Finite Group Databasebeta

← #35307547

Subgroups — #35307547

Order 21248.

364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24910768C211yesmaximal, characteristic
2#24905962C212yesmaximal
3#24905364C212yesmaximal
4#24905292C211yesmaximal, characteristic
5C83×#1995C211yesmaximal, characteristic
6#19127754C2212yes—
7#19127643—22no—
8#19127635—22no—
9C4×Dic83⋊C4—22no—
10C4×C4⋊Dic83C2212yes—
11#19127438—22no—
12#19127438—22no—
13#533×C83C2211yescharacteristic
14#423×C83C2211yescharacteristic
15#376×C83C2211yescharacteristic
16#339×C83—22no—
17C2×C4⋊Dic83—22no—
18C2×Dic83⋊C4—22no—
19C2×Dic83⋊C4—22no—
20C2×C4×Dic83—22no—
21C4⋊(C83⋊C8)—22no—
22C22⋊(C83⋊C8)—22no—
23C4×C83⋊C8—22no—
24C83⋊#95—22no—
25C83⋊#95—22no—
26C83⋊#95D412yes—
27C83⋊#95D412yes—
28C2×M16×C83—21no—
29C4⋊Q8×C83Q812yes—
30#125×C83—21no—
31C22⋊Q8×C83—22no—
32C4×Q8×C83—22no—
33#117×C83—21no—
34C2×C42×C83D412yes—
35C2×C42×C83C2311yescharacteristic
36C4⋊C8×C83—22no—
37#95×C83—22no—
38C22×Dic83—22no—
39C22×Dic83—22no—
40C2×C83⋊C8—42no—
41C4⋊Dic83—44no—
42Dic83⋊C4—44no—
43Dic83⋊C4—44no—
44C4×Dic83—42no—
45C4×Dic83—42no—
46C2×Q8×C83—22no—
47C22×C4×C83—22no—
48C22×C4×C83C2×D412yes—
49C22×C4×C83C2×D411yescharacteristic
50M16×C83—42no—
51C2×C8×C83—41no—
52C4⋊C4×C83—22no—
53C4⋊C4×C83—22no—
54C4⋊C4×C83—42no—
55C22⋊C4×C83—41no—
56C42×C83—22no—
57C42×C83—22no—
58C42×C83—41no—
59C42×C83C2×Q811yescharacteristic
60C42×C83#4112yes—
61C42×C83#4111yescharacteristic
62C23×C83#12011yescharacteristic
63Q8×C83—82no—
64C2×C4×C83—42no—
65C2×C4×C83—42no—
66C2×C4×C83—42no—
67C2×C4×C83—42no—
68C2×C4×C83—42no—
69C2×C4×C83C22⋊Q812yes—
70C2×C4×C83C22⋊Q811yescharacteristic
71C2×C4×C83#12412yes—
72C2×C4×C83#12411yescharacteristic
73C2×C4×C83#13512yes—
74C2×C4×C83#13712yes—
75C2×Dic83—24no—
76C2×Dic83—42no—
77C2×Dic83—42no—
78C2×Dic83—42no—
79C2×Dic83—42no—
80C2×Dic83—42no—
81C8×C83—81no—
82C83⋊C8—82no—
83C22×C83—22no—
84C22×C83#39311yescharacteristic
85C22×C83#45212yes—
86C4×C83—22no—
87C4×C83—22no—
88C4×C83—82no—
89C4×C83—82no—
90C4×C83#47912yes—
91C4×C83#48811yescharacteristic
92C4×C83#49111yescharacteristic
93Dic83—44no—
94Dic83—82no—
95#10373—831nomaximal, Sylow
96C2×C83—22no—
97C2×C83#202611yescharacteristic
98C2×C83#203112yes—
99#2402—831no—
100#1995D8311yescharacteristic
101#1503—832no—
102#1303—832no—
103#1274—831no—
104C83#1037311yescharacteristic, complemented, Sylow
105#533C2×D8311yescharacteristic
106#431—832no—
107#423C2×D8311yescharacteristic
108#400—1662no—
109#398—1662no—
110C4×C4⋊C4—832no—
111C4×C4⋊C4—1662no—
112#376C2×D8311yescharacteristic
113#339—22no—
114#328—1662no—
115#328—1662no—
116C2×M16—21no—
117C4⋊Q8Dic16612yes—
118#125—21no—
119C22⋊Q8—22no—
120C4×Q8—22no—
121#117—21no—
122C2×C4⋊C4—1662no—
123C2×C4⋊C4—1662no—
124C2×C4⋊C4—1662no—
125C2×C42—1662no—
126C2×C42C22⋊D8312yes—
127C2×C42C22×D8311yescharacteristic
128C4⋊C8—22no—
129C4⋊C8—1662no—
130C22⋊C8—1662no—
131C4×C8—1662no—
132#95—22no—
133#95—832no—
134#95—832no—
135#95—1662no—
136#95—1662no—
137C2×Q8—22no—
138C22×C4—22no—
139C22×C4—1662no—
140C22×C4—1662no—
141C22×C4D4×D8312yes—
142C22×C4C2×C22⋊D8311yescharacteristic
143M16—42no—
144C2×C8—41no—
145C2×C8—3322no—
146C4⋊C4—22no—
147C4⋊C4—22no—
148C4⋊C4—42no—
149C4⋊C4—3324no—
150C4⋊C4—3324no—
151C4⋊C4—3324no—
152C22⋊C4—41no—
153C42—22no—
154C42—22no—
155C42—41no—
156C42—3322no—
157C42—3322no—
158C42C2×Dic16611yescharacteristic
159C42#1305058912yes—
160C42#1305059011yescharacteristic
161C23#1458176011yescharacteristic
162Q8—82no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—3322no—
169C2×C4—3322no—
170C2×C4—3322no—
171C2×C4—3322no—
172C2×C4—3322no—
173C2×C4—1664no—
174C2×C4#1458176912yes—
175C2×C4#1458177111yescharacteristic
176C2×C4#1458177812yes—
177C2×C4#1458177911yescharacteristic
178C2×C4#1458181212yes—
179C2×C4#1458182312yes—
180C8—81no—
181C8—6642no—
182C22—22no—
183C22#1912761311yescharacteristic
184C22#1912786112yes—
185C4—22no—
186C4—22no—
187C4—82no—
188C4—82no—
189C4—3324no—
190C4—6642no—
191C4#1912800812yes—
192C4#1912805511yescharacteristic
193C4#1912806911yescharacteristic
194C2—22no—
195C2#2490861411yescharacteristic
196C2#2490863312yes—
subgroupG/H
centerC2×C4#14581779
commutator, cosocleC2×C42×C83C23
FrattiniC2×C42C22×D83
FittingC83×#1995C2
socleC22×C83#393
prime radicalC23×C83#120
hypercenter#1995D83
hypocenterC83#10373
LCSG ▷ C2×C42×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
104. C83#10373semidirect

Maximal subgroups

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

subgroupindex
#249107682
#249059622
#249053642
#249052922
C83×#19952
#1037383