Finite Group Databasebeta

← #35302086

Subgroups — #35302086

Order 21248.

468 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 103 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#24916548C211yesmaximal, characteristic
2#24912448C211yesmaximal, characteristic
3#24906188C212yesmaximal
4#24905318C212yesmaximal
5C83×#1467C211yesmaximal, characteristic
6C2×#14581792C2211yescharacteristic
7C2×#14581790C412yes—
8#19127832—24no—
9#19127758—21no—
10#19127758C2212yes—
11#19127754—21no—
12#19127631—21no—
13#19127631—21no—
14#19127606C412yes—
15#19127599—21no—
16#19127599—21no—
17C4×C4⋊Dic83C2211yescharacteristic
18#19127449—24no—
19C2×C4×Q8×C83C2211yescharacteristic
20#432×C83C2212yes—
21#324×C83—21no—
22#324×C83—21no—
23C22×Dic166C2×C412yes—
24#14581792—22no—
25#14581792—22no—
26#14581790—44no—
27C2×C4⋊Dic83—21no—
28C2×C4⋊Dic83—21no—
29C2×C4⋊Dic83—21no—
30C2×Dic83⋊C4—22no—
31C2×Dic83⋊C4—22no—
32C2×C4×Dic83C2×C412yes—
33C4⋊(C83⋊C8)—22no—
34C4⋊(C83⋊C8)—22no—
35C4⋊(C83⋊C8)D414yes—
36C22⋊(C83⋊C8)—22no—
37#14581703—22no—
38#14581703—22no—
39C4×C83⋊C8—22no—
40C83⋊#95—22no—
41C83⋊#95—22no—
42C83⋊#95—21no—
43C22×Q8×C83C2×C411yescharacteristic
44C4×Q8×C83—22no—
45C4×Q8×C83—22no—
46C2×C4⋊C4×C83C2×C411yescharacteristic
47C2×C4⋊C4×C83D411yescharacteristic
48C2×C4⋊C4×C83D411yescharacteristic
49C2×C42×C83D411yescharacteristic
50C2×C42×C83D411yescharacteristic
51C2×C42×C83C2311yescharacteristic
52C4⋊C8×C83—22no—
53C22⋊C8×C83—22no—
54#97×C83—22no—
55C2×Dic166—24no—
56C2×Dic166—42no—
57C2×Dic166—42no—
58C22×Dic83—22no—
59C22×Dic83—22no—
60C2×C83⋊C8—24no—
61C4⋊Dic83—24no—
62C4⋊Dic83—41no—
63C4⋊Dic83—42no—
64C4⋊Dic83—41no—
65Dic83⋊C4—44no—
66Dic83⋊C4—44no—
67C4×Dic83—42no—
68C2×Q8×C83—22no—
69C2×Q8×C83—22no—
70C2×Q8×C83—41no—
71C22×C4×C83C22⋊C411yescharacteristic
72C22×C4×C83C22⋊C411yescharacteristic
73C22×C4×C83C22⋊C411yescharacteristic
74C22×C4×C83C22⋊C411yescharacteristic
75C22×C4×C83C22×C411yescharacteristic
76C22×C4×C83C2×D411yescharacteristic
77C22×C4×C83C2×D411yescharacteristic
78C2×C8×C83—42no—
79C4⋊C4×C83—22no—
80C4⋊C4×C83—22no—
81C4⋊C4×C83—22no—
82C42×C83—21no—
83C42×C83—21no—
84C42×C83—21no—
85C42×C83—21no—
86C42×C83C2×D412yes—
87C42×C83#4112yes—
88C23×C83C2×C22⋊C411yescharacteristic
89Q8×C83—44no—
90C2×C4×C83—21no—
91C2×C4×C83—21no—
92C2×C4×C83—21no—
93C2×C4×C83—21no—
94C2×C4×C83—22no—
95C2×C4×C83—21no—
96C2×C4×C83—21no—
97C2×C4×C83—21no—
98C2×C4×C83—21no—
99C2×C4×C83—21no—
100C2×C4×C83—41no—
101C2×C4×C83—41no—
102C2×C4×C83—41no—
103C2×C4×C83#10012yes—
104C2×C4×C83C4×D412yes—
105C2×C4×C83#12011yescharacteristic
106C2×C4×C83#12112yes—
107C2×C4×C83#12311yescharacteristic
108C2×Dic83—24no—
109C2×Dic83—42no—
110C2×Dic83—42no—
111C2×Dic83—42no—
112C2×Dic83—42no—
113C2×Dic83—42no—
114Dic166—84no—
115C8×C83—82no—
116C83⋊C8—44no—
117C22×C83—21no—
118C22×C83—21no—
119C22×C83#38611yescharacteristic
120C22×C83C2×#10011yescharacteristic
121C22×C83#41311yescharacteristic
122C4×C83—21no—
123C4×C83—22no—
124C4×C83—22no—
125C4×C83—22no—
126C4×C83—41no—
127C4×C83—41no—
128C4×C83—41no—
129C4×C83#45612yes—
130Dic83—44no—
131Dic83—82no—
132#9452—831nomaximal, Sylow
133C2×C83—21no—
134C2×C83—21no—
135C2×C83#188611yescharacteristic
136C2×C83#190011yescharacteristic
137C2×C83#190911yescharacteristic
138#2983—831no—
139#2546—831no—
140#1558—832no—
141#1467D8311yescharacteristic
142#1285—832no—
143C83#945211yescharacteristic, complemented, Sylow
144C2×C4⋊Q8—832no—
145C2×C4⋊Q8—831no—
146C2×C4×Q8C2×D8311yescharacteristic
147#446—1664no—
148#432—832no—
149#432—1661no—
150#432C2×D8312yes—
151#431—1661no—
152#398—1661no—
153#398—1661no—
154#391—832no—
155#389—1661no—
156#389—1661no—
157C4×C4⋊C4—831no—
158#333—1664no—
159#324—21no—
160#324—21no—
161C22×Q8—832no—
162C22×Q8C4×D8311yescharacteristic
163C4⋊Q8—3324no—
164C4⋊Q8—1662no—
165C4⋊Q8—1662no—
166C4×Q8—22no—
167C4×Q8—22no—
168C2×C4⋊C4—1662no—
169C2×C4⋊C4—1662no—
170C2×C4⋊C4—1661no—
171C2×C4⋊C4—1661no—
172C2×C4⋊C4—1661no—
173C2×C4⋊C4C4×D8311yescharacteristic
174C2×C4⋊C4C22⋊D8311yescharacteristic
175C2×C4⋊C4C22⋊D8311yescharacteristic
176C2×C42—832no—
177C2×C42D33211yescharacteristic
178C2×C42D33211yescharacteristic
179C2×C42C22×D8311yescharacteristic
180C4⋊C8—22no—
181C4⋊C8—834no—
182C4⋊C8—1662no—
183C4⋊C8—1662no—
184C22⋊C8—22no—
185C22⋊C8—1662no—
186#97—22no—
187#97—1662no—
188#97—1662no—
189C4×C8—1662no—
190#95—1662no—
191#95—1662no—
192#95—1661no—
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—41no—
196C2×Q8—3322no—
197C2×Q8—3322no—
198C2×Q8—1664no—
199C22×C4—1662no—
200C22×C4—1662no—
201C22×C4(C2×D83)⋊C411yescharacteristic
202C22×C4(C2×D83)⋊C411yescharacteristic
203C22×C4(C2×D83)⋊C411yescharacteristic
204C22×C4(C2×D83)⋊C411yescharacteristic
205C22×C4C2×C4×D8311yescharacteristic
206C22×C4C2×C22⋊D8311yescharacteristic
207C22×C4C2×D33211yescharacteristic
208C2×C8—42no—
209C2×C8—1664no—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—3324no—
214C4⋊C4—3321no—
215C4⋊C4—3322no—
216C4⋊C4—3321no—
217C4⋊C4—3324no—
218C4⋊C4—1664no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—3322no—
224C42D4×D8312yes—
225C42#1305058912yes—
226C23C2×(C2×D83)⋊C411yescharacteristic
227Q8—44no—
228Q8—6644no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—3322no—
243C2×C4—3322no—
244C2×C4—3322no—
245C2×C4—3322no—
246C2×C4—3322no—
247C2×C4—1664no—
248C2×C4#1458170812yes—
249C2×C4(C22⋊D83)⋊C412yes—
250C2×C4#1458176211yescharacteristic
251C2×C4#1458176412yes—
252C2×C4#1458177611yescharacteristic
253C8—82no—
254C8—3324no—
255C22—21no—
256C22—21no—
257C22#1912757811yescharacteristic
258C22C2×#1458170811yescharacteristic
259C22#1912768311yescharacteristic
260C4—21no—
261C4—22no—
262C4—22no—
263C4—22no—
264C4—41no—
265C4—41no—
266C4—41no—
267C4—3324no—
268C4—6642no—
269C4#1912788612yes—
270C2—21no—
271C2—21no—
272C2#2490785411yescharacteristic
273C2#2490792411yescharacteristic
274C2#2490798311yescharacteristic
subgroupG/H
centerC22#19127578
commutatorC22×C4×C83C22×C4
FrattiniC2×C42C22×D83
FittingC83×#1467C2
socleC22×C83#386
prime radicalC23×C83C2×C22⋊C4
cosocleC2×C42×C83C23
hypercenter#1467D83
hypocenterC83#9452
LCSG ▷ C22×C4×C83 ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
143. C83#9452semidirect

Maximal subgroups

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

subgroupindex
#249165482
#249124482
#249061882
#249053182
C83×#14672
#945283