Subgroups — #21426390

Order 7552.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837236	C₂	1	3	yes	maximal, complemented
2	C₂×C₅₉⋊C₃₂	C₂	1	3	yes	maximal, complemented
3	C₅₉×#504	C₂	1	1	yes	maximal, characteristic
4	C₅₉⋊C₃₂	C₂²	1	1	yes	characteristic
5	C₅₉⋊C₃₂	C₂²	1	3	yes	—
6	#131×C₅₉	C₄	1	1	yes	characteristic
7	M₃₂×C₅₉	C₄	1	3	yes	—
8	C₂×C₁₆×C₅₉	C₂²	1	3	yes	—
9	#41×C₅₉	C₈	1	1	yes	characteristic
10	M₁₆×C₅₉	C₈	1	3	yes	—
11	C₂×C₈×C₅₉	C₂×C₄	1	3	yes	—
12	C₁₆×C₅₉	C₂×C₄	1	3	yes	—
13	C₁₆×C₅₉	C₂³	1	1	yes	characteristic
14	Q₈×C₅₉	C₁₆	1	1	yes	characteristic
15	D₄×C₅₉	C₁₆	1	3	yes	—
16	C₂×C₄×C₅₉	C₂×C₈	1	3	yes	—
17	C₈×C₅₉	C₂×C₈	1	3	yes	—
18	C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
19	C₂²×C₅₉	C₂×C₁₆	1	3	yes	—
20	C₄×C₅₉	C₂×C₁₆	1	3	yes	—
21	C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
22	#2258	—	59	1	no	maximal, Sylow
23	C₂×C₅₉	—	2	3	no	—
24	C₂×C₅₉	C₂²×C₁₆	1	1	yes	characteristic
25	#504	D₅₉	1	1	yes	characteristic
26	M₆₄	—	59	3	no	—
27	C₂×C₃₂	—	59	3	no	—
28	C₅₉	#2258	1	1	yes	characteristic, complemented, Sylow
29	#131	Dic₅₉	1	1	yes	characteristic
30	M₃₂	Dic₅₉	1	3	yes	—
31	C₂×C₁₆	C₂×D₅₉	1	3	yes	—
32	C₃₂	—	59	1	no	—
33	C₃₂	—	59	3	no	—
34	#41	C₅₉⋊C₈	1	1	yes	characteristic
35	M₁₆	C₅₉⋊C₈	1	3	yes	—
36	C₂×C₈	C₂×Dic₅₉	1	3	yes	—
37	C₁₆	C₂×Dic₅₉	1	3	yes	—
38	C₁₆	C₂²×D₅₉	1	1	yes	characteristic
39	Q₈	C₅₉⋊C₁₆	1	1	yes	characteristic
40	D₄	C₅₉⋊C₁₆	1	3	yes	—
41	C₂×C₄	C₂×C₅₉⋊C₈	1	3	yes	—
42	C₈	C₂×C₅₉⋊C₈	1	3	yes	—
43	C₈	C₂²×Dic₅₉	1	1	yes	characteristic
44	C₂²	C₂×C₅₉⋊C₁₆	1	3	yes	—
45	C₄	C₂×C₅₉⋊C₁₆	1	3	yes	—
46	C₄	C₂²×C₅₉⋊C₈	1	1	yes	characteristic
47	C₂	—	2	3	no	—
48	C₂	C₂²×C₅₉⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₁₆	C₂²×D₅₉
commutator, socle	C₂×C₅₉	C₂²×C₁₆
Fitting	C₅₉×#504	C₂
hypercenter	#504	D₅₉
hypocenter	C₅₉	#2258
LCS	G ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₁₆ ◁ #504

Complements

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

N	H ≅ G/N	type
1. #16837236	C₂	semidirect
2. C₂×C₅₉⋊C₃₂	C₂	semidirect
28. C₅₉	#2258	semidirect