Finite Group Databasebeta

← #14910858

Subgroups — #14910858

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#13080303C211yesmaximal, characteristic
2#13070855C211yesmaximal, characteristic, complemented
3#13070818C211yesmaximal, characteristic, complemented
4#13070796C211yesmaximal, characteristic, complemented
5#13070750C211yesmaximal, characteristic, complemented
6#13070731C211yesmaximal, characteristic, complemented
7#13070705C211yesmaximal, characteristic, complemented
8#13070678C211yesmaximal, characteristic, complemented
9#13070554C211yesmaximal, characteristic, complemented
10#13070544C211yesmaximal, characteristic, complemented
11#13070478C211yesmaximal, characteristic, complemented
12#13070442C211yesmaximal, characteristic, complemented
13#13070326C211yesmaximal, characteristic, complemented
14C2×#10622129C211yesmaximal, characteristic, complemented
15C11×#3338C211yesmaximal, characteristic, complemented
16C11×#554—21no—
17C2×#66957C2211yescharacteristic
18C22×D88C2211yescharacteristic
19#10623081—21no—
20C11×#500C2211yescharacteristic, complemented
21C11×#484—21no—
22C11×#484—21no—
23C11×#477—21no—
24C11×#467C2211yescharacteristic
25C11×#467C2211yescharacteristic, complemented
26C4×C11×Q16C2211yescharacteristic, complemented
27C8×D4×C11C2211yescharacteristic
28C2×C11×#107C2211yescharacteristic
29C2×C11×#107C2211yescharacteristic, complemented
30C2×#66893C2211yescharacteristic, complemented
31C2×#66892C2211yescharacteristic
32C2×#66892C2211yescharacteristic
33#10622729C2211yescharacteristic
34#10622728C2211yescharacteristic
35C2×#66876C2211yescharacteristic, complemented
36C22×C11⋊C16C2211yescharacteristic
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#10622127C2211yescharacteristic, complemented
55#10622127C2211yescharacteristic, 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×#125—41no—
66C11×C22⋊Q8—21no—
67C11×C22⋊Q8—21no—
68C11×C22⋊Q8—41no—
69C11×C22⋊Q8—41no—
70C4×Q8×C11—21no—
71C4×D4×C11—41no—
72C4×D4×C11D411yescharacteristic
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—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×#107—21no—
95C11×#107—21no—
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#107C2311yescharacteristic
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#33881—111nomaximal, Sylow
120C23×D11—41no—
121C2×Q8×C11—21no—
122C2×Q8×C11—41no—
123C2×D4×C11D811yescharacteristic
124C22×C4×C11—41no—
125C22×C4×C11—41no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C2×C22⋊D11—41no—
129C2×C22⋊D11—41no—
130#4339—42no—
131#4339—81no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44—42no—
135C2×D44—41no—
136C2×D44—81no—
137C2×C4×D11—41no—
138C2×C4×D11—41no—
139C2×Dic22—21no—
140C11×Q16—21no—
141C11×Q16—21no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11C2×D411yescharacteristic
147C2×C8×C11C2×D411yescharacteristic
148C2×C8×C11C2×D411yescharacteristic
149C2×C8×C11C2411yescharacteristic
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—41no—
154C11×C4⋊C4—41no—
155C11×C4⋊C4—41no—
156C11×C4⋊C4—41no—
157C11×C4⋊C4—41no—
158C11×C4⋊C4—41no—
159C11×C4⋊C4D811yescharacteristic
160C11×C22⋊C4—41no—
161C11×C22⋊C4—41no—
162C11×C22⋊C4D811yescharacteristic
163C11×C22⋊C4D811yescharacteristic
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#3338D1111yescharacteristic, complemented
187#3280—111no—
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×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—161no—
211D4×C11—22no—
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×C11—161no—
221C2×C4×C11—161no—
222C2×C4×C11C2×D811yescharacteristic
223C2×C4×C11C2×D811yescharacteristic
224C2×C4×C11C2×D811yescharacteristic
225C2×C4×C11C2×D811yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C22⋊D11—82no—
228C22⋊D11—161no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231D44—22no—
232D44—41no—
233D44—41no—
234D44—41no—
235D44—82no—
236C4×D11—82no—
237C4×D11—161no—
238Dic22—41no—
239Dic22—41no—
240C8×C11—21no—
241C8×C11—21no—
242C8×C11—21no—
243C8×C11C2×#4111yescharacteristic
244C8×C11H(5,𝔽2)11yescharacteristic
245C2×#135—111no—
246C22×D8—111no—
247#554—21no—
248#546—221no—
249C2×Q32—111no—
250C2×SD32—111no—
251C2×SD32—111no—
252C2×M32—111no—
253C22×C16—111no—
254#500C2×D1111yescharacteristic, complemented
255#495—111no—
256#484—21no—
257#484—21no—
258#477—21no—
259#467—111no—
260#467C2×D1111yescharacteristic
261#467C2×D1111yescharacteristic, complemented
262#466—111no—
263#463—221no—
264#450—221no—
265#449—221no—
266C4×Q16C2×D1111yescharacteristic, complemented
267C4×D8—111no—
268C8×D4C2×D1111yescharacteristic
269C2×#107C2×D1111yescharacteristic
270C2×#107C2×D1111yescharacteristic, complemented
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#51012yes—
294C22×C11C22×D811yescharacteristic
295C2×D11—42no—
296C2×D11—81no—
297C2×D11—81no—
298C2×D11—81no—
299C2×D11—81no—
300C2×D11—81no—
301C2×D11—164no—
302C4×C11—21no—
303C4×C11—21no—
304C4×C11—21no—
305C4×C11—21no—
306C4×C11—81no—
307C4×C11—81no—
308C4×C11—81no—
309C4×C11—81no—
310C4×C11#54611yescharacteristic
311C4×C11#57711yescharacteristic
312Dic11—81no—
313Dic11—81no—
314C2×#41—221no—
315C22×D4—221no—
316#135—222no—
317#135—441no—
318C2×Q16—111no—
319C2×Q16C22×D1111yescharacteristic
320C2×SD16—221no—
321C2×SD16—221no—
322C2×D8—111no—
323C2×D8—111no—
324C2×D8—222no—
325C2×D8—221no—
326C2×D8—441no—
327C22×C8C22×D1111yescharacteristic
328C22×C8C22×D1111yescharacteristic
329C4⋊Q8—21no—
330#125—41no—
331#124—221no—
332#123—441no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C22⋊Q8—41no—
336C22⋊Q8—41no—
337C22⋊Q8—221no—
338#121—221no—
339#121—441no—
340#120—441no—
341C4×Q8—21no—
342C4×D4—41no—
343C4×D4—221no—
344C4×D4C22⋊D1111yescharacteristic
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C22⋊C4—441no—
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—21no—
358#107—21no—
359#107—21no—
360#107—111no—
361#107C22×D1111yescharacteristic
362#107C22×D1111yescharacteristic
363#107C22×D1111yescharacteristic
364C4⋊C8C22⋊D1111yescharacteristic
365#103—21no—
366#103—21no—
367#103—21no—
368#103—221no—
369#102—221no—
370#102—221no—
371C22⋊C8C22⋊D1111yescharacteristic
372C22⋊C8C22⋊D1111yescharacteristic
373C4×C8C22×D1111yescharacteristic
374C2×C11—22no—
375C2×C11—41no—
376C2×C11#329411yescharacteristic
377C2×C11C2×#51011yescharacteristic
378C2×C11#341511yescharacteristic
379D11—82no—
380D11—161no—
381C24—441no—
382#41—442no—
383#41—881no—
384C2×Q8—21no—
385C2×Q8—41no—
386C2×Q8—221no—
387C2×D4—221no—
388C2×D4—221no—
389C2×D4—442no—
390C2×D4—441no—
391C2×D4—441no—
392C2×D4—441no—
393C2×D4—881no—
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—442no—
406SD16—881no—
407D8—112no—
408D8—221no—
409D8—221no—
410D8—221no—
411D8—442no—
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—21no—
422C4⋊C4—21no—
423C4⋊C4—41no—
424C4⋊C4—41no—
425C4⋊C4—41no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4—221no—
430C4⋊C4—441no—
431C4⋊C4#432311yescharacteristic
432C22⋊C4—41no—
433C22⋊C4—41no—
434C22⋊C4—441no—
435C22⋊C4—441no—
436C22⋊C4—441no—
437C22⋊C4—441no—
438C22⋊C4—441no—
439C22⋊C4#432311yescharacteristic
440C22⋊C4#432311yescharacteristic
441C42—41no—
442C42C2×C22⋊D1111yescharacteristic
443C16—221no—
444C16—221no—
445C16—221no—
446C16—221no—
447C11#3388111yescharacteristic, complemented, Sylow
448C23—441no—
449C23—441no—
450C23—882no—
451C23—882no—
452C23—1761no—
453C23C2×#432311yescharacteristic
454C23C2×#432311yescharacteristic
455Q8—41no—
456Q8—41no—
457Q8—161no—
458Q8—441no—
459Q8—441no—
460D4—22no—
461D4—222no—
462D4—441no—
463D4—441no—
464D4—441no—
465D4—882no—
466D4—882no—
467D4—1761no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—161no—
477C2×C4—161no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—882no—
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—
490C8#41×D1111yescharacteristic
491C8#6704211yescharacteristic
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—442no—
498C22—881no—
499C22—881no—
500C22—881no—
501C22—881no—
502C22—881no—
503C22—1764no—
504C22#1062279212yes—
505C22C22×#432311yescharacteristic
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—81no—
511C4—81no—
512C4—81no—
513C4—81no—
514C4—881no—
515C4—881no—
516C4#1062336011yescharacteristic
517C4#1062336811yescharacteristic
518C2—22no—
519C2—41no—
520C2—882no—
521C2—1761no—
522C2#1308042311yescharacteristic
523C2C2×#1062279211yescharacteristic
524C2#1308175511yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3338C2
socleC22×C11C22×D8
prime radical#13080303C2
hypercenter#3338D11
hypocenterC11#33881
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3338

Complements

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

NH ≅ G/Ntype
2. #13070855C2semidirect
3. #13070818C2semidirect
4. #13070796C2semidirect
5. #13070750C2semidirect
6. #13070731C2semidirect
7. #13070705C2semidirect
8. #13070678C2semidirect
9. #13070554C2semidirect
10. #13070544C2semidirect
11. #13070478C2semidirect
12. #13070442C2semidirect
13. #13070326C2semidirect
14. C2×#10622129C2semidirect
15. C11×#3338C2semidirect
20. C11×#500C22semidirect
25. C11×#467C22semidirect
26. C4×C11×Q16C22semidirect
29. C2×C11×#107C22semidirect
30. C2×#66893C22semidirect
35. C2×#66876C22semidirect
42. #10622202C22semidirect
44. C22⋊(C11⋊C16)C22semidirect
45. #10622130C22semidirect
46. #10622130C22semidirect
47. #10622130C22semidirect
54. #10622127C22semidirect
55. #10622127C22semidirect
56. #10622127C22semidirect
57. C4⋊(C11⋊C16)C22semidirect
58. #10622099C22semidirect
186. #3338D11semidirect
254. #500C2×D11semidirect
261. #467C2×D11semidirect
266. C4×Q16C2×D11semidirect
270. C2×#107C2×D11semidirect
447. C11#33881semidirect

Maximal subgroups

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

subgroupindex
#130803032
#130708552
#130708182
#130707962
#130707502
#130707312
#130707052
#130706782
#130705542
#130705442
#130704782
#130704422
#130703262
C2×#106221292
C11×#33382
#3388111