Subgroups — #21425676

Order 7552.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837451	C₂	1	1	yes	maximal, characteristic
2	#16837172	C₂	1	2	yes	maximal
3	#16837167	C₂	1	2	yes	maximal
4	C₅₉⋊#338	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#424	C₂	1	1	yes	maximal, characteristic
6	C₂×#11745664	C₂²	1	2	yes	—
7	C₂×#11745664	C₂²	1	2	yes	—
8	#14273663	—	2	2	no	—
9	C₂×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
11	#117×C₅₉	C₂²	1	1	yes	characteristic
12	C₄⋊C₈×C₅₉	—	2	2	no	—
13	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
14	M₁₆×C₅₉	—	2	2	no	—
15	C₂×C₈×C₅₉	—	2	1	no	—
16	C₂×C₈×C₅₉	—	2	2	no	—
17	C₂×C₈×C₅₉	D₄	1	2	yes	—
18	C₄⋊C₄×C₅₉	—	2	1	no	—
19	C₂²⋊C₄×C₅₉	Q₈	1	2	yes	—
20	C₄²×C₅₉	—	2	1	no	—
21	#11745664	—	2	2	no	—
22	#11745664	—	2	2	no	—
23	#11745664	—	2	2	no	—
24	#11745664	—	2	2	no	—
25	C₂×C₅₉⋊C₈	—	2	2	no	—
26	C₂×C₅₉⋊C₈	—	2	2	no	—
27	C₂³×C₅₉	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₄×C₅₉	—	2	2	no	—
29	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₅₉	#41	1	1	yes	characteristic
31	C₂×C₄×C₅₉	#41	1	2	yes	—
32	C₂×C₄×C₅₉	#41	1	2	yes	—
33	C₈×C₅₉	—	2	2	no	—
34	C₈×C₅₉	—	4	1	no	—
35	C₅₉⋊C₈	—	4	2	no	—
36	C₅₉⋊C₈	—	4	2	no	—
37	C₂²×C₅₉	—	4	1	no	—
38	C₂²×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
39	C₂²×C₅₉	#125	1	2	yes	—
40	C₄×C₅₉	—	4	2	no	—
41	C₄×C₅₉	#123	1	1	yes	characteristic
42	C₄×C₅₉	#124	1	1	yes	characteristic
43	C₄×C₅₉	#126	1	2	yes	—
44	#2103	—	59	1	no	maximal, Sylow
45	C₂×C₅₉	—	2	1	no	—
46	C₂×C₅₉	—	2	2	no	—
47	C₂×C₅₉	#400	1	1	yes	characteristic
48	#430	—	59	1	no	—
49	#424	D₅₉	1	1	yes	characteristic
50	#344	—	59	2	no	—
51	#341	—	59	2	no	—
52	#338	—	59	1	no	—
53	C₅₉	#2103	1	1	yes	characteristic, complemented, Sylow
54	C₂×M₁₆	—	59	2	no	—
55	C₂×M₁₆	—	59	2	no	—
56	C₂×M₁₆	C₂×D₅₉	1	1	yes	characteristic
57	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
58	#117	C₂×D₅₉	1	1	yes	characteristic
59	#108	—	118	2	no	—
60	C₄⋊C₈	—	2	2	no	—
61	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
62	M₁₆	—	2	2	no	—
63	M₁₆	—	118	2	no	—
64	M₁₆	—	118	2	no	—
65	M₁₆	—	118	2	no	—
66	M₁₆	—	118	2	no	—
67	C₂×C₈	—	2	2	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	118	2	no	—
70	C₂×C₈	—	118	2	no	—
71	C₂×C₈	C₂²⋊D₅₉	1	2	yes	—
72	C₄⋊C₄	—	2	1	no	—
73	C₂²⋊C₄	Dic₁₁₈	1	2	yes	—
74	C₄²	—	2	1	no	—
75	C₂³	C₂×Dic₁₁₈	1	1	yes	characteristic
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	#11745685	1	1	yes	characteristic
78	C₂×C₄	#11745687	1	2	yes	—
79	C₂×C₄	#11745689	1	2	yes	—
80	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
81	C₈	—	2	2	no	—
82	C₈	—	4	1	no	—
83	C₈	—	236	2	no	—
84	C₈	—	236	2	no	—
85	C₂²	—	4	1	no	—
86	C₂²	#14273706	1	1	yes	characteristic
87	C₂²	#14273718	1	2	yes	—
88	C₄	—	4	2	no	—
89	C₄	#14273708	1	1	yes	characteristic
90	C₄	#14273716	1	1	yes	characteristic
91	C₄	#14273722	1	2	yes	—
92	C₂	—	2	1	no	—
93	C₂	—	2	2	no	—
94	C₂	#16837341	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14273716
commutator	C₂²×C₄×C₅₉	C₂³
Frattini	C₂²×C₄	C₂²×D₅₉
Fitting	C₅₉×#424	C₂
socle	C₂×C₅₉	#400
hypercenter	#424	D₅₉
hypocenter	C₅₉	#2103
LCS	G ▷ C₂²×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #424

Complements

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

N	H ≅ G/N	type
53. C₅₉	#2103	semidirect