Subgroups — #21426371

Order 7552.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837807	C₂	1	2	yes	maximal
2	#16837228	C₂	1	4	yes	maximal
3	C₄×C₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic
4	#14273727	—	2	2	no	—
5	#14273661	—	2	2	no	—
6	#14273661	C₂²	1	4	yes	—
7	C₂×C₁₆×C₅₉	C₂²	1	2	yes	—
8	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
9	C₂×Dic₁₁₈	—	4	2	no	—
10	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
11	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
12	C₄²×C₅₉	D₄	1	1	yes	characteristic
13	C₄⋊Dic₅₉	—	2	4	no	—
14	C₄⋊Dic₅₉	—	4	2	no	—
15	C₁₆×C₅₉	Q₈	1	4	yes	complemented
16	C₂×C₄×C₅₉	D₈	1	1	yes	characteristic
17	C₂×C₄×C₅₉	D₈	1	1	yes	characteristic
18	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
19	C₂×Dic₅₉	—	4	4	no	—
20	Dic₁₁₈	—	8	4	no	—
21	C₈×C₅₉	Q₁₆	1	2	yes	—
22	C₈×C₅₉	C₂×Q₈	1	2	yes	—
23	C₂²×C₅₉	C₂×D₈	1	1	yes	characteristic
24	C₄×C₅₉	D₁₆	1	2	yes	—
25	C₄×C₅₉	Q₃₂	1	2	yes	—
26	C₄×C₅₉	C₄⋊Q₈	1	1	yes	characteristic
27	C₄×C₅₉	C₂×Q₁₆	1	1	yes	characteristic
28	Dic₅₉	—	8	4	no	—
29	#2252	—	59	1	no	maximal, Sylow
30	C₂×C₅₉	#500	1	1	yes	characteristic
31	C₂×C₅₉	C₂×D₁₆	1	1	yes	characteristic
32	C₂×C₅₉	C₂×Q₃₂	1	1	yes	characteristic
33	#500	—	59	2	no	—
34	#366	—	59	4	no	—
35	C₄×C₁₆	D₅₉	1	1	yes	characteristic
36	C₅₉	#2252	1	1	yes	characteristic, complemented, Sylow
37	C₄⋊Q₈	—	118	2	no	—
38	C₂×C₁₆	C₂×D₅₉	1	2	yes	—
39	#107	—	59	4	no	—
40	#107	—	118	2	no	—
41	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
42	C₂×Q₈	—	236	2	no	—
43	C₂×C₈	D₂₃₆	1	1	yes	characteristic
44	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
45	C₄⋊C₄	—	118	4	no	—
46	C₄⋊C₄	—	236	2	no	—
47	C₄²	D₂₃₆	1	1	yes	characteristic
48	C₁₆	Dic₁₁₈	1	4	yes	complemented
49	Q₈	—	472	4	no	—
50	C₂×C₄	—	236	4	no	—
51	C₂×C₄	D₄₇₂	1	1	yes	characteristic
52	C₂×C₄	D₄₇₂	1	1	yes	characteristic
53	C₂×C₄	C₂×D₂₃₆	1	1	yes	characteristic
54	C₈	Dic₂₃₆	1	2	yes	—
55	C₈	C₂×Dic₁₁₈	1	2	yes	—
56	C₂²	C₂×D₄₇₂	1	1	yes	characteristic
57	C₄	—	472	4	no	—
58	C₄	D₉₄₄	1	2	yes	—
59	C₄	Dic₄₇₂	1	2	yes	—
60	C₄	#14273727	1	1	yes	characteristic
61	C₄	C₂×Dic₂₃₆	1	1	yes	characteristic
62	C₂	#16837807	1	1	yes	characteristic
63	C₂	C₂×D₉₄₄	1	1	yes	characteristic
64	C₂	C₂×Dic₄₇₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄₇₂
commutator	C₂×C₈×C₅₉	C₂³
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₄×C₁₆×C₅₉	C₂
socle	C₂²×C₅₉	C₂×D₈
hypercenter	C₄×C₁₆	D₅₉
hypocenter	C₅₉	#2252
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
15. C₁₆×C₅₉	Q₈	semidirect
36. C₅₉	#2252	semidirect
48. C₁₆	Dic₁₁₈	semidirect