Finite Group Databasebeta

← #14724181

Subgroups — #14724181

Order 2816.

608 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#13078676C211yesmaximal, characteristic
2#13077733C211yesmaximal, characteristic, complemented
3#13077694C211yesmaximal, characteristic, complemented
4#13067527C211yesmaximal, characteristic, complemented
5#13067521C211yesmaximal, characteristic, complemented
6#13067503C211yesmaximal, characteristic, complemented
7#13067498C211yesmaximal, characteristic, complemented
8#13067483C211yesmaximal, characteristic, complemented
9#13067476C211yesmaximal, characteristic, complemented
10#13067455C211yesmaximal, characteristic, complemented
11#13067448C211yesmaximal, characteristic, complemented
12#13067402C211yesmaximal, characteristic, complemented
13#13067016C211yesmaximal, characteristic, complemented
14#13066916C211yesmaximal, characteristic, complemented
15C11×#1488C211yesmaximal, characteristic, complemented
16C4×C11×#41C2211yescharacteristic
17#10623008C2211yescharacteristic
18C11×#432C2211yescharacteristic
19C11×#431C2211yescharacteristic
20#10622851C411yescharacteristic
21#10622851C411yescharacteristic
22#10622640C411yescharacteristic
23C4×#4325C2211yescharacteristic
24C4×#4325C2211yescharacteristic
25#10622637C2211yescharacteristic
26#10622637C2211yescharacteristic
27#10622634C411yescharacteristic
28#10622628C411yescharacteristic
29C4×#4323C2211yescharacteristic
30C4×#4323C2211yescharacteristic
31#10622625C2211yescharacteristic
32#10622625C2211yescharacteristic
33#10622624—21no—
34#10622624—21no—
35#10622621C411yescharacteristic
36#10622616C411yescharacteristic
37#10622616C411yescharacteristic
38#10622539—21no—
39#10622538C2211yescharacteristic
40#10622538C2211yescharacteristic
41#10622537—21no—
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43#10622451C2211yescharacteristic
44#10622451C2211yescharacteristic
45#10622447C2211yescharacteristic
46#10622447C2211yescharacteristic
47#10622340—21no—
48#10622340—21no—
49#10622319—21no—
50#10622319—21no—
51C11×Q8⋊C8C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×D4⋊C8C2211yescharacteristic
55#10622118C2211yescharacteristic
56#10622118C2211yescharacteristic
57#10622117C2211yescharacteristic
58#10622117C2211yescharacteristic
59#10622097C2211yescharacteristic
60#10622097C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×#41C2×C411yescharacteristic
68C2×#4339—21no—
69C4×Q8×C11C2×C411yescharacteristic
70C4×Q8×C11C2311yescharacteristic
71C4×D4×C11—21no—
72C4×D4×C11—21no—
73C4×D4×C11C2×C411yescharacteristic
74C4×D4×C11C2311yescharacteristic
75C11×#117—21no—
76C11×#117C2×C411yescharacteristic
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C2×#4325C2×C411yescharacteristic
80C2×#4325C2×C411yescharacteristic
81C2×#4323C2×C411yescharacteristic
82C2×#4323C2×C411yescharacteristic
83#66983—21no—
84#66983C2×C411yescharacteristic
85#66983C2×C411yescharacteristic
86C2×#4318—21no—
87C2×#4318—21no—
88C22×C11⋊C8—21no—
89C2×#4313—21no—
90C2×#4313—21no—
91C2×C8×D11—21no—
92C2×C8×D11—21no—
93#66928—21no—
94#66927C2×C411yescharacteristic
95C4×D44—21no—
96C4×D44C2311yescharacteristic
97C4×D44C2311yescharacteristic
98#66922C2×C411yescharacteristic
99C11×C4⋊C8—21no—
100C11×C4⋊C8C2311yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×C22⋊C8—21no—
103C11×C22⋊C8—21no—
104C11×#97—21no—
105C4×C8×C11C2311yescharacteristic
106C4×C8×C11C2311yescharacteristic
107#66899C2×C411yescharacteristic
108#66899C2×C411yescharacteristic
109#66896C2×C411yescharacteristic
110#66896C2×C411yescharacteristic
111C22⋊(C11⋊C8)—21no—
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)C2×C411yescharacteristic
114C22⋊(C11⋊C8)C2×C411yescharacteristic
115C22⋊(C11⋊C8)D411yescharacteristic
116C22⋊(C11⋊C8)D411yescharacteristic
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121#66873C2×C411yescharacteristic
122#66873C2×C411yescharacteristic
123#66873C2×C411yescharacteristic
124#66873C2×C411yescharacteristic
125#66872C2×C411yescharacteristic
126#66872C2×C411yescharacteristic
127#66871C2×C411yescharacteristic
128#66871C2×C411yescharacteristic
129C4⋊(C11⋊C8)—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)C2×C411yescharacteristic
133C4⋊(C11⋊C8)C2×C411yescharacteristic
134C4⋊(C11⋊C8)D411yescharacteristic
135C4⋊(C11⋊C8)D411yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138#66867—21no—
139#66867—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17948—111nomaximal, Sylow
145C11×#41—41no—
146C11×#41—41no—
147C2×Q8×C11C22×C411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11C22×C411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C2×C22⋊D11—21no—
157C2×C22⋊D11—21no—
158#4339—81no—
159#4339—81no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44C22×C411yescharacteristic
163C2×D44C22×C411yescharacteristic
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×Dic22—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4C22×C411yescharacteristic
174C11×C4⋊C4C22×C411yescharacteristic
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11C22×C411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11#4111yescharacteristic
184C42×C11C2411yescharacteristic
185#4325—41no—
186#4325—41no—
187#4323—41no—
188#4323—41no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191(C2×D11)⋊C4—21no—
192(C2×D11)⋊C4—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11C22×C411yescharacteristic
195C4⋊Dic11C22×C411yescharacteristic
196#4318—81no—
197#4318—81no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—81no—
201C2×C11⋊C8C22×C411yescharacteristic
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209#4313—81no—
210#4313—81no—
211C8×D11—81no—
212C8×D11—81no—
213#3106—111no—
214#2989—111no—
215#2981—111no—
216#1594—111no—
217#1592—111no—
218#1590—111no—
219#1589—111no—
220#1586—111no—
221#1585—111no—
222#1582—111no—
223#1581—111no—
224#1573—111no—
225#1488D1111yescharacteristic, complemented
226#1480—111no—
227#1454—111no—
228C23×C11—21no—
229C23×C11C4×D411yescharacteristic
230C22×D11—21no—
231C22×D11—21no—
232Q8×C11—21no—
233Q8×C11—21no—
234D4×C11—21no—
235D4×C11—21no—
236D4×C11—42no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11—42no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—81no—
249C2×C4×C11C4×D411yescharacteristic
250C2×C4×C11C4×D411yescharacteristic
251C2×C4×C11C4×D411yescharacteristic
252C2×C4×C11C23×C411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C22⋊D11—81no—
256C22⋊D11—81no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259D44—21no—
260D44—21no—
261D44—21no—
262D44—21no—
263D44—81no—
264D44—81no—
265C4×D11—41no—
266C4×D11—41no—
267C4×D11—41no—
268C4×D11—41no—
269Dic22—81no—
270C8×C11—41no—
271C8×C11—41no—
272C8×C11—41no—
273C8×C11—41no—
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—21no—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284#532—111no—
285C4×#41C2×D1111yescharacteristic
286#482—111no—
287#482—111no—
288#477—111no—
289#476—111no—
290#460—111no—
291#459—111no—
292#449—111no—
293#449—111no—
294#446—111no—
295#446—111no—
296C4×SD16—111no—
297C4×SD16—111no—
298C4×D8—111no—
299C4×D8—111no—
300#436—111no—
301#436—111no—
302#436—111no—
303#436—111no—
304#435—221no—
305#435—221no—
306#435—221no—
307#435—221no—
308C8×D4—111no—
309C8×D4—111no—
310#432—221no—
311#432C2×D1111yescharacteristic
312#431—111no—
313#431—111no—
314#431C2×D1111yescharacteristic
315#423—221no—
316C2×C4⋊C8—111no—
317#408—221no—
318#408—221no—
319#335—111no—
320#335—111no—
321#334—111no—
322#334—111no—
323Q8⋊C8C2×D1111yescharacteristic
324Q8⋊C8C2×D1111yescharacteristic
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#322—111no—
334C82—111no—
335C22×C11—21no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11C2×C4×D411yescharacteristic
342C2×D11—41no—
343C2×D11—41no—
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—41no—
348C4×C11—21no—
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11#56811yescharacteristic
356C4×C11#56811yescharacteristic
357C4×C11#57611yescharacteristic
358C4×C11#57711yescharacteristic
359Dic11—41no—
360Dic11—41no—
361C2×#41—221no—
362C2×#41C4×D1111yescharacteristic
363C2×SD16—111no—
364C2×SD16—111no—
365C2×D8—111no—
366C2×D8—111no—
367C2×M16—221no—
368C2×M16—221no—
369C2×M16—221no—
370C2×M16—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×Q8C4×D1111yescharacteristic
381C4×Q8C22×D1111yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—111no—
385C4×D4—111no—
386C4×D4—221no—
387C4×D4C4×D1111yescharacteristic
388C4×D4C22×D1111yescharacteristic
389#117—21no—
390#117C4×D1111yescharacteristic
391C2×C42—21no—
392C2×C42C22×D1111yescharacteristic
393#107—111no—
394#107—111no—
395#106—111no—
396#106—111no—
397C4⋊C8—21no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—111no—
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#102—111no—
416#102—111no—
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—21no—
430#97—221no—
431#97—221no—
432C4×C8—111no—
433C4×C8—111no—
434C4×C8—111no—
435C4×C8—111no—
436C4×C8C22×D1111yescharacteristic
437C4×C8C22×D1111yescharacteristic
438C2×C11—41no—
439C2×C11—81no—
440C2×C11#293011yescharacteristic
441C2×C11#294611yescharacteristic
442C2×C11#295711yescharacteristic
443D11—81no—
444D11—81no—
445#41—41no—
446#41—41no—
447#41—881no—
448#41—881no—
449C2×Q8—221no—
450C2×Q8C2×C4×D1111yescharacteristic
451C2×D4—21no—
452C2×D4—111no—
453C2×D4—111no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4C2×C4×D1111yescharacteristic
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4C2×C4×D1111yescharacteristic
465C22×C4D4×D1111yescharacteristic
466C22×C4#434111yescharacteristic
467SD16—441no—
468SD16—441no—
469D8—441no—
470D8—441no—
471M16—881no—
472M16—881no—
473M16—881no—
474M16—881no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—111no—
482C2×C8—111no—
483C2×C8—111no—
484C2×C8—111no—
485C2×C8—111no—
486C2×C8—111no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—881no—
490C2×C8—881no—
491C2×C8—881no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—111no—
495C4⋊C4—111no—
496C4⋊C4—221no—
497C4⋊C4C2×C4×D1111yescharacteristic
498C4⋊C4C2×C4×D1111yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—221no—
503C22⋊C4—221no—
504C22⋊C4—221no—
505C22⋊C4—221no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42C2×C4×D1111yescharacteristic
510C42D4×D1111yescharacteristic
511C42#434111yescharacteristic
512C42C23×D1111yescharacteristic
513C11#1794811yescharacteristic, complemented, Sylow
514C23—21no—
515C23—221no—
516C23—221no—
517C23(C22⋊D11)⋊C411yescharacteristic
518Q8—21no—
519Q8—21no—
520Q8—881no—
521D4—21no—
522D4—21no—
523D4—42no—
524D4—221no—
525D4—221no—
526D4—221no—
527D4—221no—
528D4—881no—
529D4—881no—
530D4—881no—
531D4—881no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—81no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4(C22⋊D11)⋊C411yescharacteristic
551C2×C4(C22⋊D11)⋊C411yescharacteristic
552C2×C4(C22⋊D11)⋊C411yescharacteristic
553C2×C4C22×C4×D1111yescharacteristic
554C2×C4C2×D4×D1111yescharacteristic
555C2×C4C2×#434111yescharacteristic
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—221no—
561C8—221no—
562C8—221no—
563C8—221no—
564C8—221no—
565C8—221no—
566C8—221no—
567C8—221no—
568C8—441no—
569C8—441no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—441no—
577C22—441no—
578C22—441no—
579C22—441no—
580C22—441no—
581C22—441no—
582C22C2×(C22⋊D11)⋊C411yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—441no—
591C4—441no—
592C4#1062327611yescharacteristic
593C4#1062327611yescharacteristic
594C4#1062330011yescharacteristic
595C4#1062330111yescharacteristic
596C2—41no—
597C2—81no—
598C2—881no—
599C2—881no—
600C2#1307731511yescharacteristic
601C2#1307745111yescharacteristic
602C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1488C2
socleC22×C11C2×C4×D4
prime radical#13078676C2
cosocleC42×C11C24
hypercenter#1488D11
hypocenterC11#17948
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1488

Complements

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

NH ≅ G/Ntype
2. #13077733C2semidirect
3. #13077694C2semidirect
4. #13067527C2semidirect
5. #13067521C2semidirect
6. #13067503C2semidirect
7. #13067498C2semidirect
8. #13067483C2semidirect
9. #13067476C2semidirect
10. #13067455C2semidirect
11. #13067448C2semidirect
12. #13067402C2semidirect
13. #13067016C2semidirect
14. #13066916C2semidirect
15. C11×#1488C2semidirect
225. #1488D11semidirect
513. C11#17948semidirect

Maximal subgroups

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

subgroupindex
#130786762
#130777332
#130776942
#130675272
#130675212
#130675032
#130674982
#130674832
#130674762
#130674552
#130674482
#130674022
#130670162
#130669162
C11×#14882
#1794811