Finite Group Databasebeta

← #14910744

Subgroups — #14910744

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#13080964C211yesmaximal, characteristic, complemented
2#13070852C211yesmaximal, characteristic, complemented
3#13070811C211yesmaximal, characteristic, complemented
4#13070799C211yesmaximal, characteristic, complemented
5#13070763C211yesmaximal, characteristic, complemented
6#13070717C211yesmaximal, characteristic, complemented
7#13070714C211yesmaximal, characteristic, complemented
8#13070668C211yesmaximal, characteristic, complemented
9#13070539C211yesmaximal, characteristic, complemented
10#13070528C211yesmaximal, characteristic, complemented
11#13070490C211yesmaximal, characteristic, complemented
12#13070442C211yesmaximal, characteristic, complemented
13#13070328C211yesmaximal, characteristic, complemented
14C2×#10622200C211yesmaximal, characteristic, complemented
15C11×#3280C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C11×#546—21no—
19#10623086—21no—
20C11×#495C2211yescharacteristic
21C11×#467C2211yescharacteristic
22C11×#466C2211yescharacteristic
23C11×#463—21no—
24C11×#450—21no—
25C11×#449—21no—
26C4×C11×D8C2211yescharacteristic
27C8×D4×C11C2211yescharacteristic
28C2×#66892C2211yescharacteristic, complemented
29C2×#66890C2211yescharacteristic
30C2×#66890C2211yescharacteristic
31#10622728C2211yescharacteristic
32#10622728C2211yescharacteristic, complemented
33C2×#66882C2211yescharacteristic
34C2×#66882C2211yescharacteristic, complemented
35C2×#66876C2211yescharacteristic, complemented
36C22×C11⋊C16C2211yescharacteristic
37#10622459—21no—
38#10622349—21no—
39#10622349—21no—
40C4×D88C2211yescharacteristic, complemented
41#10622295C2211yescharacteristic, complemented
42#10622202C2211yescharacteristic, complemented
43#10622202C2211yescharacteristic, complemented
44#10622202C2211yescharacteristic, complemented
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622200C2211yescharacteristic
49#10622200C2211yescharacteristic
50#10622200C2211yescharacteristic
51C22⋊(C11⋊C16)C2211yescharacteristic
52C22⋊(C11⋊C16)C2211yescharacteristic, complemented
53#10622129C2211yescharacteristic, complemented
54#10622128C2211yescharacteristic, complemented
55#10622128C2211yescharacteristic, complemented
56#10622128C2211yescharacteristic, complemented
57C4⋊(C11⋊C16)C2211yescharacteristic, complemented
58#10622099C2211yescharacteristic, complemented
59C2×C11×#41—21no—
60C22×D4×C11—21no—
61C2×#4341—41no—
62C11×#135—22no—
63C11×#135—41no—
64C2×C11×Q16C2311yescharacteristic
65C2×C11×SD16—21no—
66C2×C11×SD16—21no—
67C2×C11×D8—22no—
68C2×C11×D8—21no—
69C2×C11×D8—41no—
70C2×C11×D8C2311yescharacteristic
71C2×C11×D8C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C11×#124—21no—
75C11×#123—41no—
76C11×C22⋊Q8—21no—
77C11×#121—21no—
78C11×#121—41no—
79C11×#120—41no—
80C4×D4×C11—21no—
81C4×D4×C11D411yescharacteristic
82C2×C11×C22⋊C4—41no—
83#66983—21no—
84#66983—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×D88C2311yescharacteristic
88#66950—41no—
89#66939—41no—
90#66939—41no—
91C4×D44—21no—
92#66922—21no—
93C11×#107C2311yescharacteristic
94C11×C4⋊C8D411yescharacteristic
95C11×#103—21no—
96C11×#102—21no—
97C11×#102—21no—
98C11×C22⋊C8D411yescharacteristic
99C11×C22⋊C8D411yescharacteristic
100C4×C8×C11C2311yescharacteristic
101#66892—41no—
102#66890—22no—
103#66890—41no—
104#66885—21no—
105#66885—21no—
106#66885—21no—
107#66882—21no—
108#66882—21no—
109#66882—21no—
110#66882C2311yescharacteristic
111#66882C2311yescharacteristic
112#66882C2311yescharacteristic
113#66876—41no—
114C2×C11⋊C16—41no—
115C2×C11⋊C16C2311yescharacteristic
116C2×C11⋊C16C2311yescharacteristic
117C2×C11⋊C16C2311yescharacteristic
118C2×C11⋊C16C2311yescharacteristic
119#33873—111nomaximal, Sylow
120C24×C11—41no—
121C11×#41—42no—
122C11×#41—81no—
123C2×Q8×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—42no—
127C2×D4×C11—41no—
128C2×D4×C11—41no—
129C2×D4×C11—41no—
130C2×D4×C11—81no—
131C2×D4×C11D811yescharacteristic
132C22×C4×C11—41no—
133C22×C4×C11—41no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C2×C22⋊D11—41no—
137C2×C22⋊D11—41no—
138C22×Dic11—41no—
139C22×Dic11—41no—
140#4341—84no—
141C2×D44—21no—
142C2×C4×D11—41no—
143C2×Dic22—41no—
144C11×Q16—21no—
145C11×Q16—21no—
146C11×SD16—42no—
147C11×SD16—81no—
148C11×D8—21no—
149C11×D8—21no—
150C11×D8—21no—
151C11×D8—42no—
152C11×D8#4112yescomplemented
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11C2×D411yescharacteristic
158C2×C8×C11C2×D411yescharacteristic
159C2×C8×C11C2×D411yescharacteristic
160C2×C8×C11C2411yescharacteristic
161C11×C4⋊C4—21no—
162C11×C4⋊C4—41no—
163C11×C4⋊C4D811yescharacteristic
164C11×C22⋊C4—41no—
165C11×C22⋊C4—41no—
166C11×C22⋊C4—41no—
167C11×C22⋊C4—41no—
168C11×C22⋊C4—41no—
169C11×C22⋊C4D811yescharacteristic
170C11×C22⋊C4D811yescharacteristic
171C42×C11C2×D411yescharacteristic
172(C2×D11)⋊C4—41no—
173(C2×D11)⋊C4—41no—
174(C2×D11)⋊C4—41no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—41no—
179C4⋊Dic11—41no—
180C4⋊Dic11—41no—
181D88—21no—
182D88—21no—
183C11⋊C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186C11⋊C16—21no—
187#3334—111no—
188#3280D1111yescharacteristic, complemented
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×C11—41no—
204C23×C11—82no—
205C23×C11—82no—
206C23×C11—161no—
207C23×C11C2×D811yescharacteristic
208C23×C11C2×D811yescharacteristic
209C22×D11—41no—
210Q8×C11—41no—
211Q8×C11—41no—
212D4×C11—22no—
213D4×C11—22no—
214D4×C11—41no—
215D4×C11—41no—
216D4×C11—41no—
217D4×C11—82no—
218D4×C11—82no—
219D4×C11—161no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—82no—
227C2×C4×C11—161no—
228C2×C4×C11C2×D811yescharacteristic
229C2×C4×C11C2×D811yescharacteristic
230C2×C4×C11C2×D811yescharacteristic
231C2×C4×C11C2×D811yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C22⋊D11—82no—
234C22⋊D11—82no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—82no—
239C2×Dic11—82no—
240D44—41no—
241D44—41no—
242C4×D11—82no—
243Dic22—82no—
244C8×C11—21no—
245C8×C11—21no—
246C8×C11—21no—
247C8×C11C2×#4111yescharacteristic
248C8×C11H(5,𝔽2)11yescharacteristic
249C2×#135C2×D1111yescharacteristic
250C22×D8C2×D1111yescharacteristic
251#547—221no—
252#546—21no—
253C2×SD32—111no—
254C2×D16—111no—
255C2×D16—111no—
256C2×M32—111no—
257C22×C16—111no—
258#500—111no—
259#495C2×D1111yescharacteristic
260#480—221no—
261#480—221no—
262#474—221no—
263#467C2×D1111yescharacteristic
264#466—111no—
265#466—111no—
266#466C2×D1111yescharacteristic
267#463—21no—
268#450—21no—
269#449—21no—
270C4×D8—111no—
271C4×D8C2×D1111yescharacteristic
272C8×D4C2×D1111yescharacteristic
273C2×#107—111no—
274C2×#107—111no—
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—42no—
298C22×C11—81no—
299C22×C11—81no—
300C22×C11—81no—
301C22×C11—81no—
302C22×C11—81no—
303C22×C11—164no—
304C22×C11#50912yes—
305C22×C11C22×D811yescharacteristic
306C2×D11—81no—
307C2×D11—81no—
308C2×D11—81no—
309C4×C11—21no—
310C4×C11—21no—
311C4×C11—21no—
312C4×C11—21no—
313C4×C11—81no—
314C4×C11—81no—
315C4×C11#54611yescharacteristic
316C4×C11#57711yescharacteristic
317Dic11—81no—
318Dic11—81no—
319Dic11—81no—
320C2×#41—21no—
321C2×#41—441no—
322C22×D4—21no—
323#135—22no—
324#135—41no—
325C2×Q16C22×D1111yescharacteristic
326C2×SD16—21no—
327C2×SD16—21no—
328C2×D8—22no—
329C2×D8—21no—
330C2×D8—41no—
331C2×D8—111no—
332C2×D8C22×D1111yescharacteristic
333C2×D8C22×D1111yescharacteristic
334C22×C8C22×D1111yescharacteristic
335C22×C8C22×D1111yescharacteristic
336C4⋊Q8—221no—
337#124—21no—
338#123—41no—
339#123—441no—
340#123—441no—
341C22⋊Q8—21no—
342C22⋊Q8—441no—
343#121—21no—
344#121—41no—
345#121—221no—
346#121—221no—
347#120—41no—
348C4×D4—21no—
349C4×D4—221no—
350C4×D4C22⋊D1111yescharacteristic
351C2×C4⋊C4—221no—
352C2×C4⋊C4—221no—
353C2×C22⋊C4—41no—
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—111no—
364#107—111no—
365#107—111no—
366#107—221no—
367#107—221no—
368#107—221no—
369#107C22×D1111yescharacteristic
370C4⋊C8C22⋊D1111yescharacteristic
371#103—21no—
372#102—21no—
373#102—21no—
374#102—221no—
375#102—221no—
376#102—221no—
377C22⋊C8C22⋊D1111yescharacteristic
378C22⋊C8C22⋊D1111yescharacteristic
379C4×C8C22×D1111yescharacteristic
380C2×C11—22no—
381C2×C11—41no—
382C2×C11—82no—
383C2×C11—161no—
384C2×C11#329411yescharacteristic
385C2×C11C2×#50911yescharacteristic
386C2×C11#341611yescharacteristic
387D11—161no—
388C24—41no—
389#41—42no—
390#41—81no—
391#41—884no—
392C2×Q8—21no—
393C2×Q8—441no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—42no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—81no—
401C2×D4—221no—
402C2×D4—441no—
403C2×D4—441no—
404C2×D4#432311yescharacteristic
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—441no—
408C22×C4—441no—
409C22×C4—441no—
410C22×C4C2×C22⋊D1111yescharacteristic
411C22×C4C2×C22⋊D1111yescharacteristic
412Q16—21no—
413Q16—21no—
414SD16—42no—
415SD16—81no—
416D8—21no—
417D8—21no—
418D8—21no—
419D8—42no—
420D8—221no—
421D8—221no—
422D8#434112yescomplemented
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—41no—
433C4⋊C4—221no—
434C4⋊C4—221no—
435C4⋊C4—221no—
436C4⋊C4—441no—
437C4⋊C4—441no—
438C4⋊C4—441no—
439C4⋊C4#432311yescharacteristic
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C22⋊C4—41no—
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—41no—
458C23—82no—
459C23—82no—
460C23—161no—
461C23—441no—
462C23C2×#432311yescharacteristic
463C23C2×#432311yescharacteristic
464Q8—41no—
465Q8—41no—
466Q8—882no—
467D4—22no—
468D4—22no—
469D4—41no—
470D4—41no—
471D4—41no—
472D4—82no—
473D4—82no—
474D4—161no—
475D4—441no—
476D4—441no—
477D4—882no—
478D4—882no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—82no—
486C2×C4—161no—
487C2×C4—441no—
488C2×C4—441no—
489C2×C4—441no—
490C2×C4—882no—
491C2×C4—882no—
492C2×C4—882no—
493C2×C4C2×#432311yescharacteristic
494C2×C4C2×#432311yescharacteristic
495C2×C4C2×#432311yescharacteristic
496C2×C4C2×#432311yescharacteristic
497C2×C4C22×C22⋊D1111yescharacteristic
498C8—21no—
499C8—21no—
500C8—21no—
501C8C2×#434111yescharacteristic
502C8#6703711yescharacteristic
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—42no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—164no—
515C22—881no—
516C22—881no—
517C22—881no—
518C22#1062280612yes—
519C22C22×#432311yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—81no—
525C4—81no—
526C4—881no—
527C4—881no—
528C4—881no—
529C4#1062333711yescharacteristic
530C4#1062336711yescharacteristic
531C2—22no—
532C2—41no—
533C2—82no—
534C2—161no—
535C2—1761no—
536C2#1308042911yescharacteristic
537C2C2×#1062280611yescharacteristic
538C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3280C2
socleC22×C11C22×D8
hypercenter#3280D11
hypocenterC11#33873
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3280

Complements

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

NH ≅ G/Ntype
1. #13080964C2semidirect
2. #13070852C2semidirect
3. #13070811C2semidirect
4. #13070799C2semidirect
5. #13070763C2semidirect
6. #13070717C2semidirect
7. #13070714C2semidirect
8. #13070668C2semidirect
9. #13070539C2semidirect
10. #13070528C2semidirect
11. #13070490C2semidirect
12. #13070442C2semidirect
13. #13070328C2semidirect
14. C2×#10622200C2semidirect
15. C11×#3280C2semidirect
28. C2×#66892C22semidirect
32. #10622728C22semidirect
34. C2×#66882C22semidirect
35. C2×#66876C22semidirect
40. C4×D88C22semidirect
41. #10622295C22semidirect
42. #10622202C22semidirect
43. #10622202C22semidirect
44. #10622202C22semidirect
52. C22⋊(C11⋊C16)C22semidirect
53. #10622129C22semidirect
54. #10622128C22semidirect
55. #10622128C22semidirect
56. #10622128C22semidirect
57. C4⋊(C11⋊C16)C22semidirect
58. #10622099C22semidirect
152. C11×D8#41semidirect
188. #3280D11semidirect
422. D8#4341semidirect
455. C11#33873semidirect

Maximal subgroups

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

subgroupindex
#130809642
#130708522
#130708112
#130707992
#130707632
#130707172
#130707142
#130706682
#130705392
#130705282
#130704902
#130704422
#130703282
C2×#106222002
C11×#32802
#3387311