Finite Group Databasebeta

← #14739191

Subgroups — #14739191

Order 2816.

758 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079534C211yesmaximal, characteristic, complemented
2#13078071C211yesmaximal, characteristic, complemented
3#13077727C211yesmaximal, characteristic, complemented
4#13068058C212yesmaximal, complemented
5#13068051C212yesmaximal, complemented
6#13067974C212yesmaximal, complemented
7#13067969C212yesmaximal, complemented
8#13067392C211yesmaximal, characteristic, complemented
9#13067294C211yesmaximal, characteristic, complemented
10C2×#10622182C211yesmaximal, characteristic, complemented
11C11×#3038C211yesmaximal, characteristic, complemented
12C2×C11×AGL(1,ℤ/8)—21no—
13C2×C11×#127C2211yescharacteristic
14C4×C11×#41C2211yescharacteristic
15C2×#67003—21no—
16#10623008C2211yescharacteristic
17C11×#460—21no—
18C11×#460C2212yes—
19C11×#459—21no—
20C11×#459C2212yes—
21C11×#423C2211yescharacteristic
22C11×#418—21no—
23#10622830—22no—
24#10622686C2212yes—
25#10622685—21no—
26#10622685—21no—
27#10622683C2212yes—
28#10622644C2211yescharacteristic, complemented
29#10622641—21no—
30#10622640C2211yescharacteristic, complemented
31Q8×C11⋊C8C2212yescomplemented
32#10622632C2211yescharacteristic, complemented
33#10622629—21no—
34#10622628C2211yescharacteristic, complemented
35D4×C11⋊C8—22no—
36D4×C11⋊C8C2212yescomplemented
37#10622615—21no—
38#10622538—21no—
39#10622538C2211yescharacteristic
40C2×C4⋊(C11⋊C8)—21no—
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43#10622182C2212yes—
44#10622182C2212yes—
45#10622123C2212yescomplemented
46#10622120C2212yescomplemented
47#10622117C2212yescomplemented
48#10622117C2212yescomplemented
49C2×C11×#41D411yescharacteristic
50C22×D4×C11—21no—
51C22×D4×C11—21no—
52C22×D4×C11—21no—
53C2×#4339—21no—
54C11×AGL(1,ℤ/8)—44no—
55C2×C11×SD16—22no—
56C2×C11×D8—22no—
57C2×C11×M16—21no—
58C11×#127—21no—
59C11×#127—21no—
60C11×#127—21no—
61C11×#127C2312yes—
62C4×Q8×C11D411yescharacteristic
63C4×Q8×C11C2311yescharacteristic
64C4×D4×C11—21no—
65C4×D4×C11—21no—
66C4×D4×C11D411yescharacteristic
67C4×D4×C11C2311yescharacteristic
68C11×#117—21no—
69C11×#117D411yescharacteristic
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72#67003—44no—
73C2×#4326—21no—
74C2×#4325—21no—
75C2×#4324—21no—
76C2×#4323—21no—
77C2×#4323—22no—
78C2×#4323—22no—
79#66983—21no—
80#66983—21no—
81C22×C11⋊C8—21no—
82C22×C11⋊C8—21no—
83C22×C11⋊C8—22no—
84#66928—21no—
85#66927C2311yescharacteristic
86C4×D44—21no—
87C4×D44—21no—
88#66922C2311yescharacteristic
89C11×C4⋊C8—21no—
90C11×C4⋊C8C2312yes—
91C11×#102—22no—
92C11×#102—22no—
93#66896—22no—
94#66896—22no—
95C22⋊(C11⋊C8)—22no—
96C22⋊(C11⋊C8)D412yes—
97#66874—21no—
98#66874—21no—
99#66873—21no—
100#66873—21no—
101C4⋊(C11⋊C8)—21no—
102C4⋊(C11⋊C8)—21no—
103C4⋊(C11⋊C8)—22no—
104C4⋊(C11⋊C8)D411yescharacteristic
105C4⋊(C11⋊C8)D411yescharacteristic
106C4⋊(C11⋊C8)C2312yes—
107C4⋊(C11⋊C8)C2311yescharacteristic
108C4⋊(C11⋊C8)C2311yescharacteristic
109C4×C11⋊C8—22no—
110C4×C11⋊C8C2312yes—
111#19410—111nomaximal, Sylow
112C24×C11—41no—
113C11×#41—22no—
114C11×#41D814yescomplemented
115C2×Q8×C11C2×D411yescharacteristic
116C2×D4×C11—21no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—41no—
121C2×D4×C11—41no—
122C2×D4×C11—41no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11—81no—
126C2×D4×C11—81no—
127C2×D4×C11—82no—
128C2×D4×C11C2×D411yescharacteristic
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11#4111yescharacteristic
135C2×C22⋊D11—41no—
136#4339—42no—
137#4339—42no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—21no—
141C2×C4×D11—41no—
142C2×Dic22—21no—
143C11×SD16—44no—
144C11×D8—44no—
145C11×M16—42no—
146C2×C8×C11—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4C2×D411yescharacteristic
150C11×C4⋊C4C2×D411yescharacteristic
151C11×C22⋊C4—21no—
152C11×C22⋊C4—21no—
153C11×C22⋊C4—21no—
154C42×C11—21no—
155C42×C11—21no—
156C42×C11—21no—
157C42×C11C2×D411yescharacteristic
158C42×C11C2×D411yescharacteristic
159C42×C11#4111yescharacteristic
160C42×C11C2411yescharacteristic
161#4326—42no—
162#4325—42no—
163#4324—42no—
164#4323—42no—
165#4323—82no—
166#4323—82no—
167(C2×D11)⋊C4—41no—
168(C2×D11)⋊C4—41no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—42no—
175C2×C11⋊C8—81no—
176C2×C11⋊C8—82no—
177C2×C11⋊C8C2×D412yes—
178C2×C11⋊C8C2×D412yes—
179#3205—111no—
180#3038D1111yescharacteristic, complemented
181#3035—111no—
182#2988—111no—
183#1682—112no—
184#1681—112no—
185#1668—112no—
186#1667—112no—
187#1571—111no—
188#1547—111no—
189C2×#331—111no—
190C23×C11—21no—
191C23×C11—42no—
192C23×C11—82no—
193C23×C11—82no—
194C23×C11—82no—
195C23×C11#12111yescharacteristic
196C22×D11—41no—
197Q8×C11—21no—
198Q8×C11C2×D812yes—
199D4×C11—24no—
200D4×C11—21no—
201D4×C11—42no—
202D4×C11—42no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—82no—
206D4×C11—82no—
207D4×C11—82no—
208D4×C11—82no—
209D4×C11C2×D812yes—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—24no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—81no—
220C2×C4×C11#12111yescharacteristic
221C2×C4×C11#12111yescharacteristic
222C2×C4×C11#12111yescharacteristic
223C2×C4×C11C2×D812yes—
224C2×C4×C11#13512yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C22⋊D11—82no—
229C2×Dic11—41no—
230D44—41no—
231D44—41no—
232D44—41no—
233D44—41no—
234D44—81no—
235C4×D11—82no—
236Dic22—41no—
237Dic22—41no—
238C8×C11—42no—
239C11⋊C8—22no—
240C11⋊C8—22no—
241C11⋊C8—41no—
242C11⋊C8—41no—
243C11⋊C8—42no—
244C2×AGL(1,ℤ/8)—21no—
245C2×#135—221no—
246#532—111no—
247C2×#127C2×D1111yescharacteristic
248C4×#41C2×D1111yescharacteristic
249#493—112no—
250#486—112no—
251#464—221no—
252#463—221no—
253#462—111no—
254#461—111no—
255#460—21no—
256#460—111no—
257#460C2×D1112yes—
258#459—21no—
259#459—111no—
260#459—221no—
261#459—221no—
262#459C2×D1112yes—
263#447—222no—
264C8×Q8—112no—
265C8×D4—112no—
266C8×D4—222no—
267#431—111no—
268#431—221no—
269#423C2×D1111yescharacteristic
270C2×C4⋊C8—111no—
271C2×C4⋊C8—111no—
272C2×C4⋊C8—221no—
273#418—21no—
274#416—221no—
275#335—112no—
276#335—112no—
277#332—112no—
278#331—112no—
279#331—112no—
280#331—112no—
281C22×C11—21no—
282C22×C11—21no—
283C22×C11—22no—
284C22×C11—41no—
285C22×C11—41no—
286C22×C11—82no—
287C22×C11—82no—
288C22×C11—82no—
289C22×C11—164no—
290C22×C11#46612yes—
291C22×C11C2×#12111yescharacteristic
292C2×D11—81no—
293C2×D11—81no—
294C2×D11—81no—
295C4×C11—21no—
296C4×C11—22no—
297C4×C11—21no—
298C4×C11—21no—
299C4×C11—41no—
300C4×C11—41no—
301C4×C11#46612yes—
302C4×C11C22×D811yescharacteristic
303C4×C11C2×#13511yescharacteristic
304C4×C11#57611yescharacteristic
305C4×C11#57711yescharacteristic
306Dic11—81no—
307C2×#41—221no—
308C2×#41C22⋊D1111yescharacteristic
309C22×D4—21no—
310C22×D4—21no—
311C22×D4—21no—
312AGL(1,ℤ/8)—44no—
313#135—444no—
314C2×Q16—221no—
315C2×SD16—22no—
316C2×SD16—221no—
317C2×SD16—221no—
318C2×D8—22no—
319C2×D8—222no—
320C2×D8—222no—
321C2×D8—221no—
322C2×M16—21no—
323C22×C8—222no—
324C22×C8—221no—
325C22×C8—221no—
326C4⋊Q8—111no—
327#127—21no—
328#127—21no—
329#127—21no—
330#127—111no—
331#127C22×D1112yes—
332#124—221no—
333#121—221no—
334#121—221no—
335C4×Q8C22⋊D1111yescharacteristic
336C4×Q8C22×D1111yescharacteristic
337C4×D4—21no—
338C4×D4—21no—
339C4×D4—221no—
340C4×D4—221no—
341C4×D4C22⋊D1111yescharacteristic
342C4×D4C22×D1111yescharacteristic
343#117—21no—
344#117C22⋊D1111yescharacteristic
345C2×C42—21no—
346C2×C42C22×D1111yescharacteristic
347C4⋊C8—21no—
348C4⋊C8—111no—
349C4⋊C8—111no—
350C4⋊C8—112no—
351C4⋊C8—111no—
352C4⋊C8—111no—
353C4⋊C8—222no—
354C4⋊C8—221no—
355C4⋊C8—221no—
356C4⋊C8C22×D1112yes—
357#103—221no—
358#103—221no—
359#102—22no—
360#102—22no—
361#102—222no—
362#102—222no—
363#102—221no—
364#102—221no—
365C22⋊C8—112no—
366C22⋊C8—222no—
367C4×C8—112no—
368C4×C8—222no—
369C2×C11—22no—
370C2×C11—42no—
371C2×C11—162no—
372C2×C11#304511yescharacteristic
373C2×C11C2×#46611yescharacteristic
374C2×C11#306811yescharacteristic
375D11—161no—
376C24—41no—
377#41—22no—
378#41—442no—
379#41—442no—
380#41#432314yescomplemented
381C2×Q8—221no—
382C2×Q8C2×C22⋊D1111yescharacteristic
383C2×D4—21no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—42no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—42no—
392C2×D4—81no—
393C2×D4—81no—
394C2×D4—82no—
395C2×D4—221no—
396C2×D4—221no—
397C2×D4—221no—
398C2×D4—441no—
399C2×D4C2×C22⋊D1111yescharacteristic
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—441no—
404C22×C4D4×D1111yescharacteristic
405C22×C4#434111yescharacteristic
406C22×C4C2×C22⋊D1111yescharacteristic
407Q16—442no—
408SD16—44no—
409SD16—442no—
410SD16—442no—
411D8—44no—
412D8—442no—
413D8—882no—
414D8—882no—
415M16—42no—
416C2×C8—22no—
417C2×C8—112no—
418C2×C8—112no—
419C2×C8—222no—
420C2×C8—221no—
421C2×C8—221no—
422C2×C8—442no—
423C2×C8—882no—
424C2×C8—881no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—221no—
428C4⋊C4—221no—
429C4⋊C4C2×C22⋊D1111yescharacteristic
430C4⋊C4C2×C22⋊D1111yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—441no—
435C22⋊C4—441no—
436C42—21no—
437C42—21no—
438C42—21no—
439C42D4×D1111yescharacteristic
440C42#434111yescharacteristic
441C42C2×C22⋊D1111yescharacteristic
442C42C23×D1111yescharacteristic
443C11#1941011yescharacteristic, complemented, Sylow
444C23—21no—
445C23—42no—
446C23—82no—
447C23—82no—
448C23—82no—
449C23—441no—
450C23#6699211yescharacteristic
451Q8—21no—
452Q8—441no—
453Q8—441no—
454Q8C2×#432312yes—
455D4—24no—
456D4—21no—
457D4—42no—
458D4—42no—
459D4—42no—
460D4—42no—
461D4—82no—
462D4—82no—
463D4—82no—
464D4—82no—
465D4—441no—
466D4—441no—
467D4—441no—
468D4—441no—
469D4—881no—
470D4—882no—
471D4C2×#432312yes—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—24no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—81no—
482C2×C4—441no—
483C2×C4—882no—
484C2×C4C2×#432312yes—
485C2×C4#6699211yescharacteristic
486C2×C4#6699211yescharacteristic
487C2×C4#6699211yescharacteristic
488C2×C4#6700312yes—
489C2×C4C2×D4×D1111yescharacteristic
490C2×C4C2×#434111yescharacteristic
491C2×C4C22×C22⋊D1111yescharacteristic
492C8—42no—
493C8—222no—
494C8—222no—
495C8—442no—
496C8—441no—
497C8—441no—
498C22—21no—
499C22—21no—
500C22—22no—
501C22—41no—
502C22—41no—
503C22—82no—
504C22—82no—
505C22—82no—
506C22—164no—
507C22—881no—
508C22—881no—
509C22—881no—
510C22#1062265112yes—
511C22C2×#6699211yescharacteristic
512C4—21no—
513C4—21no—
514C4—21no—
515C4—22no—
516C4—41no—
517C4—41no—
518C4—881no—
519C4#1062265112yes—
520C4#1062330511yescharacteristic
521C4#1062330611yescharacteristic
522C4C22×#432311yescharacteristic
523C4C2×#6700311yescharacteristic
524C2—22no—
525C2—42no—
526C2—162no—
527C2—1761no—
528C2#1307815911yescharacteristic
529C2C2×#1062265111yescharacteristic
530C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3038C2
socleC22×C11C2×#121
hypercenter#3038D11
hypocenterC11#19410
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3038

Complements

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

NH ≅ G/Ntype
1. #13079534C2semidirect
2. #13078071C2semidirect
3. #13077727C2semidirect
4. #13068058C2semidirect
5. #13068051C2semidirect
6. #13067974C2semidirect
7. #13067969C2semidirect
8. #13067392C2semidirect
9. #13067294C2semidirect
10. C2×#10622182C2semidirect
11. C11×#3038C2semidirect
28. #10622644C22semidirect
30. #10622640C22semidirect
31. Q8×C11⋊C8C22semidirect
32. #10622632C22semidirect
34. #10622628C22semidirect
36. D4×C11⋊C8C22semidirect
45. #10622123C22semidirect
46. #10622120C22semidirect
47. #10622117C22semidirect
48. #10622117C22semidirect
114. C11×#41D8semidirect
180. #3038D11semidirect
380. #41#4323semidirect
443. C11#19410semidirect

Maximal subgroups

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

subgroupindex
#130795342
#130780712
#130777272
#130680582
#130680512
#130679742
#130679692
#130673922
#130672942
C2×#106221822
C11×#30382
#1941011