Subgroups — #21423714

Order 7552.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837807	C₂	1	4	yes	maximal
2	#16837782	C₂	1	2	yes	maximal
3	C₈²×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₃₆	—	2	4	no	—
5	#14273727	C₂²	1	4	yes	—
6	#14273661	—	2	8	no	—
7	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₅₉	C₂²	1	2	yes	—
9	C₂×Dic₁₁₈	—	2	4	no	—
10	C₂×C₈×C₅₉	D₄	1	2	yes	—
11	C₂×C₈×C₅₉	D₄	1	4	yes	—
12	C₄²×C₅₉	C₂³	1	1	yes	characteristic
13	C₄⋊Dic₅₉	—	2	8	no	—
14	Dic₂₃₆	—	4	8	no	—
15	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
16	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
17	C₂×Dic₅₉	—	4	4	no	—
18	Dic₁₁₈	—	4	8	no	—
19	C₈×C₅₉	D₈	1	4	yes	—
20	C₈×C₅₉	Q₁₆	1	8	yes	complemented
21	C₂²×C₅₉	#127	1	1	yes	characteristic
22	C₄×C₅₉	C₂×D₈	1	2	yes	—
23	C₄×C₅₉	C₂×Q₁₆	1	4	yes	—
24	Dic₅₉	—	8	4	no	—
25	#1713	—	59	1	no	maximal, Sylow
26	C₂×C₅₉	#493	1	1	yes	characteristic
27	C₂×C₅₉	#494	1	2	yes	—
28	#500	—	59	4	no	—
29	#494	—	59	2	no	—
30	C₈²	D₅₉	1	1	yes	characteristic
31	C₅₉	#1713	1	1	yes	characteristic, complemented, Sylow
32	C₂×Q₁₆	—	118	4	no	—
33	C₄⋊Q₈	—	59	4	no	—
34	#107	—	118	8	no	—
35	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
36	C₄×C₈	C₂×D₅₉	1	2	yes	—
37	C₂×Q₈	—	118	4	no	—
38	Q₁₆	—	236	8	no	—
39	C₂×C₈	D₂₃₆	1	2	yes	—
40	C₂×C₈	D₂₃₆	1	4	yes	—
41	C₄⋊C₄	—	118	8	no	—
42	C₄²	C₂²×D₅₉	1	1	yes	characteristic
43	Q₈	—	236	8	no	—
44	C₂×C₄	—	236	4	no	—
45	C₂×C₄	C₂×D₂₃₆	1	1	yes	characteristic
46	C₂×C₄	C₂×D₂₃₆	1	2	yes	—
47	C₈	D₄₇₂	1	4	yes	—
48	C₈	Dic₂₃₆	1	8	yes	complemented
49	C₂²	#14273724	1	1	yes	characteristic
50	C₄	—	472	4	no	—
51	C₄	C₂×D₄₇₂	1	2	yes	—
52	C₄	C₂×Dic₂₃₆	1	4	yes	—
53	C₂	#16837779	1	1	yes	characteristic
54	C₂	#16837782	1	2	yes	—

	subgroup	G/H
center	C₂²	#14273724
commutator	C₄²×C₅₉	C₂³
Frattini	C₄²	C₂²×D₅₉
Fitting	C₈²×C₅₉	C₂
socle	C₂²×C₅₉	#127
hypercenter	C₈²	D₅₉
hypocenter	C₅₉	#1713
LCS	G ▷ C₄²×C₅₉ ▷ C₂²×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
20. C₈×C₅₉	Q₁₆	semidirect
31. C₅₉	#1713	semidirect
48. C₈	Dic₂₃₆	semidirect