Finite Group Databasebeta

← #14736585

Subgroups — #14736585

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#13078991C211yesmaximal, characteristic, complemented
2#13078624C211yesmaximal, characteristic, complemented
3C2×#10622628C211yesmaximal, characteristic
4#13068177C212yesmaximal, complemented
5#13068149C212yesmaximal, complemented
6#13068053C212yesmaximal, complemented
7#13068025C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9#13067307C211yesmaximal, characteristic, complemented
10#13067285C211yesmaximal, characteristic, complemented
11D4×C11×M16C211yesmaximal, characteristic, complemented
12C22×C11×M16—21no—
13C2×C4×D4×C11C2211yescharacteristic
14C22×#4323—21no—
15C2×#66927C2211yescharacteristic
16#10623001C2211yescharacteristic
17C11×#436C2212yescomplemented
18C11×#435—22no—
19C8×D4×C11C2212yescomplemented
20C11×#423C2211yescharacteristic
21C11×#407—21no—
22C4×C11×M16C2211yescharacteristic
23#10622831—21no—
24#10622744—21no—
25#10622744—21no—
26#10622632C2211yescharacteristic, complemented
27#10622632C2211yescharacteristic, complemented
28C4×#4324—21no—
29C4×#4324—21no—
30#10622628—21no—
31#10622628—21no—
32#10622628C2212yes—
33#10622628C2212yes—
34#10622621C2211yescharacteristic, complemented
35#10622621C2211yescharacteristic, complemented
36#10622584—21no—
37C2×#66873—21no—
38#10622538C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40#10622326—22no—
41#10622307C2212yescomplemented
42#10622307C2212yescomplemented
43#10622124C2212yescomplemented
44#10622123C2212yescomplemented
45#10622123C2212yescomplemented
46#10622119C2212yescomplemented
47#10622096C2212yescomplemented
48#10622095C2212yescomplemented
49C22×D4×C11D411yescharacteristic
50C23×C4×C11—21no—
51C22×D44—21no—
52C22×D44—21no—
53C22×D44—21no—
54C2×C11×M16—21no—
55C2×C11×M16—22no—
56C2×C11×M16—44no—
57C2×C11×M16D411yescharacteristic
58C2×C11×M16D411yescharacteristic
59C22×C8×C11—22no—
60C4×D4×C11—21no—
61C4×D4×C11—21no—
62C4×D4×C11D411yescharacteristic
63C4×D4×C11D411yescharacteristic
64C4×D4×C11C2311yescharacteristic
65C4×D4×C11C2311yescharacteristic
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C22⋊C4—21no—
68C2×C42×C11C2311yescharacteristic
69C2×#4324—21no—
70C2×#4324—21no—
71C2×#4323—22no—
72C2×#4323—22no—
73C2×#4323—44no—
74#66979—21no—
75#66977—21no—
76#66977—21no—
77C22×C11⋊C8—21no—
78#66927—21no—
79#66927—21no—
80#66927—21no—
81#66927C2312yes—
82#66923—21no—
83#66922C2311yescharacteristic
84#66922C2311yescharacteristic
85C4×Dic22—21no—
86C4×Dic22—21no—
87C11×C4⋊C8—21no—
88C11×C4⋊C8C2312yes—
89C11×C22⋊C8—22no—
90C11×C22⋊C8—22no—
91C11×#97D412yes—
92C4×C8×C11C2312yes—
93#66896—21no—
94#66896—21no—
95C22⋊(C11⋊C8)—21no—
96#66885—22no—
97#66885—22no—
98#66885—22no—
99#66885—22no—
100#66874—21no—
101#66874—21no—
102#66873—22no—
103#66873—22no—
104#66872—21no—
105#66872—21no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)C2312yes—
108C4⋊(C11⋊C8)C2311yescharacteristic
109C4⋊(C11⋊C8)C2311yescharacteristic
110C4×C11⋊C8—21no—
111#19166—111nomaximal, Sylow
112C24×C11—21no—
113C23×D11—41no—
114C2×D4×C11—22no—
115C2×D4×C11—21no—
116C2×D4×C11—41no—
117C2×D4×C11C2×D411yescharacteristic
118C2×D4×C11C2×D411yescharacteristic
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11#4111yescharacteristic
129C2×D44—22no—
130C2×D44—22no—
131C2×D44—22no—
132C2×D44—42no—
133C2×D44—42no—
134C2×D44—41no—
135C2×D44—41no—
136C2×D44—41no—
137C2×D44—42no—
138C2×D44—42no—
139C2×D44—82no—
140C2×Dic22—21no—
141C2×Dic22—21no—
142C11×M16—22no—
143C11×M16—22no—
144C11×M16—44no—
145C11×M16—42no—
146C2×C8×C11—22no—
147C2×C8×C11—44no—
148C2×C8×C11C2×D412yes—
149C2×C8×C11C2×D412yes—
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—
157C42×C11C2×D411yescharacteristic
158C42×C11C2×D411yescharacteristic
159C42×C11#4111yescharacteristic
160C42×C11C2411yescharacteristic
161C22⋊Dic11—41no—
162#4324—42no—
163#4324—42no—
164#4323—44no—
165#4323—44no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170Dic11⋊C4—41no—
171Dic11⋊C4—41no—
172C4×Dic11—41no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—42no—
177#3138—111no—
178#3101—111no—
179C2×#459—111no—
180D4×M16D1111yescharacteristic, complemented
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—81no—
193C23×C11#12111yescharacteristic
194C22×D11—42no—
195C22×D11—82no—
196C22×D11—82no—
197C22×D11—82no—
198D4×C11—21no—
199D4×C11—21no—
200D4×C11—21no—
201D4×C11—42no—
202D4×C11AGL(1,ℤ/8)12yes—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11#12111yescharacteristic
216C2×C4×C11#12111yescharacteristic
217C2×C4×C11#12111yescharacteristic
218C2×C4×C11#13512yes—
219C2×C4×C11AGL(1,ℤ/8)12yes—
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×Dic11—41no—
224C2×Dic11—41no—
225D44—42no—
226D44—42no—
227D44—42no—
228D44—42no—
229D44—82no—
230D44—82no—
231D44—82no—
232D44—82no—
233Dic22—41no—
234Dic22—41no—
235Dic22—81no—
236C8×C11—22no—
237C8×C11—22no—
238C8×C11—42no—
239C11⋊C8—42no—
240C11⋊C8—41no—
241C11⋊C8—41no—
242C22×D8—221no—
243C22×M16—21no—
244#533—111no—
245C2×#127—111no—
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—112no—
256#459—112no—
257#459—221no—
258#459—221no—
259#450—221no—
260C4×SD16—221no—
261C4×SD16—221no—
262#436C2×D1112yescomplemented
263#435—22no—
264C8×D4C2×D1112yescomplemented
265#431—111no—
266#423C2×D1111yescharacteristic
267C2×C4⋊C8—111no—
268#418—221no—
269#418—221no—
270C2×#102—221no—
271#407—21no—
272C4×M16C2×D1111yescharacteristic
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#46312yes—
289C22×C11C2×#12111yescharacteristic
290C2×D11—82no—
291C2×D11—82no—
292C2×D11—82no—
293C2×D11—164no—
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—221no—
307C22×D4—221no—
308C22×D4—221no—
309C22×D4D4411yescharacteristic
310C23×C4—21no—
311C2×SD16—221no—
312C2×SD16—221no—
313C2×D8—222no—
314C2×D8—222no—
315C2×D8—444no—
316C2×M16—21no—
317C2×M16—22no—
318C2×M16—44no—
319C2×M16C22⋊D1111yescharacteristic
320C2×M16C22⋊D1111yescharacteristic
321C22×C8—22no—
322C22×C8—221no—
323C4⋊Q8—111no—
324C4⋊Q8—111no—
325#127—112no—
326#127—221no—
327#127—221no—
328#127—221no—
329#125—221no—
330C22⋊Q8—221no—
331C22⋊Q8—221no—
332C4×Q8—221no—
333C4×Q8—221no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4D4411yescharacteristic
337C4×D4D4411yescharacteristic
338C4×D4C22×D1111yescharacteristic
339C4×D4C22×D1111yescharacteristic
340#117—221no—
341C2×C4⋊C4D4411yescharacteristic
342C2×C22⋊C4—21no—
343C2×C42C22×D1111yescharacteristic
344#106—221no—
345#106—221no—
346C4⋊C8—21no—
347C4⋊C8—111no—
348C4⋊C8—111no—
349C4⋊C8—112no—
350C4⋊C8—221no—
351C4⋊C8C22×D1112yes—
352#103—221no—
353#103—221no—
354#102—221no—
355#102—221no—
356#102—222no—
357#102—222no—
358#102—222no—
359#102—222no—
360#102—222no—
361#102—222no—
362C22⋊C8—22no—
363C22⋊C8—22no—
364C22⋊C8—221no—
365#97C22⋊D1112yes—
366C4×C8—221no—
367C4×C8C22×D1112yes—
368C2×C11—22no—
369C2×C11—42no—
370C2×C11—81no—
371C2×C11C2×#46311yescharacteristic
372C2×C11#305511yescharacteristic
373C2×C11#306811yescharacteristic
374D11—162no—
375C24—21no—
376C24—441no—
377C2×Q8—221no—
378C2×Q8—221no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—41no—
382C2×D4—222no—
383C2×D4—222no—
384C2×D4—222no—
385C2×D4—442no—
386C2×D4—442no—
387C2×D4—441no—
388C2×D4—441no—
389C2×D4—441no—
390C2×D4—442no—
391C2×D4—442no—
392C2×D4—882no—
393C2×D4C2×D4411yescharacteristic
394C2×D4C2×D4411yescharacteristic
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—42no—
401C22×C4—42no—
402C22×C4C2×D4411yescharacteristic
403C22×C4#433911yescharacteristic
404C22×C4C2×C22⋊D1111yescharacteristic
405SD16—442no—
406SD16—442no—
407D8—444no—
408D8—444no—
409M16—22no—
410M16—22no—
411M16—44no—
412M16—42no—
413C2×C8—22no—
414C2×C8—44no—
415C2×C8—221no—
416C2×C8—221no—
417C2×C8—222no—
418C2×C8—442no—
419C2×C8C2×C22⋊D1112yes—
420C2×C8C2×C22⋊D1112yes—
421C4⋊C4—21no—
422C4⋊C4—221no—
423C4⋊C4—221no—
424C4⋊C4—221no—
425C4⋊C4—221no—
426C4⋊C4—441no—
427C4⋊C4—441no—
428C4⋊C4C2×D4411yescharacteristic
429C4⋊C4C2×D4411yescharacteristic
430C22⋊C4—21no—
431C22⋊C4—21no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—441no—
435C42—441no—
436C42C2×D4411yescharacteristic
437C42#433911yescharacteristic
438C42C2×C22⋊D1111yescharacteristic
439C42C23×D1111yescharacteristic
440C11#1916611yescharacteristic, complemented, Sylow
441C23—21no—
442C23—21no—
443C23—42no—
444C23—42no—
445C23—81no—
446C23—442no—
447C23—882no—
448C23—882no—
449C23—882no—
450C23#6698311yescharacteristic
451Q8—441no—
452Q8—441no—
453Q8—881no—
454D4—21no—
455D4—21no—
456D4—21no—
457D4—42no—
458D4—442no—
459D4—442no—
460D4—442no—
461D4—442no—
462D4—882no—
463D4—882no—
464D4—882no—
465D4—882no—
466D4#6696112yes—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4#6698311yescharacteristic
482C2×C4#6698311yescharacteristic
483C2×C4#6698311yescharacteristic
484C2×C4#6698512yes—
485C2×C4#6700312yes—
486C2×C4C22×D4411yescharacteristic
487C2×C4C2×#433911yescharacteristic
488C2×C4C22×C22⋊D1111yescharacteristic
489C8—22no—
490C8—22no—
491C8—42no—
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—882no—
505C22—882no—
506C22—882no—
507C22—1764no—
508C22#1062262912yes—
509C22C2×#6698311yescharacteristic
510C4—21no—
511C4—21no—
512C4—21no—
513C4—41no—
514C4—41no—
515C4—881no—
516C4—881no—
517C4#1062262912yes—
518C4C2×#6696111yescharacteristic
519C4#1062327911yescharacteristic
520C4C2×#6698511yescharacteristic
521C4C2×#6700311yescharacteristic
522C2—22no—
523C2—42no—
524C2—81no—
525C2—1762no—
526C2C2×#1062262911yescharacteristic
527C2#1307823511yescharacteristic
528C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingD4×C11×M16C2
socleC22×C11C2×#121
prime radicalC2×#10622628C2
hypercenterD4×M16D11
hypocenterC11#19166
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
1. #13078991C2semidirect
2. #13078624C2semidirect
4. #13068177C2semidirect
5. #13068149C2semidirect
6. #13068053C2semidirect
7. #13068025C2semidirect
8. #13067368C2semidirect
9. #13067307C2semidirect
10. #13067285C2semidirect
11. D4×C11×M16C2semidirect
17. C11×#436C22semidirect
19. C8×D4×C11C22semidirect
26. #10622632C22semidirect
27. #10622632C22semidirect
34. #10622621C22semidirect
35. #10622621C22semidirect
41. #10622307C22semidirect
42. #10622307C22semidirect
43. #10622124C22semidirect
44. #10622123C22semidirect
45. #10622123C22semidirect
46. #10622119C22semidirect
47. #10622096C22semidirect
48. #10622095C22semidirect
180. D4×M16D11semidirect
262. #436C2×D11semidirect
264. C8×D4C2×D11semidirect
440. C11#19166semidirect

Maximal subgroups

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

subgroupindex
#130789912
#130786242
C2×#106226282
#130681772
#130681492
#130680532
#130680252
#130673682
#130673072
#130672852
D4×C11×M162
#1916611