Finite Group Databasebeta

← #35559437

Subgroups — #35559437

Order 21248.

554 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24918033C211yesmaximal, characteristic, complemented
2#24909671C211yesmaximal, characteristic, complemented
3#24909654C211yesmaximal, characteristic, complemented
4#24909627C211yesmaximal, characteristic, complemented
5#24909620C211yesmaximal, characteristic, complemented
6#24909525C211yesmaximal, characteristic, complemented
7#24909518C211yesmaximal, characteristic, complemented
8#24909403C211yesmaximal, characteristic, complemented
9#24909386C211yesmaximal, characteristic
10#24909337C211yesmaximal, characteristic, complemented
11#24909332C211yesmaximal, characteristic, complemented
12#24909327C211yesmaximal, characteristic, complemented
13#24909325C211yesmaximal, characteristic, complemented
14#24909266C211yesmaximal, characteristic, complemented
15C4×#135×C83C211yesmaximal, characteristic, complemented
16#19128235—21no—
17C2×#14581738C2211yescharacteristic
18C2×#14581736C2211yescharacteristic
19C2×#14581735C2211yescharacteristic
20C2×#14581733C2211yescharacteristic
21#19128103C2211yescharacteristic
22#19128085C2211yescharacteristic
23#19128056—21no—
24#19127942C2211yescharacteristic
25#19127937C2211yescharacteristic
26#19127930—21no—
27C4×Dic332C2211yescharacteristic
28C4×#13050579—21no—
29C4×D664C2211yescharacteristic
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#19127502C2211yescharacteristic
41#19127502C2211yescharacteristic
42#19127501C2211yescharacteristic
43#19127501C2211yescharacteristic
44C22⋊(C83⋊C16)C2211yescharacteristic
45C22⋊(C83⋊C16)C2211yescharacteristic
46#19127477C2211yescharacteristic
47#19127477C2211yescharacteristic
48C2×#135×C83C2211yescharacteristic
49C4×#41×C83—21no—
50C4×Q16×C83C2211yescharacteristic
51C4×Q16×C83C2211yescharacteristic
52C4×SD16×C83—21no—
53C4×SD16×C83—21no—
54C4×D8×C83C2211yescharacteristic
55C4×D8×C83C2211yescharacteristic
56#427×C83C2211yescharacteristic
57#416×C83—21no—
58C2×C4×C8×C83C2211yescharacteristic
59C2×Dic332C2311yescharacteristic
60C2×#13050579—21no—
61C2×D664C2311yescharacteristic
62#14581786—41no—
63#14581784—21no—
64#14581780—21no—
65#14581775—41no—
66#14581771—21no—
67#14581766—21no—
68C4×Dic166—21no—
69C4×D332—21no—
70C4×C22⋊D83—41no—
71#14581749—41no—
72#14581738—22no—
73#14581736—22no—
74#14581735—22no—
75#14581733—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#14581714—21no—
86#14581714—21no—
87C2×#41×C83—21no—
88#135×C83—22no—
89#135×C83—22no—
90C2×Q16×C83C2311yescharacteristic
91C2×SD16×C83—21no—
92C2×D8×C83C2311yescharacteristic
93C22×C8×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—21no—
102#117×C83—41no—
103C2×C42×C83—41no—
104C2×C42×C83D411yescharacteristic
105#107×C83C2311yescharacteristic
106#107×C83C2311yescharacteristic
107#106×C83—21no—
108#103×C83—21no—
109#103×C83—21no—
110#102×C83—21no—
111#102×C83—21no—
112C4×C8×C83D411yescharacteristic
113C4×C8×C83D411yescharacteristic
114C4×C8×C83C2311yescharacteristic
115C4×C8×C83C2311yescharacteristic
116C2×Dic166—21no—
117C2×D332—21no—
118C2×C22⋊D83—41no—
119C2×C4×D83—41no—
120Dic332—21no—
121Dic332—21no—
122#13050579—42no—
123D664—21no—
124D664—21no—
125C4⋊Dic83—21no—
126C4⋊Dic83—21no—
127Dic83⋊C4—41no—
128Dic83⋊C4—41no—
129Dic83⋊C4—41no—
130Dic83⋊C4—41no—
131C22⋊Dic83—41no—
132(C2×D83)⋊C4—41no—
133(C2×D83)⋊C4—41no—
134(C2×D83)⋊C4—41no—
135(C2×D83)⋊C4—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×C83D811yescharacteristic
150C22×C4×C83D811yescharacteristic
151C22×C4×C83C2×D411yescharacteristic
152Q16×C83—21no—
153Q16×C83#4112yes—
154SD16×C83—24no—
155D8×C83—21no—
156D8×C83#4112yes—
157C2×C8×C83—21no—
158C2×C8×C83—21no—
159C2×C8×C83—41no—
160C2×C8×C83C2×D411yescharacteristic
161C2×C8×C83C2×D411yescharacteristic
162C2×C8×C83C2×D411yescharacteristic
163C2×C8×C83C2411yescharacteristic
164C4⋊C4×C83—21no—
165C4⋊C4×C83—21no—
166C4⋊C4×C83—41no—
167C4⋊C4×C83—41no—
168C22⋊C4×C83—41no—
169C22⋊C4×C83—41no—
170C22⋊C4×C83—41no—
171C42×C83—41no—
172C42×C83—41no—
173C42×C83—41no—
174C42×C83D811yescharacteristic
175C42×C83D811yescharacteristic
176C42×C83C2×D411yescharacteristic
177C42×C83C2×D411yescharacteristic
178C23×C83—41no—
179C23×C83C2×D811yescharacteristic
180C22×D83—41no—
181Q8×C83—22no—
182Q8×C83—41no—
183D4×C83—22no—
184D4×C83—44no—
185D4×C83—41no—
186C2×C4×C83—21no—
187C2×C4×C83—21no—
188C2×C4×C83—41no—
189C2×C4×C83—41no—
190C2×C4×C83—44no—
191C2×C4×C83—41no—
192C2×C4×C83—41no—
193C2×C4×C83—41no—
194C2×C4×C83—82no—
195C2×C4×C83—82no—
196C2×C4×C83C2×D811yescharacteristic
197C2×C4×C83C2×D811yescharacteristic
198C2×C4×C83C2×D811yescharacteristic
199C2×C4×C83C2×D811yescharacteristic
200C2×C4×C83C2×D811yescharacteristic
201C2×C4×C83C22×D411yescharacteristic
202C22⋊D83—82no—
203C2×Dic83—41no—
204C2×Dic83—41no—
205C2×Dic83—41no—
206D332—41no—
207D332—41no—
208C4×D83—82no—
209Dic166—41no—
210Dic166—41no—
211C8×C83—21no—
212C8×C83—21no—
213C8×C83—21no—
214C8×C83C2×#4111yescharacteristic
215C8×C83C2×#4111yescharacteristic
216C22×C83—21no—
217C22×C83—21no—
218C22×C83—21no—
219C22×C83—42no—
220C22×C83—81no—
221C22×C83—81no—
222C22×C83C22×D811yescharacteristic
223C2×D83—81no—
224C2×D83—81no—
225C2×D83—81no—
226C4×C83—21no—
227C4×C83—21no—
228C4×C83—21no—
229C4×C83—21no—
230C4×C83—21no—
231C4×C83—42no—
232C4×C83—81no—
233C4×C83—81no—
234C4×C83#52511yescharacteristic
235C4×C83#57511yescharacteristic
236Dic83—81no—
237Dic83—81no—
238Dic83—81no—
239#33671—831nomaximal, Sylow
240C2×C83—41no—
241C2×C83—82no—
242C2×C83#310011yescharacteristic
243C2×C83#341411yescharacteristic
244C2×C83#341411yescharacteristic
245D83—161no—
246#3168—831no—
247C4×#135D8311yescharacteristic, complemented
248#2237—831no—
249#2234—831no—
250#2229—831no—
251#2228—831no—
252#2211—831no—
253#2210—831no—
254#2189—831no—
255#2186—831no—
256#2177—831no—
257#2176—831no—
258#2175—831no—
259#2175—831no—
260#2163—831no—
261C83#3367111yescharacteristic, complemented, Sylow
262C2×#135C2×D8311yescharacteristic
263#529—1661no—
264C4×#41—21no—
265C2×Q32—831no—
266C2×SD32—831no—
267C2×SD32—831no—
268C2×D16—831no—
269#499—831no—
270#495—831no—
271#488—1661no—
272#467—831no—
273#466—831no—
274#465—1661no—
275C4×Q16—831no—
276C4×Q16C2×D8311yescharacteristic
277C4×Q16C2×D8311yescharacteristic
278C4×SD16—21no—
279C4×SD16—21no—
280C4×SD16—1661no—
281C4×D8—831no—
282C4×D8C2×D8311yescharacteristic
283C4×D8C2×D8311yescharacteristic
284#427C2×D8311yescharacteristic
285#416—21no—
286C2×C4×C8C2×D8311yescharacteristic
287#367—831no—
288#367—831no—
289#366—831no—
290#366—831no—
291C4⋊C16—831no—
292C4⋊C16—831no—
293#358—831no—
294#358—831no—
295#358—831no—
296#358—831no—
297#357—831no—
298#357—831no—
299#357—831no—
300#357—831no—
301C22⋊C16—831no—
302C22⋊C16—831no—
303#346—831no—
304#346—831no—
305C2×#41—21no—
306#135—22no—
307#135—22no—
308C2×Q16—831no—
309C2×Q16C22×D8311yescharacteristic
310C2×SD16—21no—
311C2×SD16—1661no—
312C2×D8—831no—
313C2×D8C22×D8311yescharacteristic
314C22×C8C22⋊D8311yescharacteristic
315C22×C8C22×D8311yescharacteristic
316#126—3321no—
317#125—1661no—
318#124—1661no—
319#123—3321no—
320C22⋊Q8—1661no—
321#121—1661no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×Q8—1661no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—41no—
328C4×D4—41no—
329C4×D4—3321no—
330C4×D4—1661no—
331#117—21no—
332#117—41no—
333#117—3321no—
334C2×C42—41no—
335C2×C42C22⋊D8311yescharacteristic
336Q32—1662no—
337SD32—1662no—
338SD32—1662no—
339D16—1662no—
340C2×C16—831no—
341C2×C16—831no—
342C2×C16—831no—
343C2×C16—831no—
344#107—831no—
345#107—831no—
346#107C22×D8311yescharacteristic
347#107C22×D8311yescharacteristic
348#106—21no—
349#106—1661no—
350#103—21no—
351#103—21no—
352#103—1661no—
353#103—1661no—
354#102—21no—
355#102—21no—
356#102—1661no—
357#102—1661no—
358C4×C8C22⋊D8311yescharacteristic
359C4×C8C22⋊D8311yescharacteristic
360C4×C8C22×D8311yescharacteristic
361C4×C8C22×D8311yescharacteristic
362#41—24no—
363#41—42no—
364C2×Q8—21no—
365C2×Q8—1661no—
366C2×D4—21no—
367C2×D4—41no—
368C2×D4—3321no—
369C2×D4—1661no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—3321no—
374C22×C4#1305057511yescharacteristic
375C22×C4#1305057511yescharacteristic
376C22×C4C2×C22⋊D8311yescharacteristic
377Q16—21no—
378Q16—1661no—
379Q16—1661no—
380Q16#1305059012yes—
381SD16—24no—
382SD16—3322no—
383D8—21no—
384D8—1661no—
385D8—1661no—
386D8#1305059012yes—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—41no—
390C2×C8C2×C22⋊D8311yescharacteristic
391C2×C8C2×C22⋊D8311yescharacteristic
392C2×C8C2×C22⋊D8311yescharacteristic
393C2×C8C23×D8311yescharacteristic
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4—3321no—
399C4⋊C4—3321no—
400C4⋊C4—3321no—
401C4⋊C4—3321no—
402C4⋊C4—1661no—
403C4⋊C4—1661no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—41no—
407C22⋊C4—3321no—
408C22⋊C4—3321no—
409C22⋊C4—3321no—
410C22⋊C4—3321no—
411C22⋊C4—3321no—
412C42—41no—
413C42—41no—
414C42—41no—
415C42—3321no—
416C42#1305057511yescharacteristic
417C42#1305057511yescharacteristic
418C42C2×C22⋊D8311yescharacteristic
419C42C2×C22⋊D8311yescharacteristic
420C16—1661no—
421C16—1661no—
422C16—1661no—
423C16—1661no—
424C23—41no—
425C23—3321no—
426C23C2×#1305057511yescharacteristic
427Q8—22no—
428Q8—41no—
429Q8—3321no—
430Q8—3321no—
431D4—22no—
432D4—44no—
433D4—41no—
434D4—3321no—
435D4—3321no—
436D4—6642no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—44no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—82no—
446C2×C4—82no—
447C2×C4—3321no—
448C2×C4—3321no—
449C2×C4—3321no—
450C2×C4—6642no—
451C2×C4C2×#1305057511yescharacteristic
452C2×C4C2×#1305057511yescharacteristic
453C2×C4C2×#1305057511yescharacteristic
454C2×C4C2×#1305057511yescharacteristic
455C2×C4C2×#1305057511yescharacteristic
456C2×C4C22×C22⋊D8311yescharacteristic
457C8—21no—
458C8—21no—
459C8—21no—
460C8C2×#1305059011yescharacteristic
461C8C2×#1305059011yescharacteristic
462C22—21no—
463C22—21no—
464C22—21no—
465C22—42no—
466C22—81no—
467C22—81no—
468C22—6641no—
469C22—6641no—
470C22—6641no—
471C22C22×#1305057511yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—42no—
478C4—81no—
479C4—81no—
480C4—6641no—
481C4—6641no—
482C4—6641no—
483C4#1912821211yescharacteristic
484C4#1912849911yescharacteristic
485C2—41no—
486C2—82no—
487C2—13281no—
488C2#2491746311yescharacteristic
489C2#2492059711yescharacteristic
490C2#2492059711yescharacteristic
subgroupG/H
centerC22C22×#13050575
commutator, cosocleC2×C8×C83C24
FrattiniC2×C8C23×D83
FittingC4×#135×C83C2
socleC22×C83C22×D8
prime radical#24909386C2
hypercenterC4×#135D83
hypocenterC83#33671
LCSG ▷ C2×C8×C83 ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
1. #24918033C2semidirect
2. #24909671C2semidirect
3. #24909654C2semidirect
4. #24909627C2semidirect
5. #24909620C2semidirect
6. #24909525C2semidirect
7. #24909518C2semidirect
8. #24909403C2semidirect
10. #24909337C2semidirect
11. #24909332C2semidirect
12. #24909327C2semidirect
13. #24909325C2semidirect
14. #24909266C2semidirect
15. C4×#135×C83C2semidirect
247. C4×#135D83semidirect
261. C83#33671semidirect

Maximal subgroups

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

subgroupindex
#249180332
#249096712
#249096542
#249096272
#249096202
#249095252
#249095182
#249094032
#249093862
#249093372
#249093322
#249093272
#249093252
#249092662
C4×#135×C832
#3367183