Finite Group Databasebeta

← #14736199

Subgroups — #14736199

Order 2816.

672 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079176C211yesmaximal, characteristic, complemented
2#13078071C211yesmaximal, characteristic
3#41×C11⋊C8C211yesmaximal, characteristic, complemented
4#13068044C211yesmaximal, characteristic, complemented
5#13068037C211yesmaximal, characteristic, complemented
6#13068034C211yesmaximal, characteristic, complemented
7#13068027C211yesmaximal, characteristic, complemented
8#13068000C211yesmaximal, characteristic, complemented
9#13067993C211yesmaximal, characteristic, complemented
10#13067966C211yesmaximal, characteristic, complemented
11#13067959C211yesmaximal, characteristic, complemented
12C2×#10622118C211yesmaximal, characteristic, complemented
13#13067273C211yesmaximal, characteristic, complemented
14#13067266C211yesmaximal, characteristic, complemented
15C11×#3076C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18C2×#67003—21no—
19#10623008C2211yescharacteristic
20C11×#479—21no—
21C11×#478—21no—
22C11×#477C2211yescharacteristic
23C11×#476C2211yescharacteristic
24C11×#475C2211yescharacteristic
25C11×#474C2211yescharacteristic
26C11×#427—21no—
27C2×C11×C4⋊C8C2211yescharacteristic
28C11×#416—21no—
29#10622701C2211yescharacteristic
30#10622698C2211yescharacteristic
31#10622694C2211yescharacteristic
32#10622692C2211yescharacteristic
33#10622661—21no—
34#10622661—21no—
35#10622644C2211yescharacteristic
36#10622641—21no—
37#10622640C2211yescharacteristic
38C4×#4325—21no—
39C4×#4325—21no—
40Q8×C11⋊C8C2211yescharacteristic
41Q8×C11⋊C8C2211yescharacteristic
42#10622632C2211yescharacteristic
43#10622629—21no—
44#10622628C2211yescharacteristic
45D4×C11⋊C8—21no—
46D4×C11⋊C8—21no—
47D4×C11⋊C8C2211yescharacteristic
48D4×C11⋊C8C2211yescharacteristic
49#10622615—21no—
50#10622538—21no—
51#10622538C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C2×C4×C11⋊C8—21no—
54C2×C4×C11⋊C8C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622184C2211yescharacteristic
58#10622184C2211yescharacteristic
59#10622123C2211yescharacteristic
60#10622123C2211yescharacteristic
61#10622120C2211yescharacteristic
62#10622120C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622118C2211yescharacteristic
66#10622118C2211yescharacteristic
67C2×C11×#41D411yescharacteristic
68C2×#4339—21no—
69C22×C8×C11—21no—
70C11×C4⋊Q8C2311yescharacteristic
71C11×C4⋊Q8C2311yescharacteristic
72C11×#125—21no—
73C11×C22⋊Q8—21no—
74C11×C22⋊Q8—21no—
75C4×Q8×C11—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11D411yescharacteristic
78C4×Q8×C11C2311yescharacteristic
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C4×D4×C11D411yescharacteristic
82C4×D4×C11C2311yescharacteristic
83C11×#117—21no—
84C11×#117—21no—
85C11×#117D411yescharacteristic
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88#67003—44no—
89C2×#4326—21no—
90C2×#4325—21no—
91C2×#4325—21no—
92C2×#4325—21no—
93C2×#4324—21no—
94C2×#4323—21no—
95#66983—21no—
96#66983—21no—
97C22×C11⋊C8—21no—
98C22×C11⋊C8—21no—
99C22×C11⋊C8—21no—
100C22×C11⋊C8D411yescharacteristic
101C22×C11⋊C8D411yescharacteristic
102#66928—21no—
103#66927C2311yescharacteristic
104C4×D44—21no—
105C4×D44—21no—
106#66922C2311yescharacteristic
107C11×#107—21no—
108C11×#107—21no—
109C11×#106—21no—
110C11×#106—21no—
111C11×C4⋊C8—21no—
112C11×C4⋊C8C2311yescharacteristic
113C11×C4⋊C8C2311yescharacteristic
114C11×#103—21no—
115C11×#103—21no—
116C11×#102—21no—
117C11×#102—21no—
118#66899—21no—
119#66899—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122C22⋊(C11⋊C8)—21no—
123#66874—21no—
124#66874—21no—
125#66873—21no—
126#66873—21no—
127#66873—21no—
128#66873—21no—
129#66872—21no—
130#66872—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)—21no—
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8D411yescharacteristic
142C4×C11⋊C8D411yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#19124—111nomaximal, Sylow
146C11×#41—22no—
147C11×#41SD1614yescomplemented
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11C2×D411yescharacteristic
151C2×D4×C11—21no—
152C2×D4×C11C2×D411yescharacteristic
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C2×C22⋊D11—41no—
160#4339—42no—
161#4339—42no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×C4×D11—41no—
166C2×Dic22—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—42no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4—41no—
178C11×C4⋊C4C2×D411yescharacteristic
179C11×C4⋊C4C2×D411yescharacteristic
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—41no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—41no—
188C42×C11C2×D411yescharacteristic
189C42×C11C2×D411yescharacteristic
190C42×C11#4111yescharacteristic
191C42×C11C2411yescharacteristic
192#4326—42no—
193#4325—42no—
194#4325—42no—
195#4325—42no—
196#4324—42no—
197#4323—42no—
198(C2×D11)⋊C4—41no—
199(C2×D11)⋊C4—41no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—41no—
208C2×C11⋊C8—42no—
209C2×C11⋊C8—42no—
210C2×C11⋊C8—42no—
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213C2×C11⋊C8C2×D411yescharacteristic
214C2×C11⋊C8C2×D411yescharacteristic
215#3167—111no—
216#3076D1111yescharacteristic, complemented
217#3035—111no—
218C8×#41—111no—
219#1680—111no—
220#1679—111no—
221#1678—111no—
222#1677—111no—
223#1672—111no—
224#1671—111no—
225#1666—111no—
226#1665—111no—
227C2×#334—111no—
228#1542—111no—
229#1540—111no—
230C23×C11—21no—
231C23×C11#12111yescharacteristic
232C22×D11—41no—
233Q8×C11—21no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—81no—
237Q8×C11C2×SD1612yes—
238D4×C11—24no—
239D4×C11—21no—
240D4×C11C2×SD1612yes—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—24no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—41no—
248C2×C4×C11—42no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11#12111yescharacteristic
254C2×C4×C11#12111yescharacteristic
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11C2×SD1612yes—
257C2×C4×C11#13512yes—
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C22⋊D11—82no—
262C2×Dic11—41no—
263D44—41no—
264D44—41no—
265D44—41no—
266D44—41no—
267D44—81no—
268C4×D11—82no—
269Dic22—41no—
270Dic22—41no—
271C8×C11—41no—
272C8×C11—41no—
273C11⋊C8—21no—
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280C11⋊C8#13512yescomplemented
281C2×#135—221no—
282#533C2×D1111yescharacteristic
283#532—111no—
284C4×#41C2×D1111yescharacteristic
285#498—111no—
286#492—111no—
287#487—111no—
288#486—111no—
289#479—21no—
290#478—21no—
291#477C2×D1111yescharacteristic
292#476C2×D1111yescharacteristic
293#475C2×D1111yescharacteristic
294#474C2×D1111yescharacteristic
295#465—221no—
296#465—221no—
297#464—221no—
298#463—221no—
299#462—111no—
300#461—111no—
301#460—111no—
302#459—111no—
303C8×Q8—111no—
304C8×Q8—111no—
305C4×SD16—221no—
306C4×SD16—221no—
307C8×D4—111no—
308C8×D4—111no—
309C8×D4—221no—
310C8×D4—221no—
311#431—111no—
312#431—221no—
313#427—21no—
314C2×C4⋊C8—111no—
315C2×C4⋊C8C2×D1111yescharacteristic
316#416—21no—
317#416—221no—
318C2×C4×C8—111no—
319C2×C4×C8—221no—
320#334—111no—
321#334—111no—
322#334—111no—
323#334—111no—
324#333—111no—
325#333—111no—
326#332—111no—
327#332—111no—
328#332—111no—
329#332—111no—
330#331—111no—
331#331—111no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11—22no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11#46512yes—
338C22×C11C2×#12111yescharacteristic
339C2×D11—81no—
340C2×D11—81no—
341C2×D11—81no—
342C4×C11—21no—
343C4×C11—22no—
344C4×C11—21no—
345C4×C11—21no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—81no—
349C4×C11—81no—
350C4×C11#46512yes—
351C4×C11C22×SD1611yescharacteristic
352C4×C11C2×#13511yescharacteristic
353C4×C11C2×#13511yescharacteristic
354C4×C11#57511yescharacteristic
355Dic11—81no—
356C2×#41—221no—
357C2×#41C22⋊D1111yescharacteristic
358#135—444no—
359C2×Q16—221no—
360C2×SD16—221no—
361C2×SD16—221no—
362C2×SD16—221no—
363C2×SD16—221no—
364C2×D8—221no—
365C22×C8—21no—
366C22×C8—111no—
367C22×C8—111no—
368C22×C8—221no—
369C22×C8—221no—
370C22×C8—221no—
371C4⋊Q8—111no—
372C4⋊Q8C22×D1111yescharacteristic
373C4⋊Q8C22×D1111yescharacteristic
374#127—111no—
375#125—21no—
376#124—221no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379#121—221no—
380#121—221no—
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8C22⋊D1111yescharacteristic
384C4×Q8C22×D1111yescharacteristic
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—221no—
388C4×D4—221no—
389C4×D4C22⋊D1111yescharacteristic
390C4×D4C22×D1111yescharacteristic
391#117—21no—
392#117—21no—
393#117C22⋊D1111yescharacteristic
394C2×C42—21no—
395C2×C42C22×D1111yescharacteristic
396#107—21no—
397#107—21no—
398#106—21no—
399#106—21no—
400#106—221no—
401#106—221no—
402C4⋊C8—21no—
403C4⋊C8—111no—
404C4⋊C8—111no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—221no—
408C4⋊C8—221no—
409C4⋊C8—221no—
410C4⋊C8C22×D1111yescharacteristic
411C4⋊C8C22×D1111yescharacteristic
412#103—21no—
413#103—21no—
414#103—221no—
415#103—221no—
416#103—221no—
417#103—221no—
418#102—21no—
419#102—21no—
420#102—221no—
421#102—221no—
422#102—221no—
423#102—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C4×C8—111no—
428C4×C8—111no—
429C4×C8—111no—
430C4×C8—111no—
431C4×C8—221no—
432C4×C8—221no—
433C4×C8—221no—
434C2×C11—22no—
435C2×C11—42no—
436C2×C11#303511yescharacteristic
437C2×C11C2×#46511yescharacteristic
438C2×C11#306711yescharacteristic
439D11—161no—
440#41—22no—
441#41—442no—
442#41—442no—
443#41#432514yescomplemented
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—221no—
447C2×Q8C2×C22⋊D1111yescharacteristic
448C2×D4—21no—
449C2×D4—221no—
450C2×D4—221no—
451C2×D4—221no—
452C2×D4—441no—
453C2×D4C2×C22⋊D1111yescharacteristic
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—441no—
458C22×C4D4×D1111yescharacteristic
459C22×C4#434111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461Q16—442no—
462SD16—442no—
463SD16—442no—
464SD16—442no—
465SD16—442no—
466D8—442no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—42no—
470C2×C8—111no—
471C2×C8—111no—
472C2×C8—111no—
473C2×C8—111no—
474C2×C8—222no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—442no—
480C2×C8—441no—
481C2×C8—442no—
482C2×C8—442no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4C2×C22⋊D1111yescharacteristic
494C4⋊C4C2×C22⋊D1111yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—41no—
499C22⋊C4—441no—
500C22⋊C4—441no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—41no—
505C42D4×D1111yescharacteristic
506C42#434111yescharacteristic
507C42C2×C22⋊D1111yescharacteristic
508C42C23×D1111yescharacteristic
509C11#1912411yescharacteristic, complemented, Sylow
510C23—21no—
511C23—441no—
512C23#6699211yescharacteristic
513Q8—21no—
514Q8—41no—
515Q8—41no—
516Q8—81no—
517Q8—441no—
518Q8—441no—
519Q8C2×#432512yes—
520D4—24no—
521D4—21no—
522D4—441no—
523D4—441no—
524D4—441no—
525D4—441no—
526D4—881no—
527D4—882no—
528D4C2×#432512yes—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—24no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—441no—
542C2×C4—882no—
543C2×C4#6699211yescharacteristic
544C2×C4#6699211yescharacteristic
545C2×C4#6699211yescharacteristic
546C2×C4C2×#432512yes—
547C2×C4#6700312yes—
548C2×C4C2×D4×D1111yescharacteristic
549C2×C4C2×#434111yescharacteristic
550C2×C4C22×C22⋊D1111yescharacteristic
551C8—41no—
552C8—41no—
553C8—112no—
554C8—221no—
555C8—221no—
556C8—221no—
557C8—441no—
558C8—441no—
559C8—441no—
560C8—441no—
561C22—21no—
562C22—21no—
563C22—22no—
564C22—41no—
565C22—41no—
566C22—881no—
567C22—881no—
568C22—881no—
569C22#1062266112yes—
570C22C2×#6699211yescharacteristic
571C4—21no—
572C4—21no—
573C4—21no—
574C4—22no—
575C4—41no—
576C4—41no—
577C4—81no—
578C4—81no—
579C4—881no—
580C4#1062266112yes—
581C4D11×#13511yescharacteristic
582C4#1062329911yescharacteristic
583C4C22×#432511yescharacteristic
584C4C2×#6700311yescharacteristic
585C2—22no—
586C2—42no—
587C2—1761no—
588C2#1307806711yescharacteristic
589C2C2×#1062266111yescharacteristic
590C2#1307833311yescharacteristic
subgroupG/H
centerC2×C4#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3076C2
socleC22×C11C2×#121
prime radical#13078071C2
hypercenter#3076D11
hypocenterC11#19124
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3076

Complements

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

NH ≅ G/Ntype
1. #13079176C2semidirect
3. #41×C11⋊C8C2semidirect
4. #13068044C2semidirect
5. #13068037C2semidirect
6. #13068034C2semidirect
7. #13068027C2semidirect
8. #13068000C2semidirect
9. #13067993C2semidirect
10. #13067966C2semidirect
11. #13067959C2semidirect
12. C2×#10622118C2semidirect
13. #13067273C2semidirect
14. #13067266C2semidirect
15. C11×#3076C2semidirect
147. C11×#41SD16semidirect
216. #3076D11semidirect
280. C11⋊C8#135semidirect
443. #41#4325semidirect
509. C11#19124semidirect

Maximal subgroups

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

subgroupindex
#130791762
#130780712
#41×C11⋊C82
#130680442
#130680372
#130680342
#130680272
#130680002
#130679932
#130679662
#130679592
C2×#106221182
#130672732
#130672662
C11×#30762
#1912411