Subgroups — #24908865

Order 10624.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19127749	C₂	1	3	yes	maximal
2	C₂×#14581710	C₂	1	3	yes	maximal
3	#338×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₁₆₆	C₂²	1	1	yes	characteristic
5	C₂×#13050574	C₂²	1	3	yes	—
6	#14581727	—	2	6	no	—
7	#14581710	—	2	6	no	—
8	C₂×M₁₆×C₈₃	C₂²	1	3	yes	—
9	C₂×Dic₁₆₆	—	2	3	no	—
10	C₂×Dic₁₆₆	—	2	3	no	—
11	C₂²×Dic₈₃	Q₈	1	2	yes	—
12	#13050574	—	2	3	no	—
13	#13050574	D₄	1	6	yes	—
14	C₂×C₈₃⋊C₈	—	2	3	no	—
15	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
16	M₁₆×C₈₃	—	2	3	no	—
17	M₁₆×C₈₃	—	2	3	no	—
18	C₂×C₈×C₈₃	—	2	3	no	—
19	C₂³×C₈₃	C₂×Q₈	1	1	yes	characteristic
20	C₂×C₄×C₈₃	C₂×D₄	1	3	yes	—
21	C₂×C₄×C₈₃	#41	1	3	yes	—
22	C₂×Dic₈₃	—	2	6	no	—
23	Dic₁₆₆	—	4	3	no	—
24	Dic₁₆₆	—	4	1	no	—
25	C₈×C₈₃	—	4	3	no	—
26	C₈₃⋊C₈	—	2	6	no	—
27	C₂²×C₈₃	—	4	1	no	—
28	C₂²×C₈₃	C₂²⋊Q₈	1	3	yes	—
29	C₄×C₈₃	#121	1	3	yes	—
30	C₄×C₈₃	#126	1	1	yes	characteristic
31	Dic₈₃	—	4	2	no	—
32	C₂×C₈₃	—	2	3	no	—
33	C₂×C₈₃	#396	1	1	yes	characteristic
34	#2070	—	83	1	no	maximal, Sylow
35	C₈₃	#2070	1	1	yes	characteristic, complemented, Sylow
36	#430	—	83	3	no	—
37	C₂×#101	—	83	3	no	—
38	#338	D₈₃	1	1	yes	characteristic
39	C₂²×Q₈	—	83	1	no	—
40	C₂×M₁₆	—	83	3	no	—
41	C₂×M₁₆	C₂×D₈₃	1	3	yes	—
42	#108	—	166	6	no	—
43	#101	—	166	6	no	—
44	C₂×Q₈	—	166	3	no	—
45	C₂×Q₈	—	166	3	no	—
46	C₂²×C₄	—	83	2	no	—
47	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
48	M₁₆	—	2	3	no	—
49	M₁₆	—	2	3	no	—
50	M₁₆	—	83	6	no	—
51	M₁₆	—	166	3	no	—
52	C₂×C₈	—	2	3	no	—
53	C₂×C₈	—	166	3	no	—
54	C₂³	Q₈×D₈₃	1	1	yes	characteristic
55	Q₈	—	332	3	no	—
56	Q₈	—	332	1	no	—
57	C₂×C₄	—	166	6	no	—
58	C₂×C₄	D₄×D₈₃	1	3	yes	—
59	C₂×C₄	#13050590	1	3	yes	—
60	C₈	—	4	3	no	—
61	C₈	—	166	6	no	—
62	C₂²	—	4	1	no	—
63	C₂²	#14581770	1	3	yes	—
64	C₄	—	332	2	no	—
65	C₄	#14581765	1	3	yes	—
66	C₄	#14581786	1	1	yes	characteristic
67	C₂	—	2	3	no	—
68	C₂	#19127625	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19127625
commutator, cosocle	C₂²×C₄×C₈₃	C₂³
Frattini	C₂²×C₄	C₂²×D₈₃
Fitting	#338×C₈₃	C₂
socle	C₂×C₈₃	#396
prime radical	C₂³×C₈₃	C₂×Q₈
hypercenter	#338	D₈₃
hypocenter	C₈₃	#2070
LCS	G ▷ C₂²×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
35. C₈₃	#2070	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#19127749	2
C₂×#14581710	2
#338×C₈₃	2
#2070	83