Finite Group Databasebeta

← #14645739

Subgroups — #14645739

Order 2816.

1020 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068626C211yesmaximal, characteristic, complemented
2#13067265C211yesmaximal, characteristic, complemented
3#13067176C211yesmaximal, characteristic, complemented
4#13067176C211yesmaximal, characteristic, complemented
5#13067015C211yesmaximal, characteristic, complemented
6#13067007C211yesmaximal, characteristic, complemented
7C11×#3496C211yesmaximal, characteristic
8C2×C11×H(5,𝔽2)—21no—
9C11×#547—21no—
10C11×#547C412yescomplemented
11C11×#546—22no—
12C11×#546—22no—
13D42×C11—21no—
14D42×C11C412yescomplemented
15C11×#537—21no—
16C11×#534—22no—
17C11×#532C2211yescharacteristic
18C11×#532C2211yescharacteristic
19C2×C11×#121—22no—
20C2×C4×D4×C11C2211yescharacteristic
21C2×#66896—21no—
22#10622549C2211yescharacteristic, complemented
23#10622538C2211yescharacteristic, complemented
24#10622538C2211yescharacteristic, complemented
25C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
26#10622185—21no—
27#10622182—21no—
28#10622175—22no—
29#10622175—22no—
30D4⋊(C11⋊C8)—22no—
31D4⋊(C11⋊C8)—22no—
32#10622167—21no—
33C11×H(5,𝔽2)—42no—
34C11×H(5,𝔽2)—42no—
35C11×H(5,𝔽2)—42no—
36C11×H(5,𝔽2)—42no—
37C2×C11×#41—22no—
38C2×C11×#41—22no—
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C22×D4×C11—24no—
42C22×D4×C11—22no—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11D411yescharacteristic
46C23×C4×C11—21no—
47C11×C4⋊Q8C2×C411yescharacteristic
48C11×C4⋊Q8D411yescharacteristic
49C11×#127C2×C411yescharacteristic
50C11×#127D411yescharacteristic
51C11×#124—21no—
52C11×#124—21no—
53C11×#123—24no—
54C11×#123—24no—
55C11×C22⋊Q8—22no—
56C11×C22⋊Q8—22no—
57C11×#121—24no—
58C11×#121—24no—
59C11×#121—22no—
60C11×#121—22no—
61C11×#121—21no—
62C11×#121—21no—
63C11×#121—22no—
64C11×#121—22no—
65C11×#121D412yes—
66C11×#121D412yes—
67C11×#120—24no—
68C11×#120—24no—
69C4×D4×C11—21no—
70C4×D4×C11—21no—
71C4×D4×C11—21no—
72C4×D4×C11—21no—
73C4×D4×C11C2×C412yes—
74C4×D4×C11C2×C412yes—
75C4×D4×C11D412yes—
76C4×D4×C11D412yes—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C22⋊C4—24no—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C4⋊Dic11—21no—
83C22×C11⋊C8—21no—
84#66896—42no—
85C11⋊#95—21no—
86C11⋊#95—21no—
87C22⋊(C11⋊C8)—21no—
88C22⋊(C11⋊C8)—21no—
89C4⋊(C11⋊C8)—21no—
90C4⋊(C11⋊C8)—21no—
91C4⋊(C11⋊C8)—21no—
92C4⋊(C11⋊C8)—21no—
93C4×C11⋊C8—21no—
94C4×C11⋊C8—21no—
95#8428—111nomaximal, Sylow
96C24×C11—21no—
97C24×C11—24no—
98C11×#41—44no—
99C11×#41—44no—
100C11×#41—44no—
101C11×#41—44no—
102C11×#41—41no—
103C11×#41—41no—
104C11×#41—41no—
105C11×#41—41no—
106C11×#41—41no—
107C11×#41—41no—
108C11×#41—41no—
109C11×#41—41no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×D4×C11—24no—
113C2×D4×C11—24no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—24no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—44no—
125C2×D4×C11—44no—
126C2×D4×C11—44no—
127C2×D4×C11—48no—
128C2×D4×C11—48no—
129C2×D4×C11—44no—
130C2×D4×C11—84no—
131C2×D4×C11C22⋊C412yes—
132C2×D4×C11C22⋊C412yes—
133C2×D4×C11C22⋊C412yes—
134C2×D4×C11D812yes—
135C2×D4×C11SD1612yes—
136C22×C4×C11—24no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—82no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×Dic11—41no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4C22⋊C412yes—
152C11×C4⋊C4C22⋊C412yes—
153C11×C4⋊C4C22⋊C412yes—
154C11×C22⋊C4—24no—
155C11×C22⋊C4—24no—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—22no—
158C11×C22⋊C4—22no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—22no—
162C42×C11C22×C411yescharacteristic
163C42×C11C2×D411yescharacteristic
164C42×C11C2×D411yescharacteristic
165C42×C11C2×D411yescharacteristic
166C4⋊Dic11—41no—
167C4⋊Dic11—41no—
168C2×C11⋊C8—41no—
169C2×C11⋊C8—41no—
170C2×C11⋊C8—41no—
171C2×C11⋊C8—41no—
172C2×C11⋊C8—41no—
173#3496D1111yescharacteristic
174#1804—111no—
175#1540—111no—
176#1517—111no—
177#1517—111no—
178#1480—111no—
179#1478—111no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—48no—
186C23×C11—81no—
187C23×C11—81no—
188C23×C11—84no—
189C23×C11—84no—
190C23×C11#12011yescharacteristic
191Q8×C11—41no—
192Q8×C11—41no—
193Q8×C11—41no—
194Q8×C11—41no—
195D4×C11—22no—
196D4×C11—22no—
197D4×C11—22no—
198D4×C11—42no—
199D4×C11—42no—
200D4×C11—42no—
201D4×C11—48no—
202D4×C11—48no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—42no—
206D4×C11—42no—
207D4×C11—41no—
208D4×C11—41no—
209D4×C11—41no—
210D4×C11—41no—
211D4×C11—81no—
212D4×C11—84no—
213D4×C11#10214yes—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—44no—
220C2×C4×C11—48no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—82no—
226C2×C4×C11—81no—
227C2×C4×C11C2×C22⋊C411yescharacteristic
228C2×C4×C11C2×C22⋊C411yescharacteristic
229C2×C4×C11C2×C22⋊C411yescharacteristic
230C2×C4×C11#12011yescharacteristic
231C2×C4×C11#12011yescharacteristic
232C2×C4×C11#12011yescharacteristic
233C2×C4×C11C2×D811yescharacteristic
234C2×C4×C11C2×SD1611yescharacteristic
235C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
236C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
237C2×Dic11—81no—
238C2×Dic11—81no—
239C2×Dic11—81no—
240C11⋊C8—81no—
241C11⋊C8—81no—
242C11⋊C8—81no—
243C2×H(5,𝔽2)—21no—
244#547—21no—
245#547Dic1112yescomplemented
246#546—22no—
247#546—22no—
248D42—21no—
249D42Dic1112yescomplemented
250#537—21no—
251#534—22no—
252#532C2×D1111yescharacteristic
253#532C2×D1111yescharacteristic
254C2×#121—22no—
255C2×C4×D4C2×D1111yescharacteristic
256#431—111no—
257#431—111no—
258C2×C4⋊C8—111no—
259C2×#102—221no—
260#382—111no—
261#340—221no—
262#332—221no—
263#331—221no—
264#327—222no—
265#327—222no—
266D4⋊C8—222no—
267D4⋊C8—222no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—24no—
271C22×C11—42no—
272C22×C11—42no—
273C22×C11—42no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11—82no—
280C22×C11—82no—
281C22×C11—168no—
282C22×C11#37911yescharacteristic
283C22×C11#44711yescharacteristic
284C22×C11#45011yescharacteristic
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11—42no—
292C4×C11C2×#10211yescharacteristic
293C4×C11#41811yescharacteristic
294C4×C11#44711yescharacteristic
295C4×C11#45011yescharacteristic
296Dic11—161no—
297H(5,𝔽2)—42no—
298H(5,𝔽2)—42no—
299H(5,𝔽2)—42no—
300H(5,𝔽2)—42no—
301C2×#41—22no—
302C2×#41—22no—
303C2×#41—21no—
304C2×#41—21no—
305C22×D4—24no—
306C22×D4—22no—
307C22×D4—22no—
308C22×D4—22no—
309C22×D4C22⋊D1111yescharacteristic
310C23×C4—21no—
311C22×C8—221no—
312C4⋊Q8C2×Dic1111yescharacteristic
313C4⋊Q8C22⋊D1111yescharacteristic
314#127C2×Dic1111yescharacteristic
315#127C22⋊D1111yescharacteristic
316#124—21no—
317#124—21no—
318#123—24no—
319#123—24no—
320C22⋊Q8—22no—
321C22⋊Q8—22no—
322#121—24no—
323#121—24no—
324#121—22no—
325#121—22no—
326#121—21no—
327#121—21no—
328#121—22no—
329#121—22no—
330#121C22⋊D1112yes—
331#121C22⋊D1112yes—
332#120—24no—
333#120—24no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4C2×Dic1112yes—
339C4×D4C2×Dic1112yes—
340C4×D4C22⋊D1112yes—
341C4×D4C22⋊D1112yes—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4C22⋊D1111yescharacteristic
345C2×C22⋊C4—24no—
346C2×C22⋊C4—21no—
347C2×C42C22×D1111yescharacteristic
348C4⋊C8—221no—
349C4⋊C8—221no—
350C4⋊C8—221no—
351C4⋊C8—221no—
352#102—442no—
353C22⋊C8—221no—
354C22⋊C8—221no—
355C4×C8—221no—
356C4×C8—221no—
357#95—221no—
358#95—221no—
359C2×C11—21no—
360C2×C11—21no—
361C2×C11—44no—
362C2×C11—82no—
363C2×C11—82no—
364C2×C11#178611yescharacteristic
365C2×C11#179411yescharacteristic
366C2×C11#179511yescharacteristic
367C24—21no—
368C24—24no—
369#41—44no—
370#41—44no—
371#41—44no—
372#41—44no—
373#41—41no—
374#41—41no—
375#41—41no—
376#41—41no—
377#41—41no—
378#41—41no—
379#41—41no—
380#41—41no—
381C2×Q8—21no—
382C2×Q8—21no—
383C2×D4—24no—
384C2×D4—24no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—24no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—44no—
396C2×D4—44no—
397C2×D4—44no—
398C2×D4—48no—
399C2×D4—48no—
400C2×D4—44no—
401C2×D4—84no—
402C2×D4#432312yes—
403C2×D4#432412yes—
404C2×D4C22⋊Dic1112yes—
405C2×D4C22⋊Dic1112yes—
406C2×D4C22⋊Dic1112yes—
407C22×C4—24no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—82no—
414C22×C4—441no—
415C22×C4C2×C22⋊D1111yescharacteristic
416C22×C4C2×C22⋊D1111yescharacteristic
417C22×C4C2×C22⋊D1111yescharacteristic
418C2×C8—441no—
419C2×C8—441no—
420C2×C8—441no—
421C2×C8—441no—
422C2×C8—441no—
423C4⋊C4—24no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—441no—
428C4⋊C4—441no—
429C4⋊C4C22⋊Dic1112yes—
430C4⋊C4C22⋊Dic1112yes—
431C4⋊C4C22⋊Dic1112yes—
432C22⋊C4—24no—
433C22⋊C4—24no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C42C22×Dic1111yescharacteristic
441C42C2×C22⋊D1111yescharacteristic
442C42C2×C22⋊D1111yescharacteristic
443C42C2×C22⋊D1111yescharacteristic
444C11#842811yescharacteristic, complemented, Sylow
445C23—22no—
446C23—22no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—48no—
451C23—81no—
452C23—81no—
453C23—84no—
454C23—84no—
455C23#6700611yescharacteristic
456Q8—41no—
457Q8—41no—
458Q8—41no—
459Q8—41no—
460D4—22no—
461D4—22no—
462D4—22no—
463D4—42no—
464D4—42no—
465D4—42no—
466D4—48no—
467D4—48no—
468D4—42no—
469D4—42no—
470D4—42no—
471D4—42no—
472D4—41no—
473D4—41no—
474D4—41no—
475D4—41no—
476D4—81no—
477D4—84no—
478D4#6689614yes—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—44no—
485C2×C4—48no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—82no—
491C2×C4—81no—
492C2×C4—881no—
493C2×C4—881no—
494C2×C4—881no—
495C2×C4C2×#432311yescharacteristic
496C2×C4#6698511yescharacteristic
497C2×C4#6698511yescharacteristic
498C2×C4C2×#432411yescharacteristic
499C2×C4C2×C22⋊Dic1111yescharacteristic
500C2×C4C2×C22⋊Dic1111yescharacteristic
501C2×C4C2×C22⋊Dic1111yescharacteristic
502C2×C4#6700611yescharacteristic
503C2×C4#6700611yescharacteristic
504C2×C4#6700611yescharacteristic
505C8—881no—
506C8—881no—
507C8—881no—
508C22—21no—
509C22—21no—
510C22—24no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—82no—
520C22—82no—
521C22—168no—
522C22#1062283011yescharacteristic
523C22#1062283111yescharacteristic
524C22#1062286011yescharacteristic
525C4—21no—
526C4—21no—
527C4—21no—
528C4—21no—
529C4—42no—
530C4—42no—
531C4—42no—
532C4—1761no—
533C4C2×#6689611yescharacteristic
534C4#1062282811yescharacteristic
535C4#1062283011yescharacteristic
536C4#1062283111yescharacteristic
537C2—21no—
538C2—21no—
539C2—44no—
540C2—82no—
541C2—82no—
542C2#1306854711yescharacteristic
543C2#1306858011yescharacteristic
544C2#1306858611yescharacteristic
subgroupG/H
centerC22#10622860
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3496C2
socleC22×C11#379
cosocleC2×C42×C11C23
hypercenter#3496D11
hypocenterC11#8428
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. #13068626C2semidirect
2. #13067265C2semidirect
3. #13067176C2semidirect
4. #13067176C2semidirect
5. #13067015C2semidirect
6. #13067007C2semidirect
10. C11×#547C4semidirect
14. D42×C11C4semidirect
22. #10622549C22semidirect
23. #10622538C22semidirect
24. #10622538C22semidirect
25. C2×C4⋊(C11⋊C8)C22semidirect
245. #547Dic11semidirect
249. D42Dic11semidirect
444. C11#8428semidirect

Maximal subgroups

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

subgroupindex
#130686262
#130672652
#130671762
#130670152
#130670072
C11×#34962
#842811