Finite Group Databasebeta

← #14724887

Subgroups — #14724887

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#13078674C211yesmaximal, characteristic
2#13077635C211yesmaximal, characteristic, complemented
3#13077361C211yesmaximal, characteristic, complemented
4#13067528C211yesmaximal, characteristic, complemented
5#13067500C211yesmaximal, characteristic, complemented
6#13067482C211yesmaximal, characteristic, complemented
7#13067456C211yesmaximal, characteristic, complemented
8#13067442C211yesmaximal, characteristic, complemented
9#13067426C211yesmaximal, characteristic, complemented
10SD16×C11⋊C8C211yesmaximal, characteristic, complemented
11#13067400C211yesmaximal, characteristic, complemented
12#13067083C211yesmaximal, characteristic, complemented
13#13067002C211yesmaximal, characteristic, complemented
14#13066912C211yesmaximal, characteristic, complemented
15C11×#1588C211yesmaximal, characteristic, complemented
16C2×#66960—21no—
17C4×#4343C2211yescharacteristic
18#10623079C2211yescharacteristic
19C8×Q8×C11C2211yescharacteristic
20C4×C11×SD16C2211yescharacteristic
21C11×#436C2211yescharacteristic
22#10622785C411yescharacteristic
23#10622776C411yescharacteristic
24#10622740—21no—
25C4×#4325C2211yescharacteristic
26Q8×C11⋊C8C2211yescharacteristic
27C4×#4323C2211yescharacteristic
28D4×C11⋊C8C2211yescharacteristic
29#10622483C411yescharacteristic
30#10622479C411yescharacteristic
31#10622451—21no—
32#10622451C2211yescharacteristic
33#10622451C2211yescharacteristic
34#10622448—21no—
35#10622448C2211yescharacteristic
36D11×C4⋊C8C2211yescharacteristic
37#10622424C411yescharacteristic
38#10622407C411yescharacteristic
39#10622399C411yescharacteristic
40#10622397C411yescharacteristic
41#10622343—21no—
42#10622340—21no—
43C4×D88C2211yescharacteristic
44#10622301—21no—
45#10622301C2211yescharacteristic
46C4×#4313—21no—
47C4×#4313C2211yescharacteristic
48C8×D44C2211yescharacteristic
49#10622298C2211yescharacteristic
50#10622298C2211yescharacteristic
51C11×#335C2211yescharacteristic
52C11×Q8⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55Q8⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic
63#10622095C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4343C2×C411yescharacteristic
68C2×#4339—21no—
69C2×C11×SD16C2×C411yescharacteristic
70C2×C11×M16—21no—
71C4×Q8×C11C2311yescharacteristic
72C4×D4×C11C2311yescharacteristic
73Q8×Dic11C2×C411yescharacteristic
74C2×#4325C2×C411yescharacteristic
75#66993C2×C411yescharacteristic
76#66991C2×C411yescharacteristic
77C2×#4323C2×C411yescharacteristic
78C4×C22⋊D11—21no—
79C22×C11⋊C8—21no—
80#66960—44no—
81C2×D88C2×C411yescharacteristic
82C2×#4313—21no—
83C2×#4313—21no—
84C2×#4313—21no—
85C2×#4313D411yescharacteristic
86C2×#4313D411yescharacteristic
87C2×C8×D11—21no—
88C2×C8×D11—21no—
89#66948C2×C411yescharacteristic
90#66946—21no—
91#66946C2×C411yescharacteristic
92#66945—21no—
93#66945C2×C411yescharacteristic
94#66941C2×C411yescharacteristic
95#66938—21no—
96#66937—21no—
97C4×D44—21no—
98C4×D44C2311yescharacteristic
99C4×D44C2311yescharacteristic
100C42×D11—21no—
101C42×D11C2311yescharacteristic
102C11×#106C2×C411yescharacteristic
103C11×C4⋊C8—21no—
104C11×C4⋊C8C2311yescharacteristic
105C11×C4⋊C8C2311yescharacteristic
106C11×#103C2×C411yescharacteristic
107C11×#102C2×C411yescharacteristic
108C11×C22⋊C8—21no—
109C4×C8×C11—21no—
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113#66899C2×C411yescharacteristic
114#66896C2×C411yescharacteristic
115C22⋊(C11⋊C8)—21no—
116#66885C2×C411yescharacteristic
117#66885C2×C411yescharacteristic
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8—21no—
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8C2×C411yescharacteristic
125(C2×D11)⋊C8C2×C411yescharacteristic
126#66882C2×C411yescharacteristic
127#66879—21no—
128#66879D411yescharacteristic
129#66879D411yescharacteristic
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8C2×C411yescharacteristic
133Dic11⋊C8C2×C411yescharacteristic
134#66873C2×C411yescharacteristic
135#66873C2×C411yescharacteristic
136#66872C2×C411yescharacteristic
137#66871C2×C411yescharacteristic
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18011—111nomaximal, Sylow
146C2×Q8×C11C22×C411yescharacteristic
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C2×C22⋊D11—21no—
150C2×C22⋊D11—21no—
151C2×C22⋊D11—21no—
152#4343—22no—
153#4343—41no—
154#4339—42no—
155#4339—42no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44C22×C411yescharacteristic
159C2×D44C22×C411yescharacteristic
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11C22×C411yescharacteristic
165C2×C4×D11C2×D411yescharacteristic
166C2×C4×D11#4111yescharacteristic
167C2×Dic22—21no—
168C11×SD16—22no—
169C11×M16—42no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11C22×C411yescharacteristic
174C2×C8×C11C22×C411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C11×C4⋊C4—21no—
178C11×C4⋊C4C22×C411yescharacteristic
179C11×C4⋊C4C22×C411yescharacteristic
180C11×C22⋊C4—21no—
181C42×C11—21no—
182C42×C11C2411yescharacteristic
183C22⋊Dic11—21no—
184#4325—22no—
185#4323—41no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11C22×C411yescharacteristic
193C4⋊Dic11C22×C411yescharacteristic
194Dic11⋊C4—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—42no—
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208D88—41no—
209#4313—22no—
210#4313—41no—
211#4313—42no—
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#1588D1111yescharacteristic, complemented
222#1586—111no—
223#1583—111no—
224#1581—111no—
225SD16⋊C8—111no—
226C8×SD16—111no—
227#1573—111no—
228#1496—111no—
229#1477—111no—
230#1453—111no—
231C23×C11—21no—
232C22×D11—21no—
233C22×D11—21no—
234C22×D11C4×D411yescharacteristic
235Q8×C11—21no—
236Q8×C11#13112yescomplemented
237D4×C11—21no—
238D4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11C23×C411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C22⋊D11—42no—
248C22⋊D11—42no—
249C22⋊D11—81no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11C4×D411yescharacteristic
253C2×Dic11C4×D411yescharacteristic
254C2×Dic11C4×D411yescharacteristic
255D44—21no—
256D44—21no—
257D44—21no—
258D44—21no—
259D44—42no—
260D44—42no—
261C4×D11—21no—
262C4×D11—21no—
263C4×D11—21no—
264C4×D11—21no—
265C4×D11—41no—
266C4×D11—42no—
267C4×D11—41no—
268C4×D11—41no—
269C4×D11—41no—
270C4×D11—41no—
271C4×D11—81no—
272Dic22—42no—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—21no—
276C8×C11—21no—
277C8×C11—41no—
278C8×C11—41no—
279C8×C11—41no—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—21no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C11⋊C8—41no—
286C11⋊C8AGL(1,ℤ/8)12yes—
287C2×#131—221no—
288#532—111no—
289C4×#41—111no—
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×Q8C2×D1111yescharacteristic
300C4×SD16—111no—
301C4×SD16C2×D1111yescharacteristic
302C4×D8—111no—
303C4×D8—111no—
304#436—111no—
305#436—111no—
306#436—111no—
307#436—221no—
308#436—221no—
309#436C2×D1111yescharacteristic
310#435—221no—
311#435—221no—
312C8×D4—111no—
313C8×D4—111no—
314#432—111no—
315#432—221no—
316#431—111no—
317#431—111no—
318C2×C4⋊C8—111no—
319#408—221no—
320C4×M16—111no—
321C4×M16—221no—
322#335—111no—
323#335C2×D1111yescharacteristic
324#334—111no—
325#334—111no—
326Q8⋊C8—111no—
327Q8⋊C8C2×D1111yescharacteristic
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331D4⋊C8—111no—
332D4⋊C8—111no—
333D4⋊C8C2×D1111yescharacteristic
334#322—111no—
335#322—111no—
336#322C2×D1111yescharacteristic
337C82—111no—
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—
348C2×D11—41no—
349C2×D11—41no—
350C2×D11—41no—
351C4×C11—22no—
352C4×C11—21no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11C2×#13111yescharacteristic
356C4×C11#56811yescharacteristic
357C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
358C4×C11#57511yescharacteristic
359Dic11—21no—
360Dic11—21no—
361Dic11—21no—
362Dic11—41no—
363Dic11—41no—
364C2×#41—111no—
365C2×#41—221no—
366C2×SD16—111no—
367C2×SD16C4×D1111yescharacteristic
368C2×D8—111no—
369C2×D8—111no—
370#131—444no—
371C2×M16—21no—
372C2×M16—111no—
373C2×M16—111no—
374C2×M16—221no—
375C2×M16—221no—
376C2×M16—221no—
377C22×C8—221no—
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×Q8—111no—
387C4×Q8C22×D1111yescharacteristic
388C4×D4—111no—
389C4×D4—111no—
390C4×D4—111no—
391C4×D4—221no—
392C4×D4—221no—
393C4×D4—221no—
394C4×D4C22×D1111yescharacteristic
395#117—111no—
396#117—221no—
397C2×C42—111no—
398C2×C42—221no—
399#107—111no—
400#107—111no—
401#106—111no—
402#106C4×D1111yescharacteristic
403C4⋊C8—21no—
404C4⋊C8—111no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—221no—
409C4⋊C8—221no—
410C4⋊C8—221no—
411C4⋊C8C22×D1111yescharacteristic
412C4⋊C8C22×D1111yescharacteristic
413#103—111no—
414#103C4×D1111yescharacteristic
415#102—111no—
416#102—111no—
417#102—111no—
418#102—111no—
419#102—111no—
420#102C4×D1111yescharacteristic
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—21no—
435C4×C8—111no—
436C4×C8—111no—
437C4×C8—111no—
438C4×C8—221no—
439C4×C8C22×D1111yescharacteristic
440C4×C8C22×D1111yescharacteristic
441C4×C8C22×D1111yescharacteristic
442C2×C11—81no—
443C2×C11#293311yescharacteristic
444C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
445C2×C11#295711yescharacteristic
446D11—41no—
447D11—81no—
448D11—81no—
449#41—222no—
450#41—442no—
451#41—442no—
452#41—441no—
453C2×Q8—221no—
454C2×Q8C2×C4×D1111yescharacteristic
455C2×D4—111no—
456C2×D4—111no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—221no—
462C2×D4C2×C4×D1111yescharacteristic
463C22×C4—21no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—221no—
471SD16—22no—
472SD16—222no—
473D8—441no—
474D8—441no—
475M16—42no—
476M16—222no—
477M16—441no—
478M16—442no—
479M16—442no—
480M16—442no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—111no—
485C2×C8—111no—
486C2×C8—111no—
487C2×C8—111no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—442no—
492C2×C8—442no—
493C2×C8—442no—
494C2×C8C2×C4×D1111yescharacteristic
495C2×C8C2×C4×D1111yescharacteristic
496C2×C8D4×D1111yescharacteristic
497C2×C8D4×D1111yescharacteristic
498C4⋊C4—21no—
499C4⋊C4—111no—
500C4⋊C4—111no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4C2×C4×D1111yescharacteristic
504C4⋊C4C2×C4×D1111yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—221no—
507C22⋊C4—221no—
508C22⋊C4—221no—
509C22⋊C4—221no—
510C22⋊C4—221no—
511C22⋊C4—221no—
512C42—21no—
513C42—111no—
514C42—111no—
515C42—111no—
516C42—221no—
517C42—221no—
518C42C23×D1111yescharacteristic
519C11#1801111yescharacteristic, complemented, Sylow
520C23—21no—
521C23—111no—
522C23—221no—
523C23—221no—
524Q8—21no—
525Q8—442no—
526Q8#6696012yescomplemented
527D4—21no—
528D4—21no—
529D4—221no—
530D4—221no—
531D4—221no—
532D4—221no—
533D4—442no—
534D4—442no—
535D4—442no—
536D4—442no—
537D4—881no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—111no—
544C2×C4—111no—
545C2×C4—111no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—441no—
553C2×C4—442no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—881no—
559C2×C4C22×C4×D1111yescharacteristic
560C2×C4C2×D4×D1111yescharacteristic
561C2×C4#41×D1111yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—41no—
567C8—41no—
568C8—41no—
569C8—112no—
570C8—221no—
571C8—221no—
572C8—221no—
573C8—441no—
574C8—441no—
575C8—441no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—221no—
580C22—221no—
581C22—221no—
582C22—441no—
583C22—441no—
584C22—441no—
585C22—441no—
586C22—441no—
587C22—441no—
588C22C4×D4×D1111yescharacteristic
589C4—21no—
590C4—22no—
591C4—41no—
592C4—41no—
593C4—221no—
594C4—221no—
595C4—221no—
596C4—441no—
597C4—441no—
598C4C2×#6696011yescharacteristic
599C4#1062328111yescharacteristic
600C4D11×AGL(1,ℤ/8)11yescharacteristic
601C4#1062330811yescharacteristic
602C2—81no—
603C2—441no—
604C2—881no—
605C2—881no—
606C2#1307734211yescharacteristic
607C2#1307742111yescharacteristic
608C2#1307752811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1588C2
socleC22×C11C2×C4×D4
prime radical#13078674C2
cosocleC42×C11C24
hypercenter#1588D11
hypocenterC11#18011
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1588

Complements

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

NH ≅ G/Ntype
2. #13077635C2semidirect
3. #13077361C2semidirect
4. #13067528C2semidirect
5. #13067500C2semidirect
6. #13067482C2semidirect
7. #13067456C2semidirect
8. #13067442C2semidirect
9. #13067426C2semidirect
10. SD16×C11⋊C8C2semidirect
11. #13067400C2semidirect
12. #13067083C2semidirect
13. #13067002C2semidirect
14. #13066912C2semidirect
15. C11×#1588C2semidirect
221. #1588D11semidirect
236. Q8×C11#131semidirect
519. C11#18011semidirect
526. Q8#66960semidirect

Maximal subgroups

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

subgroupindex
#130786742
#130776352
#130773612
#130675282
#130675002
#130674822
#130674562
#130674422
#130674262
SD16×C11⋊C82
#130674002
#130670832
#130670022
#130669122
C11×#15882
#1801111