Subgroups — #21424248

Order 7552.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊(C₅₉⋊C₈)	C₂	1	6	yes	maximal
2	C₄³×C₅₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅₉⋊C₈	C₂²	1	4	yes	—
4	C₄⋊(C₅₉⋊C₈)	—	2	12	no	—
5	C₂×C₄²×C₅₉	C₄	1	3	yes	—
6	C₂×C₄²×C₅₉	C₄	1	1	yes	characteristic
7	C₂×C₄²×C₅₉	C₂²	1	3	yes	—
8	C₂²×C₄×C₅₉	C₂×C₄	1	3	yes	—
9	C₂²×C₄×C₅₉	C₂×C₄	1	3	yes	—
10	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
11	C₄²×C₅₉	—	2	6	no	—
12	C₄²×C₅₉	C₈	1	4	yes	complemented
13	C₄²×C₅₉	D₄	1	6	yes	—
14	C₄²×C₅₉	Q₈	1	6	yes	—
15	C₂×C₅₉⋊C₈	—	2	12	no	—
16	C₂³×C₅₉	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₄×C₅₉	—	2	6	no	—
18	C₂×C₄×C₅₉	C₄⋊C₄	1	6	yes	—
19	C₂×C₄×C₅₉	C₄⋊C₄	1	6	yes	—
20	C₂×C₄×C₅₉	C₂×C₈	1	6	yes	—
21	C₂×C₄×C₅₉	M₁₆	1	6	yes	—
22	C₂×C₄×C₅₉	C₂×D₄	1	3	yes	—
23	C₂×C₄×C₅₉	C₂×Q₈	1	3	yes	—
24	C₅₉⋊C₈	—	4	4	no	—
25	C₂²×C₅₉	C₂×C₄⋊C₄	1	3	yes	—
26	C₂²×C₅₉	C₂²×C₈	1	1	yes	characteristic
27	C₂²×C₅₉	C₂×M₁₆	1	3	yes	—
28	C₄×C₅₉	—	2	6	no	—
29	C₄×C₅₉	C₄⋊C₈	1	12	yes	complemented
30	C₄×C₅₉	#127	1	1	yes	characteristic
31	C₄×C₅₉	C₄⋊Q₈	1	3	yes	—
32	#1842	—	59	1	no	maximal, Sylow
33	C₂×C₅₉	#384	1	1	yes	characteristic
34	C₂×C₅₉	C₂×C₄⋊C₈	1	3	yes	—
35	C₂×C₅₉	#423	1	3	yes	—
36	C₂×C₄⋊C₈	—	59	6	no	—
37	C₄³	D₅₉	1	1	yes	characteristic
38	C₅₉	#1842	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₈	—	59	4	no	—
40	C₂×C₄²	Dic₅₉	1	3	yes	—
41	C₂×C₄²	Dic₅₉	1	1	yes	characteristic
42	C₂×C₄²	C₂×D₅₉	1	3	yes	—
43	C₄⋊C₈	—	118	12	no	—
44	C₂²×C₄	C₂×Dic₅₉	1	3	yes	—
45	C₂²×C₄	C₂×Dic₅₉	1	3	yes	—
46	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
47	C₂×C₈	—	118	12	no	—
48	C₄²	—	2	6	no	—
49	C₄²	C₅₉⋊C₈	1	4	yes	complemented
50	C₄²	Dic₁₁₈	1	6	yes	—
51	C₄²	D₂₃₆	1	6	yes	—
52	C₂³	C₂²×Dic₅₉	1	1	yes	characteristic
53	C₂×C₄	—	2	6	no	—
54	C₂×C₄	C₂×C₅₉⋊C₈	1	6	yes	—
55	C₂×C₄	#11745664	1	6	yes	—
56	C₂×C₄	C₄⋊Dic₅₉	1	6	yes	—
57	C₂×C₄	C₄⋊Dic₅₉	1	6	yes	—
58	C₂×C₄	C₂×Dic₁₁₈	1	3	yes	—
59	C₂×C₄	C₂×D₂₃₆	1	3	yes	—
60	C₈	—	236	4	no	—
61	C₂²	C₂×C₄⋊Dic₅₉	1	3	yes	—
62	C₂²	C₂²×C₅₉⋊C₈	1	1	yes	characteristic
63	C₂²	C₂×#11745664	1	3	yes	—
64	C₄	—	2	6	no	—
65	C₄	C₄⋊(C₅₉⋊C₈)	1	12	yes	complemented
66	C₄	#14273724	1	1	yes	characteristic
67	C₄	#14273727	1	3	yes	—
68	C₂	#16837272	1	1	yes	characteristic
69	C₂	C₂×C₄⋊(C₅₉⋊C₈)	1	3	yes	—
70	C₂	#16837426	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₅₉
commutator	C₂²×C₅₉	C₂²×C₈
Fitting	C₄³×C₅₉	C₂
socle	C₂³×C₅₉	C₂²×C₄
hypercenter	C₄³	D₅₉
hypocenter	C₅₉	#1842
LCS	G ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³

Complements

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

N	H ≅ G/N	type
12. C₄²×C₅₉	C₈	semidirect
29. C₄×C₅₉	C₄⋊C₈	semidirect
38. C₅₉	#1842	semidirect
49. C₄²	C₅₉⋊C₈	semidirect
65. C₄	C₄⋊(C₅₉⋊C₈)	semidirect