Finite Group Databasebeta

← #14910224

Subgroups — #14910224

Order 2816.

760 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622524C211yesmaximal, characteristic, complemented
2C22×#66890C211yesmaximal, characteristic, complemented
3#13080301C211yesmaximal, characteristic, complemented
4#13080290C211yesmaximal, characteristic, complemented
5#13070879C211yesmaximal, characteristic, complemented
6#13070718C211yesmaximal, characteristic, complemented
7#13070710C211yesmaximal, characteristic, complemented
8#13070670C211yesmaximal, characteristic, complemented
9#13070649C211yesmaximal, characteristic, complemented
10#13070547C211yesmaximal, characteristic, complemented
11#13070540C211yesmaximal, characteristic, complemented
12#13070526C211yesmaximal, characteristic, complemented
13#13070489C211yesmaximal, characteristic, complemented
14#13070438C211yesmaximal, characteristic, complemented
15C11×#2184C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic, complemented
17#10623337—21no—
18C2×#66965C2211yescharacteristic, complemented
19C2×D8×D11C2211yescharacteristic, complemented
20C22×D88C2211yescharacteristic
21#10623140—21no—
22C2×C11×D16C2211yescharacteristic, complemented
23C2×C11×D16C2211yescharacteristic, complemented
24C11×#466C2211yescharacteristic
25#10622831—21no—
26#10622771—21no—
27#10622770C2211yescharacteristic, complemented
28#10622768C2211yescharacteristic, complemented
29#10622766—21no—
30#10622764C2211yescharacteristic, complemented
31D8×Dic11C2211yescharacteristic, complemented
32C2×#66891C2211yescharacteristic, complemented
33C2×#66890—24no—
34C2×#66890C2211yescharacteristic
35C2×#66890C2211yescharacteristic
36C2×#66890C2211yescharacteristic, complemented
37C2×#66890C2211yescharacteristic, complemented
38#10622729C2211yescharacteristic, complemented
39C8×C22⋊D11C2211yescharacteristic
40C22×C11⋊C16C2211yescharacteristic, complemented
41#10622649—21no—
42#10622524—24no—
43C2×#66864C2211yescharacteristic, complemented
44C2×#66864C2211yescharacteristic, complemented
45C2×#66862C2211yescharacteristic, complemented
46#10622496C2211yescharacteristic, complemented
47#10622485C2211yescharacteristic, complemented
48#10622399—21no—
49#10622386—21no—
50C11×#357C2211yescharacteristic, complemented
51C11×#357C2211yescharacteristic, complemented
52C11×C22⋊C16C2211yescharacteristic, complemented
53#10622200C2211yescharacteristic, complemented
54#10622147C2211yescharacteristic, complemented
55#10622147C2211yescharacteristic, complemented
56(C2×D11)⋊C16C2211yescharacteristic, complemented
57#10622140C2211yescharacteristic, complemented
58Dic11⋊C16C2211yescharacteristic, complemented
59#10622130C2211yescharacteristic, complemented
60#10622128C2211yescharacteristic, complemented
61C22×D4×C11—21no—
62C2×#4341—21no—
63C2×D4×D11—21no—
64C2×D4×D11—41no—
65C22×D44—21no—
66C2×C11×D8—22no—
67C2×C11×D8—21no—
68C2×C11×D8—41no—
69C2×C11×D8C2311yescharacteristic
70C2×C11×D8C2311yescharacteristic
71C2×C11×D8C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×#121—21no—
74#67006—41no—
75C2×C22⋊Dic11—41no—
76#66993—21no—
77#66992—41no—
78#66991—21no—
79#66990—41no—
80#66989—21no—
81#66988—41no—
82D4×Dic11—21no—
83C2×#4324—21no—
84C2×#4324—21no—
85C2×#4323—21no—
86C2×#4323—21no—
87C4×C22⋊D11D411yescharacteristic
88#66977—21no—
89#66965—22no—
90#66965—41no—
91D8×D11—22no—
92D8×D11—41no—
93C2×Dic44C2311yescharacteristic
94C2×D88—22no—
95C2×D88—21no—
96C2×D88—41no—
97C2×D88C2311yescharacteristic
98C2×D88C2311yescharacteristic
99C2×C8×D11C2311yescharacteristic
100#66948—21no—
101#66946—21no—
102#66937—41no—
103#66935—41no—
104C11×D16—22no—
105C11×D16—41no—
106C2×C11×C16C2311yescharacteristic
107C2×C11×C16C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#102—21no—
110#66896—21no—
111#66896—21no—
112C22⋊(C11⋊C8)D411yescharacteristic
113#66891—22no—
114#66890—22no—
115#66890—22no—
116#66890—22no—
117#66890D414yescomplemented
118(C2×D11)⋊C8D411yescharacteristic
119#66882C2311yescharacteristic
120#66880—21no—
121Dic11⋊C8D411yescharacteristic
122C8×Dic11C2311yescharacteristic
123C2×C11⋊C16—22no—
124C2×C11⋊C16C2311yescharacteristic
125C2×C11⋊C16C2311yescharacteristic
126#66873—21no—
127#66873—21no—
128#66864—22no—
129#66864—41no—
130#66862—22no—
131#33830—111nomaximal, Sylow
132C24×C11—41no—
133C23×D11—41no—
134C23×D11—41no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—42no—
139C2×D4×C11—41no—
140C2×D4×C11—41no—
141C2×D4×C11—81no—
142C22×C4×C11C2×D411yescharacteristic
143C2×C22⋊D11—41no—
144C2×C22⋊D11—41no—
145C2×C22⋊D11—41no—
146C2×C22⋊D11—41no—
147C2×C22⋊D11—41no—
148C2×C22⋊D11D811yescharacteristic
149C22×Dic11—41no—
150C22×Dic11—41no—
151#4341—42no—
152#4341—81no—
153D4×D11—42no—
154D4×D11—81no—
155D4×D11—84no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—42no—
159C2×D44—41no—
160C2×D44—41no—
161C2×D44—81no—
162C2×C4×D11—41no—
163C2×C4×D11C2×D411yescharacteristic
164C2×Dic22—21no—
165C11×D8—21no—
166C11×D8—21no—
167C11×D8—21no—
168C11×D8—21no—
169C11×D8—21no—
170C11×D8—42no—
171C11×D8C2×D412yescomplemented
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2411yescharacteristic
176C11×C4⋊C4—21no—
177C11×C22⋊C4—41no—
178C22⋊Dic11—41no—
179C22⋊Dic11—41no—
180C22⋊Dic11—41no—
181C22⋊Dic11—41no—
182C22⋊Dic11—41no—
183C22⋊Dic11D811yescharacteristic
184#4324—42no—
185#4324—81no—
186#4323—42no—
187#4323—81no—
188(C2×D11)⋊C4—41no—
189(C2×D11)⋊C4—41no—
190(C2×D11)⋊C4D811yescharacteristic
191C4⋊Dic11—21no—
192Dic11⋊C4—41no—
193Dic11⋊C4D811yescharacteristic
194C4×Dic11C2×D411yescharacteristic
195C2×C11⋊C8C2×D411yescharacteristic
196C2×C11⋊C8C2×D411yescharacteristic
197Dic44—21no—
198Dic44—21no—
199D88—21no—
200D88—21no—
201D88—21no—
202D88—42no—
203D88C2×D412yes—
204C8×D11—21no—
205C8×D11—21no—
206C11×C16—21no—
207C11×C16—21no—
208C11⋊C16—21no—
209C11⋊C16C2×D412yescomplemented
210C2×#509—111no—
211C22×D16—111no—
212#3280—111no—
213D4×D8—111no—
214#2250—111no—
215#2218—111no—
216#2217—111no—
217#2210—111no—
218#2206—111no—
219#2187—111no—
220#2186—111no—
221#2184—111no—
222#2184D1111yescharacteristic, complemented
223#2177—111no—
224#2168—111no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—82no—
229C23×C11—82no—
230C23×C11—161no—
231C23×C11C2×D811yescharacteristic
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—82no—
235C22×D11—82no—
236C22×D11—82no—
237C22×D11—82no—
238C22×D11—161no—
239C22×D11—161no—
240C22×D11C2×D811yescharacteristic
241D4×C11—22no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—41no—
247D4×C11—82no—
248D4×C11—82no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11C2×D811yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C22⋊D11—22no—
255C22⋊D11—82no—
256C22⋊D11—82no—
257C22⋊D11—82no—
258C22⋊D11—161no—
259C22⋊D11—161no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—82no—
263C2×Dic11—161no—
264C2×Dic11C2×D811yescharacteristic
265C2×Dic11C2×D811yescharacteristic
266C2×Dic11C2×D811yescharacteristic
267D44—22no—
268D44—41no—
269D44—41no—
270D44—41no—
271D44—82no—
272D44—82no—
273C4×D11—21no—
274C4×D11—21no—
275C4×D11—82no—
276Dic22—41no—
277Dic22—41no—
278C8×C11—21no—
279C8×C11C22×D411yescharacteristic
280C8×C11H(5,𝔽2)11yescharacteristic
281C11⋊C8—21no—
282C11⋊C8—21no—
283C2×#135—111no—
284C22×D8—111no—
285C22×D8—111no—
286C22×D8C2×D1111yescharacteristic, complemented
287#546—221no—
288D42—221no—
289#509—224no—
290C2×SD32—111no—
291C2×SD32—111no—
292C2×SD32—111no—
293C2×D16—111no—
294C2×D16—111no—
295C2×D16—111no—
296C2×D16—111no—
297C2×D16—224no—
298C2×D16C2×D1111yescharacteristic, complemented
299C2×D16C2×D1111yescharacteristic, complemented
300C2×M32—111no—
301C22×C16—111no—
302#495—111no—
303#493—111no—
304#467—111no—
305#466—111no—
306#466—111no—
307#466C2×D1111yescharacteristic
308#463—221no—
309#459—221no—
310#450—221no—
311#449—221no—
312#447—221no—
313#447—221no—
314C4×D8—111no—
315C4×D8—111no—
316C8×D4—111no—
317#367—111no—
318C4⋊C16—111no—
319#358—111no—
320#357—111no—
321#357—111no—
322#357—111no—
323#357C2×D1111yescharacteristic, complemented
324#357C2×D1111yescharacteristic, complemented
325C22⋊C16—111no—
326C22⋊C16C2×D1111yescharacteristic, complemented
327#346—111no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—42no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11—81no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11—164no—
340C22×C11#50912yescomplemented
341C22×C11C22×D811yescharacteristic
342C2×D11—21no—
343C2×D11—21no—
344C2×D11—21no—
345C2×D11—42no—
346C2×D11—81no—
347C2×D11—81no—
348C2×D11—81no—
349C2×D11—81no—
350C2×D11—81no—
351C2×D11—164no—
352C2×D11—164no—
353C4×C11—21no—
354C4×C11—81no—
355C4×C11D4211yescharacteristic
356C4×C11#57611yescharacteristic
357Dic11—21no—
358Dic11—21no—
359Dic11—21no—
360Dic11—81no—
361Dic11—81no—
362C2×#41—221no—
363C22×D4—21no—
364C22×D4—221no—
365C22×D4—221no—
366C22×D4—441no—
367#135—222no—
368#135—441no—
369C2×Q16—111no—
370C2×SD16—221no—
371C2×SD16—221no—
372C2×D8—22no—
373C2×D8—21no—
374C2×D8—41no—
375C2×D8—111no—
376C2×D8—111no—
377C2×D8—222no—
378C2×D8—221no—
379C2×D8—221no—
380C2×D8—222no—
381C2×D8—221no—
382C2×D8—441no—
383C2×D8—441no—
384C2×D8C22×D1111yescharacteristic
385C2×D8C22×D1111yescharacteristic
386C2×D8C22×D1111yescharacteristic
387C22×C8—111no—
388C22×C8C22×D1111yescharacteristic
389#127—221no—
390#124—221no—
391#123—441no—
392C22⋊Q8—221no—
393#121—21no—
394#121—221no—
395#121—221no—
396#121—441no—
397#121—441no—
398#120—441no—
399#120—441no—
400#120—441no—
401C4×D4—111no—
402C4×D4—221no—
403C4×D4—221no—
404C2×C22⋊C4—441no—
405SD32—222no—
406SD32—222no—
407SD32—441no—
408D16—22no—
409D16—41no—
410D16—114no—
411D16—222no—
412D16—222no—
413D16—222no—
414M32—222no—
415C2×C16—111no—
416C2×C16—111no—
417C2×C16—222no—
418C2×C16C22×D1111yescharacteristic
419C2×C16C22×D1111yescharacteristic
420#107—111no—
421#107C22×D1111yescharacteristic
422C4⋊C8—111no—
423#103—221no—
424#102—21no—
425#102—221no—
426#102—221no—
427#102—221no—
428#102—221no—
429C22⋊C8—111no—
430C22⋊C8—111no—
431C4×C8—111no—
432C2×C11—22no—
433C2×C11—82no—
434C2×C11—161no—
435C2×C11—161no—
436C2×C11D4×D811yescharacteristic
437C2×C11C2×#50911yescharacteristic
438C2×C11#341511yescharacteristic
439D11—41no—
440D11—82no—
441D11—161no—
442C24—41no—
443C24—441no—
444C24—441no—
445#41—442no—
446#41—881no—
447C2×Q8—221no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—42no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—81no—
455C2×D4—111no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—442no—
459C2×D4—441no—
460C2×D4—441no—
461C2×D4—441no—
462C2×D4—441no—
463C2×D4—442no—
464C2×D4—441no—
465C2×D4—441no—
466C2×D4—441no—
467C2×D4—881no—
468C2×D4—881no—
469C2×D4—884no—
470C22×C4—111no—
471C22×C4—441no—
472C22×C4—441no—
473C22×C4—441no—
474C22×C4D4×D1111yescharacteristic
475Q16—221no—
476Q16—221no—
477SD16—442no—
478SD16—881no—
479D8—21no—
480D8—21no—
481D8—21no—
482D8—21no—
483D8—21no—
484D8—42no—
485D8—112no—
486D8—221no—
487D8—221no—
488D8—221no—
489D8—442no—
490D8—442no—
491D8—881no—
492D8D4×D1112yescomplemented
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—111no—
496C2×C8—111no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8D4×D1111yescharacteristic
500C2×C8C23×D1111yescharacteristic
501C4⋊C4—21no—
502C4⋊C4—111no—
503C4⋊C4—221no—
504C4⋊C4—441no—
505C22⋊C4—41no—
506C22⋊C4—111no—
507C22⋊C4—111no—
508C22⋊C4—441no—
509C22⋊C4—441no—
510C22⋊C4—441no—
511C22⋊C4—441no—
512C22⋊C4—441no—
513C22⋊C4—441no—
514C22⋊C4—441no—
515C42—111no—
516C16—21no—
517C16—21no—
518C16—112no—
519C16—221no—
520C11#3383011yescharacteristic, complemented, Sylow
521C23—41no—
522C23—41no—
523C23—41no—
524C23—82no—
525C23—82no—
526C23—111no—
527C23—161no—
528C23—441no—
529C23—441no—
530C23—882no—
531C23—882no—
532C23—882no—
533C23—882no—
534C23—1761no—
535C23—1761no—
536C23D8×D1111yescharacteristic
537Q8—441no—
538Q8—441no—
539D4—22no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—82no—
546D4—82no—
547D4—222no—
548D4—222no—
549D4—441no—
550D4—441no—
551D4—441no—
552D4—882no—
553D4—882no—
554D4—882no—
555D4—882no—
556D4—882no—
557D4—1761no—
558D4—1761no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—41no—
562C2×C4—111no—
563C2×C4—111no—
564C2×C4—111no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—882no—
570C2×C4—882no—
571C2×C4—1761no—
572C2×C4D8×D1111yescharacteristic
573C2×C4C2×D4×D1111yescharacteristic
574C8—21no—
575C8—221no—
576C8—221no—
577C8C2×D4×D1111yescharacteristic
578C8#6703711yescharacteristic
579C22—21no—
580C22—21no—
581C22—42no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—164no—
591C22—221no—
592C22—221no—
593C22—221no—
594C22—442no—
595C22—881no—
596C22—881no—
597C22—881no—
598C22—881no—
599C22—881no—
600C22—1764no—
601C22—1764no—
602C22#1062252412yescomplemented
603C22C2×D8×D1111yescharacteristic
604C4—21no—
605C4—81no—
606C4—221no—
607C4—221no—
608C4—221no—
609C4—881no—
610C4—881no—
611C4#1062312111yescharacteristic
612C4#1062330511yescharacteristic
613C2—22no—
614C2—82no—
615C2—161no—
616C2—161no—
617C2—441no—
618C2—882no—
619C2—1761no—
620C2#1308028611yescharacteristic
621C2C2×#1062252411yescharacteristic
622C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2184C2
socleC22×C11C22×D8
hypercenter#2184D11
hypocenterC11#33830
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2184

Complements

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

NH ≅ G/Ntype
1. C2×#10622524C2semidirect
2. C22×#66890C2semidirect
3. #13080301C2semidirect
4. #13080290C2semidirect
5. #13070879C2semidirect
6. #13070718C2semidirect
7. #13070710C2semidirect
8. #13070670C2semidirect
9. #13070649C2semidirect
10. #13070547C2semidirect
11. #13070540C2semidirect
12. #13070526C2semidirect
13. #13070489C2semidirect
14. #13070438C2semidirect
15. C11×#2184C2semidirect
16. C22×C11×D8C22semidirect
18. C2×#66965C22semidirect
19. C2×D8×D11C22semidirect
22. C2×C11×D16C22semidirect
23. C2×C11×D16C22semidirect
27. #10622770C22semidirect
28. #10622768C22semidirect
30. #10622764C22semidirect
31. D8×Dic11C22semidirect
32. C2×#66891C22semidirect
36. C2×#66890C22semidirect
37. C2×#66890C22semidirect
38. #10622729C22semidirect
40. C22×C11⋊C16C22semidirect
43. C2×#66864C22semidirect
44. C2×#66864C22semidirect
45. C2×#66862C22semidirect
46. #10622496C22semidirect
47. #10622485C22semidirect
50. C11×#357C22semidirect
51. C11×#357C22semidirect
52. C11×C22⋊C16C22semidirect
53. #10622200C22semidirect
54. #10622147C22semidirect
55. #10622147C22semidirect
56. (C2×D11)⋊C16C22semidirect
57. #10622140C22semidirect
58. Dic11⋊C16C22semidirect
59. #10622130C22semidirect
60. #10622128C22semidirect
117. #66890D4semidirect
171. C11×D8C2×D4semidirect
209. C11⋊C16C2×D4semidirect
222. #2184D11semidirect
286. C22×D8C2×D11semidirect
298. C2×D16C2×D11semidirect
299. C2×D16C2×D11semidirect
323. #357C2×D11semidirect
324. #357C2×D11semidirect
326. C22⋊C16C2×D11semidirect
340. C22×C11#509semidirect
492. D8D4×D11semidirect
520. C11#33830semidirect
602. C22#10622524semidirect

Maximal subgroups

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

subgroupindex
C2×#106225242
C22×#668902
#130803012
#130802902
#130708792
#130707182
#130707102
#130706702
#130706492
#130705472
#130705402
#130705262
#130704892
#130704382
C11×#21842
#3383011