Finite Group Databasebeta

← #14910287

Subgroups — #14910287

Order 2816.

702 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622760C211yesmaximal, characteristic, complemented
2C2×#10622807C211yesmaximal, characteristic, complemented
3#13080376C211yesmaximal, characteristic, complemented
4#13070883C211yesmaximal, characteristic, complemented
5#13070731C211yesmaximal, characteristic, complemented
6#13070700C211yesmaximal, characteristic, complemented
7#13070675C211yesmaximal, characteristic, complemented
8#13070651C211yesmaximal, characteristic, complemented
9#13070554C211yesmaximal, characteristic, complemented
10#13070539C211yesmaximal, characteristic, complemented
11#13070537C211yesmaximal, characteristic, complemented
12#13070528C211yesmaximal, characteristic, complemented
13#13070480C211yesmaximal, characteristic, complemented
14#13070442C211yesmaximal, characteristic, complemented
15C11×#3280C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C11×#546—21no—
19C2×#66957C2211yescharacteristic
20C2×#66957C2211yescharacteristic, complemented
21#10623084—21no—
22C11×#495C2211yescharacteristic
23C11×#467C2211yescharacteristic
24C11×#466C2211yescharacteristic
25C11×#463—21no—
26C11×#450—21no—
27C11×#449—21no—
28C4×C11×D8C2211yescharacteristic
29C8×D4×C11C2211yescharacteristic
30#10622807—24no—
31C2×#66893C2211yescharacteristic, complemented
32C2×#66892C2211yescharacteristic, complemented
33C2×#66892C2211yescharacteristic, complemented
34C2×#66891C2211yescharacteristic
35C2×#66891C2211yescharacteristic
36#10622760—24no—
37C2×#66890C2211yescharacteristic
38C2×#66890C2211yescharacteristic
39C2×#66890C2211yescharacteristic
40C2×#66890C2211yescharacteristic
41#10622728C2211yescharacteristic
42#10622728C2211yescharacteristic, complemented
43C2×#66876C2211yescharacteristic
44C22×C11⋊C16C2211yescharacteristic, complemented
45#10622461—21no—
46#10622347—21no—
47#10622347—21no—
48C4×Dic44C2211yescharacteristic, complemented
49#10622308C2211yescharacteristic, complemented
50#10622202C2211yescharacteristic, complemented
51#10622200C2211yescharacteristic
52#10622200C2211yescharacteristic
53C22⋊(C11⋊C16)C2211yescharacteristic
54C22⋊(C11⋊C16)C2211yescharacteristic, complemented
55#10622130C2211yescharacteristic, complemented
56#10622129C2211yescharacteristic, complemented
57#10622129C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C4⋊(C11⋊C16)C2211yescharacteristic, complemented
60#10622099C2211yescharacteristic, complemented
61C2×C11×#41—21no—
62C22×D4×C11—21no—
63C2×#4339—21no—
64C2×#4339—21no—
65C11×#135—22no—
66C11×#135—41no—
67C2×C11×Q16C2311yescharacteristic
68C2×C11×SD16—21no—
69C2×C11×SD16—21no—
70C2×C11×D8—22no—
71C2×C11×D8—21no—
72C2×C11×D8—41no—
73C2×C11×D8C2311yescharacteristic
74C2×C11×D8C2311yescharacteristic
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×#124—21no—
78C11×#123—41no—
79C11×C22⋊Q8—21no—
80C11×#121—21no—
81C11×#121—41no—
82C11×#120—41no—
83C4×D4×C11—21no—
84C4×D4×C11D411yescharacteristic
85C2×C11×C22⋊C4—41no—
86#66993—41no—
87#66983—21no—
88#66983—21no—
89C2×Dic44C2311yescharacteristic
90#66957—22no—
91#66957—22no—
92#66957—41no—
93#66957—41no—
94C2×D88—21no—
95C2×D88C2311yescharacteristic
96C2×D88C2311yescharacteristic
97C2×#4314—21no—
98C2×#4314—21no—
99#66946—41no—
100#66937—41no—
101#66937—41no—
102#66927—21no—
103C4×Dic22—21no—
104C11×#107C2311yescharacteristic
105C11×C4⋊C8D411yescharacteristic
106C11×#103—21no—
107C11×#102—21no—
108C11×#102—21no—
109C11×C22⋊C8D411yescharacteristic
110C11×C22⋊C8D411yescharacteristic
111C4×C8×C11C2311yescharacteristic
112#66893—22no—
113#66892—22no—
114#66892—41no—
115#66891—22no—
116#66891D414yescomplemented
117#66890—22no—
118#66890—22no—
119#66890—22no—
120#66890—41no—
121#66885—21no—
122#66885—21no—
123#66882C2311yescharacteristic
124#66880—21no—
125#66876—22no—
126C2×C11⋊C16—22no—
127C2×C11⋊C16C2311yescharacteristic
128C2×C11⋊C16C2311yescharacteristic
129C2×C11⋊C16C2311yescharacteristic
130C2×C11⋊C16C2311yescharacteristic
131#33834—111nomaximal, Sylow
132C24×C11—41no—
133C11×#41—42no—
134C11×#41—81no—
135C2×Q8×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—41no—
142C2×D4×C11—81no—
143C2×D4×C11D811yescharacteristic
144C22×C4×C11—41no—
145C22×C4×C11—41no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C2×C22⋊D11—41no—
149C2×C22⋊D11—41no—
150C2×C22⋊D11—41no—
151C2×C22⋊D11—41no—
152#4339—42no—
153#4339—42no—
154#4339—81no—
155#4339—81no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—41no—
159C2×D44—41no—
160C2×C4×D11—41no—
161C2×C4×D11—41no—
162C2×Dic22—21no—
163C11×Q16—21no—
164C11×Q16—21no—
165C11×SD16—42no—
166C11×SD16—81no—
167C11×D8—21no—
168C11×D8—21no—
169C11×D8—21no—
170C11×D8—42no—
171C11×D8C2×D412yes—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11C2×D411yescharacteristic
177C2×C8×C11C2×D411yescharacteristic
178C2×C8×C11C2×D411yescharacteristic
179C2×C8×C11C2411yescharacteristic
180C11×C4⋊C4—21no—
181C11×C4⋊C4—41no—
182C11×C4⋊C4D811yescharacteristic
183C11×C22⋊C4—41no—
184C11×C22⋊C4—41no—
185C11×C22⋊C4—41no—
186C11×C22⋊C4—41no—
187C11×C22⋊C4—41no—
188C11×C22⋊C4D811yescharacteristic
189C11×C22⋊C4D811yescharacteristic
190C42×C11C2×D411yescharacteristic
191(C2×D11)⋊C4—41no—
192(C2×D11)⋊C4—41no—
193C4⋊Dic11—21no—
194Dic11⋊C4—41no—
195C4×Dic11—41no—
196Dic44—21no—
197Dic44C2×D412yes—
198D88—21no—
199D88—21no—
200D88—21no—
201D88—21no—
202D88—81no—
203#4314—42no—
204#4314—42no—
205C11⋊C16—21no—
206C11⋊C16—21no—
207C11⋊C16—21no—
208C11⋊C16C2×D412yes—
209C2×#509—111no—
210C2×#508—111no—
211#3287—111no—
212#3280D1111yescharacteristic, complemented
213#2250—111no—
214#2220—111no—
215#2215—111no—
216#2211—111no—
217#2206—111no—
218#2189—111no—
219#2186—111no—
220#2186—111no—
221#2184—111no—
222#2175—111no—
223#2168—111no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—82no—
227C23×C11—82no—
228C23×C11—161no—
229C23×C11C2×D811yescharacteristic
230C23×C11C2×D811yescharacteristic
231C22×D11—41no—
232C22×D11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235D4×C11—22no—
236D4×C11—41no—
237D4×C11—41no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—82no—
241D4×C11—82no—
242D4×C11—161no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—82no—
250C2×C4×C11—161no—
251C2×C4×C11C2×D811yescharacteristic
252C2×C4×C11C2×D811yescharacteristic
253C2×C4×C11C2×D811yescharacteristic
254C2×C4×C11C2×D811yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C22⋊D11—82no—
257C22⋊D11—82no—
258C22⋊D11—161no—
259C22⋊D11—161no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262D44—41no—
263D44—41no—
264D44—41no—
265D44—41no—
266D44—82no—
267D44—161no—
268C4×D11—82no—
269C4×D11—82no—
270Dic22—22no—
271Dic22—41no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11C22×D411yescharacteristic
276C8×C11H(5,𝔽2)11yescharacteristic
277C2×#135—111no—
278C2×#135—111no—
279C2×#135C2×D1111yescharacteristic
280C22×D8C2×D1111yescharacteristic
281#550—221no—
282#546—21no—
283#509—224no—
284#508—224no—
285C2×Q32—111no—
286C2×SD32—111no—
287C2×SD32—111no—
288C2×SD32—111no—
289C2×SD32—111no—
290C2×D16—111no—
291C2×D16—111no—
292C2×D16—111no—
293C2×D16—111no—
294C2×M32—111no—
295C22×C16—111no—
296#495C2×D1111yescharacteristic
297#493—111no—
298#467C2×D1111yescharacteristic
299#466—111no—
300#466—111no—
301#466C2×D1111yescharacteristic
302#463—21no—
303#460—221no—
304#450—21no—
305#449—21no—
306#449—221no—
307#449—221no—
308C4×Q16—111no—
309C4×D8C2×D1111yescharacteristic
310C8×D4C2×D1111yescharacteristic
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—
321#346—111no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—42no—
329C22×C11—81no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11—164no—
335C22×C11C22×D811yescharacteristic
336C2×D11—81no—
337C2×D11—81no—
338C2×D11—81no—
339C2×D11—81no—
340C2×D11—81no—
341C2×D11—81no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—21no—
345C4×C11—21no—
346C4×C11—81no—
347C4×C11—81no—
348C4×C11D4211yescharacteristic
349C4×C11#57611yescharacteristic
350Dic11—42no—
351Dic11—81no—
352C2×#41—21no—
353C2×#41—221no—
354C2×#41—221no—
355C22×D4—21no—
356#135—22no—
357#135—41no—
358#135—222no—
359#135—222no—
360#135—441no—
361#135—441no—
362C2×Q16—111no—
363C2×Q16C22×D1111yescharacteristic
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—221no—
367C2×SD16—221no—
368C2×D8—22no—
369C2×D8—21no—
370C2×D8—41no—
371C2×D8—111no—
372C2×D8—111no—
373C2×D8—221no—
374C2×D8C22×D1111yescharacteristic
375C2×D8C22×D1111yescharacteristic
376C22×C8C22×D1111yescharacteristic
377C22×C8C22×D1111yescharacteristic
378#127—221no—
379#127—441no—
380#124—21no—
381#123—41no—
382C22⋊Q8—21no—
383#121—21no—
384#121—41no—
385#121—221no—
386#121—221no—
387#121—441no—
388#121—441no—
389#120—41no—
390C4×Q8—221no—
391C4×D4—21no—
392C4×D4—441no—
393C4×D4C22⋊D1111yescharacteristic
394C2×C22⋊C4—41no—
395Q32—222no—
396SD32—114no—
397SD32—222no—
398SD32—222no—
399SD32—441no—
400D16—222no—
401D16—222no—
402D16—222no—
403D16—441no—
404M32—222no—
405C2×C16—111no—
406C2×C16—111no—
407C2×C16—111no—
408C2×C16—111no—
409C2×C16—222no—
410#107—111no—
411#107C22×D1111yescharacteristic
412C4⋊C8C22⋊D1111yescharacteristic
413#103—21no—
414#103—221no—
415#102—21no—
416#102—21no—
417#102—221no—
418#102—221no—
419C22⋊C8C22⋊D1111yescharacteristic
420C22⋊C8C22⋊D1111yescharacteristic
421C4×C8C22×D1111yescharacteristic
422C2×C11—41no—
423C2×C11—41no—
424C2×C11—82no—
425C2×C11—161no—
426C2×C11D4×D811yescharacteristic
427C2×C11#341411yescharacteristic
428C2×C11#341511yescharacteristic
429D11—161no—
430D11—161no—
431C24—41no—
432#41—42no—
433#41—81no—
434#41—442no—
435#41—442no—
436#41—881no—
437#41—881no—
438C2×Q8—21no—
439C2×Q8—221no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—42no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—41no—
446C2×D4—81no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—441no—
450C2×D4—441no—
451C2×D4—441no—
452C2×D4—441no—
453C2×D4—441no—
454C2×D4—441no—
455C2×D4#432311yescharacteristic
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—441no—
459C22×C4—441no—
460C22×C4C2×C22⋊D1111yescharacteristic
461C22×C4C2×C22⋊D1111yescharacteristic
462Q16—21no—
463Q16—21no—
464Q16—112no—
465Q16—221no—
466SD16—42no—
467SD16—81no—
468SD16—442no—
469SD16—442no—
470D8—21no—
471D8—21no—
472D8—21no—
473D8—42no—
474D8—221no—
475D8—221no—
476D8—221no—
477D8—221no—
478D8—881no—
479D8D4×D1112yes—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8C2×C22⋊D1111yescharacteristic
485C2×C8C2×C22⋊D1111yescharacteristic
486C2×C8C2×C22⋊D1111yescharacteristic
487C2×C8C23×D1111yescharacteristic
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—221no—
491C4⋊C4—441no—
492C4⋊C4#432311yescharacteristic
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—441no—
499C22⋊C4—441no—
500C22⋊C4#432311yescharacteristic
501C22⋊C4#432311yescharacteristic
502C42—441no—
503C42C2×C22⋊D1111yescharacteristic
504C16—112no—
505C16—221no—
506C16—221no—
507C16—221no—
508C11#3383411yescharacteristic, complemented, Sylow
509C23—41no—
510C23—41no—
511C23—82no—
512C23—82no—
513C23—161no—
514C23—441no—
515C23—441no—
516C23C2×#432311yescharacteristic
517C23C2×#432311yescharacteristic
518Q8—41no—
519Q8—41no—
520Q8—222no—
521Q8—441no—
522D4—22no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—82no—
528D4—82no—
529D4—161no—
530D4—441no—
531D4—441no—
532D4—441no—
533D4—441no—
534D4—882no—
535D4—882no—
536D4—882no—
537D4—1761no—
538D4—1761no—
539D4—1761no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—82no—
547C2×C4—161no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—882no—
551C2×C4—882no—
552C2×C4C2×#432311yescharacteristic
553C2×C4C2×#432311yescharacteristic
554C2×C4C2×#432311yescharacteristic
555C2×C4C2×#432311yescharacteristic
556C2×C4C22×C22⋊D1111yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8C2×D4×D1111yescharacteristic
561C8#6703711yescharacteristic
562C22—21no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—42no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—164no—
575C22—881no—
576C22—881no—
577C22—881no—
578C22—881no—
579C22—881no—
580C22—881no—
581C22C22×#432311yescharacteristic
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—81no—
587C4—81no—
588C4—442no—
589C4—881no—
590C4D4×C22⋊D1111yescharacteristic
591C4#1062336611yescharacteristic
592C2—41no—
593C2—41no—
594C2—82no—
595C2—161no—
596C2—1761no—
597C2—1761no—
598C2D4×#432311yescharacteristic
599C2#1308175011yescharacteristic
600C2#1308175511yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3280C2
socleC22×C11C22×D8
hypercenter#3280D11
hypocenterC11#33834
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3280

Complements

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

NH ≅ G/Ntype
1. C2×#10622760C2semidirect
2. C2×#10622807C2semidirect
3. #13080376C2semidirect
4. #13070883C2semidirect
5. #13070731C2semidirect
6. #13070700C2semidirect
7. #13070675C2semidirect
8. #13070651C2semidirect
9. #13070554C2semidirect
10. #13070539C2semidirect
11. #13070537C2semidirect
12. #13070528C2semidirect
13. #13070480C2semidirect
14. #13070442C2semidirect
15. C11×#3280C2semidirect
20. C2×#66957C22semidirect
31. C2×#66893C22semidirect
32. C2×#66892C22semidirect
33. C2×#66892C22semidirect
42. #10622728C22semidirect
44. C22×C11⋊C16C22semidirect
48. C4×Dic44C22semidirect
49. #10622308C22semidirect
50. #10622202C22semidirect
54. C22⋊(C11⋊C16)C22semidirect
55. #10622130C22semidirect
56. #10622129C22semidirect
57. #10622129C22semidirect
58. #10622127C22semidirect
59. C4⋊(C11⋊C16)C22semidirect
60. #10622099C22semidirect
116. #66891D4semidirect
212. #3280D11semidirect
508. C11#33834semidirect

Maximal subgroups

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

subgroupindex
C2×#106227602
C2×#106228072
#130803762
#130708832
#130707312
#130707002
#130706752
#130706512
#130705542
#130705392
#130705372
#130705282
#130704802
#130704422
C11×#32802
#3383411