Subgroups — #24905648

Order 10624.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128133	C₂	1	1	yes	maximal, characteristic
2	#19127531	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₂×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#14581814	—	2	1	no	—
5	Dic₆₆₄	C₄	1	1	yes	characteristic
6	#14581737	—	2	1	no	—
7	D₁₃₂₈	C₄	1	1	yes	characteristic
8	#14581728	—	2	1	no	—
9	C₂×C₁₆×C₈₃	C₂²	1	1	yes	characteristic
10	C₃₂×C₈₃	—	2	1	no	—
11	#13050590	—	4	1	no	—
12	Dic₃₃₂	—	2	1	no	—
13	#13050579	—	4	1	no	—
14	D₆₆₄	—	2	1	no	—
15	#13050574	—	4	1	no	—
16	C₂×C₈×C₈₃	D₄	1	1	yes	characteristic
17	C₁₆×C₈₃	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₈₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₈₃	D₈	1	1	yes	characteristic
20	C₂²⋊D₈₃	—	8	1	no	—
21	D₃₃₂	—	4	1	no	—
22	C₄×D₈₃	—	8	1	no	—
23	Dic₁₆₆	—	4	1	no	—
24	C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₈₃	SD₁₆	1	1	yes	characteristic
26	C₈₃⋊C₈	—	8	1	no	—
27	C₂²×C₈₃	SD₃₂	1	1	yes	characteristic
28	C₂×D₈₃	—	8	1	no	—
29	C₄×C₈₃	#102	1	1	yes	characteristic
30	C₄×C₈₃	D₁₆	1	1	yes	characteristic
31	Dic₈₃	—	8	1	no	—
32	C₂×C₈₃	—	2	1	no	—
33	C₂×C₈₃	#357	1	1	yes	characteristic
34	D₈₃	—	16	1	no	—
35	#1417	—	83	1	no	maximal, Sylow
36	C₈₃	#1417	1	1	yes	characteristic, complemented, Sylow
37	#508	—	83	1	no	—
38	C₂×C₃₂	D₈₃	1	1	yes	characteristic, complemented
39	#368	—	83	1	no	—
40	#135	—	166	1	no	—
41	Q₃₂	—	83	1	no	—
42	SD₃₂	—	166	1	no	—
43	D₁₆	—	83	1	no	—
44	C₂×C₁₆	C₂×D₈₃	1	1	yes	characteristic
45	#108	—	166	1	no	—
46	C₃₂	—	2	1	no	—
47	#41	—	332	1	no	—
48	Q₁₆	—	166	1	no	—
49	SD₁₆	—	332	1	no	—
50	D₈	—	166	1	no	—
51	M₁₆	—	332	1	no	—
52	C₂×C₈	D₃₃₂	1	1	yes	characteristic
53	C₁₆	C₄×D₈₃	1	1	yes	characteristic
54	C₁₆	C₂²⋊D₈₃	1	1	yes	characteristic
55	Q₈	—	332	1	no	—
56	D₄	—	332	1	no	—
57	D₄	—	664	1	no	—
58	C₂×C₄	—	664	1	no	—
59	C₂×C₄	D₆₆₄	1	1	yes	characteristic
60	C₈	—	664	1	no	—
61	C₈	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
62	C₈	#13050579	1	1	yes	characteristic
63	C₂²	—	664	1	no	—
64	C₂²	#14581737	1	1	yes	characteristic
65	C₄	—	664	1	no	—
66	C₄	#14581714	1	1	yes	characteristic
67	C₄	D₁₃₂₈	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	1328	1	no	—
70	C₂	#19127503	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₁₃₂₈
commutator	C₁₆×C₈₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₈₃
Fitting	C₂×C₃₂×C₈₃	C₂
socle	C₂×C₈₃	#357
prime radical	#19128133	C₂
cosocle	C₂×C₁₆×C₈₃	C₂²
hypercenter	C₂×C₃₂	D₈₃
hypocenter	C₈₃	#1417
LCS	G ▷ C₁₆×C₈₃ ▷ C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #19127531	C₂	semidirect
3. C₂×C₃₂×C₈₃	C₂	semidirect
36. C₈₃	#1417	semidirect
38. C₂×C₃₂	D₈₃	semidirect