Finite Group Databasebeta

← C83×#9319 #35237143

Subgroups — C83×#9319 #35237143

Order 21248.

458 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C83×#3079C211yesmaximal, characteristic
2C83×#2989C211yesmaximal, characteristic
3C83×#1987C211yesmaximal, characteristic, complemented
4C83×#1806C211yesmaximal, characteristic
5C83×#1548C211yesmaximal, characteristic, complemented
6C83×#1303C211yesmaximal, characteristic, complemented
7C83×#1292C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C83C2211yescharacteristic
9C4×#41×C83C2211yescharacteristic
10#477×C83—21no—
11#476×C83—21no—
12#475×C83C412yescomplemented
13#474×C83C412yescomplemented
14#446×C83—21no—
15#436×C83—21no—
16#435×C83—22no—
17#432×C83—21no—
18#431×C83C2211yescharacteristic
19#428×C83—21no—
20#423×C83—21no—
21#423×C83C2211yescharacteristic
22#423×C83C2211yescharacteristic
23C2×C4⋊C8×C83C2211yescharacteristic
24C2×#104×C83—21no—
25#417×C83—21no—
26C4×C4⋊C4×C83C2211yescharacteristic
27#340×C83—22no—
28#339×C83—21no—
29#333×C83—21no—
30#333×C83—21no—
31C2×#41×C83D411yescharacteristic
32C22×Q8×C83—21no—
33C2×M16×C83—21no—
34C2×M16×C83—22no—
35C2×M16×C83—21no—
36C22×C8×C83D412yes—
37C4⋊Q8×C83—21no—
38C4⋊Q8×C83—21no—
39C4⋊Q8×C83—21no—
40C4⋊Q8×C83C2×C412yes—
41C4×Q8×C83C2×C411yescharacteristic
42C4×Q8×C83D411yescharacteristic
43C4×D4×C83—21no—
44C4×D4×C83—21no—
45C4×D4×C83C2×C411yescharacteristic
46C4×D4×C83D411yescharacteristic
47#117×C83—21no—
48#117×C83D411yescharacteristic
49C2×C4⋊C4×C83—21no—
50C2×C4⋊C4×C83—21no—
51C2×C4⋊C4×C83—21no—
52C2×C42×C83—21no—
53C2×C42×C83—21no—
54C2×C42×C83C2311yescharacteristic
55#107×C83—22no—
56#106×C83—22no—
57C4⋊C8×C83—22no—
58C4⋊C8×C83—21no—
59C4⋊C8×C83—21no—
60C4⋊C8×C83—21no—
61C4⋊C8×C83—21no—
62C4⋊C8×C83—21no—
63C4⋊C8×C83C2×C412yes—
64C4⋊C8×C83D411yescharacteristic
65C4⋊C8×C83D411yescharacteristic
66#104×C83—42no—
67#103×C83—22no—
68#102×C83—22no—
69C22⋊C8×C83—22no—
70C22⋊C8×C83—21no—
71#97×C83—22no—
72C4×C8×C83—21no—
73#95×C83—21no—
74#41×C83—21no—
75#41×C83—21no—
76#41×C83—21no—
77#41×C83—21no—
78C2×Q8×C83—22no—
79C2×Q8×C83—41no—
80C2×Q8×C83—82no—
81C2×Q8×C83C22⋊C411yescharacteristic
82C2×D4×C83—21no—
83C2×D4×C83C22⋊C411yescharacteristic
84C22×C4×C83—21no—
85C22×C4×C83—21no—
86C22×C4×C83—21no—
87C22×C4×C83—41no—
88C22×C4×C83—41no—
89C22×C4×C83C2×D411yescharacteristic
90C22×C4×C83C2×D411yescharacteristic
91C22×C4×C83#4111yescharacteristic
92M16×C83—41no—
93M16×C83—41no—
94M16×C83—41no—
95M16×C83—41no—
96M16×C83—82no—
97C2×C8×C83—22no—
98C2×C8×C83—21no—
99C2×C8×C83—21no—
100C2×C8×C83—22no—
101C2×C8×C83—42no—
102C2×C8×C83—41no—
103C4⋊C4×C83—21no—
104C4⋊C4×C83—21no—
105C4⋊C4×C83—22no—
106C4⋊C4×C83—22no—
107C4⋊C4×C83—22no—
108C4⋊C4×C83—41no—
109C4⋊C4×C83—41no—
110C4⋊C4×C83—41no—
111C4⋊C4×C83C22⋊C411yescharacteristic
112C4⋊C4×C83C22⋊C411yescharacteristic
113C22⋊C4×C83—21no—
114C22⋊C4×C83—21no—
115C22⋊C4×C83—21no—
116C42×C83—21no—
117C42×C83—21no—
118C42×C83—21no—
119C42×C83—41no—
120C42×C83—41no—
121C42×C83C22×C411yescharacteristic
122C42×C83C2×D411yescharacteristic
123C42×C83C2×D411yescharacteristic
124C42×C83#4111yescharacteristic
125C23×C83—21no—
126C23×C83#12111yescharacteristic
127Q8×C83—21no—
128Q8×C83—21no—
129Q8×C83—82no—
130Q8×C83—82no—
131D4×C83—21no—
132D4×C83—21no—
133D4×C83—41no—
134D4×C83—41no—
135C2×C4×C83—21no—
136C2×C4×C83—21no—
137C2×C4×C83—21no—
138C2×C4×C83—21no—
139C2×C4×C83—21no—
140C2×C4×C83—41no—
141C2×C4×C83—41no—
142C2×C4×C83—41no—
143C2×C4×C83—41no—
144C2×C4×C83—41no—
145C2×C4×C83—42no—
146C2×C4×C83—42no—
147C2×C4×C83—81no—
148C2×C4×C83—81no—
149C2×C4×C83—82no—
150C2×C4×C83—81no—
151C2×C4×C83C2×C22⋊C411yescharacteristic
152C2×C4×C83C4×D411yescharacteristic
153C2×C4×C83C4×D411yescharacteristic
154C2×C4×C83#12011yescharacteristic
155C2×C4×C83#12111yescharacteristic
156C2×C4×C83#12311yescharacteristic
157C2×C4×C83AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C83#13711yescharacteristic
159C2×C4×C83#13711yescharacteristic
160C2×C4×C83#13711yescharacteristic
161C8×C83—42no—
162C8×C83—42no—
163C8×C83—41no—
164C8×C83—41no—
165C8×C83—81no—
166C22×C83—21no—
167C22×C83—21no—
168C22×C83—41no—
169C22×C83—41no—
170C22×C83—41no—
171C22×C83#38611yescharacteristic
172C22×C83#46811yescharacteristic
173C22×C83#47011yescharacteristic
174C4×C83—21no—
175C4×C83—21no—
176C4×C83—21no—
177C4×C83—41no—
178C4×C83—41no—
179C4×C83—41no—
180C4×C83—82no—
181C4×C83—82no—
182C4×C83#41711yescharacteristic
183C4×C83#41911yescharacteristic
184C4×C83#45511yescharacteristic
185C4×C83#45611yescharacteristic
186C4×C83#46811yescharacteristic
187C4×C83#47011yescharacteristic
188#9319C8311yesmaximal, characteristic, direct product factor, Sylow
189C2×C83—21no—
190C2×C83—21no—
191C2×C83—81no—
192C2×C83#188211yescharacteristic
193C2×C83#189411yescharacteristic
194C2×C83#190311yescharacteristic
195#3079C2×C8311yescharacteristic
196#2989C2×C8311yescharacteristic
197#1987C2×C8311yescharacteristic, complemented
198#1806C2×C8311yescharacteristic
199#1548C2×C8311yescharacteristic, complemented
200#1303C2×C8311yescharacteristic, complemented
201#1292C2×C8311yescharacteristic, complemented
202C83#931911yescharacteristic, direct product factor, Sylow
203C2×C4⋊Q8C22×C8311yescharacteristic
204C4×#41C22×C8311yescharacteristic
205#477—21no—
206#476—21no—
207#475C4×C8312yescomplemented
208#474C4×C8312yescomplemented
209#446—21no—
210#436—21no—
211#435—22no—
212#432—21no—
213#431C22×C8311yescharacteristic
214#428—21no—
215#423—21no—
216#423C22×C8311yescharacteristic
217#423C22×C8311yescharacteristic
218C2×C4⋊C8C22×C8311yescharacteristic
219C2×#104—21no—
220#417—21no—
221C4×C4⋊C4C22×C8311yescharacteristic
222#340—22no—
223#339—21no—
224#333—21no—
225#333—21no—
226C2×#41D4×C8311yescharacteristic
227C22×Q8—21no—
228C2×M16—21no—
229C2×M16—22no—
230C2×M16—21no—
231C22×C8D4×C8312yes—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8—21no—
235C4⋊Q8C2×C4×C8312yes—
236C4×Q8C2×C4×C8311yescharacteristic
237C4×Q8D4×C8311yescharacteristic
238C4×D4—21no—
239C4×D4—21no—
240C4×D4C2×C4×C8311yescharacteristic
241C4×D4D4×C8311yescharacteristic
242#117—21no—
243#117D4×C8311yescharacteristic
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C42—21no—
248C2×C42—21no—
249C2×C42C23×C8311yescharacteristic
250#107—22no—
251#106—22no—
252C4⋊C8—22no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8C2×C4×C8312yes—
259C4⋊C8D4×C8311yescharacteristic
260C4⋊C8D4×C8311yescharacteristic
261#104—42no—
262#103—22no—
263#102—22no—
264C22⋊C8—22no—
265C22⋊C8—21no—
266#97—22no—
267C4×C8—21no—
268#95—21no—
269#41—21no—
270#41—21no—
271#41—21no—
272#41—21no—
273C2×Q8—22no—
274C2×Q8—41no—
275C2×Q8—82no—
276C2×Q8C22⋊C4×C8311yescharacteristic
277C2×D4—21no—
278C2×D4C22⋊C4×C8311yescharacteristic
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4C2×D4×C8311yescharacteristic
285C22×C4C2×D4×C8311yescharacteristic
286C22×C4#41×C8311yescharacteristic
287M16—41no—
288M16—41no—
289M16—41no—
290M16—41no—
291M16—82no—
292C2×C8—22no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—22no—
296C2×C8—42no—
297C2×C8—41no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4C22⋊C4×C8311yescharacteristic
307C4⋊C4C22⋊C4×C8311yescharacteristic
308C22⋊C4—21no—
309C22⋊C4—21no—
310C22⋊C4—21no—
311C42—21no—
312C42—21no—
313C42—21no—
314C42—41no—
315C42—41no—
316C42C22×C4×C8311yescharacteristic
317C42C2×D4×C8311yescharacteristic
318C42C2×D4×C8311yescharacteristic
319C42#41×C8311yescharacteristic
320C23—21no—
321C23#121×C8311yescharacteristic
322Q8—21no—
323Q8—21no—
324Q8—82no—
325Q8—82no—
326D4—21no—
327D4—21no—
328D4—41no—
329D4—41no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—82no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4C2×C22⋊C4×C8311yescharacteristic
347C2×C4C4×D4×C8311yescharacteristic
348C2×C4C4×D4×C8311yescharacteristic
349C2×C4#120×C8311yescharacteristic
350C2×C4#121×C8311yescharacteristic
351C2×C4#123×C8311yescharacteristic
352C2×C4AGL(1,ℤ/8)×C8311yescharacteristic
353C2×C4#137×C8311yescharacteristic
354C2×C4#137×C8311yescharacteristic
355C2×C4#137×C8311yescharacteristic
356C8—42no—
357C8—42no—
358C8—41no—
359C8—41no—
360C8—81no—
361C22—21no—
362C22—21no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22#386×C8311yescharacteristic
367C22#468×C8311yescharacteristic
368C22#470×C8311yescharacteristic
369C4—21no—
370C4—21no—
371C4—21no—
372C4—41no—
373C4—41no—
374C4—41no—
375C4—82no—
376C4—82no—
377C4#417×C8311yescharacteristic
378C4#419×C8311yescharacteristic
379C4#455×C8311yescharacteristic
380C4#456×C8311yescharacteristic
381C4#468×C8311yescharacteristic
382C4#470×C8311yescharacteristic
383C2—21no—
384C2—21no—
385C2—81no—
386C2C83×#188211yescharacteristic
387C2C83×#189411yescharacteristic
388C2C83×#190311yescharacteristic
subgroupG/H
center, socleC22×C83#386
commutatorC42C22×C4×C83
Frattini, cosocleC2×C42C23×C83
prime radicalC2×#41×C83D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C83 ◁ C2×C42×C83 ◁ G

Complements

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

NH ≅ G/Ntype
3. C83×#1987C2semidirect
5. C83×#1548C2semidirect
6. C83×#1303C2semidirect
7. C83×#1292C2semidirect
12. #475×C83C4semidirect
13. #474×C83C4semidirect
188. #9319C83direct (N × H)
197. #1987C2×C83semidirect
199. #1548C2×C83semidirect
200. #1303C2×C83semidirect
201. #1292C2×C83semidirect
202. C83#9319direct (N × H)
207. #475C4×C83semidirect
208. #474C4×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#30792
C83×#29892
C83×#19872
C83×#18062
C83×#15482
C83×#13032
C83×#12922
#931983