Finite Group Databasebeta

← #14736581

Subgroups — #14736581

Order 2816.

758 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078990C211yesmaximal, characteristic, complemented
2#13078624C211yesmaximal, characteristic, complemented
3D4×#4318C211yesmaximal, characteristic, complemented
4#13068175C212yesmaximal, complemented
5#13068147C212yesmaximal, complemented
6#13068051C212yesmaximal, complemented
7#13068023C212yesmaximal, complemented
8#13067366C211yesmaximal, characteristic, complemented
9#13067304C211yesmaximal, characteristic, complemented
10#13067284C211yesmaximal, characteristic, complemented
11C2×C11×#459C211yesmaximal, characteristic
12C22×C11×D8—21no—
13C2×C11×#127C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C22×#4318—21no—
16#10623001C2211yescharacteristic
17C11×#459—21no—
18C11×#459—21no—
19C11×#459C2212yes—
20C11×#459C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#102—21no—
23#10622831—21no—
24#10622828—21no—
25#10622828—21no—
26#10622820—21no—
27#10622684—22no—
28#10622683C2212yescomplemented
29#10622683C2212yescomplemented
30#10622632C2211yescharacteristic, complemented
31#10622632C2211yescharacteristic, complemented
32C4×#4324—21no—
33C4×#4324—21no—
34#10622625C2212yescomplemented
35#10622624—22no—
36D4×C11⋊C8C2212yescomplemented
37#10622621C2211yescharacteristic, complemented
38#10622621C2211yescharacteristic, complemented
39#10622584—21no—
40#10622538C2211yescharacteristic
41#10622537C2211yescharacteristic
42C4×#4318C2211yescharacteristic
43#10622182C2212yescomplemented
44#10622182C2212yescomplemented
45#10622120C2212yescomplemented
46#10622119C2212yescomplemented
47#10622118C2212yescomplemented
48#10622117C2212yescomplemented
49C22×D4×C11—21no—
50C22×D4×C11—21no—
51C22×D4×C11—21no—
52C22×D4×C11D411yescharacteristic
53C23×C4×C11—21no—
54C2×C11×D8—22no—
55C2×C11×D8—22no—
56C2×C11×D8—44no—
57C22×C8×C11—21no—
58C11×#127—21no—
59C11×#127—21no—
60C11×#127—21no—
61C11×#127C2312yes—
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64C4×D4×C11D411yescharacteristic
65C4×D4×C11D411yescharacteristic
66C4×D4×C11C2311yescharacteristic
67C4×D4×C11C2311yescharacteristic
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C22⋊C4—21no—
70C2×C42×C11C2311yescharacteristic
71C2×#4324—21no—
72C2×#4324—21no—
73#66979—21no—
74#66977—21no—
75#66977—21no—
76C2×#4318—21no—
77C2×#4318—22no—
78C2×#4318—44no—
79C2×#4318D411yescharacteristic
80C2×#4318D411yescharacteristic
81C22×C11⋊C8—22no—
82#66923—21no—
83#66922C2311yescharacteristic
84#66922C2311yescharacteristic
85C4×Dic22—21no—
86C4×Dic22—21no—
87C11×C4⋊C8—21no—
88C11×C4⋊C8C2312yes—
89C11×#102—22no—
90C11×#102—22no—
91#66896—21no—
92#66896—21no—
93#66896—22no—
94#66896—22no—
95#66896—22no—
96#66896—22no—
97C22⋊(C11⋊C8)—21no—
98C22⋊(C11⋊C8)—22no—
99C22⋊(C11⋊C8)—22no—
100#66874—21no—
101#66874—21no—
102#66872—21no—
103#66872—21no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)C2312yes—
106C4⋊(C11⋊C8)C2311yescharacteristic
107C4⋊(C11⋊C8)C2311yescharacteristic
108#66867D412yes—
109C4×C11⋊C8—21no—
110C4×C11⋊C8C2312yes—
111#19166—111nomaximal, Sylow
112C24×C11—21no—
113C24×C11—41no—
114C2×D4×C11—22no—
115C2×D4×C11—21no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—41no—
120C2×D4×C11—42no—
121C2×D4×C11—42no—
122C2×D4×C11—41no—
123C2×D4×C11—41no—
124C2×D4×C11—41no—
125C2×D4×C11—42no—
126C2×D4×C11—42no—
127C2×D4×C11—82no—
128C2×D4×C11C2×D411yescharacteristic
129C2×D4×C11C2×D411yescharacteristic
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—42no—
136C22×C4×C11—42no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11#4111yescharacteristic
140C2×Dic22—21no—
141C2×Dic22—21no—
142C11×D8—44no—
143C11×D8—44no—
144C2×C8×C11—22no—
145C2×C8×C11—42no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4C2×D411yescharacteristic
148C11×C4⋊C4C2×D411yescharacteristic
149C11×C22⋊C4—21no—
150C11×C22⋊C4—21no—
151C11×C22⋊C4—21no—
152C11×C22⋊C4—21no—
153C42×C11C2×D411yescharacteristic
154C42×C11C2×D411yescharacteristic
155C42×C11#4111yescharacteristic
156C42×C11C2411yescharacteristic
157C22⋊Dic11—41no—
158#4324—42no—
159#4324—42no—
160C4⋊Dic11—21no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164Dic11⋊C4—41no—
165Dic11⋊C4—41no—
166C4×Dic11—41no—
167#4318—22no—
168#4318—22no—
169#4318—44no—
170#4318—42no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—44no—
175C2×C11⋊C8C2×D412yes—
176C2×C11⋊C8C2×D412yes—
177#3138—111no—
178#3101—111no—
179C2×#459D1111yescharacteristic
180D4×M16—111no—
181#1701—112no—
182#1697—112no—
183#1681—112no—
184#1677—112no—
185#1565—111no—
186#1550—111no—
187#1545—111no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—81no—
194C23×C11—82no—
195C23×C11—82no—
196C23×C11—82no—
197C23×C11#12111yescharacteristic
198D4×C11—21no—
199D4×C11—21no—
200D4×C11—21no—
201D4×C11—42no—
202D4×C11—42no—
203D4×C11—42no—
204D4×C11—42no—
205D4×C11—42no—
206D4×C11—82no—
207D4×C11—82no—
208D4×C11—82no—
209D4×C11—82no—
210D4×C11AGL(1,ℤ/8)12yes—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—41no—
216C2×C4×C11—42no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11#12111yescharacteristic
224C2×C4×C11#12111yescharacteristic
225C2×C4×C11#12111yescharacteristic
226C2×C4×C11#13512yes—
227C2×C4×C11AGL(1,ℤ/8)12yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×Dic11—41no—
232C2×Dic11—41no—
233Dic22—41no—
234Dic22—41no—
235Dic22—81no—
236C8×C11—42no—
237C11⋊C8—22no—
238C11⋊C8—22no—
239C11⋊C8—42no—
240C11⋊C8—41no—
241C11⋊C8—41no—
242C22×D8—21no—
243C22×M16—221no—
244#533—111no—
245C2×#127C2×D1111yescharacteristic
246C2×C4×D4C2×D1111yescharacteristic
247#490—222no—
248#486—112no—
249#486—112no—
250#483—221no—
251#476—111no—
252#476—111no—
253#461—111no—
254#461—111no—
255#459—21no—
256#459—21no—
257#459C2×D1112yes—
258#459C2×D1112yes—
259#450—221no—
260C4×SD16—221no—
261C4×SD16—221no—
262#436—112no—
263#435—222no—
264C8×D4—112no—
265#431—111no—
266#423—111no—
267C2×C4⋊C8C2×D1111yescharacteristic
268#418—221no—
269#418—221no—
270C2×#102—21no—
271#407—221no—
272C4×M16—111no—
273#335—112no—
274#334—112no—
275#333—112no—
276#332—112no—
277#331—112no—
278#331—112no—
279C22×C11—21no—
280C22×C11—21no—
281C22×C11—22no—
282C22×C11—41no—
283C22×C11—41no—
284C22×C11—41no—
285C22×C11—41no—
286C22×C11—41no—
287C22×C11—84no—
288C22×C11—82no—
289C22×C11—82no—
290C22×C11—82no—
291C22×C11—164no—
292C22×C11#46312yes—
293C22×C11C2×#12111yescharacteristic
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—21no—
297C4×C11—41no—
298C4×C11—41no—
299C4×C11#46312yes—
300C4×C11C2×#13511yescharacteristic
301C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
302C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
303C4×C11#57511yescharacteristic
304Dic11—81no—
305Dic11—81no—
306C22×D4—21no—
307C22×D4—21no—
308C22×D4—21no—
309C22×D4C22⋊D1111yescharacteristic
310C23×C4—21no—
311C2×SD16—221no—
312C2×SD16—221no—
313C2×D8—22no—
314C2×D8—22no—
315C2×D8—44no—
316C2×M16—111no—
317C2×M16—111no—
318C2×M16—222no—
319C2×M16—221no—
320C2×M16—444no—
321C22×C8—21no—
322C22×C8—222no—
323C4⋊Q8—111no—
324C4⋊Q8—111no—
325#127—21no—
326#127—21no—
327#127—21no—
328#127C22×D1112yes—
329#125—221no—
330C22⋊Q8—221no—
331C22⋊Q8—221no—
332C4×Q8—221no—
333C4×Q8—221no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4C22⋊D1111yescharacteristic
337C4×D4C22⋊D1111yescharacteristic
338C4×D4C22×D1111yescharacteristic
339C4×D4C22×D1111yescharacteristic
340#117—221no—
341C2×C4⋊C4C22⋊D1111yescharacteristic
342C2×C22⋊C4—21no—
343C2×C42C22×D1111yescharacteristic
344#106—221no—
345#106—221no—
346C4⋊C8—21no—
347C4⋊C8—112no—
348C4⋊C8—111no—
349C4⋊C8—111no—
350C4⋊C8—221no—
351C4⋊C8C22×D1112yes—
352#103—221no—
353#103—221no—
354#102—22no—
355#102—22no—
356#102—222no—
357#102—222no—
358#102—222no—
359#102—222no—
360#102—221no—
361#102—221no—
362C22⋊C8—222no—
363C22⋊C8—222no—
364C22⋊C8—221no—
365#97—112no—
366C4×C8—112no—
367C4×C8—221no—
368C2×C11—22no—
369C2×C11—42no—
370C2×C11—81no—
371C2×C11—162no—
372C2×C11C2×#46311yescharacteristic
373C2×C11#305511yescharacteristic
374C2×C11#306811yescharacteristic
375C24—21no—
376C24—41no—
377C2×Q8—221no—
378C2×Q8—221no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—41no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4—42no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—82no—
393C2×D4C2×C22⋊D1111yescharacteristic
394C2×D4C2×C22⋊D1111yescharacteristic
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4D4×D1111yescharacteristic
403C22×C4#434111yescharacteristic
404C22×C4C2×C22⋊D1111yescharacteristic
405SD16—442no—
406SD16—442no—
407D8—44no—
408D8—44no—
409M16—222no—
410M16—222no—
411M16—444no—
412M16—442no—
413C2×C8—22no—
414C2×C8—42no—
415C2×C8—112no—
416C2×C8—112no—
417C2×C8—222no—
418C2×C8—221no—
419C2×C8—221no—
420C2×C8—444no—
421C4⋊C4—21no—
422C4⋊C4—221no—
423C4⋊C4—221no—
424C4⋊C4—221no—
425C4⋊C4—221no—
426C4⋊C4—441no—
427C4⋊C4—441no—
428C4⋊C4C2×C22⋊D1111yescharacteristic
429C4⋊C4C2×C22⋊D1111yescharacteristic
430C22⋊C4—21no—
431C22⋊C4—21no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—441no—
435C42—441no—
436C42D4×D1111yescharacteristic
437C42#434111yescharacteristic
438C42C2×C22⋊D1111yescharacteristic
439C42C23×D1111yescharacteristic
440C11#1916611yescharacteristic, complemented, Sylow
441C23—21no—
442C23—21no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—81no—
447C23—82no—
448C23—82no—
449C23—82no—
450C23#6699211yescharacteristic
451Q8—441no—
452Q8—441no—
453Q8—881no—
454D4—21no—
455D4—21no—
456D4—21no—
457D4—42no—
458D4—42no—
459D4—42no—
460D4—42no—
461D4—42no—
462D4—82no—
463D4—82no—
464D4—82no—
465D4—82no—
466D4#6698512yes—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4#6696412yes—
482C2×C4#6696512yes—
483C2×C4#6699211yescharacteristic
484C2×C4#6699211yescharacteristic
485C2×C4#6699211yescharacteristic
486C2×C4C2×D4×D1111yescharacteristic
487C2×C4C2×#434111yescharacteristic
488C2×C4C22×C22⋊D1111yescharacteristic
489C8—42no—
490C8—222no—
491C8—222no—
492C8—442no—
493C8—441no—
494C8—441no—
495C22—21no—
496C22—21no—
497C22—22no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—84no—
504C22—82no—
505C22—82no—
506C22—82no—
507C22—164no—
508C22#1062276612yes—
509C22C2×#6699211yescharacteristic
510C4—21no—
511C4—21no—
512C4—21no—
513C4—41no—
514C4—41no—
515C4—881no—
516C4—881no—
517C4#1062276612yes—
518C4C2×#6696411yescharacteristic
519C4C2×#6696511yescharacteristic
520C4C2×#6698511yescharacteristic
521C4#1062335311yescharacteristic
522C2—22no—
523C2—42no—
524C2—81no—
525C2—162no—
526C2C2×#1062276611yescharacteristic
527C2#1307823111yescharacteristic
528C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC2×C11×#459C2
socleC22×C11C2×#121
hypercenterC2×#459D11
hypocenterC11#19166
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. #13078990C2semidirect
2. #13078624C2semidirect
3. D4×#4318C2semidirect
4. #13068175C2semidirect
5. #13068147C2semidirect
6. #13068051C2semidirect
7. #13068023C2semidirect
8. #13067366C2semidirect
9. #13067304C2semidirect
10. #13067284C2semidirect
28. #10622683C22semidirect
29. #10622683C22semidirect
30. #10622632C22semidirect
31. #10622632C22semidirect
34. #10622625C22semidirect
36. D4×C11⋊C8C22semidirect
37. #10622621C22semidirect
38. #10622621C22semidirect
43. #10622182C22semidirect
44. #10622182C22semidirect
45. #10622120C22semidirect
46. #10622119C22semidirect
47. #10622118C22semidirect
48. #10622117C22semidirect
440. C11#19166semidirect

Maximal subgroups

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

subgroupindex
#130789902
#130786242
D4×#43182
#130681752
#130681472
#130680512
#130680232
#130673662
#130673042
#130672842
C2×C11×#4592
#1916611