Subgroups — #35319145

Order 21248.

238 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24909745	C₂	1	2	yes	maximal
2	#24909738	C₂	1	2	yes	maximal
3	#24907073	C₂	1	2	yes	maximal
4	C₈×C₁₆×C₈₃	C₂	1	1	yes	maximal, characteristic
5	#19128106	C₂²	1	4	yes	—
6	#19128052	—	2	4	no	—
7	#19127529	—	2	4	no	—
8	#19127527	—	2	4	no	—
9	C₄×C₁₆×C₈₃	C₂²	1	1	yes	characteristic
10	C₄×C₁₆×C₈₃	C₂²	1	1	yes	characteristic
11	C₈²×C₈₃	C₂²	1	1	yes	characteristic
12	#14581792	—	2	4	no	—
13	#14581726	—	2	4	no	—
14	#14581726	—	2	4	no	—
15	#14581717	—	4	8	no	—
16	C₂×C₁₆×C₈₃	D₄	1	2	yes	—
17	C₂×C₁₆×C₈₃	D₄	1	2	yes	—
18	C₄×C₈×C₈₃	D₄	1	2	yes	—
19	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
20	C₂×Dic₁₆₆	—	4	4	no	—
21	C₄⋊Dic₈₃	—	4	4	no	—
22	C₄⋊Dic₈₃	—	4	4	no	—
23	C₂×C₈×C₈₃	D₈	1	4	yes	—
24	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
25	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
26	C₄²×C₈₃	C₂×D₄	1	1	yes	characteristic
27	C₁₆×C₈₃	Q₁₆	1	4	yes	—
28	C₁₆×C₈₃	Q₁₆	1	4	yes	—
29	C₂×C₄×C₈₃	#127	1	1	yes	characteristic
30	C₂×C₄×C₈₃	C₂×D₈	1	2	yes	—
31	C₂×Dic₈₃	—	8	4	no	—
32	Dic₁₆₆	—	8	8	no	—
33	C₈×C₈₃	—	2	4	no	—
34	C₈×C₈₃	C₂×Q₁₆	1	2	yes	—
35	C₈×C₈₃	C₂×Q₁₆	1	2	yes	—
36	C₂²×C₈₃	#493	1	1	yes	characteristic
37	C₄×C₈₃	#494	1	1	yes	characteristic
38	C₄×C₈₃	#494	1	1	yes	characteristic
39	C₄×C₈₃	#508	1	4	yes	—
40	Dic₈₃	—	16	4	no	—
41	#12522	—	83	1	no	maximal, Sylow
42	C₂×C₈₃	#1713	1	1	yes	characteristic
43	C₂×C₈₃	#2249	1	2	yes	—
44	#2254	—	83	2	no	—
45	#2252	—	83	2	no	—
46	#1710	—	83	2	no	—
47	C₈×C₁₆	D₈₃	1	1	yes	characteristic
48	C₈₃	#12522	1	1	yes	characteristic, complemented, Sylow
49	#500	—	83	4	no	—
50	#487	—	166	4	no	—
51	#367	—	166	4	no	—
52	#366	—	166	4	no	—
53	C₄×C₁₆	C₂×D₈₃	1	1	yes	characteristic
54	C₄×C₁₆	C₂×D₈₃	1	1	yes	characteristic
55	C₈²	C₂×D₈₃	1	1	yes	characteristic
56	C₄⋊Q₈	—	166	4	no	—
57	C₂×C₁₆	D₃₃₂	1	2	yes	—
58	C₂×C₁₆	D₃₃₂	1	2	yes	—
59	#107	—	166	4	no	—
60	#107	—	166	4	no	—
61	#103	—	332	8	no	—
62	C₄×C₈	D₃₃₂	1	2	yes	—
63	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
64	C₂×Q₈	—	332	4	no	—
65	C₂×C₈	D₆₆₄	1	4	yes	—
66	C₂×C₈	C₂×D₃₃₂	1	1	yes	characteristic
67	C₂×C₈	C₂×D₃₃₂	1	1	yes	characteristic
68	C₄⋊C₄	—	332	4	no	—
69	C₄⋊C₄	—	332	4	no	—
70	C₄²	C₂×D₃₃₂	1	1	yes	characteristic
71	C₁₆	Dic₃₃₂	1	4	yes	—
72	C₁₆	Dic₃₃₂	1	4	yes	—
73	Q₈	—	664	8	no	—
74	C₂×C₄	—	664	4	no	—
75	C₂×C₄	#14581789	1	1	yes	characteristic
76	C₂×C₄	C₂×D₆₆₄	1	2	yes	—
77	C₈	—	2	4	no	—
78	C₈	C₂×Dic₃₃₂	1	2	yes	—
79	C₈	C₂×Dic₃₃₂	1	2	yes	—
80	C₂²	#19128078	1	1	yes	characteristic
81	C₄	—	1328	4	no	—
82	C₄	#19128081	1	1	yes	characteristic
83	C₄	#19128081	1	1	yes	characteristic
84	C₄	#19128133	1	4	yes	—
85	C₂	#24907081	1	1	yes	characteristic
86	C₂	#24909724	1	2	yes	—

	subgroup	G/H
center	C₂²	#19128078
commutator, cosocle	C₄×C₈×C₈₃	C₂³
Frattini	C₄×C₈	C₂²×D₈₃
Fitting	C₈×C₁₆×C₈₃	C₂
socle, prime radical	C₂²×C₈₃	#493
hypercenter	C₈×C₁₆	D₈₃
hypocenter	C₈₃	#12522
LCS	G ▷ C₄×C₈×C₈₃ ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ C₈×C₁₆

Complements

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

N	H ≅ G/N	type
48. C₈₃	#12522	semidirect

Maximal subgroups

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

subgroup	index
#24909745	2
#24909738	2
#24907073	2
C₈×C₁₆×C₈₃	2
#12522	83