Finite Group Databasebeta

← #14910227

Subgroups — #14910227

Order 2816.

760 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622760C211yesmaximal, characteristic, complemented
2C22×#66890C211yesmaximal, characteristic, complemented
3#13080303C211yesmaximal, characteristic, complemented
4#13070880C211yesmaximal, characteristic, complemented
5#13070717C211yesmaximal, characteristic, complemented
6#13070710C211yesmaximal, characteristic, complemented
7#13070671C211yesmaximal, characteristic, complemented
8#13070648C211yesmaximal, characteristic, complemented
9#13070545C211yesmaximal, characteristic, complemented
10#13070537C211yesmaximal, characteristic, complemented
11#13070528C211yesmaximal, characteristic, complemented
12#13070527C211yesmaximal, characteristic, complemented
13#13070490C211yesmaximal, characteristic, complemented
14#13070442C211yesmaximal, characteristic, complemented
15D4×C11×D8C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic, complemented
18D42×C11—21no—
19C2×#66957C2211yescharacteristic, complemented
20C22×D88C2211yescharacteristic, complemented
21#10623081—21no—
22C11×#493C2211yescharacteristic, complemented
23C11×#466C2211yescharacteristic
24C11×#466C2211yescharacteristic, complemented
25C11×#459—21no—
26C11×#447—21no—
27C11×#447—21no—
28C4×C11×D8C2211yescharacteristic, complemented
29C8×D4×C11C2211yescharacteristic
30C2×#66891C2211yescharacteristic, complemented
31C2×#66891C2211yescharacteristic, complemented
32C2×#66891C2211yescharacteristic, complemented
33#10622760—24no—
34C2×#66890—24no—
35C2×#66890C2211yescharacteristic
36C2×#66890C2211yescharacteristic
37C2×#66890C2211yescharacteristic, complemented
38C2×#66890C2211yescharacteristic, complemented
39C2×#66890C2211yescharacteristic, complemented
40C2×#66890C2211yescharacteristic, complemented
41#10622729C2211yescharacteristic, complemented
42#10622728C2211yescharacteristic, complemented
43C2×#66876C2211yescharacteristic, complemented
44C22×C11⋊C16C2211yescharacteristic, complemented
45#10622457—21no—
46#10622347—21no—
47#10622344—21no—
48#10622309C2211yescharacteristic, complemented
49C4×D88C2211yescharacteristic, complemented
50#10622200C2211yescharacteristic, complemented
51#10622200C2211yescharacteristic, complemented
52#10622200C2211yescharacteristic, complemented
53C22⋊(C11⋊C16)C2211yescharacteristic, complemented
54C22⋊(C11⋊C16)C2211yescharacteristic, complemented
55#10622130C2211yescharacteristic, complemented
56#10622129C2211yescharacteristic, complemented
57#10622129C2211yescharacteristic, complemented
58#10622128C2211yescharacteristic, complemented
59C4⋊(C11⋊C16)C2211yescharacteristic, complemented
60#10622099C2211yescharacteristic, complemented
61C22×D4×C11—21no—
62C22×D4×C11—21no—
63C22×D4×C11—41no—
64C2×#4339—21no—
65C22×D44—21no—
66C2×C11×D8—22no—
67C2×C11×D8—22no—
68C2×C11×D8—21no—
69C2×C11×D8—21no—
70C2×C11×D8—21no—
71C2×C11×D8—41no—
72C2×C11×D8—41no—
73C2×C11×D8C2311yescharacteristic
74C2×C11×D8C2311yescharacteristic
75C2×C11×D8C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C11×#127—21no—
79C11×#121—21no—
80C11×#121—21no—
81C11×#121—41no—
82C11×#120—41no—
83C11×#120—41no—
84C4×D4×C11—21no—
85C4×D4×C11D411yescharacteristic
86#66990—41no—
87#66983—21no—
88#66977—21no—
89C2×Dic44C2311yescharacteristic
90#66957—22no—
91#66957—41no—
92C2×D88—22no—
93C2×D88—21no—
94C2×D88—41no—
95C2×D88C2311yescharacteristic
96C2×D88C2311yescharacteristic
97C2×#4314—21no—
98C2×#4314—21no—
99#66947—41no—
100#66937—41no—
101C22⋊C4×D11—41no—
102#66928—21no—
103C4×D44—21no—
104C11×#107C2311yescharacteristic
105C11×C4⋊C8D411yescharacteristic
106C11×#102—21no—
107C11×#102—21no—
108C11×#102—21no—
109C11×C22⋊C8D411yescharacteristic
110C11×C22⋊C8D411yescharacteristic
111C4×C8×C11C2311yescharacteristic
112#66891—22no—
113#66891—22no—
114#66891—41no—
115#66890—22no—
116#66890—22no—
117#66890—22no—
118#66890—22no—
119#66890—41no—
120#66890D414yescomplemented
121#66885—21no—
122#66885—21no—
123#66882C2311yescharacteristic
124#66880—21no—
125#66876—22no—
126C2×C11⋊C16—22no—
127C2×C11⋊C16C2311yescharacteristic
128C2×C11⋊C16C2311yescharacteristic
129C2×C11⋊C16C2311yescharacteristic
130C2×C11⋊C16C2311yescharacteristic
131#33830—111nomaximal, Sylow
132C24×C11—41no—
133C24×C11—41no—
134C23×D11—41no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—42no—
139C2×D4×C11—42no—
140C2×D4×C11—41no—
141C2×D4×C11—41no—
142C2×D4×C11—41no—
143C2×D4×C11—41no—
144C2×D4×C11—41no—
145C2×D4×C11—41no—
146C2×D4×C11—81no—
147C2×D4×C11—81no—
148C2×D4×C11—84no—
149C2×D4×C11D811yescharacteristic
150C22×C4×C11—41no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C2×C22⋊D11—41no—
154C2×C22⋊D11—41no—
155#4339—42no—
156#4339—81no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—42no—
160C2×D44—41no—
161C2×D44—81no—
162C2×C4×D11—41no—
163C2×C4×D11—41no—
164C2×Dic22—21no—
165C11×D8—21no—
166C11×D8—21no—
167C11×D8—21no—
168C11×D8—21no—
169C11×D8—21no—
170C11×D8—42no—
171C11×D8—42no—
172C11×D8—81no—
173C11×D8C2×D412yes—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11C2×D411yescharacteristic
179C2×C8×C11C2×D411yescharacteristic
180C2×C8×C11C2×D411yescharacteristic
181C2×C8×C11C2411yescharacteristic
182C11×C4⋊C4—21no—
183C11×C4⋊C4D811yescharacteristic
184C11×C22⋊C4—41no—
185C11×C22⋊C4—41no—
186C11×C22⋊C4—41no—
187C11×C22⋊C4D811yescharacteristic
188C11×C22⋊C4D811yescharacteristic
189C42×C11C2×D411yescharacteristic
190C22⋊Dic11—41no—
191(C2×D11)⋊C4—41no—
192(C2×D11)⋊C4—41no—
193(C2×D11)⋊C4—41no—
194(C2×D11)⋊C4—41no—
195C4⋊Dic11—21no—
196Dic11⋊C4—41no—
197Dic44—21no—
198Dic44—21no—
199D88—21no—
200D88—21no—
201D88—21no—
202D88—42no—
203D88C2×D412yescomplemented
204#4314—42no—
205#4314—81no—
206C11⋊C16—21no—
207C11⋊C16—21no—
208C11⋊C16—21no—
209C11⋊C16C2×D412yescomplemented
210C2×#509—111no—
211C22×D16—111no—
212#3280—111no—
213D4×D8D1111yescharacteristic, complemented
214#2250—111no—
215#2218—111no—
216#2217—111no—
217#2210—111no—
218#2206—111no—
219#2187—111no—
220#2186—111no—
221#2184—111no—
222#2184—111no—
223#2177—111no—
224#2168—111no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—82no—
229C23×C11—82no—
230C23×C11—82no—
231C23×C11—82no—
232C23×C11—161no—
233C23×C11—161no—
234C23×C11C2×D811yescharacteristic
235C23×C11C2×D811yescharacteristic
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—82no—
239C22×D11—82no—
240C22×D11—161no—
241D4×C11—22no—
242D4×C11—22no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—41no—
247D4×C11—41no—
248D4×C11—82no—
249D4×C11—82no—
250D4×C11—82no—
251D4×C11—82no—
252D4×C11—82no—
253D4×C11—161no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—41no—
259C2×C4×C11—82no—
260C2×C4×C11C2×D811yescharacteristic
261C2×C4×C11C2×D811yescharacteristic
262C2×C4×C11C2×D811yescharacteristic
263C2×C4×C11C2×D811yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C22⋊D11—82no—
266C22⋊D11—161no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269D44—22no—
270D44—41no—
271D44—41no—
272D44—41no—
273D44—82no—
274C4×D11—82no—
275C4×D11—161no—
276Dic22—41no—
277Dic22—41no—
278C8×C11—21no—
279C8×C11—21no—
280C8×C11—21no—
281C8×C11C22×D411yescharacteristic
282C8×C11H(5,𝔽2)11yescharacteristic
283C2×#135—111no—
284C22×D8—111no—
285C22×D8C2×D1111yescharacteristic
286C22×D8C2×D1111yescharacteristic, complemented
287#546—221no—
288D42—21no—
289#509—224no—
290C2×SD32—111no—
291C2×SD32—111no—
292C2×SD32—111no—
293C2×D16—111no—
294C2×D16—111no—
295C2×D16—111no—
296C2×D16—111no—
297C2×D16—111no—
298C2×D16—111no—
299C2×D16—224no—
300C2×M32—111no—
301C22×C16—111no—
302#495—111no—
303#493C2×D1111yescharacteristic, complemented
304#467—111no—
305#466—111no—
306#466C2×D1111yescharacteristic
307#466C2×D1111yescharacteristic, complemented
308#463—221no—
309#459—21no—
310#450—221no—
311#449—221no—
312#447—21no—
313#447—21no—
314C4×D8—111no—
315C4×D8C2×D1111yescharacteristic, complemented
316C8×D4C2×D1111yescharacteristic
317#367—111no—
318C4⋊C16—111no—
319#358—111no—
320#357—111no—
321#357—111no—
322#357—111no—
323#357—111no—
324#357—111no—
325C22⋊C16—111no—
326C22⋊C16—111no—
327#346—111no—
328C22×C11—21no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—42no—
334C22×C11—81no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11—81no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11—164no—
343C22×C11—164no—
344C22×C11#50912yescomplemented
345C22×C11C22×D811yescharacteristic
346C2×D11—42no—
347C2×D11—81no—
348C2×D11—81no—
349C2×D11—81no—
350C2×D11—81no—
351C2×D11—81no—
352C2×D11—164no—
353C4×C11—21no—
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—21no—
357C4×C11—81no—
358C4×C11D4211yescharacteristic
359C4×C11#57611yescharacteristic
360Dic11—81no—
361Dic11—81no—
362C2×#41—221no—
363C22×D4—21no—
364C22×D4—21no—
365C22×D4—41no—
366C22×D4—221no—
367#135—222no—
368#135—441no—
369C2×Q16—111no—
370C2×SD16—221no—
371C2×SD16—221no—
372C2×D8—22no—
373C2×D8—22no—
374C2×D8—21no—
375C2×D8—21no—
376C2×D8—21no—
377C2×D8—41no—
378C2×D8—41no—
379C2×D8—111no—
380C2×D8—111no—
381C2×D8—222no—
382C2×D8—221no—
383C2×D8—441no—
384C2×D8C22×D1111yescharacteristic
385C2×D8C22×D1111yescharacteristic
386C2×D8C22×D1111yescharacteristic
387C22×C8C22×D1111yescharacteristic
388C22×C8C22×D1111yescharacteristic
389#127—21no—
390#124—221no—
391#123—441no—
392C22⋊Q8—221no—
393#121—21no—
394#121—21no—
395#121—41no—
396#121—221no—
397#121—441no—
398#120—41no—
399#120—41no—
400#120—441no—
401C4×D4—21no—
402C4×D4—221no—
403C4×D4C22⋊D1111yescharacteristic
404C2×C22⋊C4—441no—
405SD32—222no—
406SD32—222no—
407SD32—441no—
408D16—114no—
409D16—222no—
410D16—222no—
411D16—222no—
412D16—222no—
413D16—441no—
414M32—222no—
415C2×C16—111no—
416C2×C16—111no—
417C2×C16—111no—
418C2×C16—111no—
419C2×C16—222no—
420#107—111no—
421#107C22×D1111yescharacteristic
422C4⋊C8C22⋊D1111yescharacteristic
423#103—221no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—221no—
428#102—221no—
429C22⋊C8C22⋊D1111yescharacteristic
430C22⋊C8C22⋊D1111yescharacteristic
431C4×C8C22×D1111yescharacteristic
432C2×C11—22no—
433C2×C11—41no—
434C2×C11—82no—
435C2×C11—161no—
436C2×C11—161no—
437C2×C11D4×D811yescharacteristic
438C2×C11C2×#50911yescharacteristic
439C2×C11#341511yescharacteristic
440D11—82no—
441D11—161no—
442C24—41no—
443C24—41no—
444C24—441no—
445#41—442no—
446#41—881no—
447C2×Q8—221no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—81no—
460C2×D4—81no—
461C2×D4—84no—
462C2×D4—221no—
463C2×D4—221no—
464C2×D4—442no—
465C2×D4—441no—
466C2×D4—441no—
467C2×D4—441no—
468C2×D4—881no—
469C2×D4#432311yescharacteristic
470C22×C4—41no—
471C22×C4—441no—
472C22×C4—441no—
473C22×C4C2×C22⋊D1111yescharacteristic
474C22×C4C2×C22⋊D1111yescharacteristic
475Q16—221no—
476Q16—221no—
477SD16—442no—
478SD16—881no—
479D8—21no—
480D8—21no—
481D8—21no—
482D8—21no—
483D8—21no—
484D8—42no—
485D8—42no—
486D8—81no—
487D8—112no—
488D8—221no—
489D8—221no—
490D8—221no—
491D8—442no—
492D8D4×D1112yes—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8C2×C22⋊D1111yescharacteristic
498C2×C8C2×C22⋊D1111yescharacteristic
499C2×C8C2×C22⋊D1111yescharacteristic
500C2×C8C23×D1111yescharacteristic
501C4⋊C4—21no—
502C4⋊C4—221no—
503C4⋊C4—441no—
504C4⋊C4#432311yescharacteristic
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—441no—
509C22⋊C4—441no—
510C22⋊C4—441no—
511C22⋊C4—441no—
512C22⋊C4—441no—
513C22⋊C4#432311yescharacteristic
514C22⋊C4#432311yescharacteristic
515C42C2×C22⋊D1111yescharacteristic
516C16—112no—
517C16—221no—
518C16—221no—
519C16—221no—
520C11#3383011yescharacteristic, complemented, Sylow
521C23—41no—
522C23—41no—
523C23—41no—
524C23—82no—
525C23—82no—
526C23—82no—
527C23—82no—
528C23—161no—
529C23—161no—
530C23—441no—
531C23—441no—
532C23—882no—
533C23—882no—
534C23—1761no—
535C23C2×#432311yescharacteristic
536C23C2×#432311yescharacteristic
537Q8—441no—
538Q8—441no—
539D4—22no—
540D4—22no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—82no—
547D4—82no—
548D4—82no—
549D4—82no—
550D4—82no—
551D4—161no—
552D4—222no—
553D4—441no—
554D4—441no—
555D4—441no—
556D4—882no—
557D4—882no—
558D4—1761no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—82no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—882no—
568C2×C4—1761no—
569C2×C4C2×#432311yescharacteristic
570C2×C4C2×#432311yescharacteristic
571C2×C4C2×#432311yescharacteristic
572C2×C4C2×#432311yescharacteristic
573C2×C4C22×C22⋊D1111yescharacteristic
574C8—21no—
575C8—21no—
576C8—21no—
577C8C2×D4×D1111yescharacteristic
578C8#6703711yescharacteristic
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—42no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22—81no—
593C22—164no—
594C22—164no—
595C22—442no—
596C22—881no—
597C22—881no—
598C22—881no—
599C22—881no—
600C22—881no—
601C22—1764no—
602C22#1062276012yescomplemented
603C22C22×#432311yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—21no—
608C4—81no—
609C4—881no—
610C4—881no—
611C4D4×C22⋊D1111yescharacteristic
612C4#1062336611yescharacteristic
613C2—22no—
614C2—41no—
615C2—82no—
616C2—161no—
617C2—161no—
618C2—882no—
619C2—1761no—
620C2D4×#432311yescharacteristic
621C2C2×#1062276011yescharacteristic
622C2#1308175511yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingD4×C11×D8C2
socleC22×C11C22×D8
hypercenterD4×D8D11
hypocenterC11#33830
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ D4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#10622760C2semidirect
2. C22×#66890C2semidirect
3. #13080303C2semidirect
4. #13070880C2semidirect
5. #13070717C2semidirect
6. #13070710C2semidirect
7. #13070671C2semidirect
8. #13070648C2semidirect
9. #13070545C2semidirect
10. #13070537C2semidirect
11. #13070528C2semidirect
12. #13070527C2semidirect
13. #13070490C2semidirect
14. #13070442C2semidirect
15. D4×C11×D8C2semidirect
17. C22×C11×D8C22semidirect
19. C2×#66957C22semidirect
20. C22×D88C22semidirect
22. C11×#493C22semidirect
24. C11×#466C22semidirect
28. C4×C11×D8C22semidirect
30. C2×#66891C22semidirect
31. C2×#66891C22semidirect
32. C2×#66891C22semidirect
37. C2×#66890C22semidirect
38. C2×#66890C22semidirect
39. C2×#66890C22semidirect
40. C2×#66890C22semidirect
41. #10622729C22semidirect
42. #10622728C22semidirect
43. C2×#66876C22semidirect
44. C22×C11⋊C16C22semidirect
48. #10622309C22semidirect
49. C4×D88C22semidirect
50. #10622200C22semidirect
51. #10622200C22semidirect
52. #10622200C22semidirect
53. C22⋊(C11⋊C16)C22semidirect
54. C22⋊(C11⋊C16)C22semidirect
55. #10622130C22semidirect
56. #10622129C22semidirect
57. #10622129C22semidirect
58. #10622128C22semidirect
59. C4⋊(C11⋊C16)C22semidirect
60. #10622099C22semidirect
120. #66890D4semidirect
203. D88C2×D4semidirect
209. C11⋊C16C2×D4semidirect
213. D4×D8D11semidirect
286. C22×D8C2×D11semidirect
303. #493C2×D11semidirect
307. #466C2×D11semidirect
315. C4×D8C2×D11semidirect
344. C22×C11#509semidirect
520. C11#33830semidirect
602. C22#10622760semidirect

Maximal subgroups

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

subgroupindex
C2×#106227602
C22×#668902
#130803032
#130708802
#130707172
#130707102
#130706712
#130706482
#130705452
#130705372
#130705282
#130705272
#130704902
#130704422
D4×C11×D82
#3383011