Finite Group Databasebeta

← #14909614

Subgroups — #14909614

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#13078260C211yesmaximal, characteristic, complemented
2#13078259C211yesmaximal, characteristic, complemented
3#13070808C211yesmaximal, characteristic, complemented
4#13070806C211yesmaximal, characteristic, complemented
5#13070805C211yesmaximal, characteristic, complemented
6#13070804C211yesmaximal, characteristic, complemented
7#13070718C211yesmaximal, characteristic, complemented
8#13070716C211yesmaximal, characteristic, complemented
9#13070701C211yesmaximal, characteristic, complemented
10#13070699C211yesmaximal, characteristic, complemented
11#13070528C211yesmaximal, characteristic, complemented
12#13070526C211yesmaximal, characteristic, complemented
13#13070526C211yesmaximal, characteristic, complemented
14#13070228C211yesmaximal, characteristic, complemented
15C11×#2184C211yesmaximal, characteristic, complemented
16C22×C11×D8C2211yescharacteristic, complemented
17#10623336—21no—
18C2×D8×D11C2211yescharacteristic, complemented
19C2×#66954C2211yescharacteristic
20#10623138—21no—
21C2×C11×D16C2211yescharacteristic
22C2×C11×D16C2211yescharacteristic
23C11×#466C2211yescharacteristic
24#10622828—21no—
25#10622772—21no—
26#10622772—21no—
27#10622770C2211yescharacteristic
28#10622770C2211yescharacteristic
29#10622770C2211yescharacteristic, complemented
30#10622770C2211yescharacteristic, complemented
31#10622770C2211yescharacteristic, complemented
32C2×#66890C2211yescharacteristic
33C2×#66890C2211yescharacteristic
34#10622728C2211yescharacteristic
35#10622719C2211yescharacteristic, complemented
36#10622652—21no—
37C2×#66862C2211yescharacteristic, complemented
38C2×C16×D11C2211yescharacteristic, complemented
39#10622496C2211yescharacteristic, complemented
40#10622493C2211yescharacteristic, complemented
41#10622395—21no—
42#10622383—21no—
43C11×#357C2211yescharacteristic, complemented
44C11×#357C2211yescharacteristic, complemented
45C11×C22⋊C16C2211yescharacteristic, complemented
46#10622200C2211yescharacteristic, complemented
47#10622200C2211yescharacteristic, complemented
48#10622200C2211yescharacteristic, complemented
49#10622200C2211yescharacteristic, complemented
50C22⋊(C11⋊C16)C2211yescharacteristic, complemented
51#10622147C2211yescharacteristic, complemented
52#10622147C2211yescharacteristic, complemented
53(C2×D11)⋊C16C2211yescharacteristic, complemented
54(C2×D11)⋊C16C2211yescharacteristic, complemented
55#10622143C2211yescharacteristic, complemented
56#10622142C2211yescharacteristic, complemented
57#10622128C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C22×D4×C11—21no—
60C2×D4×D11—21no—
61C2×#4339D411yescharacteristic
62C2×C11×D8—21no—
63C2×C11×D8—41no—
64C2×C11×D8—41no—
65C2×C11×D8C2311yescharacteristic
66C2×C11×D8C2311yescharacteristic
67C2×C11×D8C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×#121—21no—
70#67006—41no—
71#67006—41no—
72#66993—41no—
73#66993—41no—
74#66991—21no—
75#66991—21no—
76#66991—21no—
77#66991—21no—
78#66991—21no—
79#66990—41no—
80#66989—41no—
81C2×#4323—21no—
82#66983—21no—
83#66979—21no—
84C2×#4318D411yescharacteristic
85D8×D11—41no—
86D8×D11—41no—
87C2×D88C2311yescharacteristic
88#66954—41no—
89#66954—41no—
90C2×#4313D411yescharacteristic
91C2×#4313D411yescharacteristic
92C2×C8×D11C2311yescharacteristic
93C2×C8×D11C2311yescharacteristic
94#66948—21no—
95#66945—21no—
96#66938—41no—
97#66935—41no—
98C11×D16—41no—
99C11×D16—41no—
100C2×C11×C16C2311yescharacteristic
101C2×C11×C16C2311yescharacteristic
102C11×#107C2311yescharacteristic
103C11×#102—21no—
104#66896—21no—
105#66896—21no—
106#66896—21no—
107#66896—21no—
108#66896—21no—
109#66890—41no—
110#66890—41no—
111#66885—21no—
112#66882C2311yescharacteristic
113#66882C2311yescharacteristic
114#66882C2311yescharacteristic
115#66881—21no—
116C2×C11⋊C16C2311yescharacteristic
117C2×C11⋊C16C2311yescharacteristic
118#66873—21no—
119#66872—21no—
120#66862—41no—
121C16×D11—41no—
122#33765—111nomaximal, Sylow
123C24×C11—41no—
124C23×D11—41no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C2×D4×C11—41no—
131C2×D4×C11—41no—
132C22×C4×C11C2×D411yescharacteristic
133C2×C22⋊D11—41no—
134C2×C22⋊D11—41no—
135C2×C22⋊D11—41no—
136C2×C22⋊D11—41no—
137C2×C22⋊D11—41no—
138C2×C22⋊D11—41no—
139C2×C22⋊D11—41no—
140C2×C22⋊D11D811yescharacteristic
141C2×C22⋊D11D811yescharacteristic
142D4×D11—42no—
143D4×D11—42no—
144#4339—41no—
145#4339—41no—
146C2×D44—21no—
147C2×D44—41no—
148C2×D44D811yescharacteristic
149C2×C4×D11C2×D411yescharacteristic
150C2×C4×D11C2×D411yescharacteristic
151C2×Dic22D811yescharacteristic
152C11×D8—21no—
153C11×D8—21no—
154C11×D8—21no—
155C11×D8—21no—
156C11×D8—21no—
157C11×D8—21no—
158C11×D8—42no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11C2×D411yescharacteristic
162C2×C8×C11C2411yescharacteristic
163C11×C4⋊C4—21no—
164C11×C22⋊C4—41no—
165C22⋊Dic11—41no—
166C22⋊Dic11—41no—
167C22⋊Dic11—41no—
168C22⋊Dic11—41no—
169C22⋊Dic11—41no—
170C22⋊Dic11—41no—
171#4323—42no—
172(C2×D11)⋊C4—41no—
173(C2×D11)⋊C4—41no—
174(C2×D11)⋊C4—41no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4×Dic11—41no—
179C4×Dic11—41no—
180#4318—41no—
181C2×C11⋊C8C2×D411yescharacteristic
182C2×C11⋊C8C2×D411yescharacteristic
183D88—21no—
184D88—21no—
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#2234—111no—
201#2218—111no—
202#2218—111no—
203#2215—111no—
204#2215—111no—
205#2184—111no—
206#2184—111no—
207#2184—111no—
208#2184D1111yescharacteristic, complemented
209#2113—111no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—82no—
214C23×C11—161no—
215C23×C11—161no—
216C23×C11C2×D811yescharacteristic
217C22×D11—41no—
218C22×D11—82no—
219C22×D11—161no—
220C22×D11—161no—
221C22×D11C2×D811yescharacteristic
222C22×D11C2×D811yescharacteristic
223D4×C11—41no—
224D4×C11—41no—
225D4×C11—41no—
226D4×C11—41no—
227D4×C11—41no—
228D4×C11—41no—
229D4×C11—82no—
230D4×C11—161no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—41no—
234C2×C4×C11C2×D811yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C22⋊D11—41no—
237C22⋊D11—41no—
238C22⋊D11—82no—
239C22⋊D11—161no—
240C22⋊D11—161no—
241C22⋊D11—161no—
242C22⋊D11—161no—
243C22⋊D11—161no—
244C22⋊D11—161no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11C2×D811yescharacteristic
249C2×Dic11C2×D811yescharacteristic
250D44—41no—
251D44—41no—
252D44—41no—
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×D8C2×D1111yescharacteristic, complemented
266C2×#131—111no—
267#535—221no—
268#535—221no—
269C2×D16—111no—
270C2×D16—111no—
271C2×D16C2×D1111yescharacteristic
272C2×D16C2×D1111yescharacteristic
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#427—111no—
289#418—221no—
290#418—221no—
291#367—111no—
292#367—111no—
293#366—111no—
294#366—111no—
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×C11—81no—
314C22×C11—81no—
315C22×C11—81no—
316C22×C11—81no—
317C22×C11—81no—
318C22×C11—81no—
319C22×C11—164no—
320C22×C11C22×D811yescharacteristic
321C2×D11—21no—
322C2×D11—21no—
323C2×D11—21no—
324C2×D11—21no—
325C2×D11—21no—
326C2×D11—21no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—81no—
330C2×D11—164no—
331C4×C11—21no—
332C4×C11—81no—
333C4×C11#53411yescharacteristic
334C4×C11#57511yescharacteristic
335Dic11—21no—
336Dic11—21no—
337Dic11—81no—
338Dic11—81no—
339Dic11—81no—
340C2×#41—111no—
341C22×D4—21no—
342C22×D4—221no—
343C2×D8—21no—
344C2×D8—41no—
345C2×D8—41no—
346C2×D8—111no—
347C2×D8—221no—
348C2×D8—441no—
349C2×D8—441no—
350C2×D8C22×D1111yescharacteristic
351C2×D8C22×D1111yescharacteristic
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—221no—
378#117—221no—
379D16—41no—
380D16—41no—
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#107—111no—
391#107—111no—
392#107C22×D1111yescharacteristic
393#106—221no—
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—161no—
406C2×C11—161no—
407C2×C11#318611yescharacteristic
408C2×C11#341511yescharacteristic
409C2×C11#341511yescharacteristic
410D11—41no—
411D11—41no—
412D11—161no—
413C24—41no—
414C24—441no—
415#41—441no—
416#41—441no—
417C2×Q8—111no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—111no—
426C2×D4—111no—
427C2×D4—111no—
428C2×D4—221no—
429C2×D4—441no—
430C2×D4—441no—
431C2×D4—442no—
432C2×D4—442no—
433C2×D4—441no—
434C2×D4—441no—
435C2×D4—441no—
436C2×D4—441no—
437C2×D4—441no—
438C2×D4—441no—
439C22×C4—111no—
440C22×C4—111no—
441C22×C4D4×D1111yescharacteristic
442D8—21no—
443D8—21no—
444D8—21no—
445D8—21no—
446D8—21no—
447D8—21no—
448D8—42no—
449D8—221no—
450D8—221no—
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—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C22⋊C4—41no—
470C22⋊C4—441no—
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—441no—
480C42—441no—
481C16—21no—
482C16—21no—
483C16—221no—
484C16—221no—
485C11#3376511yescharacteristic, complemented, Sylow
486C23—41no—
487C23—41no—
488C23—41no—
489C23—82no—
490C23—111no—
491C23—111no—
492C23—161no—
493C23—161no—
494C23—441no—
495C23—882no—
496C23—1761no—
497C23—1761no—
498C23D8×D1111yescharacteristic
499Q8—441no—
500D4—41no—
501D4—41no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—82no—
507D4—161no—
508D4—441no—
509D4—441no—
510D4—441no—
511D4—441no—
512D4—441no—
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—111no—
525C2×C4—111no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4D8×D1111yescharacteristic
534C2×C4C2×D4×D1111yescharacteristic
535C8—21no—
536C8—221no—
537C8—221no—
538C8#6703711yescharacteristic
539C8#6703711yescharacteristic
540C22—21no—
541C22—21no—
542C22—21no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—164no—
553C22—221no—
554C22—221no—
555C22—221no—
556C22—221no—
557C22—221no—
558C22—221no—
559C22—881no—
560C22—881no—
561C22—881no—
562C22—1764no—
563C22C2×D8×D1111yescharacteristic
564C4—21no—
565C4—81no—
566C4—221no—
567C4—221no—
568C4—881no—
569C4—881no—
570C4—881no—
571C4#1062312011yescharacteristic
572C4#1062330411yescharacteristic
573C2—41no—
574C2—161no—
575C2—161no—
576C2—161no—
577C2—441no—
578C2—441no—
579C2—1761no—
580C2#1307936511yescharacteristic
581C2#1308175311yescharacteristic
582C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2184C2
socleC22×C11C22×D8
hypercenter#2184D11
hypocenterC11#33765
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2184

Complements

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

NH ≅ G/Ntype
1. #13078260C2semidirect
2. #13078259C2semidirect
3. #13070808C2semidirect
4. #13070806C2semidirect
5. #13070805C2semidirect
6. #13070804C2semidirect
7. #13070718C2semidirect
8. #13070716C2semidirect
9. #13070701C2semidirect
10. #13070699C2semidirect
11. #13070528C2semidirect
12. #13070526C2semidirect
13. #13070526C2semidirect
14. #13070228C2semidirect
15. C11×#2184C2semidirect
16. C22×C11×D8C22semidirect
18. C2×D8×D11C22semidirect
29. #10622770C22semidirect
30. #10622770C22semidirect
31. #10622770C22semidirect
35. #10622719C22semidirect
37. C2×#66862C22semidirect
38. C2×C16×D11C22semidirect
39. #10622496C22semidirect
40. #10622493C22semidirect
43. C11×#357C22semidirect
44. C11×#357C22semidirect
45. C11×C22⋊C16C22semidirect
46. #10622200C22semidirect
47. #10622200C22semidirect
48. #10622200C22semidirect
49. #10622200C22semidirect
50. C22⋊(C11⋊C16)C22semidirect
51. #10622147C22semidirect
52. #10622147C22semidirect
53. (C2×D11)⋊C16C22semidirect
54. (C2×D11)⋊C16C22semidirect
55. #10622143C22semidirect
56. #10622142C22semidirect
57. #10622128C22semidirect
58. #10622127C22semidirect
208. #2184D11semidirect
265. C22×D8C2×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
#130782602
#130782592
#130708082
#130708062
#130708052
#130708042
#130707182
#130707162
#130707012
#130706992
#130705282
#130705262
#130702282
C11×#21842
#3376511