Finite Group Databasebeta

← #14910258

Subgroups — #14910258

Order 2816.

686 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622531C211yesmaximal, characteristic, complemented
2C22×#66864C211yesmaximal, characteristic, complemented
3#13080365C211yesmaximal, characteristic, complemented
4#13080298C211yesmaximal, characteristic
5#13070884C211yesmaximal, characteristic, complemented
6#13070730C211yesmaximal, characteristic, complemented
7#13070681C211yesmaximal, characteristic, complemented
8#13070660C211yesmaximal, characteristic, complemented
9#13070559C211yesmaximal, characteristic, complemented
10#13070549C211yesmaximal, characteristic, complemented
11#13070544C211yesmaximal, characteristic, complemented
12#13070534C211yesmaximal, characteristic, complemented
13#13070479C211yesmaximal, characteristic, complemented
14#13070441C211yesmaximal, characteristic, complemented
15C11×#2216C211yesmaximal, characteristic, complemented
16C2×#66972C2211yescharacteristic
17C2×Q16×D11C2211yescharacteristic, complemented
18C22×Dic44C2211yescharacteristic
19C22×D88C2211yescharacteristic
20#10623163—21no—
21#10623161—21no—
22C2×C11×Q32C2211yescharacteristic, complemented
23C22×C11×C16C2211yescharacteristic
24C11×#467C2211yescharacteristic
25C11×#467C2211yescharacteristic
26#10622804C2211yescharacteristic
27#10622794C2211yescharacteristic, complemented
28C2×#66893C2211yescharacteristic, complemented
29C2×#66893C2211yescharacteristic, complemented
30C2×#66892C2211yescharacteristic
31C2×#66892C2211yescharacteristic
32C8×C22⋊D11C2211yescharacteristic
33#10622663—21no—
34#10622659—21no—
35#10622531—24no—
36C2×#66864—24no—
37C2×#66864C2211yescharacteristic
38C2×#66864C2211yescharacteristic
39C2×#66864C2211yescharacteristic
40C2×#66864C2211yescharacteristic
41C2×#66862C2211yescharacteristic, complemented
42#10622500C2211yescharacteristic, complemented
43#10622496C2211yescharacteristic
44#10622486C2211yescharacteristic, complemented
45#10622485C2211yescharacteristic
46#10622432—21no—
47#10622424—21no—
48#10622421—21no—
49#10622406—21no—
50C11×#366C2211yescharacteristic, complemented
51C11×#358C2211yescharacteristic, complemented
52C11×#358C2211yescharacteristic, complemented
53C22⋊(C11⋊C16)C2211yescharacteristic
54(C2×D11)⋊C16C2211yescharacteristic, complemented
55#10622140C2211yescharacteristic, complemented
56Dic11⋊C16C2211yescharacteristic, complemented
57#10622130C2211yescharacteristic, complemented
58#10622130C2211yescharacteristic, complemented
59#10622129C2211yescharacteristic
60#10622129C2211yescharacteristic
61C2×#4343—21no—
62C2×Q8×D11—21no—
63C22×D44—21no—
64C22×Dic22—21no—
65C2×C11×Q16C2311yescharacteristic
66C2×C11×Q16C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×C22⋊Q8—21no—
69C11×C22⋊Q8—21no—
70#67000—21no—
71#66997—21no—
72C2×#4326—21no—
73C2×#4326—21no—
74C2×#4325—21no—
75C2×#4325—21no—
76C4×C22⋊D11D411yescharacteristic
77#66972—22no—
78#66972—41no—
79Q16×D11—22no—
80Q16×D11—41no—
81C2×Dic44—22no—
82C2×Dic44—21no—
83C2×Dic44—41no—
84C2×Dic44C2311yescharacteristic
85C2×Dic44C2311yescharacteristic
86C2×D88—22no—
87C2×D88—21no—
88C2×D88—41no—
89C2×D88C2311yescharacteristic
90C2×D88C2311yescharacteristic
91C2×C8×D11C2311yescharacteristic
92#66950—21no—
93#66949—41no—
94#66948—21no—
95#66948—41no—
96#66947—41no—
97#66946—21no—
98#66941—41no—
99#66940—21no—
100#66935—41no—
101(C22⋊D11)⋊C4—41no—
102C22⋊C4×D11—41no—
103#66931—41no—
104C11×Q32—22no—
105C2×C11×C16—22no—
106C2×C11×C16C2311yescharacteristic
107C2×C11×C16C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#107C2311yescharacteristic
110C11×#103—21no—
111C11×#103—21no—
112C22⋊(C11⋊C8)D411yescharacteristic
113#66893—22no—
114#66893—41no—
115#66892—22no—
116#66892—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—
126#66864—22no—
127#66864—22no—
128#66864—22no—
129#66864D414yescomplemented
130#66862—22no—
131#33832—111nomaximal, Sylow
132C23×D11—41no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C22×C4×C11C2×D411yescharacteristic
136C2×C22⋊D11D811yescharacteristic
137C22×Dic11—41no—
138#4343—42no—
139#4343—81no—
140Q8×D11—42no—
141Q8×D11—81no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—42no—
145C2×D44—41no—
146C2×D44—41no—
147C2×D44—41no—
148C2×D44—81no—
149C2×C4×D11—41no—
150C2×C4×D11—41no—
151C2×C4×D11—41no—
152C2×C4×D11C2×D411yescharacteristic
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—42no—
156C2×Dic22—41no—
157C2×Dic22—41no—
158C2×Dic22—81no—
159C11×Q16—21no—
160C11×Q16—21no—
161C11×Q16—21no—
162C11×Q16—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11C2×D411yescharacteristic
166C2×C8×C11C2411yescharacteristic
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—41no—
170C11×C4⋊C4—41no—
171C11×C22⋊C4—41no—
172C11×C22⋊C4—41no—
173C22⋊Dic11D811yescharacteristic
174#4326—42no—
175#4326—81no—
176#4325—42no—
177#4325—81no—
178(C2×D11)⋊C4—41no—
179(C2×D11)⋊C4—41no—
180(C2×D11)⋊C4—41no—
181(C2×D11)⋊C4—41no—
182(C2×D11)⋊C4—41no—
183(C2×D11)⋊C4D811yescharacteristic
184C4⋊Dic11—41no—
185Dic11⋊C4—41no—
186Dic11⋊C4—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—
196Dic44—42no—
197Dic44C2×D412yes—
198D88—21no—
199D88—21no—
200D88—21no—
201D88—42no—
202D88C2×D412yes—
203C8×D11—21no—
204C8×D11—21no—
205C11×C16—21no—
206C11×C16C2×D412yes—
207C11⋊C16—21no—
208C11⋊C16—21no—
209C2×#510—111no—
210C22×SD32—111no—
211D4×Q16—111no—
212#3280—111no—
213#2251—111no—
214#2220—111no—
215#2216D1111yescharacteristic, complemented
216#2211—111no—
217#2208—111no—
218#2189—111no—
219#2188—111no—
220#2187—111no—
221#2185—111no—
222#2175—111no—
223#2168—111no—
224C23×C11C2×D811yescharacteristic
225C22×D11—41no—
226C22×D11—41no—
227C22×D11—82no—
228C22×D11—82no—
229C22×D11—161no—
230C22×D11C2×D811yescharacteristic
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11C2×D811yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C22⋊D11—22no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—82no—
247C2×Dic11C2×D811yescharacteristic
248C2×Dic11C2×D811yescharacteristic
249C2×Dic11C2×D811yescharacteristic
250D44—22no—
251D44—41no—
252D44—41no—
253D44—41no—
254D44—82no—
255D44—82no—
256D44—161no—
257C4×D11—21no—
258C4×D11—21no—
259C4×D11—82no—
260C4×D11—82no—
261C4×D11—161no—
262Dic22—22no—
263Dic22—41no—
264Dic22—41no—
265Dic22—41no—
266Dic22—82no—
267Dic22—82no—
268C8×C11—21no—
269C8×C11C22×D411yescharacteristic
270C8×C11H(5,𝔽2)11yescharacteristic
271C11⋊C8—21no—
272C11⋊C8—21no—
273C2×#135—111no—
274C22×Q16—111no—
275C22×Q16—111no—
276C22×D8—111no—
277D4×Q8—221no—
278#546—221no—
279#510—224no—
280C2×Q32—111no—
281C2×Q32—111no—
282C2×Q32C2×D1111yescharacteristic, complemented
283C2×SD32—111no—
284C2×SD32—111no—
285C2×SD32—111no—
286C2×SD32—111no—
287C2×SD32—111no—
288C2×SD32—111no—
289C2×SD32—224no—
290C2×M32—111no—
291C22×C16C2×D1111yescharacteristic
292#495—111no—
293#494—111no—
294#467—111no—
295#467C2×D1111yescharacteristic
296#467C2×D1111yescharacteristic
297#466—111no—
298#463—221no—
299#462—221no—
300#451—221no—
301#451—221no—
302#450—221no—
303#449—221no—
304C4×Q16—111no—
305C4×D8—111no—
306C8×D4—111no—
307#366C2×D1111yescharacteristic, complemented
308C4⋊C16—111no—
309#358—111no—
310#358—111no—
311#358C2×D1111yescharacteristic, complemented
312#358C2×D1111yescharacteristic, complemented
313#357—111no—
314#357—111no—
315C22⋊C16—111no—
316C22⋊C16—111no—
317#346—111no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11#51012yescomplemented
321C22×C11C22×D811yescharacteristic
322C2×D11—21no—
323C2×D11—21no—
324C2×D11—21no—
325C2×D11—42no—
326C2×D11—81no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—81no—
330C2×D11—81no—
331C2×D11—164no—
332C4×C11—21no—
333C4×C11—81no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11D4211yescharacteristic
338C4×C11#57611yescharacteristic
339Dic11—21no—
340Dic11—21no—
341Dic11—21no—
342Dic11—42no—
343Dic11—81no—
344C2×#41—221no—
345C22×Q8—221no—
346C22×Q8—221no—
347C22×D4—221no—
348#135—222no—
349#135—441no—
350C2×Q16—111no—
351C2×Q16—111no—
352C2×Q16—222no—
353C2×Q16—221no—
354C2×Q16—221no—
355C2×Q16—222no—
356C2×Q16—221no—
357C2×Q16—441no—
358C2×Q16—441no—
359C2×Q16C22×D1111yescharacteristic
360C2×Q16C22×D1111yescharacteristic
361C2×SD16—221no—
362C2×SD16—221no—
363C2×D8—111no—
364C2×D8—111no—
365C2×D8—222no—
366C2×D8—221no—
367C2×D8—441no—
368C22×C8—111no—
369C22×C8C22×D1111yescharacteristic
370C4⋊Q8—221no—
371C4⋊Q8—441no—
372#124—221no—
373#123—441no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8—221no—
377C22⋊Q8—441no—
378C22⋊Q8—441no—
379#121—221no—
380#121—441no—
381#120—441no—
382C4×Q8—221no—
383C4×D4—111no—
384C4×D4—221no—
385C4×D4—441no—
386C2×C22⋊C4—441no—
387Q32—22no—
388Q32—222no—
389Q32—441no—
390SD32—114no—
391SD32—222no—
392SD32—222no—
393SD32—222no—
394SD32—222no—
395SD32—441no—
396M32—222no—
397C2×C16—22no—
398C2×C16—111no—
399C2×C16—111no—
400C2×C16C22×D1111yescharacteristic
401C2×C16C22×D1111yescharacteristic
402#107C22×D1111yescharacteristic
403#107C22×D1111yescharacteristic
404C4⋊C8—111no—
405#103—21no—
406#103—21no—
407#103—221no—
408#103—221no—
409#102—221no—
410#102—221no—
411C22⋊C8—111no—
412C22⋊C8—111no—
413C4×C8—111no—
414C2×C11—22no—
415C2×C11D4×D811yescharacteristic
416C2×C11C2×#51011yescharacteristic
417C2×C11#341611yescharacteristic
418D11—41no—
419D11—82no—
420D11—161no—
421C24—441no—
422#41—442no—
423#41—881no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—221no—
427C2×Q8—221no—
428C2×Q8—442no—
429C2×Q8—441no—
430C2×Q8—442no—
431C2×Q8—441no—
432C2×Q8—881no—
433C2×Q8—881no—
434C2×D4—111no—
435C2×D4—221no—
436C2×D4—221no—
437C2×D4—442no—
438C2×D4—441no—
439C2×D4—441no—
440C2×D4—441no—
441C2×D4—881no—
442C22×C4—111no—
443C22×C4—441no—
444C22×C4—441no—
445C22×C4—441no—
446C22×C4—441no—
447C22×C4D4×D1111yescharacteristic
448Q16—21no—
449Q16—21no—
450Q16—21no—
451Q16—21no—
452Q16—112no—
453Q16—221no—
454Q16—221no—
455Q16—221no—
456Q16—442no—
457Q16—442no—
458Q16—881no—
459SD16—442no—
460SD16—881no—
461D8—112no—
462D8—221no—
463D8—221no—
464D8—221no—
465D8—442no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—111no—
469C2×C8—111no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8D4×D1111yescharacteristic
473C2×C8C23×D1111yescharacteristic
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—111no—
479C4⋊C4—441no—
480C4⋊C4—441no—
481C4⋊C4—441no—
482C4⋊C4—441no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—111no—
486C22⋊C4—111no—
487C22⋊C4—441no—
488C22⋊C4—441no—
489C22⋊C4—441no—
490C22⋊C4—441no—
491C22⋊C4—441no—
492C42—111no—
493C42—441no—
494C16—21no—
495C16—221no—
496C16—221no—
497C16D4×D1112yes—
498C11#3383211yescharacteristic, complemented, Sylow
499C23—111no—
500C23—441no—
501C23—441no—
502C23—882no—
503C23—882no—
504C23—1761no—
505C23D8×D1111yescharacteristic
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—222no—
511Q8—441no—
512Q8—441no—
513Q8—441no—
514Q8—882no—
515Q8—882no—
516D4—222no—
517D4—222no—
518D4—441no—
519D4—441no—
520D4—441no—
521D4—882no—
522D4—882no—
523D4—1761no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—111no—
531C2×C4—111no—
532C2×C4—111no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—882no—
538C2×C4—882no—
539C2×C4—882no—
540C2×C4—1761no—
541C2×C4D8×D1111yescharacteristic
542C2×C4C2×D4×D1111yescharacteristic
543C8—21no—
544C8—221no—
545C8—221no—
546C8C2×D4×D1111yescharacteristic
547C8#6704211yescharacteristic
548C22—21no—
549C22—21no—
550C22—221no—
551C22—221no—
552C22—221no—
553C22—442no—
554C22—881no—
555C22—881no—
556C22—881no—
557C22—881no—
558C22—881no—
559C22—1764no—
560C22#1062253112yescomplemented
561C22C2×D8×D1111yescharacteristic
562C4—21no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4—221no—
568C4—221no—
569C4—221no—
570C4—442no—
571C4—881no—
572C4#1062314011yescharacteristic
573C4#1062330011yescharacteristic
574C2—22no—
575C2—441no—
576C2—882no—
577C2—1761no—
578C2#1308029011yescharacteristic
579C2C2×#1062253111yescharacteristic
580C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2216C2
socleC22×C11C22×D8
prime radical#13080298C2
hypercenter#2216D11
hypocenterC11#33832
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2216

Complements

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

NH ≅ G/Ntype
1. C2×#10622531C2semidirect
2. C22×#66864C2semidirect
3. #13080365C2semidirect
5. #13070884C2semidirect
6. #13070730C2semidirect
7. #13070681C2semidirect
8. #13070660C2semidirect
9. #13070559C2semidirect
10. #13070549C2semidirect
11. #13070544C2semidirect
12. #13070534C2semidirect
13. #13070479C2semidirect
14. #13070441C2semidirect
15. C11×#2216C2semidirect
17. C2×Q16×D11C22semidirect
22. C2×C11×Q32C22semidirect
27. #10622794C22semidirect
28. C2×#66893C22semidirect
29. C2×#66893C22semidirect
41. C2×#66862C22semidirect
42. #10622500C22semidirect
44. #10622486C22semidirect
50. C11×#366C22semidirect
51. C11×#358C22semidirect
52. C11×#358C22semidirect
54. (C2×D11)⋊C16C22semidirect
55. #10622140C22semidirect
56. Dic11⋊C16C22semidirect
57. #10622130C22semidirect
58. #10622130C22semidirect
129. #66864D4semidirect
215. #2216D11semidirect
282. C2×Q32C2×D11semidirect
307. #366C2×D11semidirect
311. #358C2×D11semidirect
312. #358C2×D11semidirect
320. C22×C11#510semidirect
498. C11#33832semidirect
560. C22#10622531semidirect

Maximal subgroups

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

subgroupindex
C2×#106225312
C22×#668642
#130803652
#130802982
#130708842
#130707302
#130706812
#130706602
#130705592
#130705492
#130705442
#130705342
#130704792
#130704412
C11×#22162
#3383211