Finite Group Databasebeta

← C83×#3307 #24904992

Subgroups — C83×#3307 #24904992

Order 10624.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#553×C83C211yesmaximal, characteristic, complemented
2#547×C83C211yesmaximal, characteristic, complemented
3#491×C83C211yesmaximal, characteristic, complemented
4#485×C83C211yesmaximal, characteristic, complemented
5#483×C83C211yesmaximal, characteristic, complemented
6#478×C83C211yesmaximal, characteristic, complemented
7#468×C83C211yesmaximal, characteristic, complemented
8#465×C83C211yesmaximal, characteristic, complemented
9#461×C83C211yesmaximal, characteristic, complemented
10#449×C83C211yesmaximal, characteristic, complemented
11#449×C83C211yesmaximal, characteristic, complemented
12#442×C83C211yesmaximal, characteristic, complemented
13#435×C83C211yesmaximal, characteristic, complemented
14#417×C83C211yesmaximal, characteristic, complemented
15#416×C83C211yesmaximal, characteristic, complemented
16C2×#41×C83C2211yescharacteristic
17C2×#41×C83C2211yescharacteristic
18C2×SD16×C83C2211yescharacteristic
19C2×SD16×C83C2211yescharacteristic
20C2×D8×C83C2211yescharacteristic
21C2×M16×C83C2211yescharacteristic
22C22×C8×C83C2211yescharacteristic
23C4⋊Q8×C83C2211yescharacteristic
24#126×C83—21no—
25#125×C83C2211yescharacteristic
26#123×C83—21no—
27#123×C83—21no—
28#123×C83—21no—
29C22⋊Q8×C83C2211yescharacteristic
30C22⋊Q8×C83C2211yescharacteristic
31#121×C83—21no—
32#121×C83—21no—
33#121×C83C2211yescharacteristic
34#121×C83C2211yescharacteristic
35C4×D4×C83—21no—
36C4×D4×C83C2211yescharacteristic
37C4×D4×C83C2211yescharacteristic
38C4×D4×C83C2211yescharacteristic
39#117×C83C2211yescharacteristic
40C2×C4⋊C4×C83—21no—
41C2×C4⋊C4×C83C2211yescharacteristic
42#107×C83C2211yescharacteristic
43#106×C83C2211yescharacteristic
44#106×C83C2211yescharacteristic
45C4⋊C8×C83C2211yescharacteristic
46#103×C83C2211yescharacteristic
47#103×C83C2211yescharacteristic
48#103×C83C2211yescharacteristic
49#103×C83C2211yescharacteristic
50#103×C83C2211yescharacteristic
51#103×C83C2211yescharacteristic
52#102×C83C2211yescharacteristic
53#102×C83C2211yescharacteristic
54#102×C83C2211yescharacteristic
55#102×C83C2211yescharacteristic
56C22⋊C8×C83C2211yescharacteristic
57C22⋊C8×C83C2211yescharacteristic
58#97×C83C2211yescharacteristic
59#41×C83—22no—
60#41×C83—22no—
61#41×C83—41no—
62#41×C83—41no—
63C2×Q8×C83C2311yescharacteristic
64C2×Q8×C83C2311yescharacteristic
65C2×D4×C83—21no—
66C2×D4×C83—21no—
67C2×D4×C83—21no—
68C2×D4×C83—21no—
69C2×D4×C83D411yescharacteristic
70C2×D4×C83C2311yescharacteristic
71C2×D4×C83C2311yescharacteristic
72C22×C4×C83—21no—
73C22×C4×C83—21no—
74C22×C4×C83—21no—
75C22×C4×C83—21no—
76C22×C4×C83—21no—
77C22×C4×C83C2311yescharacteristic
78C22×C4×C83C2311yescharacteristic
79SD16×C83—41no—
80SD16×C83—41no—
81D8×C83—22no—
82M16×C83—41no—
83C2×C8×C83—41no—
84C2×C8×C83C2311yescharacteristic
85C2×C8×C83C2311yescharacteristic
86C2×C8×C83C2311yescharacteristic
87C2×C8×C83C2311yescharacteristic
88C4⋊C4×C83—21no—
89C4⋊C4×C83—21no—
90C4⋊C4×C83—21no—
91C4⋊C4×C83—21no—
92C4⋊C4×C83—21no—
93C4⋊C4×C83—21no—
94C4⋊C4×C83—21no—
95C4⋊C4×C83D411yescharacteristic
96C4⋊C4×C83C2311yescharacteristic
97C4⋊C4×C83C2311yescharacteristic
98C4⋊C4×C83C2311yescharacteristic
99C4⋊C4×C83C2311yescharacteristic
100C22⋊C4×C83—21no—
101C22⋊C4×C83—21no—
102C22⋊C4×C83—21no—
103C22⋊C4×C83—21no—
104C22⋊C4×C83—21no—
105C22⋊C4×C83—21no—
106C22⋊C4×C83—21no—
107C22⋊C4×C83D411yescharacteristic
108C22⋊C4×C83D411yescharacteristic
109C42×C83—21no—
110C42×C83C2311yescharacteristic
111C23×C83—21no—
112C23×C83—21no—
113C23×C83C2×D411yescharacteristic
114C23×C83C2×D411yescharacteristic
115Q8×C83—21no—
116Q8×C83—21no—
117Q8×C83—21no—
118Q8×C83—21no—
119D4×C83—21no—
120D4×C83—21no—
121D4×C83—21no—
122D4×C83—41no—
123D4×C83—42no—
124D4×C83—42no—
125D4×C83—42no—
126D4×C83—81no—
127D4×C83#4112yes—
128C2×C4×C83—21no—
129C2×C4×C83—21no—
130C2×C4×C83—21no—
131C2×C4×C83—21no—
132C2×C4×C83—21no—
133C2×C4×C83—21no—
134C2×C4×C83—21no—
135C2×C4×C83—21no—
136C2×C4×C83—21no—
137C2×C4×C83—21no—
138C2×C4×C83—42no—
139C2×C4×C83—42no—
140C2×C4×C83—42no—
141C2×C4×C83—81no—
142C2×C4×C83—81no—
143C2×C4×C83C2×D411yescharacteristic
144C2×C4×C83C2×D411yescharacteristic
145C2×C4×C83C2×D411yescharacteristic
146C2×C4×C83C2×D411yescharacteristic
147C2×C4×C83C2411yescharacteristic
148C8×C83—21no—
149C8×C83—21no—
150C8×C83—21no—
151C8×C83—21no—
152C22×C83—21no—
153C22×C83—21no—
154C22×C83—22no—
155C22×C83—21no—
156C22×C83—21no—
157C22×C83—21no—
158C22×C83—21no—
159C22×C83—41no—
160C22×C83—41no—
161C22×C83—41no—
162C22×C83—41no—
163C22×C83—41no—
164C22×C83C22×D411yescharacteristic
165C4×C83—21no—
166C4×C83—21no—
167C4×C83—21no—
168C4×C83—21no—
169C4×C83—41no—
170C4×C83—41no—
171C4×C83—41no—
172C4×C83—41no—
173C4×C83—41no—
174C4×C83—41no—
175C4×C83C2×#4111yescharacteristic
176C4×C83H(5,𝔽2)11yescharacteristic
177C2×C83—41no—
178C2×C83—41no—
179C2×C83—42no—
180C2×C83—81no—
181C2×C83#54611yescharacteristic
182C2×C83#57511yescharacteristic
183C2×C83#57711yescharacteristic
184#3307C8311yesmaximal, characteristic, direct product factor, Sylow
185C83#330711yescharacteristic, direct product factor, Sylow
186#553C2×C8311yescharacteristic, complemented
187#547C2×C8311yescharacteristic, complemented
188#491C2×C8311yescharacteristic, complemented
189#485C2×C8311yescharacteristic, complemented
190#483C2×C8311yescharacteristic, complemented
191#478C2×C8311yescharacteristic, complemented
192#468C2×C8311yescharacteristic, complemented
193#465C2×C8311yescharacteristic, complemented
194#461C2×C8311yescharacteristic, complemented
195#449C2×C8311yescharacteristic, complemented
196#449C2×C8311yescharacteristic, complemented
197#442C2×C8311yescharacteristic, complemented
198#435C2×C8311yescharacteristic, complemented
199#417C2×C8311yescharacteristic, complemented
200#416C2×C8311yescharacteristic, complemented
201C2×#41C22×C8311yescharacteristic
202C2×#41C22×C8311yescharacteristic
203C2×SD16C22×C8311yescharacteristic
204C2×SD16C22×C8311yescharacteristic
205C2×D8C22×C8311yescharacteristic
206C2×M16C22×C8311yescharacteristic
207C22×C8C22×C8311yescharacteristic
208C4⋊Q8C22×C8311yescharacteristic
209#126—21no—
210#125C22×C8311yescharacteristic
211#123—21no—
212#123—21no—
213#123—21no—
214C22⋊Q8C22×C8311yescharacteristic
215C22⋊Q8C22×C8311yescharacteristic
216#121—21no—
217#121—21no—
218#121C22×C8311yescharacteristic
219#121C22×C8311yescharacteristic
220C4×D4—21no—
221C4×D4C22×C8311yescharacteristic
222C4×D4C22×C8311yescharacteristic
223C4×D4C22×C8311yescharacteristic
224#117C22×C8311yescharacteristic
225C2×C4⋊C4—21no—
226C2×C4⋊C4C22×C8311yescharacteristic
227#107C22×C8311yescharacteristic
228#106C22×C8311yescharacteristic
229#106C22×C8311yescharacteristic
230C4⋊C8C22×C8311yescharacteristic
231#103C22×C8311yescharacteristic
232#103C22×C8311yescharacteristic
233#103C22×C8311yescharacteristic
234#103C22×C8311yescharacteristic
235#103C22×C8311yescharacteristic
236#103C22×C8311yescharacteristic
237#102C22×C8311yescharacteristic
238#102C22×C8311yescharacteristic
239#102C22×C8311yescharacteristic
240#102C22×C8311yescharacteristic
241C22⋊C8C22×C8311yescharacteristic
242C22⋊C8C22×C8311yescharacteristic
243#97C22×C8311yescharacteristic
244#41—22no—
245#41—22no—
246#41—41no—
247#41—41no—
248C2×Q8C23×C8311yescharacteristic
249C2×Q8C23×C8311yescharacteristic
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4D4×C8311yescharacteristic
255C2×D4C23×C8311yescharacteristic
256C2×D4C23×C8311yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4C23×C8311yescharacteristic
263C22×C4C23×C8311yescharacteristic
264SD16—41no—
265SD16—41no—
266D8—22no—
267M16—41no—
268C2×C8—41no—
269C2×C8C23×C8311yescharacteristic
270C2×C8C23×C8311yescharacteristic
271C2×C8C23×C8311yescharacteristic
272C2×C8C23×C8311yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4D4×C8311yescharacteristic
281C4⋊C4C23×C8311yescharacteristic
282C4⋊C4C23×C8311yescharacteristic
283C4⋊C4C23×C8311yescharacteristic
284C4⋊C4C23×C8311yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4D4×C8311yescharacteristic
293C22⋊C4D4×C8311yescharacteristic
294C42—21no—
295C42C23×C8311yescharacteristic
296C23—21no—
297C23—21no—
298C23C2×D4×C8311yescharacteristic
299C23C2×D4×C8311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—21no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—41no—
308D4—42no—
309D4—42no—
310D4—42no—
311D4—81no—
312D4#41×C8312yes—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4C2×D4×C8311yescharacteristic
329C2×C4C2×D4×C8311yescharacteristic
330C2×C4C2×D4×C8311yescharacteristic
331C2×C4C2×D4×C8311yescharacteristic
332C2×C4C24×C8311yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—22no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22C22×D4×C8311yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4C2×#41×C8311yescharacteristic
361C4H(5,𝔽2)×C8311yescharacteristic
362C2—41no—
363C2—41no—
364C2—42no—
365C2—81no—
366C2#546×C8311yescharacteristic
367C2#575×C8311yescharacteristic
368C2#577×C8311yescharacteristic
subgroupG/H
center, socleC22×C83C22×D4
commutator, Frattini, cosocleC2×C4C24×C83
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C83 ◁ C4×D4×C83 ◁ G

Complements

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

NH ≅ G/Ntype
1. #553×C83C2semidirect
2. #547×C83C2semidirect
3. #491×C83C2semidirect
4. #485×C83C2semidirect
5. #483×C83C2semidirect
6. #478×C83C2semidirect
7. #468×C83C2semidirect
8. #465×C83C2semidirect
9. #461×C83C2semidirect
10. #449×C83C2semidirect
11. #449×C83C2semidirect
12. #442×C83C2semidirect
13. #435×C83C2semidirect
14. #417×C83C2semidirect
15. #416×C83C2semidirect
184. #3307C83direct (N × H)
185. C83#3307direct (N × H)
186. #553C2×C83semidirect
187. #547C2×C83semidirect
188. #491C2×C83semidirect
189. #485C2×C83semidirect
190. #483C2×C83semidirect
191. #478C2×C83semidirect
192. #468C2×C83semidirect
193. #465C2×C83semidirect
194. #461C2×C83semidirect
195. #449C2×C83semidirect
196. #449C2×C83semidirect
197. #442C2×C83semidirect
198. #435C2×C83semidirect
199. #417C2×C83semidirect
200. #416C2×C83semidirect

Maximal subgroups

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

subgroupindex
#553×C832
#547×C832
#491×C832
#485×C832
#483×C832
#478×C832
#468×C832
#465×C832
#461×C832
#449×C832
#442×C832
#435×C832
#417×C832
#416×C832
#330783