Subgroups — #21423683

Order 7552.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837800	C₂	1	3	yes	maximal, complemented
2	#16837775	C₂	1	3	yes	maximal
3	C₈²×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11745660	—	2	6	no	—
5	#14273727	C₂²	1	3	yes	—
6	#14273724	C₂²	1	1	yes	characteristic
7	#14273659	—	2	6	no	—
8	C₄×C₈×C₅₉	C₂²	1	3	yes	—
9	C₂×D₂₃₆	—	2	3	no	—
10	C₂×Dic₁₁₈	—	2	3	no	—
11	C₂×C₈×C₅₉	D₄	1	6	yes	—
12	C₄²×C₅₉	C₂³	1	1	yes	characteristic
13	C₄⋊Dic₅₉	—	2	6	no	—
14	#11745660	—	4	12	no	—
15	C₂²×D₅₉	—	4	1	no	—
16	C₂×C₄×C₅₉	C₂×D₄	1	3	yes	—
17	C₂×Dic₅₉	—	4	3	no	—
18	D₂₃₆	—	4	6	no	—
19	Dic₁₁₈	—	4	6	no	—
20	C₈×C₅₉	SD₁₆	1	12	yes	complemented
21	C₂²×C₅₉	#127	1	1	yes	characteristic
22	C₂×D₅₉	—	8	3	no	—
23	C₄×C₅₉	C₂×SD₁₆	1	6	yes	—
24	Dic₅₉	—	8	3	no	—
25	#1705	—	59	1	no	maximal, Sylow
26	C₂×C₅₉	#492	1	3	yes	—
27	D₅₉	—	16	1	no	—
28	#498	—	59	3	no	—
29	#492	—	59	3	no	—
30	C₈²	D₅₉	1	1	yes	characteristic, complemented
31	C₅₉	#1705	1	1	yes	characteristic, complemented, Sylow
32	C₂×SD₁₆	—	118	6	no	—
33	C₄⋊Q₈	—	59	3	no	—
34	#127	—	59	1	no	—
35	#106	—	118	6	no	—
36	C₄×C₈	C₂×D₅₉	1	3	yes	—
37	C₂×Q₈	—	118	3	no	—
38	C₂×D₄	—	118	3	no	—
39	SD₁₆	—	236	12	no	—
40	C₂×C₈	D₂₃₆	1	6	yes	—
41	C₄⋊C₄	—	118	6	no	—
42	C₄²	C₂²×D₅₉	1	1	yes	characteristic
43	C₂³	—	236	1	no	—
44	Q₈	—	236	6	no	—
45	D₄	—	236	6	no	—
46	C₂×C₄	—	236	3	no	—
47	C₂×C₄	C₂×D₂₃₆	1	3	yes	—
48	C₈	#11745660	1	12	yes	complemented
49	C₂²	—	472	3	no	—
50	C₂²	#14273724	1	1	yes	characteristic
51	C₄	—	472	3	no	—
52	C₄	C₂×#11745660	1	6	yes	—
53	C₂	—	944	1	no	—
54	C₂	#16837775	1	3	yes	—

	subgroup	G/H
center	C₂²	#14273724
commutator	C₄²×C₅₉	C₂³
Frattini	C₄²	C₂²×D₅₉
Fitting	C₈²×C₅₉	C₂
socle	C₂²×C₅₉	#127
hypercenter	C₈²	D₅₉
hypocenter	C₅₉	#1705
LCS	G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
1. #16837800	C₂	semidirect
3. C₈²×C₅₉	C₂	semidirect
20. C₈×C₅₉	SD₁₆	semidirect
30. C₈²	D₅₉	semidirect
31. C₅₉	#1705	semidirect
48. C₈	#11745660	semidirect