Subgroups — #21425862

Order 7552.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14273667	C₂	1	2	yes	maximal
2	#16837223	C₂	1	4	yes	maximal, complemented
3	C₅₉×#405	C₂	1	1	yes	maximal, characteristic
4	#14273667	—	2	2	no	—
5	#14273667	C₂²	1	4	yes	—
6	C₂×C₅₉⋊C₁₆	—	2	2	no	—
7	C₂×M₁₆×C₅₉	C₄	1	1	yes	characteristic
8	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
9	#117×C₅₉	C₄	1	1	yes	characteristic
10	#97×C₅₉	C₄	1	2	yes	—
11	C₄×C₈×C₅₉	C₂²	1	2	yes	—
12	C₂²×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
13	M₁₆×C₅₉	C₈	1	4	yes	—
14	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₅₉	C₂×C₄	1	2	yes	—
16	C₂×C₈×C₅₉	D₄	1	2	yes	—
17	C₂×C₈×C₅₉	Q₈	1	2	yes	—
18	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
19	C₄⋊C₄×C₅₉	—	2	1	no	—
20	C₂²⋊C₄×C₅₉	—	2	1	no	—
21	C₄²×C₅₉	C₂×C₄	1	2	yes	—
22	C₅₉⋊C₁₆	—	2	4	no	—
23	C₂³×C₅₉	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₅₉	—	2	2	no	—
25	C₂×C₄×C₅₉	C₄⋊C₄	1	2	yes	—
26	C₂×C₄×C₅₉	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₅₉	M₁₆	1	1	yes	characteristic
28	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
29	C₈×C₅₉	C₄⋊C₄	1	2	yes	—
30	C₈×C₅₉	C₂×C₈	1	4	yes	—
31	C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
32	C₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
33	C₂²×C₅₉	—	4	1	no	—
34	C₂²×C₅₉	C₄⋊C₈	1	2	yes	—
35	C₂²×C₅₉	C₂×M₁₆	1	1	yes	characteristic
36	C₄×C₅₉	—	4	2	no	—
37	C₄×C₅₉	C₄⋊C₈	1	2	yes	—
38	C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
40	#2153	—	59	1	no	maximal, Sylow
41	C₂×C₅₉	—	2	1	no	—
42	C₂×C₅₉	—	2	2	no	—
43	C₂×C₅₉	C₂×C₄⋊C₈	1	1	yes	characteristic
44	C₂×M₃₂	—	59	2	no	—
45	#405	D₅₉	1	1	yes	characteristic
46	#364	—	59	4	no	—
47	C₅₉	#2153	1	1	yes	characteristic, complemented, Sylow
48	C₂×M₁₆	Dic₅₉	1	1	yes	characteristic
49	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
50	#117	Dic₅₉	1	1	yes	characteristic
51	M₃₂	—	59	4	no	—
52	M₃₂	—	118	2	no	—
53	C₂×C₁₆	—	118	2	no	—
54	#97	Dic₅₉	1	2	yes	—
55	C₄×C₈	C₂×D₅₉	1	2	yes	—
56	C₂²×C₄	C₂×Dic₅₉	1	1	yes	characteristic
57	M₁₆	C₅₉⋊C₈	1	4	yes	—
58	C₂×C₈	Dic₁₁₈	1	2	yes	—
59	C₂×C₈	D₂₃₆	1	2	yes	—
60	C₂×C₈	C₂×Dic₅₉	1	2	yes	—
61	C₂×C₈	C₂×Dic₅₉	1	1	yes	characteristic
62	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
63	C₄⋊C₄	—	2	1	no	—
64	C₂²⋊C₄	—	2	1	no	—
65	C₄²	C₂×Dic₅₉	1	2	yes	—
66	C₁₆	—	118	4	no	—
67	C₂³	#11745664	1	1	yes	characteristic
68	C₂×C₄	—	2	2	no	—
69	C₂×C₄	C₂×C₅₉⋊C₈	1	2	yes	—
70	C₂×C₄	#11745664	1	1	yes	characteristic
71	C₂×C₄	C₄⋊Dic₅₉	1	2	yes	—
72	C₂×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
73	C₈	C₂×C₅₉⋊C₈	1	4	yes	—
74	C₈	C₄⋊Dic₅₉	1	2	yes	—
75	C₈	C₂×Dic₁₁₈	1	1	yes	characteristic
76	C₈	C₂×D₂₃₆	1	1	yes	characteristic
77	C₂²	—	4	1	no	—
78	C₂²	C₄⋊(C₅₉⋊C₈)	1	2	yes	—
79	C₂²	C₂×#11745664	1	1	yes	characteristic
80	C₄	—	4	2	no	—
81	C₄	C₄⋊(C₅₉⋊C₈)	1	2	yes	—
82	C₄	C₂×C₄⋊Dic₅₉	1	1	yes	characteristic
83	C₄	C₂²×C₅₉⋊C₈	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	2	2	no	—
86	C₂	C₂×C₄⋊(C₅₉⋊C₈)	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₂₃₆
commutator	C₄×C₅₉	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₅₉×#405	C₂
socle	C₂×C₅₉	C₂×C₄⋊C₈
hypercenter	#405	D₅₉
hypocenter	C₅₉	#2153
LCS	G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
2. #16837223	C₂	semidirect
47. C₅₉	#2153	semidirect