Finite Group Databasebeta

← #14910819

Subgroups — #14910819

Order 2816.

562 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081047C211yesmaximal, characteristic, complemented
2#13070852C211yesmaximal, characteristic, complemented
3#13070821C211yesmaximal, characteristic, complemented
4#13070804C211yesmaximal, characteristic, complemented
5#13070763C211yesmaximal, characteristic, complemented
6#13070722C211yesmaximal, characteristic, complemented
7#13070710C211yesmaximal, characteristic, complemented
8#13070675C211yesmaximal, characteristic, complemented
9#13070556C211yesmaximal, characteristic, complemented
10#13070545C211yesmaximal, characteristic, complemented
11#13070480C211yesmaximal, characteristic, complemented
12#13070442C211yesmaximal, characteristic, complemented
13#13070332C211yesmaximal, characteristic, complemented
14#13070323C211yesmaximal, characteristic, complemented
15C11×#3280C211yesmaximal, characteristic
16C2×C11×#135C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C11×#546—21no—
19#10623073—21no—
20C11×#495C2211yescharacteristic
21C11×#467C2211yescharacteristic
22C11×#466C2211yescharacteristic
23C11×#463—21no—
24C11×#450—21no—
25C11×#449—21no—
26C4×C11×D8C2211yescharacteristic
27C8×D4×C11C2211yescharacteristic
28C2×#66893C2211yescharacteristic, complemented
29C2×#66891C2211yescharacteristic
30C2×#66891C2211yescharacteristic
31#10622729C2211yescharacteristic
32#10622729C2211yescharacteristic, complemented
33#10622719C2211yescharacteristic
34#10622719C2211yescharacteristic, complemented
35C2×#66876C2211yescharacteristic
36C22×C11⋊C16C2211yescharacteristic, complemented
37#10622464—21no—
38#10622336—21no—
39#10622336—21no—
40C4×Dic44C2211yescharacteristic, complemented
41#10622295C2211yescharacteristic, complemented
42#10622202C2211yescharacteristic, complemented
43#10622202C2211yescharacteristic, complemented
44#10622202C2211yescharacteristic, complemented
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622200C2211yescharacteristic
49#10622200C2211yescharacteristic
50#10622200C2211yescharacteristic
51C22⋊(C11⋊C16)C2211yescharacteristic
52C22⋊(C11⋊C16)C2211yescharacteristic, complemented
53#10622130C2211yescharacteristic, complemented
54#10622128C2211yescharacteristic, complemented
55#10622128C2211yescharacteristic, complemented
56#10622127C2211yescharacteristic, complemented
57C4⋊(C11⋊C16)C2211yescharacteristic, complemented
58#10622099C2211yescharacteristic, complemented
59C2×C11×#41—21no—
60C22×D4×C11—21no—
61C11×#135—22no—
62C11×#135—41no—
63C2×C11×Q16C2311yescharacteristic
64C2×C11×SD16—21no—
65C2×C11×SD16—21no—
66C2×C11×D8—22no—
67C2×C11×D8—21no—
68C2×C11×D8—41no—
69C2×C11×D8C2311yescharacteristic
70C2×C11×D8C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×#124—21no—
74C11×#123—41no—
75C11×C22⋊Q8—21no—
76C11×#121—21no—
77C11×#121—41no—
78C11×#120—41no—
79C4×D4×C11—21no—
80C4×D4×C11D411yescharacteristic
81C2×C11×C22⋊C4—41no—
82#66989—41no—
83#66979—21no—
84#66979—21no—
85#66977—21no—
86#66977—21no—
87C2×Dic44C2311yescharacteristic
88#66940—41no—
89#66932—41no—
90#66932—41no—
91#66922—21no—
92C4×Dic22—21no—
93C11×#107C2311yescharacteristic
94C11×C4⋊C8D411yescharacteristic
95C11×#103—21no—
96C11×#102—21no—
97C11×#102—21no—
98C11×C22⋊C8D411yescharacteristic
99C11×C22⋊C8D411yescharacteristic
100C4×C8×C11C2311yescharacteristic
101#66893—41no—
102#66891—22no—
103#66891—41no—
104#66882—21no—
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66881—21no—
109#66881—21no—
110#66880—21no—
111#66880—21no—
112#66880—21no—
113#66876—41no—
114C2×C11⋊C16—41no—
115C2×C11⋊C16C2311yescharacteristic
116C2×C11⋊C16C2311yescharacteristic
117C2×C11⋊C16C2311yescharacteristic
118C2×C11⋊C16C2311yescharacteristic
119#33878—111nomaximal, Sylow
120C24×C11—41no—
121C11×#41—42no—
122C11×#41—81no—
123C2×Q8×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—42no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11—81no—
131C2×D4×C11D811yescharacteristic
132C22×C4×C11—41no—
133C22×C4×C11—41no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C2×Dic22—21no—
137C2×Dic22—41no—
138C11×Q16—21no—
139C11×Q16—21no—
140C11×SD16—42no—
141C11×SD16—81no—
142C11×D8—21no—
143C11×D8—21no—
144C11×D8—21no—
145C11×D8—42no—
146C11×D8#4112yes—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11C2×D411yescharacteristic
152C2×C8×C11C2×D411yescharacteristic
153C2×C8×C11C2×D411yescharacteristic
154C2×C8×C11C2411yescharacteristic
155C11×C4⋊C4—21no—
156C11×C4⋊C4—41no—
157C11×C4⋊C4D811yescharacteristic
158C11×C22⋊C4—41no—
159C11×C22⋊C4—41no—
160C11×C22⋊C4—41no—
161C11×C22⋊C4—41no—
162C11×C22⋊C4—41no—
163C11×C22⋊C4D811yescharacteristic
164C11×C22⋊C4D811yescharacteristic
165C42×C11C2×D411yescharacteristic
166C22⋊Dic11—41no—
167C22⋊Dic11—41no—
168C22⋊Dic11—41no—
169C22⋊Dic11—41no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—41no—
174Dic11⋊C4—41no—
175Dic11⋊C4—41no—
176Dic11⋊C4—41no—
177C4×Dic11—41no—
178C4×Dic11—41no—
179C4×Dic11—41no—
180Dic44—21no—
181Dic44—21no—
182C11⋊C16—21no—
183C11⋊C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3342—111no—
187#3280D1111yescharacteristic
188#2243—111no—
189#2237—111no—
190#2234—111no—
191#2226—111no—
192#2219—111no—
193#2217—111no—
194#2211—111no—
195#2189—111no—
196#2187—111no—
197#2175—111no—
198#2168—111no—
199#2140—111no—
200#2138—111no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—82no—
204C23×C11—82no—
205C23×C11—161no—
206C23×C11C2×D811yescharacteristic
207C23×C11C2×D811yescharacteristic
208Q8×C11—41no—
209Q8×C11—41no—
210D4×C11—22no—
211D4×C11—41no—
212D4×C11—41no—
213D4×C11—41no—
214D4×C11—41no—
215D4×C11—82no—
216D4×C11—82no—
217D4×C11—161no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—82no—
225C2×C4×C11—161no—
226C2×C4×C11C2×D811yescharacteristic
227C2×C4×C11C2×D811yescharacteristic
228C2×C4×C11C2×D811yescharacteristic
229C2×C4×C11C2×D811yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235Dic22—41no—
236Dic22—41no—
237Dic22—82no—
238C8×C11—21no—
239C8×C11—21no—
240C8×C11—21no—
241C8×C11C2×#4111yescharacteristic
242C8×C11H(5,𝔽2)11yescharacteristic
243C2×#135C2×D1111yescharacteristic
244C22×D8C2×D1111yescharacteristic
245#556—221no—
246#546—21no—
247C2×Q32—111no—
248C2×SD32—111no—
249C2×SD32—111no—
250C2×M32—111no—
251C22×C16—111no—
252#500—111no—
253#495C2×D1111yescharacteristic
254#485—221no—
255#485—221no—
256#475—221no—
257#467—111no—
258#467—111no—
259#467C2×D1111yescharacteristic
260#466C2×D1111yescharacteristic
261#463—21no—
262#450—21no—
263#449—21no—
264C4×Q16—111no—
265C4×D8C2×D1111yescharacteristic
266C8×D4C2×D1111yescharacteristic
267#427—111no—
268#427—111no—
269#367—111no—
270#367—111no—
271#366—111no—
272C4⋊C16—111no—
273#358—111no—
274#358—111no—
275#358—111no—
276#358—111no—
277#357—111no—
278#357—111no—
279#357—111no—
280#357—111no—
281#357—111no—
282#357—111no—
283C22⋊C16—111no—
284C22⋊C16—111no—
285#346—111no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—42no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11—164no—
299C22×C11C22×D811yescharacteristic
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—21no—
304C4×C11—81no—
305C4×C11—81no—
306C4×C11#54611yescharacteristic
307C4×C11#57711yescharacteristic
308Dic11—81no—
309Dic11—81no—
310Dic11—81no—
311Dic11—81no—
312C2×#41—21no—
313C22×D4—21no—
314#135—22no—
315#135—41no—
316C2×Q16—111no—
317C2×Q16C22×D1111yescharacteristic
318C2×SD16—21no—
319C2×SD16—21no—
320C2×D8—22no—
321C2×D8—21no—
322C2×D8—41no—
323C2×D8C22×D1111yescharacteristic
324C2×D8C22×D1111yescharacteristic
325C22×C8C22×D1111yescharacteristic
326C22×C8C22×D1111yescharacteristic
327C4⋊Q8—221no—
328#126—441no—
329#126—441no—
330#124—21no—
331#124—441no—
332#123—41no—
333C22⋊Q8—21no—
334C22⋊Q8—221no—
335C22⋊Q8—221no—
336#121—21no—
337#121—41no—
338#120—41no—
339C4×Q8—221no—
340C4×Q8—441no—
341C4×D4—21no—
342C4×D4C22⋊D1111yescharacteristic
343#117—221no—
344#117—221no—
345C2×C22⋊C4—41no—
346Q32—441no—
347SD32—222no—
348SD32—441no—
349M32—441no—
350C2×C16—111no—
351C2×C16—111no—
352C2×C16—111no—
353C2×C16—111no—
354C2×C16—441no—
355#107—111no—
356#107—111no—
357#107—111no—
358#107—221no—
359#107C22×D1111yescharacteristic
360#106—221no—
361#106—221no—
362C4⋊C8C22⋊D1111yescharacteristic
363#103—21no—
364#103—221no—
365#103—221no—
366#103—221no—
367#102—21no—
368#102—21no—
369C22⋊C8C22⋊D1111yescharacteristic
370C22⋊C8C22⋊D1111yescharacteristic
371C4×C8C22×D1111yescharacteristic
372C2×C11—41no—
373C2×C11—41no—
374C2×C11—82no—
375C2×C11—161no—
376C2×C11#329411yescharacteristic
377C2×C11#341411yescharacteristic
378C2×C11#341611yescharacteristic
379C24—41no—
380#41—42no—
381#41—81no—
382C2×Q8—21no—
383C2×Q8—221no—
384C2×Q8—441no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—42no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—81no—
392C2×D4#432311yescharacteristic
393C22×C4—41no—
394C22×C4—41no—
395C22×C4C2×C22⋊D1111yescharacteristic
396C22×C4C2×C22⋊D1111yescharacteristic
397Q16—21no—
398Q16—21no—
399Q16—221no—
400Q16—221no—
401SD16—42no—
402SD16—81no—
403D8—21no—
404D8—21no—
405D8—21no—
406D8—42no—
407D8#434112yes—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—21no—
412C2×C8C2×C22⋊D1111yescharacteristic
413C2×C8C2×C22⋊D1111yescharacteristic
414C2×C8C2×C22⋊D1111yescharacteristic
415C2×C8C23×D1111yescharacteristic
416C4⋊C4—21no—
417C4⋊C4—41no—
418C4⋊C4—221no—
419C4⋊C4—221no—
420C4⋊C4—221no—
421C4⋊C4—441no—
422C4⋊C4—441no—
423C4⋊C4—441no—
424C4⋊C4—441no—
425C4⋊C4#432311yescharacteristic
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—441no—
432C22⋊C4—441no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C22⋊C4#432311yescharacteristic
436C22⋊C4#432311yescharacteristic
437C42—441no—
438C42—441no—
439C42—441no—
440C42C2×C22⋊D1111yescharacteristic
441C16—221no—
442C16—221no—
443C16—221no—
444C16—221no—
445C11#3387811yescharacteristic, complemented, Sylow
446C23—41no—
447C23—41no—
448C23—82no—
449C23—82no—
450C23—161no—
451C23C2×#432311yescharacteristic
452C23C2×#432311yescharacteristic
453Q8—41no—
454Q8—41no—
455Q8—441no—
456Q8—441no—
457Q8—882no—
458D4—22no—
459D4—41no—
460D4—41no—
461D4—41no—
462D4—41no—
463D4—82no—
464D4—82no—
465D4—161no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—82no—
473C2×C4—161no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4C2×#432311yescharacteristic
479C2×C4C2×#432311yescharacteristic
480C2×C4C2×#432311yescharacteristic
481C2×C4C2×#432311yescharacteristic
482C2×C4C22×C22⋊D1111yescharacteristic
483C8—21no—
484C8—21no—
485C8—21no—
486C8C2×#434111yescharacteristic
487C8#6703711yescharacteristic
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—42no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—81no—
499C22—81no—
500C22—164no—
501C22C22×#432311yescharacteristic
502C4—21no—
503C4—21no—
504C4—21no—
505C4—21no—
506C4—81no—
507C4—81no—
508C4—881no—
509C4—881no—
510C4—881no—
511C4—881no—
512C4#1062333711yescharacteristic
513C4#1062336711yescharacteristic
514C2—41no—
515C2—41no—
516C2—82no—
517C2—161no—
518C2#1308042911yescharacteristic
519C2#1308175011yescharacteristic
520C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC11×#3280C2
socleC22×C11C22×D8
hypercenter#3280D11
hypocenterC11#33878
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3280

Complements

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

NH ≅ G/Ntype
1. #13081047C2semidirect
2. #13070852C2semidirect
3. #13070821C2semidirect
4. #13070804C2semidirect
5. #13070763C2semidirect
6. #13070722C2semidirect
7. #13070710C2semidirect
8. #13070675C2semidirect
9. #13070556C2semidirect
10. #13070545C2semidirect
11. #13070480C2semidirect
12. #13070442C2semidirect
13. #13070332C2semidirect
14. #13070323C2semidirect
28. C2×#66893C22semidirect
32. #10622729C22semidirect
34. #10622719C22semidirect
36. C22×C11⋊C16C22semidirect
40. C4×Dic44C22semidirect
41. #10622295C22semidirect
42. #10622202C22semidirect
43. #10622202C22semidirect
44. #10622202C22semidirect
52. C22⋊(C11⋊C16)C22semidirect
53. #10622130C22semidirect
54. #10622128C22semidirect
55. #10622128C22semidirect
56. #10622127C22semidirect
57. C4⋊(C11⋊C16)C22semidirect
58. #10622099C22semidirect
445. C11#33878semidirect

Maximal subgroups

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

subgroupindex
#130810472
#130708522
#130708212
#130708042
#130707632
#130707222
#130707102
#130706752
#130705562
#130705452
#130704802
#130704422
#130703322
#130703232
C11×#32802
#3387811