Finite Group Databasebeta

← #14723866

Subgroups — #14723866

Order 2816.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078672C211yesmaximal, characteristic
2#13077723C211yesmaximal, characteristic, complemented
3#13077693C211yesmaximal, characteristic, complemented
4#13067496C211yesmaximal, characteristic, complemented
5#13067457C211yesmaximal, characteristic, complemented
6#13067445C211yesmaximal, characteristic, complemented
7#13067437C211yesmaximal, characteristic, complemented
8#13067425C211yesmaximal, characteristic, complemented
9#13067415C211yesmaximal, characteristic, complemented
10D8×C11⋊C8C211yesmaximal, characteristic, complemented
11#13067398C211yesmaximal, characteristic, complemented
12#13067047C211yesmaximal, characteristic, complemented
13#13067013C211yesmaximal, characteristic, complemented
14#13066917C211yesmaximal, characteristic, complemented
15C11×#1586C211yesmaximal, characteristic, complemented
16#10623079C2211yescharacteristic
17C4×#4341C2211yescharacteristic
18C4×C11×D8C2211yescharacteristic
19C11×#436C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic
21#10622771C411yescharacteristic
22#10622763C411yescharacteristic
23#10622742—21no—
24#10622740—21no—
25C8×C22⋊D11—21no—
26C2×Dic11⋊C8—21no—
27C4×#4324C2211yescharacteristic
28C4×#4323C2211yescharacteristic
29D4×C11⋊C8C2211yescharacteristic
30D4×C11⋊C8C2211yescharacteristic
31#10622498C411yescharacteristic
32#10622488C411yescharacteristic
33#10622448C2211yescharacteristic
34#10622447C2211yescharacteristic
35D11×C4⋊C8C2211yescharacteristic
36#10622443C2211yescharacteristic
37#10622394C411yescharacteristic
38#10622392C411yescharacteristic
39#10622375C411yescharacteristic
40#10622374C411yescharacteristic
41#10622343—21no—
42#10622340—21no—
43(C22⋊D11)⋊C8—21no—
44#10622331—21no—
45C4×#4314C2211yescharacteristic
46#10622301C2211yescharacteristic
47#10622298C2211yescharacteristic
48#10622298C2211yescharacteristic
49#10622298C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622096C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622093C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4341C2×C411yescharacteristic
68C2×#4339—21no—
69C2×C11×D8C2×C411yescharacteristic
70C2×C11×M16—21no—
71C22×C8×C11—21no—
72C4×D4×C11C2311yescharacteristic
73C4×D4×C11C2311yescharacteristic
74#66993C2×C411yescharacteristic
75#66991C2×C411yescharacteristic
76D4×Dic11C2×C411yescharacteristic
77C2×#4324C2×C411yescharacteristic
78C2×#4323C2×C411yescharacteristic
79C4×C22⋊D11—21no—
80C4×C22⋊D11—21no—
81C2×C4×Dic11—21no—
82C22×C11⋊C8—21no—
83C22×C11⋊C8—21no—
84C2×#4314C2×C411yescharacteristic
85C2×#4313—21no—
86C2×C8×D11—21no—
87C2×C8×D11—21no—
88#66948C2×C411yescharacteristic
89#66945C2×C411yescharacteristic
90#66941C2×C411yescharacteristic
91#66940C2×C411yescharacteristic
92#66938—21no—
93#66937—21no—
94(C22⋊D11)⋊C4—21no—
95#66930—21no—
96C4×D44C2311yescharacteristic
97C42×D11C2311yescharacteristic
98C4×Dic22C2311yescharacteristic
99C11×#107C2×C411yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×#102C2×C411yescharacteristic
103C11×#102C2×C411yescharacteristic
104C11×C22⋊C8—21no—
105C11×C22⋊C8—21no—
106C4×C8×C11C2311yescharacteristic
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109#66896C2×C411yescharacteristic
110#66896C2×C411yescharacteristic
111C22⋊(C11⋊C8)—21no—
112C22⋊(C11⋊C8)—21no—
113#66885C2×C411yescharacteristic
114(C2×D11)⋊C8—21no—
115(C2×D11)⋊C8—21no—
116(C2×D11)⋊C8—21no—
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8C2×C411yescharacteristic
119(C2×D11)⋊C8C2×C411yescharacteristic
120(C2×D11)⋊C8D411yescharacteristic
121(C2×D11)⋊C8D411yescharacteristic
122#66881C2×C411yescharacteristic
123#66880C2×C411yescharacteristic
124#66879—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127Dic11⋊C8—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8C2×C411yescharacteristic
130Dic11⋊C8C2×C411yescharacteristic
131Dic11⋊C8D411yescharacteristic
132Dic11⋊C8D411yescharacteristic
133C8×Dic11—21no—
134C8×Dic11—21no—
135#66874C2×C411yescharacteristic
136#66873C2×C411yescharacteristic
137#66872C2×C411yescharacteristic
138#66871C2×C411yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17920—111nomaximal, Sylow
145C2×D4×C11C22×C411yescharacteristic
146C2×D4×C11C22×C411yescharacteristic
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C2×C22⋊D11—21no—
150C2×C22⋊D11—21no—
151C2×C22⋊D11—21no—
152C2×C22⋊D11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155#4341—22no—
156#4341—22no—
157#4339—81no—
158#4339—81no—
159C2×D44—21no—
160C2×D44C22×C411yescharacteristic
161C2×C4×D11—21no—
162C2×C4×D11C22×C411yescharacteristic
163C2×C4×D11C2×D411yescharacteristic
164C2×C4×D11#4111yescharacteristic
165C2×Dic22—21no—
166C2×Dic22C22×C411yescharacteristic
167C11×D8—22no—
168C11×M16—81no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—81no—
173C2×C8×C11C22×C411yescharacteristic
174C2×C8×C11C22×C411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C11×C4⋊C4C22×C411yescharacteristic
178C11×C4⋊C4C22×C411yescharacteristic
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C42×C11C2411yescharacteristic
182C22⋊Dic11—21no—
183C22⋊Dic11—21no—
184#4324—22no—
185#4323—22no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189C4⋊Dic11C22×C411yescharacteristic
190C4⋊Dic11C22×C411yescharacteristic
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11C22×C411yescharacteristic
198C4×Dic11C2×D411yescharacteristic
199C4×Dic11#4111yescharacteristic
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—81no—
204C2×C11⋊C8—81no—
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209#4314—22no—
210#4313—81no—
211C8×D11—81no—
212C8×D11—81no—
213#3106—111no—
214#2988—111no—
215#2981—111no—
216#1588—111no—
217#1586D1111yescharacteristic, complemented
218#1583—111no—
219#1581—111no—
220#1580—111no—
221SD16⋊C8—111no—
222C8×SD16—111no—
223C8×D8—111no—
224#1573—111no—
225#1488—111no—
226#1480—111no—
227#1454—111no—
228C23×C11—21no—
229C23×C11—21no—
230C22×D11—21no—
231C22×D11C4×D411yescharacteristic
232D4×C11—21no—
233D4×C11—21no—
234D4×C11—21no—
235D4×C11#13112yes—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11C23×C411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C22⋊D11—24no—
246C22⋊D11—81no—
247C22⋊D11—81no—
248C22⋊D11—81no—
249C2×Dic11—24no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—81no—
254C2×Dic11C4×D411yescharacteristic
255C2×Dic11C4×D411yescharacteristic
256C2×Dic11C4×D411yescharacteristic
257D44—21no—
258D44—21no—
259D44—81no—
260C4×D11—21no—
261C4×D11—21no—
262C4×D11—21no—
263C4×D11—21no—
264C4×D11—41no—
265C4×D11—41no—
266C4×D11—41no—
267Dic22—21no—
268Dic22—81no—
269Dic22#13112yes—
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—41no—
275C8×C11—41no—
276C8×C11—41no—
277C11⋊C8—21no—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284#532—111no—
285C4×#41—111no—
286#482—111no—
287#482—111no—
288#477—111no—
289#476—111no—
290#460—111no—
291#459—111no—
292#449—111no—
293#449—111no—
294C8×Q8—111no—
295C8×Q8—111no—
296C4×SD16—111no—
297C4×SD16—111no—
298C4×D8—111no—
299C4×D8C2×D1111yescharacteristic
300#436—111no—
301#436C2×D1111yescharacteristic
302#435—221no—
303#435—221no—
304C8×D4—111no—
305C8×D4—111no—
306C8×D4—111no—
307C8×D4—221no—
308C8×D4—221no—
309C8×D4C2×D1111yescharacteristic
310#432—111no—
311#431—111no—
312#431—111no—
313#431—111no—
314#431—221no—
315C2×C4⋊C8—111no—
316C2×C4⋊C8—221no—
317#408—221no—
318#408—221no—
319#335—111no—
320#335—111no—
321#334—111no—
322#334C2×D1111yescharacteristic
323Q8⋊C8—111no—
324Q8⋊C8—111no—
325D4⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8C2×D1111yescharacteristic
330D4⋊C8C2×D1111yescharacteristic
331#322—111no—
332#322—111no—
333#322C2×D1111yescharacteristic
334C82—111no—
335C22×C11—22no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11C2×C4×D411yescharacteristic
342C2×D11—21no—
343C2×D11—21no—
344C2×D11—21no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—41no—
348C4×C11—21no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11C2×#13111yescharacteristic
352C4×C11C2×#13111yescharacteristic
353C4×C11#57611yescharacteristic
354C4×C11#57711yescharacteristic
355Dic11—22no—
356Dic11—21no—
357Dic11—21no—
358Dic11—21no—
359Dic11—41no—
360Dic11—41no—
361C2×#41—111no—
362C2×#41—221no—
363C2×SD16—111no—
364C2×SD16—111no—
365C2×D8—111no—
366C2×D8C4×D1111yescharacteristic
367C2×M16—21no—
368C2×M16—221no—
369C22×C8—21no—
370C22×C8—221no—
371C22×C8—221no—
372C22×C8—221no—
373C22×C8—221no—
374C4⋊Q8—111no—
375#127—111no—
376#124—221no—
377#121—111no—
378#121—111no—
379#121—221no—
380C4×Q8—111no—
381C4×Q8—111no—
382C4×D4—111no—
383C4×D4—111no—
384C4×D4—221no—
385C4×D4—221no—
386C4×D4—221no—
387C4×D4C22×D1111yescharacteristic
388C4×D4C22×D1111yescharacteristic
389#117—111no—
390#117—221no—
391C2×C42—111no—
392C2×C42—221no—
393#107—111no—
394#107C4×D1111yescharacteristic
395#106—111no—
396#106—111no—
397C4⋊C8—111no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—221no—
404C4⋊C8—221no—
405C4⋊C8—221no—
406C4⋊C8—221no—
407C4⋊C8C22×D1111yescharacteristic
408C4⋊C8C22×D1111yescharacteristic
409#103—111no—
410#103—111no—
411#102—111no—
412#102—111no—
413#102—111no—
414#102—111no—
415#102C4×D1111yescharacteristic
416#102C4×D1111yescharacteristic
417C22⋊C8—21no—
418C22⋊C8—21no—
419C22⋊C8—111no—
420C22⋊C8—111no—
421C22⋊C8—111no—
422C22⋊C8—111no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428C22⋊C8—221no—
429#97—221no—
430C4×C8—111no—
431C4×C8—111no—
432C4×C8—111no—
433C4×C8—221no—
434C4×C8—221no—
435C4×C8C22×D1111yescharacteristic
436C4×C8C22×D1111yescharacteristic
437C4×C8C22×D1111yescharacteristic
438C2×C11—42no—
439C2×C11—81no—
440C2×C11#292911yescharacteristic
441C2×C11#294611yescharacteristic
442C2×C11#295711yescharacteristic
443D11—41no—
444D11—81no—
445#41—222no—
446#41—222no—
447#41—881no—
448#41—881no—
449C2×Q8—111no—
450C2×Q8—221no—
451C2×D4—111no—
452C2×D4—221no—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4C2×C4×D1111yescharacteristic
458C2×D4C2×C4×D1111yescharacteristic
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—111no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—221no—
467SD16—222no—
468SD16—222no—
469D8—22no—
470D8—222no—
471M16—81no—
472M16—881no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—81no—
477C2×C8—111no—
478C2×C8—111no—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—881no—
485C2×C8—881no—
486C2×C8—881no—
487C2×C8—881no—
488C2×C8C2×C4×D1111yescharacteristic
489C2×C8C2×C4×D1111yescharacteristic
490C2×C8D4×D1111yescharacteristic
491C2×C8D4×D1111yescharacteristic
492C4⋊C4—111no—
493C4⋊C4—111no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4C2×C4×D1111yescharacteristic
498C4⋊C4C2×C4×D1111yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—221no—
502C22⋊C4—221no—
503C22⋊C4—221no—
504C22⋊C4—221no—
505C22⋊C4—221no—
506C42—111no—
507C42—111no—
508C42—111no—
509C42—221no—
510C42—221no—
511C42—221no—
512C42C23×D1111yescharacteristic
513C11#1792011yescharacteristic, complemented, Sylow
514C23—21no—
515C23—21no—
516C23—111no—
517C23—221no—
518Q8—112no—
519Q8—221no—
520Q8—881no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—224no—
525D4—221no—
526D4—221no—
527D4—881no—
528D4—881no—
529D4—881no—
530D4—881no—
531D4#6696012yes—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—111no—
539C2×C4—111no—
540C2×C4—111no—
541C2×C4—224no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—881no—
553C2×C4C22×C4×D1111yescharacteristic
554C2×C4C2×D4×D1111yescharacteristic
555C2×C4#41×D1111yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—221no—
564C8—221no—
565C8—221no—
566C8—221no—
567C8—441no—
568C8—441no—
569C8—441no—
570C22—22no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—221no—
577C22—221no—
578C22—221no—
579C22—441no—
580C22—441no—
581C22—441no—
582C22C4×D4×D1111yescharacteristic
583C4—21no—
584C4—41no—
585C4—41no—
586C4—221no—
587C4—221no—
588C4—222no—
589C4—221no—
590C4—441no—
591C4—441no—
592C4C2×#6696011yescharacteristic
593C4D11×#13111yescharacteristic
594C4#1062330511yescharacteristic
595C4#1062330611yescharacteristic
596C2—42no—
597C2—81no—
598C2—441no—
599C2—881no—
600C2#1307730711yescharacteristic
601C2#1307744511yescharacteristic
602C2#1307752811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1586C2
socleC22×C11C2×C4×D4
prime radical#13078672C2
cosocleC42×C11C24
hypercenter#1586D11
hypocenterC11#17920
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
2. #13077723C2semidirect
3. #13077693C2semidirect
4. #13067496C2semidirect
5. #13067457C2semidirect
6. #13067445C2semidirect
7. #13067437C2semidirect
8. #13067425C2semidirect
9. #13067415C2semidirect
10. D8×C11⋊C8C2semidirect
11. #13067398C2semidirect
12. #13067047C2semidirect
13. #13067013C2semidirect
14. #13066917C2semidirect
15. C11×#1586C2semidirect
217. #1586D11semidirect
513. C11#17920semidirect

Maximal subgroups

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

subgroupindex
#130786722
#130777232
#130776932
#130674962
#130674572
#130674452
#130674372
#130674252
#130674152
D8×C11⋊C82
#130673982
#130670472
#130670132
#130669172
C11×#15862
#1792011