Subgroups — #21422015

Order 7552.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅₉⋊C₁₆	C₄	1	2	yes	—
5	C₄×C₅₉⋊C₈	C₄	1	1	yes	characteristic
6	C₄×C₅₉⋊C₈	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₅₉	C₄	1	2	yes	—
8	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
10	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
11	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₅₉⋊C₈	C₈	1	2	yes	—
13	C₂×C₅₉⋊C₈	C₈	1	2	yes	—
14	C₁₆×C₅₉	—	2	2	no	—
15	C₅₉⋊C₁₆	—	2	2	no	—
16	C₂×C₄×C₅₉	C₄²	1	1	yes	characteristic
17	C₂×C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
18	C₂×C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
19	C₈×C₅₉	M₁₆	1	2	yes	—
20	C₈×C₅₉	M₁₆	1	2	yes	—
21	C₅₉⋊C₈	—	2	2	no	—
22	C₅₉⋊C₈	C₁₆	1	4	yes	complemented
23	C₂²×C₅₉	C₄×C₈	1	1	yes	characteristic
24	C₄×C₅₉	#97	1	1	yes	characteristic
25	C₄×C₅₉	#97	1	1	yes	characteristic
26	C₄×C₅₉	C₂×C₁₆	1	2	yes	—
27	C₄×C₅₉	M₃₂	1	2	yes	—
28	#1312	—	59	1	no	maximal, Sylow
29	C₂×C₅₉	#322	1	1	yes	characteristic
30	C₂×C₅₉	C₄×C₁₆	1	1	yes	characteristic
31	C₂×C₅₉	#346	1	1	yes	characteristic
32	C₄×C₁₆	—	59	1	no	—
33	C₄×C₁₆	D₅₉	1	1	yes	characteristic
34	C₈²	—	59	1	no	—
35	C₅₉	#1312	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₁₆	—	59	2	no	—
37	C₂×C₁₆	Dic₅₉	1	2	yes	—
38	C₄×C₈	—	59	1	no	—
39	C₄×C₈	—	59	1	no	—
40	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
41	C₂×C₈	—	59	2	no	—
42	C₂×C₈	—	59	2	no	—
43	C₂×C₈	C₄×D₅₉	1	1	yes	characteristic
44	C₂×C₈	C₂×Dic₅₉	1	1	yes	characteristic
45	C₄²	C₄×D₅₉	1	1	yes	characteristic
46	C₁₆	—	2	2	no	—
47	C₁₆	—	118	2	no	—
48	C₂×C₄	C₈×D₅₉	1	1	yes	characteristic
49	C₂×C₄	C₈×D₅₉	1	1	yes	characteristic
50	C₂×C₄	C₄×Dic₅₉	1	1	yes	characteristic
51	C₈	—	59	4	no	—
52	C₈	—	118	2	no	—
53	C₈	#11745659	1	2	yes	—
54	C₈	#11745664	1	2	yes	—
55	C₂²	C₈×Dic₅₉	1	1	yes	characteristic
56	C₄	#14273637	1	1	yes	characteristic
57	C₄	#14273638	1	1	yes	characteristic
58	C₄	C₁₆×D₅₉	1	2	yes	—
59	C₄	#14273666	1	2	yes	—
60	C₂	#16837124	1	1	yes	characteristic
61	C₂	C₁₆×Dic₅₉	1	1	yes	characteristic
62	C₂	#16837177	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄×C₈	C₂×D₅₉
commutator	C₂×C₅₉	C₄×C₁₆
Fitting	C₄×C₁₆×C₅₉	C₂
socle	C₂²×C₅₉	C₄×C₈
hypercenter	C₄×C₁₆	D₅₉
hypocenter	C₅₉	#1312
LCS	G ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
22. C₅₉⋊C₈	C₁₆	semidirect
35. C₅₉	#1312	semidirect