Finite Group Databasebeta

← #14910843

Subgroups — #14910843

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#13080359C211yesmaximal, characteristic
2#13070855C211yesmaximal, characteristic, complemented
3#13070824C211yesmaximal, characteristic, complemented
4#13070807C211yesmaximal, characteristic, complemented
5#13070765C211yesmaximal, characteristic, complemented
6#13070731C211yesmaximal, characteristic, complemented
7#13070705C211yesmaximal, characteristic, complemented
8#13070678C211yesmaximal, characteristic, complemented
9#13070554C211yesmaximal, characteristic, complemented
10#13070549C211yesmaximal, characteristic, complemented
11#13070485C211yesmaximal, characteristic, complemented
12#13070442C211yesmaximal, characteristic, complemented
13#13070335C211yesmaximal, characteristic, complemented
14#13070321C211yesmaximal, characteristic, complemented
15C11×#3342C211yesmaximal, characteristic, complemented
16C11×#556—21no—
17C22×Dic44C2211yescharacteristic
18C2×#66957C2211yescharacteristic
19#10623083—21no—
20C11×#500C2211yescharacteristic
21C11×#485—21no—
22C11×#485—21no—
23C11×#475—21no—
24C11×#467C2211yescharacteristic
25C11×#467C2211yescharacteristic
26C4×C11×Q16C2211yescharacteristic
27C8×D4×C11C2211yescharacteristic
28C11×#427C2211yescharacteristic
29C11×#427C2211yescharacteristic
30C2×#66893C2211yescharacteristic
31C2×#66893C2211yescharacteristic
32C2×#66892C2211yescharacteristic
33#10622729C2211yescharacteristic
34#10622728C2211yescharacteristic
35C2×#66876C2211yescharacteristic
36C22×C11⋊C16C2211yescharacteristic
37#10622458—21no—
38#10622351—21no—
39#10622346—21no—
40C4×Dic44C2211yescharacteristic
41#10622309C2211yescharacteristic
42#10622202C2211yescharacteristic
43C22⋊(C11⋊C16)C2211yescharacteristic
44C22⋊(C11⋊C16)C2211yescharacteristic
45#10622130C2211yescharacteristic
46#10622130C2211yescharacteristic
47#10622130C2211yescharacteristic
48#10622130C2211yescharacteristic
49#10622130C2211yescharacteristic
50#10622130C2211yescharacteristic
51#10622129C2211yescharacteristic
52#10622129C2211yescharacteristic
53#10622129C2211yescharacteristic
54#10622128C2211yescharacteristic
55#10622127C2211yescharacteristic
56#10622127C2211yescharacteristic
57C4⋊(C11⋊C16)C2211yescharacteristic
58#10622099C2211yescharacteristic
59C2×#4339—21no—
60C22×Dic22—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#66992—41no—
76#66983—21no—
77#66977—21no—
78C2×Dic44—22no—
79C2×Dic44—21no—
80C2×Dic44—41no—
81C2×Dic44C2311yescharacteristic
82C2×Dic44C2311yescharacteristic
83#66957—22no—
84#66957—41no—
85C2×D88C2311yescharacteristic
86C2×#4314—21no—
87C2×#4314—21no—
88#66949—41no—
89#66938—41no—
90(C22⋊D11)⋊C4—41no—
91#66928—21no—
92C4×Dic22—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—22no—
107#66893—41no—
108#66892—41no—
109#66885—21no—
110#66882C2311yescharacteristic
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
120C2×Q8×C11—21no—
121C2×Q8×C11—41no—
122C2×D4×C11D811yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C2×C22⋊D11—41no—
126C2×C22⋊D11—41no—
127C22×Dic11—41no—
128#4339—42no—
129#4339—81no—
130C2×D44—21no—
131C2×C4×D11—41no—
132C2×Dic22—21no—
133C2×Dic22—21no—
134C2×Dic22—42no—
135C2×Dic22—41no—
136C2×Dic22—81no—
137C11×Q16—21no—
138C11×Q16—21no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11—21no—
142C2×C8×C11—21no—
143C2×C8×C11C2×D411yescharacteristic
144C2×C8×C11C2×D411yescharacteristic
145C2×C8×C11C2×D411yescharacteristic
146C2×C8×C11C2411yescharacteristic
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—41no—
151C11×C4⋊C4—41no—
152C11×C4⋊C4—41no—
153C11×C4⋊C4—41no—
154C11×C4⋊C4D811yescharacteristic
155C11×C22⋊C4—41no—
156C11×C22⋊C4—41no—
157C11×C22⋊C4—41no—
158C11×C22⋊C4—41no—
159C11×C22⋊C4D811yescharacteristic
160C11×C22⋊C4D811yescharacteristic
161C42×C11—41no—
162C42×C11—41no—
163C42×C11—41no—
164C42×C11C2×D411yescharacteristic
165C22⋊Dic11—41no—
166(C2×D11)⋊C4—41no—
167(C2×D11)⋊C4—41no—
168(C2×D11)⋊C4—41no—
169C4⋊Dic11—21no—
170Dic11⋊C4—41no—
171Dic11⋊C4—41no—
172C4×Dic11—41no—
173Dic44—21no—
174Dic44—21no—
175Dic44—21no—
176Dic44—42no—
177Dic44#4112yes—
178D88—21no—
179D88—21no—
180#4314—42no—
181#4314—81no—
182C11⋊C16—21no—
183C11⋊C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3342D1111yescharacteristic, complemented
187#3285—111no—
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×C11C2×D811yescharacteristic
202C23×C11C2×D811yescharacteristic
203C22×D11—41no—
204Q8×C11—41no—
205Q8×C11—41no—
206Q8×C11—82no—
207D4×C11—41no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11C2×D811yescharacteristic
217C2×C4×C11C2×D811yescharacteristic
218C2×C4×C11C2×D811yescharacteristic
219C2×C4×C11C2×D811yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C22⋊D11—82no—
222C22⋊D11—82no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—82no—
227D44—41no—
228D44—41no—
229C4×D11—82no—
230Dic22—22no—
231Dic22—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×#135—111no—
241C22×Q16—111no—
242#556—21no—
243#548—221no—
244C2×Q32—111no—
245C2×Q32—111no—
246C2×SD32—111no—
247C2×M32—111no—
248C22×C16—111no—
249#500C2×D1111yescharacteristic
250#495—111no—
251#485—21no—
252#485—21no—
253#475—21no—
254#467—111no—
255#467C2×D1111yescharacteristic
256#467C2×D1111yescharacteristic
257#466—111no—
258#464—221no—
259#452—221no—
260#448—221no—
261C4×Q16—111no—
262C4×Q16C2×D1111yescharacteristic
263C8×D4C2×D1111yescharacteristic
264#427C2×D1111yescharacteristic
265#427C2×D1111yescharacteristic
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×C11C22×D811yescharacteristic
290C2×D11—81no—
291C2×D11—81no—
292C2×D11—81no—
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—21no—
297C4×C11—81no—
298C4×C11—81no—
299C4×C11—81no—
300C4×C11—81no—
301C4×C11#54611yescharacteristic
302C4×C11#57711yescharacteristic
303Dic11—42no—
304Dic11—81no—
305Dic11—81no—
306C2×#41—221no—
307C22×Q8—221no—
308#135—222no—
309#135—441no—
310C2×Q16—111no—
311C2×Q16—111no—
312C2×Q16—222no—
313C2×Q16—221no—
314C2×Q16—441no—
315C2×Q16C22×D1111yescharacteristic
316C2×SD16—221no—
317C2×SD16—221no—
318C2×D8—111no—
319C22×C8C22×D1111yescharacteristic
320C22×C8C22×D1111yescharacteristic
321C4⋊Q8—21no—
322#126—41no—
323#126—41no—
324#124—41no—
325#124—221no—
326#124—441no—
327C22⋊Q8—21no—
328C22⋊Q8—21no—
329C22⋊Q8—221no—
330C22⋊Q8—441no—
331#121—221no—
332#121—441no—
333C4×Q8—21no—
334C4×Q8—41no—
335C4×Q8—221no—
336C4×D4—441no—
337C4×D4C22⋊D1111yescharacteristic
338#117—21no—
339#117—21no—
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—21no—
350#107—111no—
351#107C22×D1111yescharacteristic
352#107C22×D1111yescharacteristic
353#107C22×D1111yescharacteristic
354#106—21no—
355#106—21no—
356C4⋊C8C22⋊D1111yescharacteristic
357#103—21no—
358#103—21no—
359#103—21no—
360#103—221no—
361#103—221no—
362#102—221no—
363C22⋊C8C22⋊D1111yescharacteristic
364C22⋊C8C22⋊D1111yescharacteristic
365C4×C8C22×D1111yescharacteristic
366C2×C11—41no—
367C2×C11—41no—
368C2×C11#329411yescharacteristic
369C2×C11#341411yescharacteristic
370C2×C11#341711yescharacteristic
371D11—161no—
372#41—442no—
373#41—881no—
374C2×Q8—21no—
375C2×Q8—41no—
376C2×Q8—221no—
377C2×Q8—221no—
378C2×Q8—442no—
379C2×Q8—441no—
380C2×Q8—881no—
381C2×D4—221no—
382C2×D4—441no—
383C2×D4—441no—
384C2×D4#432311yescharacteristic
385C22×C4—441no—
386C22×C4—441no—
387C22×C4C2×C22⋊D1111yescharacteristic
388C22×C4C2×C22⋊D1111yescharacteristic
389Q16—21no—
390Q16—21no—
391Q16—112no—
392Q16—221no—
393Q16—221no—
394Q16—221no—
395Q16—442no—
396SD16—442no—
397SD16—881no—
398D8—221no—
399D8—221no—
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—21no—
410C4⋊C4—21no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4—221no—
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—41no—
431C42—41no—
432C42—441no—
433C42C2×C22⋊D1111yescharacteristic
434C16—221no—
435C16—221no—
436C16—221no—
437C16—221no—
438C11#3388011yescharacteristic, complemented, Sylow
439C23—441no—
440C23C2×#432311yescharacteristic
441C23C2×#432311yescharacteristic
442Q8—41no—
443Q8—41no—
444Q8—82no—
445Q8—222no—
446Q8—441no—
447Q8—441no—
448Q8—441no—
449Q8—882no—
450D4—41no—
451D4—441no—
452D4—441no—
453D4—882no—
454D4—882no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—882no—
467C2×C4—882no—
468C2×C4C2×#432311yescharacteristic
469C2×C4C2×#432311yescharacteristic
470C2×C4C2×#432311yescharacteristic
471C2×C4C2×#432311yescharacteristic
472C2×C4C22×C22⋊D1111yescharacteristic
473C8—21no—
474C8—21no—
475C8—21no—
476C8#41×D1111yescharacteristic
477C8#6704211yescharacteristic
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—881no—
485C22—881no—
486C22—881no—
487C22C22×#432311yescharacteristic
488C4—21no—
489C4—21no—
490C4—21no—
491C4—21no—
492C4—81no—
493C4—81no—
494C4—81no—
495C4—81no—
496C4—442no—
497C4—881no—
498C4—881no—
499C4#1062336011yescharacteristic
500C4#1062336811yescharacteristic
501C2—41no—
502C2—41no—
503C2—1761no—
504C2#1308042311yescharacteristic
505C2#1308175011yescharacteristic
506C2#1308176711yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3342C2
socleC22×C11C22×D8
prime radical#13080359C2
hypercenter#3342D11
hypocenterC11#33880
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. #13070765C2semidirect
6. #13070731C2semidirect
7. #13070705C2semidirect
8. #13070678C2semidirect
9. #13070554C2semidirect
10. #13070549C2semidirect
11. #13070485C2semidirect
12. #13070442C2semidirect
13. #13070335C2semidirect
14. #13070321C2semidirect
15. C11×#3342C2semidirect
186. #3342D11semidirect
438. C11#33880semidirect

Maximal subgroups

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

subgroupindex
#130803592
#130708552
#130708242
#130708072
#130707652
#130707312
#130707052
#130706782
#130705542
#130705492
#130704852
#130704422
#130703352
#130703212
C11×#33422
#3388011