Subgroups — #21424270

Order 7552.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14273662	C₂	1	4	yes	maximal
2	#16837426	C₂	1	1	yes	maximal, characteristic
3	C₂×#14273638	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#423	C₂	1	1	yes	maximal, characteristic
5	C₂×#11745664	C₂²	1	2	yes	—
6	C₂²×C₅₉⋊C₈	C₂²	1	2	yes	—
7	#14273662	—	2	8	no	—
8	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
9	#14273638	C₄	1	4	yes	—
10	C₂×M₁₆×C₅₉	C₂²	1	2	yes	—
11	C₂×C₄²×C₅₉	C₂²	1	1	yes	characteristic
12	C₄⋊C₈×C₅₉	—	2	2	no	—
13	C₂²×C₄×C₅₉	Q₈	1	2	yes	—
14	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
15	M₁₆×C₅₉	—	2	4	no	—
16	C₂×C₈×C₅₉	—	2	2	no	—
17	C₄²×C₅₉	C₂×C₄	1	2	yes	—
18	C₄²×C₅₉	D₄	1	2	yes	—
19	#11745664	—	2	4	no	—
20	C₂×C₅₉⋊C₈	—	2	2	no	—
21	C₂×C₅₉⋊C₈	C₂×C₄	1	4	yes	—
22	C₂×C₅₉⋊C₈	D₄	1	4	yes	—
23	C₂×C₅₉⋊C₈	Q₈	1	4	yes	—
24	C₂³×C₅₉	C₂×Q₈	1	1	yes	characteristic
25	C₂×C₄×C₅₉	—	4	2	no	—
26	C₂×C₄×C₅₉	C₄⋊C₄	1	4	yes	—
27	C₂×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₅₉	C₂×D₄	1	2	yes	—
29	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₅₉	C₂×Q₈	1	2	yes	—
31	C₈×C₅₉	—	4	2	no	—
32	C₅₉⋊C₈	—	4	2	no	—
33	C₅₉⋊C₈	C₄⋊C₄	1	8	yes	—
34	C₂²×C₅₉	—	2	2	no	—
35	C₂²×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂²×C₅₉	C₄⋊Q₈	1	2	yes	—
37	C₄×C₅₉	—	2	4	no	—
38	C₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
39	C₄×C₅₉	#127	1	1	yes	characteristic
40	C₄×C₅₉	C₄⋊Q₈	1	1	yes	characteristic
41	#1849	—	59	1	no	maximal, Sylow
42	C₂×C₅₉	—	2	2	no	—
43	C₂×C₅₉	#384	1	1	yes	characteristic
44	C₂×C₅₉	#430	1	2	yes	—
45	C₂×#108	—	59	4	no	—
46	#423	—	59	1	no	—
47	#423	D₅₉	1	1	yes	characteristic
48	C₂×#97	—	59	1	no	—
49	C₅₉	#1849	1	1	yes	characteristic, complemented, Sylow
50	C₂×M₁₆	—	59	2	no	—
51	C₂×M₁₆	C₂×D₅₉	1	2	yes	—
52	C₂²×C₈	—	59	2	no	—
53	C₂×C₄²	C₂×D₅₉	1	1	yes	characteristic
54	#108	—	118	8	no	—
55	C₄⋊C₈	—	2	2	no	—
56	C₄⋊C₈	—	118	2	no	—
57	#97	—	59	4	no	—
58	C₂²×C₄	Dic₁₁₈	1	2	yes	—
59	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
60	M₁₆	—	2	4	no	—
61	M₁₆	—	118	4	no	—
62	C₂×C₈	—	2	2	no	—
63	C₂×C₈	—	59	4	no	—
64	C₂×C₈	—	59	4	no	—
65	C₂×C₈	—	59	4	no	—
66	C₂×C₈	—	118	2	no	—
67	C₄²	C₄×D₅₉	1	2	yes	—
68	C₄²	C₂²⋊D₅₉	1	2	yes	—
69	C₂³	C₂×Dic₁₁₈	1	1	yes	characteristic
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	Dic₅₉⋊C₄	1	4	yes	—
72	C₂×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
73	C₂×C₄	D₄×D₅₉	1	2	yes	—
74	C₂×C₄	Q₈×D₅₉	1	2	yes	—
75	C₂×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
76	C₈	—	4	2	no	—
77	C₈	—	59	8	no	—
78	C₈	—	236	2	no	—
79	C₂²	—	2	2	no	—
80	C₂²	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
81	C₂²	#14273726	1	2	yes	—
82	C₄	—	2	4	no	—
83	C₄	C₄⋊C₄×D₅₉	1	2	yes	—
84	C₄	#14273723	1	1	yes	characteristic
85	C₄	#14273725	1	1	yes	characteristic
86	C₂	—	2	2	no	—
87	C₂	#16837271	1	1	yes	characteristic
88	C₂	#16837450	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₅₉
Fitting	C₅₉×#423	C₂
socle	C₂²×C₅₉	C₂×C₄⋊C₄
hypercenter	#423	D₅₉
hypocenter	C₅₉	#1849
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
49. C₅₉	#1849	semidirect