Finite Group Databasebeta

← #14910849

Subgroups — #14910849

Order 2816.

540 conjugacy classes of subgroups.

The subgroup lattice has 508 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#13070768C211yesmaximal, characteristic, complemented
6#13070727C211yesmaximal, characteristic, complemented
7#13070705C211yesmaximal, characteristic, complemented
8#13070675C211yesmaximal, characteristic, complemented
9#13070556C211yesmaximal, characteristic, complemented
10#13070550C211yesmaximal, characteristic, complemented
11#13070485C211yesmaximal, characteristic, complemented
12#13070442C211yesmaximal, characteristic, complemented
13#13070336C211yesmaximal, characteristic, complemented
14#13070323C211yesmaximal, characteristic, complemented
15C11×#3285C211yesmaximal, characteristic
16C2×C11×#135C2211yescharacteristic
17C22×C11×Q16C2211yescharacteristic
18C11×#548—21no—
19#10623073—21no—
20C11×#495C2211yescharacteristic
21C11×#467C2211yescharacteristic
22C11×#466C2211yescharacteristic
23C11×#464—21no—
24C11×#452—21no—
25C11×#448—21no—
26C4×C11×Q16C2211yescharacteristic
27C8×D4×C11C2211yescharacteristic
28C2×#66893C2211yescharacteristic
29C2×#66893C2211yescharacteristic
30C2×#66891C2211yescharacteristic
31#10622729C2211yescharacteristic
32#10622729C2211yescharacteristic
33#10622719C2211yescharacteristic
34#10622719C2211yescharacteristic
35C2×#66876C2211yescharacteristic
36C22×C11⋊C16C2211yescharacteristic
37#10622464—21no—
38#10622336—21no—
39#10622336—21no—
40C4×Dic44C2211yescharacteristic
41#10622295C2211yescharacteristic
42#10622202C2211yescharacteristic
43#10622202C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622202C2211yescharacteristic
47#10622202C2211yescharacteristic
48#10622200C2211yescharacteristic
49#10622200C2211yescharacteristic
50#10622200C2211yescharacteristic
51C22⋊(C11⋊C16)C2211yescharacteristic
52C22⋊(C11⋊C16)C2211yescharacteristic
53#10622130C2211yescharacteristic
54#10622128C2211yescharacteristic
55#10622127C2211yescharacteristic
56#10622127C2211yescharacteristic
57C4⋊(C11⋊C16)C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×C11×#41—21no—
60C22×Q8×C11—21no—
61C11×#135—22no—
62C11×#135—41no—
63C2×C11×Q16—22no—
64C2×C11×Q16—21no—
65C2×C11×Q16—41no—
66C2×C11×Q16C2311yescharacteristic
67C2×C11×Q16C2311yescharacteristic
68C2×C11×SD16—21no—
69C2×C11×SD16—21no—
70C2×C11×D8C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×#124—21no—
74C11×#124—41no—
75C11×C22⋊Q8—21no—
76C11×C22⋊Q8—41no—
77C11×#121—21no—
78C11×#121—41no—
79C4×Q8×C11—21no—
80C4×D4×C11—41no—
81C4×D4×C11D411yescharacteristic
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×#103—21no—
97C11×#102—21no—
98C11×C22⋊C8D411yescharacteristic
99C11×C22⋊C8D411yescharacteristic
100C4×C8×C11C2311yescharacteristic
101#66893—22no—
102#66893—41no—
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#33880—111nomaximal, Sylow
120C11×#41—42no—
121C11×#41—81no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—42no—
125C2×Q8×C11—41no—
126C2×Q8×C11—81no—
127C2×D4×C11—21no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11D811yescharacteristic
131C22×C4×C11—41no—
132C22×C4×C11—41no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C2×Dic22—21no—
136C2×Dic22—41no—
137C11×Q16—21no—
138C11×Q16—21no—
139C11×Q16—21no—
140C11×Q16—42no—
141C11×Q16#4112yes—
142C11×SD16—42no—
143C11×SD16—81no—
144C11×D8—21no—
145C11×D8—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11C2×D411yescharacteristic
151C2×C8×C11C2×D411yescharacteristic
152C2×C8×C11C2×D411yescharacteristic
153C2×C8×C11C2411yescharacteristic
154C11×C4⋊C4—21no—
155C11×C4⋊C4—41no—
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⋊C4D811yescharacteristic
163C11×C22⋊C4D811yescharacteristic
164C42×C11—41no—
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#3285D1111yescharacteristic
188#2243—111no—
189#2237—111no—
190#2234—111no—
191#2227—111no—
192#2220—111no—
193#2216—111no—
194#2211—111no—
195#2189—111no—
196#2188—111no—
197#2176—111no—
198#2168—111no—
199#2141—111no—
200#2138—111no—
201C23×C11—41no—
202C23×C11C2×D811yescharacteristic
203C23×C11C2×D811yescharacteristic
204Q8×C11—22no—
205Q8×C11—41no—
206Q8×C11—41no—
207Q8×C11—41no—
208Q8×C11—82no—
209D4×C11—41no—
210D4×C11—41no—
211D4×C11—41no—
212D4×C11—82no—
213D4×C11—82no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—82no—
222C2×C4×C11—82no—
223C2×C4×C11C2×D811yescharacteristic
224C2×C4×C11C2×D811yescharacteristic
225C2×C4×C11C2×D811yescharacteristic
226C2×C4×C11C2×D811yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—41no—
232Dic22—41no—
233Dic22—41no—
234Dic22—82no—
235C8×C11—21no—
236C8×C11—21no—
237C8×C11—21no—
238C8×C11C2×#4111yescharacteristic
239C8×C11H(5,𝔽2)11yescharacteristic
240C2×#135C2×D1111yescharacteristic
241C22×Q16C2×D1111yescharacteristic
242#556—221no—
243#548—21no—
244C2×Q32—111no—
245C2×Q32—111no—
246C2×SD32—111no—
247C2×M32—111no—
248C22×C16—111no—
249#500—111no—
250#495C2×D1111yescharacteristic
251#485—221no—
252#485—221no—
253#475—221no—
254#467—111no—
255#467—111no—
256#467C2×D1111yescharacteristic
257#466C2×D1111yescharacteristic
258#464—21no—
259#452—21no—
260#448—21no—
261C4×Q16—111no—
262C4×Q16C2×D1111yescharacteristic
263C8×D4C2×D1111yescharacteristic
264#427—111no—
265#427—111no—
266#367—111no—
267#366—111no—
268#366—111no—
269C4⋊C16—111no—
270#358—111no—
271#358—111no—
272#358—111no—
273#358—111no—
274#358—111no—
275#358—111no—
276#358—111no—
277#357—111no—
278#357—111no—
279#357—111no—
280C22⋊C16—111no—
281C22⋊C16—111no—
282#346—111no—
283C22×C11—21no—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—21no—
289C22×C11—81no—
290C22×C11—81no—
291C22×C11—81no—
292C22×C11C22×D811yescharacteristic
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—21no—
297C4×C11—42no—
298C4×C11—81no—
299C4×C11—81no—
300C4×C11#54611yescharacteristic
301C4×C11#57711yescharacteristic
302Dic11—81no—
303Dic11—81no—
304Dic11—81no—
305Dic11—81no—
306C2×#41—21no—
307C22×Q8—21no—
308#135—22no—
309#135—41no—
310C2×Q16—22no—
311C2×Q16—21no—
312C2×Q16—41no—
313C2×Q16—111no—
314C2×Q16C22×D1111yescharacteristic
315C2×Q16C22×D1111yescharacteristic
316C2×SD16—21no—
317C2×SD16—21no—
318C2×D8C22×D1111yescharacteristic
319C22×C8C22×D1111yescharacteristic
320C22×C8C22×D1111yescharacteristic
321C4⋊Q8—221no—
322#126—441no—
323#126—441no—
324#124—21no—
325#124—41no—
326#124—441no—
327C22⋊Q8—21no—
328C22⋊Q8—41no—
329C22⋊Q8—221no—
330C22⋊Q8—221no—
331#121—21no—
332#121—41no—
333C4×Q8—21no—
334C4×Q8—221no—
335C4×Q8—441no—
336C4×D4—41no—
337C4×D4C22⋊D1111yescharacteristic
338#117—221no—
339#117—221no—
340Q32—222no—
341Q32—441no—
342SD32—441no—
343M32—441no—
344C2×C16—111no—
345C2×C16—111no—
346C2×C16—111no—
347C2×C16—111no—
348C2×C16—441no—
349#107—111no—
350#107—111no—
351#107—111no—
352#107—221no—
353#107C22×D1111yescharacteristic
354#106—221no—
355#106—221no—
356C4⋊C8C22⋊D1111yescharacteristic
357#103—21no—
358#103—21no—
359#103—221no—
360#103—221no—
361#103—221no—
362#102—21no—
363C22⋊C8C22⋊D1111yescharacteristic
364C22⋊C8C22⋊D1111yescharacteristic
365C4×C8C22×D1111yescharacteristic
366C2×C11—41no—
367C2×C11—41no—
368C2×C11—161no—
369C2×C11#329411yescharacteristic
370C2×C11#341411yescharacteristic
371C2×C11#341711yescharacteristic
372#41—42no—
373#41—81no—
374C2×Q8—21no—
375C2×Q8—21no—
376C2×Q8—42no—
377C2×Q8—41no—
378C2×Q8—81no—
379C2×Q8—221no—
380C2×Q8—441no—
381C2×D4—21no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4#432311yescharacteristic
385C22×C4—41no—
386C22×C4—41no—
387C22×C4C2×C22⋊D1111yescharacteristic
388C22×C4C2×C22⋊D1111yescharacteristic
389Q16—21no—
390Q16—21no—
391Q16—21no—
392Q16—42no—
393Q16—221no—
394Q16—221no—
395Q16#434112yes—
396SD16—42no—
397SD16—81no—
398D8—21no—
399D8—21no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8C2×C22⋊D1111yescharacteristic
405C2×C8C2×C22⋊D1111yescharacteristic
406C2×C8C2×C22⋊D1111yescharacteristic
407C2×C8C23×D1111yescharacteristic
408C4⋊C4—21no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C4⋊C4—221no—
414C4⋊C4—441no—
415C4⋊C4—441no—
416C4⋊C4—441no—
417C4⋊C4—441no—
418C4⋊C4#432311yescharacteristic
419C22⋊C4—41no—
420C22⋊C4—41no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—441no—
424C22⋊C4—441no—
425C22⋊C4—441no—
426C22⋊C4—441no—
427C22⋊C4#432311yescharacteristic
428C22⋊C4#432311yescharacteristic
429C42—41no—
430C42—441no—
431C42—441no—
432C42—441no—
433C42C2×C22⋊D1111yescharacteristic
434C16—221no—
435C16—221no—
436C16—221no—
437C16—221no—
438C11#3388011yescharacteristic, complemented, Sylow
439C23—41no—
440C23C2×#432311yescharacteristic
441C23C2×#432311yescharacteristic
442Q8—22no—
443Q8—41no—
444Q8—41no—
445Q8—41no—
446Q8—82no—
447Q8—441no—
448Q8—441no—
449Q8—882no—
450D4—41no—
451D4—41no—
452D4—41no—
453D4—82no—
454D4—82no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—82no—
463C2×C4—82no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4C2×#432311yescharacteristic
469C2×C4C2×#432311yescharacteristic
470C2×C4C2×#432311yescharacteristic
471C2×C4C2×#432311yescharacteristic
472C2×C4C22×C22⋊D1111yescharacteristic
473C8—21no—
474C8—21no—
475C8—21no—
476C8C2×#434111yescharacteristic
477C8#6703711yescharacteristic
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—81no—
485C22—81no—
486C22—81no—
487C22C22×#432311yescharacteristic
488C4—21no—
489C4—21no—
490C4—21no—
491C4—21no—
492C4—42no—
493C4—81no—
494C4—81no—
495C4—881no—
496C4—881no—
497C4—881no—
498C4—881no—
499C4#1062333711yescharacteristic
500C4#1062336711yescharacteristic
501C2—41no—
502C2—41no—
503C2—161no—
504C2#1308042911yescharacteristic
505C2#1308175011yescharacteristic
506C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
Fitting, prime radicalC11×#3285C2
socleC22×C11C22×D8
hypercenter#3285D11
hypocenterC11#33880
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3285

Complements

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

NH ≅ G/Ntype
1. #13081047C2semidirect
2. #13070852C2semidirect
3. #13070821C2semidirect
4. #13070804C2semidirect
5. #13070768C2semidirect
6. #13070727C2semidirect
7. #13070705C2semidirect
8. #13070675C2semidirect
9. #13070556C2semidirect
10. #13070550C2semidirect
11. #13070485C2semidirect
12. #13070442C2semidirect
13. #13070336C2semidirect
14. #13070323C2semidirect
438. C11#33880semidirect

Maximal subgroups

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

subgroupindex
#130810472
#130708522
#130708212
#130708042
#130707682
#130707272
#130707052
#130706752
#130705562
#130705502
#130704852
#130704422
#130703362
#130703232
C11×#32852
#3388011