Finite Group Databasebeta

← #14910359

Subgroups — #14910359

Order 2816.

712 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
1C2×#10622521C211yesmaximal, characteristic, complemented
2C2×#10622527C211yesmaximal, characteristic, complemented
3#13080304C211yesmaximal, characteristic, complemented
4#13080298C211yesmaximal, characteristic, complemented
5#13070876C211yesmaximal, characteristic, complemented
6#13070730C211yesmaximal, characteristic, complemented
7#13070674C211yesmaximal, characteristic, complemented
8#13070670C211yesmaximal, characteristic, complemented
9#13070559C211yesmaximal, characteristic, complemented
10#13070554C211yesmaximal, characteristic, complemented
11#13070529C211yesmaximal, characteristic, complemented
12#13070527C211yesmaximal, characteristic, complemented
13#13070462C211yesmaximal, characteristic, complemented
14#13070446C211yesmaximal, characteristic, complemented
15C11×#2220C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C2×D8×D11C2211yescharacteristic, complemented
18C2×#66957C2211yescharacteristic
19C22×D88C2211yescharacteristic, complemented
20#10623161—21no—
21#10623143—21no—
22C2×C11×SD32C2211yescharacteristic, complemented
23C2×C11×M32C2211yescharacteristic, complemented
24C11×#467C2211yescharacteristic, complemented
25C11×#466C2211yescharacteristic
26#10622804C2211yescharacteristic, complemented
27C2×#66893C2211yescharacteristic, complemented
28C2×#66892C2211yescharacteristic, complemented
29#10622768C2211yescharacteristic, complemented
30C2×#66890C2211yescharacteristic
31C2×#66890C2211yescharacteristic
32C8×C22⋊D11C2211yescharacteristic
33#10622659—21no—
34#10622650—21no—
35#10622527—24no—
36#10622521—24no—
37C2×#66864C2211yescharacteristic, complemented
38C2×#66864C2211yescharacteristic, complemented
39C2×D176C2211yescharacteristic
40C2×D176C2211yescharacteristic
41C2×#66862C2211yescharacteristic, complemented
42#10622500C2211yescharacteristic, complemented
43#10622496C2211yescharacteristic
44#10622485C2211yescharacteristic, complemented
45#10622485C2211yescharacteristic, complemented
46#10622432—21no—
47#10622424—21no—
48#10622400—21no—
49#10622389—21no—
50C11×#366C2211yescharacteristic, complemented
51C11×#358C2211yescharacteristic, complemented
52C11×#357C2211yescharacteristic, complemented
53C22⋊(C11⋊C16)C2211yescharacteristic, complemented
54(C2×D11)⋊C16C2211yescharacteristic, complemented
55Dic11⋊C16C2211yescharacteristic, complemented
56C16×Dic11C2211yescharacteristic, complemented
57#10622130C2211yescharacteristic, complemented
58#10622129C2211yescharacteristic, complemented
59#10622129C2211yescharacteristic, complemented
60#10622129C2211yescharacteristic, complemented
61C2×#4343—21no—
62C2×D4×D11—21no—
63C2×#4339—21no—
64C22×D44—21no—
65C2×C11×Q16C2311yescharacteristic
66C2×C11×D8C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×C22⋊Q8—21no—
69C11×#121—21no—
70#67000—21no—
71C2×#4325—21no—
72C2×#4325—21no—
73#66991—41no—
74#66990—41no—
75#66989—21no—
76C2×#4324—21no—
77C2×#4323—21no—
78C4×C22⋊D11D411yescharacteristic
79#66972—22no—
80#66972—41no—
81D8×D11—22no—
82D8×D11—41no—
83C2×Dic44C2311yescharacteristic
84#66957—22no—
85#66957—41no—
86C2×D88—22no—
87C2×D88—21no—
88C2×D88—41no—
89C2×D88C2311yescharacteristic
90C2×D88C2311yescharacteristic
91C2×D88C2311yescharacteristic
92C2×#4314—21no—
93C2×C8×D11C2311yescharacteristic
94#66950—21no—
95#66948—21no—
96#66948—41no—
97#66947—41no—
98#66946—21no—
99#66946—21no—
100#66936—41no—
101#66935—41no—
102C22⋊C4×D11—41no—
103C22⋊C4×D11—41no—
104C11×SD32—22no—
105C11×M32—22no—
106C2×C11×C16C2311yescharacteristic
107C2×C11×C16C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#107C2311yescharacteristic
110C11×#103—21no—
111C11×#102—21no—
112C22⋊(C11⋊C8)D411yescharacteristic
113#66893—41no—
114#66892—22no—
115#66890—22no—
116#66890—41no—
117(C2×D11)⋊C8D411yescharacteristic
118Dic11⋊C8D411yescharacteristic
119C8×Dic11C2311yescharacteristic
120C2×C11⋊C16C2311yescharacteristic
121C2×C11⋊C16C2311yescharacteristic
122#66874—21no—
123#66873—21no—
124#66873—21no—
125#66873—21no—
126#66864—22no—
127#66864—22no—
128D176—22no—
129D176D414yescomplemented
130#66862—22no—
131#33839—111nomaximal, Sylow
132C23×D11—41no—
133C23×D11—41no—
134C2×Q8×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—41no—
137C22×C4×C11C2×D411yescharacteristic
138C2×C22⋊D11—41no—
139C2×C22⋊D11—41no—
140C2×C22⋊D11D811yescharacteristic
141#4343—42no—
142#4343—81no—
143D4×D11—42no—
144D4×D11—81no—
145#4339—42no—
146#4339—81no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—42no—
151C2×D44—41no—
152C2×D44—41no—
153C2×D44—41no—
154C2×D44—81no—
155C2×C4×D11—41no—
156C2×C4×D11—41no—
157C2×C4×D11—41no—
158C2×C4×D11—41no—
159C2×C4×D11C2×D411yescharacteristic
160C2×Dic22—21no—
161C11×Q16—21no—
162C11×Q16—21no—
163C11×D8—21no—
164C11×D8—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2411yescharacteristic
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—41no—
172C11×C22⋊C4—41no—
173C11×C22⋊C4—41no—
174C22⋊Dic11—41no—
175C22⋊Dic11—41no—
176C22⋊Dic11D811yescharacteristic
177#4325—42no—
178#4325—81no—
179#4324—81no—
180#4323—42no—
181(C2×D11)⋊C4—41no—
182(C2×D11)⋊C4—41no—
183(C2×D11)⋊C4—41no—
184(C2×D11)⋊C4—41no—
185(C2×D11)⋊C4—41no—
186(C2×D11)⋊C4—41no—
187(C2×D11)⋊C4D811yescharacteristic
188C4⋊Dic11—41no—
189Dic11⋊C4D811yescharacteristic
190C4×Dic11C2×D411yescharacteristic
191C2×C11⋊C8C2×D411yescharacteristic
192C2×C11⋊C8C2×D411yescharacteristic
193Dic44—21no—
194Dic44—21no—
195D88—21no—
196D88—21no—
197D88—21no—
198D88—21no—
199D88—42no—
200D88C2×D412yes—
201D88C2×D412yes—
202#4314—42no—
203C8×D11—21no—
204C8×D11—21no—
205C11×C16—21no—
206C11×C16C2×D412yes—
207C11⋊C16—21no—
208C11⋊C16—21no—
209C2×#509—111no—
210C2×#509—111no—
211#3280—111no—
212#3280—111no—
213#2249—111no—
214#2220—111no—
215#2220D1111yescharacteristic, complemented
216#2210—111no—
217#2210—111no—
218#2189—111no—
219#2189—111no—
220#2184—111no—
221#2184—111no—
222C4×D16—111no—
223#2169—111no—
224C23×C11—41no—
225C23×C11C2×D811yescharacteristic
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—82no—
230C22×D11—82no—
231C22×D11—82no—
232C22×D11—82no—
233C22×D11—161no—
234C22×D11—161no—
235C22×D11C2×D811yescharacteristic
236Q8×C11—41no—
237Q8×C11—41no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—161no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11C2×D811yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C22⋊D11—41no—
249C22⋊D11—82no—
250C22⋊D11—82no—
251C2×Dic11—41no—
252C2×Dic11C2×D811yescharacteristic
253C2×Dic11C2×D811yescharacteristic
254C2×Dic11C2×D811yescharacteristic
255D44—22no—
256D44—22no—
257D44—41no—
258D44—41no—
259D44—41no—
260D44—41no—
261D44—82no—
262D44—82no—
263D44—161no—
264C4×D11—21no—
265C4×D11—21no—
266C4×D11—82no—
267C4×D11—82no—
268C4×D11—161no—
269C4×D11—161no—
270Dic22—41no—
271Dic22—41no—
272C8×C11—21no—
273C8×C11C22×D411yescharacteristic
274C8×C11H(5,𝔽2)11yescharacteristic
275C11⋊C8—21no—
276C11⋊C8—21no—
277C2×#135—111no—
278C2×#135—111no—
279C22×D8—111no—
280C22×D8—111no—
281#546—221no—
282#546—221no—
283#509—224no—
284#509—224no—
285C2×Q32—111no—
286C2×SD32—111no—
287C2×SD32—111no—
288C2×SD32—111no—
289C2×SD32C2×D1111yescharacteristic, complemented
290C2×D16—111no—
291C2×D16—111no—
292C2×D16—111no—
293C2×D16—111no—
294C2×M32—111no—
295C2×M32C2×D1111yescharacteristic, complemented
296#495—111no—
297#495—111no—
298#467—111no—
299#467C2×D1111yescharacteristic, complemented
300#466—111no—
301#466C2×D1111yescharacteristic
302#463—221no—
303#463—221no—
304#450—221no—
305#450—221no—
306#449—221no—
307#449—221no—
308C4×D8—111no—
309C4×D8—111no—
310C8×D4—111no—
311#366C2×D1111yescharacteristic, complemented
312C4⋊C16—111no—
313#358—111no—
314#358C2×D1111yescharacteristic, complemented
315#357—111no—
316#357—111no—
317#357—111no—
318#357C2×D1111yescharacteristic, complemented
319C22⋊C16—111no—
320C22⋊C16—111no—
321C4×C16—111no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—81no—
326C22×C11—81no—
327C22×C11—81no—
328C22×C11C22×D811yescharacteristic
329C2×D11—21no—
330C2×D11—21no—
331C2×D11—21no—
332C2×D11—42no—
333C2×D11—42no—
334C2×D11—81no—
335C2×D11—81no—
336C2×D11—81no—
337C2×D11—81no—
338C2×D11—81no—
339C2×D11—81no—
340C2×D11—81no—
341C2×D11—164no—
342C2×D11—164no—
343C4×C11—21no—
344C4×C11—81no—
345C4×C11—81no—
346C4×C11—81no—
347C4×C11D4211yescharacteristic
348C4×C11#57611yescharacteristic
349Dic11—21no—
350Dic11—21no—
351Dic11—21no—
352Dic11—81no—
353C2×#41—221no—
354C2×#41—221no—
355C22×D4—221no—
356C22×D4—221no—
357#135—222no—
358#135—222no—
359#135—441no—
360#135—441no—
361C2×Q16—111no—
362C2×Q16C22×D1111yescharacteristic
363C2×SD16—221no—
364C2×SD16—221no—
365C2×SD16—221no—
366C2×SD16—221no—
367C2×D8—111no—
368C2×D8—111no—
369C2×D8—111no—
370C2×D8—222no—
371C2×D8—221no—
372C2×D8—222no—
373C2×D8—221no—
374C2×D8—441no—
375C2×D8—441no—
376C2×D8C22×D1111yescharacteristic
377C22×C8—111no—
378C22×C8C22×D1111yescharacteristic
379#124—221no—
380#124—221no—
381#123—441no—
382#123—441no—
383C22⋊Q8—21no—
384C22⋊Q8—221no—
385#121—21no—
386#121—221no—
387#121—441no—
388#121—441no—
389#120—441no—
390#120—441no—
391C4×D4—111no—
392C4×D4—221no—
393C4×D4—221no—
394C2×C22⋊C4—441no—
395C2×C22⋊C4—441no—
396Q32—441no—
397SD32—22no—
398SD32—222no—
399SD32—222no—
400SD32—222no—
401D16—114no—
402D16—222no—
403D16—222no—
404D16—441no—
405M32—22no—
406M32—222no—
407C2×C16—111no—
408C2×C16—111no—
409C2×C16C22×D1111yescharacteristic
410C2×C16C22×D1111yescharacteristic
411#107C22×D1111yescharacteristic
412#107C22×D1111yescharacteristic
413C4⋊C8—111no—
414#103—21no—
415#103—221no—
416#102—21no—
417#102—221no—
418#102—221no—
419#102—221no—
420C22⋊C8—111no—
421C22⋊C8—111no—
422C4×C8—111no—
423C2×C11—41no—
424C2×C11—161no—
425C2×C11D4×D811yescharacteristic
426C2×C11#341411yescharacteristic
427C2×C11#341511yescharacteristic
428D11—41no—
429D11—82no—
430D11—82no—
431D11—161no—
432C24—441no—
433C24—441no—
434#41—442no—
435#41—442no—
436#41—881no—
437#41—881no—
438C2×Q8—21no—
439C2×Q8—221no—
440C2×D4—21no—
441C2×D4—41no—
442C2×D4—111no—
443C2×D4—221no—
444C2×D4—221no—
445C2×D4—221no—
446C2×D4—442no—
447C2×D4—441no—
448C2×D4—441no—
449C2×D4—441no—
450C2×D4—442no—
451C2×D4—441no—
452C2×D4—441no—
453C2×D4—881no—
454C2×D4—881no—
455C22×C4—111no—
456C22×C4—441no—
457C22×C4—441no—
458C22×C4—441no—
459C22×C4—441no—
460C22×C4D4×D1111yescharacteristic
461Q16—21no—
462Q16—21no—
463Q16—221no—
464Q16—221no—
465SD16—442no—
466SD16—442no—
467SD16—881no—
468SD16—881no—
469D8—21no—
470D8—21no—
471D8—112no—
472D8—112no—
473D8—221no—
474D8—221no—
475D8—221no—
476D8—221no—
477D8—442no—
478D8—442no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—111no—
482C2×C8—111no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8D4×D1111yescharacteristic
486C2×C8C23×D1111yescharacteristic
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—111no—
491C4⋊C4—441no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C22⋊C4—111no—
495C22⋊C4—111no—
496C22⋊C4—441no—
497C22⋊C4—441no—
498C22⋊C4—441no—
499C22⋊C4—441no—
500C22⋊C4—441no—
501C22⋊C4—441no—
502C22⋊C4—441no—
503C22⋊C4—441no—
504C42—111no—
505C16—21no—
506C16—221no—
507C16—221no—
508C16D4×D1112yes—
509C11#3383911yescharacteristic, complemented, Sylow
510C23—41no—
511C23—111no—
512C23—441no—
513C23—441no—
514C23—441no—
515C23—882no—
516C23—882no—
517C23—882no—
518C23—882no—
519C23—1761no—
520C23—1761no—
521C23D8×D1111yescharacteristic
522Q8—41no—
523Q8—41no—
524Q8—441no—
525Q8—441no—
526D4—41no—
527D4—41no—
528D4—161no—
529D4—222no—
530D4—222no—
531D4—441no—
532D4—441no—
533D4—441no—
534D4—441no—
535D4—441no—
536D4—882no—
537D4—882no—
538D4—882no—
539D4—882no—
540D4—1761no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—111no—
547C2×C4—111no—
548C2×C4—111no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—441no—
552C2×C4—882no—
553C2×C4—882no—
554C2×C4—1761no—
555C2×C4—1761no—
556C2×C4D8×D1111yescharacteristic
557C2×C4C2×D4×D1111yescharacteristic
558C8—21no—
559C8—221no—
560C8—221no—
561C8C2×D4×D1111yescharacteristic
562C8#6704211yescharacteristic
563C22—21no—
564C22—21no—
565C22—21no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22—221no—
570C22—221no—
571C22—221no—
572C22—442no—
573C22—442no—
574C22—881no—
575C22—881no—
576C22—881no—
577C22—881no—
578C22—881no—
579C22—881no—
580C22—881no—
581C22—1764no—
582C22—1764no—
583C22C2×D8×D1111yescharacteristic
584C4—21no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4—221no—
589C4—221no—
590C4—221no—
591C4—881no—
592C4#1062314011yescharacteristic
593C4#1062330011yescharacteristic
594C2—41no—
595C2—161no—
596C2—441no—
597C2—882no—
598C2—882no—
599C2—1761no—
600C2#1308029011yescharacteristic
601C2#1308175111yescharacteristic
602C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2220C2
socleC22×C11C22×D8
hypercenter#2220D11
hypocenterC11#33839
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2220

Complements

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

NH ≅ G/Ntype
1. C2×#10622521C2semidirect
2. C2×#10622527C2semidirect
3. #13080304C2semidirect
4. #13080298C2semidirect
5. #13070876C2semidirect
6. #13070730C2semidirect
7. #13070674C2semidirect
8. #13070670C2semidirect
9. #13070559C2semidirect
10. #13070554C2semidirect
11. #13070529C2semidirect
12. #13070527C2semidirect
13. #13070462C2semidirect
14. #13070446C2semidirect
15. C11×#2220C2semidirect
17. C2×D8×D11C22semidirect
19. C22×D88C22semidirect
22. C2×C11×SD32C22semidirect
23. C2×C11×M32C22semidirect
24. C11×#467C22semidirect
26. #10622804C22semidirect
27. C2×#66893C22semidirect
28. C2×#66892C22semidirect
29. #10622768C22semidirect
37. C2×#66864C22semidirect
38. C2×#66864C22semidirect
41. C2×#66862C22semidirect
42. #10622500C22semidirect
44. #10622485C22semidirect
45. #10622485C22semidirect
50. C11×#366C22semidirect
51. C11×#358C22semidirect
52. C11×#357C22semidirect
53. C22⋊(C11⋊C16)C22semidirect
54. (C2×D11)⋊C16C22semidirect
55. Dic11⋊C16C22semidirect
56. C16×Dic11C22semidirect
57. #10622130C22semidirect
58. #10622129C22semidirect
59. #10622129C22semidirect
60. #10622129C22semidirect
129. D176D4semidirect
215. #2220D11semidirect
289. C2×SD32C2×D11semidirect
295. C2×M32C2×D11semidirect
299. #467C2×D11semidirect
311. #366C2×D11semidirect
314. #358C2×D11semidirect
318. #357C2×D11semidirect
509. C11#33839semidirect

Maximal subgroups

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

subgroupindex
C2×#106225212
C2×#106225272
#130803042
#130802982
#130708762
#130707302
#130706742
#130706702
#130705592
#130705542
#130705292
#130705272
#130704622
#130704462
C11×#22202
#3383911