Finite Group Databasebeta

← #14732446

Subgroups — #14732446

Order 2816.

1288 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079534C211yesmaximal, characteristic, complemented
2#13078616C211yesmaximal, characteristic, complemented
3#13078088C211yesmaximal, characteristic, complemented
4#13067809C214yesmaximal, complemented
5#13067681C214yesmaximal, complemented
6#13067284C211yesmaximal, characteristic, complemented
7#13067041C211yesmaximal, characteristic, complemented
8#13067011C211yesmaximal, characteristic, complemented
9C2×C11×#550C211yesmaximal, characteristic, complemented
10C22×C11×#41—21no—
11C11×#550—22no—
12C11×#550—22no—
13C11×#550—22no—
14C11×#550C2214yes—
15C2×C11×#127—21no—
16C2×C11×#127C2211yescharacteristic
17C2×C11×#121—22no—
18C2×C11×#121—21no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66995—21no—
23#10623008C2211yescharacteristic
24#10622830—21no—
25#10622830—22no—
26#10622686C2212yescomplemented
27#10622685—22no—
28#10622683C2212yescomplemented
29#10622644C2212yescomplemented
30#10622641—22no—
31#10622640C2212yescomplemented
32#10622628C2212yescomplemented
33C4×#4323—22no—
34#10622620C2212yescomplemented
35#10622580—21no—
36#10622579—21no—
37#10622538C2211yescharacteristic
38#10622538C2211yescharacteristic
39#10622537C2211yescharacteristic
40#10622182C2214yescomplemented
41Q8⋊(C11⋊C8)C2214yescomplemented
42D4⋊(C11⋊C8)C2214yescomplemented
43C2×C11×#41—24no—
44C2×C11×#41—24no—
45C2×C11×#41—44no—
46C2×C11×#41—44no—
47C22×Q8×C11D411yescharacteristic
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11—21no—
51C22×D4×C11—21no—
52C22×D4×C11D411yescharacteristic
53C22×D4×C11D412yes—
54C23×C4×C11—22no—
55C23×C4×C11—21no—
56C2×#4339—21no—
57C11×#127—24no—
58C11×#127—24no—
59C11×#127—21no—
60C11×#127—21no—
61C11×#127D412yes—
62C11×#127C2312yes—
63C11×#121—24no—
64C11×#121—28no—
65C11×#121—28no—
66C11×#121—24no—
67C4×Q8×C11—21no—
68C4×Q8×C11—21no—
69C4×Q8×C11D412yes—
70C4×Q8×C11C2312yes—
71C4×D4×C11—24no—
72C4×D4×C11—24no—
73C4×D4×C11—21no—
74C4×D4×C11—21no—
75C4×D4×C11D412yes—
76C4×D4×C11C2312yes—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—21no—
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C2×#4326—22no—
85#66995—44no—
86C2×#4325—22no—
87C2×#4323—22no—
88C2×#4323—24no—
89#66983—21no—
90#66983—21no—
91C2×#4318—21no—
92#66928—21no—
93#66927C2311yescharacteristic
94C4×D44—21no—
95C4×D44—21no—
96#66922C2311yescharacteristic
97#66896—22no—
98#66896—24no—
99C22⋊(C11⋊C8)—21no—
100C22⋊(C11⋊C8)—21no—
101#66874—22no—
102#66873—22no—
103#66873—22no—
104#66871—22no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)C2312yes—
108C4⋊(C11⋊C8)C2312yes—
109C4×C11⋊C8—21no—
110C4×C11⋊C8C2312yes—
111#18766—111nomaximal, Sylow
112C24×C11—22no—
113C24×C11—21no—
114C11×#41—48no—
115C11×#41—416no—
116C11×#41—48no—
117C2×Q8×C11—21no—
118C2×Q8×C11—22no—
119C2×Q8×C11D814yescomplemented
120C2×Q8×C11C2×D412yes—
121C2×D4×C11—28no—
122C2×D4×C11—28no—
123C2×D4×C11—21no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—42no—
130C2×D4×C11—44no—
131C2×D4×C11—48no—
132C2×D4×C11—42no—
133C2×D4×C11—42no—
134C2×D4×C11—82no—
135C2×D4×C11—84no—
136C2×D4×C11C2×D412yes—
137C2×D4×C11C2×D414yes—
138C22×C4×C11—21no—
139C22×C4×C11—28no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—48no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C2×C22⋊D11—41no—
151#4339—42no—
152#4339—42no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×C4×D11—41no—
157C2×Dic22—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4C2×D412yes—
163C11×C4⋊C4C2×D412yes—
164C11×C22⋊C4—28no—
165C11×C22⋊C4—22no—
166C11×C22⋊C4—22no—
167C42×C11—22no—
168C42×C11—22no—
169C42×C11C2×D411yescharacteristic
170C42×C11C2×D411yescharacteristic
171C42×C11C2×D411yescharacteristic
172C42×C11C2411yescharacteristic
173#4326—44no—
174#4325—44no—
175#4323—44no—
176#4323—84no—
177(C2×D11)⋊C4—41no—
178(C2×D11)⋊C4—41no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181#4318—42no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×#550D1111yescharacteristic, complemented
186#3205—111no—
187#3100—111no—
188#3037—111no—
189#1641—114no—
190#1621—114no—
191#1545—111no—
192#1486—111no—
193#1479—111no—
194C23×C11—22no—
195C23×C11—24no—
196C23×C11—42no—
197C23×C11—44no—
198C23×C11—44no—
199C23×C11—42no—
200C23×C11—44no—
201C23×C11—42no—
202C23×C11#12011yescharacteristic
203C22×D11—41no—
204Q8×C11—22no—
205Q8×C11—24no—
206Q8×C11C2×D814yes—
207D4×C11—22no—
208D4×C11—22no—
209D4×C11—44no—
210D4×C11—42no—
211D4×C11—44no—
212D4×C11—416no—
213D4×C11—42no—
214D4×C11—42no—
215D4×C11—44no—
216D4×C11—44no—
217D4×C11—82no—
218D4×C11—88no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—41no—
225C2×C4×C11—416no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—44no—
231C2×C4×C11#12011yescharacteristic
232C2×C4×C11#12011yescharacteristic
233C2×C4×C11#12011yescharacteristic
234C2×C4×C11C2×D812yes—
235C2×C4×C11AGL(1,ℤ/8)12yes—
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C22⋊D11—82no—
240C2×Dic11—41no—
241D44—42no—
242D44—41no—
243D44—41no—
244D44—42no—
245C4×D11—82no—
246Dic22—41no—
247Dic22—41no—
248C11⋊C8—42no—
249C11⋊C8—42no—
250C11⋊C8—42no—
251C22×#41—21no—
252C2×#137—221no—
253#550—22no—
254#550—22no—
255#550—22no—
256#550C2×D1114yes—
257#532—111no—
258C2×#127—21no—
259C2×#127C2×D1111yescharacteristic
260C2×#121—22no—
261C2×#121—21no—
262C2×C4×Q8C2×D1111yescharacteristic
263C2×C4×D4—21no—
264C2×C4×D4C2×D1111yescharacteristic
265#493—112no—
266#486—112no—
267#480—221no—
268#474—112no—
269#464—222no—
270#462—112no—
271#460—112no—
272#459—112no—
273#459—222no—
274#447—221no—
275#447—222no—
276C4×D8—222no—
277#431—111no—
278#431—111no—
279#423—111no—
280#417—221no—
281#331—114no—
282Q8⋊C8—114no—
283D4⋊C8—114no—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11—44no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—44no—
290C22×C11—44no—
291C22×C11—42no—
292C22×C11—84no—
293C22×C11—88no—
294C22×C11#44712yes—
295C22×C11C2×#12011yescharacteristic
296C2×D11—81no—
297C2×D11—81no—
298C2×D11—81no—
299C4×C11—24no—
300C4×C11—21no—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—42no—
304C4×C11—42no—
305C4×C11#44712yes—
306C4×C11C22×D811yescharacteristic
307C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
308C4×C11#57512yes—
309Dic11—81no—
310C2×#41—24no—
311C2×#41—24no—
312C2×#41—44no—
313C2×#41—44no—
314C2×#41—221no—
315C22×Q8C22⋊D1111yescharacteristic
316C22×D4—22no—
317C22×D4—22no—
318C22×D4—21no—
319C22×D4—21no—
320C22×D4C22⋊D1111yescharacteristic
321C22×D4C22⋊D1112yes—
322C23×C4—22no—
323C23×C4—21no—
324#137—444no—
325C2×Q16—222no—
326C2×SD16—222no—
327C2×D8—222no—
328C2×D8—224no—
329C2×M16—221no—
330C4⋊Q8—111no—
331#127—24no—
332#127—24no—
333#127—21no—
334#127—21no—
335#127—111no—
336#127C22⋊D1112yes—
337#127C22×D1112yes—
338#124—221no—
339#121—24no—
340#121—28no—
341#121—28no—
342#121—24no—
343#121—221no—
344#121—221no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8C22⋊D1112yes—
348C4×Q8C22×D1112yes—
349C4×D4—24no—
350C4×D4—24no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4—221no—
354C4×D4—221no—
355C4×D4C22⋊D1112yes—
356C4×D4C22×D1112yes—
357C2×C4⋊C4—21no—
358C2×C4⋊C4C22⋊D1111yescharacteristic
359C2×C4⋊C4C22⋊D1111yescharacteristic
360C2×C22⋊C4—22no—
361C2×C22⋊C4—21no—
362C2×C42—21no—
363C2×C42C22×D1111yescharacteristic
364#107—222no—
365C4⋊C8—112no—
366C4⋊C8—112no—
367C4⋊C8—221no—
368C4⋊C8—221no—
369#103—222no—
370#102—222no—
371#102—224no—
372#102—222no—
373#102—222no—
374C22⋊C8—221no—
375C22⋊C8—221no—
376C4×C8—112no—
377C4×C8—221no—
378C2×C11—22no—
379C2×C11—82no—
380C2×C11—84no—
381C2×C11C2×#44711yescharacteristic
382C2×C11#300511yescharacteristic
383C2×C11#301911yescharacteristic
384D11—161no—
385C24—22no—
386C24—21no—
387#41—48no—
388#41—416no—
389#41—48no—
390#41—442no—
391#41—442no—
392C2×Q8—22no—
393C2×Q8—21no—
394C2×Q8—221no—
395C2×Q8#432314yescomplemented
396C2×Q8C2×C22⋊D1112yes—
397C2×D4—28no—
398C2×D4—28no—
399C2×D4—21no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—42no—
406C2×D4—48no—
407C2×D4—44no—
408C2×D4—42no—
409C2×D4—42no—
410C2×D4—82no—
411C2×D4—84no—
412C2×D4—221no—
413C2×D4—221no—
414C2×D4—221no—
415C2×D4—441no—
416C2×D4C2×C22⋊D1112yes—
417C2×D4C2×C22⋊D1114yes—
418C22×C4—21no—
419C22×C4—28no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—48no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—441no—
428C22×C4C2×C22⋊D1111yescharacteristic
429C22×C4C2×C22⋊D1111yescharacteristic
430C22×C4C2×C22⋊D1111yescharacteristic
431Q16—444no—
432SD16—444no—
433D8—444no—
434D8—884no—
435M16—442no—
436C2×C8—222no—
437C2×C8—222no—
438C2×C8—222no—
439C4⋊C4—22no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—221no—
444C4⋊C4—221no—
445C4⋊C4C2×C22⋊D1112yes—
446C4⋊C4C2×C22⋊D1112yes—
447C22⋊C4—28no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—441no—
451C22⋊C4—441no—
452C42—22no—
453C42—22no—
454C42C2×C22⋊D1111yescharacteristic
455C42C2×C22⋊D1111yescharacteristic
456C42C2×C22⋊D1111yescharacteristic
457C42C23×D1111yescharacteristic
458C11#1876611yescharacteristic, complemented, Sylow
459C23—22no—
460C23—24no—
461C23—42no—
462C23—44no—
463C23—44no—
464C23—42no—
465C23—44no—
466C23—42no—
467C23—441no—
468C23#6700611yescharacteristic
469Q8—22no—
470Q8—24no—
471Q8—441no—
472Q8—441no—
473Q8C2×#432314yes—
474D4—22no—
475D4—22no—
476D4—44no—
477D4—42no—
478D4—44no—
479D4—416no—
480D4—42no—
481D4—42no—
482D4—44no—
483D4—44no—
484D4—82no—
485D4—88no—
486D4—442no—
487D4—441no—
488D4—441no—
489D4—442no—
490D4—882no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—41no—
497C2×C4—416no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—44no—
503C2×C4—441no—
504C2×C4—882no—
505C2×C4C2×#432312yes—
506C2×C4#6698512yes—
507C2×C4#6700611yescharacteristic
508C2×C4#6700611yescharacteristic
509C2×C4#6700611yescharacteristic
510C2×C4C22×C22⋊D1111yescharacteristic
511C2×C4C22×C22⋊D1111yescharacteristic
512C2×C4C22×C22⋊D1111yescharacteristic
513C8—442no—
514C8—442no—
515C8—442no—
516C22—21no—
517C22—21no—
518C22—44no—
519C22—42no—
520C22—42no—
521C22—44no—
522C22—44no—
523C22—42no—
524C22—84no—
525C22—88no—
526C22—881no—
527C22—881no—
528C22—881no—
529C22#1062283012yes—
530C22C2×#6700611yescharacteristic
531C4—24no—
532C4—21no—
533C4—21no—
534C4—21no—
535C4—42no—
536C4—42no—
537C4—881no—
538C4#1062283012yes—
539C4C22×#432311yescharacteristic
540C4C2×#6698511yescharacteristic
541C4#1062335312yes—
542C2—22no—
543C2—82no—
544C2—84no—
545C2—1761no—
546C2C2×#1062283011yescharacteristic
547C2#1307785811yescharacteristic
548C2#1307797311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#550C2
socleC22×C11C2×#120
hypercenterC2×#550D11
hypocenterC11#18766
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. #13079534C2semidirect
2. #13078616C2semidirect
3. #13078088C2semidirect
4. #13067809C2semidirect
5. #13067681C2semidirect
6. #13067284C2semidirect
7. #13067041C2semidirect
8. #13067011C2semidirect
9. C2×C11×#550C2semidirect
26. #10622686C22semidirect
28. #10622683C22semidirect
29. #10622644C22semidirect
31. #10622640C22semidirect
32. #10622628C22semidirect
34. #10622620C22semidirect
40. #10622182C22semidirect
41. Q8⋊(C11⋊C8)C22semidirect
42. D4⋊(C11⋊C8)C22semidirect
119. C2×Q8×C11D8semidirect
185. C2×#550D11semidirect
395. C2×Q8#4323semidirect
458. C11#18766semidirect

Maximal subgroups

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

subgroupindex
#130795342
#130786162
#130780882
#130678092
#130676812
#130672842
#130670412
#130670112
C2×C11×#5502
#1876611