Subgroups — #21424268

Order 7552.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14273663	C₂	1	4	yes	maximal
2	#16837426	C₂	1	2	yes	maximal
3	C₂×C₄×C₈×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#11745664	C₂²	1	4	yes	—
5	#14273663	—	2	8	no	—
6	C₄⋊(C₅₉⋊C₈)	—	2	4	no	—
7	C₂²×C₈×C₅₉	C₂²	1	2	yes	—
8	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₅₉	C₄	1	2	yes	—
10	C₄×C₈×C₅₉	C₄	1	2	yes	—
11	C₂²×C₄×C₅₉	Q₈	1	2	yes	—
12	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
13	C₂×C₈×C₅₉	C₂×C₄	1	4	yes	—
14	C₂×C₈×C₅₉	D₄	1	4	yes	—
15	C₂×C₈×C₅₉	Q₈	1	4	yes	—
16	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
17	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
18	C₄²×C₅₉	D₄	1	2	yes	—
19	#11745664	—	2	8	no	—
20	C₂×C₅₉⋊C₈	—	2	4	no	—
21	C₂³×C₅₉	C₂×Q₈	1	1	yes	characteristic
22	C₂×C₄×C₅₉	—	2	4	no	—
23	C₂×C₄×C₅₉	C₄⋊C₄	1	2	yes	—
24	C₂×C₄×C₅₉	C₄⋊C₄	1	2	yes	—
25	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
27	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₅₉	C₂×Q₈	1	2	yes	—
29	C₈×C₅₉	C₄⋊C₄	1	8	yes	—
30	C₅₉⋊C₈	—	4	4	no	—
31	C₂²×C₅₉	—	2	2	no	—
32	C₂²×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
33	C₂²×C₅₉	C₄⋊Q₈	1	2	yes	—
34	C₄×C₅₉	—	2	2	no	—
35	C₄×C₅₉	#108	1	4	yes	complemented
36	C₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
37	C₄×C₅₉	#127	1	1	yes	characteristic
38	C₄×C₅₉	C₄⋊Q₈	1	1	yes	characteristic
39	#1848	—	59	1	no	maximal, Sylow
40	C₂×C₅₉	—	2	2	no	—
41	C₂×C₅₉	#384	1	1	yes	characteristic
42	C₂×C₅₉	C₂×#108	1	2	yes	—
43	C₂×#108	—	59	4	no	—
44	#423	—	59	2	no	—
45	C₂×C₄×C₈	D₅₉	1	1	yes	characteristic
46	C₅₉	#1848	1	1	yes	characteristic, complemented, Sylow
47	C₂×M₁₆	—	59	4	no	—
48	C₂²×C₈	C₂×D₅₉	1	2	yes	—
49	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
50	#108	—	118	8	no	—
51	C₄⋊C₈	—	118	4	no	—
52	C₄×C₈	Dic₅₉	1	2	yes	—
53	C₄×C₈	Dic₅₉	1	2	yes	—
54	C₂²×C₄	Dic₁₁₈	1	2	yes	—
55	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
56	M₁₆	—	118	8	no	—
57	C₂×C₈	—	118	4	no	—
58	C₂×C₈	Dic₁₁₈	1	4	yes	—
59	C₂×C₈	D₂₃₆	1	4	yes	—
60	C₂×C₈	C₂×Dic₅₉	1	4	yes	—
61	C₄²	D₂₃₆	1	2	yes	—
62	C₄²	C₂×Dic₅₉	1	1	yes	characteristic
63	C₄²	C₂×Dic₅₉	1	1	yes	characteristic
64	C₂³	C₂×Dic₁₁₈	1	1	yes	characteristic
65	C₂×C₄	—	2	4	no	—
66	C₂×C₄	C₄⋊Dic₅₉	1	2	yes	—
67	C₂×C₄	C₄⋊Dic₅₉	1	2	yes	—
68	C₂×C₄	C₂×Dic₁₁₈	1	2	yes	—
69	C₂×C₄	C₂×D₂₃₆	1	2	yes	—
70	C₂×C₄	C₂×D₂₃₆	1	1	yes	characteristic
71	C₂×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
72	C₈	—	236	4	no	—
73	C₈	C₄⋊Dic₅₉	1	8	yes	—
74	C₂²	—	2	2	no	—
75	C₂²	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
76	C₂²	#14273727	1	2	yes	—
77	C₄	—	2	2	no	—
78	C₄	#14273663	1	4	yes	complemented
79	C₄	C₂×C₄⋊Dic₅₉	1	2	yes	—
80	C₄	#14273724	1	1	yes	characteristic
81	C₄	#14273727	1	1	yes	characteristic
82	C₂	—	2	2	no	—
83	C₂	#16837272	1	1	yes	characteristic
84	C₂	C₂×#14273663	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₂₃₆
commutator	C₂×C₄×C₅₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₅₉
Fitting	C₂×C₄×C₈×C₅₉	C₂
socle	C₂²×C₅₉	C₂×C₄⋊C₄
hypercenter	C₂×C₄×C₈	D₅₉
hypocenter	C₅₉	#1848
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
35. C₄×C₅₉	#108	semidirect
46. C₅₉	#1848	semidirect
78. C₄	#14273663	semidirect