Finite Group Databasebeta

← #14910864

Subgroups — #14910864

Order 2816.

570 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081009C211yesmaximal, characteristic, complemented
2#13070852C211yesmaximal, characteristic, complemented
3#13070816C211yesmaximal, characteristic, complemented
4#13070794C211yesmaximal, characteristic, complemented
5#13070753C211yesmaximal, characteristic, complemented
6#13070727C211yesmaximal, characteristic, complemented
7#13070705C211yesmaximal, characteristic, complemented
8#13070675C211yesmaximal, characteristic, complemented
9#13070556C211yesmaximal, characteristic, complemented
10#13070545C211yesmaximal, characteristic, complemented
11#13070480C211yesmaximal, characteristic, complemented
12#13070442C211yesmaximal, characteristic, complemented
13#13070328C211yesmaximal, characteristic, complemented
14C2×#10622200C211yesmaximal, characteristic, complemented
15C11×#3280C211yesmaximal, characteristic
16C2×C11×#135C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C11×#546—21no—
19#10623074—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
33C2×#66882C2211yescharacteristic
34C2×#66882C2211yescharacteristic, complemented
35C2×#66876C2211yescharacteristic, complemented
36C22×C11⋊C16C2211yescharacteristic
37#10622463—21no—
38#10622335—21no—
39#10622335—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#10622127C2211yescharacteristic, complemented
55#10622127C2211yescharacteristic, 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—
82D4×Dic11—41no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85#66977—21no—
86#66977—21no—
87C2×Dic44C2311yescharacteristic
88#66943—41no—
89#66931—41no—
90#66931—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#66882—21no—
106#66882—21no—
107#66882C2311yescharacteristic
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
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#33881—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
136C22×Dic11—41no—
137C22×Dic11—41no—
138C2×Dic22—21no—
139C2×Dic22—41no—
140C11×Q16—21no—
141C11×Q16—21no—
142C11×SD16—42no—
143C11×SD16—81no—
144C11×D8—21no—
145C11×D8—21no—
146C11×D8—21no—
147C11×D8—42no—
148C11×D8#4112yes—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11C2×D411yescharacteristic
154C2×C8×C11C2×D411yescharacteristic
155C2×C8×C11C2×D411yescharacteristic
156C2×C8×C11C2411yescharacteristic
157C11×C4⋊C4—21no—
158C11×C4⋊C4—41no—
159C11×C4⋊C4D811yescharacteristic
160C11×C22⋊C4—41no—
161C11×C22⋊C4—41no—
162C11×C22⋊C4—41no—
163C11×C22⋊C4—41no—
164C11×C22⋊C4—41no—
165C11×C22⋊C4D811yescharacteristic
166C11×C22⋊C4D811yescharacteristic
167C42×C11C2×D411yescharacteristic
168C22⋊Dic11—41no—
169C22⋊Dic11—41no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—41no—
174C4⋊Dic11—41no—
175C4⋊Dic11—41no—
176Dic11⋊C4—41no—
177Dic11⋊C4—41no—
178Dic11⋊C4—41no—
179C4×Dic11—41no—
180Dic44—21no—
181Dic44—21no—
182C11⋊C16—21no—
183C11⋊C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3338—111no—
187#3280D1111yescharacteristic
188#2243—111no—
189#2236—111no—
190#2232—111no—
191#2224—111no—
192#2220—111no—
193#2216—111no—
194#2211—111no—
195#2189—111no—
196#2187—111no—
197#2175—111no—
198#2168—111no—
199#2139—111no—
200C2×#357—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—22no—
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—
235C2×Dic11—161no—
236C2×Dic11—161no—
237Dic22—41no—
238Dic22—41no—
239Dic22—161no—
240C8×C11—21no—
241C8×C11—21no—
242C8×C11—21no—
243C8×C11C2×#4111yescharacteristic
244C8×C11H(5,𝔽2)11yescharacteristic
245C2×#135C2×D1111yescharacteristic
246C22×D8C2×D1111yescharacteristic
247#554—221no—
248#546—21no—
249C2×Q32—111no—
250C2×SD32—111no—
251C2×SD32—111no—
252C2×M32—111no—
253C22×C16—111no—
254#500—111no—
255#495C2×D1111yescharacteristic
256#484—221no—
257#484—221no—
258#477—221no—
259#467—111no—
260#467—111no—
261#467C2×D1111yescharacteristic
262#466C2×D1111yescharacteristic
263#463—21no—
264#450—21no—
265#449—21no—
266C4×Q16—111no—
267C4×D8C2×D1111yescharacteristic
268C8×D4C2×D1111yescharacteristic
269C2×#107—111no—
270C2×#107—111no—
271#366—111no—
272#366—111no—
273#366—111no—
274C4⋊C16—111no—
275#358—111no—
276#358—111no—
277#358—111no—
278#358—111no—
279#357—111no—
280#357—111no—
281#357—111no—
282#357—111no—
283#357—111no—
284#357—111no—
285C22⋊C16—111no—
286C22⋊C16—111no—
287#346—111no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—21no—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11—42no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—164no—
300C22×C11#51012yes—
301C22×C11C22×D811yescharacteristic
302C4×C11—21no—
303C4×C11—21no—
304C4×C11—21no—
305C4×C11—21no—
306C4×C11—81no—
307C4×C11—81no—
308C4×C11#54611yescharacteristic
309C4×C11#57711yescharacteristic
310Dic11—81no—
311Dic11—81no—
312Dic11—81no—
313Dic11—81no—
314C2×#41—21no—
315C22×D4—21no—
316#135—22no—
317#135—41no—
318C2×Q16—111no—
319C2×Q16C22×D1111yescharacteristic
320C2×SD16—21no—
321C2×SD16—21no—
322C2×D8—22no—
323C2×D8—21no—
324C2×D8—41no—
325C2×D8C22×D1111yescharacteristic
326C2×D8C22×D1111yescharacteristic
327C22×C8C22×D1111yescharacteristic
328C22×C8C22×D1111yescharacteristic
329C4⋊Q8—221no—
330#125—441no—
331#124—21no—
332#123—41no—
333C22⋊Q8—21no—
334C22⋊Q8—221no—
335C22⋊Q8—221no—
336C22⋊Q8—441no—
337C22⋊Q8—441no—
338#121—21no—
339#121—41no—
340#120—41no—
341C4×Q8—221no—
342C4×D4—21no—
343C4×D4—441no—
344C4×D4C22⋊D1111yescharacteristic
345C2×C4⋊C4—221no—
346C2×C4⋊C4—221no—
347C2×C22⋊C4—41no—
348Q32—441no—
349SD32—222no—
350SD32—441no—
351M32—441no—
352C2×C16—111no—
353C2×C16—111no—
354C2×C16—111no—
355C2×C16—111no—
356C2×C16—441no—
357#107—111no—
358#107—111no—
359#107—111no—
360#107—221no—
361#107—221no—
362#107—221no—
363#107C22×D1111yescharacteristic
364C4⋊C8C22⋊D1111yescharacteristic
365#103—21no—
366#103—221no—
367#103—221no—
368#103—221no—
369#102—21no—
370#102—21no—
371C22⋊C8C22⋊D1111yescharacteristic
372C22⋊C8C22⋊D1111yescharacteristic
373C4×C8C22×D1111yescharacteristic
374C2×C11—22no—
375C2×C11—41no—
376C2×C11—82no—
377C2×C11—161no—
378C2×C11#329411yescharacteristic
379C2×C11C2×#51011yescharacteristic
380C2×C11#341511yescharacteristic
381C24—41no—
382#41—42no—
383#41—81no—
384C2×Q8—21no—
385C2×Q8—221no—
386C2×Q8—441no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—42no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—81no—
394C2×D4#432311yescharacteristic
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—441no—
398C22×C4—441no—
399C22×C4C2×C22⋊D1111yescharacteristic
400C22×C4C2×C22⋊D1111yescharacteristic
401Q16—21no—
402Q16—21no—
403Q16—221no—
404Q16—221no—
405SD16—42no—
406SD16—81no—
407D8—21no—
408D8—21no—
409D8—21no—
410D8—42no—
411D8#434112yes—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8—21no—
415C2×C8—21no—
416C2×C8C2×C22⋊D1111yescharacteristic
417C2×C8C2×C22⋊D1111yescharacteristic
418C2×C8C2×C22⋊D1111yescharacteristic
419C2×C8C23×D1111yescharacteristic
420C4⋊C4—21no—
421C4⋊C4—41no—
422C4⋊C4—221no—
423C4⋊C4—221no—
424C4⋊C4—221no—
425C4⋊C4—441no—
426C4⋊C4—441no—
427C4⋊C4—441no—
428C4⋊C4—441no—
429C4⋊C4—441no—
430C4⋊C4—441no—
431C4⋊C4#432311yescharacteristic
432C22⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—441no—
438C22⋊C4—441no—
439C22⋊C4#432311yescharacteristic
440C22⋊C4#432311yescharacteristic
441C42—441no—
442C42C2×C22⋊D1111yescharacteristic
443C16—221no—
444C16—221no—
445C16—221no—
446C16—221no—
447C11#3388111yescharacteristic, complemented, Sylow
448C23—41no—
449C23—41no—
450C23—82no—
451C23—82no—
452C23—161no—
453C23C2×#432311yescharacteristic
454C23C2×#432311yescharacteristic
455Q8—41no—
456Q8—41no—
457Q8—441no—
458Q8—441no—
459Q8—1761no—
460D4—22no—
461D4—22no—
462D4—41no—
463D4—41no—
464D4—41no—
465D4—82no—
466D4—82no—
467D4—161no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—82no—
475C2×C4—161no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—1761no—
481C2×C4—1761no—
482C2×C4C2×#432311yescharacteristic
483C2×C4C2×#432311yescharacteristic
484C2×C4C2×#432311yescharacteristic
485C2×C4C2×#432311yescharacteristic
486C2×C4C22×C22⋊D1111yescharacteristic
487C8—21no—
488C8—21no—
489C8—21no—
490C8C2×#434111yescharacteristic
491C8#6703711yescharacteristic
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—42no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—164no—
504C22#1062280812yes—
505C22C22×#432311yescharacteristic
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—81no—
511C4—81no—
512C4—881no—
513C4—881no—
514C4—881no—
515C4—881no—
516C4#1062333711yescharacteristic
517C4#1062336711yescharacteristic
518C2—22no—
519C2—41no—
520C2—82no—
521C2—161no—
522C2#1308042911yescharacteristic
523C2C2×#1062280811yescharacteristic
524C2#1308175511yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC11×#3280C2
socleC22×C11C22×D8
hypercenter#3280D11
hypocenterC11#33881
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. #13081009C2semidirect
2. #13070852C2semidirect
3. #13070816C2semidirect
4. #13070794C2semidirect
5. #13070753C2semidirect
6. #13070727C2semidirect
7. #13070705C2semidirect
8. #13070675C2semidirect
9. #13070556C2semidirect
10. #13070545C2semidirect
11. #13070480C2semidirect
12. #13070442C2semidirect
13. #13070328C2semidirect
14. C2×#10622200C2semidirect
28. C2×#66893C22semidirect
32. #10622729C22semidirect
34. C2×#66882C22semidirect
35. C2×#66876C22semidirect
40. C4×Dic44C22semidirect
41. #10622295C22semidirect
42. #10622202C22semidirect
43. #10622202C22semidirect
44. #10622202C22semidirect
52. C22⋊(C11⋊C16)C22semidirect
53. #10622130C22semidirect
54. #10622127C22semidirect
55. #10622127C22semidirect
56. #10622127C22semidirect
57. C4⋊(C11⋊C16)C22semidirect
58. #10622099C22semidirect
447. C11#33881semidirect

Maximal subgroups

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

subgroupindex
#130810092
#130708522
#130708162
#130707942
#130707532
#130707272
#130707052
#130706752
#130705562
#130705452
#130704802
#130704422
#130703282
C2×#106222002
C11×#32802
#3388111