₂×D₄	1	3	yes	—
19	D₁₇₂	—	4	6	no	—
20	C₄₃⋊C₈	—	4	3	no	—
21	C₂²×C₄₃	#120	1	1	yes	characteristic
22	C₂×D₄₃	—	8	3	no	—
23	C₄×C₄₃	—	2	3	no	—
24	C₄×C₄₃	—	4	6	no	—
25	#1658	—	43	1	no	maximal, Sylow
26	C₂×C₄₃	#454	1	3	yes	—
27	D₄₃	—	16	1	no	—
28	#564	D₄₃	1	1	yes	characteristic, complemented
29	#490	—	43	3	no	—
30	#330	—	43	3	no	—
31	C₄₃	#1658	1	1	yes	characteristic, complemented, Sylow
32	#127	—	43	1	no	—
33	#125	—	2	6	no	—
34	#125	C₂×D₄₃	1	3	yes	—
35	#102	—	86	6	no	—
36	#97	—	43	3	no	—
37	C₂×D₄	—	86	3	no	—
38	C₂×C₈	—	86	3	no	—
39	C₄⋊C₄	—	2	6	no	—
40	C₄⋊C₄	—	2	6	no	—
41	C₄⋊C₄	C₂²⋊D₄₃	1	6	yes	—
42	C₄²	—	2	2	no	—
43	C₄²	C₂²×D₄₃	1	1	yes	characteristic
44	C₂³	—	172	1	no	—
45	D₄	—	172	6	no	—
46	C₂×C₄	—	2	6	no	—
47	C₂×C₄	C₂×C₂²⋊D₄₃	1	3	yes	—
48	C₈	—	172	3	no	—
49	C₂²	—	344	3	no	—
50	C₂²	#13063294	1	1	yes	characteristic
51	C₄	—	2	3	no	—
52	C₄	—	4	6	no	—
53	C₂	—	688	1	no	—
54	C₂	#14583072	1	3	yes	—

	subgroup	G/H
center	C₂²	#13063294
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#564	C₂
socle	C₂²×C₄₃	#120
hypercenter	#564	D₄₃
hypocenter	C₄₃	#1658
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #564

Complements

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

N	H ≅ G/N	type
2. #14582641	C₂	semidirect
3. C₄₃×#564	C₂	semidirect
28. #564	D₄₃	semidirect
31. C₄₃	#1658	semidirect