Finite Group Databasebeta

← #14736781

Subgroups — #14736781

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079335C211yesmaximal, characteristic, complemented
2#13078071C211yesmaximal, characteristic
3#13077636C211yesmaximal, characteristic, complemented
4#13068179C211yesmaximal, characteristic, complemented
5#13068161C211yesmaximal, characteristic, complemented
6#13068127C211yesmaximal, characteristic, complemented
7#13068083C211yesmaximal, characteristic, complemented
8#13068062C211yesmaximal, characteristic, complemented
9#13068044C211yesmaximal, characteristic, complemented
10#13068008C211yesmaximal, characteristic, complemented
11#13067966C211yesmaximal, characteristic, complemented
12#13067369C211yesmaximal, characteristic, complemented
13#13067319C211yesmaximal, characteristic, complemented
14#13067316C211yesmaximal, characteristic, complemented
15C11×#3107C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18C2×#67003—21no—
19#10623008C2211yescharacteristic
20C11×#485—21no—
21C11×#475C2211yescharacteristic
22C11×#474C2211yescharacteristic
23C11×#462C2211yescharacteristic
24C11×#461C2211yescharacteristic
25C11×#452—21no—
26C4×C11×Q16—21no—
27C4×C11×SD16—21no—
28C11×#431C2211yescharacteristic
29#10622701C2211yescharacteristic
30#10622698C2211yescharacteristic
31#10622694C2211yescharacteristic
32#10622691C2211yescharacteristic
33#10622662—21no—
34#10622662—21no—
35#10622644C2211yescharacteristic
36#10622641—21no—
37#10622640C2211yescharacteristic
38#10622639—21no—
39#10622639—21no—
40Q8×C11⋊C8C2211yescharacteristic
41Q8×C11⋊C8C2211yescharacteristic
42#10622632C2211yescharacteristic
43#10622629—21no—
44#10622628C2211yescharacteristic
45#10622625—21no—
46#10622625—21no—
47#10622625C2211yescharacteristic
48#10622625C2211yescharacteristic
49#10622615—21no—
50#10622539—21no—
51#10622539C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53C4×#4318—21no—
54C4×#4318C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622185C2211yescharacteristic
58#10622185C2211yescharacteristic
59#10622123C2211yescharacteristic
60#10622123C2211yescharacteristic
61#10622120C2211yescharacteristic
62#10622120C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×#41D411yescharacteristic
68C2×#4339—21no—
69C2×C11×Q16—21no—
70C2×C11×SD16—21no—
71C11×C4⋊Q8C2311yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×#125—21no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8—21no—
76C4×Q8×C11—21no—
77C4×Q8×C11—21no—
78C4×Q8×C11D411yescharacteristic
79C4×Q8×C11C2311yescharacteristic
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11D411yescharacteristic
83C4×D4×C11C2311yescharacteristic
84C11×#117—21no—
85C11×#117—21no—
86C11×#117D411yescharacteristic
87C2×C42×C11—21no—
88C2×C42×C11C2311yescharacteristic
89#67003—44no—
90C2×#4326—21no—
91C2×#4325—21no—
92C2×#4325—21no—
93C2×#4325—21no—
94C2×#4324—21no—
95C2×#4323—21no—
96#66983—21no—
97#66983—21no—
98C2×#4318—21no—
99C2×#4318—21no—
100C2×#4318D411yescharacteristic
101C2×#4318D411yescharacteristic
102C22×C11⋊C8—21no—
103#66928—21no—
104#66927C2311yescharacteristic
105C4×D44—21no—
106C4×D44—21no—
107#66922C2311yescharacteristic
108C11×#107—21no—
109C11×#106—21no—
110C11×C4⋊C8C2311yescharacteristic
111C11×C4⋊C8C2311yescharacteristic
112C11×#103—21no—
113C11×#103—21no—
114C11×#103—21no—
115C11×#102—21no—
116C11×C22⋊C8—21no—
117C4×C8×C11—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#66871—21no—
130#66871—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
138#66867—21no—
139#66867D411yescharacteristic
140#66867D411yescharacteristic
141C4×C11⋊C8—21no—
142C4×C11⋊C8—21no—
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#19182—111nomaximal, Sylow
146C11×#41—22no—
147C11×#41—41no—
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—
167C11×Q16—42no—
168C11×SD16—42no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—41no—
178C11×C4⋊C4—41no—
179C11×C4⋊C4C2×D411yescharacteristic
180C11×C4⋊C4C2×D411yescharacteristic
181C11×C22⋊C4—21no—
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—41no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—41no—
189C42×C11C2×D411yescharacteristic
190C42×C11C2×D411yescharacteristic
191C42×C11#4111yescharacteristic
192C42×C11C2411yescharacteristic
193#4326—42no—
194#4325—42no—
195#4325—42no—
196#4325—42no—
197#4324—42no—
198#4323—42no—
199(C2×D11)⋊C4—41no—
200(C2×D11)⋊C4—41no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203#4318—22no—
204#4318—41no—
205#4318—42no—
206#4318—42no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—42no—
212C2×C11⋊C8C2×D411yescharacteristic
213C2×C11⋊C8C2×D411yescharacteristic
214C2×C11⋊C8C2×D411yescharacteristic
215C2×C11⋊C8C2×D411yescharacteristic
216#3182—111no—
217#3107D1111yescharacteristic, complemented
218#3035—111no—
219#2971—111no—
220#1701—111no—
221#1699—111no—
222#1693—111no—
223#1685—111no—
224#1682—111no—
225#1680—111no—
226#1674—111no—
227#1666—111no—
228#1565—111no—
229#1553—111no—
230#1552—111no—
231C23×C11—21no—
232C23×C11#12111yescharacteristic
233C22×D11—41no—
234Q8×C11—21no—
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11—41no—
238Q8×C11—41no—
239Q8×C11AGL(1,ℤ/8)12yes—
240D4×C11—21no—
241D4×C11—21no—
242D4×C11—42no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—41no—
251C2×C4×C11—42no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—81no—
257C2×C4×C11#12111yescharacteristic
258C2×C4×C11#12111yescharacteristic
259C2×C4×C11#12111yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C22⋊D11—82no—
264C2×Dic11—41no—
265D44—41no—
266D44—41no—
267D44—41no—
268D44—41no—
269D44—81no—
270C4×D11—82no—
271Dic22—41no—
272Dic22—41no—
273C8×C11—41no—
274C8×C11—41no—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—21no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C11⋊C8#13512yescomplemented
283C2×#135—221no—
284#533C2×D1111yescharacteristic
285#532—111no—
286C4×#41C2×D1111yescharacteristic
287#500—111no—
288#492—111no—
289#487—111no—
290#486—111no—
291#485—21no—
292#475C2×D1111yescharacteristic
293#474C2×D1111yescharacteristic
294#468—221no—
295#468—221no—
296#464—221no—
297#463—221no—
298#462—111no—
299#462C2×D1111yescharacteristic
300#461—111no—
301#461C2×D1111yescharacteristic
302#460—111no—
303#459—111no—
304#452—21no—
305C8×Q8—111no—
306C8×Q8—111no—
307#440—221no—
308#440—221no—
309C4×Q16—21no—
310C4×SD16—21no—
311#436—111no—
312#436—111no—
313#436—221no—
314#436—221no—
315#432—111no—
316#432—221no—
317#431C2×D1111yescharacteristic
318C2×C4⋊C8—111no—
319#416—221no—
320C4×M16—111no—
321C4×M16—221no—
322#335—111no—
323#335—111no—
324#334—111no—
325#334—111no—
326#332—111no—
327#332—111no—
328#332—111no—
329#332—111no—
330#332—111no—
331#332—111no—
332#331—111no—
333#331—111no—
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—21no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11C2×#12111yescharacteristic
341C2×D11—81no—
342C2×D11—81no—
343C2×D11—81no—
344C4×C11—21no—
345C4×C11—21no—
346C4×C11—22no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—81no—
352C4×C11—81no—
353C4×C11C2×#13511yescharacteristic
354C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
355C4×C11#57511yescharacteristic
356C4×C11#57511yescharacteristic
357Dic11—81no—
358C2×#41—221no—
359C2×#41C22⋊D1111yescharacteristic
360#135—444no—
361C2×Q16—21no—
362C2×Q16—221no—
363C2×SD16—21no—
364C2×SD16—221no—
365C2×SD16—221no—
366C2×SD16—221no—
367C2×SD16—221no—
368C2×D8—221no—
369C2×M16—111no—
370C2×M16—111no—
371C2×M16—221no—
372C2×M16—221no—
373C22×C8—221no—
374C4⋊Q8—111no—
375C4⋊Q8C22×D1111yescharacteristic
376C4⋊Q8C22×D1111yescharacteristic
377#127—111no—
378#125—21no—
379#124—221no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382#121—221no—
383#121—221no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8C22⋊D1111yescharacteristic
387C4×Q8C22×D1111yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—221no—
391C4×D4—221no—
392C4×D4C22⋊D1111yescharacteristic
393C4×D4C22×D1111yescharacteristic
394#117—21no—
395#117—21no—
396#117C22⋊D1111yescharacteristic
397C2×C42—21no—
398C2×C42C22×D1111yescharacteristic
399#107—21no—
400#107—221no—
401#107—221no—
402#106—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—21no—
415#103—221no—
416#103—221no—
417#103—221no—
418#103—221no—
419#102—21no—
420#102—221no—
421#102—221no—
422#102—221no—
423#102—221no—
424C22⋊C8—21no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428#97—111no—
429#97—111no—
430#97—221no—
431C4×C8—21no—
432C4×C8—111no—
433C4×C8—111no—
434C4×C8—221no—
435C4×C8—221no—
436C2×C11—41no—
437C2×C11—81no—
438C2×C11#303511yescharacteristic
439C2×C11#305511yescharacteristic
440C2×C11#306911yescharacteristic
441D11—161no—
442#41—22no—
443#41—41no—
444#41—442no—
445#41—442no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—221no—
449C2×Q8C2×C22⋊D1111yescharacteristic
450C2×D4—21no—
451C2×D4—221no—
452C2×D4—221no—
453C2×D4—221no—
454C2×D4—441no—
455C2×D4C2×C22⋊D1111yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—441no—
460C22×C4D4×D1111yescharacteristic
461C22×C4#434111yescharacteristic
462C22×C4C2×C22⋊D1111yescharacteristic
463Q16—42no—
464Q16—442no—
465SD16—42no—
466SD16—442no—
467SD16—442no—
468SD16—442no—
469SD16—442no—
470D8—442no—
471M16—222no—
472M16—442no—
473M16—441no—
474M16—442no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—111no—
478C2×C8—111no—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—442no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4C2×C22⋊D1111yescharacteristic
497C4⋊C4C2×C22⋊D1111yescharacteristic
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—41no—
502C22⋊C4—441no—
503C22⋊C4—441no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—41no—
508C42D4×D1111yescharacteristic
509C42#434111yescharacteristic
510C42C2×C22⋊D1111yescharacteristic
511C42C23×D1111yescharacteristic
512C11#1918211yescharacteristic, complemented, Sylow
513C23—21no—
514C23—441no—
515C23#6699211yescharacteristic
516Q8—21no—
517Q8—41no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—441no—
522Q8—441no—
523Q8#6700212yes—
524D4—21no—
525D4—21no—
526D4—42no—
527D4—441no—
528D4—441no—
529D4—441no—
530D4—441no—
531D4—881no—
532D4—882no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—81no—
547C2×C4—441no—
548C2×C4—882no—
549C2×C4#6699211yescharacteristic
550C2×C4#6699211yescharacteristic
551C2×C4#6699211yescharacteristic
552C2×C4C2×D4×D1111yescharacteristic
553C2×C4C2×#434111yescharacteristic
554C2×C4C22×C22⋊D1111yescharacteristic
555C8—41no—
556C8—41no—
557C8—112no—
558C8—221no—
559C8—221no—
560C8—221no—
561C8—441no—
562C8—441no—
563C8—441no—
564C8—441no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—881no—
572C22—881no—
573C22—881no—
574C22C2×#6699211yescharacteristic
575C4—21no—
576C4—21no—
577C4—21no—
578C4—21no—
579C4—22no—
580C4—41no—
581C4—41no—
582C4—81no—
583C4—81no—
584C4—881no—
585C4D11×#13511yescharacteristic
586C4#1062329911yescharacteristic
587C4C2×#6700211yescharacteristic
588C4#1062335311yescharacteristic
589C2—41no—
590C2—81no—
591C2—1761no—
592C2#1307806711yescharacteristic
593C2#1307823711yescharacteristic
594C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3107C2
socleC22×C11C2×#121
prime radical#13078071C2
hypercenter#3107D11
hypocenterC11#19182
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3107

Complements

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

NH ≅ G/Ntype
1. #13079335C2semidirect
3. #13077636C2semidirect
4. #13068179C2semidirect
5. #13068161C2semidirect
6. #13068127C2semidirect
7. #13068083C2semidirect
8. #13068062C2semidirect
9. #13068044C2semidirect
10. #13068008C2semidirect
11. #13067966C2semidirect
12. #13067369C2semidirect
13. #13067319C2semidirect
14. #13067316C2semidirect
15. C11×#3107C2semidirect
217. #3107D11semidirect
282. C11⋊C8#135semidirect
512. C11#19182semidirect

Maximal subgroups

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

subgroupindex
#130793352
#130780712
#130776362
#130681792
#130681612
#130681272
#130680832
#130680622
#130680442
#130680082
#130679662
#130673692
#130673192
#130673162
C11×#31072
#1918211