Finite Group Databasebeta

← #14724878

Subgroups — #14724878

Order 2816.

660 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078676C211yesmaximal, characteristic
2#13077636C211yesmaximal, characteristic, complemented
3#13077359C211yesmaximal, characteristic, complemented
4#13067527C211yesmaximal, characteristic, complemented
5#13067498C211yesmaximal, characteristic, complemented
6#13067491C211yesmaximal, characteristic, complemented
7#13067483C211yesmaximal, characteristic, complemented
8#13067456C211yesmaximal, characteristic, complemented
9#13067448C211yesmaximal, characteristic, complemented
10#13067431C211yesmaximal, characteristic, complemented
11#13067413C211yesmaximal, characteristic, complemented
12#13067399C211yesmaximal, characteristic, complemented
13#13067086C211yesmaximal, characteristic, complemented
14#13066911C211yesmaximal, characteristic, complemented
15C11×#1477C211yesmaximal, characteristic, complemented
16C4×C11×#41C2211yescharacteristic
17C2×#66954—21no—
18#10623008C2211yescharacteristic
19C11×#431C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21#10622851C411yescharacteristic
22#10622851C411yescharacteristic
23#10622723—21no—
24#10622640C411yescharacteristic
25C4×#4325C2211yescharacteristic
26C4×#4325C2211yescharacteristic
27Q8×C11⋊C8C2211yescharacteristic
28Q8×C11⋊C8C2211yescharacteristic
29#10622634C411yescharacteristic
30#10622628C411yescharacteristic
31C4×#4323C2211yescharacteristic
32C4×#4323C2211yescharacteristic
33#10622625—21no—
34#10622625—21no—
35#10622625C2211yescharacteristic
36#10622625C2211yescharacteristic
37#10622621C411yescharacteristic
38#10622616C411yescharacteristic
39#10622616C411yescharacteristic
40#10622539—21no—
41#10622539C2211yescharacteristic
42#10622538C2211yescharacteristic
43C4×#4318—21no—
44C4×#4318C2211yescharacteristic
45#10622451C2211yescharacteristic
46#10622451C2211yescharacteristic
47#10622449—21no—
48#10622449—21no—
49#10622447C2211yescharacteristic
50#10622447C2211yescharacteristic
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—
69C22×C8×C11—21no—
70C4×Q8×C11C2×C411yescharacteristic
71C4×Q8×C11C2311yescharacteristic
72C4×D4×C11—21no—
73C4×D4×C11—21no—
74C4×D4×C11C2×C411yescharacteristic
75C4×D4×C11C2311yescharacteristic
76C11×#117—21no—
77C11×#117C2×C411yescharacteristic
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80C2×#4325C2×C411yescharacteristic
81C2×#4325C2×C411yescharacteristic
82C2×#4323C2×C411yescharacteristic
83C2×#4323C2×C411yescharacteristic
84#66983—21no—
85#66983C2×C411yescharacteristic
86#66983C2×C411yescharacteristic
87C2×#4318—21no—
88C2×#4318—21no—
89C2×#4318D411yescharacteristic
90C2×#4318D411yescharacteristic
91#66954—44no—
92C2×#4313—21no—
93C2×#4313—21no—
94C2×C8×D11—21no—
95C2×C8×D11—21no—
96#66928—21no—
97#66927C2×C411yescharacteristic
98C4×D44—21no—
99C4×D44C2311yescharacteristic
100C4×D44C2311yescharacteristic
101#66922C2×C411yescharacteristic
102C11×C4⋊C8—21no—
103C11×C4⋊C8—21no—
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×C22⋊C8—21no—
107C4×C8×C11C2311yescharacteristic
108C4×C8×C11C2311yescharacteristic
109#66899C2×C411yescharacteristic
110#66899C2×C411yescharacteristic
111#66896C2×C411yescharacteristic
112#66896C2×C411yescharacteristic
113C22⋊(C11⋊C8)—21no—
114C22⋊(C11⋊C8)—21no—
115C22⋊(C11⋊C8)—21no—
116C22⋊(C11⋊C8)C2×C411yescharacteristic
117C22⋊(C11⋊C8)C2×C411yescharacteristic
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122#66873C2×C411yescharacteristic
123#66873C2×C411yescharacteristic
124#66873C2×C411yescharacteristic
125#66873C2×C411yescharacteristic
126#66872C2×C411yescharacteristic
127#66872C2×C411yescharacteristic
128#66871C2×C411yescharacteristic
129#66871C2×C411yescharacteristic
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)C2×C411yescharacteristic
133C4⋊(C11⋊C8)C2×C411yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136#66867—21no—
137#66867D411yescharacteristic
138#66867D411yescharacteristic
139C4×C11⋊C8—21no—
140C4×C11⋊C8—21no—
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18011—111nomaximal, Sylow
146C11×#41—22no—
147C11×#41—41no—
148C2×Q8×C11C22×C411yescharacteristic
149C2×D4×C11—21no—
150C2×D4×C11C22×C411yescharacteristic
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11C22×C411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11#4111yescharacteristic
157C2×C22⋊D11—21no—
158C2×C22⋊D11—21no—
159#4339—42no—
160#4339—42no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44C22×C411yescharacteristic
164C2×D44C22×C411yescharacteristic
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×Dic22—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—42no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4C22×C411yescharacteristic
176C11×C4⋊C4C22×C411yescharacteristic
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11C22×C411yescharacteristic
184C42×C11C2×D411yescharacteristic
185C42×C11#4111yescharacteristic
186C42×C11C2411yescharacteristic
187#4325—22no—
188#4325—22no—
189#4323—41no—
190#4323—41no—
191(C2×D11)⋊C4—21no—
192(C2×D11)⋊C4—21no—
193(C2×D11)⋊C4—21no—
194(C2×D11)⋊C4—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11C22×C411yescharacteristic
197C4⋊Dic11C22×C411yescharacteristic
198#4318—22no—
199#4318—41no—
200#4318—42no—
201#4318—42no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212#4313—42no—
213#4313—42no—
214C8×D11—42no—
215C8×D11—42no—
216#3106—111no—
217#2971—111no—
218#2935—111no—
219#1594—111no—
220#1589—111no—
221#1588—111no—
222#1586—111no—
223#1583—111no—
224#1581—111no—
225SD16⋊C8—111no—
226C8×SD16—111no—
227#1573—111no—
228#1496—111no—
229#1477D1111yescharacteristic, complemented
230#1453—111no—
231C23×C11—21no—
232C23×C11C4×D411yescharacteristic
233C22×D11—21no—
234C22×D11—21no—
235Q8×C11—21no—
236Q8×C11#13112yescomplemented
237D4×C11—21no—
238D4×C11—21no—
239D4×C11—42no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
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—81no—
252C2×C4×C11C4×D411yescharacteristic
253C2×C4×C11C4×D411yescharacteristic
254C2×C4×C11C4×D411yescharacteristic
255C2×C4×C11C23×C411yescharacteristic
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C22⋊D11—42no—
259C22⋊D11—42no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262D44—21no—
263D44—21no—
264D44—21no—
265D44—21no—
266D44—42no—
267D44—81no—
268C4×D11—41no—
269C4×D11—41no—
270C4×D11—41no—
271C4×D11—41no—
272Dic22—42no—
273C8×C11—41no—
274C8×C11—41no—
275C8×C11—41no—
276C8×C11—41no—
277C11⋊C8—21no—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—21no—
283C11⋊C8—21no—
284C11⋊C8—41no—
285C11⋊C8—41no—
286C11⋊C8AGL(1,ℤ/8)12yes—
287C2×#131—221no—
288#532—111no—
289C4×#41C2×D1111yescharacteristic
290#482—111no—
291#482—111no—
292#477—111no—
293#476—111no—
294#460—111no—
295#459—111no—
296#449—111no—
297#449—111no—
298C8×Q8—111no—
299C8×Q8—111no—
300C4×SD16—111no—
301C4×SD16—111no—
302C4×D8—111no—
303C4×D8—111no—
304#436—111no—
305#436—111no—
306#436—111no—
307#436—111no—
308#436—221no—
309#436—221no—
310#435—221no—
311#435—221no—
312C8×D4—111no—
313C8×D4—111no—
314#432—111no—
315#432—221no—
316#431—111no—
317#431C2×D1111yescharacteristic
318C2×C4⋊C8C2×D1111yescharacteristic
319#408—221no—
320C4×M16—111no—
321C4×M16—221no—
322#335—111no—
323#335—111no—
324#334—111no—
325#334—111no—
326Q8⋊C8C2×D1111yescharacteristic
327Q8⋊C8C2×D1111yescharacteristic
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331D4⋊C8—111no—
332D4⋊C8C2×D1111yescharacteristic
333D4⋊C8C2×D1111yescharacteristic
334#322—111no—
335#322—111no—
336#322—111no—
337C82—111no—
338C22×C11—21no—
339C22×C11—21no—
340C22×C11—21no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11C2×C4×D411yescharacteristic
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—41no—
350C2×D11—41no—
351C4×C11—21no—
352C4×C11—22no—
353C4×C11—21no—
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11C2×#13111yescharacteristic
359C4×C11#56811yescharacteristic
360C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
361C4×C11#57511yescharacteristic
362Dic11—41no—
363Dic11—41no—
364C2×#41—221no—
365C2×#41C4×D1111yescharacteristic
366C2×SD16—111no—
367C2×SD16—111no—
368C2×D8—111no—
369C2×D8—111no—
370#131—444no—
371C2×M16—111no—
372C2×M16—111no—
373C2×M16—221no—
374C2×M16—221no—
375C2×M16—221no—
376C2×M16—221no—
377C22×C8—21no—
378C22×C8—221no—
379C22×C8—221no—
380C4⋊Q8—111no—
381#127—111no—
382#124—221no—
383#121—111no—
384#121—111no—
385#121—221no—
386C4×Q8C4×D1111yescharacteristic
387C4×Q8C22×D1111yescharacteristic
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—111no—
391C4×D4—111no—
392C4×D4—221no—
393C4×D4C4×D1111yescharacteristic
394C4×D4C22×D1111yescharacteristic
395#117—21no—
396#117C4×D1111yescharacteristic
397C2×C42—21no—
398C2×C42C22×D1111yescharacteristic
399#107—111no—
400#107—111no—
401#106—111no—
402#106—111no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—111no—
409C4⋊C8—221no—
410C4⋊C8—221no—
411C4⋊C8C22×D1111yescharacteristic
412C4⋊C8C22×D1111yescharacteristic
413#103—111no—
414#103—111no—
415#102—111no—
416#102—111no—
417#102—111no—
418#102—111no—
419#102—111no—
420#102—111no—
421C22⋊C8—21no—
422C22⋊C8—111no—
423C22⋊C8—111no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428C22⋊C8—221no—
429C22⋊C8—221no—
430C22⋊C8—221no—
431#97—111no—
432#97—111no—
433#97—221no—
434C4×C8—111no—
435C4×C8—111no—
436C4×C8—111no—
437C4×C8—111no—
438C4×C8—221no—
439C4×C8—221no—
440C4×C8C22×D1111yescharacteristic
441C4×C8C22×D1111yescharacteristic
442C2×C11—41no—
443C2×C11—81no—
444C2×C11#293311yescharacteristic
445C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
446C2×C11#295711yescharacteristic
447D11—81no—
448D11—81no—
449#41—22no—
450#41—41no—
451#41—442no—
452#41—442no—
453C2×Q8—221no—
454C2×Q8C2×C4×D1111yescharacteristic
455C2×D4—21no—
456C2×D4—111no—
457C2×D4—111no—
458C2×D4—221no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—221no—
462C2×D4C2×C4×D1111yescharacteristic
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4C2×C4×D1111yescharacteristic
469C22×C4D4×D1111yescharacteristic
470C22×C4#434111yescharacteristic
471SD16—222no—
472SD16—222no—
473D8—441no—
474D8—441no—
475M16—222no—
476M16—442no—
477M16—442no—
478M16—442no—
479M16—441no—
480M16—442no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—42no—
486C2×C8—111no—
487C2×C8—111no—
488C2×C8—111no—
489C2×C8—111no—
490C2×C8—111no—
491C2×C8—111no—
492C2×C8—111no—
493C2×C8—111no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—442no—
497C2×C8—442no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—111no—
501C4⋊C4—111no—
502C4⋊C4—221no—
503C4⋊C4C2×C4×D1111yescharacteristic
504C4⋊C4C2×C4×D1111yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—221no—
509C22⋊C4—221no—
510C22⋊C4—221no—
511C22⋊C4—221no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42C2×C4×D1111yescharacteristic
516C42D4×D1111yescharacteristic
517C42#434111yescharacteristic
518C42C23×D1111yescharacteristic
519C11#1801111yescharacteristic, complemented, Sylow
520C23—21no—
521C23—221no—
522C23—221no—
523C23(C22⋊D11)⋊C411yescharacteristic
524Q8—21no—
525Q8—442no—
526Q8#6695412yescomplemented
527D4—21no—
528D4—21no—
529D4—42no—
530D4—221no—
531D4—221no—
532D4—221no—
533D4—221no—
534D4—442no—
535D4—442no—
536D4—442no—
537D4—881no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—81no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4(C22⋊D11)⋊C411yescharacteristic
557C2×C4(C22⋊D11)⋊C411yescharacteristic
558C2×C4(C22⋊D11)⋊C411yescharacteristic
559C2×C4C22×C4×D1111yescharacteristic
560C2×C4C2×D4×D1111yescharacteristic
561C2×C4C2×#434111yescharacteristic
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—112no—
567C8—221no—
568C8—221no—
569C8—221no—
570C8—221no—
571C8—221no—
572C8—221no—
573C8—221no—
574C8—441no—
575C8—441no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—441no—
583C22—441no—
584C22—441no—
585C22—441no—
586C22—441no—
587C22—441no—
588C22C2×(C22⋊D11)⋊C411yescharacteristic
589C4—21no—
590C4—21no—
591C4—21no—
592C4—22no—
593C4—21no—
594C4—41no—
595C4—41no—
596C4—441no—
597C4—441no—
598C4C2×#6695411yescharacteristic
599C4#1062327611yescharacteristic
600C4D11×AGL(1,ℤ/8)11yescharacteristic
601C4#1062330811yescharacteristic
602C2—41no—
603C2—81no—
604C2—881no—
605C2—881no—
606C2#1307733711yescharacteristic
607C2#1307742911yescharacteristic
608C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1477C2
socleC22×C11C2×C4×D4
prime radical#13078676C2
cosocleC42×C11C24
hypercenter#1477D11
hypocenterC11#18011
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1477

Complements

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

NH ≅ G/Ntype
2. #13077636C2semidirect
3. #13077359C2semidirect
4. #13067527C2semidirect
5. #13067498C2semidirect
6. #13067491C2semidirect
7. #13067483C2semidirect
8. #13067456C2semidirect
9. #13067448C2semidirect
10. #13067431C2semidirect
11. #13067413C2semidirect
12. #13067399C2semidirect
13. #13067086C2semidirect
14. #13066911C2semidirect
15. C11×#1477C2semidirect
229. #1477D11semidirect
236. Q8×C11#131semidirect
519. C11#18011semidirect
526. Q8#66954semidirect

Maximal subgroups

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

subgroupindex
#130786762
#130776362
#130773592
#130675272
#130674982
#130674912
#130674832
#130674562
#130674482
#130674312
#130674132
#130673992
#130670862
#130669112
C11×#14772
#1801111