Subgroups — #21422014

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	2	yes	maximal
2	C₈²×C₅₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅₉⋊C₁₆	C₄	1	4	yes	—
4	C₄×C₈×C₅₉	C₄	1	1	yes	characteristic
5	C₄×C₈×C₅₉	C₄	1	1	yes	characteristic
6	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₅₉	C₈	1	2	yes	—
8	C₂×C₈×C₅₉	C₈	1	2	yes	—
9	C₂×C₈×C₅₉	C₂×C₄	1	2	yes	—
10	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
11	C₅₉⋊C₁₆	—	2	4	no	—
12	C₂×C₄×C₅₉	C₄²	1	1	yes	characteristic
13	C₂×C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
14	C₂×C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
15	C₈×C₅₉	—	2	2	no	—
16	C₈×C₅₉	C₁₆	1	4	yes	complemented
17	C₈×C₅₉	M₁₆	1	4	yes	—
18	C₂²×C₅₉	C₄×C₈	1	1	yes	characteristic
19	C₄×C₅₉	#97	1	2	yes	—
20	C₄×C₅₉	C₂×C₁₆	1	2	yes	—
21	C₄×C₅₉	M₃₂	1	2	yes	—
22	#1312	—	59	1	no	maximal, Sylow
23	C₂×C₅₉	#322	1	1	yes	characteristic
24	C₂×C₅₉	C₄×C₁₆	1	1	yes	characteristic
25	C₂×C₅₉	#346	1	1	yes	characteristic
26	C₄×C₁₆	—	59	2	no	—
27	C₈²	D₅₉	1	1	yes	characteristic
28	C₅₉	#1312	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₁₆	—	59	4	no	—
30	C₄×C₈	Dic₅₉	1	1	yes	characteristic
31	C₄×C₈	Dic₅₉	1	1	yes	characteristic
32	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
33	C₂×C₈	C₅₉⋊C₈	1	2	yes	—
34	C₂×C₈	C₅₉⋊C₈	1	2	yes	—
35	C₂×C₈	C₄×D₅₉	1	2	yes	—
36	C₄²	C₂×Dic₅₉	1	1	yes	characteristic
37	C₁₆	—	118	4	no	—
38	C₂×C₄	C₂×C₅₉⋊C₈	1	1	yes	characteristic
39	C₂×C₄	C₂×C₅₉⋊C₈	1	1	yes	characteristic
40	C₂×C₄	C₄×Dic₅₉	1	1	yes	characteristic
41	C₈	—	2	2	no	—
42	C₈	C₅₉⋊C₁₆	1	4	yes	complemented
43	C₈	#11745659	1	4	yes	—
44	C₂²	C₄×C₅₉⋊C₈	1	1	yes	characteristic
45	C₄	#14273637	1	2	yes	—
46	C₄	C₂×C₅₉⋊C₁₆	1	2	yes	—
47	C₄	#14273667	1	2	yes	—
48	C₂	#16837123	1	1	yes	characteristic
49	C₂	C₄×C₅₉⋊C₁₆	1	1	yes	characteristic
50	C₂	#16837178	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄×C₈	C₂×D₅₉
commutator	C₂×C₅₉	C₄×C₁₆
Fitting	C₈²×C₅₉	C₂
socle	C₂²×C₅₉	C₄×C₈
hypercenter	C₈²	D₅₉
hypocenter	C₅₉	#1312
LCS	G ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄×C₈ ◁ C₈²

Complements

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

N	H ≅ G/N	type
16. C₈×C₅₉	C₁₆	semidirect
28. C₅₉	#1312	semidirect
42. C₈	C₅₉⋊C₁₆	semidirect