Finite Group Databasebeta

← #14909615

Subgroups — #14909615

Order 2816.

616 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078265C211yesmaximal, characteristic, complemented
2#13078259C211yesmaximal, characteristic, complemented
3#13070810C211yesmaximal, characteristic, complemented
4#13070809C211yesmaximal, characteristic, complemented
5#13070807C211yesmaximal, characteristic, complemented
6#13070720C211yesmaximal, characteristic, complemented
7#13070718C211yesmaximal, characteristic, complemented
8#13070703C211yesmaximal, characteristic, complemented
9#13070701C211yesmaximal, characteristic, complemented
10#13070530C211yesmaximal, characteristic, complemented
11#13070529C211yesmaximal, characteristic, complemented
12#13070529C211yesmaximal, characteristic, complemented
13#13070527C211yesmaximal, characteristic, complemented
14#13070228C211yesmaximal, characteristic, complemented
15C11×#2234C211yesmaximal, characteristic, complemented
16C2×D8×D11C2211yescharacteristic, complemented
17C22×D88C2211yescharacteristic, complemented
18C2×#66954C2211yescharacteristic
19#10623138—21no—
20#10623056—21no—
21C11×#466C2211yescharacteristic
22C11×#427C2211yescharacteristic, complemented
23#10622770C2211yescharacteristic, complemented
24C2×#66890C2211yescharacteristic
25C2×#66890C2211yescharacteristic
26#10622728C2211yescharacteristic
27#10622652—21no—
28#10622614—21no—
29C2×D176C2211yescharacteristic
30C2×D176C2211yescharacteristic
31C2×#66862C2211yescharacteristic, complemented
32C2×C16×D11C2211yescharacteristic, complemented
33#10622496C2211yescharacteristic
34#10622496C2211yescharacteristic
35#10622496C2211yescharacteristic, complemented
36#10622496C2211yescharacteristic, complemented
37#10622496C2211yescharacteristic, complemented
38#10622493C2211yescharacteristic, complemented
39#10622478—21no—
40#10622478—21no—
41#10622395—21no—
42#10622383—21no—
43C11×#367C2211yescharacteristic, complemented
44C11×#366C2211yescharacteristic, complemented
45C11×#357C2211yescharacteristic, complemented
46C11×#357C2211yescharacteristic, complemented
47C11×C22⋊C16C2211yescharacteristic, complemented
48C22⋊(C11⋊C16)C2211yescharacteristic, complemented
49#10622147C2211yescharacteristic, complemented
50#10622147C2211yescharacteristic, complemented
51(C2×D11)⋊C16C2211yescharacteristic, complemented
52(C2×D11)⋊C16C2211yescharacteristic, complemented
53#10622129C2211yescharacteristic, complemented
54#10622129C2211yescharacteristic, complemented
55#10622129C2211yescharacteristic, complemented
56#10622129C2211yescharacteristic, complemented
57#10622128C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C2×D4×D11—21no—
60C2×#4339D411yescharacteristic
61C22×D44—21no—
62C2×C11×D8C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×#121—21no—
65C11×#117—21no—
66#66993—41no—
67#66991—21no—
68#66990—41no—
69C2×#4323—21no—
70#66983—21no—
71C2×#4318D411yescharacteristic
72D8×D11—41no—
73D8×D11—41no—
74C2×D88—21no—
75C2×D88—41no—
76C2×D88—41no—
77C2×D88C2311yescharacteristic
78C2×D88C2311yescharacteristic
79C2×D88C2311yescharacteristic
80#66954—41no—
81#66954—41no—
82C2×#4313D411yescharacteristic
83C2×#4313D411yescharacteristic
84C2×C8×D11C2311yescharacteristic
85C2×C8×D11C2311yescharacteristic
86#66948—21no—
87#66948—21no—
88#66948—21no—
89#66948—21no—
90#66948—21no—
91#66945—21no—
92#66938—41no—
93#66935—41no—
94#66935—41no—
95#66935—41no—
96#66928—41no—
97#66927—41no—
98C2×C11×C16C2311yescharacteristic
99C2×C11×C16C2311yescharacteristic
100C11×#107C2311yescharacteristic
101C11×#107C2311yescharacteristic
102C11×#107C2311yescharacteristic
103C11×#106—21no—
104C11×#102—21no—
105#66896—21no—
106#66890—41no—
107#66890—41no—
108#66885—21no—
109#66882C2311yescharacteristic
110C2×C11⋊C16C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112#66873—21no—
113#66873—21no—
114#66873—21no—
115#66873—21no—
116#66873—21no—
117#66872—21no—
118D176—41no—
119D176—41no—
120#66862—41no—
121C16×D11—41no—
122#33765—111nomaximal, Sylow
123C23×D11—41no—
124C23×D11—41no—
125C2×D4×C11—21no—
126C2×D4×C11—41no—
127C22×C4×C11C2×D411yescharacteristic
128C2×C22⋊D11—41no—
129C2×C22⋊D11—41no—
130C2×C22⋊D11—41no—
131C2×C22⋊D11D811yescharacteristic
132C2×C22⋊D11D811yescharacteristic
133D4×D11—42no—
134D4×D11—42no—
135#4339—41no—
136#4339—41no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—42no—
141C2×D44—42no—
142C2×D44—41no—
143C2×D44—41no—
144C2×D44—41no—
145C2×D44—41no—
146C2×D44—41no—
147C2×D44—41no—
148C2×D44D811yescharacteristic
149C2×C4×D11C2×D411yescharacteristic
150C2×C4×D11C2×D411yescharacteristic
151C2×Dic22D811yescharacteristic
152C11×D8—21no—
153C11×D8—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11C2×D411yescharacteristic
157C2×C8×C11C2411yescharacteristic
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C22⋊C4—41no—
162C11×C22⋊C4—41no—
163C42×C11—41no—
164C22⋊Dic11—41no—
165#4323—42no—
166(C2×D11)⋊C4—41no—
167(C2×D11)⋊C4—41no—
168(C2×D11)⋊C4—41no—
169(C2×D11)⋊C4—41no—
170(C2×D11)⋊C4—41no—
171(C2×D11)⋊C4—41no—
172(C2×D11)⋊C4—41no—
173C4⋊Dic11—21no—
174C4×Dic11—41no—
175#4318—41no—
176C2×C11⋊C8C2×D411yescharacteristic
177C2×C11⋊C8C2×D411yescharacteristic
178D88—21no—
179D88—21no—
180D88—21no—
181D88—21no—
182D88—21no—
183D88—21no—
184D88—42no—
185#4313—41no—
186#4313—41no—
187C8×D11—21no—
188C8×D11—21no—
189C8×D11—21no—
190C8×D11—21no—
191C11×C16—21no—
192C11×C16—21no—
193C11⋊C16—21no—
194C11⋊C16—21no—
195#3058—111no—
196#3058—111no—
197#2234—111no—
198#2234—111no—
199#2234—111no—
200#2234D1111yescharacteristic, complemented
201#2218—111no—
202#2218—111no—
203#2215—111no—
204#2215—111no—
205#2184—111no—
206#2184—111no—
207#2184—111no—
208#2184—111no—
209#2113—111no—
210C23×C11—41no—
211C23×C11C2×D811yescharacteristic
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—82no—
216C22×D11—82no—
217C22×D11—161no—
218C22×D11—161no—
219C22×D11—161no—
220C22×D11—161no—
221C22×D11C2×D811yescharacteristic
222C22×D11C2×D811yescharacteristic
223D4×C11—41no—
224D4×C11—41no—
225D4×C11—161no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11C2×D811yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C22⋊D11—41no—
234C22⋊D11—41no—
235C22⋊D11—82no—
236C22⋊D11—161no—
237C22⋊D11—161no—
238C2×Dic11—41no—
239C2×Dic11C2×D811yescharacteristic
240C2×Dic11C2×D811yescharacteristic
241D44—41no—
242D44—41no—
243D44—41no—
244D44—41no—
245D44—41no—
246D44—41no—
247D44—41no—
248D44—82no—
249D44—161no—
250D44—161no—
251D44—161no—
252D44—161no—
253D44—161no—
254C4×D11—21no—
255C4×D11—21no—
256C4×D11—21no—
257C4×D11—21no—
258Dic22—41no—
259C8×C11—21no—
260C8×C11H(5,𝔽2)11yescharacteristic
261C8×C11H(5,𝔽2)11yescharacteristic
262C11⋊C8—21no—
263C11⋊C8—21no—
264C22×D8—111no—
265C22×D8—111no—
266C2×#131—111no—
267#535—221no—
268#535—221no—
269C2×D16—111no—
270C2×D16—111no—
271C2×D16—111no—
272C2×D16—111no—
273C2×M32—111no—
274C22×C16—111no—
275#469—221no—
276#469—221no—
277#469—221no—
278#469—221no—
279#466—111no—
280#466—111no—
281#466—111no—
282#466—111no—
283#466—111no—
284#466—111no—
285#466—111no—
286#466C2×D1111yescharacteristic
287#427—111no—
288#427C2×D1111yescharacteristic, complemented
289#418—221no—
290#418—221no—
291#367—111no—
292#367C2×D1111yescharacteristic, complemented
293#366—111no—
294#366C2×D1111yescharacteristic, complemented
295#357—111no—
296#357—111no—
297#357—111no—
298#357—111no—
299#357—111no—
300#357—111no—
301#357C2×D1111yescharacteristic, complemented
302#357C2×D1111yescharacteristic, complemented
303C22⋊C16—111no—
304C22⋊C16—111no—
305C22⋊C16—111no—
306C22⋊C16C2×D1111yescharacteristic, complemented
307C22×C11—21no—
308C22×C11—21no—
309C22×C11—21no—
310C22×C11—81no—
311C22×C11—81no—
312C22×C11—81no—
313C22×C11C22×D811yescharacteristic
314C2×D11—21no—
315C2×D11—21no—
316C2×D11—21no—
317C2×D11—21no—
318C2×D11—21no—
319C2×D11—21no—
320C2×D11—81no—
321C2×D11—81no—
322C2×D11—81no—
323C2×D11—81no—
324C2×D11—81no—
325C2×D11—81no—
326C2×D11—81no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—164no—
330C2×D11—164no—
331C4×C11—21no—
332C4×C11—81no—
333C4×C11—81no—
334C4×C11—81no—
335C4×C11#53411yescharacteristic
336C4×C11#57511yescharacteristic
337Dic11—21no—
338Dic11—21no—
339Dic11—81no—
340C2×#41—111no—
341C22×D4—221no—
342C22×D4—221no—
343C2×D8—111no—
344C2×D8—111no—
345C2×D8—111no—
346C2×D8—221no—
347C2×D8—221no—
348C2×D8—441no—
349C2×D8—441no—
350C2×D8—441no—
351C2×D8—441no—
352C2×D8C22×D1111yescharacteristic
353#131—441no—
354#131—441no—
355C2×M16—111no—
356C2×M16—111no—
357C2×M16—111no—
358C22×C8—111no—
359C22×C8—111no—
360C22×C8C22×D1111yescharacteristic
361#127—441no—
362#127—441no—
363#124—441no—
364#124—441no—
365#121—21no—
366#121—221no—
367#121—221no—
368#121—221no—
369#121—221no—
370#121—221no—
371#121—221no—
372#121—221no—
373#120—441no—
374#120—441no—
375#120—441no—
376#120—441no—
377#117—21no—
378#117—221no—
379D16—441no—
380D16—441no—
381D16—441no—
382D16—441no—
383M32—441no—
384C2×C16—111no—
385C2×C16—111no—
386C2×C16—441no—
387C2×C16C22×D1111yescharacteristic
388C2×C16C22×D1111yescharacteristic
389#107—111no—
390#107C22×D1111yescharacteristic
391#107C22×D1111yescharacteristic
392#107C22×D1111yescharacteristic
393#106—21no—
394#106—221no—
395#102—21no—
396#102—221no—
397#102—221no—
398#102—221no—
399#102—221no—
400#102—221no—
401#102—221no—
402#102—221no—
403C2×C11—41no—
404C2×C11—161no—
405C2×C11#318611yescharacteristic
406C2×C11#341511yescharacteristic
407C2×C11#341511yescharacteristic
408D11—41no—
409D11—41no—
410D11—161no—
411D11—161no—
412D11—161no—
413C24—441no—
414C24—441no—
415#41—441no—
416#41—441no—
417C2×Q8—111no—
418C2×D4—21no—
419C2×D4—41no—
420C2×D4—111no—
421C2×D4—111no—
422C2×D4—111no—
423C2×D4—221no—
424C2×D4—221no—
425C2×D4—221no—
426C2×D4—442no—
427C2×D4—442no—
428C2×D4—441no—
429C2×D4—441no—
430C2×D4—441no—
431C2×D4—441no—
432C2×D4—441no—
433C2×D4—441no—
434C2×D4—442no—
435C2×D4—442no—
436C2×D4—441no—
437C2×D4—441no—
438C2×D4—441no—
439C22×C4—111no—
440C22×C4—111no—
441C22×C4D4×D1111yescharacteristic
442D8—21no—
443D8—21no—
444D8—221no—
445D8—221no—
446D8—221no—
447D8—221no—
448D8—221no—
449D8—221no—
450D8—442no—
451D8—442no—
452M16—441no—
453M16—441no—
454M16—441no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—111no—
458C2×C8—111no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8D4×D1111yescharacteristic
464C2×C8C23×D1111yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—221no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C22⋊C4—441no—
472C22⋊C4—441no—
473C22⋊C4—441no—
474C22⋊C4—441no—
475C22⋊C4—441no—
476C22⋊C4—441no—
477C22⋊C4—441no—
478C22⋊C4—441no—
479C42—41no—
480C42—441no—
481C16—21no—
482C16—21no—
483C16—221no—
484C16—221no—
485C11#3376511yescharacteristic, complemented, Sylow
486C23—41no—
487C23—111no—
488C23—111no—
489C23—441no—
490C23—441no—
491C23—441no—
492C23—882no—
493C23—882no—
494C23—1761no—
495C23—1761no—
496C23—1761no—
497C23—1761no—
498C23D8×D1111yescharacteristic
499Q8—441no—
500D4—41no—
501D4—41no—
502D4—161no—
503D4—441no—
504D4—441no—
505D4—441no—
506D4—441no—
507D4—441no—
508D4—441no—
509D4—441no—
510D4—441no—
511D4—441no—
512D4—882no—
513D4—882no—
514D4—1761no—
515D4—1761no—
516D4—1761no—
517D4—1761no—
518D4—1761no—
519D4—1761no—
520D4—1761no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—111no—
527C2×C4—111no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—441no—
533C2×C4D8×D1111yescharacteristic
534C2×C4C2×D4×D1111yescharacteristic
535C8—21no—
536C8—221no—
537C8—221no—
538C8#6704211yescharacteristic
539C8#6704211yescharacteristic
540C22—21no—
541C22—21no—
542C22—21no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—221no—
547C22—221no—
548C22—221no—
549C22—221no—
550C22—221no—
551C22—221no—
552C22—881no—
553C22—881no—
554C22—881no—
555C22—881no—
556C22—881no—
557C22—881no—
558C22—881no—
559C22—881no—
560C22—881no—
561C22—1764no—
562C22—1764no—
563C22C2×D8×D1111yescharacteristic
564C4—21no—
565C4—81no—
566C4—81no—
567C4—81no—
568C4—221no—
569C4—221no—
570C4—881no—
571C4#1062318411yescharacteristic
572C4#1062330811yescharacteristic
573C2—41no—
574C2—161no—
575C2—441no—
576C2—441no—
577C2—1761no—
578C2—1761no—
579C2—1761no—
580C2#1307936611yescharacteristic
581C2#1308175411yescharacteristic
582C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2234C2
socleC22×C11C22×D8
hypercenter#2234D11
hypocenterC11#33765
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2234

Complements

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

NH ≅ G/Ntype
1. #13078265C2semidirect
2. #13078259C2semidirect
3. #13070810C2semidirect
4. #13070809C2semidirect
5. #13070807C2semidirect
6. #13070720C2semidirect
7. #13070718C2semidirect
8. #13070703C2semidirect
9. #13070701C2semidirect
10. #13070530C2semidirect
11. #13070529C2semidirect
12. #13070529C2semidirect
13. #13070527C2semidirect
14. #13070228C2semidirect
15. C11×#2234C2semidirect
16. C2×D8×D11C22semidirect
17. C22×D88C22semidirect
22. C11×#427C22semidirect
23. #10622770C22semidirect
31. C2×#66862C22semidirect
32. C2×C16×D11C22semidirect
35. #10622496C22semidirect
36. #10622496C22semidirect
37. #10622496C22semidirect
38. #10622493C22semidirect
43. C11×#367C22semidirect
44. C11×#366C22semidirect
45. C11×#357C22semidirect
46. C11×#357C22semidirect
47. C11×C22⋊C16C22semidirect
48. C22⋊(C11⋊C16)C22semidirect
49. #10622147C22semidirect
50. #10622147C22semidirect
51. (C2×D11)⋊C16C22semidirect
52. (C2×D11)⋊C16C22semidirect
53. #10622129C22semidirect
54. #10622129C22semidirect
55. #10622129C22semidirect
56. #10622129C22semidirect
57. #10622128C22semidirect
58. #10622127C22semidirect
200. #2234D11semidirect
288. #427C2×D11semidirect
292. #367C2×D11semidirect
294. #366C2×D11semidirect
301. #357C2×D11semidirect
302. #357C2×D11semidirect
306. C22⋊C16C2×D11semidirect
485. C11#33765semidirect

Maximal subgroups

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

subgroupindex
#130782652
#130782592
#130708102
#130708092
#130708072
#130707202
#130707182
#130707032
#130707012
#130705302
#130705292
#130705272
#130702282
C11×#22342
#3376511