Subgroups — #35292054

Order 21248.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24909738	C₂	1	1	yes	maximal, characteristic
2	#24905535	C₂	1	1	yes	maximal, characteristic
3	C₈₃×C₄⋊C₃₂	C₂	1	1	yes	maximal, characteristic
4	#19128106	—	2	1	no	—
5	#19127527	—	2	1	no	—
6	#19127527	C₄	1	2	yes	—
7	#19127454	—	2	1	no	—
8	C₂×C₃₂×C₈₃	—	2	1	no	—
9	C₄×C₁₆×C₈₃	C₂²	1	1	yes	characteristic
10	#14581792	—	4	1	no	—
11	#14581726	—	2	2	no	—
12	#14581726	—	4	1	no	—
13	C₄⋊(C₈₃⋊C₈)	—	4	1	no	—
14	C₂×C₁₆×C₈₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₁₆×C₈₃	D₄	1	1	yes	characteristic
16	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
17	C₃₂×C₈₃	—	4	1	no	—
18	C₂×Dic₁₆₆	—	8	1	no	—
19	C₂×C₈₃⋊C₈	—	8	1	no	—
20	C₄⋊Dic₈₃	—	4	2	no	—
21	C₄⋊Dic₈₃	—	8	1	no	—
22	C₂×C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₈×C₈₃	SD₁₆	1	1	yes	characteristic
24	C₄²×C₈₃	D₈	1	1	yes	characteristic
25	C₁₆×C₈₃	—	2	1	no	—
26	C₁₆×C₈₃	SD₁₆	1	1	yes	characteristic
27	C₁₆×C₈₃	Q₁₆	1	1	yes	characteristic
28	C₂×C₄×C₈₃	#102	1	1	yes	characteristic
29	C₂×C₄×C₈₃	D₁₆	1	1	yes	characteristic
30	C₂×C₄×C₈₃	SD₃₂	1	1	yes	characteristic
31	C₂×Dic₈₃	—	8	2	no	—
32	Dic₁₆₆	—	16	1	no	—
33	Dic₁₆₆	—	16	1	no	—
34	C₈×C₈₃	—	2	1	no	—
35	C₈×C₈₃	#101	1	1	yes	characteristic
36	C₈×C₈₃	#103	1	1	yes	characteristic
37	C₈₃⋊C₈	—	16	1	no	—
38	C₂²×C₈₃	#357	1	1	yes	characteristic
39	C₄×C₈₃	—	2	1	no	—
40	C₄×C₈₃	#332	1	1	yes	characteristic
41	C₄×C₈₃	#362	1	1	yes	characteristic
42	C₄×C₈₃	D₃₂	1	1	yes	characteristic
43	C₄×C₈₃	SD₆₄	1	1	yes	characteristic
44	Dic₈₃	—	16	2	no	—
45	#7450	—	83	1	no	maximal, Sylow
46	C₂×C₈₃	#1364	1	1	yes	characteristic
47	C₂×C₈₃	#1415	1	1	yes	characteristic
48	C₂×C₈₃	#1420	1	1	yes	characteristic
49	#2252	—	83	1	no	—
50	C₄⋊C₃₂	D₈₃	1	1	yes	characteristic
51	#1371	—	83	1	no	—
52	C₈₃	#7450	1	1	yes	characteristic, complemented, Sylow
53	#500	—	166	1	no	—
54	C₂×C₃₂	—	2	1	no	—
55	#366	—	83	2	no	—
56	#366	—	166	1	no	—
57	C₄×C₁₆	C₂×D₈₃	1	1	yes	characteristic
58	#335	—	166	1	no	—
59	C₄⋊Q₈	—	332	1	no	—
60	C₂×C₁₆	C₄×D₈₃	1	1	yes	characteristic
61	C₂×C₁₆	C₂²⋊D₈₃	1	1	yes	characteristic
62	#107	—	332	1	no	—
63	#107	—	166	2	no	—
64	C₄⋊C₈	—	332	1	no	—
65	C₄×C₈	D₃₃₂	1	1	yes	characteristic
66	C₃₂	—	4	1	no	—
67	C₂×Q₈	—	664	1	no	—
68	C₂×C₈	—	664	1	no	—
69	C₂×C₈	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
70	C₂×C₈	#13050579	1	1	yes	characteristic
71	C₄⋊C₄	—	332	2	no	—
72	C₄⋊C₄	—	664	1	no	—
73	C₄²	D₆₆₄	1	1	yes	characteristic
74	C₁₆	—	2	1	no	—
75	C₁₆	#13050578	1	1	yes	characteristic
76	C₁₆	#13050580	1	1	yes	characteristic
77	Q₈	—	1328	1	no	—
78	Q₈	—	1328	1	no	—
79	C₂×C₄	—	664	2	no	—
80	C₂×C₄	#14581714	1	1	yes	characteristic
81	C₂×C₄	D₁₃₂₈	1	1	yes	characteristic
82	C₂×C₄	#14581737	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	1328	1	no	—
85	C₈	#14581710	1	1	yes	characteristic
86	C₈	#14581715	1	1	yes	characteristic
87	C₂²	#19127503	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	1328	2	no	—
90	C₄	#19127446	1	1	yes	characteristic
91	C₄	#19127518	1	1	yes	characteristic
92	C₄	D₂₆₅₆	1	1	yes	characteristic
93	C₄	#19127540	1	1	yes	characteristic
94	C₂	#24905517	1	1	yes	characteristic
95	C₂	#24905642	1	1	yes	characteristic
96	C₂	#24905657	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#19127503
commutator	C₂×C₁₆×C₈₃	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₈₃
Fitting	C₈₃×C₄⋊C₃₂	C₂
socle, prime radical	C₂²×C₈₃	#357
cosocle	C₄×C₁₆×C₈₃	C₂²
hypercenter	C₄⋊C₃₂	D₈₃
hypocenter	C₈₃	#7450
LCS	G ▷ C₂×C₁₆×C₈₃ ▷ C₂×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ C₄⋊C₃₂

Complements

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

N	H ≅ G/N	type
52. C₈₃	#7450	semidirect

Maximal subgroups

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

subgroup	index
#24909738	2
#24905535	2
C₈₃×C₄⋊C₃₂	2
#7450	83