Finite Group Databasebeta

← #14736771

Subgroups — #14736771

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#13078681C211yesmaximal, characteristic, complemented
2#13078065C211yesmaximal, characteristic
3#13077634C211yesmaximal, characteristic, complemented
4#13068174C211yesmaximal, characteristic, complemented
5#13068160C211yesmaximal, characteristic, complemented
6#13068126C211yesmaximal, characteristic, complemented
7#13068078C211yesmaximal, characteristic, complemented
8#13068057C211yesmaximal, characteristic, complemented
9#13068043C211yesmaximal, characteristic, complemented
10#13068007C211yesmaximal, characteristic, complemented
11#13067961C211yesmaximal, characteristic, complemented
12#13067368C211yesmaximal, characteristic, complemented
13#13067321C211yesmaximal, characteristic, complemented
14#13067316C211yesmaximal, characteristic, complemented
15C11×#3182C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C11×#532C2211yescharacteristic
18C2×#67003—21no—
19C4×#4339C2211yescharacteristic
20C11×#500C2211yescharacteristic
21C11×#492C2211yescharacteristic
22C11×#487C2211yescharacteristic
23C11×#486C2211yescharacteristic
24C11×#468—21no—
25C11×#468—21no—
26C11×#440—21no—
27C11×#440—21no—
28C4×C11×M16C2211yescharacteristic
29#10622846—21no—
30#10622741—21no—
31#10622741—21no—
32#10622707C2211yescharacteristic
33#10622703C2211yescharacteristic
34#10622703C2211yescharacteristic
35#10622700C2211yescharacteristic
36#10622696C2211yescharacteristic
37#10622696C2211yescharacteristic
38#10622688C2211yescharacteristic
39#10622685C2211yescharacteristic
40#10622670—21no—
41#10622667—21no—
42#10622660—21no—
43#10622658—21no—
44C4×#4326—21no—
45C4×#4325—21no—
46#10622539C2211yescharacteristic
47#10622538C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622320—21no—
50#10622318—21no—
51#10622301C2211yescharacteristic
52#10622301C2211yescharacteristic
53C8×Dic22C2211yescharacteristic
54C8×Dic22C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622185C2211yescharacteristic
58#10622185C2211yescharacteristic
59#10622185C2211yescharacteristic
60#10622185C2211yescharacteristic
61#10622182C2211yescharacteristic
62#10622182C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C2×C11×#41—21no—
68C2×#4339D411yescharacteristic
69C2×C11×SD16—21no—
70C2×C11×SD16—21no—
71C2×C11×M16D411yescharacteristic
72C2×C11×M16D411yescharacteristic
73C11×C4⋊Q8C2311yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×C4⋊Q8C2311yescharacteristic
76C11×#127C2311yescharacteristic
77C11×#125—21no—
78C11×#124—21no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×#121—21no—
82C11×#121—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11—21no—
85C4×D4×C11—21no—
86C4×D4×C11—21no—
87C11×#117—21no—
88C2×C42×C11C2311yescharacteristic
89#67003—44no—
90C2×#4326—21no—
91C2×#4326—21no—
92C2×#4325—21no—
93C2×#4325—21no—
94C2×#4324—21no—
95C2×#4323—21no—
96C4×C22⋊D11—21no—
97C4×C22⋊D11—21no—
98#66979D411yescharacteristic
99C22×C11⋊C8—21no—
100C2×#4313—21no—
101C2×#4313—21no—
102C4×D44D411yescharacteristic
103C4×D44C2311yescharacteristic
104#66925—21no—
105C42×D11—21no—
106C4×Dic22D411yescharacteristic
107C4×Dic22C2311yescharacteristic
108C11×#107—21no—
109C11×#107—21no—
110C11×#103—21no—
111C11×#103—21no—
112C11×#102—21no—
113C11×#102—21no—
114C11×#97D411yescharacteristic
115C11×#97D411yescharacteristic
116C4×C8×C11C2311yescharacteristic
117C4×C8×C11C2311yescharacteristic
118#66899—21no—
119#66899—21no—
120#66899—21no—
121#66899—21no—
122#66896—21no—
123#66896—21no—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)—21no—
126(C2×D11)⋊C8—21no—
127(C2×D11)⋊C8—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130C8×Dic11—21no—
131C8×Dic11—21no—
132#66874—21no—
133#66873—21no—
134#66872—21no—
135#66871—21no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143#66867—21no—
144C4×C11⋊C8—21no—
145#19182—111nomaximal, Sylow
146C11×#41—42no—
147C11×#41—42no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—41no—
155C22×C4×C11—41no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11#4111yescharacteristic
159C2×C22⋊D11—21no—
160#4339—22no—
161#4339—41no—
162C2×D44C2×D411yescharacteristic
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×Dic22C2×D411yescharacteristic
167C11×SD16—42no—
168C11×SD16—42no—
169C11×M16—22no—
170C11×M16—41no—
171C2×C8×C11C2×D411yescharacteristic
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2×D411yescharacteristic
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—41no—
182C11×C4⋊C4—41no—
183C11×C22⋊C4—41no—
184C11×C22⋊C4—41no—
185C11×C22⋊C4—41no—
186C42×C11—41no—
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11#4111yescharacteristic
190C42×C11C2411yescharacteristic
191C22⋊Dic11—21no—
192#4326—42no—
193#4326—42no—
194#4325—42no—
195#4325—42no—
196#4324—42no—
197#4323—42no—
198(C2×D11)⋊C4—21no—
199(C2×D11)⋊C4—21no—
200C4⋊Dic11C2×D411yescharacteristic
201C4⋊Dic11C2×D411yescharacteristic
202Dic11⋊C4—21no—
203Dic11⋊C4—21no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—42no—
214#4313—42no—
215#4313—42no—
216#3182D1111yescharacteristic, complemented
217#3107—111no—
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—41no—
232C23×C11#12111yescharacteristic
233C22×D11—21no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11—41no—
238Q8×C11—41no—
239Q8×C11—41no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—81no—
245D4×C11—82no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—82no—
255C2×C4×C11#12111yescharacteristic
256C2×C4×C11#12111yescharacteristic
257C2×C4×C11#12111yescharacteristic
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C22⋊D11—42no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265D44—21no—
266D44—21no—
267C4×D11—42no—
268C4×D11—41no—
269C4×D11—41no—
270C4×D11—81no—
271Dic22—21no—
272Dic22AGL(1,ℤ/8)12yes—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—21no—
276C8×C11#13512yescomplemented
277C11⋊C8—41no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C2×#135—221no—
284#533C2×D1111yescharacteristic
285#532C2×D1111yescharacteristic
286C4×#41—111no—
287#500C2×D1111yescharacteristic
288#492C2×D1111yescharacteristic
289#487C2×D1111yescharacteristic
290#486C2×D1111yescharacteristic
291#485—221no—
292#475—111no—
293#474—111no—
294#468—21no—
295#468—21no—
296#464—221no—
297#463—221no—
298#462—111no—
299#462—111no—
300#461—111no—
301#461—111no—
302#460—111no—
303#459—111no—
304#452—221no—
305C8×Q8—111no—
306C8×Q8—111no—
307#440—21no—
308#440—21no—
309C4×Q16—221no—
310C4×SD16—221no—
311#436—111no—
312#436—111no—
313#436—221no—
314#436—221no—
315#432—111no—
316#432—221no—
317#431—111no—
318C2×C4⋊C8—111no—
319#416—221no—
320C4×M16—221no—
321C4×M16C2×D1111yescharacteristic
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—81no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11C2×#12111yescharacteristic
341C2×D11—41no—
342C2×D11—41no—
343C2×D11—41no—
344C4×C11—21no—
345C4×C11—21no—
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—81no—
349C4×C11—81no—
350C4×C11—81no—
351C4×C11C2×#13511yescharacteristic
352C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
353C4×C11#57511yescharacteristic
354C4×C11#57511yescharacteristic
355Dic11—22no—
356Dic11—41no—
357Dic11—41no—
358C2×#41—21no—
359C2×#41—111no—
360#135—444no—
361C2×Q16—221no—
362C2×Q16—221no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—221no—
366C2×SD16—221no—
367C2×SD16—221no—
368C2×D8—221no—
369C2×M16—221no—
370C2×M16—221no—
371C2×M16C22⋊D1111yescharacteristic
372C2×M16C22⋊D1111yescharacteristic
373C22×C8—221no—
374C4⋊Q8C22×D1111yescharacteristic
375C4⋊Q8C22×D1111yescharacteristic
376C4⋊Q8C22×D1111yescharacteristic
377#127C22×D1111yescharacteristic
378#125—21no—
379#124—21no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382#121—21no—
383#121—21no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8—111no—
387C4×Q8—111no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—111no—
391C4×D4—111no—
392C4×D4—221no—
393C4×D4—221no—
394#117—21no—
395#117—111no—
396#117—221no—
397C2×C42—221no—
398C2×C42C22×D1111yescharacteristic
399#107—21no—
400#107—21no—
401#107—221no—
402#106—221no—
403C4⋊C8—111no—
404C4⋊C8—111no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—111no—
409C4⋊C8—221no—
410C4⋊C8—221no—
411C4⋊C8—221no—
412#103—21no—
413#103—21no—
414#103—221no—
415#103—221no—
416#103—221no—
417#103—221no—
418#103—221no—
419#102—21no—
420#102—21no—
421#102—221no—
422#102—221no—
423#102—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428#97—221no—
429#97C22⋊D1111yescharacteristic
430#97C22⋊D1111yescharacteristic
431C4×C8—221no—
432C4×C8—221no—
433C4×C8—221no—
434C4×C8C22×D1111yescharacteristic
435C4×C8C22×D1111yescharacteristic
436C2×C11—41no—
437C2×C11—161no—
438C2×C11#303511yescharacteristic
439C2×C11#305511yescharacteristic
440C2×C11#306911yescharacteristic
441D11—81no—
442#41—42no—
443#41—42no—
444#41—222no—
445#41—441no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—111no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—41no—
454C2×D4—111no—
455C2×D4—221no—
456C22×C4—41no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4D4×D1111yescharacteristic
461C22×C4#434111yescharacteristic
462C22×C4C2×C22⋊D1111yescharacteristic
463Q16—442no—
464Q16—442no—
465SD16—42no—
466SD16—42no—
467SD16—442no—
468SD16—442no—
469SD16—442no—
470D8—442no—
471M16—22no—
472M16—41no—
473M16—442no—
474M16—442no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—442no—
482C2×C8C2×C22⋊D1111yescharacteristic
483C2×C8C2×C22⋊D1111yescharacteristic
484C2×C8C2×C22⋊D1111yescharacteristic
485C2×C8C2×C22⋊D1111yescharacteristic
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—111no—
495C4⋊C4—111no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—221no—
502C22⋊C4—221no—
503C22⋊C4—221no—
504C42—41no—
505C42—221no—
506C42—221no—
507C42—221no—
508C42D4×D1111yescharacteristic
509C42#434111yescharacteristic
510C42C2×C22⋊D1111yescharacteristic
511C42C23×D1111yescharacteristic
512C11#1918211yescharacteristic, complemented, Sylow
513C23—41no—
514C23—221no—
515C23#6699111yescharacteristic
516Q8—41no—
517Q8—41no—
518Q8—41no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522Q8—112no—
523Q8—221no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—81no—
529D4—82no—
530D4—221no—
531D4—221no—
532D4—442no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—82no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—442no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—881no—
549C2×C4#6699111yescharacteristic
550C2×C4#6699111yescharacteristic
551C2×C4#6699111yescharacteristic
552C2×C4C2×D4×D1111yescharacteristic
553C2×C4C2×#434111yescharacteristic
554C2×C4C22×C22⋊D1111yescharacteristic
555C8—21no—
556C8—21no—
557C8—21no—
558C8—441no—
559C8—441no—
560C8—441no—
561C8—441no—
562C8—441no—
563C8—441no—
564C8#6700312yescomplemented
565C22—21no—
566C22—21no—
567C22—21no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22—441no—
572C22—441no—
573C22—441no—
574C22C2×#6699111yescharacteristic
575C4—21no—
576C4—21no—
577C4—21no—
578C4—21no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—222no—
583C4—441no—
584C4—441no—
585C4D11×AGL(1,ℤ/8)11yescharacteristic
586C4#1062330411yescharacteristic
587C4C2×#6700311yescharacteristic
588C4#1062335311yescharacteristic
589C2—41no—
590C2—161no—
591C2—881no—
592C2#1307806511yescharacteristic
593C2#1307822911yescharacteristic
594C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3182C2
socleC22×C11C2×#121
prime radical#13078065C2
hypercenter#3182D11
hypocenterC11#19182
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3182

Complements

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

NH ≅ G/Ntype
1. #13078681C2semidirect
3. #13077634C2semidirect
4. #13068174C2semidirect
5. #13068160C2semidirect
6. #13068126C2semidirect
7. #13068078C2semidirect
8. #13068057C2semidirect
9. #13068043C2semidirect
10. #13068007C2semidirect
11. #13067961C2semidirect
12. #13067368C2semidirect
13. #13067321C2semidirect
14. #13067316C2semidirect
15. C11×#3182C2semidirect
216. #3182D11semidirect
276. C8×C11#135semidirect
512. C11#19182semidirect
564. C8#67003semidirect

Maximal subgroups

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

subgroupindex
#130786812
#130780652
#130776342
#130681742
#130681602
#130681262
#130680782
#130680572
#130680432
#130680072
#130679612
#130673682
#130673212
#130673162
C11×#31822
#1918211