Subgroups — #21423398

Order 7552.

182 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837768	C₂	1	3	yes	maximal
2	#16837144	C₂	1	3	yes	maximal, complemented
3	C₅₉×#564	C₂	1	1	yes	maximal, characteristic, complemented
4	#14273724	C₂²	1	1	yes	characteristic
5	#14273647	—	2	6	no	—
6	#14273638	C₂²	1	3	yes	—
7	#125×C₅₉	—	2	6	no	—
8	#125×C₅₉	C₂²	1	3	yes	—
9	C₂×D₂₃₆	—	2	3	no	—
10	C₄⋊C₄×C₅₉	—	2	6	no	—
11	C₄⋊C₄×C₅₉	—	2	6	no	—
12	C₄⋊C₄×C₅₉	D₄	1	6	yes	—
13	C₄²×C₅₉	—	2	2	no	—
14	C₄²×C₅₉	C₂³	1	1	yes	characteristic
15	C₂×C₅₉⋊C₈	—	2	3	no	—
16	C₂²×D₅₉	—	4	1	no	—
17	C₂×C₄×C₅₉	—	2	6	no	—
18	C₂×C₄×C₅₉	C₂×D₄	1	3	yes	—
19	D₂₃₆	—	4	6	no	—
20	C₅₉⋊C₈	—	4	3	no	—
21	C₂²×C₅₉	#120	1	1	yes	characteristic
22	C₂×D₅₉	—	8	3	no	—
23	C₄×C₅₉	—	2	3	no	—
24	C₄×C₅₉	—	4	6	no	—
25	#1658	—	59	1	no	maximal, Sylow
26	C₂×C₅₉	#454	1	3	yes	—
27	D₅₉	—	16	1	no	—
28	#564	D₅₉	1	1	yes	characteristic, complemented
29	#490	—	59	3	no	—
30	#330	—	59	3	no	—
31	C₅₉	#1658	1	1	yes	characteristic, complemented, Sylow
32	#127	—	59	1	no	—
33	#125	—	2	6	no	—
34	#125	C₂×D₅₉	1	3	yes	—
35	#102	—	118	6	no	—
36	#97	—	59	3	no	—
37	C₂×D₄	—	118	3	no	—
38	C₂×C₈	—	118	3	no	—
39	C₄⋊C₄	—	2	6	no	—
40	C₄⋊C₄	—	2	6	no	—
41	C₄⋊C₄	C₂²⋊D₅₉	1	6	yes	—
42	C₄²	—	2	2	no	—
43	C₄²	C₂²×D₅₉	1	1	yes	characteristic
44	C₂³	—	236	1	no	—
45	D₄	—	236	6	no	—
46	C₂×C₄	—	2	6	no	—
47	C₂×C₄	C₂×C₂²⋊D₅₉	1	3	yes	—
48	C₈	—	236	3	no	—
49	C₂²	—	472	3	no	—
50	C₂²	#14273696	1	1	yes	characteristic
51	C₄	—	2	3	no	—
52	C₄	—	4	6	no	—
53	C₂	—	944	1	no	—
54	C₂	#16837575	1	3	yes	—

	subgroup	G/H
center	C₂²	#14273696
commutator	C₄²×C₅₉	C₂³
Frattini	C₄²	C₂²×D₅₉
Fitting	C₅₉×#564	C₂
socle	C₂²×C₅₉	#120
hypercenter	#564	D₅₉
hypocenter	C₅₉	#1658
LCS	G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #564

Complements

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

N	H ≅ G/N	type
2. #16837144	C₂	semidirect
3. C₅₉×#564	C₂	semidirect
28. #564	D₅₉	semidirect
31. C₅₉	#1658	semidirect