Finite Group Databasebeta

← #14910243

Subgroups — #14910243

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622524C211yesmaximal, characteristic, complemented
2C22×#66864C211yesmaximal, characteristic, complemented
3#13080354C211yesmaximal, characteristic, complemented
4#13080290C211yesmaximal, characteristic, complemented
5#13070879C211yesmaximal, characteristic, complemented
6#13070730C211yesmaximal, characteristic, complemented
7#13070670C211yesmaximal, characteristic, complemented
8#13070655C211yesmaximal, characteristic, complemented
9#13070546C211yesmaximal, characteristic, complemented
10#13070540C211yesmaximal, characteristic, complemented
11#13070532C211yesmaximal, characteristic, complemented
12#13070527C211yesmaximal, characteristic, complemented
13#13070479C211yesmaximal, characteristic, complemented
14#13070441C211yesmaximal, characteristic, complemented
15C11×#2215C211yesmaximal, characteristic, complemented
16C2×#66965C2211yescharacteristic, complemented
17C2×D8×D11C2211yescharacteristic
18C22×Dic44C2211yescharacteristic, complemented
19C22×D88C2211yescharacteristic
20#10623140—21no—
21#10623129—21no—
22C2×C11×D16C2211yescharacteristic, complemented
23C22×C11×C16C2211yescharacteristic, complemented
24C11×#466C2211yescharacteristic
25C11×#466C2211yescharacteristic, complemented
26#10622768C2211yescharacteristic, complemented
27#10622764C2211yescharacteristic
28C2×#66891C2211yescharacteristic, complemented
29C2×#66891C2211yescharacteristic, complemented
30C2×#66890C2211yescharacteristic
31C2×#66890C2211yescharacteristic, complemented
32C8×C22⋊D11C2211yescharacteristic
33#10622653—21no—
34#10622649—21no—
35#10622524—24no—
36C2×#66864—24no—
37C2×#66864C2211yescharacteristic
38C2×#66864C2211yescharacteristic
39C2×#66864C2211yescharacteristic, complemented
40C2×#66864C2211yescharacteristic, complemented
41C2×#66862C2211yescharacteristic, complemented
42#10622500C2211yescharacteristic, complemented
43#10622496C2211yescharacteristic
44#10622486C2211yescharacteristic, complemented
45#10622485C2211yescharacteristic
46#10622399—21no—
47#10622396—21no—
48#10622386—21no—
49#10622380—21no—
50C11×#366C2211yescharacteristic, complemented
51C11×#357C2211yescharacteristic, complemented
52C11×#357C2211yescharacteristic, complemented
53C22⋊(C11⋊C16)C2211yescharacteristic, complemented
54(C2×D11)⋊C16C2211yescharacteristic, complemented
55#10622140C2211yescharacteristic, complemented
56Dic11⋊C16C2211yescharacteristic, complemented
57#10622130C2211yescharacteristic, complemented
58#10622130C2211yescharacteristic, complemented
59#10622129C2211yescharacteristic
60#10622129C2211yescharacteristic, complemented
61C2×#4341—21no—
62C2×D4×D11—21no—
63C2×D4×D11—41no—
64C22×D44—21no—
65C22×Dic22—21no—
66C2×C11×D8C2311yescharacteristic
67C2×C11×D8C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×#121—21no—
70C11×#121—21no—
71#66993—21no—
72#66992—41no—
73#66990—41no—
74#66989—21no—
75D4×Dic11—41no—
76C2×#4324—21no—
77C2×#4324—21no—
78C2×#4323—21no—
79C2×#4323—21no—
80C4×C22⋊D11D411yescharacteristic
81#66965—22no—
82#66965—41no—
83D8×D11—22no—
84D8×D11—41no—
85C2×Dic44—22no—
86C2×Dic44—21no—
87C2×Dic44—41no—
88C2×Dic44C2311yescharacteristic
89C2×Dic44C2311yescharacteristic
90C2×D88—22no—
91C2×D88—21no—
92C2×D88—41no—
93C2×D88C2311yescharacteristic
94C2×D88C2311yescharacteristic
95C2×C8×D11C2311yescharacteristic
96#66950—21no—
97#66948—21no—
98#66946—21no—
99#66940—21no—
100#66938—41no—
101#66937—41no—
102#66935—41no—
103#66931—41no—
104C11×D16—22no—
105C2×C11×C16—22no—
106C2×C11×C16C2311yescharacteristic
107C2×C11×C16C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#107C2311yescharacteristic
110C11×#102—21no—
111C11×#102—21no—
112C22⋊(C11⋊C8)D411yescharacteristic
113#66891—22no—
114#66891—41no—
115#66890—22no—
116#66890—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#33831—111nomaximal, Sylow
132C23×D11—41no—
133C23×D11—41no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—41no—
137C2×D4×C11—41no—
138C22×C4×C11C2×D411yescharacteristic
139C2×C22⋊D11—41no—
140C2×C22⋊D11—41no—
141C2×C22⋊D11—41no—
142C2×C22⋊D11—41no—
143C2×C22⋊D11D811yescharacteristic
144C22×Dic11—41no—
145C22×Dic11—41no—
146#4341—42no—
147#4341—81no—
148D4×D11—42no—
149D4×D11—81no—
150D4×D11—84no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—42no—
154C2×D44—41no—
155C2×D44—41no—
156C2×D44—81no—
157C2×C4×D11—41no—
158C2×C4×D11C2×D411yescharacteristic
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—42no—
162C2×Dic22—41no—
163C2×Dic22—81no—
164C11×D8—21no—
165C11×D8—21no—
166C11×D8—21no—
167C11×D8—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11C2×D411yescharacteristic
171C2×C8×C11C2411yescharacteristic
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C22⋊C4—41no—
175C11×C22⋊C4—41no—
176C22⋊Dic11—41no—
177C22⋊Dic11—41no—
178C22⋊Dic11D811yescharacteristic
179#4324—42no—
180#4324—81no—
181#4323—42no—
182#4323—81no—
183(C2×D11)⋊C4—41no—
184(C2×D11)⋊C4—41no—
185(C2×D11)⋊C4—41no—
186(C2×D11)⋊C4D811yescharacteristic
187C4⋊Dic11—41no—
188Dic11⋊C4—41no—
189Dic11⋊C4D811yescharacteristic
190C4×Dic11—41no—
191C4×Dic11C2×D411yescharacteristic
192C2×C11⋊C8C2×D411yescharacteristic
193C2×C11⋊C8C2×D411yescharacteristic
194Dic44—21no—
195Dic44—21no—
196Dic44—21no—
197Dic44—42no—
198Dic44C2×D412yescomplemented
199D88—21no—
200D88—21no—
201D88—21no—
202D88—42no—
203D88C2×D412yes—
204C8×D11—21no—
205C8×D11—21no—
206C11×C16—21no—
207C11×C16C2×D412yescomplemented
208C11⋊C16—21no—
209C11⋊C16—21no—
210C2×#509—111no—
211C22×SD32—111no—
212#3285—111no—
213D4×D8—111no—
214#2250—111no—
215#2220—111no—
216#2215D1111yescharacteristic, complemented
217#2210—111no—
218#2207—111no—
219#2187—111no—
220#2186—111no—
221#2185—111no—
222#2184—111no—
223#2175—111no—
224#2168—111no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11C2×D811yescharacteristic
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—82no—
231C22×D11—82no—
232C22×D11—82no—
233C22×D11—82no—
234C22×D11—161no—
235C22×D11—161no—
236C22×D11C2×D811yescharacteristic
237D4×C11—41no—
238D4×C11—41no—
239D4×C11—41no—
240D4×C11—41no—
241D4×C11—82no—
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—82no—
252C22⋊D11—82no—
253C22⋊D11—161no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—82no—
257C2×Dic11—82no—
258C2×Dic11C2×D811yescharacteristic
259C2×Dic11C2×D811yescharacteristic
260C2×Dic11C2×D811yescharacteristic
261D44—22no—
262D44—41no—
263D44—41no—
264D44—41no—
265D44—82no—
266D44—82no—
267C4×D11—21no—
268C4×D11—21no—
269C4×D11—82no—
270Dic22—22no—
271Dic22—41no—
272Dic22—41no—
273Dic22—41no—
274Dic22—82no—
275C8×C11—21no—
276C8×C11C22×D411yescharacteristic
277C8×C11H(5,𝔽2)11yescharacteristic
278C11⋊C8—21no—
279C11⋊C8—21no—
280C2×#135—111no—
281C22×Q16—111no—
282C22×D8—111no—
283C22×D8—111no—
284#548—221no—
285D42—221no—
286#509—224no—
287C2×SD32—111no—
288C2×SD32—111no—
289C2×SD32—111no—
290C2×SD32—111no—
291C2×SD32—111no—
292C2×SD32—111no—
293C2×SD32—224no—
294C2×D16—111no—
295C2×D16—111no—
296C2×D16C2×D1111yescharacteristic, complemented
297C2×M32—111no—
298C22×C16C2×D1111yescharacteristic, complemented
299#495—111no—
300#493—111no—
301#467—111no—
302#466—111no—
303#466C2×D1111yescharacteristic
304#466C2×D1111yescharacteristic, complemented
305#464—221no—
306#459—221no—
307#452—221no—
308#448—221no—
309#447—221no—
310#447—221no—
311C4×Q16—111no—
312C4×D8—111no—
313C8×D4—111no—
314#366C2×D1111yescharacteristic, complemented
315C4⋊C16—111no—
316#358—111no—
317#358—111no—
318#357—111no—
319#357—111no—
320#357C2×D1111yescharacteristic, complemented
321#357C2×D1111yescharacteristic, complemented
322C22⋊C16—111no—
323C22⋊C16—111no—
324#346—111no—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11—81no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11#50912yescomplemented
334C22×C11C22×D811yescharacteristic
335C2×D11—21no—
336C2×D11—21no—
337C2×D11—21no—
338C2×D11—42no—
339C2×D11—81no—
340C2×D11—81no—
341C2×D11—81no—
342C2×D11—81no—
343C2×D11—81no—
344C2×D11—164no—
345C2×D11—164no—
346C4×C11—21no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11D4211yescharacteristic
350C4×C11#57611yescharacteristic
351Dic11—21no—
352Dic11—21no—
353Dic11—21no—
354Dic11—42no—
355Dic11—81no—
356C2×#41—221no—
357C22×Q8—221no—
358C22×D4—221no—
359C22×D4—221no—
360C22×D4—441no—
361#135—222no—
362#135—441no—
363C2×Q16—111no—
364C2×Q16—111no—
365C2×Q16—222no—
366C2×Q16—221no—
367C2×Q16—441no—
368C2×SD16—221no—
369C2×SD16—221no—
370C2×D8—111no—
371C2×D8—111no—
372C2×D8—222no—
373C2×D8—221no—
374C2×D8—221no—
375C2×D8—222no—
376C2×D8—221no—
377C2×D8—441no—
378C2×D8—441no—
379C2×D8C22×D1111yescharacteristic
380C2×D8C22×D1111yescharacteristic
381C22×C8—111no—
382C22×C8C22×D1111yescharacteristic
383#127—221no—
384#124—221no—
385#124—441no—
386C22⋊Q8—221no—
387C22⋊Q8—441no—
388#121—21no—
389#121—21no—
390#121—221no—
391#121—441no—
392#121—441no—
393#120—441no—
394#120—441no—
395C4×Q8—221no—
396C4×D4—111no—
397C4×D4—221no—
398C4×D4—441no—
399SD32—114no—
400SD32—222no—
401SD32—222no—
402SD32—222no—
403SD32—222no—
404SD32—441no—
405D16—22no—
406D16—222no—
407D16—441no—
408M32—222no—
409C2×C16—22no—
410C2×C16—111no—
411C2×C16—111no—
412C2×C16C22×D1111yescharacteristic
413C2×C16C22×D1111yescharacteristic
414#107C22×D1111yescharacteristic
415#107C22×D1111yescharacteristic
416C4⋊C8—111no—
417#103—221no—
418#103—221no—
419#102—21no—
420#102—21no—
421#102—221no—
422#102—221no—
423C22⋊C8—111no—
424C22⋊C8—111no—
425C4×C8—111no—
426C2×C11—22no—
427C2×C11—161no—
428C2×C11—161no—
429C2×C11D4×D811yescharacteristic
430C2×C11C2×#50911yescharacteristic
431C2×C11#341611yescharacteristic
432D11—41no—
433D11—82no—
434D11—161no—
435C24—441no—
436C24—441no—
437#41—442no—
438#41—881no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×Q8—442no—
442C2×Q8—441no—
443C2×Q8—881no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—111no—
449C2×D4—221no—
450C2×D4—221no—
451C2×D4—442no—
452C2×D4—441no—
453C2×D4—441no—
454C2×D4—441no—
455C2×D4—441no—
456C2×D4—442no—
457C2×D4—441no—
458C2×D4—441no—
459C2×D4—881no—
460C2×D4—881no—
461C2×D4—884no—
462C22×C4—111no—
463C22×C4—441no—
464C22×C4—441no—
465C22×C4—441no—
466C22×C4D4×D1111yescharacteristic
467Q16—112no—
468Q16—221no—
469Q16—221no—
470Q16—221no—
471Q16—442no—
472SD16—442no—
473SD16—881no—
474D8—21no—
475D8—21no—
476D8—21no—
477D8—21no—
478D8—112no—
479D8—221no—
480D8—221no—
481D8—221no—
482D8—442no—
483D8—442no—
484D8—881no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—111no—
488C2×C8—111no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8D4×D1111yescharacteristic
492C2×C8C23×D1111yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—111no—
496C4⋊C4—441no—
497C4⋊C4—441no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—111no—
501C22⋊C4—111no—
502C22⋊C4—441no—
503C22⋊C4—441no—
504C22⋊C4—441no—
505C22⋊C4—441no—
506C22⋊C4—441no—
507C42—111no—
508C42—441no—
509C16—21no—
510C16—221no—
511C16—221no—
512C16D4×D1112yescomplemented
513C11#3383111yescharacteristic, complemented, Sylow
514C23—41no—
515C23—41no—
516C23—111no—
517C23—441no—
518C23—441no—
519C23—882no—
520C23—882no—
521C23—882no—
522C23—882no—
523C23—1761no—
524C23—1761no—
525C23D8×D1111yescharacteristic
526Q8—222no—
527Q8—441no—
528Q8—441no—
529Q8—441no—
530Q8—882no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—82no—
536D4—82no—
537D4—222no—
538D4—222no—
539D4—441no—
540D4—441no—
541D4—441no—
542D4—882no—
543D4—882no—
544D4—882no—
545D4—882no—
546D4—882no—
547D4—1761no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—111no—
553C2×C4—111no—
554C2×C4—111no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—882no—
560C2×C4—882no—
561C2×C4—882no—
562C2×C4D8×D1111yescharacteristic
563C2×C4C2×D4×D1111yescharacteristic
564C8—21no—
565C8—221no—
566C8—221no—
567C8C2×D4×D1111yescharacteristic
568C8#6704211yescharacteristic
569C22—21no—
570C22—21no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—221no—
578C22—221no—
579C22—221no—
580C22—442no—
581C22—881no—
582C22—881no—
583C22—881no—
584C22—881no—
585C22—881no—
586C22—1764no—
587C22—1764no—
588C22#1062252412yescomplemented
589C22C2×D8×D1111yescharacteristic
590C4—21no—
591C4—81no—
592C4—81no—
593C4—221no—
594C4—221no—
595C4—221no—
596C4—442no—
597C4—881no—
598C4#1062314011yescharacteristic
599C4#1062330011yescharacteristic
600C2—22no—
601C2—161no—
602C2—161no—
603C2—441no—
604C2—882no—
605C2—1761no—
606C2#1308029011yescharacteristic
607C2C2×#1062252411yescharacteristic
608C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2215C2
socleC22×C11C22×D8
hypercenter#2215D11
hypocenterC11#33831
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2215

Complements

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

NH ≅ G/Ntype
1. C2×#10622524C2semidirect
2. C22×#66864C2semidirect
3. #13080354C2semidirect
4. #13080290C2semidirect
5. #13070879C2semidirect
6. #13070730C2semidirect
7. #13070670C2semidirect
8. #13070655C2semidirect
9. #13070546C2semidirect
10. #13070540C2semidirect
11. #13070532C2semidirect
12. #13070527C2semidirect
13. #13070479C2semidirect
14. #13070441C2semidirect
15. C11×#2215C2semidirect
16. C2×#66965C22semidirect
18. C22×Dic44C22semidirect
22. C2×C11×D16C22semidirect
23. C22×C11×C16C22semidirect
25. C11×#466C22semidirect
26. #10622768C22semidirect
28. C2×#66891C22semidirect
29. C2×#66891C22semidirect
31. C2×#66890C22semidirect
39. C2×#66864C22semidirect
40. C2×#66864C22semidirect
41. C2×#66862C22semidirect
42. #10622500C22semidirect
44. #10622486C22semidirect
50. C11×#366C22semidirect
51. C11×#357C22semidirect
52. C11×#357C22semidirect
53. C22⋊(C11⋊C16)C22semidirect
54. (C2×D11)⋊C16C22semidirect
55. #10622140C22semidirect
56. Dic11⋊C16C22semidirect
57. #10622130C22semidirect
58. #10622130C22semidirect
60. #10622129C22semidirect
129. #66864D4semidirect
198. Dic44C2×D4semidirect
207. C11×C16C2×D4semidirect
216. #2215D11semidirect
296. C2×D16C2×D11semidirect
298. C22×C16C2×D11semidirect
304. #466C2×D11semidirect
314. #366C2×D11semidirect
320. #357C2×D11semidirect
321. #357C2×D11semidirect
333. C22×C11#509semidirect
512. C16D4×D11semidirect
513. C11#33831semidirect
588. C22#10622524semidirect

Maximal subgroups

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

subgroupindex
C2×#106225242
C22×#668642
#130803542
#130802902
#130708792
#130707302
#130706702
#130706552
#130705462
#130705402
#130705322
#130705272
#130704792
#130704412
C11×#22152
#3383111