Subgroups — #21422198

Order 7552.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837440	C₂	1	2	yes	maximal
2	C₂×M₃₂×C₅₉	C₂	1	1	yes	maximal, characteristic
3	#14273686	—	2	2	no	—
4	#14273661	—	2	2	no	—
5	#14273659	C₄	1	4	yes	complemented
6	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
7	M₃₂×C₅₉	—	2	2	no	—
8	C₂×C₁₆×C₅₉	C₄	1	2	yes	complemented
9	C₂²×C₄×C₅₉	D₄	1	1	yes	characteristic
10	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
11	C₂×C₈×C₅₉	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₅₉	D₄	1	2	yes	—
13	C₂×C₈×C₅₉	Q₈	1	1	yes	characteristic
14	C₂²⋊Dic₅₉	—	4	2	no	—
15	C₄⋊Dic₅₉	—	2	4	no	—
16	C₄×Dic₅₉	—	4	2	no	—
17	C₁₆×C₅₉	—	2	2	no	—
18	C₂³×C₅₉	D₈	1	1	yes	characteristic
19	C₂×C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₅₉	SD₁₆	1	2	yes	—
22	C₂×C₄×C₅₉	Q₁₆	1	1	yes	characteristic
23	C₂×Dic₅₉	—	4	4	no	—
24	C₈×C₅₉	C₄²	1	1	yes	characteristic
25	C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₅₉	C₄⋊C₄	1	2	yes	—
27	C₂²×C₅₉	—	4	1	no	—
28	C₂²×C₅₉	#102	1	2	yes	—
29	C₂²×C₅₉	#107	1	1	yes	characteristic
30	C₄×C₅₉	#95	1	1	yes	characteristic
31	C₄×C₅₉	#103	1	2	yes	—
32	C₄×C₅₉	#106	1	1	yes	characteristic
33	Dic₅₉	—	8	4	no	—
34	#1384	—	59	1	no	maximal, Sylow
35	C₂×C₅₉	—	2	2	no	—
36	C₂×C₅₉	—	2	1	no	—
37	C₂×C₅₉	#340	1	1	yes	characteristic
38	C₂×M₃₂	D₅₉	1	1	yes	characteristic
39	#427	—	59	2	no	—
40	C₅₉	#1384	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
42	#117	—	118	2	no	—
43	M₃₂	—	2	2	no	—
44	C₂×C₁₆	Dic₅₉	1	2	yes	complemented
45	#107	—	118	2	no	—
46	#106	—	59	4	no	—
47	C₂²×C₄	D₂₃₆	1	1	yes	characteristic
48	C₂×C₈	Dic₁₁₈	1	1	yes	characteristic
49	C₂×C₈	C₄×D₅₉	1	2	yes	—
50	C₂×C₈	C₂×Dic₅₉	1	1	yes	characteristic
51	C₂×C₈	C₂²⋊D₅₉	1	2	yes	—
52	C₄⋊C₄	—	118	4	no	—
53	C₂²⋊C₄	—	236	2	no	—
54	C₄²	—	236	2	no	—
55	C₁₆	—	2	2	no	—
56	C₂³	D₄₇₂	1	1	yes	characteristic
57	C₂×C₄	—	236	4	no	—
58	C₂×C₄	#11745660	1	2	yes	—
59	C₂×C₄	Dic₂₃₆	1	1	yes	characteristic
60	C₂×C₄	C₄⋊Dic₅₉	1	1	yes	characteristic
61	C₂×C₄	(C₂×D₅₉)⋊C₄	1	2	yes	—
62	C₈	C₄×Dic₅₉	1	1	yes	characteristic
63	C₈	Dic₅₉⋊C₄	1	2	yes	—
64	C₈	C₂²⋊Dic₅₉	1	1	yes	characteristic
65	C₂²	—	4	1	no	—
66	C₂²	#14273649	1	2	yes	—
67	C₂²	#14273661	1	1	yes	characteristic
68	C₄	—	472	4	no	—
69	C₄	C₅₉⋊#95	1	1	yes	characteristic
70	C₄	#14273652	1	2	yes	—
71	C₄	#14273659	1	1	yes	characteristic
72	C₂	—	2	2	no	—
73	C₂	—	2	1	no	—
74	C₂	#16837165	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14273659
commutator	C₈×C₅₉	C₄²
Frattini	C₂²×C₈	C₂×D₅₉
Fitting	C₂×M₃₂×C₅₉	C₂
socle	C₂×C₅₉	#340
hypercenter	C₂×M₃₂	D₅₉
hypocenter	C₅₉	#1384
LCS	G ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
5. #14273659	C₄	semidirect
8. C₂×C₁₆×C₅₉	C₄	semidirect
40. C₅₉	#1384	semidirect
44. C₂×C₁₆	Dic₅₉	semidirect