Finite Group Databasebeta

← #14910254

Subgroups — #14910254

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×#66892C211yesmaximal, characteristic, complemented
3Q16×C22⋊D11C211yesmaximal, characteristic, complemented
4#13080298C211yesmaximal, characteristic
5#13070884C211yesmaximal, characteristic, complemented
6#13070732C211yesmaximal, characteristic, complemented
7#13070705C211yesmaximal, characteristic, complemented
8#13070680C211yesmaximal, characteristic, complemented
9#13070660C211yesmaximal, characteristic, complemented
10#13070555C211yesmaximal, characteristic, complemented
11#13070547C211yesmaximal, characteristic, complemented
12#13070534C211yesmaximal, characteristic, complemented
13#13070483C211yesmaximal, characteristic, complemented
14#13070438C211yesmaximal, characteristic, complemented
15C11×#2188C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17Q8×C22⋊D11—21no—
18C2×#66972C2211yescharacteristic
19C2×Q16×D11C2211yescharacteristic, complemented
20C22×D88C2211yescharacteristic
21#10623161—21no—
22C2×C11×Q32C2211yescharacteristic, complemented
23C2×C11×Q32C2211yescharacteristic, complemented
24C11×#467C2211yescharacteristic
25#10622841—21no—
26#10622804C2211yescharacteristic
27#10622801C2211yescharacteristic, complemented
28#10622799—21no—
29Q16×Dic11C2211yescharacteristic, complemented
30#10622795—21no—
31#10622794C2211yescharacteristic, complemented
32C2×#66893C2211yescharacteristic, complemented
33C2×#66892—24no—
34C2×#66892C2211yescharacteristic
35C2×#66892C2211yescharacteristic
36C2×#66892C2211yescharacteristic
37C2×#66892C2211yescharacteristic
38#10622729C2211yescharacteristic
39C8×C22⋊D11C2211yescharacteristic
40C22×C11⋊C16C2211yescharacteristic
41#10622659—21no—
42#10622531—24no—
43C2×#66864C2211yescharacteristic
44C2×#66864C2211yescharacteristic
45C2×#66862C2211yescharacteristic, complemented
46#10622496C2211yescharacteristic
47#10622485C2211yescharacteristic
48#10622432—21no—
49#10622424—21no—
50C11×#358C2211yescharacteristic, complemented
51C11×#358C2211yescharacteristic, complemented
52C11×C22⋊C16C2211yescharacteristic
53#10622202C2211yescharacteristic, complemented
54#10622147C2211yescharacteristic
55#10622147C2211yescharacteristic
56(C2×D11)⋊C16C2211yescharacteristic, complemented
57#10622140C2211yescharacteristic, complemented
58Dic11⋊C16C2211yescharacteristic, complemented
59#10622130C2211yescharacteristic, complemented
60#10622127C2211yescharacteristic, complemented
61C22×Q8×C11—21no—
62C2×#4343—21no—
63C2×Q8×D11—21no—
64C22×D44—21no—
65C2×C11×Q16—22no—
66C2×C11×Q16—21no—
67C2×C11×Q16—41no—
68C2×C11×Q16C2311yescharacteristic
69C2×C11×Q16C2311yescharacteristic
70C2×C11×Q16C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C11×C22⋊Q8—21no—
73#67000—21no—
74#66999—21no—
75#66999—41no—
76Q8×Dic11—21no—
77#66997—21no—
78#66997—41no—
79C2×#4326—21no—
80C2×#4326—21no—
81C2×#4325—21no—
82C2×#4325—21no—
83C4×C22⋊D11—41no—
84C4×C22⋊D11D411yescharacteristic
85#66977—21no—
86#66977—41no—
87#66972—22no—
88#66972—41no—
89Q16×D11—22no—
90Q16×D11—41no—
91C2×Dic44C2311yescharacteristic
92C2×D88—22no—
93C2×D88—21no—
94C2×D88—41no—
95C2×D88C2311yescharacteristic
96C2×D88C2311yescharacteristic
97C2×C8×D11C2311yescharacteristic
98#66948—21no—
99#66948—41no—
100#66947—41no—
101#66946—21no—
102#66935—41no—
103C22⋊C4×D11—41no—
104C11×Q32—22no—
105C11×Q32—41no—
106C2×C11×C16C2311yescharacteristic
107C2×C11×C16C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#103—21no—
110#66899—21no—
111#66899—21no—
112C22⋊(C11⋊C8)D411yescharacteristic
113#66893—22no—
114#66892—22no—
115#66892—22no—
116#66892—22no—
117#66892D414yescomplemented
118(C2×D11)⋊C8D411yescharacteristic
119#66882C2311yescharacteristic
120#66880—21no—
121Dic11⋊C8D411yescharacteristic
122C8×Dic11C2311yescharacteristic
123C2×C11⋊C16—22no—
124C2×C11⋊C16C2311yescharacteristic
125C2×C11⋊C16C2311yescharacteristic
126#66873—21no—
127#66873—21no—
128#66864—22no—
129#66864—41no—
130#66862—22no—
131#33832—111nomaximal, Sylow
132C23×D11—41no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—42no—
137C2×Q8×C11—41no—
138C2×Q8×C11—81no—
139C22×C4×C11—41no—
140C22×C4×C11C2×D411yescharacteristic
141C2×C22⋊D11D811yescharacteristic
142#4343—42no—
143#4343—81no—
144Q8×D11—42no—
145Q8×D11—81no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—42no—
149C2×D44—41no—
150C2×D44—41no—
151C2×D44—41no—
152C2×D44—81no—
153C2×C4×D11—41no—
154C2×C4×D11—41no—
155C2×C4×D11—41no—
156C2×C4×D11C2×D411yescharacteristic
157C2×Dic22—21no—
158C2×Dic22—41no—
159C11×Q16—21no—
160C11×Q16—21no—
161C11×Q16—21no—
162C11×Q16—21no—
163C11×Q16—21no—
164C11×Q16—42no—
165C11×Q16C2×D412yes—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2411yescharacteristic
170C11×C4⋊C4—21no—
171C11×C4⋊C4—41no—
172C11×C22⋊C4—41no—
173C22⋊Dic11—41no—
174C22⋊Dic11D811yescharacteristic
175#4326—42no—
176#4326—81no—
177#4325—42no—
178#4325—81no—
179(C2×D11)⋊C4—41no—
180(C2×D11)⋊C4—41no—
181(C2×D11)⋊C4—41no—
182(C2×D11)⋊C4—41no—
183(C2×D11)⋊C4—41no—
184(C2×D11)⋊C4D811yescharacteristic
185C4⋊Dic11—21no—
186C4⋊Dic11—41no—
187Dic11⋊C4—41no—
188Dic11⋊C4—41no—
189Dic11⋊C4—41no—
190Dic11⋊C4—41no—
191Dic11⋊C4D811yescharacteristic
192C4×Dic11—41no—
193C4×Dic11C2×D411yescharacteristic
194C2×C11⋊C8C2×D411yescharacteristic
195C2×C11⋊C8C2×D411yescharacteristic
196Dic44—21no—
197Dic44—21no—
198D88—21no—
199D88—21no—
200D88—21no—
201D88—42no—
202D88C2×D412yes—
203C8×D11—21no—
204C8×D11—21no—
205C11×C16—21no—
206C11×C16—21no—
207C11⋊C16—21no—
208C11⋊C16C2×D412yes—
209C2×#510—111no—
210C22×SD32—111no—
211D4×Q16—111no—
212#3280—111no—
213#2251—111no—
214#2220—111no—
215#2216—111no—
216#2211—111no—
217#2208—111no—
218#2189—111no—
219#2188D1111yescharacteristic, complemented
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—22no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—41no—
235Q8×C11—41no—
236Q8×C11—41no—
237Q8×C11—82no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—82no—
245C2×C4×C11C2×D811yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C22⋊D11—22no—
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—
258D44—82no—
259D44—161no—
260C4×D11—21no—
261C4×D11—21no—
262C4×D11—82no—
263C4×D11—82no—
264C4×D11—161no—
265Dic22—41no—
266Dic22—41no—
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×Q16C2×D1111yescharacteristic
276C22×D8—111no—
277D4×Q8—221no—
278#546—221no—
279#510—224no—
280C2×Q32—111no—
281C2×Q32C2×D1111yescharacteristic, complemented
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×C16—111no—
292#495—111no—
293#494—111no—
294#467—111no—
295#467—111no—
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#366—111no—
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⋊C16C2×D1111yescharacteristic
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—42no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11D4211yescharacteristic
338C4×C11#57611yescharacteristic
339Dic11—21no—
340Dic11—21no—
341Dic11—21no—
342Dic11—81no—
343Dic11—81no—
344C2×#41—221no—
345C22×Q8—21no—
346C22×Q8—221no—
347C22×D4—221no—
348#135—222no—
349#135—441no—
350C2×Q16—22no—
351C2×Q16—21no—
352C2×Q16—41no—
353C2×Q16—111no—
354C2×Q16—221no—
355C2×Q16—221no—
356C2×Q16—222no—
357C2×Q16—441no—
358C2×Q16C22×D1111yescharacteristic
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—221no—
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—41no—
389Q32—222no—
390SD32—114no—
391SD32—222no—
392SD32—222no—
393SD32—222no—
394SD32—222no—
395SD32—441no—
396M32—222no—
397C2×C16—111no—
398C2×C16—111no—
399C2×C16—222no—
400C2×C16C22×D1111yescharacteristic
401C2×C16C22×D1111yescharacteristic
402#107—111no—
403#107C22×D1111yescharacteristic
404C4⋊C8—111no—
405#103—21no—
406#103—221no—
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—21no—
427C2×Q8—42no—
428C2×Q8—41no—
429C2×Q8—81no—
430C2×Q8—221no—
431C2×Q8—441no—
432C2×Q8—442no—
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—41no—
443C22×C4—111no—
444C22×C4—441no—
445C22×C4—441no—
446C22×C4—441no—
447C22×C4D4×D1111yescharacteristic
448Q16—21no—
449Q16—21no—
450Q16—21no—
451Q16—21no—
452Q16—21no—
453Q16—42no—
454Q16—221no—
455Q16—221no—
456Q16—442no—
457Q16—881no—
458Q16D4×D1112yes—
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—41no—
476C4⋊C4—111no—
477C4⋊C4—221no—
478C4⋊C4—441no—
479C4⋊C4—441no—
480C4⋊C4—441no—
481C4⋊C4—441no—
482C4⋊C4—441no—
483C22⋊C4—41no—
484C22⋊C4—111no—
485C22⋊C4—111no—
486C22⋊C4—441no—
487C22⋊C4—441no—
488C22⋊C4—441no—
489C22⋊C4—441no—
490C22⋊C4—441no—
491C22⋊C4—441no—
492C42—111no—
493C42—441no—
494C16—21no—
495C16—21no—
496C16—112no—
497C16—221no—
498C11#3383211yescharacteristic, complemented, Sylow
499C23—111no—
500C23—441no—
501C23—441no—
502C23—882no—
503C23—882no—
504C23—1761no—
505C23D8×D1111yescharacteristic
506Q8—22no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—82no—
513Q8—441no—
514Q8—441no—
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—82no—
531C2×C4—111no—
532C2×C4—111no—
533C2×C4—111no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—441no—
537C2×C4—441no—
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#6703711yescharacteristic
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—42no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4—221no—
568C4—221no—
569C4—221no—
570C4—881no—
571C4—881no—
572C4#1062312111yescharacteristic
573C4#1062330511yescharacteristic
574C2—22no—
575C2—441no—
576C2—882no—
577C2—1761no—
578C2#1308028611yescharacteristic
579C2C2×#1062253111yescharacteristic
580C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2188C2
socleC22×C11C22×D8
prime radical#13080298C2
hypercenter#2188D11
hypocenterC11#33832
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2188

Complements

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

NH ≅ G/Ntype
1. C2×#10622531C2semidirect
2. C22×#66892C2semidirect
3. Q16×C22⋊D11C2semidirect
5. #13070884C2semidirect
6. #13070732C2semidirect
7. #13070705C2semidirect
8. #13070680C2semidirect
9. #13070660C2semidirect
10. #13070555C2semidirect
11. #13070547C2semidirect
12. #13070534C2semidirect
13. #13070483C2semidirect
14. #13070438C2semidirect
15. C11×#2188C2semidirect
19. C2×Q16×D11C22semidirect
22. C2×C11×Q32C22semidirect
23. C2×C11×Q32C22semidirect
27. #10622801C22semidirect
29. Q16×Dic11C22semidirect
31. #10622794C22semidirect
32. C2×#66893C22semidirect
45. C2×#66862C22semidirect
50. C11×#358C22semidirect
51. C11×#358C22semidirect
53. #10622202C22semidirect
56. (C2×D11)⋊C16C22semidirect
57. #10622140C22semidirect
58. Dic11⋊C16C22semidirect
59. #10622130C22semidirect
60. #10622127C22semidirect
117. #66892D4semidirect
219. #2188D11semidirect
281. C2×Q32C2×D11semidirect
282. C2×Q32C2×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×#668922
Q16×C22⋊D112
#130802982
#130708842
#130707322
#130707052
#130706802
#130706602
#130705552
#130705472
#130705342
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