Finite Group Databasebeta

← #35375054

Subgroups — #35375054

Order 21248.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24918067C211yesmaximal, characteristic
2#24916611C211yesmaximal, characteristic
3#24916554C211yesmaximal, characteristic, complemented
4#24906372C211yesmaximal, characteristic, complemented
5#24906364C211yesmaximal, characteristic, complemented
6#24906357C211yesmaximal, characteristic, complemented
7#24906350C211yesmaximal, characteristic, complemented
8#24906280C211yesmaximal, characteristic, complemented
9#24906273C211yesmaximal, characteristic, complemented
10C8×#13050579C211yesmaximal, characteristic, complemented
11#24906229C211yesmaximal, characteristic, complemented
12#24905922C211yesmaximal, characteristic
13#24905916C211yesmaximal, characteristic, complemented
14C8×#13050573C211yesmaximal, characteristic, complemented
15C8×Q16×C83C211yesmaximal, characteristic, complemented
16#19128255C2211yescharacteristic
17#19128238C2211yescharacteristic
18#19128109C411yescharacteristic
19#19128094C411yescharacteristic
20#19128068C411yescharacteristic
21#19128062C411yescharacteristic
22#19127958C411yescharacteristic
23#19127956C411yescharacteristic
24#19127950C411yescharacteristic
25#19127948C411yescharacteristic
26#19127832C2211yescharacteristic
27#19127832C2211yescharacteristic
28#19127831—21no—
29#19127830—21no—
30#19127828C2211yescharacteristic
31C8×Dic166C2211yescharacteristic
32C4×#13050580C2211yescharacteristic
33C4×#13050579C2211yescharacteristic
34C4×#13050577C2211yescharacteristic
35#19127780—21no—
36#19127778C2211yescharacteristic
37#19127771—21no—
38C8×D332C2211yescharacteristic
39#19127761—21no—
40#19127760—21no—
41#19127760—21no—
42#19127757C2211yescharacteristic
43#19127752C2211yescharacteristic
44#19127726—21no—
45#19127723C2211yescharacteristic
46C4×#13050573C2211yescharacteristic
47C4×C8×D83C2211yescharacteristic
48#19127453C2211yescharacteristic
49#19127452C2211yescharacteristic
50#19127451C2211yescharacteristic
51#19127433C2211yescharacteristic
52Q8⋊(C83⋊C8)C2211yescharacteristic
53Q8⋊(C83⋊C8)C2211yescharacteristic
54#19127431C2211yescharacteristic
55#19127430C2211yescharacteristic
56#19127428C2211yescharacteristic
57#19127423C2211yescharacteristic
58#19127422C2211yescharacteristic
59C8×C83⋊C8C2211yescharacteristic
60C8×Q8×C83C2211yescharacteristic
61C8×Q8×C83C2211yescharacteristic
62C4×Q16×C83C2211yescharacteristic
63#335×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65Q8⋊C8×C83C2211yescharacteristic
66C82×C83C2211yescharacteristic
67C2×#13050580C2×C411yescharacteristic
68C2×#13050579C2×C411yescharacteristic
69C2×#13050577C2×C411yescharacteristic
70C2×#13050573—21no—
71C2×#13050573—21no—
72C2×#13050573C2×C411yescharacteristic
73C2×#13050573C2×C411yescharacteristic
74C2×C8×D83—21no—
75C2×C8×D83—21no—
76#14581791C2×C411yescharacteristic
77#14581790C2×C411yescharacteristic
78#14581787—21no—
79#14581783C2×C411yescharacteristic
80#14581782—21no—
81#14581781C2×C411yescharacteristic
82#14581777—21no—
83#14581772C2×C411yescharacteristic
84#14581770—21no—
85#14581768C2×C411yescharacteristic
86#14581768C2×C411yescharacteristic
87#14581767C2×C411yescharacteristic
88C4×Dic166—21no—
89C4×Dic166C2311yescharacteristic
90C4×D332—21no—
91C4×D332C2311yescharacteristic
92#14581749—21no—
93#14581749—21no—
94C42×D83C2311yescharacteristic
95#14581725C2×C411yescharacteristic
96#14581724C2×C411yescharacteristic
97#14581723C2×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⋊C8D411yescharacteristic
106Dic83⋊C8D411yescharacteristic
107#14581717C2×C411yescharacteristic
108#14581716C2×C411yescharacteristic
109#14581716C2×C411yescharacteristic
110#14581715C2×C411yescharacteristic
111#14581714C2×C411yescharacteristic
112#14581712C2×C411yescharacteristic
113(C2×D83)⋊C8—21no—
114(C2×D83)⋊C8—21no—
115(C2×D83)⋊C8—21no—
116(C2×D83)⋊C8D411yescharacteristic
117(C2×D83)⋊C8D411yescharacteristic
118#14581703—21no—
119#14581703—21no—
120#14581702—21no—
121#14581702—21no—
122#14581702C2×C411yescharacteristic
123#14581702C2×C411yescharacteristic
124C4×C83⋊C8C2311yescharacteristic
125C4×C83⋊C8C2311yescharacteristic
126C4×C83⋊C8C2311yescharacteristic
127C8×Dic83—21no—
128C8×Dic83—21no—
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
139C4×C8×C83—21no—
140C4×C8×C83—21no—
141C4×C8×C83C2311yescharacteristic
142C4×C8×C83C2311yescharacteristic
143C4×C8×C83C2311yescharacteristic
144C2×Dic166—21no—
145C2×Dic166C22×C411yescharacteristic
146C2×D332—21no—
147C2×D332C22×C411yescharacteristic
148C2×C4×D83—21no—
149C2×C4×D83C22×C411yescharacteristic
150C2×C4×D83C2×D411yescharacteristic
151C2×C4×D83#4111yescharacteristic
152#13050580—22no—
153#13050579—22no—
154#13050577—22no—
155#13050573—22no—
156#13050573—22no—
157#13050573—81no—
158#13050573—81no—
159C2×C83⋊C8—21no—
160C2×C83⋊C8—21no—
161C2×C83⋊C8—21no—
162C2×C83⋊C8C22×C411yescharacteristic
163C2×C83⋊C8C22×C411yescharacteristic
164C2×C83⋊C8C2×D411yescharacteristic
165C2×C83⋊C8C2×D411yescharacteristic
166C8×D83—42no—
167C8×D83—81no—
168C4⋊Dic83—21no—
169C4⋊Dic83—21no—
170C4⋊Dic83C22×C411yescharacteristic
171C4⋊Dic83C22×C411yescharacteristic
172Dic83⋊C4—21no—
173Dic83⋊C4—21no—
174Dic83⋊C4—21no—
175Dic83⋊C4—21no—
176Dic83⋊C4—21no—
177Dic83⋊C4—21no—
178Dic83⋊C4—21no—
179(C2×D83)⋊C4—21no—
180(C2×D83)⋊C4—21no—
181(C2×D83)⋊C4—21no—
182(C2×D83)⋊C4—21no—
183(C2×D83)⋊C4—21no—
184(C2×D83)⋊C4—21no—
185(C2×D83)⋊C4—21no—
186C4×Dic83—21no—
187C4×Dic83C22×C411yescharacteristic
188C4×Dic83C2×D411yescharacteristic
189C4×Dic83#4111yescharacteristic
190C2×Q8×C83C22×C411yescharacteristic
191C2×Q8×C83C22×C411yescharacteristic
192Q16×C83—22no—
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×D83—21no—
208C22×D83C4×D411yescharacteristic
209Q8×C83—21no—
210Q8×C83—21no—
211Q8×C83—21no—
212Q8×C83—21no—
213C2×C4×C83—21no—
214C2×C4×C83—21no—
215C2×C4×C83—21no—
216C2×C4×C83—21no—
217C2×C4×C83C23×C411yescharacteristic
218C2×C4×C83C22×D411yescharacteristic
219C2×C4×C83C2×#4111yescharacteristic
220C2×Dic83—21no—
221C2×Dic83—21no—
222C2×Dic83—21no—
223C2×Dic83C4×D411yescharacteristic
224C2×Dic83C4×D411yescharacteristic
225C2×Dic83C4×D411yescharacteristic
226D332—21no—
227D332—21no—
228D332—81no—
229C4×D83—21no—
230C4×D83—21no—
231C4×D83—21no—
232C4×D83—21no—
233C4×D83—41no—
234C4×D83—41no—
235C4×D83—41no—
236Dic166—21no—
237Dic166—21no—
238Dic166—81no—
239C8×C83—22no—
240C8×C83—21no—
241C8×C83—21no—
242C8×C83—21no—
243C8×C83—41no—
244C8×C83—41no—
245C8×C83#13112yes—
246C83⋊C8—21no—
247C83⋊C8—21no—
248C83⋊C8—21no—
249C83⋊C8—41no—
250C83⋊C8—41no—
251C83⋊C8—41no—
252C83⋊C8#13112yes—
253C22×C83C2×C4×D411yescharacteristic
254C2×D83—21no—
255C2×D83—21no—
256C2×D83—21no—
257C2×D83—41no—
258C2×D83—41no—
259C2×D83—41no—
260C4×C83—21no—
261C4×C83—41no—
262C4×C83—41no—
263C4×C83—41no—
264C4×C83—41no—
265C4×C83C2×#13111yescharacteristic
266C4×C83C2×#13111yescharacteristic
267C4×C83#57711yescharacteristic
268C4×C83#57811yescharacteristic
269Dic83—21no—
270Dic83—21no—
271Dic83—21no—
272Dic83—41no—
273Dic83—41no—
274Dic83—41no—
275#17969—831nomaximal, Sylow
276C2×C83#293111yescharacteristic
277C2×C83#294711yescharacteristic
278C2×C83#295611yescharacteristic
279D83—41no—
280D83—81no—
281#3172—831no—
282#2993—831no—
283#2985—831no—
284#1593—831no—
285#1592—831no—
286#1591—831no—
287#1590—831no—
288#1579—831no—
289SD16⋊C8—831no—
290C8×Q16D8311yescharacteristic, complemented
291C8×SD16—831no—
292#1569—831no—
293#1494—831no—
294#1493—831no—
295C8×M16—831no—
296C83#1796911yescharacteristic, complemented, Sylow
297#533—831no—
298#529—831no—
299#501—831no—
300#497—831no—
301#491—831no—
302#489—831no—
303#470—831no—
304#470—831no—
305#468—831no—
306#468—831no—
307#446—831no—
308#446—831no—
309#446—831no—
310#446—1661no—
311#446—1661no—
312C8×Q8—831no—
313C8×Q8C2×D8311yescharacteristic
314C8×Q8C2×D8311yescharacteristic
315C4×Q16—831no—
316C4×Q16C2×D8311yescharacteristic
317C4×SD16—831no—
318C4×SD16—831no—
319#436—831no—
320#436—1661no—
321#435—1661no—
322C8×D4—831no—
323#433—1661no—
324#433—1661no—
325#433—1661no—
326#432—831no—
327#431—831no—
328#424—1661no—
329#423—831no—
330C4×M16—831no—
331C2×C4×C8—831no—
332#335—831no—
333#335C2×D8311yescharacteristic
334#334—831no—
335#334—831no—
336Q8⋊C8—831no—
337Q8⋊C8—831no—
338Q8⋊C8—831no—
339Q8⋊C8—831no—
340Q8⋊C8C2×D8311yescharacteristic
341Q8⋊C8C2×D8311yescharacteristic
342D4⋊C8—831no—
343D4⋊C8—831no—
344#322—831no—
345#322—831no—
346C82—831no—
347C82C2×D8311yescharacteristic
348C2×Q16—831no—
349C2×Q16C4×D8311yescharacteristic
350C2×SD16—831no—
351C2×SD16—831no—
352C2×M16—831no—
353C2×M16—831no—
354C2×M16—1661no—
355C2×M16—1661no—
356C22×C8—1661no—
357C22×C8—1661no—
358C4⋊Q8—831no—
359C4⋊Q8—831no—
360#126—1661no—
361#125—831no—
362#125—1661no—
363#124—831no—
364#123—1661no—
365C22⋊Q8—831no—
366C22⋊Q8—831no—
367C22⋊Q8—831no—
368C22⋊Q8—1661no—
369#121—831no—
370C4×Q8—831no—
371C4×Q8—1661no—
372C4×Q8C22×D8311yescharacteristic
373C4×Q8C22×D8311yescharacteristic
374C4×D4—831no—
375C4×D4—1661no—
376#117—1661no—
377#117—1661no—
378C2×C42—831no—
379#107—831no—
380#107C4×D8311yescharacteristic
381#106—831no—
382#106—831no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—831no—
386C4⋊C8—831no—
387C4⋊C8—831no—
388C4⋊C8—831no—
389C4⋊C8—1661no—
390C4⋊C8—1661no—
391C4⋊C8—1661no—
392C4⋊C8—1661no—
393C4⋊C8—1661no—
394C4⋊C8C22×D8311yescharacteristic
395C4⋊C8C22×D8311yescharacteristic
396#103—831no—
397#103—831no—
398#103—831no—
399#103—831no—
400#103C4×D8311yescharacteristic
401#103C4×D8311yescharacteristic
402#102—831no—
403#102—831no—
404C22⋊C8—831no—
405C22⋊C8—831no—
406C22⋊C8—1661no—
407C22⋊C8—1661no—
408C22⋊C8—1661no—
409#97—831no—
410#97—831no—
411#97—1661no—
412#97—1661no—
413#97—1661no—
414#97—1661no—
415C4×C8—21no—
416C4×C8—21no—
417C4×C8—831no—
418C4×C8—831no—
419C4×C8—831no—
420C4×C8—1661no—
421C4×C8—1661no—
422C4×C8C22×D8311yescharacteristic
423C4×C8C22×D8311yescharacteristic
424C4×C8C22×D8311yescharacteristic
425C2×Q8—831no—
426C2×Q8—1661no—
427C2×Q8C2×C4×D8311yescharacteristic
428C2×Q8C2×C4×D8311yescharacteristic
429C2×D4—831no—
430C2×D4—1661no—
431C22×C4—831no—
432C22×C4—831no—
433C22×C4—831no—
434C22×C4—1661no—
435Q16—22no—
436Q16—1662no—
437SD16—1662no—
438SD16—1662no—
439M16—6641no—
440M16—6641no—
441M16—1662no—
442M16—1662no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—3322no—
447C2×C8—831no—
448C2×C8—831no—
449C2×C8—831no—
450C2×C8—831no—
451C2×C8—6641no—
452C2×C8—1661no—
453C2×C8—1661no—
454C2×C8—1661no—
455C2×C8C2×C4×D8311yescharacteristic
456C2×C8C2×C4×D8311yescharacteristic
457C2×C8D4×D8311yescharacteristic
458C2×C8D4×D8311yescharacteristic
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—831no—
462C4⋊C4—831no—
463C4⋊C4—1661no—
464C4⋊C4—1661no—
465C4⋊C4—1661no—
466C4⋊C4—1661no—
467C4⋊C4—1661no—
468C4⋊C4—1661no—
469C4⋊C4—1661no—
470C4⋊C4—1661no—
471C4⋊C4—1661no—
472C4⋊C4C2×C4×D8311yescharacteristic
473C4⋊C4C2×C4×D8311yescharacteristic
474C22⋊C4—1661no—
475C22⋊C4—1661no—
476C22⋊C4—1661no—
477C22⋊C4—1661no—
478C22⋊C4—1661no—
479C22⋊C4—1661no—
480C22⋊C4—1661no—
481C42—21no—
482C42—21no—
483C42—831no—
484C42—831no—
485C42—831no—
486C42—1661no—
487C42C23×D8311yescharacteristic
488C23—831no—
489C23—1661no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—6641no—
495Q8—1661no—
496Q8—1661no—
497D4—6641no—
498D4—1661no—
499D4—1661no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—3321no—
505C2×C4—3321no—
506C2×C4—3321no—
507C2×C4—831no—
508C2×C4—831no—
509C2×C4—831no—
510C2×C4—1661no—
511C2×C4—1661no—
512C2×C4—1661no—
513C2×C4—1661no—
514C2×C4—1661no—
515C2×C4—1661no—
516C2×C4—1661no—
517C2×C4C22×C4×D8311yescharacteristic
518C2×C4C2×D4×D8311yescharacteristic
519C2×C4#41×D8311yescharacteristic
520C8—22no—
521C8—21no—
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—3321no—
527C8—3321no—
528C8—3321no—
529C8—832no—
530C8—1661no—
531C8—1661no—
532C8—1661no—
533C8#1458179812yes—
534C22—3321no—
535C22—3321no—
536C22—3321no—
537C22—1661no—
538C22—1661no—
539C22—1661no—
540C22C4×D4×D8311yescharacteristic
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—3321no—
547C4—3321no—
548C4—3321no—
549C4—1661no—
550C4—1661no—
551C4—1661no—
552C4#131×D8311yescharacteristic
553C4C2×#1458179811yescharacteristic
554C4#1912850811yescharacteristic
555C4#1912851411yescharacteristic
556C2—3321no—
557C2—6641no—
558C2#2491617011yescharacteristic
559C2#2491630111yescharacteristic
560C2#2491636811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC8×Q16×C83C2
socleC22×C83C2×C4×D4
prime radical#14581767C2×C4
cosocleC42×C83C24
hypercenterC8×Q16D83
hypocenterC83#17969
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×Q16

Complements

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

NH ≅ G/Ntype
3. #24916554C2semidirect
4. #24906372C2semidirect
5. #24906364C2semidirect
6. #24906357C2semidirect
7. #24906350C2semidirect
8. #24906280C2semidirect
9. #24906273C2semidirect
10. C8×#13050579C2semidirect
11. #24906229C2semidirect
13. #24905916C2semidirect
14. C8×#13050573C2semidirect
15. C8×Q16×C83C2semidirect
290. C8×Q16D83semidirect
296. C83#17969semidirect

Maximal subgroups

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

subgroupindex
#249180672
#249166112
#249165542
#249063722
#249063642
#249063572
#249063502
#249062802
#249062732
C8×#130505792
#249062292
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