Finite Group Databasebeta

← #14909633

Subgroups — #14909633

Order 2816.

564 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078286C211yesmaximal, characteristic
2#13070824C211yesmaximal, characteristic, complemented
3#13070816C211yesmaximal, characteristic, complemented
4#13070811C211yesmaximal, characteristic, complemented
5#13070807C211yesmaximal, characteristic, complemented
6#13070731C211yesmaximal, characteristic, complemented
7#13070722C211yesmaximal, characteristic, complemented
8#13070714C211yesmaximal, characteristic, complemented
9#13070705C211yesmaximal, characteristic, complemented
10#13070554C211yesmaximal, characteristic, complemented
11#13070554C211yesmaximal, characteristic, complemented
12#13070550C211yesmaximal, characteristic, complemented
13#13070533C211yesmaximal, characteristic, complemented
14#13070230C211yesmaximal, characteristic, complemented
15C11×#3059C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17C2×C11×#131C2211yescharacteristic
18C11×#536—21no—
19#10623364—21no—
20C2×#66957C2211yescharacteristic
21C11×#470—21no—
22C11×#470—21no—
23C11×#467C2211yescharacteristic
24C11×#467C2211yescharacteristic
25C11×#467C2211yescharacteristic
26C11×#467C2211yescharacteristic
27C11×#427C2211yescharacteristic
28C11×#419—21no—
29C2×#66893C2211yescharacteristic
30C2×#66893C2211yescharacteristic
31C2×#66892C2211yescharacteristic
32C2×#66892C2211yescharacteristic
33#10622747—21no—
34#10622747—21no—
35#10622746—21no—
36#10622729C2211yescharacteristic
37#10622729C2211yescharacteristic
38#10622728C2211yescharacteristic
39#10622728C2211yescharacteristic
40C2×#66882C2211yescharacteristic
41C2×#66876C2211yescharacteristic
42C22×C11⋊C16C2211yescharacteristic
43#10622202C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622202C2211yescharacteristic
47C22⋊(C11⋊C16)C2211yescharacteristic
48C22⋊(C11⋊C16)C2211yescharacteristic
49C22⋊(C11⋊C16)C2211yescharacteristic
50C22⋊(C11⋊C16)C2211yescharacteristic
51#10622130C2211yescharacteristic
52#10622130C2211yescharacteristic
53#10622129C2211yescharacteristic
54#10622129C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×C11×#41D411yescharacteristic
60C22×Q8×C11—21no—
61C2×#4339—21no—
62C2×C11×Q16—21no—
63C2×C11×Q16—41no—
64C2×C11×Q16—41no—
65C2×C11×Q16C2311yescharacteristic
66C2×C11×Q16C2311yescharacteristic
67C11×#131—41no—
68C11×#131—41no—
69C2×C11×M16D411yescharacteristic
70C2×C11×M16D411yescharacteristic
71C2×C11×M16D411yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C11×C4⋊Q8—41no—
76C11×#124—41no—
77C11×#123—41no—
78C11×#123—41no—
79C11×C22⋊Q8—21no—
80C11×C22⋊Q8—21no—
81C11×C22⋊Q8—21no—
82C11×C22⋊Q8—21no—
83C11×#117—21no—
84#66999—41no—
85#66992—41no—
86#66992—41no—
87#66991—41no—
88#66983—21no—
89#66983—21no—
90C2×C4⋊Dic11—21no—
91#66977—21no—
92#66977—21no—
93C2×Dic44C2311yescharacteristic
94#66957—41no—
95#66957—41no—
96C2×D88C2311yescharacteristic
97C2×#4314—21no—
98C11×#107C2311yescharacteristic
99C11×#107C2311yescharacteristic
100C11×#106—21no—
101C11×#103—21no—
102C11×#103—21no—
103C11×#103—21no—
104C11×#103—21no—
105#66893—41no—
106#66893—41no—
107#66892—41no—
108#66892—41no—
109#66885—21no—
110#66885—21no—
111#66882—21no—
112#66882C2311yescharacteristic
113#66882C2311yescharacteristic
114#66880—21no—
115#66880—21no—
116#66876—41no—
117C2×C11⋊C16—41no—
118C2×C11⋊C16C2311yescharacteristic
119C2×C11⋊C16C2311yescharacteristic
120C2×C11⋊C16C2311yescharacteristic
121C2×C11⋊C16C2311yescharacteristic
122#33767—111nomaximal, Sylow
123C11×#41—41no—
124C11×#41—41no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—42no—
128C2×Q8×C11—42no—
129C2×Q8×C11—41no—
130C2×Q8×C11D811yescharacteristic
131C2×D4×C11D811yescharacteristic
132C2×D4×C11D811yescharacteristic
133C2×D4×C11D811yescharacteristic
134C22×C4×C11—41no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C2×C22⋊D11—41no—
139C2×C22⋊D11—41no—
140C2×C22⋊D11—41no—
141C22×Dic11—41no—
142#4339—42no—
143#4339—42no—
144C2×D44—21no—
145C2×C4×D11—41no—
146C2×Dic22—21no—
147C11×Q16—21no—
148C11×Q16—21no—
149C11×Q16—21no—
150C11×Q16—21no—
151C11×Q16—42no—
152C11×M16—41no—
153C11×M16—41no—
154C11×M16—41no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11C2×D411yescharacteristic
162C2×C8×C11C2×D411yescharacteristic
163C2×C8×C11C2×D411yescharacteristic
164C2×C8×C11C2411yescharacteristic
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—41no—
168C11×C4⋊C4—41no—
169C11×C4⋊C4—41no—
170C11×C4⋊C4—41no—
171C11×C22⋊C4—41no—
172C11×C22⋊C4—41no—
173C11×C22⋊C4—41no—
174C11×C22⋊C4—41no—
175C11×C22⋊C4—41no—
176C42×C11—41no—
177C22⋊Dic11—41no—
178C22⋊Dic11—41no—
179(C2×D11)⋊C4—41no—
180(C2×D11)⋊C4—41no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—41no—
184Dic11⋊C4—41no—
185Dic11⋊C4—41no—
186Dic44—21no—
187Dic44—21no—
188D88—21no—
189D88—21no—
190#4314—42no—
191C11⋊C16—21no—
192C11⋊C16—21no—
193C11⋊C16—21no—
194C11⋊C16—21no—
195#3061—111no—
196#3059D1111yescharacteristic, complemented
197#2237—111no—
198#2236—111no—
199#2235—111no—
200#2234—111no—
201#2220—111no—
202#2219—111no—
203#2217—111no—
204#2216—111no—
205#2189—111no—
206#2189—111no—
207#2188—111no—
208#2185—111no—
209#2113—111no—
210C23×C11C2×D811yescharacteristic
211C23×C11C2×D811yescharacteristic
212C23×C11C2×D811yescharacteristic
213C22×D11—41no—
214Q8×C11—41no—
215Q8×C11—41no—
216Q8×C11—41no—
217Q8×C11—41no—
218Q8×C11—41no—
219Q8×C11—82no—
220D4×C11—41no—
221D4×C11—41no—
222D4×C11—41no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—82no—
234C2×C4×C11C2×D811yescharacteristic
235C2×C4×C11C2×D811yescharacteristic
236C2×C4×C11C2×D811yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C22⋊D11—82no—
239C22⋊D11—161no—
240C22⋊D11—161no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—161no—
245D44—41no—
246D44—41no—
247C4×D11—82no—
248Dic22—41no—
249Dic22—41no—
250C8×C11—21no—
251C8×C11—21no—
252C8×C11—21no—
253C8×C11H(5,𝔽2)11yescharacteristic
254C8×C11H(5,𝔽2)11yescharacteristic
255C2×#135—111no—
256C22×Q16C2×D1111yescharacteristic
257C2×#131C2×D1111yescharacteristic
258#537—221no—
259#536—21no—
260C2×Q32—111no—
261C2×Q32—111no—
262C2×SD32—111no—
263C2×SD32—111no—
264C2×M32—111no—
265C22×C16—111no—
266#470—21no—
267#470—21no—
268#468—221no—
269#468—221no—
270#467—111no—
271#467—111no—
272#467C2×D1111yescharacteristic
273#467C2×D1111yescharacteristic
274#467C2×D1111yescharacteristic
275#467C2×D1111yescharacteristic
276#466—111no—
277#466—111no—
278#427C2×D1111yescharacteristic
279C2×#107—111no—
280#419—21no—
281#417—221no—
282#367—111no—
283#367—111no—
284#366—111no—
285#366—111no—
286#358—111no—
287#358—111no—
288#358—111no—
289#358—111no—
290#358—111no—
291#358—111no—
292#357—111no—
293#357—111no—
294C22⋊C16—111no—
295C22⋊C16—111no—
296C22⋊C16—111no—
297C22⋊C16—111no—
298C22×C11—21no—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11C22×D811yescharacteristic
308C2×D11—81no—
309C2×D11—81no—
310C2×D11—81no—
311C4×C11—21no—
312C4×C11—21no—
313C4×C11—21no—
314C4×C11—81no—
315C4×C11—81no—
316C4×C11—81no—
317C4×C11—81no—
318C4×C11#53411yescharacteristic
319C4×C11#57511yescharacteristic
320Dic11—81no—
321Dic11—81no—
322Dic11—81no—
323C2×#41—221no—
324C2×#41C22⋊D1111yescharacteristic
325C22×Q8—21no—
326#135—441no—
327#135—441no—
328C2×Q16—21no—
329C2×Q16—41no—
330C2×Q16—41no—
331C2×Q16—111no—
332C2×Q16C22×D1111yescharacteristic
333C2×Q16C22×D1111yescharacteristic
334C2×SD16—221no—
335C2×D8—111no—
336#131—41no—
337#131—41no—
338C2×M16C22⋊D1111yescharacteristic
339C2×M16C22⋊D1111yescharacteristic
340C2×M16C22⋊D1111yescharacteristic
341C22×C8C22×D1111yescharacteristic
342C22×C8C22×D1111yescharacteristic
343C22×C8C22×D1111yescharacteristic
344C4⋊Q8—41no—
345#124—41no—
346#123—41no—
347#123—41no—
348C22⋊Q8—21no—
349C22⋊Q8—21no—
350C22⋊Q8—21no—
351C22⋊Q8—21no—
352C22⋊Q8—221no—
353C22⋊Q8—221no—
354C22⋊Q8—441no—
355#121—221no—
356#121—221no—
357#121—441no—
358#121—441no—
359#121—441no—
360#117—21no—
361C2×C4⋊C4—221no—
362Q32—441no—
363Q32—441no—
364SD32—441no—
365SD32—441no—
366M32—441no—
367C2×C16—111no—
368C2×C16—111no—
369C2×C16—111no—
370C2×C16—111no—
371C2×C16—441no—
372#107—111no—
373#107—111no—
374#107—221no—
375#107C22×D1111yescharacteristic
376#107C22×D1111yescharacteristic
377#106—21no—
378#103—21no—
379#103—21no—
380#103—21no—
381#103—21no—
382#103—221no—
383#103—221no—
384#102—221no—
385#102—221no—
386C2×C11—41no—
387C2×C11—41no—
388C2×C11—41no—
389C2×C11#318611yescharacteristic
390C2×C11#341611yescharacteristic
391C2×C11#341711yescharacteristic
392D11—161no—
393#41—41no—
394#41—41no—
395#41—442no—
396#41—442no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—42no—
400C2×Q8—42no—
401C2×Q8—41no—
402C2×Q8—221no—
403C2×Q8#432311yescharacteristic
404C2×D4—221no—
405C2×D4—441no—
406C2×D4—441no—
407C2×D4—441no—
408C2×D4#432311yescharacteristic
409C2×D4#432311yescharacteristic
410C2×D4#432311yescharacteristic
411C22×C4—41no—
412C22×C4—441no—
413C22×C4—441no—
414C22×C4C2×C22⋊D1111yescharacteristic
415C22×C4C2×C22⋊D1111yescharacteristic
416C22×C4C2×C22⋊D1111yescharacteristic
417Q16—21no—
418Q16—21no—
419Q16—21no—
420Q16—21no—
421Q16—42no—
422Q16—221no—
423Q16—221no—
424SD16—442no—
425D8—221no—
426D8—221no—
427M16—41no—
428M16—41no—
429M16—41no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8C2×C22⋊D1111yescharacteristic
437C2×C8C2×C22⋊D1111yescharacteristic
438C2×C8C2×C22⋊D1111yescharacteristic
439C2×C8C23×D1111yescharacteristic
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—41no—
443C4⋊C4—41no—
444C4⋊C4—41no—
445C4⋊C4—41no—
446C4⋊C4—221no—
447C4⋊C4—221no—
448C4⋊C4—441no—
449C4⋊C4—441no—
450C4⋊C4—441no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C22⋊C4—41no—
454C22⋊C4—41no—
455C22⋊C4—41no—
456C22⋊C4—441no—
457C22⋊C4—441no—
458C22⋊C4—441no—
459C22⋊C4—441no—
460C42—41no—
461C16—221no—
462C16—221no—
463C16—221no—
464C16—221no—
465C11#3376711yescharacteristic, complemented, Sylow
466C23—441no—
467C23C2×#432311yescharacteristic
468C23C2×#432311yescharacteristic
469C23C2×#432311yescharacteristic
470Q8—41no—
471Q8—41no—
472Q8—41no—
473Q8—41no—
474Q8—41no—
475Q8—82no—
476Q8—441no—
477Q8—441no—
478D4—41no—
479D4—41no—
480D4—41no—
481D4—441no—
482D4—441no—
483D4—882no—
484D4—1761no—
485D4—1761no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—82no—
497C2×C4—441no—
498C2×C4—441no—
499C2×C4—441no—
500C2×C4—882no—
501C2×C4—1761no—
502C2×C4C2×#432311yescharacteristic
503C2×C4C2×#432311yescharacteristic
504C2×C4C2×#432311yescharacteristic
505C2×C4C22×C22⋊D1111yescharacteristic
506C8—21no—
507C8—21no—
508C8—21no—
509C8#6703711yescharacteristic
510C8#6703711yescharacteristic
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—881no—
521C22—881no—
522C22—881no—
523C22C22×#432311yescharacteristic
524C4—21no—
525C4—21no—
526C4—21no—
527C4—81no—
528C4—81no—
529C4—81no—
530C4—81no—
531C4—881no—
532C4—881no—
533C4—881no—
534C4#1062333511yescharacteristic
535C4#1062335311yescharacteristic
536C2—41no—
537C2—41no—
538C2—41no—
539C2—1761no—
540C2#1307936411yescharacteristic
541C2#1308176011yescharacteristic
542C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3059C2
socleC22×C11C22×D8
prime radical#13078286C2
hypercenter#3059D11
hypocenterC11#33767
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ #3059

Complements

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

NH ≅ G/Ntype
2. #13070824C2semidirect
3. #13070816C2semidirect
4. #13070811C2semidirect
5. #13070807C2semidirect
6. #13070731C2semidirect
7. #13070722C2semidirect
8. #13070714C2semidirect
9. #13070705C2semidirect
10. #13070554C2semidirect
11. #13070554C2semidirect
12. #13070550C2semidirect
13. #13070533C2semidirect
14. #13070230C2semidirect
15. C11×#3059C2semidirect
196. #3059D11semidirect
465. C11#33767semidirect

Maximal subgroups

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

subgroupindex
#130782862
#130708242
#130708162
#130708112
#130708072
#130707312
#130707222
#130707142
#130707052
#130705542
#130705502
#130705332
#130702302
C11×#30592
#3376711