Finite Group Databasebeta

← #14910813

Subgroups — #14910813

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#13080303C211yesmaximal, characteristic
2#13070855C211yesmaximal, characteristic, complemented
3#13070824C211yesmaximal, characteristic, complemented
4#13070807C211yesmaximal, characteristic, complemented
5#13070760C211yesmaximal, characteristic, complemented
6#13070722C211yesmaximal, characteristic, complemented
7#13070714C211yesmaximal, characteristic, complemented
8#13070678C211yesmaximal, characteristic, complemented
9#13070554C211yesmaximal, characteristic, complemented
10#13070544C211yesmaximal, characteristic, complemented
11#13070478C211yesmaximal, characteristic, complemented
12#13070442C211yesmaximal, characteristic, complemented
13#13070331C211yesmaximal, characteristic, complemented
14#13070321C211yesmaximal, characteristic, complemented
15C11×#3342C211yesmaximal, characteristic, complemented
16C11×#556—21no—
17C2×#66957C2211yescharacteristic
18C22×D88C2211yescharacteristic
19#10623081—21no—
20C11×#500C2211yescharacteristic, complemented
21C11×#485—21no—
22C11×#485—21no—
23C11×#475—21no—
24C11×#467C2211yescharacteristic
25C11×#467C2211yescharacteristic, complemented
26C4×C11×Q16C2211yescharacteristic, complemented
27C8×D4×C11C2211yescharacteristic
28C11×#427C2211yescharacteristic
29C11×#427C2211yescharacteristic, complemented
30C2×#66893C2211yescharacteristic, complemented
31C2×#66892C2211yescharacteristic
32C2×#66892C2211yescharacteristic
33#10622729C2211yescharacteristic
34#10622728C2211yescharacteristic
35C2×#66876C2211yescharacteristic
36C22×C11⋊C16C2211yescharacteristic, complemented
37#10622457—21no—
38#10622347—21no—
39#10622344—21no—
40#10622309C2211yescharacteristic
41C4×D88C2211yescharacteristic
42#10622202C2211yescharacteristic, complemented
43C22⋊(C11⋊C16)C2211yescharacteristic
44C22⋊(C11⋊C16)C2211yescharacteristic, complemented
45#10622130C2211yescharacteristic, complemented
46#10622130C2211yescharacteristic, complemented
47#10622130C2211yescharacteristic, complemented
48#10622129C2211yescharacteristic
49#10622129C2211yescharacteristic
50#10622129C2211yescharacteristic
51#10622129C2211yescharacteristic
52#10622129C2211yescharacteristic
53#10622129C2211yescharacteristic
54#10622128C2211yescharacteristic, complemented
55#10622128C2211yescharacteristic, complemented
56#10622127C2211yescharacteristic, complemented
57C4⋊(C11⋊C16)C2211yescharacteristic, complemented
58#10622099C2211yescharacteristic, complemented
59C2×#4339—21no—
60C22×D44—21no—
61C2×C11×Q16C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×C4⋊Q8—21no—
65C11×#126—41no—
66C11×#126—41no—
67C11×#124—41no—
68C11×C22⋊Q8—21no—
69C11×C22⋊Q8—21no—
70C4×Q8×C11—21no—
71C4×Q8×C11—41no—
72C4×D4×C11D411yescharacteristic
73C11×#117—21no—
74C11×#117—21no—
75#66990—41no—
76#66983—21no—
77#66977—21no—
78C2×Dic44C2311yescharacteristic
79#66957—22no—
80#66957—41no—
81C2×D88—22no—
82C2×D88—21no—
83C2×D88—41no—
84C2×D88C2311yescharacteristic
85C2×D88C2311yescharacteristic
86C2×#4314—21no—
87C2×#4314—21no—
88#66947—41no—
89#66937—41no—
90C22⋊C4×D11—41no—
91#66928—21no—
92C4×D44—21no—
93C11×#107—21no—
94C11×#107C2311yescharacteristic
95C11×#107C2311yescharacteristic
96C11×#107C2311yescharacteristic
97C11×#106—21no—
98C11×#106—21no—
99C11×C4⋊C8D411yescharacteristic
100C11×#103—21no—
101C11×#103—21no—
102C11×#103—21no—
103C11×C22⋊C8D411yescharacteristic
104C11×C22⋊C8D411yescharacteristic
105C4×C8×C11C2311yescharacteristic
106#66893—41no—
107#66892—22no—
108#66892—41no—
109#66885—21no—
110#66885—21no—
111#66882C2311yescharacteristic
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
120C23×D11—41no—
121C2×Q8×C11—21no—
122C2×Q8×C11—41no—
123C2×D4×C11D811yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C2×C22⋊D11—41no—
127C2×C22⋊D11—41no—
128#4339—42no—
129#4339—81no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44—42no—
133C2×D44—41no—
134C2×D44—81no—
135C2×C4×D11—41no—
136C2×C4×D11—41no—
137C2×Dic22—21no—
138C11×Q16—21no—
139C11×Q16—21no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2×D411yescharacteristic
147C2×C8×C11C2411yescharacteristic
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—41no—
152C11×C4⋊C4—41no—
153C11×C4⋊C4—41no—
154C11×C4⋊C4—41no—
155C11×C4⋊C4D811yescharacteristic
156C11×C22⋊C4—41no—
157C11×C22⋊C4—41no—
158C11×C22⋊C4—41no—
159C11×C22⋊C4—41no—
160C11×C22⋊C4D811yescharacteristic
161C11×C22⋊C4D811yescharacteristic
162C42×C11—41no—
163C42×C11—41no—
164C42×C11—41no—
165C42×C11C2×D411yescharacteristic
166C22⋊Dic11—41no—
167(C2×D11)⋊C4—41no—
168(C2×D11)⋊C4—41no—
169(C2×D11)⋊C4—41no—
170(C2×D11)⋊C4—41no—
171C4⋊Dic11—21no—
172Dic11⋊C4—41no—
173Dic44—21no—
174Dic44—21no—
175D88—21no—
176D88—21no—
177D88—21no—
178D88—42no—
179D88#4112yes—
180#4314—42no—
181#4314—81no—
182C11⋊C16—21no—
183C11⋊C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3342D1111yescharacteristic, complemented
187#3280—111no—
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×C11C2×D811yescharacteristic
202C23×C11C2×D811yescharacteristic
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—82no—
206C22×D11—82no—
207C22×D11—161no—
208Q8×C11—41no—
209Q8×C11—41no—
210Q8×C11—82no—
211D4×C11—41no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11C2×D811yescharacteristic
221C2×C4×C11C2×D811yescharacteristic
222C2×C4×C11C2×D811yescharacteristic
223C2×C4×C11C2×D811yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C22⋊D11—82no—
226C22⋊D11—161no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229D44—22no—
230D44—41no—
231D44—41no—
232D44—41no—
233D44—82no—
234C4×D11—82no—
235C4×D11—161no—
236Dic22—41no—
237Dic22—41no—
238C8×C11—21no—
239C8×C11—21no—
240C8×C11—21no—
241C8×C11C2×#4111yescharacteristic
242C8×C11H(5,𝔽2)11yescharacteristic
243C2×#135—111no—
244C22×D8—111no—
245#556—21no—
246#546—221no—
247C2×Q32—111no—
248C2×SD32—111no—
249C2×SD32—111no—
250C2×M32—111no—
251C22×C16—111no—
252#500C2×D1111yescharacteristic, complemented
253#495—111no—
254#485—21no—
255#485—21no—
256#475—21no—
257#467—111no—
258#467C2×D1111yescharacteristic
259#467C2×D1111yescharacteristic, complemented
260#466—111no—
261#463—221no—
262#450—221no—
263#449—221no—
264C4×Q16C2×D1111yescharacteristic, complemented
265C4×D8—111no—
266C8×D4C2×D1111yescharacteristic
267#427C2×D1111yescharacteristic
268#427C2×D1111yescharacteristic, complemented
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×C11C22×D811yescharacteristic
293C2×D11—42no—
294C2×D11—81no—
295C2×D11—81no—
296C2×D11—81no—
297C2×D11—81no—
298C2×D11—81no—
299C2×D11—164no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—21no—
304C4×C11—81no—
305C4×C11—81no—
306C4×C11—81no—
307C4×C11—81no—
308C4×C11#54611yescharacteristic
309C4×C11#57711yescharacteristic
310Dic11—81no—
311Dic11—81no—
312C2×#41—221no—
313C22×D4—221no—
314#135—222no—
315#135—441no—
316C2×Q16—111no—
317C2×Q16C22×D1111yescharacteristic
318C2×SD16—221no—
319C2×SD16—221no—
320C2×D8—111no—
321C2×D8—111no—
322C2×D8—222no—
323C2×D8—221no—
324C2×D8—441no—
325C22×C8C22×D1111yescharacteristic
326C22×C8C22×D1111yescharacteristic
327C4⋊Q8—21no—
328#126—41no—
329#126—41no—
330#124—41no—
331#124—221no—
332#123—441no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C22⋊Q8—221no—
336#121—221no—
337#121—441no—
338#120—441no—
339C4×Q8—21no—
340C4×Q8—41no—
341C4×D4—221no—
342C4×D4C22⋊D1111yescharacteristic
343#117—21no—
344#117—21no—
345C2×C22⋊C4—441no—
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—21no—
356#107—111no—
357#107C22×D1111yescharacteristic
358#107C22×D1111yescharacteristic
359#107C22×D1111yescharacteristic
360#106—21no—
361#106—21no—
362C4⋊C8C22⋊D1111yescharacteristic
363#103—21no—
364#103—21no—
365#103—21no—
366#103—221no—
367#102—221no—
368#102—221no—
369C22⋊C8C22⋊D1111yescharacteristic
370C22⋊C8C22⋊D1111yescharacteristic
371C4×C8C22×D1111yescharacteristic
372C2×C11—41no—
373C2×C11—41no—
374C2×C11#329411yescharacteristic
375C2×C11#341411yescharacteristic
376C2×C11#341611yescharacteristic
377D11—82no—
378D11—161no—
379C24—441no—
380#41—442no—
381#41—881no—
382C2×Q8—21no—
383C2×Q8—41no—
384C2×Q8—221no—
385C2×D4—221no—
386C2×D4—221no—
387C2×D4—442no—
388C2×D4—441no—
389C2×D4—441no—
390C2×D4—441no—
391C2×D4—881no—
392C2×D4#432311yescharacteristic
393C22×C4—441no—
394C22×C4—441no—
395C22×C4C2×C22⋊D1111yescharacteristic
396C22×C4C2×C22⋊D1111yescharacteristic
397Q16—21no—
398Q16—21no—
399Q16—221no—
400Q16—221no—
401SD16—442no—
402SD16—881no—
403D8—112no—
404D8—221no—
405D8—221no—
406D8—221no—
407D8—442no—
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—21no—
418C4⋊C4—21no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—221no—
424C4⋊C4—441no—
425C4⋊C4#432311yescharacteristic
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—441no—
431C22⋊C4—441no—
432C22⋊C4—441no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C22⋊C4#432311yescharacteristic
436C22⋊C4#432311yescharacteristic
437C42—41no—
438C42—41no—
439C42—41no—
440C42C2×C22⋊D1111yescharacteristic
441C16—221no—
442C16—221no—
443C16—221no—
444C16—221no—
445C11#3387811yescharacteristic, complemented, Sylow
446C23—441no—
447C23—441no—
448C23—882no—
449C23—882no—
450C23—1761no—
451C23C2×#432311yescharacteristic
452C23C2×#432311yescharacteristic
453Q8—41no—
454Q8—41no—
455Q8—82no—
456Q8—441no—
457Q8—441no—
458D4—41no—
459D4—222no—
460D4—441no—
461D4—441no—
462D4—441no—
463D4—882no—
464D4—882no—
465D4—1761no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—882no—
477C2×C4—1761no—
478C2×C4C2×#432311yescharacteristic
479C2×C4C2×#432311yescharacteristic
480C2×C4C2×#432311yescharacteristic
481C2×C4C2×#432311yescharacteristic
482C2×C4C22×C22⋊D1111yescharacteristic
483C8—21no—
484C8—21no—
485C8—21no—
486C8#41×D1111yescharacteristic
487C8#6704211yescharacteristic
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—442no—
495C22—881no—
496C22—881no—
497C22—881no—
498C22—881no—
499C22—881no—
500C22—1764no—
501C22C22×#432311yescharacteristic
502C4—21no—
503C4—21no—
504C4—21no—
505C4—21no—
506C4—81no—
507C4—81no—
508C4—81no—
509C4—81no—
510C4—881no—
511C4—881no—
512C4#1062336011yescharacteristic
513C4#1062336811yescharacteristic
514C2—41no—
515C2—41no—
516C2—882no—
517C2—1761no—
518C2#1308042311yescharacteristic
519C2#1308175011yescharacteristic
520C2#1308176011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3342C2
socleC22×C11C22×D8
prime radical#13080303C2
hypercenter#3342D11
hypocenterC11#33878
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3342

Complements

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

NH ≅ G/Ntype
2. #13070855C2semidirect
3. #13070824C2semidirect
4. #13070807C2semidirect
5. #13070760C2semidirect
6. #13070722C2semidirect
7. #13070714C2semidirect
8. #13070678C2semidirect
9. #13070554C2semidirect
10. #13070544C2semidirect
11. #13070478C2semidirect
12. #13070442C2semidirect
13. #13070331C2semidirect
14. #13070321C2semidirect
15. C11×#3342C2semidirect
20. C11×#500C22semidirect
25. C11×#467C22semidirect
26. C4×C11×Q16C22semidirect
29. C11×#427C22semidirect
30. C2×#66893C22semidirect
36. C22×C11⋊C16C22semidirect
42. #10622202C22semidirect
44. C22⋊(C11⋊C16)C22semidirect
45. #10622130C22semidirect
46. #10622130C22semidirect
47. #10622130C22semidirect
54. #10622128C22semidirect
55. #10622128C22semidirect
56. #10622127C22semidirect
57. C4⋊(C11⋊C16)C22semidirect
58. #10622099C22semidirect
186. #3342D11semidirect
252. #500C2×D11semidirect
259. #467C2×D11semidirect
264. C4×Q16C2×D11semidirect
268. #427C2×D11semidirect
445. C11#33878semidirect

Maximal subgroups

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

subgroupindex
#130803032
#130708552
#130708242
#130708072
#130707602
#130707222
#130707142
#130706782
#130705542
#130705442
#130704782
#130704422
#130703312
#130703212
C11×#33422
#3387811