Subgroups — #21422076

Order 7552.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Dic₁₁₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₅₉⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₄×Dic₁₁₈	C₄	1	1	yes	characteristic
5	C₂×C₅₉⋊C₁₆	—	2	1	no	—
6	C₄⋊(C₅₉⋊C₈)	C₄	1	1	yes	characteristic
7	Dic₅₉⋊C₈	—	2	1	no	—
8	C₈×Dic₅₉	—	2	1	no	—
9	C₂×C₁₆×C₅₉	—	2	1	no	—
10	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₁₈	C₈	1	1	yes	characteristic
12	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
13	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
14	C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
15	C₄⋊Dic₅₉	C₈	1	1	yes	characteristic
16	Dic₅₉⋊C₄	—	2	1	no	—
17	C₄×Dic₅₉	—	2	1	no	—
18	C₂×C₅₉⋊C₈	—	2	1	no	—
19	C₁₆×C₅₉	—	2	2	no	—
20	C₅₉⋊C₁₆	—	4	1	no	—
21	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₅₉	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₅₉	M₁₆	1	1	yes	characteristic
24	C₂×Dic₅₉	—	2	1	no	—
25	C₂×Dic₅₉	—	2	1	no	—
26	Dic₁₁₈	—	2	1	no	—
27	Dic₁₁₈	C₁₆	1	2	yes	complemented
28	C₈×C₅₉	—	2	1	no	—
29	C₈×C₅₉	SD₁₆	1	1	yes	characteristic
30	C₈×C₅₉	Q₁₆	1	1	yes	characteristic
31	C₅₉⋊C₈	—	4	1	no	—
32	C₂²×C₅₉	C₂²⋊C₈	1	1	yes	characteristic
33	C₄×C₅₉	—	2	1	no	—
34	C₄×C₅₉	#103	1	1	yes	characteristic
35	C₄×C₅₉	#104	1	1	yes	characteristic
36	C₄×C₅₉	C₂×C₁₆	1	1	yes	characteristic
37	C₄×C₅₉	M₃₂	1	1	yes	characteristic
38	Dic₅₉	—	2	2	no	—
39	Dic₅₉	—	4	1	no	—
40	Q₈⋊C₁₆	—	59	1	no	maximal, Sylow
41	C₂×C₅₉	Q₈⋊C₈	1	1	yes	characteristic
42	C₂×C₅₉	C₂²⋊C₁₆	1	1	yes	characteristic
43	C₂×C₅₉	#350	1	1	yes	characteristic
44	C₈×Q₈	—	59	1	no	—
45	C₄⋊C₁₆	—	59	1	no	—
46	C₄×C₁₆	D₅₉	1	1	yes	characteristic
47	C₅₉	Q₈⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
48	C₄×Q₈	—	59	1	no	—
49	C₂×C₁₆	—	2	1	no	—
50	C₂×C₁₆	—	118	1	no	—
51	C₄⋊C₈	—	59	1	no	—
52	C₄⋊C₈	—	118	1	no	—
53	C₄×C₈	—	118	1	no	—
54	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
55	C₂×Q₈	—	59	1	no	—
56	C₂×C₈	—	118	1	no	—
57	C₂×C₈	D₂₃₆	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
59	C₄⋊C₄	—	59	1	no	—
60	C₄⋊C₄	—	118	1	no	—
61	C₄²	—	118	1	no	—
62	C₄²	C₄×D₅₉	1	1	yes	characteristic
63	C₁₆	—	2	2	no	—
64	C₁₆	—	236	1	no	—
65	Q₈	—	59	2	no	—
66	Q₈	—	118	1	no	—
67	C₂×C₄	—	118	1	no	—
68	C₂×C₄	—	118	1	no	—
69	C₂×C₄	C₈×D₅₉	1	1	yes	characteristic
70	C₂×C₄	#11745659	1	1	yes	characteristic
71	C₂×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
72	C₈	—	2	1	no	—
73	C₈	—	236	1	no	—
74	C₈	#11745660	1	1	yes	characteristic
75	C₈	Dic₂₃₆	1	1	yes	characteristic
76	C₂²	(C₂×D₅₉)⋊C₈	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	118	2	no	—
79	C₄	—	236	1	no	—
80	C₄	#14273652	1	1	yes	characteristic
81	C₄	#14273655	1	1	yes	characteristic
82	C₄	C₁₆×D₅₉	1	1	yes	characteristic
83	C₄	#14273666	1	1	yes	characteristic
84	C₂	#16837134	1	1	yes	characteristic
85	C₂	(C₂×D₅₉)⋊C₁₆	1	1	yes	characteristic
86	C₂	#16837185	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₂₃₆
commutator	C₄×C₅₉	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₅₉
Fitting	C₄×C₁₆×C₅₉	C₂
socle	C₂²×C₅₉	C₂²⋊C₈
hypercenter	C₄×C₁₆	D₅₉
hypocenter	C₅₉	Q₈⋊C₁₆
LCS	G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
27. Dic₁₁₈	C₁₆	semidirect
47. C₅₉	Q₈⋊C₁₆	semidirect