Subgroups — #21424235

Order 7552.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837425	C₂	1	2	yes	maximal
2	C₂×#14273637	C₂	1	1	yes	maximal, characteristic
3	#16837167	C₂	1	1	yes	maximal, characteristic
4	#16837166	C₂	1	2	yes	maximal
5	C₅₉×#341	C₂	1	1	yes	maximal, characteristic
6	C₂×#11745664	C₂²	1	2	yes	—
7	C₂²×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₅₉	C₂²	1	1	yes	characteristic
9	Dic₅₉⋊C₈	—	2	4	no	—
10	#14273637	C₄	1	4	yes	—
11	C₂×M₁₆×C₅₉	C₂²	1	2	yes	—
12	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
14	C₂²×Dic₅₉	Q₈	1	2	yes	—
15	M₁₆×C₅₉	—	2	2	no	—
16	M₁₆×C₅₉	—	2	2	no	—
17	C₂×C₈×C₅₉	—	2	2	no	—
18	C₂×C₈×C₅₉	—	2	2	no	—
19	C₂×C₈×C₅₉	C₂×C₄	1	2	yes	—
20	C₄×Dic₅₉	C₂×C₄	1	2	yes	—
21	C₄×Dic₅₉	D₄	1	2	yes	—
22	#11745664	—	2	2	no	—
23	#11745664	—	2	2	no	—
24	C₂×C₅₉⋊C₈	—	2	2	no	—
25	C₂×C₅₉⋊C₈	—	2	2	no	—
26	C₂×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
27	C₂³×C₅₉	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₅₉	#41	1	2	yes	—
31	C₂×C₄×C₅₉	#41	1	2	yes	—
32	C₂×Dic₅₉	—	4	2	no	—
33	C₂×Dic₅₉	C₄⋊C₄	1	4	yes	—
34	C₈×C₅₉	—	2	2	no	—
35	C₈×C₅₉	—	4	2	no	—
36	C₅₉⋊C₈	—	2	2	no	—
37	C₅₉⋊C₈	—	4	2	no	—
38	C₂²×C₅₉	—	2	2	no	—
39	C₂²×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₅₉	#125	1	2	yes	—
41	C₄×C₅₉	#117	1	1	yes	characteristic
42	C₄×C₅₉	#117	1	1	yes	characteristic
43	C₄×C₅₉	#124	1	2	yes	—
44	Dic₅₉	—	2	4	no	—
45	#1838	—	59	1	no	maximal, Sylow
46	C₂×C₅₉	—	2	2	no	—
47	C₂×C₅₉	#382	1	1	yes	characteristic
48	C₂×C₅₉	#430	1	2	yes	—
49	#423	—	59	2	no	—
50	C₂×#97	—	59	1	no	—
51	#341	—	59	2	no	—
52	#341	—	59	1	no	—
53	#341	D₅₉	1	1	yes	characteristic
54	C₅₉	#1838	1	1	yes	characteristic, complemented, Sylow
55	C₂×M₁₆	—	59	2	no	—
56	C₂×M₁₆	C₂×D₅₉	1	2	yes	—
57	C₂²×C₈	—	59	1	no	—
58	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
59	C₂×C₄²	—	59	1	no	—
60	C₄⋊C₈	—	118	4	no	—
61	#97	—	59	4	no	—
62	C₂²×C₄	—	59	2	no	—
63	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
64	M₁₆	—	2	2	no	—
65	M₁₆	—	2	2	no	—
66	M₁₆	—	118	2	no	—
67	M₁₆	—	118	2	no	—
68	C₂×C₈	—	2	2	no	—
69	C₂×C₈	—	2	2	no	—
70	C₂×C₈	—	59	2	no	—
71	C₂×C₈	—	118	2	no	—
72	C₂×C₈	—	118	2	no	—
73	C₂×C₈	C₄×D₅₉	1	2	yes	—
74	C₄²	—	59	2	no	—
75	C₄²	—	59	2	no	—
76	C₂³	Q₈×D₅₉	1	1	yes	characteristic
77	C₂×C₄	—	59	4	no	—
78	C₂×C₄	—	236	2	no	—
79	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
80	C₂×C₄	#11745685	1	2	yes	—
81	C₂×C₄	D₄×D₅₉	1	1	yes	characteristic
82	C₂×C₄	#11745687	1	2	yes	—
83	C₈	—	2	2	no	—
84	C₈	—	4	2	no	—
85	C₈	—	118	2	no	—
86	C₈	—	236	2	no	—
87	C₂²	—	2	2	no	—
88	C₂²	C₄⋊C₄×D₅₉	1	1	yes	characteristic
89	C₂²	#14273717	1	2	yes	—
90	C₄	—	118	4	no	—
91	C₄	#14273683	1	1	yes	characteristic
92	C₄	#14273684	1	1	yes	characteristic
93	C₄	#14273713	1	2	yes	—
94	C₂	—	2	2	no	—
95	C₂	#16837266	1	1	yes	characteristic
96	C₂	#16837449	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₅₉
Fitting	C₅₉×#341	C₂
socle	C₂²×C₅₉	C₂×C₄⋊C₄
hypercenter	#341	D₅₉
hypocenter	C₅₉	#1838
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #341

Complements

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

N	H ≅ G/N	type
54. C₅₉	#1838	semidirect