Finite Group Databasebeta

← C83×#9464 #35237288

Subgroups — C83×#9464 #35237288

Order 21248.

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

normal subgroups only

This group has 610 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×#2501C211yesmaximal, characteristic
2C83×#2313C211yesmaximal, characteristic, complemented
3C83×#1821C211yesmaximal, characteristic, complemented
4C83×#1510C212yesmaximal
5C83×#1284C212yesmaximal, complemented
6C2×#123×C83—21no—
7C2×#123×C83—21no—
8C2×#121×C83C2211yescharacteristic
9C22×C4⋊C4×C83C2211yescharacteristic
10#407×C83C2212yes—
11#399×C83—22no—
12#390×C83C412yescomplemented
13#387×C83—24no—
14#384×C83C412yescomplemented
15#381×C83C2212yes—
16#380×C83—21no—
17C4×C22⋊C4×C83—21no—
18C4×C22⋊C4×C83C2211yescharacteristic
19#343×C83—22no—
20#327×C83—24no—
21C22×D4×C83—21no—
22C22×D4×C83C2×C411yescharacteristic
23C23×C4×C83D411yescharacteristic
24C23×C4×C83D411yescharacteristic
25C23×C4×C83C2311yescharacteristic
26C2×M16×C83—22no—
27#123×C83—44no—
28#123×C83—44no—
29#121×C83—22no—
30#121×C83—22no—
31C2×C4⋊C4×C83—22no—
32C2×C4⋊C4×C83—22no—
33C2×C4⋊C4×C83—22no—
34C2×C4⋊C4×C83—22no—
35C2×C4⋊C4×C83—22no—
36C2×C4⋊C4×C83C2×C411yescharacteristic
37C2×C4⋊C4×C83C2×C412yes—
38C2×C4⋊C4×C83D412yes—
39C2×C22⋊C4×C83—21no—
40C2×C22⋊C4×C83—22no—
41C2×C22⋊C4×C83—22no—
42C2×C22⋊C4×C83—22no—
43C2×C22⋊C4×C83—21no—
44C2×C42×C83—22no—
45C2×C42×C83C2×C412yes—
46C22⋊C8×C83—22no—
47C22⋊C8×C83—22no—
48#95×C83—22no—
49#95×C83—22no—
50#95×C83—21no—
51#95×C83—22no—
52#95×C83D414yes—
53C24×C83—21no—
54C24×C83C2×D411yescharacteristic
55C2×D4×C83—22no—
56C2×D4×C83—42no—
57C2×D4×C83—42no—
58C2×D4×C83—42no—
59C2×D4×C83—41no—
60C2×D4×C83—41no—
61C22×C4×C83—22no—
62C22×C4×C83—21no—
63C22×C4×C83—21no—
64C22×C4×C83—21no—
65C22×C4×C83—21no—
66C22×C4×C83—21no—
67C22×C4×C83—24no—
68C22×C4×C83—42no—
69C22×C4×C83—42no—
70C22×C4×C83—42no—
71C22×C4×C83C22⋊C412yes—
72C22×C4×C83C22⋊C412yes—
73C22×C4×C83C22×C411yescharacteristic
74C22×C4×C83C2×D411yescharacteristic
75C22×C4×C83C2×D412yes—
76C22×C4×C83#4112yes—
77M16×C83—44no—
78C2×C8×C83—42no—
79C4⋊C4×C83—24no—
80C4⋊C4×C83—24no—
81C4⋊C4×C83—22no—
82C4⋊C4×C83—44no—
83C4⋊C4×C83—44no—
84C4⋊C4×C83—82no—
85C22⋊C4×C83—24no—
86C22⋊C4×C83—44no—
87C22⋊C4×C83—44no—
88C22⋊C4×C83—44no—
89C22⋊C4×C83—42no—
90C42×C83—42no—
91C42×C83—82no—
92C23×C83—22no—
93C23×C83—22no—
94C23×C83—41no—
95C23×C83—41no—
96C23×C83—41no—
97C23×C83—42no—
98C23×C83—41no—
99C23×C83—42no—
100C23×C83C2×C22⋊C411yescharacteristic
101C23×C83#12011yescharacteristic
102C23×C83#12311yescharacteristic
103D4×C83—82no—
104D4×C83—82no—
105D4×C83—82no—
106C2×C4×C83—22no—
107C2×C4×C83—22no—
108C2×C4×C83—24no—
109C2×C4×C83—22no—
110C2×C4×C83—22no—
111C2×C4×C83—42no—
112C2×C4×C83—42no—
113C2×C4×C83—42no—
114C2×C4×C83—42no—
115C2×C4×C83—42no—
116C2×C4×C83—42no—
117C2×C4×C83—42no—
118C2×C4×C83—42no—
119C2×C4×C83—44no—
120C2×C4×C83—41no—
121C2×C4×C83—41no—
122C2×C4×C83—44no—
123C2×C4×C83—41no—
124C2×C4×C83—44no—
125C2×C4×C83—81no—
126C2×C4×C83—81no—
127C2×C4×C83C4×D412yes—
128C2×C4×C83#12112yes—
129C8×C83—82no—
130C22×C83—21no—
131C22×C83—21no—
132C22×C83—21no—
133C22×C83—21no—
134C22×C83—21no—
135C22×C83—21no—
136C22×C83—21no—
137C22×C83—44no—
138C22×C83—82no—
139C22×C83—82no—
140C22×C83—81no—
141C22×C83—81no—
142C22×C83—81no—
143C22×C83#38611yescharacteristic
144C22×C83#41012yes—
145C22×C83#45312yes—
146C4×C83—22no—
147C4×C83—22no—
148C4×C83—44no—
149C4×C83—42no—
150C4×C83—42no—
151C4×C83—84no—
152C4×C83—81no—
153#9464C8311yesmaximal, characteristic, direct product factor, Sylow
154C2×C83—22no—
155C2×C83—22no—
156C2×C83—41no—
157C2×C83—161no—
158C2×C83#188711yescharacteristic
159C2×C83#189911yescharacteristic
160C2×C83#191211yescharacteristic
161#2501C2×C8311yescharacteristic
162#2313C2×C8311yescharacteristic, complemented
163#1821C2×C8311yescharacteristic, complemented
164#1510C2×C8312yes—
165#1284C2×C8312yescomplemented
166C83#946411yescharacteristic, direct product factor, Sylow
167C2×#123—21no—
168C2×#123—21no—
169C2×#121C22×C8311yescharacteristic
170C22×C4⋊C4C22×C8311yescharacteristic
171#407C22×C8312yes—
172#399—22no—
173#390C4×C8312yescomplemented
174#387—24no—
175#384C4×C8312yescomplemented
176#381C22×C8312yes—
177#380—21no—
178C4×C22⋊C4—21no—
179C4×C22⋊C4C22×C8311yescharacteristic
180#343—22no—
181#327—24no—
182C22×D4—21no—
183C22×D4C2×C4×C8311yescharacteristic
184C23×C4D4×C8311yescharacteristic
185C23×C4D4×C8311yescharacteristic
186C23×C4C23×C8311yescharacteristic
187C2×M16—22no—
188#123—44no—
189#123—44no—
190#121—22no—
191#121—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4C2×C4×C8311yescharacteristic
198C2×C4⋊C4C2×C4×C8312yes—
199C2×C4⋊C4D4×C8312yes—
200C2×C22⋊C4—21no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—21no—
205C2×C42—22no—
206C2×C42C2×C4×C8312yes—
207C22⋊C8—22no—
208C22⋊C8—22no—
209#95—22no—
210#95—22no—
211#95—21no—
212#95—22no—
213#95D4×C8314yes—
214C24—21no—
215C24C2×D4×C8311yescharacteristic
216C2×D4—22no—
217C2×D4—42no—
218C2×D4—42no—
219C2×D4—42no—
220C2×D4—41no—
221C2×D4—41no—
222C22×C4—22no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—24no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4C22⋊C4×C8312yes—
233C22×C4C22⋊C4×C8312yes—
234C22×C4C22×C4×C8311yescharacteristic
235C22×C4C2×D4×C8311yescharacteristic
236C22×C4C2×D4×C8312yes—
237C22×C4#41×C8312yes—
238M16—44no—
239C2×C8—42no—
240C4⋊C4—24no—
241C4⋊C4—24no—
242C4⋊C4—22no—
243C4⋊C4—44no—
244C4⋊C4—44no—
245C4⋊C4—82no—
246C22⋊C4—24no—
247C22⋊C4—44no—
248C22⋊C4—44no—
249C22⋊C4—44no—
250C22⋊C4—42no—
251C42—42no—
252C42—82no—
253C23—22no—
254C23—22no—
255C23—41no—
256C23—41no—
257C23—41no—
258C23—42no—
259C23—41no—
260C23—42no—
261C23C2×C22⋊C4×C8311yescharacteristic
262C23#120×C8311yescharacteristic
263C23#123×C8311yescharacteristic
264D4—82no—
265D4—82no—
266D4—82no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—24no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—44no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—44no—
284C2×C4—41no—
285C2×C4—44no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4C4×D4×C8312yes—
289C2×C4#121×C8312yes—
290C8—82no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—44no—
299C22—82no—
300C22—82no—
301C22—81no—
302C22—81no—
303C22—81no—
304C22#386×C8311yescharacteristic
305C22#410×C8312yes—
306C22#453×C8312yes—
307C4—22no—
308C4—22no—
309C4—44no—
310C4—42no—
311C4—42no—
312C4—84no—
313C4—81no—
314C2—22no—
315C2—22no—
316C2—41no—
317C2—161no—
318C2C83×#188711yescharacteristic
319C2C83×#189911yescharacteristic
320C2C83×#191211yescharacteristic
subgroupG/H
center, socleC22×C83#386
commutatorC22×C4C22×C4×C83
Frattini, cosocleC23×C4C23×C83
prime radicalC2×#121×C83C22
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
2. C83×#2313C2semidirect
3. C83×#1821C2semidirect
5. C83×#1284C2semidirect
12. #390×C83C4semidirect
14. #384×C83C4semidirect
153. #9464C83direct (N × H)
162. #2313C2×C83semidirect
163. #1821C2×C83semidirect
165. #1284C2×C83semidirect
166. C83#9464direct (N × H)
173. #390C4×C83semidirect
175. #384C4×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#25012
C83×#23132
C83×#18212
C83×#15102
C83×#12842
#946483