Finite Group Databasebeta

← #14906705

Subgroups — #14906705

Order 2816.

1114 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13083385C211yesmaximal, characteristic
2C2×#10622520C211yesmaximal, characteristic, complemented
3#13077224C211yesmaximal, characteristic, complemented
4#13070345C211yesmaximal, characteristic, complemented
5#13070342C214yesmaximal, complemented
6C2×#10622205C211yesmaximal, characteristic, complemented
7C2×#10622135C211yesmaximal, characteristic, complemented
8D11×#359C214yesmaximal, complemented
9C11×#2143C211yesmaximal, characteristic, complemented
10#10623453—21no—
11C2×C11×#135C2211yescharacteristic
12#10623353—21no—
13#10623302C412yes—
14#10623301—22no—
15#10623300C412yes—
16#10623299—22no—
17D11×#135C2214yes—
18#10623297C412yes—
19#10623293—22no—
20#10623288C412yes—
21#10623276—21no—
22C2×#66957C2211yescharacteristic
23C2×#66954C2211yescharacteristic
24C2×C11×M32C2211yescharacteristic, complemented
25C2×C11×#108C2211yescharacteristic, complemented
26#10622737—21no—
27C2×#66883C2211yescharacteristic, complemented
28C22×C11⋊C16C2211yescharacteristic, complemented
29#10622520—22no—
30#10622520—22no—
31C2×#66862C2212yescomplemented
32C2×C16×D11C2212yescomplemented
33#10622506—22no—
34D11×#108C2214yescomplemented
35C11×#359C2214yescomplemented
36#10622205C2212yescomplemented
37#10622205C2212yescomplemented
38#10622148C2214yescomplemented
39#10622135C2212yescomplemented
40#10622135C2212yescomplemented
41C2×C11×#41—21no—
42#67043—22no—
43#67043—41no—
44#67042—22no—
45#67042—41no—
46#41×D11—24no—
47#41×D11—42no—
48#67040—22no—
49#67037—22no—
50#67037—42no—
51C2×#4339—21no—
52C2×#4339—42no—
53C2×#4339D411yescharacteristic
54C11×#135—21no—
55C11×#135—21no—
56C11×#135C2×C412yes—
57C11×#135C2312yes—
58C2×C11×Q16C2×C411yescharacteristic
59C2×C11×SD16—21no—
60C2×C11×D8C2×C411yescharacteristic
61C2×C11×M16—21no—
62C22×C8×C11C2311yescharacteristic
63#67004—22no—
64#67003—24no—
65#67002—22no—
66#66995—22no—
67#66985—22no—
68C2×#4318—21no—
69C2×#4318D411yescharacteristic
70#66972C2×C414yes—
71#66971—24no—
72Q16×D11C2×C414yes—
73#66969—24no—
74#66968—24no—
75#66967—24no—
76SD16×D11—24no—
77#66965C2×C414yes—
78#66964—24no—
79D8×D11C2×C414yes—
80#66960—42no—
81M16×D11—24no—
82C2×Dic44C2×C411yescharacteristic
83#66957—21no—
84#66957—21no—
85#66957C2×C412yes—
86#66957C2312yes—
87C2×D88C2×C411yescharacteristic
88C2×#4314—21no—
89#66954—42no—
90#66954C2×C412yes—
91#66954C2×C412yes—
92#66954D412yes—
93#66954D412yes—
94C2×#4313D412yes—
95C2×C8×D11C2312yes—
96C11×M32—21no—
97C11×M32—21no—
98C2×C11×C16C2312yes—
99C11×#108—21no—
100C11×#108C2312yes—
101#66886—24no—
102#66883—21no—
103#66883C2312yes—
104C2×C11⋊C16—21no—
105C2×C11⋊C16—21no—
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66862—24no—
109C16×D11—24no—
110#33385—111nomaximal, Sylow
111C11×#41—22no—
112C11×#41—22no—
113C11×#41—41no—
114C11×#41—41no—
115C2×Q8×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—41no—
118C22×C4×C11—41no—
119C22×C4×C11C2×D411yescharacteristic
120C2×C22⋊D11—44no—
121C2×C22⋊D11—41no—
122C2×C22⋊D11SD1612yes—
123#4343—24no—
124#4343—42no—
125Q8×D11—24no—
126Q8×D11—42no—
127#4341—24no—
128#4341—44no—
129#4341—44no—
130#4341—42no—
131D4×D11—24no—
132D4×D11—44no—
133D4×D11—42no—
134D4×D11—44no—
135#4339—22no—
136#4339—22no—
137#4339—44no—
138#4339—42no—
139#4339—44no—
140#4339—42no—
141#4339—41no—
142#4339—41no—
143#4339C22⋊C412yes—
144#4339C22⋊C412yes—
145#4339D812yes—
146#4339D812yes—
147C2×D44—21no—
148C2×D44—42no—
149C2×D44SD1611yescharacteristic
150C2×C4×D11—44no—
151C2×C4×D11—41no—
152C2×C4×D11C2×D412yes—
153C2×Dic22—21no—
154C2×Dic22—42no—
155C2×Dic22SD1611yescharacteristic
156C11×Q16—21no—
157C11×Q16C22×C412yes—
158C11×SD16—22no—
159C11×SD16—22no—
160C11×D8—21no—
161C11×D8C22×C412yes—
162C11×M16—22no—
163C11×M16—41no—
164C2×C8×C11—41no—
165C2×C8×C11C22×C411yescharacteristic
166C2×C8×C11C22×C411yescharacteristic
167C2×C8×C11C2×D411yescharacteristic
168C2×C8×C11C2×D411yescharacteristic
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2411yescharacteristic
171#4326—24no—
172#4325—24no—
173#4324—24no—
174#4323—24no—
175#4318—22no—
176#4318—41no—
177#4318C22⋊C412yes—
178#4318C22⋊C412yes—
179C2×C11⋊C8—41no—
180C2×C11⋊C8C2×D412yes—
181Dic44—21no—
182Dic44C22×C412yes—
183D88—21no—
184D88C22×C412yes—
185#4314—22no—
186#4314—22no—
187#4313—44no—
188#4313C22⋊C414yes—
189#4313C22⋊C414yes—
190C8×D11—44no—
191C8×D11C22×C414yes—
192C8×D11C2×D414yes—
193C11×C16—22no—
194C11⋊C16—21no—
195C11⋊C16—21no—
196#3584—111no—
197C2×#504—111no—
198#2916—111no—
199#2143—111no—
200#2143—114no—
201#2143D1111yescharacteristic, complemented
202C2×#359—111no—
203C2×#359—114no—
204C2×#359—111no—
205C23×C11—41no—
206C23×C11C2×SD1611yescharacteristic
207C22×D11—41no—
208C22×D11—44no—
209C22×D11C2×SD1612yes—
210Q8×C11—22no—
211Q8×C11—41no—
212D4×C11—22no—
213D4×C11—42no—
214D4×C11—42no—
215D4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11C2×C22⋊C411yescharacteristic
220C2×C4×C11C2×C22⋊C411yescharacteristic
221C2×C4×C11C2×D811yescharacteristic
222C2×C4×C11C2×D811yescharacteristic
223C2×C4×C11C2×SD1611yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C22⋊D11—42no—
226C22⋊D11—42no—
227C22⋊D11—44no—
228C22⋊D11—44no—
229C22⋊D11#10214yes—
230C22⋊D11#10214yes—
231C2×Dic11—41no—
232C2×Dic11—44no—
233C2×Dic11C2×SD1612yes—
234D44—22no—
235D44—44no—
236D44—41no—
237D44#10212yes—
238D44#10212yes—
239C4×D11—44no—
240C4×D11—42no—
241C4×D11—42no—
242C4×D11—44no—
243C4×D11C2×C22⋊C414yes—
244C4×D11C2×D814yes—
245Dic22—22no—
246Dic22—41no—
247Dic22—44no—
248Dic22#10212yes—
249Dic22#10212yes—
250C8×C11—42no—
251C8×C11C2×C22⋊C411yescharacteristic
252C8×C11C2×C22⋊C411yescharacteristic
253C8×C11C23×C411yescharacteristic
254C8×C11C22×D411yescharacteristic
255C11⋊C8—42no—
256C11⋊C8C2×C22⋊C414yes—
257#585—221no—
258#578—112no—
259#578—112no—
260#577—222no—
261#577—222no—
262#576—112no—
263#576—112no—
264#575—222no—
265#575—221no—
266C2×#135—114no—
267C2×#135—111no—
268C2×#135C2×D1111yescharacteristic
269#568—221no—
270C2×#131—111no—
271#504—222no—
272#504—222no—
273C2×M32—112no—
274C2×M32C2×D1111yescharacteristic, complemented
275C22×C16—111no—
276C22×C16—112no—
277#430—222no—
278#430—221no—
279C2×#108—111no—
280C2×#108—114no—
281C2×#108C2×D1111yescharacteristic, complemented
282#359—112no—
283#359—112no—
284#359—114no—
285#359—112no—
286#359—112no—
287#359C2×D1114yescomplemented
288C22×C11—41no—
289C22×C11—42no—
290C22×C11—161no—
291C22×C11C2×#10211yescharacteristic
292C22×C11C2×#10211yescharacteristic
293C22×C11C22×SD1611yescharacteristic
294C2×D11—42no—
295C2×D11—42no—
296C2×D11—164no—
297C2×D11—161no—
298C2×D11C2×#10214yes—
299C4×C11—42no—
300C4×C11C2×#10211yescharacteristic
301C4×C11C2×#10211yescharacteristic
302C4×C11C22×C22⋊C411yescharacteristic
303C4×C11C22×D811yescharacteristic
304Dic11—42no—
305Dic11C2×#10214yes—
3062−1+4—222no—
3072−1+4—222no—
3082−1+4—441no—
309H(5,𝔽2)—222no—
310H(5,𝔽2)—222no—
311H(5,𝔽2)—442no—
312H(5,𝔽2)—441no—
313C2×#41—21no—
314C2×#41—111no—
315C2×#41—224no—
316C2×#41—221no—
317C2×#41—442no—
318C2×#41—442no—
319#137—224no—
320#137—224no—
321#137—222no—
322#137—222no—
323AGL(1,ℤ/8)—224no—
324AGL(1,ℤ/8)—224no—
325AGL(1,ℤ/8)—222no—
326AGL(1,ℤ/8)—222no—
327#135—21no—
328#135—21no—
329#135—114no—
330#135—114no—
331#135—112no—
332#135—112no—
333#135—224no—
334#135—224no—
335#135—221no—
336#135—221no—
337#135C4×D1112yes—
338#135C22×D1112yes—
339C2×Q16—114no—
340C2×Q16—111no—
341C2×Q16C4×D1111yescharacteristic
342C2×SD16—21no—
343C2×SD16—224no—
344C2×SD16—221no—
345C2×D8—114no—
346C2×D8—111no—
347C2×D8C4×D1111yescharacteristic
348#131—112no—
349#131—112no—
350#131—112no—
351#131—112no—
352#131—442no—
353#131—442no—
354C2×M16—21no—
355C2×M16—111no—
356C2×M16—112no—
357C2×M16—224no—
358C2×M16—221no—
359C22×C8—112no—
360C22×C8C22×D1111yescharacteristic
361M32—21no—
362M32—21no—
363M32—224no—
364C2×C16—111no—
365C2×C16—111no—
366C2×C16—224no—
367C2×C16—221no—
368C2×C16—221no—
369C2×C16C22×D1112yes—
370#108—21no—
371#108—112no—
372#108—224no—
373#108—221no—
374#108C22×D1112yes—
375C2×C11—21no—
376C2×C11—21no—
377C2×C11—21no—
378C2×C11—82no—
379C2×C11C22×#10211yescharacteristic
380D11—24no—
381D11—82no—
382#41—22no—
383#41—22no—
384#41—41no—
385#41—41no—
386#41—112no—
387#41—112no—
388#41—112no—
389#41—112no—
390#41—224no—
391#41—224no—
392#41—222no—
393#41—222no—
394#41—444no—
395#41—444no—
396#41—442no—
397#41—442no—
398#41—444no—
399#41—444no—
400#41—442no—
401#41—442no—
402#41—441no—
403#41—441no—
404C2×Q8—21no—
405C2×Q8—111no—
406C2×Q8—224no—
407C2×Q8—221no—
408C2×Q8—442no—
409C2×Q8—442no—
410C2×D4—21no—
411C2×D4—41no—
412C2×D4—112no—
413C2×D4—111no—
414C2×D4—224no—
415C2×D4—221no—
416C2×D4—442no—
417C2×D4—444no—
418C2×D4—442no—
419C2×D4—444no—
420C2×D4—444no—
421C2×D4—441no—
422C22×C4—41no—
423C22×C4—112no—
424C22×C4—444no—
425C22×C4—441no—
426C22×C4D4×D1111yescharacteristic
427Q16—21no—
428Q16—112no—
429Q16—224no—
430Q16—221no—
431Q16C2×C4×D1112yes—
432SD16—22no—
433SD16—22no—
434SD16—224no—
435SD16—224no—
436SD16—222no—
437SD16—222no—
438D8—21no—
439D8—112no—
440D8—224no—
441D8—221no—
442D8C2×C4×D1112yes—
443M16—22no—
444M16—41no—
445M16—112no—
446M16—112no—
447M16—114no—
448M16—114no—
449M16—222no—
450M16—444no—
451M16—441no—
452C2×C8—41no—
453C2×C8—112no—
454C2×C8—114no—
455C2×C8—114no—
456C2×C8—444no—
457C2×C8—441no—
458C2×C8C2×C4×D1111yescharacteristic
459C2×C8C2×C4×D1111yescharacteristic
460C2×C8D4×D1111yescharacteristic
461C2×C8D4×D1111yescharacteristic
462C2×C8D4×D1111yescharacteristic
463C2×C8C23×D1111yescharacteristic
464C16—22no—
465C16—221no—
466C16—221no—
467C11#3338511yescharacteristic, complemented, Sylow
468C23—41no—
469C23—112no—
470C23—444no—
471C23—441no—
472C23SD16×D1111yescharacteristic
473Q8—22no—
474Q8—41no—
475Q8—112no—
476Q8—112no—
477Q8—222no—
478Q8—444no—
479Q8—441no—
480D4—22no—
481D4—42no—
482D4—42no—
483D4—41no—
484D4—114no—
485D4—114no—
486D4—112no—
487D4—112no—
488D4—222no—
489D4—444no—
490D4—444no—
491D4—444no—
492D4—442no—
493D4—442no—
494D4—441no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—112no—
499C2×C4—114no—
500C2×C4—114no—
501C2×C4—444no—
502C2×C4—444no—
503C2×C4—444no—
504C2×C4—441no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4C22⋊C4×D1111yescharacteristic
508C2×C4C22⋊C4×D1111yescharacteristic
509C2×C4D8×D1111yescharacteristic
510C2×C4D8×D1111yescharacteristic
511C2×C4SD16×D1111yescharacteristic
512C2×C4C2×D4×D1111yescharacteristic
513C8—42no—
514C8—114no—
515C8—442no—
516C8C22⋊C4×D1111yescharacteristic
517C8C22⋊C4×D1111yescharacteristic
518C8C22×C4×D1111yescharacteristic
519C8C2×D4×D1111yescharacteristic
520C22—41no—
521C22—42no—
522C22—114no—
523C22—161no—
524C22—442no—
525C22—442no—
526C22—1761no—
527C22—1764no—
528C22D11×#10211yescharacteristic
529C22D11×#10211yescharacteristic
530C22C2×SD16×D1111yescharacteristic
531C4—42no—
532C4—114no—
533C4—442no—
534C4D11×#10211yescharacteristic
535C4D11×#10211yescharacteristic
536C4C2×C22⋊C4×D1111yescharacteristic
537C4C2×D8×D1111yescharacteristic
538C2—21no—
539C2—21no—
540C2—21no—
541C2—82no—
542C2—224no—
543C2—882no—
544C2C2×D11×#10211yescharacteristic
subgroupG/H
centerC4C2×D8×D11
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2143C2
socleC2×C11C22×#102
prime radical#13083385C2
cosocleC2×C8×C11C24
hypercenter#2143D11
hypocenterC11#33385
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #2143

Complements

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

NH ≅ G/Ntype
2. C2×#10622520C2semidirect
3. #13077224C2semidirect
4. #13070345C2semidirect
5. #13070342C2semidirect
6. C2×#10622205C2semidirect
7. C2×#10622135C2semidirect
8. D11×#359C2semidirect
9. C11×#2143C2semidirect
24. C2×C11×M32C22semidirect
25. C2×C11×#108C22semidirect
27. C2×#66883C22semidirect
28. C22×C11⋊C16C22semidirect
31. C2×#66862C22semidirect
32. C2×C16×D11C22semidirect
34. D11×#108C22semidirect
35. C11×#359C22semidirect
36. #10622205C22semidirect
37. #10622205C22semidirect
38. #10622148C22semidirect
39. #10622135C22semidirect
40. #10622135C22semidirect
201. #2143D11semidirect
274. C2×M32C2×D11semidirect
281. C2×#108C2×D11semidirect
287. #359C2×D11semidirect
467. C11#33385semidirect

Maximal subgroups

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

subgroupindex
#130833852
C2×#106225202
#130772242
#130703452
#130703422
C2×#106222052
C2×#106221352
D11×#3592
C11×#21432
#3338511