Subgroups — #28476392

Order 15104.

166 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16837232	C₂	1	2	yes	maximal
2	C₂²×C₃₂×C₅₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#14273663	—	2	2	no	—
4	#16837232	—	2	2	no	—
5	#16837232	C₄	1	4	yes	—
6	C₂²×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
7	C₂×C₃₂×C₅₉	—	2	2	no	—
8	C₂×C₃₂×C₅₉	C₄	1	2	yes	—
9	C₂×#11745664	—	4	2	no	—
10	#14273663	—	2	4	no	—
11	#14273663	—	4	2	no	—
12	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
13	C₂×C₁₆×C₅₉	C₂×C₄	1	2	yes	—
14	C₂×C₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₁₆×C₅₉	D₄	1	2	yes	—
16	C₂×C₁₆×C₅₉	Q₈	1	1	yes	characteristic
17	C₃₂×C₅₉	—	2	2	no	—
18	C₂²×C₄×C₅₉	D₈	1	1	yes	characteristic
19	C₂×C₈×C₅₉	C₂²⋊C₄	1	2	yes	—
20	C₂×C₈×C₅₉	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₈×C₅₉	SD₁₆	1	2	yes	—
22	C₂×C₈×C₅₉	Q₁₆	1	1	yes	characteristic
23	#11745664	—	4	4	no	—
24	#11745664	—	8	2	no	—
25	C₂×C₅₉⋊C₈	—	8	2	no	—
26	C₁₆×C₅₉	C₄²	1	1	yes	characteristic
27	C₁₆×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₁₆×C₅₉	C₄⋊C₄	1	2	yes	—
29	C₂³×C₅₉	Q₃₂	1	1	yes	characteristic
30	C₂×C₄×C₅₉	#102	1	2	yes	—
31	C₂×C₄×C₅₉	#107	1	1	yes	characteristic
32	C₂×C₄×C₅₉	D₁₆	1	1	yes	characteristic
33	C₂×C₄×C₅₉	SD₃₂	1	2	yes	—
34	C₈×C₅₉	#95	1	1	yes	characteristic
35	C₈×C₅₉	#103	1	2	yes	—
36	C₈×C₅₉	#106	1	1	yes	characteristic
37	C₅₉⋊C₈	—	8	4	no	—
38	#7472	—	59	1	no	maximal, Sylow
39	C₂²×C₅₉	—	2	2	no	—
40	C₂²×C₅₉	#358	1	2	yes	—
41	C₂²×C₅₉	#366	1	1	yes	characteristic
42	C₄×C₅₉	#340	1	1	yes	characteristic
43	C₄×C₅₉	#357	1	2	yes	—
44	C₄×C₅₉	#367	1	1	yes	characteristic
45	C₂²×C₃₂	D₅₉	1	1	yes	characteristic
46	C₂×#368	—	59	2	no	—
47	C₂×C₅₉	—	2	2	no	—
48	C₂×C₅₉	#1380	1	1	yes	characteristic
49	C₂×C₅₉	#1425	1	2	yes	—
50	C₂²×C₁₆	C₂×D₅₉	1	1	yes	characteristic
51	C₂×#108	—	118	2	no	—
52	C₂×C₃₂	—	2	2	no	—
53	C₂×C₃₂	Dic₅₉	1	2	yes	—
54	#368	—	59	4	no	—
55	#368	—	118	2	no	—
56	C₅₉	#7472	1	1	yes	characteristic, complemented, Sylow
57	C₂×M₁₆	—	236	2	no	—
58	C₂²×C₈	D₂₃₆	1	1	yes	characteristic
59	C₂×C₁₆	Dic₁₁₈	1	1	yes	characteristic
60	C₂×C₁₆	C₄×D₅₉	1	2	yes	—
61	C₂×C₁₆	C₂×Dic₅₉	1	1	yes	characteristic
62	C₂×C₁₆	C₂²⋊D₅₉	1	2	yes	—
63	#108	—	118	4	no	—
64	#108	—	236	2	no	—
65	C₃₂	—	2	2	no	—
66	C₂²×C₄	D₄₇₂	1	1	yes	characteristic
67	M₁₆	—	472	2	no	—
68	M₁₆	—	236	4	no	—
69	C₂×C₈	—	472	2	no	—
70	C₂×C₈	#11745660	1	2	yes	—
71	C₂×C₈	Dic₂₃₆	1	1	yes	characteristic
72	C₂×C₈	C₄⋊Dic₅₉	1	1	yes	characteristic
73	C₂×C₈	(C₂×D₅₉)⋊C₄	1	2	yes	—
74	C₁₆	C₄×Dic₅₉	1	1	yes	characteristic
75	C₁₆	Dic₅₉⋊C₄	1	2	yes	—
76	C₁₆	C₂²⋊Dic₅₉	1	1	yes	characteristic
77	C₂³	Dic₄₇₂	1	1	yes	characteristic
78	C₂×C₄	#14273649	1	2	yes	—
79	C₂×C₄	#14273661	1	1	yes	characteristic
80	C₂×C₄	D₉₄₄	1	1	yes	characteristic
81	C₂×C₄	#14273672	1	2	yes	—
82	C₈	—	472	4	no	—
83	C₈	C₅₉⋊#95	1	1	yes	characteristic
84	C₈	#14273652	1	2	yes	—
85	C₈	#14273659	1	1	yes	characteristic
86	C₂²	—	2	2	no	—
87	C₂²	#16837207	1	2	yes	—
88	C₂²	#16837228	1	1	yes	characteristic
89	C₄	#16837165	1	1	yes	characteristic
90	C₄	#16837204	1	2	yes	—
91	C₄	#16837230	1	1	yes	characteristic
92	C₂	—	2	2	no	—
93	C₂	#21422188	1	1	yes	characteristic
94	C₂	#21422300	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₉₄₄
commutator	C₁₆×C₅₉	C₄²
Frattini	C₂²×C₁₆	C₂×D₅₉
Fitting	C₂²×C₃₂×C₅₉	C₂
socle	C₂²×C₅₉	#366
prime radical	C₂³×C₅₉	Q₃₂
cosocle	C₂²×C₁₆×C₅₉	C₂²
hypercenter	C₂²×C₃₂	D₅₉
hypocenter	C₅₉	#7472
LCS	G ▷ C₁₆×C₅₉ ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ C₂²×C₃₂

Complements

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

N	H ≅ G/N	type
56. C₅₉	#7472	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#16837232	2
C₂²×C₃₂×C₅₉	2
#7472	59