Finite Group Databasebeta

← C83×#9408 #35237232

Subgroups — C83×#9408 #35237232

Order 21248.

618 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 130 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×#2583C211yesmaximal, characteristic
2C83×#2274C211yesmaximal, characteristic
3C83×#1508C212yesmaximal
4C83×#1463C211yesmaximal, characteristic
5C83×#1297C212yesmaximal
6C2×C22⋊Q8×C83C2211yescharacteristic
7C2×#117×C83—21no—
8C22×C4⋊C4×C83C2211yescharacteristic
9#407×C83C2212yes—
10#398×C83C412yescomplemented
11#395×C83C412yescomplemented
12#389×C83—22no—
13#385×C83—21no—
14#385×C83—21no—
15C4×C4⋊C4×C83—24no—
16C4×C22⋊C4×C83—21no—
17C4×C22⋊C4×C83C2211yescharacteristic
18C4×C22⋊C4×C83C2212yes—
19#328×C83—24no—
20#324×C83—22no—
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—
28#117×C83—28no—
29C2×C4⋊C4×C83—22no—
30C2×C4⋊C4×C83—22no—
31C2×C4⋊C4×C83—22no—
32C2×C4⋊C4×C83—22no—
33C2×C4⋊C4×C83—21no—
34C2×C4⋊C4×C83—22no—
35C2×C4⋊C4×C83C2×C411yescharacteristic
36C2×C4⋊C4×C83C2×C412yes—
37C2×C4⋊C4×C83D412yes—
38C2×C22⋊C4×C83—22no—
39C2×C22⋊C4×C83—21no—
40C2×C22⋊C4×C83—21no—
41C2×C42×C83—22no—
42C2×C42×C83—22no—
43C2×C42×C83—22no—
44C2×C42×C83—21no—
45C22⋊C8×C83—22no—
46C22⋊C8×C83—22no—
47#95×C83—22no—
48#95×C83—22no—
49#95×C83—22no—
50#95×C83C2×C412yes—
51#95×C83D414yes—
52C24×C83C2×D411yescharacteristic
53C2×Q8×C83—22no—
54C2×Q8×C83—81no—
55C22×C4×C83—21no—
56C22×C4×C83—21no—
57C22×C4×C83—24no—
58C22×C4×C83—22no—
59C22×C4×C83—21no—
60C22×C4×C83—24no—
61C22×C4×C83—21no—
62C22×C4×C83—21no—
63C22×C4×C83—21no—
64C22×C4×C83—81no—
65C22×C4×C83—81no—
66C22×C4×C83C22⋊C412yes—
67C22×C4×C83C22⋊C412yes—
68C22×C4×C83C22×C411yescharacteristic
69C22×C4×C83C2×D412yes—
70C22×C4×C83C2×D411yescharacteristic
71C22×C4×C83#4112yes—
72M16×C83—82no—
73C2×C8×C83—42no—
74C4⋊C4×C83—28no—
75C4⋊C4×C83—24no—
76C4⋊C4×C83—24no—
77C4⋊C4×C83—22no—
78C4⋊C4×C83—44no—
79C4⋊C4×C83—42no—
80C4⋊C4×C83—82no—
81C22⋊C4×C83—24no—
82C22⋊C4×C83—28no—
83C22⋊C4×C83—41no—
84C22⋊C4×C83—41no—
85C42×C83—28no—
86C42×C83—82no—
87C42×C83—81no—
88C42×C83—82no—
89C23×C83—22no—
90C23×C83—22no—
91C23×C83—41no—
92C23×C83C2×C22⋊C411yescharacteristic
93C23×C83#12011yescharacteristic
94C23×C83#12311yescharacteristic
95Q8×C83—82no—
96C2×C4×C83—22no—
97C2×C4×C83—22no—
98C2×C4×C83—24no—
99C2×C4×C83—22no—
100C2×C4×C83—22no—
101C2×C4×C83—28no—
102C2×C4×C83—24no—
103C2×C4×C83—22no—
104C2×C4×C83—41no—
105C2×C4×C83—42no—
106C2×C4×C83—42no—
107C2×C4×C83—41no—
108C2×C4×C83—44no—
109C2×C4×C83—42no—
110C2×C4×C83—42no—
111C2×C4×C83—42no—
112C2×C4×C83—44no—
113C2×C4×C83—42no—
114C2×C4×C83—42no—
115C2×C4×C83—41no—
116C2×C4×C83—41no—
117C2×C4×C83—42no—
118C2×C4×C83—81no—
119C2×C4×C83#10414yes—
120C2×C4×C83C4×D412yes—
121C2×C4×C83#12112yes—
122C8×C83—82no—
123C22×C83—21no—
124C22×C83—21no—
125C22×C83—21no—
126C22×C83—21no—
127C22×C83—21no—
128C22×C83—21no—
129C22×C83—21no—
130C22×C83—44no—
131C22×C83#38611yescharacteristic
132C22×C83C2×#10412yes—
133C22×C83#45612yes—
134C4×C83—24no—
135C4×C83—22no—
136C4×C83—22no—
137C4×C83—48no—
138C4×C83—44no—
139C4×C83—42no—
140C4×C83—81no—
141C4×C83—81no—
142#9408C8311yesmaximal, characteristic, direct product factor, Sylow
143C2×C83—22no—
144C2×C83—22no—
145C2×C83—41no—
146C2×C83#188611yescharacteristic
147C2×C83#189611yescharacteristic
148C2×C83#191311yescharacteristic
149#2583C2×C8311yescharacteristic
150#2274C2×C8311yescharacteristic
151#1508C2×C8312yes—
152#1463C2×C8311yescharacteristic
153#1297C2×C8312yes—
154C83#940811yescharacteristic, direct product factor, Sylow
155C2×C22⋊Q8C22×C8311yescharacteristic
156C2×#117—21no—
157C22×C4⋊C4C22×C8311yescharacteristic
158#407C22×C8312yes—
159#398C4×C8312yescomplemented
160#395C4×C8312yescomplemented
161#389—22no—
162#385—21no—
163#385—21no—
164C4×C4⋊C4—24no—
165C4×C22⋊C4—21no—
166C4×C22⋊C4C22×C8311yescharacteristic
167C4×C22⋊C4C22×C8312yes—
168#328—24no—
169#324—22no—
170C22×Q8C2×C4×C8311yescharacteristic
171C23×C4D4×C8311yescharacteristic
172C23×C4D4×C8311yescharacteristic
173C23×C4C23×C8311yescharacteristic
174C2×M16—22no—
175C22⋊Q8—22no—
176C22⋊Q8—22no—
177#117—28no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4C2×C4×C8311yescharacteristic
185C2×C4⋊C4C2×C4×C8312yes—
186C2×C4⋊C4D4×C8312yes—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—21no—
189C2×C22⋊C4—21no—
190C2×C42—22no—
191C2×C42—22no—
192C2×C42—22no—
193C2×C42—21no—
194C22⋊C8—22no—
195C22⋊C8—22no—
196#95—22no—
197#95—22no—
198#95—22no—
199#95C2×C4×C8312yes—
200#95D4×C8314yes—
201C24C2×D4×C8311yescharacteristic
202C2×Q8—22no—
203C2×Q8—81no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—24no—
207C22×C4—22no—
208C22×C4—21no—
209C22×C4—24no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—81no—
214C22×C4—81no—
215C22×C4C22⋊C4×C8312yes—
216C22×C4C22⋊C4×C8312yes—
217C22×C4C22×C4×C8311yescharacteristic
218C22×C4C2×D4×C8312yes—
219C22×C4C2×D4×C8311yescharacteristic
220C22×C4#41×C8312yes—
221M16—82no—
222C2×C8—42no—
223C4⋊C4—28no—
224C4⋊C4—24no—
225C4⋊C4—24no—
226C4⋊C4—22no—
227C4⋊C4—44no—
228C4⋊C4—42no—
229C4⋊C4—82no—
230C22⋊C4—28no—
231C22⋊C4—24no—
232C22⋊C4—41no—
233C22⋊C4—41no—
234C42—28no—
235C42—82no—
236C42—81no—
237C42—82no—
238C23—22no—
239C23—22no—
240C23—41no—
241C23C2×C22⋊C4×C8311yescharacteristic
242C23#120×C8311yescharacteristic
243C23#123×C8311yescharacteristic
244Q8—82no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—24no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—28no—
251C2×C4—24no—
252C2×C4—22no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—44no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—44no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—81no—
268C2×C4#104×C8314yes—
269C2×C4C4×D4×C8312yes—
270C2×C4#121×C8312yes—
271C8—82no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—44no—
280C22#386×C8311yescharacteristic
281C22C2×#104×C8312yes—
282C22#456×C8312yes—
283C4—24no—
284C4—22no—
285C4—22no—
286C4—48no—
287C4—44no—
288C4—42no—
289C4—81no—
290C4—81no—
291C2—22no—
292C2—22no—
293C2—41no—
294C2C83×#188611yescharacteristic
295C2C83×#189611yescharacteristic
296C2C83×#191311yescharacteristic
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. #398×C83C4semidirect
11. #395×C83C4semidirect
142. #9408C83direct (N × H)
154. C83#9408direct (N × H)
159. #398C4×C83semidirect
160. #395C4×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#25832
C83×#22742
C83×#15082
C83×#14632
C83×#12972
#940883