Subgroups — #21422285

Order 7552.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₉₄₄	C₂	1	1	yes	maximal, characteristic
2	#16837236	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#368	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄₇₂	—	2	1	no	—
5	D₉₄₄	—	2	1	no	—
6	D₉₄₄	C₄	1	2	yes	—
7	C₅₉⋊C₃₂	—	2	1	no	—
8	C₂×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
9	#108×C₅₉	—	2	1	no	—
10	C₂×D₂₃₆	—	4	1	no	—
11	M₁₆×C₅₉	—	4	1	no	—
12	C₂×C₈×C₅₉	D₄	1	1	yes	characteristic
13	D₄₇₂	—	2	2	no	—
14	D₄₇₂	—	4	1	no	—
15	C₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₅₉	D₄	1	1	yes	characteristic
17	C₂²×D₅₉	—	8	1	no	—
18	C₂×C₄×C₅₉	D₈	1	1	yes	characteristic
19	D₂₃₆	—	4	2	no	—
20	D₂₃₆	—	8	1	no	—
21	C₈×C₅₉	—	8	1	no	—
22	C₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₅₉	SD₁₆	1	1	yes	characteristic
24	C₂²×C₅₉	SD₃₂	1	1	yes	characteristic
25	C₂×D₅₉	—	8	2	no	—
26	C₂×D₅₉	—	16	2	no	—
27	C₄×C₅₉	#102	1	1	yes	characteristic
28	C₄×C₅₉	D₁₆	1	1	yes	characteristic
29	#1419	—	59	1	no	maximal, Sylow
30	C₂×C₅₉	—	2	1	no	—
31	C₂×C₅₉	#357	1	1	yes	characteristic
32	D₅₉	—	16	2	no	—
33	C₂×D₁₆	—	59	1	no	—
34	M₆₄	—	59	1	no	—
35	#368	D₅₉	1	1	yes	characteristic, complemented
36	C₅₉	#1419	1	1	yes	characteristic, complemented, Sylow
37	C₂×D₈	—	118	1	no	—
38	D₁₆	—	59	2	no	—
39	D₁₆	—	118	1	no	—
40	C₂×C₁₆	C₂×D₅₉	1	1	yes	characteristic
41	#108	—	2	1	no	—
42	C₃₂	—	118	1	no	—
43	C₂×D₄	—	236	1	no	—
44	D₈	—	118	2	no	—
45	D₈	—	236	1	no	—
46	M₁₆	—	4	1	no	—
47	C₂×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
48	C₁₆	C₄×D₅₉	1	1	yes	characteristic
49	C₁₆	D₂₃₆	1	1	yes	characteristic
50	C₂³	—	472	1	no	—
51	D₄	—	472	1	no	—
52	D₄	—	236	2	no	—
53	C₂×C₄	#11745669	1	1	yes	characteristic
54	C₈	—	8	1	no	—
55	C₈	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
56	C₈	#11745671	1	1	yes	characteristic
57	C₂²	—	944	2	no	—
58	C₂²	—	472	2	no	—
59	C₂²	#14273670	1	1	yes	characteristic
60	C₄	#14273647	1	1	yes	characteristic
61	C₄	#14273668	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	944	2	no	—
64	C₂	#16837202	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#16837202
commutator	C₁₆×C₅₉	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₅₉
Fitting	C₅₉×#368	C₂
socle	C₂×C₅₉	#357
hypercenter	#368	D₅₉
hypocenter	C₅₉	#1419
LCS	G ▷ C₁₆×C₅₉ ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
2. #16837236	C₂	semidirect
3. C₅₉×#368	C₂	semidirect
35. #368	D₅₉	semidirect
36. C₅₉	#1419	semidirect