Subgroups — #21425954

Order 7552.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₇₂	C₂	1	1	yes	maximal, characteristic
2	#16837496	C₂	1	2	yes	maximal
3	#16837205	C₂	1	2	yes	maximal
4	C₁₆×Dic₅₉	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#366	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₃₆	C₂²	1	2	yes	—
7	#14273692	—	2	2	no	—
8	Dic₄₇₂	C₄	1	4	yes	complemented
9	C₂×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
10	#14273650	—	2	2	no	—
11	C₈×Dic₅₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
13	#107×C₅₉	C₂²	1	2	yes	—
14	C₂×Dic₁₁₈	—	2	2	no	—
15	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
16	C₄⋊C₄×C₅₉	—	2	2	no	—
17	Dic₅₉⋊C₄	—	4	2	no	—
18	C₄×Dic₅₉	—	4	2	no	—
19	C₄×Dic₅₉	D₄	1	1	yes	characteristic
20	C₂×C₅₉⋊C₈	D₄	1	1	yes	characteristic
21	Dic₂₃₆	—	2	2	no	—
22	Dic₂₃₆	C₂×C₄	1	4	yes	—
23	C₁₆×C₅₉	C₂×C₄	1	2	yes	—
24	C₅₉⋊C₁₆	—	2	1	no	—
25	C₂×C₄×C₅₉	—	4	2	no	—
26	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₅₉	—	4	2	no	—
28	C₂×Dic₅₉	D₈	1	1	yes	characteristic
29	C₂×Dic₅₉	D₈	1	1	yes	characteristic
30	Dic₁₁₈	—	2	4	no	—
31	Dic₁₁₈	—	4	2	no	—
32	C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₅₉	#41	1	1	yes	characteristic
34	C₅₉⋊C₈	—	2	1	no	—
35	C₂²×C₅₉	C₂×D₈	1	1	yes	characteristic
36	C₄×C₅₉	—	8	2	no	—
37	C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
38	C₄×C₅₉	#135	1	1	yes	characteristic
39	Dic₅₉	—	2	1	no	—
40	Dic₅₉	—	4	4	no	—
41	Dic₅₉	Q₃₂	1	2	yes	complemented
42	C₄×Q₃₂	—	59	1	no	maximal, Sylow
43	C₂×C₅₉	C₄×D₈	1	1	yes	characteristic
44	C₂×C₅₉	C₂×Q₃₂	1	1	yes	characteristic
45	C₂×C₅₉	#508	1	1	yes	characteristic
46	C₂×Q₃₂	—	59	1	no	—
47	C₄×Q₁₆	—	59	2	no	—
48	#366	D₅₉	1	1	yes	characteristic
49	#358	—	59	2	no	—
50	C₄×C₁₆	—	59	1	no	—
51	C₅₉	C₄×Q₃₂	1	1	yes	characteristic, complemented, Sylow
52	C₂×Q₁₆	—	59	2	no	—
53	C₄×Q₈	—	118	2	no	—
54	Q₃₂	—	59	4	no	—
55	C₂×C₁₆	—	59	1	no	—
56	C₂×C₁₆	C₂×D₅₉	1	1	yes	characteristic
57	#107	C₂×D₅₉	1	2	yes	—
58	#103	—	118	2	no	—
59	C₄×C₈	—	59	1	no	—
60	C₂×Q₈	—	118	2	no	—
61	Q₁₆	—	59	4	no	—
62	Q₁₆	—	118	2	no	—
63	C₂×C₈	—	59	1	no	—
64	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
65	C₄⋊C₄	—	2	2	no	—
66	C₄⋊C₄	—	236	2	no	—
67	C₄²	—	59	1	no	—
68	C₄²	—	236	2	no	—
69	C₁₆	—	118	1	no	—
70	C₁₆	C₄×D₅₉	1	2	yes	—
71	Q₈	—	118	4	no	—
72	Q₈	—	236	2	no	—
73	C₂×C₄	—	4	2	no	—
74	C₂×C₄	—	59	1	no	—
75	C₂×C₄	—	59	1	no	—
76	C₂×C₄	—	236	2	no	—
77	C₂×C₄	D₄×D₅₉	1	1	yes	characteristic
78	C₈	—	118	1	no	—
79	C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
80	C₈	#11745689	1	1	yes	characteristic
81	C₂²	D₈×D₅₉	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	59	2	no	—
84	C₄	—	118	1	no	—
85	C₄	—	236	4	no	—
86	C₄	#14273689	1	1	yes	characteristic
87	C₄	#14273750	1	1	yes	characteristic
88	C₂	#16837484	1	1	yes	characteristic
89	C₂	Q₃₂×D₅₉	1	1	yes	characteristic
90	C₂	#16837831	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₈×D₅₉
commutator	C₈×C₅₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₅₉×#366	C₂
socle	C₂²×C₅₉	C₂×D₈
hypercenter	#366	D₅₉
hypocenter	C₅₉	C₄×Q₃₂
LCS	G ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

Complements

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

N	H ≅ G/N	type
8. Dic₄₇₂	C₄	semidirect
41. Dic₅₉	Q₃₂	semidirect
51. C₅₉	C₄×Q₃₂	semidirect