Finite Group Databasebeta

← #14910429

Subgroups — #14910429

Order 2816.

718 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×#10622529C211yesmaximal, characteristic, complemented
2C22×#66890C211yesmaximal, characteristic, complemented
3#13080301C211yesmaximal, characteristic, complemented
4#13080298C211yesmaximal, characteristic, complemented
5#13070876C211yesmaximal, characteristic, complemented
6#13070705C211yesmaximal, characteristic, complemented
7#13070701C211yesmaximal, characteristic, complemented
8#13070673C211yesmaximal, characteristic, complemented
9#13070670C211yesmaximal, characteristic, complemented
10#13070547C211yesmaximal, characteristic, complemented
11#13070540C211yesmaximal, characteristic, complemented
12#13070538C211yesmaximal, characteristic, complemented
13#13070460C211yesmaximal, characteristic, complemented
14(C22⋊D11)⋊C16C211yesmaximal, characteristic, complemented
15C11×#2187C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17#10623337—21no—
18C2×#66972C2211yescharacteristic, complemented
19C2×#66965C2211yescharacteristic, complemented
20C22×D88C2211yescharacteristic
21#10623161—21no—
22C2×C11×SD32C2211yescharacteristic, complemented
23C2×C11×SD32C2211yescharacteristic, complemented
24C11×#467C2211yescharacteristic
25#10622831—21no—
26#10622804C2211yescharacteristic, complemented
27C2×#66893C2211yescharacteristic, complemented
28#10622771—21no—
29#10622770C2211yescharacteristic, complemented
30#10622768C2211yescharacteristic, complemented
31#10622766—21no—
32D8×Dic11C2211yescharacteristic, complemented
33C2×#66890—24no—
34C2×#66890C2211yescharacteristic
35C2×#66890C2211yescharacteristic
36C2×#66890C2211yescharacteristic
37C2×#66890C2211yescharacteristic
38#10622729C2211yescharacteristic
39C8×C22⋊D11C2211yescharacteristic
40C22×C11⋊C16C2211yescharacteristic
41#10622659—21no—
42#10622529—24no—
43C2×#66864C2211yescharacteristic, complemented
44C2×#66864C2211yescharacteristic, complemented
45C2×C16×D11C2211yescharacteristic, complemented
46#10622496C2211yescharacteristic, complemented
47#10622485C2211yescharacteristic, complemented
48#10622432—21no—
49#10622424—21no—
50C11×#357C2211yescharacteristic, complemented
51C11×#357C2211yescharacteristic, complemented
52C11×C22⋊C16C2211yescharacteristic
53#10622202C2211yescharacteristic, complemented
54#10622147C2211yescharacteristic, complemented
55#10622147C2211yescharacteristic, complemented
56(C2×D11)⋊C16C2211yescharacteristic, complemented
57Dic11⋊C16C2211yescharacteristic, complemented
58C16×Dic11C2211yescharacteristic, complemented
59#10622130C2211yescharacteristic, complemented
60#10622127C2211yescharacteristic, complemented
61C22×D4×C11—21no—
62C2×#4343—21no—
63C2×#4341—21no—
64C22×D44—21no—
65C2×C11×Q16C2311yescharacteristic
66C2×C11×D8—22no—
67C2×C11×D8—21no—
68C2×C11×D8—41no—
69C2×C11×D8C2311yescharacteristic
70C2×C11×D8C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C11×C22⋊Q8—21no—
73#67006—41no—
74C2×C22⋊Dic11—41no—
75#67000—21no—
76C2×#4325—21no—
77C2×#4325—21no—
78#66992—41no—
79#66991—21no—
80#66989—21no—
81#66988—41no—
82D4×Dic11—21no—
83C2×#4324—21no—
84C2×#4324—21no—
85C4×C22⋊D11D411yescharacteristic
86#66977—21no—
87#66972—22no—
88#66972—41no—
89#66965—22no—
90#66965—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×SD32—22no—
105C11×SD32—41no—
106C2×C11×C16C2311yescharacteristic
107C2×C11×C16C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#103—21no—
110#66896—21no—
111#66896—21no—
112C22⋊(C11⋊C8)D411yescharacteristic
113#66893—22no—
114#66890—22no—
115#66890—22no—
116#66890—22no—
117#66890D414yescomplemented
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—
130C16×D11—22no—
131#33846—111nomaximal, Sylow
132C24×C11—41no—
133C23×D11—41no—
134C2×Q8×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—42no—
138C2×D4×C11—41no—
139C2×D4×C11—81no—
140C22×C4×C11C2×D411yescharacteristic
141C2×C22⋊D11—41no—
142C2×C22⋊D11—41no—
143C2×C22⋊D11D811yescharacteristic
144C22×Dic11—41no—
145C22×Dic11—41no—
146#4343—42no—
147#4343—81no—
148#4341—42no—
149#4341—81no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—42no—
153C2×D44—41no—
154C2×D44—41no—
155C2×D44—41no—
156C2×D44—81no—
157C2×C4×D11—41no—
158C2×C4×D11—41no—
159C2×C4×D11C2×D411yescharacteristic
160C2×Dic22—21no—
161C11×Q16—21no—
162C11×Q16—21no—
163C11×D8—21no—
164C11×D8—21no—
165C11×D8—21no—
166C11×D8—42no—
167C11×D8C2×D412yes—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2411yescharacteristic
172C11×C4⋊C4—21no—
173C11×C4⋊C4—41no—
174C11×C22⋊C4—41no—
175C22⋊Dic11—41no—
176C22⋊Dic11—41no—
177C22⋊Dic11—41no—
178C22⋊Dic11—41no—
179C22⋊Dic11—41no—
180C22⋊Dic11D811yescharacteristic
181#4325—42no—
182#4325—81no—
183#4324—42no—
184#4324—81no—
185(C2×D11)⋊C4—41no—
186(C2×D11)⋊C4—41no—
187(C2×D11)⋊C4—41no—
188(C2×D11)⋊C4—41no—
189(C2×D11)⋊C4D811yescharacteristic
190C4⋊Dic11—21no—
191Dic11⋊C4—41no—
192Dic11⋊C4D811yescharacteristic
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×#508—111no—
210C22×D16—111no—
211#3280—111no—
212#3280—111no—
213#2249—111no—
214#2216—111no—
215#2215—111no—
216#2210—111no—
217#2210—111no—
218#2187—111no—
219#2187D1111yescharacteristic, complemented
220#2186—111no—
221#2186—111no—
222C4×D16—111no—
223D4×C16—111no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—82no—
227C23×C11—82no—
228C23×C11—161no—
229C23×C11C2×D811yescharacteristic
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—82no—
233C22×D11—82no—
234C22×D11—161no—
235C22×D11C2×D811yescharacteristic
236Q8×C11—41no—
237Q8×C11—41no—
238D4×C11—22no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—82no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11C2×D811yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C22⋊D11—22no—
250C22⋊D11—82no—
251C22⋊D11—161no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—82no—
255C2×Dic11—161no—
256C2×Dic11C2×D811yescharacteristic
257C2×Dic11C2×D811yescharacteristic
258C2×Dic11C2×D811yescharacteristic
259D44—22no—
260D44—41no—
261D44—41no—
262D44—41no—
263D44—82no—
264D44—82no—
265D44—161no—
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×D8C2×D1111yescharacteristic
281#546—221no—
282#546—221no—
283#508—224no—
284C2×Q32—111no—
285C2×SD32—111no—
286C2×SD32—111no—
287C2×SD32C2×D1111yescharacteristic, complemented
288C2×SD32C2×D1111yescharacteristic, complemented
289C2×D16—111no—
290C2×D16—111no—
291C2×D16—111no—
292C2×D16—111no—
293C2×D16—224no—
294C22×C16—111no—
295C22×C16—111no—
296#495—111no—
297#495—111no—
298#467—111no—
299#467C2×D1111yescharacteristic
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×D8—111no—
310C8×D4—111no—
311#366—111no—
312C4⋊C16—111no—
313#358—111no—
314#358—111no—
315#357—111no—
316#357—111no—
317#357C2×D1111yescharacteristic, complemented
318#357C2×D1111yescharacteristic, complemented
319C22⋊C16—111no—
320C22⋊C16C2×D1111yescharacteristic
321C4×C16—111no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—42no—
325C22×C11—81no—
326C22×C11—81no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11—81no—
330C22×C11—164no—
331C22×C11#50812yescomplemented
332C22×C11C22×D811yescharacteristic
333C2×D11—21no—
334C2×D11—21no—
335C2×D11—21no—
336C2×D11—42no—
337C2×D11—81no—
338C2×D11—81no—
339C2×D11—81no—
340C2×D11—81no—
341C2×D11—81no—
342C2×D11—164no—
343C4×C11—21no—
344C4×C11—81no—
345C4×C11—81no—
346C4×C11D4211yescharacteristic
347C4×C11#57611yescharacteristic
348Dic11—21no—
349Dic11—21no—
350Dic11—21no—
351Dic11—81no—
352Dic11—81no—
353C2×#41—221no—
354C2×#41—221no—
355C22×D4—21no—
356C22×D4—221no—
357#135—222no—
358#135—222no—
359#135—441no—
360#135—441no—
361C2×Q16—111no—
362C2×Q16C22×D1111yescharacteristic
363C2×SD16—221no—
364C2×SD16—221no—
365C2×SD16—221no—
366C2×SD16—221no—
367C2×D8—22no—
368C2×D8—21no—
369C2×D8—41no—
370C2×D8—111no—
371C2×D8—111no—
372C2×D8—222no—
373C2×D8—221no—
374C2×D8—441no—
375C2×D8C22×D1111yescharacteristic
376C2×D8C22×D1111yescharacteristic
377C22×C8—111no—
378C22×C8C22×D1111yescharacteristic
379#124—221no—
380#124—221no—
381#123—441no—
382#123—441no—
383C22⋊Q8—21no—
384C22⋊Q8—221no—
385#121—221no—
386#121—221no—
387#121—441no—
388#121—441no—
389#120—441no—
390#120—441no—
391C4×D4—111no—
392C4×D4—221no—
393C4×D4—221no—
394C2×C22⋊C4—441no—
395C2×C22⋊C4—441no—
396Q32—222no—
397SD32—22no—
398SD32—41no—
399SD32—222no—
400SD32—441no—
401D16—114no—
402D16—222no—
403D16—222no—
404D16—222no—
405C2×C16—111no—
406C2×C16—111no—
407C2×C16—222no—
408C2×C16—222no—
409C2×C16C22×D1111yescharacteristic
410C2×C16C22×D1111yescharacteristic
411#107—111no—
412#107C22×D1111yescharacteristic
413C4⋊C8—111no—
414#103—21no—
415#103—221no—
416#102—221no—
417#102—221no—
418#102—221no—
419#102—221no—
420C22⋊C8—111no—
421C22⋊C8—111no—
422C4×C8—111no—
423C2×C11—22no—
424C2×C11—82no—
425C2×C11—161no—
426C2×C11D4×D811yescharacteristic
427C2×C11C2×#50811yescharacteristic
428C2×C11#341511yescharacteristic
429D11—41no—
430D11—82no—
431D11—161no—
432C24—41no—
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—42no—
443C2×D4—41no—
444C2×D4—81no—
445C2×D4—111no—
446C2×D4—221no—
447C2×D4—221no—
448C2×D4—442no—
449C2×D4—441no—
450C2×D4—441no—
451C2×D4—441no—
452C2×D4—441no—
453C2×D4—441no—
454C2×D4—881no—
455C22×C4—111no—
456C22×C4—441no—
457C22×C4—441no—
458C22×C4—441no—
459C22×C4—441no—
460C22×C4D4×D1111yescharacteristic
461Q16—21no—
462Q16—21no—
463Q16—221no—
464Q16—221no—
465SD16—442no—
466SD16—442no—
467SD16—881no—
468SD16—881no—
469D8—21no—
470D8—21no—
471D8—21no—
472D8—42no—
473D8—112no—
474D8—221no—
475D8—221no—
476D8—221no—
477D8—442no—
478D8D4×D1112yes—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—111no—
482C2×C8—111no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8D4×D1111yescharacteristic
486C2×C8C23×D1111yescharacteristic
487C4⋊C4—21no—
488C4⋊C4—41no—
489C4⋊C4—111no—
490C4⋊C4—221no—
491C4⋊C4—441no—
492C22⋊C4—41no—
493C22⋊C4—111no—
494C22⋊C4—111no—
495C22⋊C4—441no—
496C22⋊C4—441no—
497C22⋊C4—441no—
498C22⋊C4—441no—
499C22⋊C4—441no—
500C22⋊C4—441no—
501C22⋊C4—441no—
502C22⋊C4—441no—
503C22⋊C4—441no—
504C42—111no—
505C16—21no—
506C16—21no—
507C16—112no—
508C16—221no—
509C11#3384611yescharacteristic, complemented, Sylow
510C23—41no—
511C23—41no—
512C23—82no—
513C23—82no—
514C23—111no—
515C23—161no—
516C23—441no—
517C23—441no—
518C23—882no—
519C23—882no—
520C23—1761no—
521C23D8×D1111yescharacteristic
522Q8—41no—
523Q8—41no—
524Q8—441no—
525Q8—441no—
526D4—22no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—82no—
531D4—222no—
532D4—222no—
533D4—441no—
534D4—441no—
535D4—441no—
536D4—882no—
537D4—882no—
538D4—882no—
539D4—1761no—
540D4—1761no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—111no—
546C2×C4—111no—
547C2×C4—111no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—882no—
553C2×C4—882no—
554C2×C4—1761no—
555C2×C4—1761no—
556C2×C4D8×D1111yescharacteristic
557C2×C4C2×D4×D1111yescharacteristic
558C8—21no—
559C8—221no—
560C8—221no—
561C8C2×D4×D1111yescharacteristic
562C8#6703711yescharacteristic
563C22—21no—
564C22—21no—
565C22—42no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22—164no—
572C22—221no—
573C22—221no—
574C22—221no—
575C22—442no—
576C22—881no—
577C22—881no—
578C22—881no—
579C22—881no—
580C22—881no—
581C22—1764no—
582C22#1062252912yescomplemented
583C22C2×D8×D1111yescharacteristic
584C4—21no—
585C4—81no—
586C4—81no—
587C4—221no—
588C4—221no—
589C4—221no—
590C4—881no—
591C4—881no—
592C4#1062312111yescharacteristic
593C4#1062330511yescharacteristic
594C2—22no—
595C2—82no—
596C2—161no—
597C2—441no—
598C2—882no—
599C2—1761no—
600C2#1308028611yescharacteristic
601C2C2×#1062252911yescharacteristic
602C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2187C2
socleC22×C11C22×D8
hypercenter#2187D11
hypocenterC11#33846
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2187

Complements

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

NH ≅ G/Ntype
1. C2×#10622529C2semidirect
2. C22×#66890C2semidirect
3. #13080301C2semidirect
4. #13080298C2semidirect
5. #13070876C2semidirect
6. #13070705C2semidirect
7. #13070701C2semidirect
8. #13070673C2semidirect
9. #13070670C2semidirect
10. #13070547C2semidirect
11. #13070540C2semidirect
12. #13070538C2semidirect
13. #13070460C2semidirect
14. (C22⋊D11)⋊C16C2semidirect
15. C11×#2187C2semidirect
18. C2×#66972C22semidirect
19. C2×#66965C22semidirect
22. C2×C11×SD32C22semidirect
23. C2×C11×SD32C22semidirect
26. #10622804C22semidirect
27. C2×#66893C22semidirect
29. #10622770C22semidirect
30. #10622768C22semidirect
32. D8×Dic11C22semidirect
43. C2×#66864C22semidirect
44. C2×#66864C22semidirect
45. C2×C16×D11C22semidirect
46. #10622496C22semidirect
47. #10622485C22semidirect
50. C11×#357C22semidirect
51. C11×#357C22semidirect
53. #10622202C22semidirect
54. #10622147C22semidirect
55. #10622147C22semidirect
56. (C2×D11)⋊C16C22semidirect
57. Dic11⋊C16C22semidirect
58. C16×Dic11C22semidirect
59. #10622130C22semidirect
60. #10622127C22semidirect
117. #66890D4semidirect
219. #2187D11semidirect
287. C2×SD32C2×D11semidirect
288. C2×SD32C2×D11semidirect
317. #357C2×D11semidirect
318. #357C2×D11semidirect
331. C22×C11#508semidirect
509. C11#33846semidirect
582. C22#10622529semidirect

Maximal subgroups

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

subgroupindex
C2×#106225292
C22×#668902
#130803012
#130802982
#130708762
#130707052
#130707012
#130706732
#130706702
#130705472
#130705402
#130705382
#130704602
(C22⋊D11)⋊C162
C11×#21872
#3384611