Subgroups — #21426413

Order 7552.

104 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, complemented
2	#16837242	C₂	1	2	yes	maximal, complemented
3	#16837240	C₂	1	2	yes	maximal, complemented
4	#16837236	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#508	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₃₆	—	2	1	no	—
7	Dic₄₇₂	—	2	1	no	—
8	Dic₄₇₂	C₂²	1	2	yes	—
9	C₅₉⋊C₃₂	C₂²	1	2	yes	—
10	#135×C₅₉	—	2	1	no	—
11	Q₃₂×C₅₉	C₂²	1	1	yes	characteristic
12	SD₃₂×C₅₉	—	2	1	no	—
13	D₁₆×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
15	#41×C₅₉	—	4	1	no	—
16	C₂×Dic₁₁₈	—	4	1	no	—
17	Q₁₆×C₅₉	—	2	1	no	—
18	SD₁₆×C₅₉	—	4	1	no	—
19	D₈×C₅₉	—	2	1	no	—
20	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
21	Dic₂₃₆	—	2	2	no	—
22	Dic₂₃₆	—	4	1	no	—
23	C₁₆×C₅₉	D₄	1	1	yes	characteristic
24	C₁₆×C₅₉	C₂³	1	1	yes	characteristic
25	Q₈×C₅₉	—	4	1	no	—
26	D₄×C₅₉	—	4	1	no	—
27	D₄×C₅₉	—	8	1	no	—
28	C₂×C₄×C₅₉	—	8	1	no	—
29	C₂×C₄×C₅₉	D₈	1	1	yes	characteristic
30	C₂×Dic₅₉	—	8	1	no	—
31	Dic₁₁₈	—	4	2	no	—
32	Dic₁₁₈	—	8	1	no	—
33	C₈×C₅₉	D₈	1	1	yes	characteristic
34	C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
35	C₂²×C₅₉	—	8	1	no	—
36	C₂²×C₅₉	D₁₆	1	1	yes	characteristic
37	C₄×C₅₉	—	8	1	no	—
38	C₄×C₅₉	D₁₆	1	1	yes	characteristic
39	C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
40	Dic₅₉	—	8	2	no	—
41	#2264	—	59	1	no	maximal, Sylow
42	C₂×C₅₉	—	2	1	no	—
43	C₂×C₅₉	—	16	1	no	—
44	C₂×C₅₉	C₂×D₁₆	1	1	yes	characteristic
45	#508	D₅₉	1	1	yes	characteristic
46	C₂×Q₃₂	—	59	1	no	—
47	Q₆₄	—	59	2	no	—
48	SD₆₄	—	59	2	no	—
49	M₆₄	—	59	1	no	—
50	C₅₉	#2264	1	1	yes	characteristic, complemented, Sylow
51	#135	—	2	1	no	—
52	C₂×Q₁₆	—	118	1	no	—
53	Q₃₂	—	59	2	no	—
54	Q₃₂	—	118	1	no	—
55	Q₃₂	C₂×D₅₉	1	1	yes	characteristic
56	SD₃₂	—	2	1	no	—
57	D₁₆	C₂×D₅₉	1	1	yes	characteristic
58	C₂×C₁₆	C₂×D₅₉	1	1	yes	characteristic
59	C₃₂	—	59	2	no	—
60	#41	—	4	1	no	—
61	C₂×Q₈	—	236	1	no	—
62	Q₁₆	—	2	1	no	—
63	Q₁₆	—	118	2	no	—
64	Q₁₆	—	236	1	no	—
65	SD₁₆	—	4	1	no	—
66	D₈	—	2	1	no	—
67	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
68	C₁₆	C₂²⋊D₅₉	1	1	yes	characteristic
69	C₁₆	C₂²×D₅₉	1	1	yes	characteristic
70	Q₈	—	4	1	no	—
71	Q₈	—	472	1	no	—
72	Q₈	—	236	2	no	—
73	D₄	—	4	1	no	—
74	D₄	—	8	1	no	—
75	C₂×C₄	—	8	1	no	—
76	C₂×C₄	—	472	1	no	—
77	C₂×C₄	#11745669	1	1	yes	characteristic
78	C₈	#11745669	1	1	yes	characteristic
79	C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
80	C₂²	—	8	1	no	—
81	C₂²	#14273668	1	1	yes	characteristic
82	C₄	—	8	1	no	—
83	C₄	—	472	2	no	—
84	C₄	#14273668	1	1	yes	characteristic
85	C₄	C₂×#11745669	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	16	1	no	—
88	C₂	C₂×#14273668	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#14273668
commutator	C₁₆×C₅₉	C₂³
Frattini	C₁₆	C₂²×D₅₉
Fitting	C₅₉×#508	C₂
socle	C₂×C₅₉	C₂×D₁₆
hypercenter	#508	D₅₉
hypocenter	C₅₉	#2264
LCS	G ▷ C₁₆×C₅₉ ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #508

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₄₇₂	C₂	semidirect
2. #16837242	C₂	semidirect
3. #16837240	C₂	semidirect
4. #16837236	C₂	semidirect
50. C₅₉	#2264	semidirect