Finite Group Databasebeta

← #35559542

Subgroups — #35559542

Order 21248.

534 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24918122C211yesmaximal, characteristic, complemented
2#24909665C211yesmaximal, characteristic, complemented
3#24909660C211yesmaximal, characteristic, complemented
4#24909627C211yesmaximal, characteristic, complemented
5#24909620C211yesmaximal, characteristic, complemented
6#24909513C211yesmaximal, characteristic, complemented
7#24909508C211yesmaximal, characteristic, complemented
8#24909403C211yesmaximal, characteristic
9#24909403C211yesmaximal, characteristic
10#24909332C211yesmaximal, characteristic, complemented
11#24909327C211yesmaximal, characteristic, complemented
12C4×#14581738C211yesmaximal, characteristic, complemented
13C4×#14581736C211yesmaximal, characteristic, complemented
14#24909270C211yesmaximal, characteristic, complemented
15C83×#2951C211yesmaximal, characteristic
16#19128313—21no—
17C2×#14581738C2211yescharacteristic
18C2×#14581738C2211yescharacteristic
19C2×#14581736C2211yescharacteristic
20C2×#14581736C2211yescharacteristic
21#19128103C2211yescharacteristic
22#19128081C2211yescharacteristic
23#19128070—21no—
24#19127959—21no—
25#19127942C2211yescharacteristic
26#19127942C2211yescharacteristic
27#19127809—21no—
28C4×Dic332C2211yescharacteristic
29C4×Dic332C2211yescharacteristic
30#19127528C2211yescharacteristic
31#19127528C2211yescharacteristic
32#19127526C2211yescharacteristic
33#19127526C2211yescharacteristic
34C4⋊(C83⋊C16)C2211yescharacteristic
35C4⋊(C83⋊C16)C2211yescharacteristic
36#19127505C2211yescharacteristic
37#19127505C2211yescharacteristic
38#19127504C2211yescharacteristic
39#19127504C2211yescharacteristic
40#19127504C2211yescharacteristic
41#19127504C2211yescharacteristic
42#19127502C2211yescharacteristic
43#19127502C2211yescharacteristic
44C22⋊(C83⋊C16)C2211yescharacteristic
45C22⋊(C83⋊C16)C2211yescharacteristic
46#19127477C2211yescharacteristic
47C4×C83⋊C16C2211yescharacteristic
48C2×#135×C83C2211yescharacteristic
49#520×C83—21no—
50#440×C83—21no—
51#440×C83—21no—
52C4×Q16×C83C2211yescharacteristic
53C4×Q16×C83C2211yescharacteristic
54C4×D8×C83C2211yescharacteristic
55C4×D8×C83C2211yescharacteristic
56C2×#107×C83C2211yescharacteristic
57#417×C83—21no—
58#405×C83C2211yescharacteristic
59C2×Dic332—21no—
60C2×Dic332C2311yescharacteristic
61C2×Dic332C2311yescharacteristic
62#14581792—21no—
63#14581785—41no—
64#14581785—41no—
65#14581784—21no—
66#14581782—41no—
67#14581782—41no—
68#14581771—21no—
69#14581771—21no—
70C4×Dic166—21no—
71C4×Dic166—21no—
72#14581738—22no—
73#14581738—22no—
74#14581736—22no—
75#14581736—22no—
76C2×C83⋊C16C2311yescharacteristic
77C2×C83⋊C16C2311yescharacteristic
78C2×C83⋊C16C2311yescharacteristic
79C2×C83⋊C16C2311yescharacteristic
80#14581726C2311yescharacteristic
81#14581726C2311yescharacteristic
82#14581724—21no—
83#14581717—21no—
84#14581717—21no—
85#14581717—21no—
86#14581717—21no—
87C2×#41×C83—21no—
88#135×C83—22no—
89#135×C83—22no—
90C2×Q16×C83C2311yescharacteristic
91C2×SD16×C83—21no—
92C2×D8×C83C2311yescharacteristic
93C2×M16×C83D411yescharacteristic
94C22×C8×C83C2311yescharacteristic
95C4×Q8×C83—21no—
96C4×Q8×C83—21no—
97C4×D4×C83—21no—
98C4×D4×C83—21no—
99C4×D4×C83—41no—
100C4×D4×C83—41no—
101#117×C83—41no—
102#117×C83D411yescharacteristic
103C2×C4⋊C4×C83—21no—
104C2×C4⋊C4×C83—41no—
105#107×C83—21no—
106#107×C83C2311yescharacteristic
107#107×C83C2311yescharacteristic
108#103×C83—21no—
109#103×C83—21no—
110#102×C83—21no—
111#102×C83—21no—
112#97×C83D411yescharacteristic
113#97×C83D411yescharacteristic
114C4×C8×C83C2311yescharacteristic
115C4×C8×C83C2311yescharacteristic
116C2×Dic166—21no—
117C2×Dic166—21no—
118Dic332—21no—
119Dic332—21no—
120Dic332—21no—
121Dic332—21no—
122Dic332—42no—
123C4⋊Dic83—21no—
124C4⋊Dic83—21no—
125C4⋊Dic83—41no—
126C4⋊Dic83—41no—
127Dic83⋊C4—41no—
128Dic83⋊C4—41no—
129Dic83⋊C4—41no—
130Dic83⋊C4—41no—
131Dic83⋊C4—41no—
132Dic83⋊C4—41no—
133C22⋊Dic83—41no—
134C22⋊Dic83—41no—
135C4×Dic83—41no—
136C4×Dic83—41no—
137C83⋊C16—21no—
138C83⋊C16—21no—
139C83⋊C16—21no—
140C83⋊C16—21no—
141#41×C83—24no—
142#41×C83—42no—
143C2×Q8×C83—21no—
144C2×D4×C83—21no—
145C2×D4×C83—41no—
146C22×C4×C83—41no—
147C22×C4×C83—41no—
148C22×C4×C83—41no—
149C22×C4×C83—41no—
150C22×C4×C83C2×D411yescharacteristic
151Q16×C83—21no—
152Q16×C83#4112yes—
153SD16×C83—24no—
154D8×C83—21no—
155D8×C83#4112yes—
156M16×C83—41no—
157C2×C8×C83—21no—
158C2×C8×C83—21no—
159C2×C8×C83C2×D411yescharacteristic
160C2×C8×C83C2×D411yescharacteristic
161C2×C8×C83C2×D411yescharacteristic
162C2×C8×C83C2411yescharacteristic
163C4⋊C4×C83—21no—
164C4⋊C4×C83—21no—
165C4⋊C4×C83—41no—
166C4⋊C4×C83—41no—
167C4⋊C4×C83—41no—
168C4⋊C4×C83D811yescharacteristic
169C4⋊C4×C83D811yescharacteristic
170C22⋊C4×C83—41no—
171C22⋊C4×C83—41no—
172C22⋊C4×C83D811yescharacteristic
173C22⋊C4×C83D811yescharacteristic
174C42×C83—41no—
175C42×C83—41no—
176C42×C83C2×D411yescharacteristic
177C42×C83C2×D411yescharacteristic
178C23×C83—41no—
179C23×C83C2×D811yescharacteristic
180Q8×C83—22no—
181Q8×C83—41no—
182D4×C83—22no—
183D4×C83—44no—
184D4×C83—41no—
185C2×C4×C83—21no—
186C2×C4×C83—21no—
187C2×C4×C83—44no—
188C2×C4×C83—41no—
189C2×C4×C83—41no—
190C2×C4×C83—41no—
191C2×C4×C83—161no—
192C2×C4×C83—161no—
193C2×C4×C83—161no—
194C2×C4×C83C2×D811yescharacteristic
195C2×C4×C83C2×D811yescharacteristic
196C2×C4×C83C2×D811yescharacteristic
197C2×C4×C83C2×D811yescharacteristic
198C2×C4×C83C2×D811yescharacteristic
199C2×C4×C83C22×D411yescharacteristic
200C2×Dic83—41no—
201C2×Dic83—41no—
202C2×Dic83—41no—
203C2×Dic83—41no—
204Dic166—41no—
205Dic166—41no—
206Dic166—41no—
207Dic166—41no—
208C8×C83—21no—
209C8×C83—21no—
210C8×C83—21no—
211C8×C83C2×#4111yescharacteristic
212C8×C83C2×#4111yescharacteristic
213C22×C83—21no—
214C22×C83—21no—
215C22×C83—21no—
216C22×C83—42no—
217C22×C83—81no—
218C22×C83—81no—
219C22×C83C22×D811yescharacteristic
220C4×C83—21no—
221C4×C83—21no—
222C4×C83—21no—
223C4×C83—21no—
224C4×C83—21no—
225C4×C83—42no—
226C4×C83—81no—
227C4×C83—81no—
228C4×C83#52511yescharacteristic
229C4×C83#57511yescharacteristic
230Dic83—81no—
231Dic83—81no—
232Dic83—81no—
233Dic83—81no—
234#33680—831nomaximal, Sylow
235C2×C83—41no—
236C2×C83—82no—
237C2×C83#310011yescharacteristic
238C2×C83#341611yescharacteristic
239C2×C83#341711yescharacteristic
240#3177—831no—
241#2951D8311yescharacteristic
242#2236—831no—
243#2235—831no—
244#2229—831no—
245#2228—831no—
246#2209—831no—
247#2208—831no—
248#2189—831no—
249#2189—831no—
250#2176—831no—
251#2175—831no—
252C4×Q32—831no—
253C4×SD32—831no—
254#2164—831no—
255C83#3368011yescharacteristic, complemented, Sylow
256C2×#135C2×D8311yescharacteristic
257#541—1661no—
258#520—21no—
259C2×Q32—831no—
260C2×Q32—831no—
261C2×SD32—831no—
262C2×SD32—831no—
263#499—831no—
264#494—831no—
265#491—1661no—
266#470—1661no—
267#467—831no—
268#467—831no—
269#441—1661no—
270#440—21no—
271#440—21no—
272C4×Q16—831no—
273C4×Q16—831no—
274C4×Q16C2×D8311yescharacteristic
275C4×Q16C2×D8311yescharacteristic
276C4×D8C2×D8311yescharacteristic
277C4×D8C2×D8311yescharacteristic
278C2×#107C2×D8311yescharacteristic
279#417—21no—
280#405C2×D8311yescharacteristic
281#367—831no—
282#367—831no—
283#366—831no—
284#366—831no—
285C4⋊C16—831no—
286C4⋊C16—831no—
287#358—831no—
288#358—831no—
289#358—831no—
290#358—831no—
291#358—831no—
292#358—831no—
293#357—831no—
294#357—831no—
295C22⋊C16—831no—
296C22⋊C16—831no—
297#346—831no—
298C4×C16—831no—
299C2×#41—21no—
300#135—22no—
301#135—22no—
302C2×Q16—831no—
303C2×Q16—831no—
304C2×Q16—1661no—
305C2×Q16C22×D8311yescharacteristic
306C2×SD16—21no—
307C2×D8C22×D8311yescharacteristic
308C2×M16C22⋊D8311yescharacteristic
309C22×C8C22×D8311yescharacteristic
310C4⋊Q8—1661no—
311#126—3321no—
312#126—3321no—
313#125—3321no—
314#125—3321no—
315#125—1661no—
316C22⋊Q8—1661no—
317C22⋊Q8—1661no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8—1661no—
321C4×Q8—1661no—
322C4×D4—21no—
323C4×D4—21no—
324C4×D4—41no—
325C4×D4—41no—
326#117—41no—
327#117C22⋊D8311yescharacteristic
328C2×C4⋊C4—21no—
329C2×C4⋊C4—41no—
330Q32—1662no—
331Q32—1662no—
332SD32—1662no—
333SD32—1662no—
334C2×C16—831no—
335C2×C16—831no—
336C2×C16—831no—
337C2×C16—831no—
338#107—21no—
339#107—831no—
340#107—831no—
341#107C22×D8311yescharacteristic
342#107C22×D8311yescharacteristic
343#106—1661no—
344#103—21no—
345#103—21no—
346#103—1661no—
347#103—1661no—
348#103—1661no—
349#103—1661no—
350#102—21no—
351#102—21no—
352#97C22⋊D8311yescharacteristic
353#97C22⋊D8311yescharacteristic
354C4×C8C22×D8311yescharacteristic
355C4×C8C22×D8311yescharacteristic
356#41—24no—
357#41—42no—
358C2×Q8—21no—
359C2×Q8—1661no—
360C2×Q8—1661no—
361C2×D4—21no—
362C2×D4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4C2×C22⋊D8311yescharacteristic
368Q16—21no—
369Q16—3322no—
370Q16—1661no—
371Q16—1661no—
372Q16—1661no—
373Q16—1661no—
374Q16#1305059012yes—
375SD16—24no—
376D8—21no—
377D8#1305059012yes—
378M16—41no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8C2×C22⋊D8311yescharacteristic
382C2×C8C2×C22⋊D8311yescharacteristic
383C2×C8C2×C22⋊D8311yescharacteristic
384C2×C8C23×D8311yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—3321no—
391C4⋊C4—3321no—
392C4⋊C4—3321no—
393C4⋊C4—3321no—
394C4⋊C4—3321no—
395C4⋊C4—3321no—
396C4⋊C4—3321no—
397C4⋊C4—3321no—
398C4⋊C4—1661no—
399C4⋊C4—1661no—
400C4⋊C4#1305057511yescharacteristic
401C4⋊C4#1305057511yescharacteristic
402C22⋊C4—41no—
403C22⋊C4—41no—
404C22⋊C4—3321no—
405C22⋊C4—3321no—
406C22⋊C4#1305057511yescharacteristic
407C22⋊C4#1305057511yescharacteristic
408C42—41no—
409C42—41no—
410C42—3321no—
411C42—3321no—
412C42C2×C22⋊D8311yescharacteristic
413C42C2×C22⋊D8311yescharacteristic
414C16—1661no—
415C16—1661no—
416C16—1661no—
417C16—1661no—
418C23—41no—
419C23C2×#1305057511yescharacteristic
420Q8—22no—
421Q8—41no—
422Q8—3321no—
423Q8—3321no—
424Q8—3321no—
425Q8—3321no—
426D4—22no—
427D4—44no—
428D4—41no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—44no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—161no—
436C2×C4—161no—
437C2×C4—161no—
438C2×C4—3321no—
439C2×C4—3321no—
440C2×C4—3321no—
441C2×C4—3321no—
442C2×C4C2×#1305057511yescharacteristic
443C2×C4C2×#1305057511yescharacteristic
444C2×C4C2×#1305057511yescharacteristic
445C2×C4C2×#1305057511yescharacteristic
446C2×C4C2×#1305057511yescharacteristic
447C2×C4C22×C22⋊D8311yescharacteristic
448C8—21no—
449C8—21no—
450C8—21no—
451C8C2×#1305059011yescharacteristic
452C8C2×#1305059011yescharacteristic
453C22—21no—
454C22—21no—
455C22—21no—
456C22—42no—
457C22—81no—
458C22—81no—
459C22C22×#1305057511yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—42no—
466C4—81no—
467C4—81no—
468C4—6641no—
469C4—6641no—
470C4—6641no—
471C4—6641no—
472C4#1912821211yescharacteristic
473C4#1912849911yescharacteristic
474C2—41no—
475C2—82no—
476C2#2491746311yescharacteristic
477C2#2492061011yescharacteristic
478C2#2492061411yescharacteristic
subgroupG/H
centerC22C22×#13050575
commutator, cosocleC2×C8×C83C24
FrattiniC2×C8C23×D83
FittingC83×#2951C2
socleC22×C83C22×D8
prime radicalC2×#135×C83C22
hypercenter#2951D83
hypocenterC83#33680
LCSG ▷ C2×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #2951

Complements

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

NH ≅ G/Ntype
1. #24918122C2semidirect
2. #24909665C2semidirect
3. #24909660C2semidirect
4. #24909627C2semidirect
5. #24909620C2semidirect
6. #24909513C2semidirect
7. #24909508C2semidirect
10. #24909332C2semidirect
11. #24909327C2semidirect
12. C4×#14581738C2semidirect
13. C4×#14581736C2semidirect
14. #24909270C2semidirect
255. C83#33680semidirect

Maximal subgroups

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

subgroupindex
#249181222
#249096652
#249096602
#249096272
#249096202
#249095132
#249095082
#249094032
#249093322
#249093272
C4×#145817382
C4×#145817362
#249092702
C83×#29512
#3368083