Finite Group Databasebeta

← C83×#9482 #35237306

Subgroups — C83×#9482 #35237306

Order 21248.

518 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C83×#2484C211yesmaximal, characteristic
2C83×#2313C211yesmaximal, characteristic
3C83×#1826C212yesmaximal
4C83×#1463C211yesmaximal, characteristic
5C83×#1284C212yesmaximal
6C2×#117×C83C2211yescharacteristic
7C22×C4⋊C4×C83C2211yescharacteristic
8#407×C83C2212yes—
9#400×C83C412yescomplemented
10#398×C83C412yescomplemented
11#387×C83—22no—
12#387×C83—24no—
13#385×C83—21no—
14#381×C83—21no—
15#381×C83—21no—
16#381×C83C2211yescharacteristic
17#380×C83—21no—
18C4×C22⋊C4×C83C2212yes—
19#339×C83—24no—
20#324×C83—22no—
21C23×C4×C83D411yescharacteristic
22C23×C4×C83D411yescharacteristic
23C23×C4×C83C2311yescharacteristic
24C2×M16×C83—22no—
25#117×C83—22no—
26#117×C83—22no—
27C2×C4⋊C4×C83—22no—
28C2×C4⋊C4×C83—22no—
29C2×C4⋊C4×C83—22no—
30C2×C4⋊C4×C83—22no—
31C2×C4⋊C4×C83C2×C411yescharacteristic
32C2×C4⋊C4×C83C2×C411yescharacteristic
33C2×C4⋊C4×C83C2×C412yes—
34C2×C4⋊C4×C83D412yes—
35C2×C22⋊C4×C83—21no—
36C2×C22⋊C4×C83—22no—
37C2×C22⋊C4×C83—21no—
38C2×C42×C83—21no—
39C2×C42×C83D414yes—
40C22⋊C8×C83—22no—
41C22⋊C8×C83—22no—
42#95×C83—22no—
43#95×C83—24no—
44#95×C83—22no—
45#95×C83—22no—
46#95×C83—22no—
47#95×C83—22no—
48#95×C83—21no—
49#95×C83C2×C412yes—
50C24×C83C2×D411yescharacteristic
51C22×C4×C83—21no—
52C22×C4×C83—21no—
53C22×C4×C83—21no—
54C22×C4×C83—21no—
55C22×C4×C83—22no—
56C22×C4×C83—21no—
57C22×C4×C83—21no—
58C22×C4×C83—24no—
59C22×C4×C83—42no—
60C22×C4×C83—42no—
61C22×C4×C83—42no—
62C22×C4×C83C22⋊C412yes—
63C22×C4×C83C22⋊C412yes—
64C22×C4×C83C22×C411yescharacteristic
65C22×C4×C83C2×D412yes—
66C22×C4×C83C2×D411yescharacteristic
67C22×C4×C83#4112yes—
68M16×C83—44no—
69C2×C8×C83—42no—
70C4⋊C4×C83—24no—
71C4⋊C4×C83—24no—
72C4⋊C4×C83—22no—
73C4⋊C4×C83—22no—
74C4⋊C4×C83—44no—
75C4⋊C4×C83—82no—
76C22⋊C4×C83—44no—
77C22⋊C4×C83—42no—
78C22⋊C4×C83—41no—
79C22⋊C4×C83—41no—
80C42×C83—44no—
81C42×C83—42no—
82C23×C83—22no—
83C23×C83—22no—
84C23×C83—41no—
85C23×C83C2×C22⋊C411yescharacteristic
86C23×C83#12011yescharacteristic
87C23×C83#12311yescharacteristic
88C2×C4×C83—24no—
89C2×C4×C83—22no—
90C2×C4×C83—22no—
91C2×C4×C83—22no—
92C2×C4×C83—22no—
93C2×C4×C83—41no—
94C2×C4×C83—41no—
95C2×C4×C83—42no—
96C2×C4×C83—42no—
97C2×C4×C83—42no—
98C2×C4×C83—42no—
99C2×C4×C83—42no—
100C2×C4×C83—42no—
101C2×C4×C83—44no—
102C2×C4×C83—42no—
103C2×C4×C83—44no—
104C2×C4×C83—42no—
105C2×C4×C83—41no—
106C2×C4×C83—41no—
107C2×C4×C83—42no—
108C2×C4×C83—42no—
109C2×C4×C83—44no—
110C2×C4×C83—81no—
111C2×C4×C83C4×D412yes—
112C2×C4×C83#12112yes—
113C8×C83—82no—
114C22×C83—21no—
115C22×C83—21no—
116C22×C83—21no—
117C22×C83—21no—
118C22×C83—21no—
119C22×C83—21no—
120C22×C83—21no—
121C22×C83—44no—
122C22×C83#38611yescharacteristic
123C22×C83#42112yes—
124C22×C83#45812yes—
125C4×C83—22no—
126C4×C83—22no—
127C4×C83—42no—
128C4×C83—42no—
129C4×C83—84no—
130C4×C83—82no—
131C4×C83—81no—
132C4×C83—81no—
133#9482C8311yesmaximal, characteristic, direct product factor, Sylow
134C2×C83—22no—
135C2×C83—22no—
136C2×C83—41no—
137C2×C83#189011yescharacteristic
138C2×C83#189711yescharacteristic
139C2×C83#191211yescharacteristic
140#2484C2×C8311yescharacteristic
141#2313C2×C8311yescharacteristic
142#1826C2×C8312yes—
143#1463C2×C8311yescharacteristic
144#1284C2×C8312yes—
145C83#948211yescharacteristic, direct product factor, Sylow
146C2×#117C22×C8311yescharacteristic
147C22×C4⋊C4C22×C8311yescharacteristic
148#407C22×C8312yes—
149#400C4×C8312yescomplemented
150#398C4×C8312yescomplemented
151#387—22no—
152#387—24no—
153#385—21no—
154#381—21no—
155#381—21no—
156#381C22×C8311yescharacteristic
157#380—21no—
158C4×C22⋊C4C22×C8312yes—
159#339—24no—
160#324—22no—
161C23×C4D4×C8311yescharacteristic
162C23×C4D4×C8311yescharacteristic
163C23×C4C23×C8311yescharacteristic
164C2×M16—22no—
165#117—22no—
166#117—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4C2×C4×C8311yescharacteristic
172C2×C4⋊C4C2×C4×C8311yescharacteristic
173C2×C4⋊C4C2×C4×C8312yes—
174C2×C4⋊C4D4×C8312yes—
175C2×C22⋊C4—21no—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—21no—
178C2×C42—21no—
179C2×C42D4×C8314yes—
180C22⋊C8—22no—
181C22⋊C8—22no—
182#95—22no—
183#95—24no—
184#95—22no—
185#95—22no—
186#95—22no—
187#95—22no—
188#95—21no—
189#95C2×C4×C8312yes—
190C24C2×D4×C8311yescharacteristic
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—24no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4C22⋊C4×C8312yes—
203C22×C4C22⋊C4×C8312yes—
204C22×C4C22×C4×C8311yescharacteristic
205C22×C4C2×D4×C8312yes—
206C22×C4C2×D4×C8311yescharacteristic
207C22×C4#41×C8312yes—
208M16—44no—
209C2×C8—42no—
210C4⋊C4—24no—
211C4⋊C4—24no—
212C4⋊C4—22no—
213C4⋊C4—22no—
214C4⋊C4—44no—
215C4⋊C4—82no—
216C22⋊C4—44no—
217C22⋊C4—42no—
218C22⋊C4—41no—
219C22⋊C4—41no—
220C42—44no—
221C42—42no—
222C23—22no—
223C23—22no—
224C23—41no—
225C23C2×C22⋊C4×C8311yescharacteristic
226C23#120×C8311yescharacteristic
227C23#123×C8311yescharacteristic
228C2×C4—24no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—44no—
242C2×C4—42no—
243C2×C4—44no—
244C2×C4—42no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—44no—
250C2×C4—81no—
251C2×C4C4×D4×C8312yes—
252C2×C4#121×C8312yes—
253C8—82no—
254C22—21no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—44no—
262C22#386×C8311yescharacteristic
263C22#421×C8312yes—
264C22#458×C8312yes—
265C4—22no—
266C4—22no—
267C4—42no—
268C4—42no—
269C4—84no—
270C4—82no—
271C4—81no—
272C4—81no—
273C2—22no—
274C2—22no—
275C2—41no—
276C2C83×#189011yescharacteristic
277C2C83×#189711yescharacteristic
278C2C83×#191211yescharacteristic
subgroupG/H
center, socleC22×C83#386
commutatorC22×C4C22×C4×C83
Frattini, cosocleC23×C4C23×C83
prime radicalC24×C83C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ C23×C4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
9. #400×C83C4semidirect
10. #398×C83C4semidirect
133. #9482C83direct (N × H)
145. C83#9482direct (N × H)
149. #400C4×C83semidirect
150. #398C4×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#24842
C83×#23132
C83×#18262
C83×#14632
C83×#12842
#948283