Finite Group Databasebeta

← #14910738

Subgroups — #14910738

Order 2816.

602 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080303C211yesmaximal, characteristic, complemented
2#13070855C211yesmaximal, characteristic, complemented
3#13070813C211yesmaximal, characteristic, complemented
4#13070801C211yesmaximal, characteristic, complemented
5#13070760C211yesmaximal, characteristic, complemented
6#13070717C211yesmaximal, characteristic, complemented
7#13070710C211yesmaximal, characteristic, complemented
8#13070671C211yesmaximal, characteristic, complemented
9#13070537C211yesmaximal, characteristic, complemented
10#13070527C211yesmaximal, characteristic, complemented
11#13070490C211yesmaximal, characteristic, complemented
12#13070442C211yesmaximal, characteristic, complemented
13#13070326C211yesmaximal, characteristic, complemented
14C2×#10622129C211yesmaximal, characteristic, complemented
15C11×#3334C211yesmaximal, characteristic, complemented
16C11×#547—21no—
17C2×#66957C2211yescharacteristic
18C22×D88C2211yescharacteristic
19#10623081—21no—
20C11×#500C2211yescharacteristic, complemented
21C11×#480—21no—
22C11×#480—21no—
23C11×#474—21no—
24C11×#466C2211yescharacteristic
25C11×#466C2211yescharacteristic, complemented
26C4×C11×D8C2211yescharacteristic, complemented
27C8×D4×C11C2211yescharacteristic
28C2×C11×#107C2211yescharacteristic
29C2×C11×#107C2211yescharacteristic, complemented
30C2×#66891C2211yescharacteristic, complemented
31C2×#66890C2211yescharacteristic
32C2×#66890C2211yescharacteristic
33#10622729C2211yescharacteristic
34#10622728C2211yescharacteristic
35C2×#66876C2211yescharacteristic, complemented
36C22×C11⋊C16C2211yescharacteristic
37#10622457—21no—
38#10622347—21no—
39#10622344—21no—
40#10622309C2211yescharacteristic
41C4×D88C2211yescharacteristic
42#10622200C2211yescharacteristic, 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#10622128C2211yescharacteristic, complemented
57C4⋊(C11⋊C16)C2211yescharacteristic, complemented
58#10622099C2211yescharacteristic, complemented
59C2×C11×#41—41no—
60C2×#4339—21no—
61C22×D44—21no—
62C2×C11×D8C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×C4⋊Q8—21no—
66C11×#123—41no—
67C11×#123—41no—
68C11×C22⋊Q8—41no—
69C11×#121—21no—
70C11×#121—21no—
71C4×D4×C11—21no—
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×#102—21no—
101C11×#102—21no—
102C11×#102—21no—
103C11×C22⋊C8D411yescharacteristic
104C11×C22⋊C8D411yescharacteristic
105C4×C8×C11C2311yescharacteristic
106#66891—41no—
107#66890—22no—
108#66890—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#33873—111nomaximal, Sylow
120C23×D11—41no—
121C11×#41—84no—
122C2×Q8×C11—41no—
123C2×D4×C11—21no—
124C2×D4×C11—41no—
125C2×D4×C11—41no—
126C2×D4×C11D811yescharacteristic
127C22×C4×C11—41no—
128C22×C4×C11—41no—
129C22×C4×C11—41no—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C2×C22⋊D11—41no—
133C2×C22⋊D11—41no—
134#4339—42no—
135#4339—81no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—42no—
139C2×D44—41no—
140C2×D44—81no—
141C2×C4×D11—41no—
142C2×C4×D11—41no—
143C2×Dic22—21no—
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—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—41no—
158C11×C4⋊C4—41no—
159C11×C4⋊C4—41no—
160C11×C4⋊C4D811yescharacteristic
161C11×C22⋊C4—41no—
162C11×C22⋊C4—41no—
163C11×C22⋊C4—41no—
164C11×C22⋊C4D811yescharacteristic
165C11×C22⋊C4D811yescharacteristic
166C42×C11C2×D411yescharacteristic
167C22⋊Dic11—41no—
168(C2×D11)⋊C4—41no—
169(C2×D11)⋊C4—41no—
170(C2×D11)⋊C4—41no—
171(C2×D11)⋊C4—41no—
172C4⋊Dic11—21no—
173Dic11⋊C4—41no—
174Dic44—21no—
175Dic44—21no—
176D88—21no—
177D88—21no—
178D88—21no—
179D88—42no—
180D88#4112yescomplemented
181#4314—42no—
182#4314—81no—
183C11⋊C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186C11⋊C16—21no—
187#3334D1111yescharacteristic, complemented
188#3280—111no—
189#2243—111no—
190#2235—111no—
191#2233—111no—
192#2226—111no—
193#2218—111no—
194#2217—111no—
195#2210—111no—
196#2186—111no—
197#2184—111no—
198#2177—111no—
199#2168—111no—
200#2139—111no—
201C2×#357—111no—
202C23×C11—41no—
203C23×C11C2×D811yescharacteristic
204C23×C11C2×D811yescharacteristic
205C22×D11—41no—
206C22×D11—41no—
207C22×D11—82no—
208C22×D11—82no—
209C22×D11—161no—
210Q8×C11—82no—
211D4×C11—22no—
212D4×C11—41no—
213D4×C11—41no—
214D4×C11—82no—
215D4×C11—82no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—82no—
224C2×C4×C11—82no—
225C2×C4×C11—82no—
226C2×C4×C11C2×D811yescharacteristic
227C2×C4×C11C2×D811yescharacteristic
228C2×C4×C11C2×D811yescharacteristic
229C2×C4×C11C2×D811yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C22⋊D11—82no—
232C22⋊D11—161no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235D44—22no—
236D44—41no—
237D44—41no—
238D44—41no—
239D44—82no—
240C4×D11—82no—
241C4×D11—161no—
242Dic22—41no—
243Dic22—41no—
244C8×C11—21no—
245C8×C11—21no—
246C8×C11—21no—
247C8×C11C2×#4111yescharacteristic
248C8×C11H(5,𝔽2)11yescharacteristic
249C2×#135—111no—
250C22×D8—111no—
251#547—21no—
252#546—221no—
253C2×SD32—111no—
254C2×D16—111no—
255C2×D16—111no—
256C2×M32—111no—
257C22×C16—111no—
258#500C2×D1111yescharacteristic, complemented
259#495—111no—
260#480—21no—
261#480—21no—
262#474—21no—
263#467—111no—
264#466—111no—
265#466C2×D1111yescharacteristic
266#466C2×D1111yescharacteristic, complemented
267#463—221no—
268#450—221no—
269#449—221no—
270C4×D8—111no—
271C4×D8C2×D1111yescharacteristic, complemented
272C8×D4C2×D1111yescharacteristic
273C2×#107C2×D1111yescharacteristic
274C2×#107C2×D1111yescharacteristic, complemented
275#367—111no—
276#367—111no—
277#367—111no—
278C4⋊C16—111no—
279#358—111no—
280#358—111no—
281#358—111no—
282#357—111no—
283#357—111no—
284#357—111no—
285#357—111no—
286#357—111no—
287#357—111no—
288#357—111no—
289C22⋊C16—111no—
290C22⋊C16—111no—
291#346—111no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11—81no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11#50912yes—
301C22×C11C22×D811yescharacteristic
302C2×D11—42no—
303C2×D11—81no—
304C2×D11—81no—
305C2×D11—81no—
306C2×D11—81no—
307C2×D11—81no—
308C2×D11—164no—
309C4×C11—21no—
310C4×C11—21no—
311C4×C11—21no—
312C4×C11—21no—
313C4×C11—81no—
314C4×C11—81no—
315C4×C11—81no—
316C4×C11#54611yescharacteristic
317C4×C11#57711yescharacteristic
318Dic11—81no—
319Dic11—81no—
320C2×#41—41no—
321C2×#41—221no—
322C22×D4—221no—
323#135—222no—
324#135—441no—
325C2×Q16—111no—
326C2×SD16—221no—
327C2×SD16—221no—
328C2×D8—111no—
329C2×D8—111no—
330C2×D8—222no—
331C2×D8—221no—
332C2×D8—441no—
333C2×D8C22×D1111yescharacteristic
334C22×C8C22×D1111yescharacteristic
335C22×C8C22×D1111yescharacteristic
336C4⋊Q8—21no—
337#124—221no—
338#123—41no—
339#123—41no—
340#123—441no—
341C22⋊Q8—41no—
342C22⋊Q8—221no—
343#121—21no—
344#121—21no—
345#121—221no—
346#121—441no—
347#120—441no—
348C4×D4—21no—
349C4×D4—221no—
350C4×D4C22⋊D1111yescharacteristic
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C22⋊C4—441no—
354SD32—441no—
355D16—222no—
356D16—441no—
357M32—441no—
358C2×C16—111no—
359C2×C16—111no—
360C2×C16—111no—
361C2×C16—111no—
362C2×C16—441no—
363#107—21no—
364#107—21no—
365#107—21no—
366#107—111no—
367#107C22×D1111yescharacteristic
368#107C22×D1111yescharacteristic
369#107C22×D1111yescharacteristic
370C4⋊C8C22⋊D1111yescharacteristic
371#103—221no—
372#102—21no—
373#102—21no—
374#102—21no—
375#102—221no—
376#102—221no—
377C22⋊C8C22⋊D1111yescharacteristic
378C22⋊C8C22⋊D1111yescharacteristic
379C4×C8C22×D1111yescharacteristic
380C2×C11—22no—
381C2×C11—41no—
382C2×C11—161no—
383C2×C11#329411yescharacteristic
384C2×C11C2×#50911yescharacteristic
385C2×C11#341611yescharacteristic
386D11—82no—
387D11—161no—
388C24—441no—
389#41—84no—
390#41—442no—
391#41—881no—
392C2×Q8—41no—
393C2×Q8—221no—
394C2×D4—21no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—221no—
398C2×D4—221no—
399C2×D4—442no—
400C2×D4—441no—
401C2×D4—441no—
402C2×D4—441no—
403C2×D4—881no—
404C2×D4#432311yescharacteristic
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—441no—
409C22×C4—441no—
410C22×C4C2×C22⋊D1111yescharacteristic
411C22×C4C2×C22⋊D1111yescharacteristic
412Q16—221no—
413Q16—221no—
414SD16—442no—
415SD16—881no—
416D8—21no—
417D8—21no—
418D8—112no—
419D8—221no—
420D8—221no—
421D8—221no—
422D8—442no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8C2×C22⋊D1111yescharacteristic
428C2×C8C2×C22⋊D1111yescharacteristic
429C2×C8C2×C22⋊D1111yescharacteristic
430C2×C8C23×D1111yescharacteristic
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—41no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C4⋊C4—221no—
438C4⋊C4—441no—
439C4⋊C4#432311yescharacteristic
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—441no—
444C22⋊C4—441no—
445C22⋊C4—441no—
446C22⋊C4—441no—
447C22⋊C4—441no—
448C22⋊C4#432311yescharacteristic
449C22⋊C4#432311yescharacteristic
450C42C2×C22⋊D1111yescharacteristic
451C16—221no—
452C16—221no—
453C16—221no—
454C16—221no—
455C11#3387311yescharacteristic, complemented, Sylow
456C23—41no—
457C23—441no—
458C23—441no—
459C23—882no—
460C23—882no—
461C23—1761no—
462C23C2×#432311yescharacteristic
463C23C2×#432311yescharacteristic
464Q8—82no—
465Q8—441no—
466Q8—441no—
467D4—22no—
468D4—41no—
469D4—41no—
470D4—82no—
471D4—82no—
472D4—222no—
473D4—441no—
474D4—441no—
475D4—441no—
476D4—882no—
477D4—882no—
478D4—1761no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—82no—
487C2×C4—82no—
488C2×C4—82no—
489C2×C4—441no—
490C2×C4—441no—
491C2×C4—882no—
492C2×C4—1761no—
493C2×C4C2×#432311yescharacteristic
494C2×C4C2×#432311yescharacteristic
495C2×C4C2×#432311yescharacteristic
496C2×C4C2×#432311yescharacteristic
497C2×C4C22×C22⋊D1111yescharacteristic
498C8—21no—
499C8—21no—
500C8—21no—
501C8#41×D1111yescharacteristic
502C8#6704211yescharacteristic
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—442no—
512C22—881no—
513C22—881no—
514C22—881no—
515C22—881no—
516C22—881no—
517C22—1764no—
518C22#1062276012yes—
519C22C22×#432311yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—81no—
525C4—81no—
526C4—81no—
527C4—881no—
528C4—881no—
529C4#1062336011yescharacteristic
530C4#1062336811yescharacteristic
531C2—22no—
532C2—41no—
533C2—161no—
534C2—882no—
535C2—1761no—
536C2#1308042311yescharacteristic
537C2C2×#1062276011yescharacteristic
538C2#1308176011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3334C2
socleC22×C11C22×D8
hypercenter#3334D11
hypocenterC11#33873
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3334

Complements

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

NH ≅ G/Ntype
1. #13080303C2semidirect
2. #13070855C2semidirect
3. #13070813C2semidirect
4. #13070801C2semidirect
5. #13070760C2semidirect
6. #13070717C2semidirect
7. #13070710C2semidirect
8. #13070671C2semidirect
9. #13070537C2semidirect
10. #13070527C2semidirect
11. #13070490C2semidirect
12. #13070442C2semidirect
13. #13070326C2semidirect
14. C2×#10622129C2semidirect
15. C11×#3334C2semidirect
20. C11×#500C22semidirect
25. C11×#466C22semidirect
26. C4×C11×D8C22semidirect
29. C2×C11×#107C22semidirect
30. C2×#66891C22semidirect
35. C2×#66876C22semidirect
42. #10622200C22semidirect
44. C22⋊(C11⋊C16)C22semidirect
45. #10622130C22semidirect
46. #10622130C22semidirect
47. #10622130C22semidirect
54. #10622128C22semidirect
55. #10622128C22semidirect
56. #10622128C22semidirect
57. C4⋊(C11⋊C16)C22semidirect
58. #10622099C22semidirect
180. D88#41semidirect
187. #3334D11semidirect
258. #500C2×D11semidirect
266. #466C2×D11semidirect
271. C4×D8C2×D11semidirect
274. C2×#107C2×D11semidirect
455. C11#33873semidirect

Maximal subgroups

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

subgroupindex
#130803032
#130708552
#130708132
#130708012
#130707602
#130707172
#130707102
#130706712
#130705372
#130705272
#130704902
#130704422
#130703262
C2×#106221292
C11×#33342
#3387311