Finite Group Databasebeta

← #14910356

Subgroups — #14910356

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×#10622524C211yesmaximal, characteristic, complemented
2#13080301C211yesmaximal, characteristic, complemented
3#13080295C211yesmaximal, characteristic, complemented
4#13070876C211yesmaximal, characteristic, complemented
5#13070729C211yesmaximal, characteristic, complemented
6#13070726C211yesmaximal, characteristic, complemented
7#13070673C211yesmaximal, characteristic, complemented
8#13070669C211yesmaximal, characteristic, complemented
9#13070556C211yesmaximal, characteristic, complemented
10#13070553C211yesmaximal, characteristic, complemented
11#13070528C211yesmaximal, characteristic, complemented
12#13070526C211yesmaximal, characteristic, complemented
13D16×Dic11C211yesmaximal, characteristic, complemented
14#13070446C211yesmaximal, characteristic, complemented
15C2×C11×#509C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic, complemented
18#10623360—21no—
19#10623337—21no—
20C2×#66965C2211yescharacteristic
21C2×D8×D11C2211yescharacteristic, complemented
22C11×#509—24no—
23C2×C11×SD32C2211yescharacteristic, complemented
24C2×C11×SD32C2211yescharacteristic, complemented
25C2×C11×D16C2211yescharacteristic
26C2×C11×D16C2211yescharacteristic
27C2×C11×M32C2211yescharacteristic, complemented
28#10622851—21no—
29#10622831—21no—
30#10622804C2211yescharacteristic, complemented
31#10622801C2211yescharacteristic, complemented
32C2×#66893C2211yescharacteristic, complemented
33#10622782—21no—
34#10622778—21no—
35#10622771—21no—
36#10622770C2211yescharacteristic
37#10622768C2211yescharacteristic, complemented
38#10622766—21no—
39D8×Dic11C2211yescharacteristic, complemented
40D8×Dic11C2211yescharacteristic, complemented
41C2×#66891C2211yescharacteristic, complemented
42C2×#66890C2211yescharacteristic
43C2×#66890C2211yescharacteristic
44#10622729C2211yescharacteristic, complemented
45#10622728C2211yescharacteristic
46C8×C22⋊D11C2211yescharacteristic
47#10622524—24no—
48C2×#66864C2211yescharacteristic, complemented
49C2×#66862C2211yescharacteristic, complemented
50#10622202C2211yescharacteristic, complemented
51#10622200C2211yescharacteristic, complemented
52#10622200C2211yescharacteristic, complemented
53#10622200C2211yescharacteristic, complemented
54C22⋊(C11⋊C16)C2211yescharacteristic, complemented
55#10622147C2211yescharacteristic, complemented
56(C2×D11)⋊C16C2211yescharacteristic, complemented
57#10622142C2211yescharacteristic, complemented
58#10622141C2211yescharacteristic, complemented
59Dic11⋊C16C2211yescharacteristic, complemented
60C16×Dic11C2211yescharacteristic, complemented
61C2×C11×#41—21no—
62C22×D4×C11—21no—
63C2×#4341—21no—
64C2×D4×D11—21no—
65C11×#135—22no—
66C11×#135—41no—
67C2×C11×Q16C2311yescharacteristic
68C2×C11×SD16—21no—
69C2×C11×D8—22no—
70C2×C11×D8—21no—
71C2×C11×D8—41no—
72C2×C11×D8C2311yescharacteristic
73C2×C11×D8C2311yescharacteristic
74C2×C11×D8C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76#67006—41no—
77C2×C22⋊Dic11—41no—
78#67000—21no—
79#66999—21no—
80C2×#4325—21no—
81#66992—41no—
82#66992—41no—
83#66991—21no—
84#66990—41no—
85#66989—21no—
86#66988—41no—
87D4×Dic11—21no—
88D4×Dic11—21no—
89C2×#4324—21no—
90C2×#4324—21no—
91C2×#4323—21no—
92#66983—21no—
93#66982—41no—
94C4×C22⋊D11D411yescharacteristic
95C2×(C2×D11)⋊C4—41no—
96#66977—21no—
97#66965—22no—
98#66965—41no—
99D8×D11—22no—
100D8×D11—41no—
101C2×Dic44C2311yescharacteristic
102C2×D88C2311yescharacteristic
103C2×C8×D11C2311yescharacteristic
104C11×SD32—22no—
105C11×SD32—22no—
106C11×D16—22no—
107C11×D16D414yescomplemented
108C11×M32—22no—
109C2×C11×C16C2311yescharacteristic
110C2×C11×C16C2311yescharacteristic
111#66899—21no—
112#66896—21no—
113#66896—21no—
114#66896—21no—
115C22⋊(C11⋊C8)D411yescharacteristic
116#66893—41no—
117#66891—22no—
118#66890—22no—
119#66890—41no—
120#66885—21no—
121(C2×D11)⋊C8D411yescharacteristic
122#66882C2311yescharacteristic
123#66882C2311yescharacteristic
124#66880—21no—
125Dic11⋊C8D411yescharacteristic
126C8×Dic11C2311yescharacteristic
127C2×C11⋊C16C2311yescharacteristic
128C2×C11⋊C16C2311yescharacteristic
129#66864—22no—
130#66862—22no—
131#33839—111nomaximal, Sylow
132C24×C11—41no—
133C23×D11—41no—
134C11×#41—42no—
135C11×#41—81no—
136C2×Q8×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—42no—
141C2×D4×C11—41no—
142C2×D4×C11—41no—
143C2×D4×C11—81no—
144C22×C4×C11—41no—
145C22×C4×C11C2×D411yescharacteristic
146C2×C22⋊D11—41no—
147C2×C22⋊D11—41no—
148C2×C22⋊D11—41no—
149C2×C22⋊D11—41no—
150C2×C22⋊D11D811yescharacteristic
151C22×Dic11—41no—
152C22×Dic11—41no—
153C22×Dic11—41no—
154#4341—42no—
155#4341—81no—
156D4×D11—42no—
157D4×D11—81no—
158C2×D44—21no—
159C2×C4×D11C2×D411yescharacteristic
160C2×Dic22—21no—
161C11×Q16—21no—
162C11×Q16—21no—
163C11×SD16—42no—
164C11×D8—21no—
165C11×D8—21no—
166C11×D8—21no—
167C11×D8—21no—
168C11×D8—42no—
169C11×D8C2×D412yes—
170C11×D8C2×D412yes—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11C2×D411yescharacteristic
174C2×C8×C11C2411yescharacteristic
175C22⋊Dic11—41no—
176C22⋊Dic11—41no—
177C22⋊Dic11—41no—
178C22⋊Dic11—41no—
179C22⋊Dic11—41no—
180C22⋊Dic11—41no—
181C22⋊Dic11D811yescharacteristic
182#4325—81no—
183#4324—42no—
184#4324—81no—
185#4323—42no—
186(C2×D11)⋊C4—41no—
187(C2×D11)⋊C4—41no—
188(C2×D11)⋊C4—41no—
189(C2×D11)⋊C4—41no—
190(C2×D11)⋊C4D811yescharacteristic
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193Dic11⋊C4—41no—
194Dic11⋊C4—41no—
195Dic11⋊C4D811yescharacteristic
196C4×Dic11C2×D411yescharacteristic
197C2×C11⋊C8C2×D411yescharacteristic
198C2×C11⋊C8C2×D411yescharacteristic
199Dic44—21no—
200Dic44—21no—
201D88—21no—
202D88—21no—
203C8×D11—21no—
204C8×D11—21no—
205C11×C16—21no—
206C11×C16C2×D412yes—
207C11⋊C16—21no—
208C11⋊C16—21no—
209C2×#509—111no—
210C2×#509D1111yescharacteristic, complemented
211#3280—111no—
212#3280—111no—
213#2249—111no—
214#2220—111no—
215#2220—111no—
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×C11—41no—
226C23×C11—41no—
227C23×C11—82no—
228C23×C11—82no—
229C23×C11—161no—
230C23×C11C2×D811yescharacteristic
231C22×D11—41no—
232C22×D11—82no—
233C22×D11—82no—
234C22×D11—161no—
235C22×D11C2×D811yescharacteristic
236Q8×C11—41no—
237Q8×C11—41no—
238D4×C11—22no—
239D4×C11—22no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—82no—
245D4×C11—82no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—41no—
249C2×C4×C11—82no—
250C2×C4×C11C2×D811yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C22⋊D11—41no—
253C22⋊D11—82no—
254C22⋊D11—82no—
255C22⋊D11—161no—
256C22⋊D11—161no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—82no—
261C2×Dic11—161no—
262C2×Dic11—161no—
263C2×Dic11C2×D811yescharacteristic
264C2×Dic11C2×D811yescharacteristic
265C2×Dic11C2×D811yescharacteristic
266D44—41no—
267D44—41no—
268C4×D11—21no—
269C4×D11—21no—
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×#135C2×D1111yescharacteristic
279C22×D8—111no—
280C22×D8C2×D1111yescharacteristic, complemented
281#546—221no—
282#546—221no—
283#509—24no—
284#509—224no—
285C2×Q32—111no—
286C2×SD32—111no—
287C2×SD32—111no—
288C2×SD32C2×D1111yescharacteristic, complemented
289C2×SD32C2×D1111yescharacteristic, complemented
290C2×D16—111no—
291C2×D16—111no—
292C2×D16C2×D1111yescharacteristic
293C2×D16C2×D1111yescharacteristic
294C2×M32—111no—
295C2×M32C2×D1111yescharacteristic, complemented
296#495—111no—
297#495—111no—
298#467—111no—
299#467—111no—
300#466—111no—
301#466—111no—
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#366—111no—
312C4⋊C16—111no—
313#358—111no—
314#358—111no—
315#357—111no—
316#357—111no—
317#357—111no—
318#357—111no—
319C22⋊C16—111no—
320C22⋊C16—111no—
321C4×C16—111no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11—81no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11—164no—
335C22×C11C22×D811yescharacteristic
336C2×D11—21no—
337C2×D11—21no—
338C2×D11—21no—
339C2×D11—81no—
340C2×D11—81no—
341C2×D11—81no—
342C2×D11—164no—
343C4×C11—21no—
344C4×C11—81no—
345C4×C11D4211yescharacteristic
346C4×C11#57611yescharacteristic
347Dic11—21no—
348Dic11—21no—
349Dic11—21no—
350Dic11—81no—
351Dic11—81no—
352Dic11—81no—
353C2×#41—21no—
354C2×#41—221no—
355C22×D4—21no—
356C22×D4—221no—
357#135—22no—
358#135—41no—
359#135—222no—
360#135—441no—
361C2×Q16—111no—
362C2×Q16C22×D1111yescharacteristic
363C2×SD16—21no—
364C2×SD16—221no—
365C2×SD16—221no—
366C2×SD16—221no—
367C2×D8—22no—
368C2×D8—21no—
369C2×D8—41no—
370C2×D8—111no—
371C2×D8—221no—
372C2×D8—222no—
373C2×D8—441no—
374C2×D8C22×D1111yescharacteristic
375C2×D8C22×D1111yescharacteristic
376C2×D8C22×D1111yescharacteristic
377C22×C8—111no—
378C22×C8C22×D1111yescharacteristic
379#124—221no—
380#124—221no—
381#123—441no—
382#123—441no—
383C22⋊Q8—221no—
384C22⋊Q8—221no—
385#121—221no—
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—22no—
399SD32—222no—
400SD32—222no—
401D16—22no—
402D16—222no—
403D16—441no—
404D16C22⋊D1114yescomplemented
405M32—22no—
406M32—222no—
407C2×C16—111no—
408C2×C16—111no—
409C2×C16C22×D1111yescharacteristic
410C2×C16C22×D1111yescharacteristic
411#107—111no—
412#107—111no—
413C4⋊C8—111no—
414#103—221no—
415#103—221no—
416#102—221no—
417#102—221no—
418#102—221no—
419#102—221no—
420C22⋊C8—111no—
421C22⋊C8—111no—
422C4×C8—111no—
423C2×C11—41no—
424C2×C11—82no—
425C2×C11—82no—
426C2×C11—161no—
427C2×C11D4×D811yescharacteristic
428C2×C11#341411yescharacteristic
429C2×C11#341511yescharacteristic
430D11—41no—
431D11—161no—
432C24—41no—
433C24—441no—
434#41—42no—
435#41—81no—
436#41—442no—
437#41—881no—
438C2×Q8—21no—
439C2×Q8—221no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—42no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—81no—
447C2×D4—111no—
448C2×D4—221no—
449C2×D4—441no—
450C2×D4—442no—
451C2×D4—441no—
452C2×D4—441no—
453C2×D4—441no—
454C2×D4—881no—
455C22×C4—41no—
456C22×C4—111no—
457C22×C4—441no—
458C22×C4—441no—
459C22×C4—441no—
460C22×C4D4×D1111yescharacteristic
461Q16—21no—
462Q16—21no—
463Q16—221no—
464Q16—221no—
465SD16—42no—
466SD16—442no—
467SD16—881no—
468SD16—881no—
469D8—21no—
470D8—21no—
471D8—21no—
472D8—21no—
473D8—42no—
474D8—221no—
475D8—221no—
476D8—442no—
477D8C2×C22⋊D1112yes—
478D8C2×C22⋊D1112yes—
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—111no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—441no—
491C4⋊C4—441no—
492C22⋊C4—111no—
493C22⋊C4—111no—
494C22⋊C4—441no—
495C22⋊C4—441no—
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—
508C16C2×C22⋊D1112yes—
509C11#3383911yescharacteristic, complemented, Sylow
510C23—41no—
511C23—41no—
512C23—41no—
513C23—82no—
514C23—82no—
515C23—111no—
516C23—161no—
517C23—441no—
518C23—882no—
519C23—882no—
520C23—1761no—
521C23D8×D1111yescharacteristic
522Q8—41no—
523Q8—41no—
524Q8—441no—
525Q8—441no—
526D4—22no—
527D4—22no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—82no—
533D4—82no—
534D4—441no—
535D4—441no—
536D4—441no—
537D4—882no—
538D4—882no—
539D4—1761no—
540D4—1761no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—82no—
545C2×C4—111no—
546C2×C4—111no—
547C2×C4—111no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—882no—
554C2×C4—1761no—
555C2×C4—1761no—
556C2×C4D8×D1111yescharacteristic
557C2×C4C2×D4×D1111yescharacteristic
558C8—21no—
559C8—221no—
560C8—221no—
561C8#6703711yescharacteristic
562C8C22×C22⋊D1111yescharacteristic
563C22—21no—
564C22—21no—
565C22—21no—
566C22—42no—
567C22—42no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—164no—
576C22—221no—
577C22—221no—
578C22—221no—
579C22—881no—
580C22—881no—
581C22—881no—
582C22—1764no—
583C22C2×D8×D1111yescharacteristic
584C4—21no—
585C4—81no—
586C4—221no—
587C4—221no—
588C4—221no—
589C4—881no—
590C4—881no—
591C4—881no—
592C4#1062328811yescharacteristic
593C4D4×C22⋊D1111yescharacteristic
594C2—41no—
595C2—82no—
596C2—82no—
597C2—161no—
598C2—441no—
599C2—1761no—
600C2D8×C22⋊D1111yescharacteristic
601C2#1308174811yescharacteristic
602C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#509C2
socleC22×C11C22×D8
hypercenterC2×#509D11
hypocenterC11#33839
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

Complements

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

NH ≅ G/Ntype
1. C2×#10622524C2semidirect
2. #13080301C2semidirect
3. #13080295C2semidirect
4. #13070876C2semidirect
5. #13070729C2semidirect
6. #13070726C2semidirect
7. #13070673C2semidirect
8. #13070669C2semidirect
9. #13070556C2semidirect
10. #13070553C2semidirect
11. #13070528C2semidirect
12. #13070526C2semidirect
13. D16×Dic11C2semidirect
14. #13070446C2semidirect
15. C2×C11×#509C2semidirect
17. C22×C11×D8C22semidirect
21. C2×D8×D11C22semidirect
23. C2×C11×SD32C22semidirect
24. C2×C11×SD32C22semidirect
27. C2×C11×M32C22semidirect
30. #10622804C22semidirect
31. #10622801C22semidirect
32. C2×#66893C22semidirect
37. #10622768C22semidirect
39. D8×Dic11C22semidirect
40. D8×Dic11C22semidirect
41. C2×#66891C22semidirect
44. #10622729C22semidirect
48. C2×#66864C22semidirect
49. C2×#66862C22semidirect
50. #10622202C22semidirect
51. #10622200C22semidirect
52. #10622200C22semidirect
53. #10622200C22semidirect
54. C22⋊(C11⋊C16)C22semidirect
55. #10622147C22semidirect
56. (C2×D11)⋊C16C22semidirect
57. #10622142C22semidirect
58. #10622141C22semidirect
59. Dic11⋊C16C22semidirect
60. C16×Dic11C22semidirect
107. C11×D16D4semidirect
210. C2×#509D11semidirect
280. C22×D8C2×D11semidirect
288. C2×SD32C2×D11semidirect
289. C2×SD32C2×D11semidirect
295. C2×M32C2×D11semidirect
404. D16C22⋊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×#106225242
#130803012
#130802952
#130708762
#130707292
#130707262
#130706732
#130706692
#130705562
#130705532
#130705282
#130705262
D16×Dic112
#130704462
C2×C11×#5092
#3383911