Subgroups — #21426353

Order 7552.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14273670	C₂	1	4	yes	maximal, complemented
2	#16837779	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄₇₂	—	2	1	no	—
6	C₂×D₄₇₂	C₂²	1	2	yes	—
7	#14273724	—	2	1	no	—
8	#14273670	—	2	8	no	—
9	C₂×C₅₉⋊C₁₆	C₂²	1	2	yes	—
10	C₂×Q₁₆×C₅₉	—	2	1	no	—
11	C₂×Q₁₆×C₅₉	C₂²	1	2	yes	—
12	C₄⋊Q₈×C₅₉	—	2	1	no	—
13	C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×Q₈×C₅₉	—	2	2	no	—
15	C₂×D₂₃₆	—	2	2	no	—
16	C₂×D₂₃₆	—	4	2	no	—
17	Q₁₆×C₅₉	—	2	4	no	—
18	Q₁₆×C₅₉	—	4	2	no	—
19	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
20	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
21	C₄⋊C₄×C₅₉	—	4	2	no	—
22	C₄²×C₅₉	D₄	1	1	yes	characteristic
23	D₄₇₂	—	2	4	no	—
24	D₄₇₂	—	4	2	no	—
25	C₅₉⋊C₁₆	D₄	1	4	yes	complemented
26	C₂²×D₅₉	—	4	2	no	—
27	Q₈×C₅₉	—	4	2	no	—
28	Q₈×C₅₉	—	4	2	no	—
29	C₂×C₄×C₅₉	—	4	2	no	—
30	C₂×C₄×C₅₉	D₈	1	2	yes	—
31	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
32	D₂₃₆	—	4	2	no	—
33	D₂₃₆	—	4	2	no	—
34	D₂₃₆	—	8	4	no	—
35	C₈×C₅₉	D₈	1	2	yes	—
36	C₈×C₅₉	C₂×D₄	1	2	yes	—
37	C₂²×C₅₉	C₂×D₈	1	1	yes	characteristic
38	C₂×D₅₉	—	8	2	no	—
39	C₂×D₅₉	—	8	4	no	—
40	C₄×C₅₉	—	8	2	no	—
41	C₄×C₅₉	SD₃₂	1	4	yes	complemented
42	C₄×C₅₉	#127	1	1	yes	characteristic
43	C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
44	#2248	—	59	1	no	maximal, Sylow
45	C₂×C₅₉	#493	1	1	yes	characteristic
46	C₂×C₅₉	C₂×SD₃₂	1	2	yes	—
47	D₅₉	—	16	2	no	—
48	C₂×SD₃₂	—	59	4	no	—
49	#494	D₅₉	1	1	yes	characteristic, complemented
50	#493	—	59	1	no	—
51	C₄×C₁₆	—	59	1	no	—
52	C₅₉	#2248	1	1	yes	characteristic, complemented, Sylow
53	C₂×Q₁₆	—	2	1	no	—
54	C₂×Q₁₆	C₂×D₅₉	1	2	yes	—
55	C₂×D₈	—	59	2	no	—
56	C₂×D₈	—	118	1	no	—
57	C₄⋊Q₈	—	2	1	no	—
58	#127	—	118	1	no	—
59	SD₃₂	—	118	8	no	—
60	C₂×C₁₆	—	59	2	no	—
61	C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
62	C₂×Q₈	—	2	2	no	—
63	C₂×D₄	—	118	2	no	—
64	C₂×D₄	—	236	2	no	—
65	Q₁₆	—	2	4	no	—
66	Q₁₆	—	4	2	no	—
67	D₈	—	118	4	no	—
68	D₈	—	236	2	no	—
69	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
70	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
71	C₄⋊C₄	—	4	2	no	—
72	C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
73	C₁₆	—	59	4	no	—
74	C₂³	—	236	2	no	—
75	Q₈	—	4	2	no	—
76	Q₈	—	4	2	no	—
77	D₄	—	472	4	no	—
78	D₄	—	236	2	no	—
79	D₄	—	236	2	no	—
80	C₂×C₄	—	4	2	no	—
81	C₂×C₄	#11745669	1	2	yes	—
82	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
83	C₈	#11745669	1	2	yes	—
84	C₈	D₄×D₅₉	1	2	yes	—
85	C₂²	—	472	2	no	—
86	C₂²	—	472	4	no	—
87	C₂²	C₂×#11745669	1	1	yes	characteristic
88	C₄	—	8	2	no	—
89	C₄	#14273670	1	4	yes	complemented
90	C₄	#14273723	1	1	yes	characteristic
91	C₄	C₂×#11745669	1	1	yes	characteristic
92	C₂	—	944	2	no	—
93	C₂	#16837778	1	1	yes	characteristic
94	C₂	C₂×#14273670	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#11745669
commutator	C₂×C₈×C₅₉	C₂³
Frattini	C₂×C₈	C₂²×D₅₉
Fitting	C₅₉×#494	C₂
socle	C₂²×C₅₉	C₂×D₈
hypercenter	#494	D₅₉
hypocenter	C₅₉	#2248
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
1. C₂×#14273670	C₂	semidirect
3. C₄×C₅₉⋊C₁₆	C₂	semidirect
4. C₅₉×#494	C₂	semidirect
25. C₅₉⋊C₁₆	D₄	semidirect
41. C₄×C₅₉	SD₃₂	semidirect
49. #494	D₅₉	semidirect
52. C₅₉	#2248	semidirect
89. C₄	#14273670	semidirect