Subgroups — #21422073

Order 7552.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837520	C₂	1	1	yes	maximal, characteristic
2	#16837223	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#322	C₂	1	1	yes	maximal, characteristic, complemented
4	#14273749	C₄	1	1	yes	characteristic
5	#14273733	—	2	1	no	—
6	#14273667	—	2	1	no	—
7	#14273663	C₄	1	1	yes	characteristic
8	#14273655	—	2	1	no	—
9	C₄×C₈×C₅₉	—	2	1	no	—
10	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
11	#11745685	—	2	1	no	—
12	C₂×C₈×C₅₉	—	2	2	no	—
13	C₂×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
15	C₄²×C₅₉	D₄	1	1	yes	characteristic
16	#11745664	—	2	1	no	—
17	Dic₂₃₆	C₈	1	1	yes	characteristic, complemented
18	D₄₇₂	C₈	1	1	yes	characteristic, complemented
19	#11745660	—	2	1	no	—
20	#11745659	—	4	1	no	—
21	C₈×D₅₉	—	4	1	no	—
22	C₅₉⋊C₁₆	—	4	1	no	—
23	C₂×C₄×C₅₉	—	2	1	no	—
24	C₂×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂²⋊D₅₉	—	4	1	no	—
26	D₂₃₆	—	2	1	no	—
27	C₄×D₅₉	—	4	1	no	—
28	Dic₁₁₈	—	2	1	no	—
29	C₈×C₅₉	—	4	2	no	—
30	C₈×C₅₉	C₂×C₈	1	1	yes	characteristic
31	C₈×C₅₉	M₁₆	1	1	yes	characteristic
32	C₈×C₅₉	D₈	1	1	yes	characteristic
33	C₈×C₅₉	SD₁₆	1	1	yes	characteristic
34	C₅₉⋊C₈	—	4	1	no	—
35	C₂²×C₅₉	#104	1	1	yes	characteristic
36	C₂×D₅₉	—	4	1	no	—
37	C₄×C₅₉	—	2	2	no	—
38	C₄×C₅₉	C₂²⋊C₈	1	1	yes	characteristic
39	C₄×C₅₉	#102	1	1	yes	characteristic
40	Dic₅₉	—	4	1	no	—
41	#1336	—	59	1	no	maximal, Sylow
42	C₂×C₅₉	—	2	1	no	—
43	C₂×C₅₉	D₄⋊C₈	1	1	yes	characteristic
44	D₅₉	—	8	1	no	—
45	#443	—	59	1	no	—
46	#364	—	59	1	no	—
47	#322	D₅₉	1	1	yes	characteristic, complemented
48	C₅₉	#1336	1	1	yes	characteristic, complemented, Sylow
49	#135	—	59	1	no	—
50	#131	—	118	1	no	—
51	M₃₂	—	118	1	no	—
52	#108	—	59	1	no	—
53	#104	—	118	1	no	—
54	C₄×C₈	—	2	1	no	—
55	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
56	#41	—	118	1	no	—
57	Q₁₆	—	59	1	no	—
58	SD₁₆	—	118	1	no	—
59	D₈	—	59	1	no	—
60	M₁₆	—	118	1	no	—
61	M₁₆	—	236	1	no	—
62	C₂×C₈	—	2	2	no	—
63	C₂×C₈	—	236	1	no	—
64	C₂×C₈	C₄×D₅₉	1	1	yes	characteristic
65	C₂×C₈	D₂₃₆	1	1	yes	characteristic
66	C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
67	C₁₆	—	236	1	no	—
68	Q₈	—	118	1	no	—
69	D₄	—	118	1	no	—
70	D₄	—	236	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	236	1	no	—
73	C₂×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
74	C₈	—	4	2	no	—
75	C₈	—	236	1	no	—
76	C₈	C₈×D₅₉	1	1	yes	characteristic
77	C₈	#11745659	1	1	yes	characteristic
78	C₈	#11745660	1	1	yes	characteristic
79	C₈	D₄₇₂	1	1	yes	characteristic
80	C₂²	—	236	1	no	—
81	C₂²	#14273655	1	1	yes	characteristic
82	C₄	—	2	2	no	—
83	C₄	—	236	1	no	—
84	C₄	(C₂×D₅₉)⋊C₈	1	1	yes	characteristic
85	C₄	#14273649	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	472	1	no	—
88	C₂	#16837131	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14273649
commutator	C₈×C₅₉	C₂×C₈
Frattini	C₄×C₈	C₂×D₅₉
Fitting	C₅₉×#322	C₂
socle	C₂×C₅₉	D₄⋊C₈
hypercenter	#322	D₅₉
hypocenter	C₅₉	#1336
LCS	G ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #322

Complements

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

N	H ≅ G/N	type
2. #16837223	C₂	semidirect
3. C₅₉×#322	C₂	semidirect
17. Dic₂₃₆	C₈	semidirect
18. D₄₇₂	C₈	semidirect
47. #322	D₅₉	semidirect
48. C₅₉	#1336	semidirect