Finite Group Databasebeta

← #35376217

Subgroups — #35376217

Order 21248.

578 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24918046C211yesmaximal, characteristic
2#24916411C211yesmaximal, characteristic
3#24916405C211yesmaximal, characteristic
4#24906370C211yesmaximal, characteristic, complemented
5#24906369C211yesmaximal, characteristic, complemented
6#24906336C211yesmaximal, characteristic, complemented
7#24906335C211yesmaximal, characteristic, complemented
8#24906333C211yesmaximal, characteristic, complemented
9#24906280C211yesmaximal, characteristic, complemented
10#24906279C211yesmaximal, characteristic, complemented
11#334×D83C211yesmaximal, characteristic
12#24905864C211yesmaximal, characteristic
13#24905864C211yesmaximal, characteristic
14#24905751C211yesmaximal, characteristic
15C83×#1587C211yesmaximal, characteristic, complemented
16#19128255C2211yescharacteristic
17#19128255C2211yescharacteristic
18#19128105C411yescharacteristic
19#19128079C411yescharacteristic
20#19128050C411yescharacteristic
21#19128050C411yescharacteristic
22#19127943C411yescharacteristic
23#19127941C411yescharacteristic
24#19127941C411yescharacteristic
25#19127939C411yescharacteristic
26#19127832C2211yescharacteristic
27#19127831—21no—
28#19127831C2211yescharacteristic
29#19127830—21no—
30#19127829—21no—
31#19127828—21no—
32#19127828C2211yescharacteristic
33Q8×C83⋊C8C2211yescharacteristic
34C8×Dic166C2211yescharacteristic
35#19127825C2211yescharacteristic
36C4×Dic332C2211yescharacteristic
37C4×#13050580C2211yescharacteristic
38C4×#13050580C2211yescharacteristic
39#19127752C2211yescharacteristic
40#19127726—21no—
41#19127726—21no—
42C4⋊C8×D83C2211yescharacteristic
43C4⋊C8×D83C2211yescharacteristic
44#19127658—21no—
45#19127655—21no—
46C4×#13050573C2211yescharacteristic
47C4×C8×D83C2211yescharacteristic
48#19127452C2211yescharacteristic
49#19127451C2211yescharacteristic
50#19127451C2211yescharacteristic
51#19127433C2211yescharacteristic
52#19127433C2211yescharacteristic
53Q8⋊(C83⋊C8)C2211yescharacteristic
54Q8⋊(C83⋊C8)C2211yescharacteristic
55#19127431C2211yescharacteristic
56#19127431C2211yescharacteristic
57#19127423C2211yescharacteristic
58#19127423C2211yescharacteristic
59#19127423C2211yescharacteristic
60#446×C83C2211yescharacteristic
61C8×Q8×C83C2211yescharacteristic
62C4×Q16×C83C2211yescharacteristic
63#334×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65Q8⋊C8×C83C2211yescharacteristic
66#322×C83C2211yescharacteristic
67C2×Dic332C2×C411yescharacteristic
68C2×#13050580C2×C411yescharacteristic
69C2×#13050580C2×C411yescharacteristic
70C2×#13050573D411yescharacteristic
71C2×#13050573D411yescharacteristic
72C2×C8×D83—21no—
73C2×C8×D83—21no—
74C2×C8×D83C2×C411yescharacteristic
75C2×C8×D83C2×C411yescharacteristic
76#14581791C2×C411yescharacteristic
77#14581791C2×C411yescharacteristic
78#14581790C2×C411yescharacteristic
79#14581790C2×C411yescharacteristic
80#14581782—21no—
81#14581782—21no—
82#14581772C2×C411yescharacteristic
83#14581772C2×C411yescharacteristic
84#14581770—21no—
85#14581770—21no—
86#14581768C2×C411yescharacteristic
87#14581768C2×C411yescharacteristic
88C4×Dic166—21no—
89C4×Dic166—21no—
90C4×Dic166C2311yescharacteristic
91C4×Dic166C2311yescharacteristic
92#14581749—21no—
93#14581749—21no—
94C42×D83C2311yescharacteristic
95#14581726C2×C411yescharacteristic
96#14581725C2×C411yescharacteristic
97#14581725C2×C411yescharacteristic
98C4⋊(C83⋊C8)—21no—
99C4⋊(C83⋊C8)—21no—
100C4⋊(C83⋊C8)C2311yescharacteristic
101C4⋊(C83⋊C8)C2311yescharacteristic
102Dic83⋊C8—21no—
103Dic83⋊C8—21no—
104Dic83⋊C8—21no—
105Dic83⋊C8—21no—
106Dic83⋊C8—21no—
107Dic83⋊C8—21no—
108Dic83⋊C8—21no—
109#14581717C2×C411yescharacteristic
110#14581717C2×C411yescharacteristic
111#14581716C2×C411yescharacteristic
112#14581716C2×C411yescharacteristic
113#14581715C2×C411yescharacteristic
114#14581715C2×C411yescharacteristic
115(C2×D83)⋊C8—21no—
116#14581703—21no—
117#14581702—21no—
118#14581702—21no—
119#14581702D411yescharacteristic
120#14581702D411yescharacteristic
121C4×C83⋊C8—21no—
122C4×C83⋊C8C2311yescharacteristic
123C4×C83⋊C8C2311yescharacteristic
124C4×C83⋊C8C2311yescharacteristic
125C8×Dic83—21no—
126C8×Dic83—21no—
127C8×Dic83C2×C411yescharacteristic
128C8×Dic83C2×C411yescharacteristic
129C2×Q16×C83C2×C411yescharacteristic
130C4×Q8×C83C2311yescharacteristic
131C4×Q8×C83C2311yescharacteristic
132#107×C83C2×C411yescharacteristic
133C4⋊C8×C83—21no—
134C4⋊C8×C83—21no—
135C4⋊C8×C83C2311yescharacteristic
136C4⋊C8×C83C2311yescharacteristic
137#103×C83C2×C411yescharacteristic
138#103×C83C2×C411yescharacteristic
139#97×C83—21no—
140C4×C8×C83—21no—
141C4×C8×C83C2311yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144C2×Dic166—21no—
145C2×Dic166—21no—
146C2×Dic166C22×C411yescharacteristic
147C2×Dic166C22×C411yescharacteristic
148C2×C4×D83C22×C411yescharacteristic
149C2×C4×D83C2×D411yescharacteristic
150C2×C4×D83#4111yescharacteristic
151Dic332—41no—
152#13050580—22no—
153#13050580—22no—
154#13050573—22no—
155#13050573—22no—
156C2×C83⋊C8—21no—
157C2×C83⋊C8—21no—
158C2×C83⋊C8—21no—
159C2×C83⋊C8C22×C411yescharacteristic
160C2×C83⋊C8C22×C411yescharacteristic
161C2×C83⋊C8C2×D411yescharacteristic
162C2×C83⋊C8C2×D411yescharacteristic
163C8×D83—22no—
164C8×D83—41no—
165C8×D83—42no—
166C8×D83—42no—
167C4⋊Dic83—21no—
168C4⋊Dic83—21no—
169C4⋊Dic83C22×C411yescharacteristic
170C4⋊Dic83C22×C411yescharacteristic
171Dic83⋊C4—21no—
172Dic83⋊C4—21no—
173Dic83⋊C4—21no—
174Dic83⋊C4—21no—
175Dic83⋊C4—21no—
176Dic83⋊C4—21no—
177Dic83⋊C4—21no—
178Dic83⋊C4—21no—
179Dic83⋊C4—21no—
180Dic83⋊C4—21no—
181(C2×D83)⋊C4—21no—
182(C2×D83)⋊C4—21no—
183(C2×D83)⋊C4—21no—
184(C2×D83)⋊C4—21no—
185C4×Dic83—21no—
186C4×Dic83—21no—
187C4×Dic83C22×C411yescharacteristic
188C4×Dic83C2×D411yescharacteristic
189C4×Dic83#4111yescharacteristic
190C2×Q8×C83C22×C411yescharacteristic
191C2×Q8×C83C22×C411yescharacteristic
192Q16×C83—41no—
193C2×C8×C83—21no—
194C2×C8×C83—21no—
195C2×C8×C83—21no—
196C2×C8×C83C22×C411yescharacteristic
197C2×C8×C83C22×C411yescharacteristic
198C2×C8×C83C2×D411yescharacteristic
199C2×C8×C83C2×D411yescharacteristic
200C4⋊C4×C83—21no—
201C4⋊C4×C83—21no—
202C4⋊C4×C83C22×C411yescharacteristic
203C4⋊C4×C83C22×C411yescharacteristic
204C42×C83—21no—
205C42×C83—21no—
206C42×C83C2411yescharacteristic
207C22×D83C4×D411yescharacteristic
208Q8×C83—21no—
209Q8×C83—21no—
210Q8×C83—21no—
211Q8×C83—21no—
212C2×C4×C83—21no—
213C2×C4×C83—21no—
214C2×C4×C83—21no—
215C2×C4×C83—21no—
216C2×C4×C83C23×C411yescharacteristic
217C2×C4×C83C22×D411yescharacteristic
218C2×C4×C83C2×#4111yescharacteristic
219C2×Dic83—21no—
220C2×Dic83—21no—
221C2×Dic83—21no—
222C2×Dic83—21no—
223C2×Dic83C4×D411yescharacteristic
224C2×Dic83C4×D411yescharacteristic
225C2×Dic83C4×D411yescharacteristic
226C4×D83—21no—
227C4×D83—21no—
228C4×D83—41no—
229C4×D83#13712yes—
230C4×D83#13712yes—
231Dic166—21no—
232Dic166—21no—
233Dic166—21no—
234Dic166—21no—
235Dic166—81no—
236Dic166—81no—
237C8×C83—21no—
238C8×C83—21no—
239C8×C83—21no—
240C8×C83—21no—
241C8×C83—41no—
242C8×C83—41no—
243C8×C83—41no—
244C83⋊C8—21no—
245C83⋊C8—21no—
246C83⋊C8—21no—
247C83⋊C8—41no—
248C83⋊C8—41no—
249C83⋊C8—41no—
250C83⋊C8#13112yes—
251C22×C83C2×C4×D411yescharacteristic
252C2×D83—21no—
253C2×D83—21no—
254C2×D83#44112yes—
255C4×C83—21no—
256C4×C83—41no—
257C4×C83—41no—
258C4×C83—41no—
259C4×C83—41no—
260C4×C83C2×#13111yescharacteristic
261C4×C83#56811yescharacteristic
262C4×C83C2×#13711yescharacteristic
263C4×C83C2×#13711yescharacteristic
264Dic83—21no—
265Dic83—21no—
266Dic83—41no—
267Dic83—41no—
268Dic83—41no—
269Dic83—41no—
270Dic83#44112yes—
271#18072—831nomaximal, Sylow
272C2×C83#293511yescharacteristic
273C2×C83C2×#44111yescharacteristic
274C2×C83#295711yescharacteristic
275D83—22no—
276#3170—831no—
277#2962—831no—
278#2962—831no—
279#1593—831no—
280#1593—831no—
281#1587—831no—
282#1587—831no—
283#1587—831no—
284#1587D8311yescharacteristic, complemented
285#1579—831no—
286#1579—831no—
287C2×#334—831no—
288#1481—831no—
289#1481—831no—
290#1451—831no—
291C83#1807211yescharacteristic, complemented, Sylow
292#533—831no—
293#533—831no—
294#500—831no—
295#494—831no—
296#487—831no—
297#487—831no—
298#467—831no—
299#467—831no—
300#467—831no—
301#467—831no—
302#446—831no—
303#446—831no—
304#446—831no—
305#446—1661no—
306#446—1661no—
307#446—1661no—
308#446—1661no—
309#446C2×D8311yescharacteristic
310C8×Q8—831no—
311C8×Q8—831no—
312C8×Q8—831no—
313C8×Q8C2×D8311yescharacteristic
314C4×Q16—831no—
315C4×Q16—831no—
316C4×Q16—831no—
317C4×Q16C2×D8311yescharacteristic
318#431—831no—
319#424—1661no—
320#424—1661no—
321C2×C4⋊C8—831no—
322C2×C4⋊C8—831no—
323#405—1661no—
324#405—1661no—
325C4×M16—831no—
326C2×C4×C8—831no—
327#334—831no—
328#334—831no—
329#334—831no—
330#334C2×D8311yescharacteristic
331Q8⋊C8—831no—
332Q8⋊C8—831no—
333Q8⋊C8—831no—
334Q8⋊C8—831no—
335Q8⋊C8—831no—
336Q8⋊C8—831no—
337Q8⋊C8C2×D8311yescharacteristic
338Q8⋊C8C2×D8311yescharacteristic
339#322—831no—
340#322—831no—
341#322—831no—
342#322C2×D8311yescharacteristic
343C2×Q16—831no—
344C2×Q16—831no—
345C2×Q16—831no—
346C2×Q16C4×D8311yescharacteristic
347C2×M16—831no—
348C2×M16—831no—
349C22×C8—831no—
350C22×C8—831no—
351C22×C8—1661no—
352C22×C8—1661no—
353C4⋊Q8—831no—
354C4⋊Q8—831no—
355C4⋊Q8—831no—
356C4⋊Q8—831no—
357#125—1661no—
358#125—1661no—
359C22⋊Q8—831no—
360C22⋊Q8—831no—
361C22⋊Q8—831no—
362C22⋊Q8—831no—
363C22⋊Q8—1661no—
364C22⋊Q8—1661no—
365C4×Q8—831no—
366C4×Q8—831no—
367C4×Q8—1661no—
368C4×Q8—1661no—
369C4×Q8C22×D8311yescharacteristic
370C4×Q8C22×D8311yescharacteristic
371#117—1661no—
372#117—1661no—
373C2×C42—831no—
374#107—831no—
375#107—831no—
376#107—831no—
377#107C4×D8311yescharacteristic
378C4⋊C8—21no—
379C4⋊C8—21no—
380C4⋊C8—831no—
381C4⋊C8—831no—
382C4⋊C8—1661no—
383C4⋊C8—1661no—
384C4⋊C8—1661no—
385C4⋊C8—1661no—
386C4⋊C8—1661no—
387C4⋊C8—1661no—
388C4⋊C8—1661no—
389C4⋊C8—1661no—
390C4⋊C8—1661no—
391C4⋊C8C22×D8311yescharacteristic
392C4⋊C8C22×D8311yescharacteristic
393#103—831no—
394#103—831no—
395#103—831no—
396#103—831no—
397#103—831no—
398#103—831no—
399#103C4×D8311yescharacteristic
400#103C4×D8311yescharacteristic
401C22⋊C8—1661no—
402#97—21no—
403#97—831no—
404#97—831no—
405#97—1661no—
406#97—1661no—
407#97—1661no—
408C4×C8—21no—
409C4×C8—831no—
410C4×C8—831no—
411C4×C8—831no—
412C4×C8—831no—
413C4×C8—831no—
414C4×C8—1661no—
415C4×C8—1661no—
416C4×C8—1661no—
417C4×C8C22×D8311yescharacteristic
418C4×C8C22×D8311yescharacteristic
419C4×C8C22×D8311yescharacteristic
420C2×Q8—831no—
421C2×Q8—831no—
422C2×Q8—1661no—
423C2×Q8—1661no—
424C2×Q8C2×C4×D8311yescharacteristic
425C2×Q8C2×C4×D8311yescharacteristic
426C22×C4—831no—
427C22×C4—831no—
428C22×C4—831no—
429Q16—41no—
430Q16—3321no—
431Q16—1662no—
432Q16—1662no—
433M16—1662no—
434M16—1662no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—3321no—
439C2×C8—3322no—
440C2×C8—3322no—
441C2×C8—831no—
442C2×C8—831no—
443C2×C8—831no—
444C2×C8—831no—
445C2×C8—1662no—
446C2×C8—1661no—
447C2×C8—1661no—
448C2×C8—1661no—
449C2×C8C2×C4×D8311yescharacteristic
450C2×C8C2×C4×D8311yescharacteristic
451C2×C8D4×D8311yescharacteristic
452C2×C8D4×D8311yescharacteristic
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—831no—
456C4⋊C4—831no—
457C4⋊C4—1661no—
458C4⋊C4—1661no—
459C4⋊C4—1661no—
460C4⋊C4—1661no—
461C4⋊C4—1661no—
462C4⋊C4—1661no—
463C4⋊C4—1661no—
464C4⋊C4—1661no—
465C4⋊C4—1661no—
466C4⋊C4—1661no—
467C4⋊C4—1661no—
468C4⋊C4—1661no—
469C4⋊C4C2×C4×D8311yescharacteristic
470C4⋊C4C2×C4×D8311yescharacteristic
471C22⋊C4—1661no—
472C22⋊C4—1661no—
473C22⋊C4—1661no—
474C22⋊C4—1661no—
475C42—21no—
476C42—21no—
477C42—831no—
478C42—831no—
479C42—831no—
480C42—1661no—
481C42—1661no—
482C42C23×D8311yescharacteristic
483C23—831no—
484Q8—21no—
485Q8—21no—
486Q8—21no—
487Q8—21no—
488Q8—6641no—
489Q8—6641no—
490Q8—1661no—
491Q8—1661no—
492Q8—1661no—
493Q8—1661no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—3321no—
499C2×C4—831no—
500C2×C4—832no—
501C2×C4—832no—
502C2×C4—831no—
503C2×C4—831no—
504C2×C4—1661no—
505C2×C4—1661no—
506C2×C4—1661no—
507C2×C4—1661no—
508C2×C4—1661no—
509C2×C4—1661no—
510C2×C4C22×C4×D8311yescharacteristic
511C2×C4C2×D4×D8311yescharacteristic
512C2×C4#41×D8311yescharacteristic
513C8—21no—
514C8—21no—
515C8—21no—
516C8—21no—
517C8—41no—
518C8—41no—
519C8—41no—
520C8—3321no—
521C8—3321no—
522C8—3321no—
523C8—832no—
524C8—1661no—
525C8—1661no—
526C8—1661no—
527C22—832no—
528C22—1661no—
529C22—1661no—
530C22C4×D4×D8311yescharacteristic
531C4—21no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—3321no—
537C4—3321no—
538C4—3321no—
539C4—3321no—
540C4—832no—
541C4—1661no—
542C4—1661no—
543C4#131×D8311yescharacteristic
544C4#1912846711yescharacteristic
545C4#137×D8311yescharacteristic
546C4#137×D8311yescharacteristic
547C2—1662no—
548C2#2491620411yescharacteristic
549C2#441×D8311yescharacteristic
550C2#2491637511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1587C2
socleC22×C83C2×C4×D4
prime radicalC22×D83C4×D4
cosocleC42×C83C24
hypercenter#1587D83
hypocenterC83#18072
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
4. #24906370C2semidirect
5. #24906369C2semidirect
6. #24906336C2semidirect
7. #24906335C2semidirect
8. #24906333C2semidirect
9. #24906280C2semidirect
10. #24906279C2semidirect
15. C83×#1587C2semidirect
284. #1587D83semidirect
291. C83#18072semidirect

Maximal subgroups

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

subgroupindex
#249180462
#249164112
#249164052
#249063702
#249063692
#249063362
#249063352
#249063332
#249062802
#249062792
#334×D832
#249058642
#249057512
C83×#15872
#1807283