Finite Group Databasebeta

← #14738526

Subgroups — #14738526

Order 2816.

776 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079631C211yesmaximal, characteristic, complemented
2C2×#10622686C211yesmaximal, characteristic, complemented
3#13077592C211yesmaximal, characteristic, complemented
4#13068098C212yesmaximal, complemented
5#13068093C212yesmaximal, complemented
6#13067974C212yesmaximal, complemented
7#13067969C212yesmaximal, complemented
8#13067377C211yesmaximal, characteristic, complemented
9#13067330C211yesmaximal, characteristic, complemented
10#13067329C211yesmaximal, characteristic, complemented
11C11×#3217C211yesmaximal, characteristic, complemented
12C2×C11×#127C2211yescharacteristic
13C11×#529C2211yescharacteristic
14C22×#4323—21no—
15C22×#4323—21no—
16C2×#66927C2211yescharacteristic
17C11×#496—21no—
18C11×#490—21no—
19C11×#460C2212yescomplemented
20C11×#459C2212yescomplemented
21C11×#450—21no—
22C11×#447—21no—
23C11×#432C2211yescharacteristic
24#10622686—21no—
25#10622686—21no—
26#10622686C2212yes—
27#10622686C2212yes—
28#10622680—21no—
29#10622671—21no—
30#10622659—21no—
31#10622649—21no—
32#10622640C2212yescomplemented
33#10622637C2211yescharacteristic, complemented
34Q8×C11⋊C8C2211yescharacteristic, complemented
35#10622628C2212yescomplemented
36#10622625C2211yescharacteristic, complemented
37#10622624—21no—
38D4×C11⋊C8—21no—
39D4×C11⋊C8C2211yescharacteristic, complemented
40#10622613—21no—
41#10622610—21no—
42#10622539C2211yescharacteristic
43#10622539C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622182C2212yescomplemented
46#10622182C2212yescomplemented
47#10622123C2212yescomplemented
48#10622123C2212yescomplemented
49#10622118C2212yescomplemented
50#10622117C2212yescomplemented
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C22×D4×C11—21no—
54C22×D44—21no—
55C22×D44—21no—
56C22×D44—21no—
57C2×C11×SD16—22no—
58C2×C11×D8—22no—
59C11×#127—21no—
60C11×#127—21no—
61C11×#127—21no—
62C11×#127C2312yes—
63C11×#126—21no—
64C11×#125D411yescharacteristic
65C11×#124D411yescharacteristic
66C11×#123—21no—
67C11×C22⋊Q8D411yescharacteristic
68C11×#121D411yescharacteristic
69C4×Q8×C11C2311yescharacteristic
70C4×D4×C11—21no—
71C4×D4×C11C2311yescharacteristic
72C11×#117—21no—
73C2×C42×C11C2311yescharacteristic
74C2×#4325—22no—
75C2×#4323—22no—
76C2×#4323—22no—
77C2×#4323—22no—
78C2×#4323—22no—
79C2×#4323—22no—
80C2×#4323—44no—
81C2×#4323—44no—
82C2×#4318—21no—
83C22×C11⋊C8—21no—
84C22×C11⋊C8D411yescharacteristic
85C22×C11⋊C8D411yescharacteristic
86#66927—21no—
87#66927—21no—
88#66927—21no—
89#66927C2312yes—
90C11×C4⋊C8C2312yes—
91C11×#102—22no—
92C11×#102—22no—
93C11×C22⋊C8—21no—
94C11×#97—21no—
95C22⋊(C11⋊C8)—21no—
96C22⋊(C11⋊C8)—21no—
97C22⋊(C11⋊C8)—21no—
98C22⋊(C11⋊C8)—21no—
99#66873—22no—
100#66873—22no—
101C4⋊(C11⋊C8)—21no—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)C2311yescharacteristic
104C4⋊(C11⋊C8)C2311yescharacteristic
105C4⋊(C11⋊C8)C2312yes—
106#66867—21no—
107#66867—21no—
108#66867—21no—
109C4×C11⋊C8—21no—
110C4×C11⋊C8D411yescharacteristic
111C4×C11⋊C8D411yescharacteristic
112C4×C11⋊C8C2311yescharacteristic
113C4×C11⋊C8C2311yescharacteristic
114#19353—111nomaximal, Sylow
115C24×C11—41no—
116C23×D11—41no—
117C2×Q8×C11C2×D411yescharacteristic
118C2×D4×C11—21no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—42no—
123C2×D4×C11—42no—
124C2×D4×C11—41no—
125C2×D4×C11—41no—
126C2×D4×C11—41no—
127C2×D4×C11—82no—
128C2×D4×C11—82no—
129C2×D4×C11C2×D411yescharacteristic
130C22×C4×C11—21no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11#4111yescharacteristic
134C2×D44—22no—
135C2×D44—22no—
136C2×D44—22no—
137C2×D44—42no—
138C2×D44—42no—
139C2×D44—41no—
140C2×D44—41no—
141C2×D44—41no—
142C2×D44—82no—
143C2×D44—82no—
144C11×SD16—82no—
145C11×D8—82no—
146C2×C8×C11—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4C2×D411yescharacteristic
152C11×C4⋊C4C2×D411yescharacteristic
153C11×C22⋊C4—21no—
154C11×C22⋊C4—21no—
155C11×C22⋊C4—21no—
156C11×C22⋊C4—21no—
157C11×C22⋊C4—21no—
158C42×C11—21no—
159C42×C11C2×D411yescharacteristic
160C42×C11C2×D411yescharacteristic
161C42×C11#4111yescharacteristic
162C42×C11C2411yescharacteristic
163#4325—82no—
164#4323—44no—
165#4323—44no—
166#4323—44no—
167#4323—44no—
168#4323—82no—
169#4318—42no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—42no—
176C2×C11⋊C8C2×D411yescharacteristic
177C2×C11⋊C8C2×D411yescharacteristic
178C2×C11⋊C8C2×D411yescharacteristic
179C2×C11⋊C8C2×D411yescharacteristic
180#3217—111no—
181#3217D1111yescharacteristic, complemented
182C2×#493—111no—
183#2966—111no—
184#1688—112no—
185#1687—112no—
186#1668—112no—
187#1667—112no—
188#1568—111no—
189#1555—111no—
190#1555—111no—
191C23×C11—21no—
192C23×C11—42no—
193C23×C11—82no—
194C23×C11—82no—
195C23×C11—82no—
196C23×C11#12111yescharacteristic
197C22×D11—42no—
198C22×D11—82no—
199C22×D11—82no—
200C22×D11—82no—
201Q8×C11—22no—
202D4×C11—22no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—42no—
206D4×C11—42no—
207D4×C11—42no—
208D4×C11—82no—
209D4×C11—82no—
210D4×C11—82no—
211D4×C11—82no—
212C2×C4×C11—22no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—22no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11#12111yescharacteristic
222C2×C4×C11#12111yescharacteristic
223C2×C4×C11#12111yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C2×#4111yescharacteristic
227D44—42no—
228D44—42no—
229D44—42no—
230D44—42no—
231D44—82no—
232D44—82no—
233D44—82no—
234D44—82no—
235C8×C11—42no—
236C11⋊C8—21no—
237C11⋊C8—21no—
238C11⋊C8—41no—
239C11⋊C8—41no—
240C11⋊C8—42no—
241C11⋊C8AGL(1,ℤ/8)12yes—
242C11⋊C8AGL(1,ℤ/8)12yes—
243C22×D8—221no—
244C22×D8—221no—
245C2×#127—111no—
246C2×#127C2×D1111yescharacteristic
247#529C2×D1111yescharacteristic
248#496—21no—
249#496—221no—
250#493—112no—
251#493—112no—
252#493—221no—
253#493—221no—
254#490—21no—
255#490—221no—
256#460—112no—
257#460C2×D1112yescomplemented
258#459—112no—
259#459C2×D1112yescomplemented
260#450—21no—
261#450—221no—
262#447—21no—
263#447—221no—
264#446—111no—
265C8×Q8—111no—
266#436—111no—
267#435—221no—
268C8×D4—111no—
269C8×D4—221no—
270#433—221no—
271#432—111no—
272#432—111no—
273#432C2×D1111yescharacteristic
274#405—221no—
275C2×C4×C8—111no—
276#335—112no—
277#334—112no—
278#331—112no—
279#331—112no—
280#331—112no—
281#331—112no—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—41no—
285C22×C11—41no—
286C22×C11—41no—
287C22×C11—82no—
288C22×C11—82no—
289C22×C11—82no—
290C22×C11—164no—
291C22×C11#47212yes—
292C22×C11C2×#12111yescharacteristic
293C2×D11—82no—
294C2×D11—82no—
295C2×D11—82no—
296C2×D11—164no—
297C4×C11—21no—
298C4×C11—21no—
299C4×C11—21no—
300C4×C11—21no—
301C4×C11—41no—
302C4×C11—41no—
303C4×C11—41no—
304C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
305C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
306C4×C11#57612yes—
307C22×D4—21no—
308C22×D4—21no—
309C22×D4—21no—
310C22×D4—221no—
311C22×D4—221no—
312C22×D4—221no—
313C2×SD16—22no—
314C2×SD16—222no—
315C2×D8—22no—
316C2×D8—222no—
317C2×D8—222no—
318C2×D8—222no—
319C2×D8—222no—
320C2×D8—222no—
321C2×D8—444no—
322C2×D8—444no—
323C2×M16—221no—
324C22×C8—111no—
325C22×C8—111no—
326C22×C8—221no—
327#127—21no—
328#127—21no—
329#127—21no—
330#127—112no—
331#127—221no—
332#127—221no—
333#127—221no—
334#127C22×D1112yes—
335#126—21no—
336#125C22⋊D1111yescharacteristic
337#124C22⋊D1111yescharacteristic
338#123—21no—
339C22⋊Q8C22⋊D1111yescharacteristic
340#121C22⋊D1111yescharacteristic
341C4×Q8C22×D1111yescharacteristic
342C4×D4—21no—
343C4×D4C22×D1111yescharacteristic
344#117—21no—
345C2×C42C22×D1111yescharacteristic
346C4⋊C8—111no—
347C4⋊C8—111no—
348C4⋊C8—112no—
349C4⋊C8—221no—
350C4⋊C8—221no—
351C4⋊C8C22×D1112yes—
352#102—22no—
353#102—22no—
354#102—222no—
355#102—222no—
356C22⋊C8—21no—
357C22⋊C8—221no—
358C22⋊C8—221no—
359C22⋊C8—221no—
360C22⋊C8—221no—
361#97—21no—
362#97—221no—
363#97—221no—
364#97—221no—
365C4×C8—111no—
366C4×C8—111no—
367C4×C8—111no—
368C4×C8—111no—
369C4×C8—221no—
370C2×C11—22no—
371C2×C11—81no—
372C2×C11—162no—
373C2×C11#303811yescharacteristic
374C2×C11#305811yescharacteristic
375C2×C11C2×#47211yescharacteristic
376D11—162no—
377C24—41no—
378C24—441no—
379C2×Q8C2×C22⋊D1111yescharacteristic
380C2×D4—21no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—82no—
390C2×D4—82no—
391C2×D4—222no—
392C2×D4—222no—
393C2×D4—222no—
394C2×D4—442no—
395C2×D4—442no—
396C2×D4—441no—
397C2×D4—441no—
398C2×D4—441no—
399C2×D4—882no—
400C2×D4—882no—
401C2×D4C2×C22⋊D1111yescharacteristic
402C22×C4—21no—
403C22×C4D4×D1111yescharacteristic
404C22×C4#434111yescharacteristic
405C22×C4C2×C22⋊D1111yescharacteristic
406SD16—82no—
407SD16—882no—
408D8—82no—
409D8—444no—
410D8—444no—
411D8—444no—
412D8—444no—
413D8—882no—
414M16—442no—
415C2×C8—22no—
416C2×C8—111no—
417C2×C8—111no—
418C2×C8—111no—
419C2×C8—111no—
420C2×C8—222no—
421C2×C8—222no—
422C2×C8—221no—
423C2×C8—221no—
424C2×C8—222no—
425C2×C8—442no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4C2×C22⋊D1111yescharacteristic
431C4⋊C4C2×C22⋊D1111yescharacteristic
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—21no—
437C42—21no—
438C42D4×D1111yescharacteristic
439C42#434111yescharacteristic
440C42C2×C22⋊D1111yescharacteristic
441C42C23×D1111yescharacteristic
442C11#1935311yescharacteristic, complemented, Sylow
443C23—21no—
444C23—42no—
445C23—82no—
446C23—82no—
447C23—82no—
448C23—442no—
449C23—882no—
450C23—882no—
451C23—882no—
452C23#6699211yescharacteristic
453Q8—22no—
454D4—22no—
455D4—42no—
456D4—42no—
457D4—42no—
458D4—42no—
459D4—42no—
460D4—82no—
461D4—82no—
462D4—82no—
463D4—82no—
464D4—442no—
465D4—442no—
466D4—442no—
467D4—442no—
468D4—882no—
469D4—882no—
470D4—882no—
471D4—882no—
472C2×C4—22no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4#6699211yescharacteristic
482C2×C4#6699211yescharacteristic
483C2×C4#6699211yescharacteristic
484C2×C4C2×D4×D1111yescharacteristic
485C2×C4C2×#434111yescharacteristic
486C2×C4C22×C22⋊D1111yescharacteristic
487C8—42no—
488C8—112no—
489C8—112no—
490C8—221no—
491C8—221no—
492C8—441no—
493C8—441no—
494C8—442no—
495C22—21no—
496C22—21no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—82no—
501C22—82no—
502C22—82no—
503C22—164no—
504C22—882no—
505C22—882no—
506C22—882no—
507C22—1764no—
508C22#1062281212yes—
509C22C2×#6699211yescharacteristic
510C4—21no—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—41no—
515C4—41no—
516C4—41no—
517C4D11×AGL(1,ℤ/8)11yescharacteristic
518C4D11×AGL(1,ℤ/8)11yescharacteristic
519C4#1062336612yes—
520C2—22no—
521C2—81no—
522C2—162no—
523C2—1762no—
524C2#1307809411yescharacteristic
525C2#1307826111yescharacteristic
526C2C2×#1062281211yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3217C2
socleC22×C11C2×#121
hypercenter#3217D11
hypocenterC11#19353
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3217

Complements

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

NH ≅ G/Ntype
1. #13079631C2semidirect
2. C2×#10622686C2semidirect
3. #13077592C2semidirect
4. #13068098C2semidirect
5. #13068093C2semidirect
6. #13067974C2semidirect
7. #13067969C2semidirect
8. #13067377C2semidirect
9. #13067330C2semidirect
10. #13067329C2semidirect
11. C11×#3217C2semidirect
19. C11×#460C22semidirect
20. C11×#459C22semidirect
32. #10622640C22semidirect
33. #10622637C22semidirect
34. Q8×C11⋊C8C22semidirect
35. #10622628C22semidirect
36. #10622625C22semidirect
39. D4×C11⋊C8C22semidirect
45. #10622182C22semidirect
46. #10622182C22semidirect
47. #10622123C22semidirect
48. #10622123C22semidirect
49. #10622118C22semidirect
50. #10622117C22semidirect
181. #3217D11semidirect
257. #460C2×D11semidirect
259. #459C2×D11semidirect
442. C11#19353semidirect

Maximal subgroups

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

subgroupindex
#130796312
C2×#106226862
#130775922
#130680982
#130680932
#130679742
#130679692
#130673772
#130673302
#130673292
C11×#32172
#1935311