Finite Group Databasebeta

← #14910465

Subgroups — #14910465

Order 2816.

696 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622517C211yesmaximal, characteristic, complemented
2C2×D11×SD32C211yesmaximal, characteristic, complemented
3#13080360C211yesmaximal, characteristic, complemented
4#13080304C211yesmaximal, characteristic, complemented
5#13070876C211yesmaximal, characteristic, complemented
6#13070713C211yesmaximal, characteristic, complemented
7#13070677C211yesmaximal, characteristic, complemented
8#13070674C211yesmaximal, characteristic, complemented
9#13070554C211yesmaximal, characteristic, complemented
10#13070551C211yesmaximal, characteristic, complemented
11#13070537C211yesmaximal, characteristic, complemented
12#13070529C211yesmaximal, characteristic, complemented
13#13070467C211yesmaximal, characteristic, complemented
14C16×C22⋊D11C211yesmaximal, characteristic, complemented
15C11×#2217C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic
17C2×D8×D11C2211yescharacteristic
18C2×#66957C2211yescharacteristic
19C2×#66957C2211yescharacteristic, complemented
20#10623164—21no—
21#10623143—21no—
22C2×C11×SD32C2211yescharacteristic
23C22×C11×C16C2211yescharacteristic, complemented
24C11×#467C2211yescharacteristic, complemented
25C11×#466C2211yescharacteristic
26#10622804C2211yescharacteristic, complemented
27C2×#66893C2211yescharacteristic, complemented
28C2×#66892C2211yescharacteristic
29#10622768C2211yescharacteristic
30C2×#66891C2211yescharacteristic
31C2×#66890C2211yescharacteristic
32C8×C22⋊D11C2211yescharacteristic
33#10622660—21no—
34#10622650—21no—
35D11×SD32—24no—
36C2×Dic88C2211yescharacteristic, complemented
37#10622517—24no—
38C2×#66864C2211yescharacteristic
39C2×#66864C2211yescharacteristic, complemented
40C2×D176C2211yescharacteristic
41C2×C16×D11C2211yescharacteristic
42#10622500C2211yescharacteristic
43#10622496C2211yescharacteristic
44#10622486C2211yescharacteristic, complemented
45#10622485C2211yescharacteristic
46#10622419—21no—
47#10622411—21no—
48#10622400—21no—
49#10622389—21no—
50C11×#367C2211yescharacteristic, complemented
51C11×#358C2211yescharacteristic, complemented
52C11×#357C2211yescharacteristic
53C22⋊(C11⋊C16)C2211yescharacteristic, complemented
54(C2×D11)⋊C16C2211yescharacteristic
55Dic11⋊C16C2211yescharacteristic, complemented
56C16×Dic11C2211yescharacteristic, complemented
57#10622130C2211yescharacteristic, complemented
58#10622130C2211yescharacteristic, complemented
59#10622129C2211yescharacteristic
60#10622129C2211yescharacteristic, complemented
61C2×Q8×D11—21no—
62C2×D4×D11—21no—
63C2×#4339—21no—
64C2×#4339—21no—
65C2×C11×Q16C2311yescharacteristic
66C2×C11×D8C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×C22⋊Q8—21no—
69C11×#121—21no—
70#67000—21no—
71C2×#4326—21no—
72C2×#4325—21no—
73#66991—41no—
74#66990—41no—
75#66989—21no—
76C2×#4324—21no—
77C2×#4323—21no—
78C4×C22⋊D11D411yescharacteristic
79Q16×D11—22no—
80Q16×D11—41no—
81D8×D11—22no—
82D8×D11—41no—
83C2×Dic44C2311yescharacteristic
84C2×Dic44C2311yescharacteristic
85#66957—22no—
86#66957—22no—
87#66957—41no—
88#66957—41no—
89C2×D88C2311yescharacteristic
90C2×D88C2311yescharacteristic
91C2×#4314—21no—
92C2×#4314—21no—
93C2×C8×D11C2311yescharacteristic
94#66950—21no—
95#66949—41no—
96#66948—21no—
97#66946—21no—
98#66946—41no—
99#66940—21no—
100#66938—41no—
101#66937—41no—
102#66936—41no—
103C22⋊C4×D11—41no—
104C11×SD32—22no—
105C2×C11×C16—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#66891—22no—
116#66890—41no—
117(C2×D11)⋊C8D411yescharacteristic
118Dic11⋊C8D411yescharacteristic
119C8×Dic11C2311yescharacteristic
120C2×C11⋊C16C2311yescharacteristic
121C2×C11⋊C16C2311yescharacteristic
122#66874—21no—
123#66874—21no—
124#66873—21no—
125#66873—21no—
126Dic88—22no—
127#66864—22no—
128#66864D414yescomplemented
129D176—22no—
130C16×D11—22no—
131#33848—111nomaximal, Sylow
132C23×D11—41no—
133C2×Q8×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—41no—
136C22×C4×C11C2×D411yescharacteristic
137C2×C22⋊D11—41no—
138C2×C22⋊D11—41no—
139C2×C22⋊D11—41no—
140C2×C22⋊D11D811yescharacteristic
141Q8×D11—42no—
142Q8×D11—81no—
143D4×D11—42no—
144D4×D11—81no—
145#4339—42no—
146#4339—42no—
147#4339—81no—
148#4339—81no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—41no—
152C2×C4×D11—41no—
153C2×C4×D11—41no—
154C2×C4×D11—41no—
155C2×C4×D11—41no—
156C2×C4×D11C2×D411yescharacteristic
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—41no—
160C11×Q16—21no—
161C11×Q16—21no—
162C11×D8—21no—
163C11×D8—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11C2×D411yescharacteristic
167C2×C8×C11C2411yescharacteristic
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—41no—
171C11×C22⋊C4—41no—
172C11×C22⋊C4—41no—
173C22⋊Dic11—41no—
174C22⋊Dic11—41no—
175C22⋊Dic11D811yescharacteristic
176#4326—42no—
177#4325—81no—
178#4324—81no—
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)⋊C4D811yescharacteristic
186C4⋊Dic11—41no—
187Dic11⋊C4—41no—
188Dic11⋊C4D811yescharacteristic
189C4×Dic11—41no—
190C4×Dic11C2×D411yescharacteristic
191C2×C11⋊C8C2×D411yescharacteristic
192C2×C11⋊C8C2×D411yescharacteristic
193Dic44—21no—
194Dic44—21no—
195Dic44—21no—
196Dic44C2×D412yes—
197D88—21no—
198D88—21no—
199D88—21no—
200D88C2×D412yes—
201#4314—42no—
202#4314—42no—
203C8×D11—21no—
204C8×D11—21no—
205C11×C16—21no—
206C11×C16C2×D412yes—
207C11⋊C16—21no—
208C11⋊C16—21no—
209C2×#508—111no—
210C22×SD32—111no—
211#3285—111no—
212#3280—111no—
213#2249—111no—
214#2217—111no—
215#2217D1111yescharacteristic, complemented
216#2211—111no—
217#2210—111no—
218#2189—111no—
219#2188—111no—
220#2186—111no—
221#2184—111no—
222C4×SD32—111no—
223D4×C16—111no—
224C23×C11—41no—
225C23×C11C2×D811yescharacteristic
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—82no—
229C22×D11—82no—
230C22×D11—161no—
231C22×D11C2×D811yescharacteristic
232Q8×C11—41no—
233Q8×C11—41no—
234D4×C11—41no—
235D4×C11—41no—
236D4×C11—161no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11C2×D811yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C22⋊D11—22no—
245C22⋊D11—82no—
246C22⋊D11—82no—
247C22⋊D11—82no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11C2×D811yescharacteristic
251C2×Dic11C2×D811yescharacteristic
252C2×Dic11C2×D811yescharacteristic
253D44—22no—
254D44—41no—
255D44—41no—
256D44—41no—
257D44—82no—
258C4×D11—21no—
259C4×D11—21no—
260C4×D11—82no—
261C4×D11—82no—
262C4×D11—82no—
263C4×D11—161no—
264Dic22—22no—
265Dic22—41no—
266Dic22—41no—
267Dic22—41no—
268Dic22—82no—
269C8×C11—21no—
270C8×C11C22×D411yescharacteristic
271C8×C11H(5,𝔽2)11yescharacteristic
272C11⋊C8—21no—
273C11⋊C8—21no—
274C2×#135—111no—
275C2×#135—111no—
276C22×Q16—111no—
277C22×D8—111no—
278#548—221no—
279#546—221no—
280#508—224no—
281C2×Q32—111no—
282C2×Q32—111no—
283C2×SD32—111no—
284C2×SD32—111no—
285C2×SD32—111no—
286C2×SD32—111no—
287C2×SD32—224no—
288C2×SD32C2×D1111yescharacteristic
289C2×D16—111no—
290C2×D16—111no—
291C22×C16—111no—
292C22×C16C2×D1111yescharacteristic, complemented
293#495—111no—
294#495—111no—
295#467—111no—
296#467C2×D1111yescharacteristic, complemented
297#466—111no—
298#466C2×D1111yescharacteristic
299#464—221no—
300#463—221no—
301#452—221no—
302#450—221no—
303#449—221no—
304#448—221no—
305C4×Q16—111no—
306C4×D8—111no—
307C8×D4—111no—
308#367C2×D1111yescharacteristic, complemented
309C4⋊C16—111no—
310#358—111no—
311#358—111no—
312#358C2×D1111yescharacteristic, complemented
313#357—111no—
314#357—111no—
315#357C2×D1111yescharacteristic
316C22⋊C16—111no—
317C22⋊C16—111no—
318C4×C16—111no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—81no—
323C22×C11—81no—
324C22×C11—81no—
325C22×C11C22×D811yescharacteristic
326C2×D11—21no—
327C2×D11—21no—
328C2×D11—42no—
329C2×D11—81no—
330C2×D11—81no—
331C2×D11—81no—
332C2×D11—81no—
333C2×D11—81no—
334C2×D11—164no—
335C2×D11#50812yescomplemented
336C4×C11—21no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11D4211yescharacteristic
341C4×C11#57611yescharacteristic
342Dic11—21no—
343Dic11—21no—
344Dic11—21no—
345Dic11—42no—
346Dic11—81no—
347C2×#41—221no—
348C2×#41—221no—
349C22×Q8—221no—
350C22×D4—221no—
351#135—222no—
352#135—222no—
353#135—441no—
354#135—441no—
355C2×Q16—111no—
356C2×Q16—111no—
357C2×Q16—221no—
358C2×Q16—222no—
359C2×Q16—441no—
360C2×Q16C22×D1111yescharacteristic
361C2×SD16—221no—
362C2×SD16—221no—
363C2×SD16—221no—
364C2×SD16—221no—
365C2×D8—111no—
366C2×D8—111no—
367C2×D8—221no—
368C2×D8—222no—
369C2×D8—441no—
370C2×D8C22×D1111yescharacteristic
371C22×C8—111no—
372C22×C8C22×D1111yescharacteristic
373#124—221no—
374#124—221no—
375#124—441no—
376#123—441no—
377C22⋊Q8—21no—
378C22⋊Q8—221no—
379C22⋊Q8—441no—
380#121—21no—
381#121—221no—
382#121—441no—
383#121—441no—
384#120—441no—
385C4×Q8—221no—
386C4×D4—111no—
387C4×D4—221no—
388C4×D4—441no—
389C2×C22⋊C4—441no—
390Q32—222no—
391Q32—441no—
392SD32—22no—
393SD32—114no—
394SD32—222no—
395SD32—222no—
396SD32—222no—
397D16—222no—
398D16—441no—
399C2×C16—22no—
400C2×C16—111no—
401C2×C16—111no—
402C2×C16—222no—
403C2×C16C22×D1111yescharacteristic
404C2×C16C22×D1111yescharacteristic
405#107C22×D1111yescharacteristic
406#107C22×D1111yescharacteristic
407C4⋊C8—111no—
408#103—21no—
409#103—221no—
410#103—221no—
411#102—21no—
412#102—221no—
413#102—221no—
414C22⋊C8—111no—
415C22⋊C8—111no—
416C4×C8—111no—
417C2×C11—41no—
418C2×C11—161no—
419C2×C11D4×D811yescharacteristic
420C2×C11C2×#50811yescharacteristic
421C2×C11#341611yescharacteristic
422D11—22no—
423D11—82no—
424D11—161no—
425C24—441no—
426#41—442no—
427#41—442no—
428#41—881no—
429#41—881no—
430C2×Q8—21no—
431C2×Q8—221no—
432C2×Q8—221no—
433C2×Q8—441no—
434C2×Q8—442no—
435C2×Q8—881no—
436C2×D4—21no—
437C2×D4—41no—
438C2×D4—111no—
439C2×D4—221no—
440C2×D4—221no—
441C2×D4—441no—
442C2×D4—441no—
443C2×D4—442no—
444C2×D4—441no—
445C2×D4—441no—
446C2×D4—881no—
447C22×C4—111no—
448C22×C4—441no—
449C22×C4—441no—
450C22×C4—441no—
451C22×C4—441no—
452C22×C4D4×D1111yescharacteristic
453Q16—21no—
454Q16—21no—
455Q16—112no—
456Q16—221no—
457Q16—221no—
458Q16—221no—
459Q16—442no—
460SD16—442no—
461SD16—442no—
462SD16—881no—
463SD16—881no—
464D8—21no—
465D8—21no—
466D8—112no—
467D8—221no—
468D8—221no—
469D8—221no—
470D8—442no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—111no—
474C2×C8—111no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8D4×D1111yescharacteristic
478C2×C8C23×D1111yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—41no—
482C4⋊C4—111no—
483C4⋊C4—441no—
484C4⋊C4—441no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—111no—
488C22⋊C4—111no—
489C22⋊C4—441no—
490C22⋊C4—441no—
491C22⋊C4—441no—
492C22⋊C4—441no—
493C22⋊C4—441no—
494C22⋊C4—441no—
495C22⋊C4—441no—
496C42—111no—
497C42—441no—
498C16—21no—
499C16—221no—
500C16—221no—
501C16D4×D1112yes—
502C11#3384811yescharacteristic, complemented, Sylow
503C23—41no—
504C23—111no—
505C23—441no—
506C23—441no—
507C23—882no—
508C23—882no—
509C23—1761no—
510C23D8×D1111yescharacteristic
511Q8—41no—
512Q8—41no—
513Q8—222no—
514Q8—441no—
515Q8—441no—
516Q8—441no—
517Q8—882no—
518D4—41no—
519D4—41no—
520D4—161no—
521D4—222no—
522D4—222no—
523D4—441no—
524D4—441no—
525D4—441no—
526D4—882no—
527D4—882no—
528D4—882no—
529D4—882no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—111no—
536C2×C4—111no—
537C2×C4—111no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—882no—
543C2×C4—882no—
544C2×C4—882no—
545C2×C4—1761no—
546C2×C4D8×D1111yescharacteristic
547C2×C4C2×D4×D1111yescharacteristic
548C8—21no—
549C8—221no—
550C8—221no—
551C8C2×D4×D1111yescharacteristic
552C8#6704211yescharacteristic
553C22—21no—
554C22—21no—
555C22—21no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—112no—
560C22—221no—
561C22—221no—
562C22—442no—
563C22—881no—
564C22—881no—
565C22—881no—
566C22—881no—
567C22—881no—
568C22—1764no—
569C22C2×D8×D1111yescharacteristic
570C4—21no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—221no—
575C4—221no—
576C4—221no—
577C4—442no—
578C4—881no—
579C4#1062314011yescharacteristic
580C4#1062330011yescharacteristic
581C2—41no—
582C2—161no—
583C2—222no—
584C2—882no—
585C2—1761no—
586C2#1308029011yescharacteristic
587C2D11×#50811yescharacteristic
588C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2217C2
socleC22×C11C22×D8
hypercenter#2217D11
hypocenterC11#33848
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2217

Complements

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

NH ≅ G/Ntype
1. C2×#10622517C2semidirect
2. C2×D11×SD32C2semidirect
3. #13080360C2semidirect
4. #13080304C2semidirect
5. #13070876C2semidirect
6. #13070713C2semidirect
7. #13070677C2semidirect
8. #13070674C2semidirect
9. #13070554C2semidirect
10. #13070551C2semidirect
11. #13070537C2semidirect
12. #13070529C2semidirect
13. #13070467C2semidirect
14. C16×C22⋊D11C2semidirect
15. C11×#2217C2semidirect
19. C2×#66957C22semidirect
23. C22×C11×C16C22semidirect
24. C11×#467C22semidirect
26. #10622804C22semidirect
27. C2×#66893C22semidirect
36. C2×Dic88C22semidirect
39. C2×#66864C22semidirect
44. #10622486C22semidirect
50. C11×#367C22semidirect
51. C11×#358C22semidirect
53. C22⋊(C11⋊C16)C22semidirect
55. Dic11⋊C16C22semidirect
56. C16×Dic11C22semidirect
57. #10622130C22semidirect
58. #10622130C22semidirect
60. #10622129C22semidirect
128. #66864D4semidirect
215. #2217D11semidirect
292. C22×C16C2×D11semidirect
296. #467C2×D11semidirect
308. #367C2×D11semidirect
312. #358C2×D11semidirect
335. C2×D11#508semidirect
502. C11#33848semidirect

Maximal subgroups

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

subgroupindex
C2×#106225172
C2×D11×SD322
#130803602
#130803042
#130708762
#130707132
#130706772
#130706742
#130705542
#130705512
#130705372
#130705292
#130704672
C16×C22⋊D112
C11×#22172
#3384811