Finite Group Databasebeta

← #35376272

Subgroups — #35376272

Order 21248.

588 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24918067C211yesmaximal, characteristic
2#24916466C211yesmaximal, characteristic
3#24916405C211yesmaximal, characteristic, complemented
4#24906367C211yesmaximal, characteristic, complemented
5#24906360C211yesmaximal, characteristic, complemented
6#24906341C211yesmaximal, characteristic, complemented
7#24906334C211yesmaximal, characteristic, complemented
8#24906316C211yesmaximal, characteristic, complemented
9#24906302C211yesmaximal, characteristic, complemented
10#24906262C211yesmaximal, characteristic, complemented
11#24906212C211yesmaximal, characteristic, complemented
12#24905882C211yesmaximal, characteristic, complemented
13#24905875C211yesmaximal, characteristic
14#24905767C211yesmaximal, characteristic, complemented
15C83×#1579C211yesmaximal, 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#19127831C2211yescharacteristic
30#19127830—21no—
31#19127825C2211yescharacteristic
32C4×#13050580C2211yescharacteristic
33C4×#13050579C2211yescharacteristic
34C4×#13050577C2211yescharacteristic
35#19127780—21no—
36#19127780C2211yescharacteristic
37#19127771—21no—
38#19127766C2211yescharacteristic
39#19127761—21no—
40#19127753C2211yescharacteristic
41#19127726—21no—
42C4⋊C8×D83C2211yescharacteristic
43#19127655—21no—
44#19127655—21no—
45C4×#13050573C2211yescharacteristic
46C4×#13050573C2211yescharacteristic
47C4×#13050573C2211yescharacteristic
48#19127454C2211yescharacteristic
49#19127453C2211yescharacteristic
50#19127451C2211yescharacteristic
51#19127433C2211yescharacteristic
52Q8⋊(C83⋊C8)C2211yescharacteristic
53Q8⋊(C83⋊C8)C2211yescharacteristic
54#19127431C2211yescharacteristic
55#19127430C2211yescharacteristic
56#19127428C2211yescharacteristic
57#19127423C2211yescharacteristic
58#19127423C2211yescharacteristic
59C8×C83⋊C8C2211yescharacteristic
60C8×Q8×C83C2211yescharacteristic
61C8×Q8×C83C2211yescharacteristic
62C4×Q16×C83C2211yescharacteristic
63#334×C83C2211yescharacteristic
64Q8⋊C8×C83C2211yescharacteristic
65Q8⋊C8×C83C2211yescharacteristic
66#322×C83C2211yescharacteristic
67C2×#13050580C2×C411yescharacteristic
68C2×#13050579C2×C411yescharacteristic
69C2×#13050577C2×C411yescharacteristic
70C2×#13050573—21no—
71C2×#13050573—21no—
72C2×#13050573C2×C411yescharacteristic
73C2×#13050573C2×C411yescharacteristic
74C2×#13050573D411yescharacteristic
75C2×#13050573D411yescharacteristic
76C2×C8×D83—21no—
77C2×C8×D83—21no—
78#14581791C2×C411yescharacteristic
79#14581790C2×C411yescharacteristic
80#14581787—21no—
81#14581783C2×C411yescharacteristic
82#14581782—21no—
83#14581781C2×C411yescharacteristic
84#14581777—21no—
85#14581772C2×C411yescharacteristic
86#14581770—21no—
87#14581768C2×C411yescharacteristic
88#14581768C2×C411yescharacteristic
89#14581767C2×C411yescharacteristic
90C4×Dic166—21no—
91C4×Dic166C2311yescharacteristic
92C4×D332—21no—
93C4×D332C2311yescharacteristic
94#14581749—21no—
95#14581749—21no—
96C42×D83C2311yescharacteristic
97#14581725C2×C411yescharacteristic
98#14581724C2×C411yescharacteristic
99#14581723C2×C411yescharacteristic
100C4⋊(C83⋊C8)—21no—
101C4⋊(C83⋊C8)—21no—
102C4⋊(C83⋊C8)C2311yescharacteristic
103C4⋊(C83⋊C8)C2311yescharacteristic
104Dic83⋊C8—21no—
105Dic83⋊C8—21no—
106Dic83⋊C8—21no—
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#14581703—21no—
117#14581703—21no—
118#14581702—21no—
119#14581702—21no—
120#14581702C2×C411yescharacteristic
121#14581702C2×C411yescharacteristic
122#14581702D411yescharacteristic
123#14581702D411yescharacteristic
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—41no—
153#13050579—22no—
154#13050577—41no—
155#13050573—22no—
156#13050573—22no—
157#13050573—41no—
158#13050573—41no—
159#13050573—42no—
160#13050573—42no—
161C2×C83⋊C8—21no—
162C2×C83⋊C8—21no—
163C2×C83⋊C8—21no—
164C2×C83⋊C8C22×C411yescharacteristic
165C2×C83⋊C8C22×C411yescharacteristic
166C2×C83⋊C8C2×D411yescharacteristic
167C2×C83⋊C8C2×D411yescharacteristic
168C8×D83—42no—
169C8×D83—42no—
170C4⋊Dic83—21no—
171C4⋊Dic83—21no—
172C4⋊Dic83C22×C411yescharacteristic
173C4⋊Dic83C22×C411yescharacteristic
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—
185(C2×D83)⋊C4—21no—
186(C2×D83)⋊C4—21no—
187(C2×D83)⋊C4—21no—
188C4×Dic83—21no—
189C4×Dic83C22×C411yescharacteristic
190C4×Dic83C2×D411yescharacteristic
191C4×Dic83#4111yescharacteristic
192C2×Q8×C83C22×C411yescharacteristic
193C2×Q8×C83C22×C411yescharacteristic
194Q16×C83—22no—
195C2×C8×C83—21no—
196C2×C8×C83—21no—
197C2×C8×C83—21no—
198C2×C8×C83C22×C411yescharacteristic
199C2×C8×C83C22×C411yescharacteristic
200C2×C8×C83C2×D411yescharacteristic
201C2×C8×C83C2×D411yescharacteristic
202C4⋊C4×C83—21no—
203C4⋊C4×C83—21no—
204C4⋊C4×C83C22×C411yescharacteristic
205C4⋊C4×C83C22×C411yescharacteristic
206C42×C83—21no—
207C42×C83—21no—
208C42×C83C2411yescharacteristic
209C22×D83—21no—
210C22×D83C4×D411yescharacteristic
211Q8×C83—21no—
212Q8×C83—21no—
213Q8×C83—21no—
214Q8×C83—21no—
215C2×C4×C83—21no—
216C2×C4×C83—21no—
217C2×C4×C83—21no—
218C2×C4×C83—21no—
219C2×C4×C83C23×C411yescharacteristic
220C2×C4×C83C22×D411yescharacteristic
221C2×C4×C83C2×#4111yescharacteristic
222C2×Dic83—21no—
223C2×Dic83—21no—
224C2×Dic83—21no—
225C2×Dic83C4×D411yescharacteristic
226C2×Dic83C4×D411yescharacteristic
227C2×Dic83C4×D411yescharacteristic
228D332—21no—
229D332—21no—
230D332—81no—
231C4×D83—21no—
232C4×D83—21no—
233C4×D83—21no—
234C4×D83—21no—
235C4×D83—41no—
236C4×D83—41no—
237C4×D83—41no—
238Dic166—21no—
239Dic166—21no—
240Dic166—81no—
241C8×C83—21no—
242C8×C83—21no—
243C8×C83—21no—
244C8×C83—41no—
245C8×C83—41no—
246C8×C83—41no—
247C8×C83#13112yes—
248C83⋊C8—22no—
249C83⋊C8—21no—
250C83⋊C8—21no—
251C83⋊C8—21no—
252C83⋊C8—41no—
253C83⋊C8—41no—
254C83⋊C8#13712yes—
255C22×C83C2×C4×D411yescharacteristic
256C2×D83—21no—
257C2×D83—21no—
258C2×D83—21no—
259C2×D83—41no—
260C2×D83—41no—
261C2×D83—41no—
262C4×C83—21no—
263C4×C83—41no—
264C4×C83—41no—
265C4×C83—41no—
266C4×C83—41no—
267C4×C83C2×#13111yescharacteristic
268C4×C83#56811yescharacteristic
269C4×C83C2×#13711yescharacteristic
270C4×C83#57511yescharacteristic
271Dic83—21no—
272Dic83—21no—
273Dic83—21no—
274Dic83—41no—
275Dic83—41no—
276Dic83—41no—
277#18077—831nomaximal, Sylow
278C2×C83#293511yescharacteristic
279C2×C83C4×#13711yescharacteristic
280C2×C83#295611yescharacteristic
281D83—41no—
282D83—81no—
283#3172—831no—
284#2969—831no—
285#2962—831no—
286#1592—831no—
287#1591—831no—
288#1588—831no—
289#1587—831no—
290#1584—831no—
291#1582—831no—
292#1579D8311yescharacteristic, complemented
293C8×SD16—831no—
294#1565—831no—
295#1485—831no—
296#1483—831no—
297#1455—831no—
298C83#1807711yescharacteristic, complemented, Sylow
299#533—831no—
300#529—831no—
301#501—831no—
302#497—831no—
303#491—831no—
304#489—831no—
305#470—831no—
306#470—831no—
307#468—831no—
308#468—831no—
309#446—831no—
310#446—831no—
311#446—831no—
312#446—1661no—
313#446—1661no—
314C8×Q8—831no—
315C8×Q8C2×D8311yescharacteristic
316C8×Q8C2×D8311yescharacteristic
317C4×Q16—831no—
318C4×Q16C2×D8311yescharacteristic
319C4×SD16—831no—
320C4×SD16—831no—
321#436—831no—
322#436—1661no—
323#435—1661no—
324C8×D4—831no—
325#433—1661no—
326#431—831no—
327#424—1661no—
328C2×C4⋊C8—831no—
329#405—1661no—
330#405—1661no—
331C4×M16—831no—
332C4×M16—831no—
333C4×M16—831no—
334#335—831no—
335#335—831no—
336#334—831no—
337#334C2×D8311yescharacteristic
338Q8⋊C8—831no—
339Q8⋊C8—831no—
340Q8⋊C8—831no—
341Q8⋊C8—831no—
342Q8⋊C8C2×D8311yescharacteristic
343Q8⋊C8C2×D8311yescharacteristic
344D4⋊C8—831no—
345D4⋊C8—831no—
346#322—831no—
347#322—831no—
348#322C2×D8311yescharacteristic
349C82—831no—
350C2×Q16—831no—
351C2×Q16C4×D8311yescharacteristic
352C2×SD16—831no—
353C2×SD16—831no—
354C2×M16—831no—
355C2×M16—831no—
356C2×M16—831no—
357C2×M16—831no—
358C2×M16—1661no—
359C2×M16—1661no—
360C22×C8—1661no—
361C22×C8—1661no—
362C4⋊Q8—831no—
363C4⋊Q8—831no—
364#126—1661no—
365#125—831no—
366#125—1661no—
367#124—831no—
368#123—1661no—
369C22⋊Q8—831no—
370C22⋊Q8—831no—
371C22⋊Q8—831no—
372C22⋊Q8—1661no—
373#121—831no—
374C4×Q8—831no—
375C4×Q8—1661no—
376C4×Q8C22×D8311yescharacteristic
377C4×Q8C22×D8311yescharacteristic
378C4×D4—831no—
379C4×D4—1661no—
380#117—1661no—
381#117—1661no—
382C2×C42—831no—
383#107—831no—
384#107C4×D8311yescharacteristic
385#106—831no—
386#106—831no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8—831no—
390C4⋊C8—831no—
391C4⋊C8—1661no—
392C4⋊C8—1661no—
393C4⋊C8—1661no—
394C4⋊C8—1661no—
395C4⋊C8—1661no—
396C4⋊C8C22×D8311yescharacteristic
397C4⋊C8C22×D8311yescharacteristic
398#103—831no—
399#103—831no—
400#103—831no—
401#103—831no—
402#103C4×D8311yescharacteristic
403#103C4×D8311yescharacteristic
404#102—831no—
405#102—831no—
406C22⋊C8—1661no—
407C22⋊C8—1661no—
408C22⋊C8—1661no—
409#97—831no—
410#97—831no—
411#97—831no—
412#97—831no—
413#97—1661no—
414#97—1661no—
415#97—1661no—
416#97—1661no—
417C4×C8—21no—
418C4×C8—21no—
419C4×C8—831no—
420C4×C8—831no—
421C4×C8—831no—
422C4×C8—1661no—
423C4×C8—1661no—
424C4×C8C22×D8311yescharacteristic
425C4×C8C22×D8311yescharacteristic
426C4×C8C22×D8311yescharacteristic
427C2×Q8—831no—
428C2×Q8—1661no—
429C2×Q8C2×C4×D8311yescharacteristic
430C2×Q8C2×C4×D8311yescharacteristic
431C2×D4—831no—
432C2×D4—1661no—
433C22×C4—831no—
434C22×C4—831no—
435C22×C4—831no—
436C22×C4—1661no—
437Q16—22no—
438Q16—3321no—
439SD16—3321no—
440SD16—1662no—
441M16—3322no—
442M16—3321no—
443M16—3321no—
444M16—3322no—
445M16—1662no—
446M16—1662no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—3322no—
451C2×C8—3322no—
452C2×C8—831no—
453C2×C8—831no—
454C2×C8—831no—
455C2×C8—831no—
456C2×C8—1661no—
457C2×C8—1661no—
458C2×C8—1661no—
459C2×C8C2×C4×D8311yescharacteristic
460C2×C8C2×C4×D8311yescharacteristic
461C2×C8D4×D8311yescharacteristic
462C2×C8D4×D8311yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—831no—
466C4⋊C4—831no—
467C4⋊C4—1661no—
468C4⋊C4—1661no—
469C4⋊C4—1661no—
470C4⋊C4—1661no—
471C4⋊C4—1661no—
472C4⋊C4—1661no—
473C4⋊C4—1661no—
474C4⋊C4—1661no—
475C4⋊C4—1661no—
476C4⋊C4C2×C4×D8311yescharacteristic
477C4⋊C4C2×C4×D8311yescharacteristic
478C22⋊C4—1661no—
479C22⋊C4—1661no—
480C22⋊C4—1661no—
481C22⋊C4—1661no—
482C22⋊C4—1661no—
483C22⋊C4—1661no—
484C22⋊C4—1661no—
485C42—21no—
486C42—21no—
487C42—831no—
488C42—831no—
489C42—831no—
490C42—1661no—
491C42C23×D8311yescharacteristic
492C23—831no—
493C23—1661no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—6641no—
499Q8—1661no—
500Q8—1661no—
501D4—6641no—
502D4—1661no—
503D4—1661no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—3321no—
509C2×C4—3321no—
510C2×C4—3321no—
511C2×C4—831no—
512C2×C4—831no—
513C2×C4—831no—
514C2×C4—1661no—
515C2×C4—1661no—
516C2×C4—1661no—
517C2×C4—1661no—
518C2×C4—1661no—
519C2×C4—1661no—
520C2×C4—1661no—
521C2×C4C22×C4×D8311yescharacteristic
522C2×C4C2×D4×D8311yescharacteristic
523C2×C4#41×D8311yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—3321no—
531C8—3321no—
532C8—832no—
533C8—1662no—
534C8—1661no—
535C8—1661no—
536C8—1661no—
537C8#1458179812yes—
538C22—3321no—
539C22—3321no—
540C22—3321no—
541C22—1661no—
542C22—1661no—
543C22—1661no—
544C22C4×D4×D8311yescharacteristic
545C4—21no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—3321no—
551C4—3321no—
552C4—3321no—
553C4—1661no—
554C4—1661no—
555C4—1661no—
556C4C2×#1458179811yescharacteristic
557C4#1912846611yescharacteristic
558C4#137×D8311yescharacteristic
559C4#1912850011yescharacteristic
560C2—3321no—
561C2—6641no—
562C2#2491620211yescharacteristic
563C2#2491627911yescharacteristic
564C2#2491637111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D83
commutatorC2×C4×C83C23×C4
FrattiniC42C23×D83
FittingC83×#1579C2
socleC22×C83C2×C4×D4
prime radical#14581767C2×C4
cosocleC42×C83C24
hypercenter#1579D83
hypocenterC83#18077
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1579

Complements

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

NH ≅ G/Ntype
3. #24916405C2semidirect
4. #24906367C2semidirect
5. #24906360C2semidirect
6. #24906341C2semidirect
7. #24906334C2semidirect
8. #24906316C2semidirect
9. #24906302C2semidirect
10. #24906262C2semidirect
11. #24906212C2semidirect
12. #24905882C2semidirect
14. #24905767C2semidirect
15. C83×#1579C2semidirect
292. #1579D83semidirect
298. C83#18077semidirect

Maximal subgroups

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

subgroupindex
#249180672
#249164662
#249164052
#249063672
#249063602
#249063412
#249063342
#249063162
#249063022
#249062622
#249062122
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