Subgroups — #21426323

Order 7552.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837807	C₂	1	1	yes	maximal, characteristic
2	#16837206	C₂	1	4	yes	maximal
3	C₄×C₅₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#494	C₂	1	1	yes	maximal, characteristic
5	#14273727	—	2	1	no	—
6	C₂×C₅₉⋊C₁₆	C₂²	1	2	yes	—
7	#14273661	—	2	1	no	—
8	#14273661	C₂²	1	2	yes	—
9	C₂×Q₁₆×C₅₉	—	2	1	no	—
10	C₂×Q₁₆×C₅₉	C₂²	1	2	yes	—
11	C₄⋊Q₈×C₅₉	—	2	1	no	—
12	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
13	C₂×Q₈×C₅₉	—	2	2	no	—
14	C₂×Dic₁₁₈	—	4	1	no	—
15	Q₁₆×C₅₉	—	2	4	no	—
16	Q₁₆×C₅₉	—	4	2	no	—
17	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
18	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
19	C₄⋊C₄×C₅₉	—	4	1	no	—
20	C₄⋊C₄×C₅₉	—	4	1	no	—
21	C₄²×C₅₉	D₄	1	1	yes	characteristic
22	C₄⋊Dic₅₉	—	2	2	no	—
23	C₄⋊Dic₅₉	—	4	1	no	—
24	C₅₉⋊C₁₆	—	2	2	no	—
25	Q₈×C₅₉	—	4	2	no	—
26	Q₈×C₅₉	—	4	2	no	—
27	C₂×C₄×C₅₉	—	4	2	no	—
28	C₂×C₄×C₅₉	D₈	1	1	yes	characteristic
29	C₂×C₄×C₅₉	D₈	1	1	yes	characteristic
30	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
31	C₂×Dic₅₉	—	4	2	no	—
32	Dic₁₁₈	—	8	2	no	—
33	C₈×C₅₉	SD₁₆	1	2	yes	—
34	C₈×C₅₉	#41	1	2	yes	—
35	C₂²×C₅₉	C₂×D₈	1	1	yes	characteristic
36	C₄×C₅₉	—	8	2	no	—
37	C₄×C₅₉	SD₃₂	1	2	yes	—
38	C₄×C₅₉	Q₃₂	1	2	yes	—
39	C₄×C₅₉	#124	1	1	yes	characteristic
40	C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
41	Dic₅₉	—	8	2	no	—
42	#2241	—	59	1	no	maximal, Sylow
43	C₂×C₅₉	#486	1	1	yes	characteristic
44	C₂×C₅₉	C₂×SD₃₂	1	1	yes	characteristic
45	C₂×C₅₉	C₂×Q₃₂	1	1	yes	characteristic
46	#500	—	59	1	no	—
47	#494	D₅₉	1	1	yes	characteristic
48	#358	—	59	4	no	—
49	C₄×C₁₆	—	59	1	no	—
50	C₅₉	#2241	1	1	yes	characteristic, complemented, Sylow
51	C₂×Q₁₆	—	2	1	no	—
52	C₂×Q₁₆	C₂×D₅₉	1	2	yes	—
53	C₄⋊Q₈	—	2	1	no	—
54	C₄⋊Q₈	—	118	1	no	—
55	C₂×C₁₆	—	59	2	no	—
56	#107	—	59	2	no	—
57	#107	—	118	1	no	—
58	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
59	C₂×Q₈	—	2	2	no	—
60	C₂×Q₈	—	236	1	no	—
61	Q₁₆	—	2	4	no	—
62	Q₁₆	—	4	2	no	—
63	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
64	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
65	C₄⋊C₄	—	4	1	no	—
66	C₄⋊C₄	—	4	1	no	—
67	C₄⋊C₄	—	118	2	no	—
68	C₄⋊C₄	—	236	1	no	—
69	C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
70	C₁₆	—	118	2	no	—
71	Q₈	—	4	2	no	—
72	Q₈	—	4	2	no	—
73	Q₈	—	472	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	236	2	no	—
76	C₂×C₄	#11745669	1	1	yes	characteristic
77	C₂×C₄	#11745669	1	1	yes	characteristic
78	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
79	C₈	#11745670	1	2	yes	—
80	C₈	#11745687	1	2	yes	—
81	C₂²	C₂×#11745669	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	472	2	no	—
84	C₄	#14273670	1	2	yes	—
85	C₄	#14273673	1	2	yes	—
86	C₄	#14273714	1	1	yes	characteristic
87	C₄	C₂×#11745670	1	1	yes	characteristic
88	C₂	#16837748	1	1	yes	characteristic
89	C₂	C₂×#14273670	1	1	yes	characteristic
90	C₂	C₂×#14273673	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#11745669
commutator	C₂×C₈×C₅₉	C₂³
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₅₉×#494	C₂
socle	C₂²×C₅₉	C₂×D₈
hypercenter	#494	D₅₉
hypocenter	C₅₉	#2241
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
50. C₅₉	#2241	semidirect