Finite Group Databasebeta

← #14910226

Subgroups — #14910226

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×#10622524C211yesmaximal, characteristic, complemented
2C2×D11×D16C211yesmaximal, characteristic, complemented
3#13080302C211yesmaximal, characteristic, complemented
4#13080291C211yesmaximal, characteristic, complemented
5#13070880C211yesmaximal, characteristic, complemented
6#13070718C211yesmaximal, characteristic, complemented
7#13070711C211yesmaximal, characteristic, complemented
8#13070672C211yesmaximal, characteristic, complemented
9#13070546C211yesmaximal, characteristic, complemented
10#13070536C211yesmaximal, characteristic, complemented
11#13070529C211yesmaximal, characteristic, complemented
12#13070526C211yesmaximal, characteristic, complemented
13#13070490C211yesmaximal, characteristic, complemented
14#13070440C211yesmaximal, characteristic, complemented
15C11×#2206C211yesmaximal, characteristic, complemented
16C2×#66965C2211yescharacteristic, complemented
17C2×D8×D11C2211yescharacteristic
18C2×D8×D11C2211yescharacteristic, complemented
19C2×D8×D11C2211yescharacteristic, complemented
20#10623248—21no—
21#10623085—21no—
22C2×C11×D16C2211yescharacteristic, complemented
23C2×C11×D16C2211yescharacteristic, complemented
24C11×#493C2211yescharacteristic, complemented
25C4×C11×D8C2211yescharacteristic, complemented
26#10622770C2211yescharacteristic
27#10622770C2211yescharacteristic, complemented
28#10622769—21no—
29#10622769—21no—
30C2×#66891C2211yescharacteristic, complemented
31C2×#66891C2211yescharacteristic, complemented
32C2×#66890C2211yescharacteristic
33C2×#66890C2211yescharacteristic, complemented
34C2×#66890C2211yescharacteristic, complemented
35#10622685—21no—
36#10622629—21no—
37#10622524—24no—
38D11×D16—24no—
39C2×#66864C2211yescharacteristic, complemented
40C2×D176C2211yescharacteristic
41C2×#66862C2211yescharacteristic, complemented
42C2×C16×D11C2211yescharacteristic, complemented
43#10622500C2211yescharacteristic, complemented
44#10622496C2211yescharacteristic, complemented
45#10622394—21no—
46#10622389—21no—
47#10622309C2211yescharacteristic, complemented
48C4×D88C2211yescharacteristic, complemented
49C8×D44C2211yescharacteristic
50C11×C4⋊C16C2211yescharacteristic, complemented
51C11×#357C2211yescharacteristic, complemented
52C11×#357C2211yescharacteristic, complemented
53#10622200C2211yescharacteristic, complemented
54#10622147C2211yescharacteristic, complemented
55(C2×D11)⋊C16C2211yescharacteristic, complemented
56(C2×D11)⋊C16C2211yescharacteristic, complemented
57#10622141C2211yescharacteristic, complemented
58#10622129C2211yescharacteristic, complemented
59#10622128C2211yescharacteristic, complemented
60#10622099C2211yescharacteristic, complemented
61C2×#4341—21no—
62C2×D4×D11—21no—
63C2×D4×D11—21no—
64C2×D4×D11—21no—
65C2×D4×D11—41no—
66C2×C11×D8—21no—
67C2×C11×D8C2311yescharacteristic
68C2×C11×D8C2311yescharacteristic
69C2×C11×D8C2311yescharacteristic
70C11×#127—21no—
71C4×D4×C11—21no—
72#66991—21no—
73#66991—21no—
74#66991—41no—
75#66990—41no—
76#66990—41no—
77C2×#4324—21no—
78C2×#4323—21no—
79C2×#4323—21no—
80C2×#4323—21no—
81#66983—41no—
82C2×(C2×D11)⋊C4—41no—
83#66965—22no—
84#66965—41no—
85D8×D11—22no—
86D8×D11—22no—
87D8×D11—22no—
88D8×D11—41no—
89D8×D11—41no—
90D8×D11—41no—
91C2×Dic44C2311yescharacteristic
92C2×D88C2311yescharacteristic
93C2×D88C2311yescharacteristic
94C2×#4314—21no—
95C2×C8×D11C2311yescharacteristic
96C2×C8×D11C2311yescharacteristic
97#66950—21no—
98#66948—21no—
99#66939—41no—
100#66935—41no—
101#66928—21no—
102C4×D44—21no—
103C4×D44D411yescharacteristic
104C11×D16—22no—
105C11×D16—22no—
106C2×C11×C16C2311yescharacteristic
107C2×C11×C16C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#102—21no—
110C4×C8×C11C2311yescharacteristic
111#66896—21no—
112#66896—21no—
113#66891—22no—
114#66891—41no—
115#66890—22no—
116#66890—41no—
117#66890D414yescomplemented
118#66885—21no—
119(C2×D11)⋊C8D411yescharacteristic
120(C2×D11)⋊C8D411yescharacteristic
121#66882C2311yescharacteristic
122C2×C11⋊C16C2311yescharacteristic
123C2×C11⋊C16C2311yescharacteristic
124#66874—21no—
125#66873—21no—
126C4⋊(C11⋊C8)D411yescharacteristic
127#66864—22no—
128D176—22no—
129#66862—22no—
130C16×D11—22no—
131#33830—111nomaximal, Sylow
132C23×D11—41no—
133C23×D11—41no—
134C23×D11—41no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—41no—
139C2×D4×C11—41no—
140C22×C4×C11—41no—
141C2×C22⋊D11—41no—
142C2×C22⋊D11—41no—
143C2×C22⋊D11—41no—
144C2×C22⋊D11—41no—
145C2×C22⋊D11—41no—
146C2×C22⋊D11—41no—
147C22×Dic11—41no—
148#4341—42no—
149#4341—81no—
150D4×D11—42no—
151D4×D11—42no—
152D4×D11—42no—
153D4×D11—81no—
154D4×D11—81no—
155D4×D11—81no—
156D4×D11—84no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—41no—
160C2×D44D811yescharacteristic
161C2×C4×D11—41no—
162C2×C4×D11C2×D411yescharacteristic
163C2×C4×D11C2×D411yescharacteristic
164C2×Dic22—21no—
165C11×D8—21no—
166C11×D8—21no—
167C11×D8—21no—
168C11×D8—21no—
169C11×D8—21no—
170C11×D8—81no—
171C11×D8C2×D412yescomplemented
172C2×C8×C11C2×D411yescharacteristic
173C2×C8×C11C2411yescharacteristic
174C11×C4⋊C4—21no—
175C11×C22⋊C4—41no—
176C42×C11C2×D411yescharacteristic
177C22⋊Dic11—41no—
178C22⋊Dic11—41no—
179#4324—42no—
180#4323—42no—
181#4323—42no—
182#4323—42no—
183(C2×D11)⋊C4—41no—
184(C2×D11)⋊C4—41no—
185(C2×D11)⋊C4—41no—
186(C2×D11)⋊C4—41no—
187(C2×D11)⋊C4—41no—
188(C2×D11)⋊C4D811yescharacteristic
189(C2×D11)⋊C4D811yescharacteristic
190C4⋊Dic11—21no—
191C4⋊Dic11—41no—
192C4⋊Dic11D811yescharacteristic
193C2×C11⋊C8C2×D411yescharacteristic
194C2×C11⋊C8C2×D411yescharacteristic
195Dic44—21no—
196Dic44—21no—
197D88—21no—
198D88—21no—
199D88—21no—
200D88C2×D412yes—
201#4314—81no—
202C8×D11—21no—
203C8×D11—21no—
204C8×D11—21no—
205C8×D11—21no—
206C11×C16—21no—
207C11×C16—21no—
208C11⋊C16—21no—
209C11⋊C16C2×D412yescomplemented
210C2×#509—111no—
211C22×D16—111no—
212#3280—111no—
213D4×D8—111no—
214#2250—111no—
215#2218—111no—
216#2217—111no—
217#2210—111no—
218#2206D1111yescharacteristic, complemented
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—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—82no—
231C22×D11—82no—
232C22×D11—82no—
233C22×D11—82no—
234C22×D11—82no—
235C22×D11—82no—
236C22×D11—161no—
237C22×D11—161no—
238C22×D11—161no—
239C22×D11C2×D811yescharacteristic
240C22×D11C2×D811yescharacteristic
241D4×C11—22no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—41no—
247D4×C11—82no—
248D4×C11—161no—
249C2×C4×C11—41no—
250C2×C4×C11—161no—
251C2×C4×C11C2×D811yescharacteristic
252C2×C4×C11C2×D811yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C22⋊D11—82no—
255C22⋊D11—82no—
256C22⋊D11—82no—
257C22⋊D11—82no—
258C22⋊D11—82no—
259C22⋊D11—82no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—82no—
263C2×Dic11C2×D811yescharacteristic
264C2×Dic11C2×D811yescharacteristic
265D44—22no—
266D44—22no—
267D44—41no—
268D44—41no—
269D44—41no—
270D44—161no—
271C4×D11—21no—
272C4×D11—21no—
273C4×D11—21no—
274C4×D11—21no—
275C4×D11—82no—
276Dic22—41no—
277Dic22—41no—
278C8×C11—21no—
279C8×C11C22×D411yescharacteristic
280C8×C11H(5,𝔽2)11yescharacteristic
281C11⋊C8—21no—
282C11⋊C8—21no—
283C2×#135—111no—
284C22×D8—111no—
285C22×D8—111no—
286C22×D8—111no—
287#546—221no—
288D42—221no—
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—224no—
298C2×D16C2×D1111yescharacteristic, complemented
299C2×D16C2×D1111yescharacteristic, complemented
300C2×M32—111no—
301C22×C16—111no—
302#495—111no—
303#493C2×D1111yescharacteristic, complemented
304#467—111no—
305#466—111no—
306#466—111no—
307#466—111no—
308#463—221no—
309#459—221no—
310#450—221no—
311#449—221no—
312#447—221no—
313#447—221no—
314C4×D8—111no—
315C4×D8C2×D1111yescharacteristic, complemented
316C8×D4—111no—
317#367—111no—
318C4⋊C16C2×D1111yescharacteristic, complemented
319#358—111no—
320#357—111no—
321#357—111no—
322#357—111no—
323#357C2×D1111yescharacteristic, complemented
324#357C2×D1111yescharacteristic, complemented
325C22⋊C16—111no—
326C22⋊C16—111no—
327#346—111no—
328C22×C11—42no—
329C22×C11—81no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11—81no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11C22×D811yescharacteristic
338C2×D11—21no—
339C2×D11—21no—
340C2×D11—21no—
341C2×D11—21no—
342C2×D11—21no—
343C2×D11—42no—
344C2×D11—81no—
345C2×D11—81no—
346C2×D11—81no—
347C2×D11—81no—
348C2×D11—81no—
349C2×D11—164no—
350C2×D11—164no—
351C2×D11—164no—
352C2×D11#50912yescomplemented
353C4×C11—21no—
354C4×C11—21no—
355C4×C11—81no—
356C4×C11D4211yescharacteristic
357C4×C11#57611yescharacteristic
358Dic11—21no—
359Dic11—21no—
360Dic11—81no—
361Dic11—81no—
362C2×#41—221no—
363C22×D4—221no—
364C22×D4—221no—
365C22×D4—221no—
366C22×D4—441no—
367#135—222no—
368#135—441no—
369C2×Q16—111no—
370C2×SD16—221no—
371C2×SD16—221no—
372C2×D8—21no—
373C2×D8—111no—
374C2×D8—111no—
375C2×D8—221no—
376C2×D8—221no—
377C2×D8—221no—
378C2×D8—222no—
379C2×D8—222no—
380C2×D8—222no—
381C2×D8—441no—
382C2×D8—441no—
383C2×D8—441no—
384C2×D8C22×D1111yescharacteristic
385C2×D8C22×D1111yescharacteristic
386C2×D8C22×D1111yescharacteristic
387C22×C8—111no—
388C22×C8—111no—
389#127—21no—
390#124—221no—
391#123—441no—
392C22⋊Q8—221no—
393#121—221no—
394#121—221no—
395#121—221no—
396#121—441no—
397#121—441no—
398#120—441no—
399#120—441no—
400#120—441no—
401C4×D4—21no—
402C4×D4—111no—
403C4×D4—221no—
404C2×C22⋊C4—441no—
405SD32—222no—
406SD32—222no—
407SD32—441no—
408D16—22no—
409D16—22no—
410D16—114no—
411D16—222no—
412D16—222no—
413D16—441no—
414M32—222no—
415C2×C16—111no—
416C2×C16—111no—
417C2×C16—222no—
418C2×C16C22×D1111yescharacteristic
419C2×C16C22×D1111yescharacteristic
420#107—111no—
421#107C22×D1111yescharacteristic
422C4⋊C8—111no—
423#103—221no—
424#102—21no—
425#102—221no—
426#102—221no—
427#102—221no—
428#102—221no—
429C22⋊C8—111no—
430C22⋊C8—111no—
431C4×C8C22×D1111yescharacteristic
432C2×C11—82no—
433C2×C11—161no—
434C2×C11—161no—
435C2×C11D4×D811yescharacteristic
436C2×C11C2×#50911yescharacteristic
437C2×C11#341511yescharacteristic
438D11—22no—
439D11—41no—
440D11—82no—
441D11—161no—
442C24—441no—
443C24—441no—
444C24—441no—
445#41—442no—
446#41—881no—
447C2×Q8—221no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—111no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—441no—
457C2×D4—441no—
458C2×D4—441no—
459C2×D4—441no—
460C2×D4—442no—
461C2×D4—442no—
462C2×D4—442no—
463C2×D4—441no—
464C2×D4—441no—
465C2×D4—441no—
466C2×D4—881no—
467C2×D4—881no—
468C2×D4—881no—
469C2×D4—884no—
470C22×C4—41no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—441no—
474C22×C4—441no—
475Q16—221no—
476Q16—221no—
477SD16—442no—
478SD16—881no—
479D8—21no—
480D8—21no—
481D8—21no—
482D8—21no—
483D8—21no—
484D8—81no—
485D8—112no—
486D8—221no—
487D8—221no—
488D8—221no—
489D8—442no—
490D8—442no—
491D8—442no—
492D8D4×D1112yescomplemented
493C2×C8—111no—
494C2×C8—111no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8D4×D1111yescharacteristic
500C2×C8C23×D1111yescharacteristic
501C4⋊C4—21no—
502C4⋊C4—111no—
503C4⋊C4—221no—
504C4⋊C4—441no—
505C22⋊C4—41no—
506C22⋊C4—111no—
507C22⋊C4—111no—
508C22⋊C4—441no—
509C22⋊C4—441no—
510C22⋊C4—441no—
511C22⋊C4—441no—
512C22⋊C4—441no—
513C22⋊C4—441no—
514C22⋊C4—441no—
515C42D4×D1111yescharacteristic
516C16—21no—
517C16—21no—
518C16—112no—
519C16—221no—
520C11#3383011yescharacteristic, complemented, Sylow
521C23—41no—
522C23—41no—
523C23—41no—
524C23—111no—
525C23—111no—
526C23—441no—
527C23—441no—
528C23—882no—
529C23—882no—
530C23—882no—
531C23—882no—
532C23—882no—
533C23—882no—
534C23—1761no—
535C23—1761no—
536C23—1761no—
537Q8—441no—
538Q8—441no—
539D4—22no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—82no—
546D4—161no—
547D4—222no—
548D4—222no—
549D4—441no—
550D4—441no—
551D4—441no—
552D4—882no—
553D4—882no—
554D4—882no—
555D4—882no—
556D4—882no—
557D4—882no—
558D4—1761no—
559C2×C4—41no—
560C2×C4—111no—
561C2×C4—111no—
562C2×C4—161no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—882no—
570C2×C4—882no—
571C2×C4D8×D1111yescharacteristic
572C2×C4D8×D1111yescharacteristic
573C2×C4C2×D4×D1111yescharacteristic
574C8—21no—
575C8—221no—
576C8—221no—
577C8C2×D4×D1111yescharacteristic
578C8#6704211yescharacteristic
579C22—42no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—112no—
589C22—221no—
590C22—221no—
591C22—221no—
592C22—221no—
593C22—221no—
594C22—442no—
595C22—881no—
596C22—881no—
597C22—881no—
598C22—881no—
599C22—881no—
600C22—1764no—
601C22—1764no—
602C22—1764no—
603C22C2×D8×D1111yescharacteristic
604C4—21no—
605C4—21no—
606C4—81no—
607C4—221no—
608C4—221no—
609C4—881no—
610C4—881no—
611C4#1062314011yescharacteristic
612C4#1062330511yescharacteristic
613C2—82no—
614C2—161no—
615C2—161no—
616C2—222no—
617C2—441no—
618C2—882no—
619C2—1761no—
620C2#1308028811yescharacteristic
621C2D11×#50911yescharacteristic
622C2#1308175311yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2206C2
socleC22×C11C22×D8
hypercenter#2206D11
hypocenterC11#33830
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2206

Complements

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

NH ≅ G/Ntype
1. C2×#10622524C2semidirect
2. C2×D11×D16C2semidirect
3. #13080302C2semidirect
4. #13080291C2semidirect
5. #13070880C2semidirect
6. #13070718C2semidirect
7. #13070711C2semidirect
8. #13070672C2semidirect
9. #13070546C2semidirect
10. #13070536C2semidirect
11. #13070529C2semidirect
12. #13070526C2semidirect
13. #13070490C2semidirect
14. #13070440C2semidirect
15. C11×#2206C2semidirect
16. C2×#66965C22semidirect
18. C2×D8×D11C22semidirect
19. C2×D8×D11C22semidirect
22. C2×C11×D16C22semidirect
23. C2×C11×D16C22semidirect
24. C11×#493C22semidirect
25. C4×C11×D8C22semidirect
27. #10622770C22semidirect
30. C2×#66891C22semidirect
31. C2×#66891C22semidirect
33. C2×#66890C22semidirect
34. C2×#66890C22semidirect
39. C2×#66864C22semidirect
41. C2×#66862C22semidirect
42. C2×C16×D11C22semidirect
43. #10622500C22semidirect
44. #10622496C22semidirect
47. #10622309C22semidirect
48. C4×D88C22semidirect
50. C11×C4⋊C16C22semidirect
51. C11×#357C22semidirect
52. C11×#357C22semidirect
53. #10622200C22semidirect
54. #10622147C22semidirect
55. (C2×D11)⋊C16C22semidirect
56. (C2×D11)⋊C16C22semidirect
57. #10622141C22semidirect
58. #10622129C22semidirect
59. #10622128C22semidirect
60. #10622099C22semidirect
117. #66890D4semidirect
171. C11×D8C2×D4semidirect
209. C11⋊C16C2×D4semidirect
218. #2206D11semidirect
298. C2×D16C2×D11semidirect
299. C2×D16C2×D11semidirect
303. #493C2×D11semidirect
315. C4×D8C2×D11semidirect
318. C4⋊C16C2×D11semidirect
323. #357C2×D11semidirect
324. #357C2×D11semidirect
352. C2×D11#509semidirect
492. D8D4×D11semidirect
520. C11#33830semidirect

Maximal subgroups

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

subgroupindex
C2×#106225242
C2×D11×D162
#130803022
#130802912
#130708802
#130707182
#130707112
#130706722
#130705462
#130705362
#130705292
#130705262
#130704902
#130704402
C11×#22062
#3383011