Subgroups — #35292059

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	C₄⋊(C₈₃⋊C₃₂)	C₂	1	1	yes	maximal, characteristic
3	C₈₃×#1371	C₂	1	1	yes	maximal, characteristic
4	#19128106	—	2	1	no	—
5	C₂×C₈₃⋊C₃₂	—	2	1	no	—
6	#19127527	—	2	1	no	—
7	#19127527	C₄	1	2	yes	—
8	C₄×C₁₆×C₈₃	C₂²	1	1	yes	characteristic
9	#335×C₈₃	—	2	1	no	—
10	#14581792	—	4	1	no	—
11	#14581726	—	2	2	no	—
12	#14581726	—	4	1	no	—
13	C₈₃⋊C₃₂	—	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	—	4	1	no	—
17	C₄×C₈×C₈₃	D₄	1	1	yes	characteristic
18	C₂×Dic₁₆₆	—	8	1	no	—
19	C₄⋊Dic₈₃	—	4	2	no	—
20	C₄⋊Dic₈₃	—	8	1	no	—
21	C₂×C₈×C₈₃	—	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	2	no	—
33	C₈×C₈₃	—	2	1	no	—
34	C₈×C₈₃	—	16	1	no	—
35	C₈×C₈₃	#101	1	1	yes	characteristic
36	C₈×C₈₃	#103	1	1	yes	characteristic
37	C₂²×C₈₃	#357	1	1	yes	characteristic
38	C₄×C₈₃	—	2	1	no	—
39	C₄×C₈₃	#332	1	1	yes	characteristic
40	C₄×C₈₃	#362	1	1	yes	characteristic
41	C₄×C₈₃	SD₆₄	1	1	yes	characteristic
42	C₄×C₈₃	Q₆₄	1	1	yes	characteristic
43	Dic₈₃	—	16	2	no	—
44	#7451	—	83	1	no	maximal, Sylow
45	C₂×C₈₃	#1364	1	1	yes	characteristic
46	C₂×C₈₃	#1416	1	1	yes	characteristic
47	C₂×C₈₃	#1419	1	1	yes	characteristic
48	#2252	—	83	1	no	—
49	C₄⋊C₃₂	—	83	1	no	—
50	#1371	D₈₃	1	1	yes	characteristic
51	C₈₃	#7451	1	1	yes	characteristic, complemented, Sylow
52	#500	—	166	1	no	—
53	C₂×C₃₂	—	166	1	no	—
54	#366	—	83	2	no	—
55	#366	—	166	1	no	—
56	C₄×C₁₆	C₂×D₈₃	1	1	yes	characteristic
57	#335	—	2	1	no	—
58	C₄⋊Q₈	—	332	1	no	—
59	C₂×C₁₆	C₄×D₈₃	1	1	yes	characteristic
60	C₂×C₁₆	D₃₃₂	1	1	yes	characteristic
61	#107	—	332	1	no	—
62	#107	—	166	2	no	—
63	C₄⋊C₈	—	4	1	no	—
64	C₄×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
65	C₃₂	—	332	1	no	—
66	C₂×Q₈	—	664	1	no	—
67	C₂×C₈	—	8	1	no	—
68	C₂×C₈	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
69	C₂×C₈	#13050577	1	1	yes	characteristic
70	C₄⋊C₄	—	332	2	no	—
71	C₄⋊C₄	—	664	1	no	—
72	C₄²	#13050575	1	1	yes	characteristic
73	C₁₆	—	2	1	no	—
74	C₁₆	#13050579	1	1	yes	characteristic
75	C₁₆	Dic₃₃₂	1	1	yes	characteristic
76	Q₈	—	1328	2	no	—
77	C₂×C₄	—	664	2	no	—
78	C₂×C₄	#14581712	1	1	yes	characteristic
79	C₂×C₄	#14581733	1	1	yes	characteristic
80	C₂×C₄	#14581735	1	1	yes	characteristic
81	C₈	—	2	1	no	—
82	C₈	—	16	1	no	—
83	C₈	#14581710	1	1	yes	characteristic
84	C₈	#14581717	1	1	yes	characteristic
85	C₂²	#19127501	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	1328	2	no	—
88	C₄	#19127448	1	1	yes	characteristic
89	C₄	#19127516	1	1	yes	characteristic
90	C₄	#19127539	1	1	yes	characteristic
91	C₄	#19127541	1	1	yes	characteristic
92	C₂	#24905519	1	1	yes	characteristic
93	C₂	#24905643	1	1	yes	characteristic
94	C₂	#24905652	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#19127501
commutator	C₂×C₁₆×C₈₃	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₈₃
Fitting	C₈₃×#1371	C₂
socle, prime radical	C₂²×C₈₃	#357
cosocle	C₄×C₁₆×C₈₃	C₂²
hypercenter	#1371	D₈₃
hypocenter	C₈₃	#7451
LCS	G ▷ C₂×C₁₆×C₈₃ ▷ C₂×C₈×C₈₃ ▷ C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1371

Complements

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

N	H ≅ G/N	type
51. C₈₃	#7451	semidirect

Maximal subgroups

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

subgroup	index
#24909738	2
C₄⋊(C₈₃⋊C₃₂)	2
C₈₃×#1371	2
#7451	83