Subgroups — #24905604

Order 10624.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128117	C₂	1	1	yes	maximal, characteristic
2	#19127535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₂×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#14581798	C₄	1	1	yes	characteristic
5	#14581732	C₄	1	1	yes	characteristic
6	#14581731	—	2	1	no	—
7	C₁₆×D₈₃	—	2	1	no	—
8	C₈₃⋊C₃₂	—	2	1	no	—
9	C₂×C₁₆×C₈₃	C₂²	1	1	yes	characteristic
10	C₃₂×C₈₃	—	2	1	no	—
11	#13050590	C₈	1	1	yes	characteristic
12	#13050574	C₈	1	1	yes	characteristic
13	#13050573	—	2	1	no	—
14	C₈×D₈₃	—	2	1	no	—
15	C₈₃⋊C₁₆	—	2	1	no	—
16	C₂×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
17	C₁₆×C₈₃	D₄	1	1	yes	characteristic
18	C₁₆×C₈₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₈₃	C₂×C₈	1	1	yes	characteristic
20	C₂²⋊D₈₃	—	2	1	no	—
21	D₃₃₂	C₁₆	1	1	yes	characteristic
22	C₄×D₈₃	—	2	1	no	—
23	Dic₁₆₆	C₁₆	1	1	yes	characteristic
24	C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₈₃	M₁₆	1	1	yes	characteristic
26	C₈₃⋊C₈	—	2	1	no	—
27	C₂²×C₈₃	M₃₂	1	1	yes	characteristic
28	C₂×D₈₃	—	2	1	no	—
29	C₄×C₈₃	C₂²⋊C₈	1	1	yes	characteristic
30	C₄×C₈₃	C₂×C₁₆	1	1	yes	characteristic
31	Dic₈₃	—	2	1	no	—
32	C₂×C₈₃	—	2	1	no	—
33	C₂×C₈₃	C₂²⋊C₁₆	1	1	yes	characteristic
34	D₈₃	—	4	1	no	—
35	#1401	—	83	1	no	maximal, Sylow
36	C₈₃	#1401	1	1	yes	characteristic, complemented, Sylow
37	#504	—	83	1	no	—
38	M₆₄	—	83	1	no	—
39	C₂×C₃₂	D₈₃	1	1	yes	characteristic, complemented
40	#131	—	83	1	no	—
41	M₃₂	—	83	1	no	—
42	M₃₂	—	166	1	no	—
43	C₂×C₁₆	—	166	1	no	—
44	C₂×C₁₆	C₂×D₈₃	1	1	yes	characteristic
45	C₃₂	—	2	1	no	—
46	C₃₂	—	166	1	no	—
47	#41	—	83	1	no	—
48	M₁₆	—	83	1	no	—
49	M₁₆	—	166	1	no	—
50	C₂×C₈	—	166	1	no	—
51	C₂×C₈	C₄×D₈₃	1	1	yes	characteristic
52	C₁₆	—	166	1	no	—
53	C₁₆	D₃₃₂	1	1	yes	characteristic
54	C₁₆	C₂²⋊D₈₃	1	1	yes	characteristic
55	Q₈	—	83	1	no	—
56	D₄	—	83	1	no	—
57	D₄	—	166	1	no	—
58	C₂×C₄	—	166	1	no	—
59	C₂×C₄	C₈×D₈₃	1	1	yes	characteristic
60	C₈	—	166	1	no	—
61	C₈	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
62	C₈	#13050573	1	1	yes	characteristic
63	C₂²	—	166	1	no	—
64	C₂²	#14581731	1	1	yes	characteristic
65	C₄	—	166	1	no	—
66	C₄	(C₂×D₈₃)⋊C₈	1	1	yes	characteristic
67	C₄	C₁₆×D₈₃	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	332	1	no	—
70	C₂	(C₂×D₈₃)⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	D₃₃₂
commutator	C₄×C₈₃	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₈₃
Fitting	C₂×C₃₂×C₈₃	C₂
socle	C₂×C₈₃	C₂²⋊C₁₆
prime radical	#13050590	C₈
cosocle	C₂×C₁₆×C₈₃	C₂²
hypercenter	C₂×C₃₂	D₈₃
hypocenter	C₈₃	#1401
LCS	G ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #19127535	C₂	semidirect
3. C₂×C₃₂×C₈₃	C₂	semidirect
36. C₈₃	#1401	semidirect
39. C₂×C₃₂	D₈₃	semidirect