Finite Group Databasebeta

← #14910357

Subgroups — #14910357

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×#10622527C211yesmaximal, characteristic, complemented
2C2×#10622524C211yesmaximal, characteristic, complemented
3#13080302C211yesmaximal, characteristic, complemented
4#13080300C211yesmaximal, characteristic, complemented
5#13070875C211yesmaximal, characteristic, complemented
6#13070732C211yesmaximal, characteristic, complemented
7#13070728C211yesmaximal, characteristic, complemented
8#13070672C211yesmaximal, characteristic, complemented
9#13070559C211yesmaximal, characteristic, complemented
10#13070553C211yesmaximal, characteristic, complemented
11#13070529C211yesmaximal, characteristic, complemented
12#13070526C211yesmaximal, characteristic, complemented
13C4×#66890C211yesmaximal, characteristic, complemented
14#13070447C211yesmaximal, characteristic, complemented
15C11×#2210C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C2×#66965C2211yescharacteristic
18C2×D8×D11C2211yescharacteristic, complemented
19C2×D8×D11C2211yescharacteristic, complemented
20#10623207—21no—
21#10623085—21no—
22C2×C11×SD32C2211yescharacteristic, complemented
23C2×C11×D16C2211yescharacteristic
24C11×#495C2211yescharacteristic, complemented
25C4×C11×D8C2211yescharacteristic, complemented
26#10622801C2211yescharacteristic, complemented
27C2×#66893C2211yescharacteristic, complemented
28C2×#66892C2211yescharacteristic, complemented
29#10622785—21no—
30#10622782—21no—
31#10622770C2211yescharacteristic
32C2×#66891C2211yescharacteristic, complemented
33C2×#66890C2211yescharacteristic
34C2×#66890C2211yescharacteristic
35#10622670—21no—
36#10622629—21no—
37#10622527—24no—
38#10622524—24no—
39C2×#66864C2211yescharacteristic, complemented
40C2×D176C2211yescharacteristic
41C2×#66862C2211yescharacteristic, complemented
42C2×#66862C2211yescharacteristic, complemented
43#10622500C2211yescharacteristic, complemented
44#10622496C2211yescharacteristic
45#10622394—21no—
46#10622389—21no—
47#10622309C2211yescharacteristic, complemented
48C4×D88C2211yescharacteristic, complemented
49C8×D44C2211yescharacteristic
50C11×C4⋊C16C2211yescharacteristic, complemented
51C11×#358C2211yescharacteristic, complemented
52C11×#357C2211yescharacteristic, complemented
53#10622200C2211yescharacteristic, complemented
54#10622147C2211yescharacteristic, complemented
55(C2×D11)⋊C16C2211yescharacteristic, complemented
56(C2×D11)⋊C16C2211yescharacteristic, complemented
57#10622141C2211yescharacteristic, complemented
58#10622129C2211yescharacteristic, complemented
59#10622127C2211yescharacteristic, complemented
60C4×C11⋊C16C2211yescharacteristic, complemented
61C2×#4343—21no—
62C2×#4341—21no—
63C2×D4×D11—21no—
64C2×D4×D11—21no—
65C2×C11×Q16C2311yescharacteristic
66C2×C11×SD16—21no—
67C2×C11×D8C2311yescharacteristic
68C2×C11×D8C2311yescharacteristic
69C11×#124—21no—
70C4×D4×C11—21no—
71#66999—21no—
72C2×#4325—21no—
73#66991—21no—
74C2×#4324—21no—
75C2×#4323—21no—
76C2×#4323—21no—
77#66983—41no—
78C2×(C2×D11)⋊C4—41no—
79#66972—22no—
80#66972—41no—
81#66965—22no—
82#66965—41no—
83D8×D11—22no—
84D8×D11—22no—
85D8×D11—41no—
86D8×D11—41no—
87C2×Dic44C2311yescharacteristic
88C2×D88C2311yescharacteristic
89C2×D88C2311yescharacteristic
90C2×#4314—21no—
91C2×C8×D11C2311yescharacteristic
92C2×C8×D11C2311yescharacteristic
93#66950—21no—
94#66948—21no—
95#66939—41no—
96#66937—41no—
97#66936—41no—
98#66935—41no—
99#66935—41no—
100C22⋊C4×D11—41no—
101#66928—21no—
102C4×D44—21no—
103C4×D44D411yescharacteristic
104C11×SD32—22no—
105C11×D16—22no—
106C2×C11×C16C2311yescharacteristic
107C2×C11×C16C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#102—21no—
110C4×C8×C11C2311yescharacteristic
111#66899—21no—
112#66896—21no—
113#66893—41no—
114#66892—22no—
115#66891—22no—
116#66890—41no—
117#66890D414yescomplemented
118#66885—21no—
119(C2×D11)⋊C8D411yescharacteristic
120(C2×D11)⋊C8D411yescharacteristic
121#66882C2311yescharacteristic
122C2×C11⋊C16C2311yescharacteristic
123C2×C11⋊C16C2311yescharacteristic
124#66874—21no—
125#66873—21no—
126C4⋊(C11⋊C8)D411yescharacteristic
127#66864—22no—
128D176—22no—
129#66862—22no—
130#66862—22no—
131#33839—111nomaximal, Sylow
132C23×D11—41no—
133C23×D11—41no—
134C2×Q8×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C22×C4×C11—41no—
138C2×C22⋊D11—41no—
139C2×C22⋊D11—41no—
140C2×C22⋊D11—41no—
141C2×C22⋊D11—41no—
142C22×Dic11—41no—
143#4343—42no—
144#4343—81no—
145#4341—42no—
146#4341—81no—
147D4×D11—42no—
148D4×D11—42no—
149D4×D11—81no—
150D4×D11—81no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—41no—
154C2×D44—41no—
155C2×D44D811yescharacteristic
156C2×C4×D11—41no—
157C2×C4×D11—41no—
158C2×C4×D11C2×D411yescharacteristic
159C2×C4×D11C2×D411yescharacteristic
160C2×Dic22—21no—
161C11×Q16—21no—
162C11×Q16—21no—
163C11×SD16—81no—
164C11×D8—21no—
165C11×D8—21no—
166C11×D8—21no—
167C11×D8C2×D412yes—
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2411yescharacteristic
170C11×C4⋊C4—21no—
171C11×C22⋊C4—41no—
172C11×C22⋊C4—41no—
173C11×C22⋊C4—41no—
174C42×C11C2×D411yescharacteristic
175C22⋊Dic11—41no—
176#4325—42no—
177#4324—42no—
178#4323—42no—
179#4323—42no—
180(C2×D11)⋊C4—41no—
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)⋊C4D811yescharacteristic
187(C2×D11)⋊C4D811yescharacteristic
188C4⋊Dic11—21no—
189C4⋊Dic11—41no—
190C4⋊Dic11D811yescharacteristic
191Dic11⋊C4—41no—
192C2×C11⋊C8C2×D411yescharacteristic
193C2×C11⋊C8C2×D411yescharacteristic
194Dic44—21no—
195Dic44—21no—
196D88—21no—
197D88—21no—
198D88—21no—
199D88C2×D412yes—
200#4314—81no—
201C8×D11—21no—
202C8×D11—21no—
203C8×D11—21no—
204C8×D11—21no—
205C11×C16—21no—
206C11×C16—21no—
207C11⋊C16—21no—
208C11⋊C16C2×D412yes—
209C2×#509—111no—
210C2×#509—111no—
211#3280—111no—
212#3280—111no—
213#2249—111no—
214#2220—111no—
215#2220—111no—
216#2210—111no—
217#2210D1111yescharacteristic, complemented
218#2189—111no—
219#2189—111no—
220#2184—111no—
221#2184—111no—
222C4×D16—111no—
223#2169—111no—
224C23×C11—41no—
225C23×C11—41no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—82no—
229C22×D11—82no—
230C22×D11—82no—
231C22×D11—82no—
232C22×D11—161no—
233C22×D11—161no—
234C22×D11C2×D811yescharacteristic
235C22×D11C2×D811yescharacteristic
236Q8×C11—41no—
237Q8×C11—41no—
238D4×C11—22no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—161no—
245C2×C4×C11C2×D811yescharacteristic
246C2×C4×C11C2×D811yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C22⋊D11—82no—
249C22⋊D11—82no—
250C22⋊D11—82no—
251C22⋊D11—161no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—82no—
255C2×Dic11C2×D811yescharacteristic
256C2×Dic11C2×D811yescharacteristic
257D44—22no—
258D44—41no—
259D44—41no—
260D44—41no—
261D44—41no—
262D44—82no—
263D44—161no—
264C4×D11—21no—
265C4×D11—21no—
266C4×D11—21no—
267C4×D11—21no—
268C4×D11—82no—
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×D16C2×D1111yescharacteristic
294C2×M32—111no—
295C2×M32—111no—
296#495—111no—
297#495C2×D1111yescharacteristic, complemented
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×D8C2×D1111yescharacteristic, complemented
310C8×D4—111no—
311#366—111no—
312C4⋊C16C2×D1111yescharacteristic, complemented
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—42no—
323C22×C11—81no—
324C22×C11—81no—
325C22×C11—81no—
326C22×C11—81no—
327C22×C11—81no—
328C22×C11C22×D811yescharacteristic
329C2×D11—21no—
330C2×D11—21no—
331C2×D11—21no—
332C2×D11—21no—
333C2×D11—21no—
334C2×D11—21no—
335C2×D11—42no—
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—21no—
345C4×C11—81no—
346C4×C11—81no—
347C4×C11D4211yescharacteristic
348C4×C11#57611yescharacteristic
349Dic11—21no—
350Dic11—21no—
351Dic11—81no—
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—21no—
364C2×SD16—221no—
365C2×SD16—221no—
366C2×SD16—221no—
367C2×D8—111no—
368C2×D8—111no—
369C2×D8—221no—
370C2×D8—221no—
371C2×D8—222no—
372C2×D8—222no—
373C2×D8—441no—
374C2×D8—441no—
375C2×D8C22×D1111yescharacteristic
376C2×D8C22×D1111yescharacteristic
377C22×C8—111no—
378C22×C8—111no—
379#124—21no—
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—21no—
392C4×D4—111no—
393C4×D4—221no—
394C2×C22⋊C4—441no—
395C2×C22⋊C4—441no—
396Q32—441no—
397SD32—22no—
398SD32—222no—
399SD32—222no—
400SD32—222no—
401D16—22no—
402D16—114no—
403D16—222no—
404D16—441no—
405M32—222no—
406M32—222no—
407C2×C16—111no—
408C2×C16—111no—
409C2×C16C22×D1111yescharacteristic
410C2×C16C22×D1111yescharacteristic
411#107—111no—
412#107C22×D1111yescharacteristic
413C4⋊C8—111no—
414#103—221no—
415#103—221no—
416#102—21no—
417#102—221no—
418#102—221no—
419#102—221no—
420C22⋊C8—111no—
421C22⋊C8—111no—
422C4×C8C22×D1111yescharacteristic
423C2×C11—82no—
424C2×C11—161no—
425C2×C11D4×D811yescharacteristic
426C2×C11#341411yescharacteristic
427C2×C11#341511yescharacteristic
428D11—41no—
429D11—41no—
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—21no—
442C2×D4—111no—
443C2×D4—221no—
444C2×D4—221no—
445C2×D4—441no—
446C2×D4—441no—
447C2×D4—441no—
448C2×D4—441no—
449C2×D4—442no—
450C2×D4—442no—
451C2×D4—441no—
452C2×D4—441no—
453C2×D4—881no—
454C2×D4—881no—
455C22×C4—41no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—441no—
459C22×C4—441no—
460C22×C4—441no—
461Q16—21no—
462Q16—21no—
463Q16—221no—
464Q16—221no—
465SD16—81no—
466SD16—442no—
467SD16—442no—
468SD16—881no—
469D8—21no—
470D8—21no—
471D8—21no—
472D8—112no—
473D8—221no—
474D8—221no—
475D8—221no—
476D8—442no—
477D8—442no—
478D8D4×D1112yes—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8D4×D1111yescharacteristic
486C2×C8C23×D1111yescharacteristic
487C4⋊C4—21no—
488C4⋊C4—111no—
489C4⋊C4—221no—
490C4⋊C4—441no—
491C4⋊C4—441no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—111no—
496C22⋊C4—111no—
497C22⋊C4—441no—
498C22⋊C4—441no—
499C22⋊C4—441no—
500C22⋊C4—441no—
501C22⋊C4—441no—
502C22⋊C4—441no—
503C22⋊C4—441no—
504C42D4×D1111yescharacteristic
505C16—21no—
506C16—21no—
507C16—112no—
508C16—221no—
509C11#3383911yescharacteristic, complemented, Sylow
510C23—41no—
511C23—41no—
512C23—111no—
513C23—111no—
514C23—441no—
515C23—441no—
516C23—882no—
517C23—882no—
518C23—882no—
519C23—882no—
520C23—1761no—
521C23—1761no—
522Q8—41no—
523Q8—41no—
524Q8—441no—
525Q8—441no—
526D4—22no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—222no—
531D4—441no—
532D4—441no—
533D4—441no—
534D4—441no—
535D4—882no—
536D4—882no—
537D4—882no—
538D4—882no—
539D4—1761no—
540D4—1761no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—111no—
544C2×C4—111no—
545C2×C4—161no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—882no—
553C2×C4—882no—
554C2×C4—1761no—
555C2×C4D8×D1111yescharacteristic
556C2×C4D8×D1111yescharacteristic
557C2×C4C2×D4×D1111yescharacteristic
558C8—21no—
559C8—221no—
560C8—221no—
561C8C2×D4×D1111yescharacteristic
562C8#6704211yescharacteristic
563C22—42no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22—221no—
570C22—221no—
571C22—221no—
572C22—221no—
573C22—221no—
574C22—221no—
575C22—442no—
576C22—881no—
577C22—881no—
578C22—881no—
579C22—881no—
580C22—881no—
581C22—1764no—
582C22—1764no—
583C22C2×D8×D1111yescharacteristic
584C4—21no—
585C4—21no—
586C4—81no—
587C4—81no—
588C4—221no—
589C4—221no—
590C4—881no—
591C4—881no—
592C4#1062314011yescharacteristic
593C4#1062330511yescharacteristic
594C2—82no—
595C2—161no—
596C2—441no—
597C2—441no—
598C2—882no—
599C2—1761no—
600C2#1308028811yescharacteristic
601C2#1308174911yescharacteristic
602C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2210C2
socleC22×C11C22×D8
hypercenter#2210D11
hypocenterC11#33839
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2210

Complements

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

NH ≅ G/Ntype
1. C2×#10622527C2semidirect
2. C2×#10622524C2semidirect
3. #13080302C2semidirect
4. #13080300C2semidirect
5. #13070875C2semidirect
6. #13070732C2semidirect
7. #13070728C2semidirect
8. #13070672C2semidirect
9. #13070559C2semidirect
10. #13070553C2semidirect
11. #13070529C2semidirect
12. #13070526C2semidirect
13. C4×#66890C2semidirect
14. #13070447C2semidirect
15. C11×#2210C2semidirect
18. C2×D8×D11C22semidirect
19. C2×D8×D11C22semidirect
22. C2×C11×SD32C22semidirect
24. C11×#495C22semidirect
25. C4×C11×D8C22semidirect
26. #10622801C22semidirect
27. C2×#66893C22semidirect
28. C2×#66892C22semidirect
32. C2×#66891C22semidirect
39. C2×#66864C22semidirect
41. C2×#66862C22semidirect
42. C2×#66862C22semidirect
43. #10622500C22semidirect
47. #10622309C22semidirect
48. C4×D88C22semidirect
50. C11×C4⋊C16C22semidirect
51. C11×#358C22semidirect
52. C11×#357C22semidirect
53. #10622200C22semidirect
54. #10622147C22semidirect
55. (C2×D11)⋊C16C22semidirect
56. (C2×D11)⋊C16C22semidirect
57. #10622141C22semidirect
58. #10622129C22semidirect
59. #10622127C22semidirect
60. C4×C11⋊C16C22semidirect
117. #66890D4semidirect
217. #2210D11semidirect
289. C2×SD32C2×D11semidirect
297. #495C2×D11semidirect
309. C4×D8C2×D11semidirect
312. C4⋊C16C2×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×#106225272
C2×#106225242
#130803022
#130803002
#130708752
#130707322
#130707282
#130706722
#130705592
#130705532
#130705292
#130705262
C4×#668902
#130704472
C11×#22102
#3383911