Finite Group Databasebeta

← C83×#9460 #35237284

Subgroups — C83×#9460 #35237284

Order 21248.

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

normal subgroups only

This group has 512 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×#2503C211yesmaximal, characteristic
2C83×#2313C211yesmaximal, characteristic
3C83×#1821C211yesmaximal, characteristic
4C83×#1511C212yesmaximal
5C83×#1284C212yesmaximal
6C2×C22⋊Q8×C83C2211yescharacteristic
7C22×C4⋊C4×C83C2211yescharacteristic
8#407×C83C2212yes—
9#400×C83—22no—
10#391×C83C412yescomplemented
11#387×C83—24no—
12#382×C83C412yescomplemented
13#381×C83—21no—
14#381×C83—21no—
15#381×C83C2212yes—
16#380×C83—21no—
17C4×C22⋊C4×C83—21no—
18C4×C22⋊C4×C83C2211yescharacteristic
19#343×C83—22no—
20#328×C83—24no—
21C22×Q8×C83C2×C411yescharacteristic
22C23×C4×C83D411yescharacteristic
23C23×C4×C83D411yescharacteristic
24C23×C4×C83C2311yescharacteristic
25C2×M16×C83—22no—
26C22⋊Q8×C83—22no—
27C22⋊Q8×C83—22no—
28C2×C4⋊C4×C83—22no—
29C2×C4⋊C4×C83—22no—
30C2×C4⋊C4×C83—21no—
31C2×C4⋊C4×C83—22no—
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—22no—
39C2×C42×C83C2×C412yes—
40C22⋊C8×C83—22no—
41C22⋊C8×C83—22no—
42#95×C83—22no—
43#95×C83—22no—
44#95×C83—22no—
45#95×C83—22no—
46#95×C83—22no—
47#95×C83—22no—
48#95×C83—21no—
49#95×C83—22no—
50#95×C83D414yes—
51C24×C83C2×D411yescharacteristic
52C2×Q8×C83—22no—
53C2×Q8×C83—42no—
54C22×C4×C83—21no—
55C22×C4×C83—21no—
56C22×C4×C83—21no—
57C22×C4×C83—21no—
58C22×C4×C83—22no—
59C22×C4×C83—21no—
60C22×C4×C83—21no—
61C22×C4×C83—24no—
62C22×C4×C83—42no—
63C22×C4×C83—42no—
64C22×C4×C83—42no—
65C22×C4×C83C22⋊C412yes—
66C22×C4×C83C22⋊C412yes—
67C22×C4×C83C22×C411yescharacteristic
68C22×C4×C83C2×D411yescharacteristic
69C22×C4×C83C2×D412yes—
70C22×C4×C83#4112yes—
71M16×C83—44no—
72C2×C8×C83—42no—
73C4⋊C4×C83—24no—
74C4⋊C4×C83—24no—
75C4⋊C4×C83—22no—
76C4⋊C4×C83—42no—
77C4⋊C4×C83—82no—
78C22⋊C4×C83—44no—
79C22⋊C4×C83—42no—
80C22⋊C4×C83—41no—
81C22⋊C4×C83—41no—
82C42×C83—42no—
83C42×C83—82no—
84C23×C83—22no—
85C23×C83—22no—
86C23×C83—41no—
87C23×C83C2×C22⋊C411yescharacteristic
88C23×C83#12011yescharacteristic
89C23×C83#12311yescharacteristic
90Q8×C83—82no—
91C2×C4×C83—22no—
92C2×C4×C83—22no—
93C2×C4×C83—22no—
94C2×C4×C83—22no—
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—42no—
102C2×C4×C83—44no—
103C2×C4×C83—42no—
104C2×C4×C83—44no—
105C2×C4×C83—42no—
106C2×C4×C83—41no—
107C2×C4×C83—41no—
108C2×C4×C83—42no—
109C2×C4×C83—42no—
110C2×C4×C83—44no—
111C2×C4×C83—81no—
112C2×C4×C83—81no—
113C2×C4×C83C4×D412yes—
114C2×C4×C83#12112yes—
115C8×C83—82no—
116C22×C83—21no—
117C22×C83—21no—
118C22×C83—21no—
119C22×C83—21no—
120C22×C83—21no—
121C22×C83—21no—
122C22×C83—21no—
123C22×C83—44no—
124C22×C83#38611yescharacteristic
125C22×C83#41012yes—
126C22×C83#45512yes—
127C4×C83—22no—
128C4×C83—22no—
129C4×C83—42no—
130C4×C83—42no—
131C4×C83—84no—
132C4×C83—82no—
133C4×C83—81no—
134C4×C83—81no—
135#9460C8311yesmaximal, characteristic, direct product factor, Sylow
136C2×C83—22no—
137C2×C83—22no—
138C2×C83—41no—
139C2×C83#188511yescharacteristic
140C2×C83#189911yescharacteristic
141C2×C83#191211yescharacteristic
142#2503C2×C8311yescharacteristic
143#2313C2×C8311yescharacteristic
144#1821C2×C8311yescharacteristic
145#1511C2×C8312yes—
146#1284C2×C8312yes—
147C83#946011yescharacteristic, direct product factor, Sylow
148C2×C22⋊Q8C22×C8311yescharacteristic
149C22×C4⋊C4C22×C8311yescharacteristic
150#407C22×C8312yes—
151#400—22no—
152#391C4×C8312yescomplemented
153#387—24no—
154#382C4×C8312yescomplemented
155#381—21no—
156#381—21no—
157#381C22×C8312yes—
158#380—21no—
159C4×C22⋊C4—21no—
160C4×C22⋊C4C22×C8311yescharacteristic
161#343—22no—
162#328—24no—
163C22×Q8C2×C4×C8311yescharacteristic
164C23×C4D4×C8311yescharacteristic
165C23×C4D4×C8311yescharacteristic
166C23×C4C23×C8311yescharacteristic
167C2×M16—22no—
168C22⋊Q8—22no—
169C22⋊Q8—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4C2×C4×C8311yescharacteristic
175C2×C4⋊C4C2×C4×C8312yes—
176C2×C4⋊C4D4×C8312yes—
177C2×C22⋊C4—21no—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—21no—
180C2×C42—22no—
181C2×C42C2×C4×C8312yes—
182C22⋊C8—22no—
183C22⋊C8—22no—
184#95—22no—
185#95—22no—
186#95—22no—
187#95—22no—
188#95—22no—
189#95—22no—
190#95—21no—
191#95—22no—
192#95D4×C8314yes—
193C24C2×D4×C8311yescharacteristic
194C2×Q8—22no—
195C2×Q8—42no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—22no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—24no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4C22⋊C4×C8312yes—
208C22×C4C22⋊C4×C8312yes—
209C22×C4C22×C4×C8311yescharacteristic
210C22×C4C2×D4×C8311yescharacteristic
211C22×C4C2×D4×C8312yes—
212C22×C4#41×C8312yes—
213M16—44no—
214C2×C8—42no—
215C4⋊C4—24no—
216C4⋊C4—24no—
217C4⋊C4—22no—
218C4⋊C4—42no—
219C4⋊C4—82no—
220C22⋊C4—44no—
221C22⋊C4—42no—
222C22⋊C4—41no—
223C22⋊C4—41no—
224C42—42no—
225C42—82no—
226C23—22no—
227C23—22no—
228C23—41no—
229C23C2×C22⋊C4×C8311yescharacteristic
230C23#120×C8311yescharacteristic
231C23#123×C8311yescharacteristic
232Q8—82no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—44no—
245C2×C4—42no—
246C2×C4—44no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—44no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4C4×D4×C8312yes—
256C2×C4#121×C8312yes—
257C8—82no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—44no—
266C22#386×C8311yescharacteristic
267C22#410×C8312yes—
268C22#455×C8312yes—
269C4—22no—
270C4—22no—
271C4—42no—
272C4—42no—
273C4—84no—
274C4—82no—
275C4—81no—
276C4—81no—
277C2—22no—
278C2—22no—
279C2—41no—
280C2C83×#188511yescharacteristic
281C2C83×#189911yescharacteristic
282C2C83×#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
10. #391×C83C4semidirect
12. #382×C83C4semidirect
135. #9460C83direct (N × H)
147. C83#9460direct (N × H)
152. #391C4×C83semidirect
154. #382C4×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#25032
C83×#23132
C83×#18212
C83×#15112
C83×#12842
#946083