Finite Group Databasebeta

← #14909031

Subgroups — #14909031

Order 2816.

524 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079230C211yesmaximal, characteristic, complemented
2#13077514C211yesmaximal, characteristic, complemented
3#13070834C211yesmaximal, characteristic, complemented
4#13070829C211yesmaximal, characteristic, complemented
5#13070788C211yesmaximal, characteristic, complemented
6#13070787C211yesmaximal, characteristic, complemented
7#13070682C211yesmaximal, characteristic, complemented
8#13070565C211yesmaximal, characteristic, complemented
9#13070560C211yesmaximal, characteristic
10#13070517C211yesmaximal, characteristic, complemented
11#13070515C211yesmaximal, characteristic, complemented
12#13070510C211yesmaximal, characteristic, complemented
13#13070508C211yesmaximal, characteristic, complemented
14#13070431C211yesmaximal, characteristic, complemented
15C11×#2212C211yesmaximal, characteristic, complemented
16#10623299C2211yescharacteristic
17D11×#131—21no—
18#10623213—21no—
19C11×#510C2211yescharacteristic
20C11×#509C2211yescharacteristic
21C11×#495C2211yescharacteristic, complemented
22C11×#443C2211yescharacteristic
23#10622810C2211yescharacteristic
24#10622802C2211yescharacteristic
25#10622797C2211yescharacteristic, complemented
26#10622792C2211yescharacteristic
27#10622784—21no—
28SD16×Dic11—21no—
29#10622772C2211yescharacteristic
30#10622765C2211yescharacteristic, complemented
31#10622760C2211yescharacteristic
32#10622757—21no—
33#10622668—21no—
34#10622507C2211yescharacteristic
35#10622506C2211yescharacteristic
36#10622436—21no—
37#10622434—21no—
38#10622313C2211yescharacteristic
39#10622302C2211yescharacteristic
40#10622293C2211yescharacteristic, complemented
41C11×#364C2211yescharacteristic, complemented
42C11×#362C2211yescharacteristic, complemented
43C11×#361C2211yescharacteristic, complemented
44#10622204C2211yescharacteristic
45#10622204C2211yescharacteristic
46#10622203C2211yescharacteristic, complemented
47#10622201C2211yescharacteristic, complemented
48#10622156C2211yescharacteristic
49#10622156C2211yescharacteristic
50#10622152C2211yescharacteristic
51#10622152C2211yescharacteristic
52#10622151C2211yescharacteristic, complemented
53#10622151C2211yescharacteristic, complemented
54#10622150C2211yescharacteristic, complemented
55#10622150C2211yescharacteristic, complemented
56#10622132C2211yescharacteristic, complemented
57#10622132C2211yescharacteristic, complemented
58#10622101C2211yescharacteristic, complemented
59#41×D11—21no—
60C11×#135C2311yescharacteristic
61C2×C11×Q16C2311yescharacteristic
62C2×C11×SD16—21no—
63C2×C11×D8C2311yescharacteristic
64C11×#131—21no—
65C11×#124—21no—
66#67003—21no—
67#67001—21no—
68#66999—21no—
69Q8×Dic11—21no—
70#66991—21no—
71D4×Dic11—21no—
72#66971—21no—
73#66968—21no—
74#66967—21no—
75#66964—21no—
76#66960—21no—
77#66960—41no—
78M16×D11—21no—
79M16×D11—41no—
80#66957C2311yescharacteristic
81#66954—21no—
82#66954—41no—
83C2×#4313C2311yescharacteristic
84C2×C8×D11—41no—
85C2×C8×D11D411yescharacteristic
86#66939—41no—
87#66938—41no—
88#66932—41no—
89#66931—41no—
90#66925D411yescharacteristic
91#66922—21no—
92C11×Q32—21no—
93C11×SD32—21no—
94C11×SD32—21no—
95C11×D16—21no—
96C11×M32C2311yescharacteristic
97C11×M32C2311yescharacteristic
98C11×#108C2311yescharacteristic
99C11×#104—21no—
100C4×C8×C11C2311yescharacteristic
101#66901—21no—
102#66899—21no—
103#66899—21no—
104#66896—21no—
105#66896—21no—
106#66893—21no—
107#66892—21no—
108#66891—21no—
109#66890—21no—
110#66889—21no—
111#66886—21no—
112#66883C2311yescharacteristic
113#66881—21no—
114#66881C2311yescharacteristic
115#66881C2311yescharacteristic
116#66879C2311yescharacteristic
117C8×Dic11D411yescharacteristic
118#66876C2311yescharacteristic
119#66876C2311yescharacteristic
120#66869—21no—
121#66867D411yescharacteristic
122#33691—111nomaximal, Sylow
123C11×#41—21no—
124C2×Q8×C11—21no—
125C2×D4×C11—21no—
126C2×C22⋊D11—41no—
127C22×Dic11—41no—
128#4343—21no—
129Q8×D11—21no—
130#4341—21no—
131#4341—41no—
132D4×D11—21no—
133D4×D11—41no—
134#4339—21no—
135#4339—41no—
136C2×C4×D11—41no—
137C2×C4×D11C2×D411yescharacteristic
138C2×Dic22—41no—
139C11×Q16—21no—
140C11×Q16—21no—
141C11×Q16#4111yescharacteristic
142C11×SD16—21no—
143C11×SD16—41no—
144C11×SD16—41no—
145C11×D8—21no—
146C11×D8—21no—
147C11×D8#4111yescharacteristic
148C11×M16—21no—
149C11×M16—41no—
150C2×C8×C11—41no—
151C2×C8×C11C2×D411yescharacteristic
152C2×C8×C11C2411yescharacteristic
153C11×C22⋊C4—41no—
154C11×C22⋊C4—41no—
155C42×C11C2×D411yescharacteristic
156C22⋊Dic11—41no—
157C22⋊Dic11—41no—
158#4326—21no—
159#4325—21no—
160#4324—21no—
161#4323—21no—
162(C2×D11)⋊C4—21no—
163(C2×D11)⋊C4—41no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—41no—
167C4⋊Dic11—41no—
168Dic11⋊C4—21no—
169Dic11⋊C4—41no—
170C4×Dic11—41no—
171C4×Dic11C2×D411yescharacteristic
172#4318—21no—
173#4318—41no—
174C2×C11⋊C8—41no—
175C2×C11⋊C8C2×D411yescharacteristic
176C2×C11⋊C8C2×D411yescharacteristic
177Dic44#4111yescharacteristic
178D88#4111yescharacteristic
179#4314—21no—
180#4313—21no—
181#4313—21no—
182#4313—41no—
183#4313—41no—
184#4313—41no—
185C8×D11—21no—
186C8×D11—21no—
187C8×D11—41no—
188C8×D11—41no—
189C8×D11—41no—
190C11×C16—21no—
191C11×C16—21no—
192C11⋊C16—21no—
193C11⋊C16—21no—
194#3173—111no—
195#2955—111no—
196#2239—111no—
197#2238—111no—
198#2230—111no—
199#2230—111no—
200#2212—111no—
201#2212D1111yescharacteristic, complemented
202#2191—111no—
203#2190—111no—
204AGL(1,ℤ/16)—111no—
205AGL(1,ℤ/16)—111no—
206#2180—111no—
207#2180—111no—
208#2166—111no—
209C23×C11—41no—
210C22×D11—41no—
211C22×D11AGL(1,ℤ/8)11yescharacteristic
212Q8×C11—21no—
213Q8×C11—41no—
214Q8×C11—41no—
215D4×C11—21no—
216D4×C11—41no—
217D4×C11—41no—
218D4×C11—41no—
219C2×C4×C11—21no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11C22×D411yescharacteristic
223C22⋊D11—41no—
224C22⋊D11—41no—
225C22⋊D11—41no—
226C22⋊D11—161no—
227C2×Dic11—21no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231C2×Dic11—161no—
232C2×Dic11AGL(1,ℤ/8)11yescharacteristic
233D44—21no—
234D44—41no—
235C4×D11—21no—
236C4×D11—21no—
237C4×D11—41no—
238C4×D11—41no—
239C4×D11—41no—
240Dic22—21no—
241Dic22—41no—
242Dic22—161no—
243C8×C11—41no—
244C8×C11AGL(1,ℤ/8)11yescharacteristic
245C8×C11AGL(1,ℤ/8)11yescharacteristic
246C8×C11C2×#4111yescharacteristic
247C8×C11C2×#4111yescharacteristic
248C11⋊C8—21no—
249C11⋊C8—21no—
250C11⋊C8—41no—
251#575—111no—
252C2×#131—221no—
253#542—221no—
254#510—111no—
255#510C2×D1111yescharacteristic
256#509—111no—
257#509C2×D1111yescharacteristic
258#498—111no—
259#495C2×D1111yescharacteristic, complemented
260#489—221no—
261#470—111no—
262#469—111no—
263#465—221no—
264#444—111no—
265#444—111no—
266#444—221no—
267#443—111no—
268#443—221no—
269#443C2×D1111yescharacteristic
270#442—111no—
271#441—111no—
272C4×SD16—221no—
273#430—111no—
274#421—221no—
275#405—111no—
276#365—111no—
277#365—111no—
278#365—111no—
279#365—111no—
280#364—111no—
281#364C2×D1111yescharacteristic, complemented
282#362—111no—
283#362C2×D1111yescharacteristic, complemented
284#361—111no—
285#361C2×D1111yescharacteristic, complemented
286#360—111no—
287#360—111no—
288#360—111no—
289#360—111no—
290#349—111no—
291#349—111no—
292#347—111no—
293#347—111no—
294C22×C11—41no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11—81no—
298C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
299C2×D11—21no—
300C2×D11—41no—
301C2×D11—41no—
302C2×D11—82no—
303C4×C11—41no—
304C4×C11—41no—
305C4×C11—81no—
306C4×C11#52511yescharacteristic
307C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
308Dic11—21no—
309Dic11—41no—
310Dic11—41no—
311Dic11—81no—
312Dic11—81no—
313C2×#41—221no—
314#137—221no—
315#137—221no—
316AGL(1,ℤ/8)—221no—
317AGL(1,ℤ/8)—221no—
318#135—111no—
319#135—221no—
320#135C22×D1111yescharacteristic
321C2×Q16C22×D1111yescharacteristic
322C2×SD16—21no—
323C2×D8C22×D1111yescharacteristic
324#131—21no—
325#131—221no—
326#131—221no—
327#131—221no—
328#131—441no—
329#131—441no—
330C2×M16—111no—
331C2×M16—221no—
332C2×M16—441no—
333C22×C8—111no—
334C22×C8—441no—
335C4⋊Q8—221no—
336#126—441no—
337#124—21no—
338#124—441no—
339#123—441no—
340C22⋊Q8—221no—
341C22⋊Q8—441no—
342#121—221no—
343C4×Q8—221no—
344C4×D4—221no—
345#117—111no—
346Q32—21no—
347Q32—221no—
348SD32—21no—
349SD32—21no—
350SD32—221no—
351SD32—221no—
352D16—21no—
353D16—221no—
354M32—111no—
355M32—111no—
356M32C22×D1111yescharacteristic
357M32C22×D1111yescharacteristic
358#108—111no—
359#108—221no—
360#108C22×D1111yescharacteristic
361#106—111no—
362#106—111no—
363#106—221no—
364#104—21no—
365#104—221no—
366#104—221no—
367#104—221no—
368#103—221no—
369#103—221no—
370#102—221no—
371#102—221no—
372#97—111no—
373#97—111no—
374C4×C8—111no—
375C4×C8C22×D1111yescharacteristic
376C2×C11—21no—
377C2×C11—81no—
378C2×C11—161no—
379C2×C11#310911yescharacteristic
380D11—41no—
381D11—81no—
382#41—21no—
383#41—221no—
384#41—221no—
385#41—221no—
386#41—441no—
387#41—441no—
388C2×Q8—21no—
389C2×Q8—221no—
390C2×Q8—441no—
391C2×D4—21no—
392C2×D4—221no—
393C2×D4—441no—
394C2×D4—441no—
395C22×C4—111no—
396C22×C4—441no—
397C22×C4—441no—
398Q16—21no—
399Q16—21no—
400Q16—111no—
401Q16—221no—
402Q16#434111yescharacteristic
403SD16—21no—
404SD16—41no—
405SD16—41no—
406SD16—221no—
407SD16—221no—
408SD16—221no—
409D8—21no—
410D8—21no—
411D8—111no—
412D8—221no—
413D8#434111yescharacteristic
414M16—21no—
415M16—41no—
416M16—221no—
417M16—221no—
418M16—221no—
419M16—441no—
420M16—441no—
421M16—441no—
422M16—441no—
423C2×C8—41no—
424C2×C8—111no—
425C2×C8—111no—
426C2×C8—221no—
427C2×C8—221no—
428C2×C8—441no—
429C2×C8—441no—
430C2×C8—441no—
431C2×C8—441no—
432C2×C8D4×D1111yescharacteristic
433C2×C8C23×D1111yescharacteristic
434C4⋊C4—221no—
435C4⋊C4—221no—
436C4⋊C4—221no—
437C4⋊C4—441no—
438C4⋊C4—441no—
439C4⋊C4—441no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—221no—
443C22⋊C4—441no—
444C22⋊C4—441no—
445C22⋊C4—441no—
446C42—111no—
447C42—441no—
448C42D4×D1111yescharacteristic
449C16—21no—
450C16—21no—
451C16—221no—
452C16—221no—
453C11#3369111yescharacteristic, complemented, Sylow
454C23—41no—
455C23—111no—
456C23—441no—
457Q8—21no—
458Q8—41no—
459Q8—41no—
460Q8—221no—
461Q8—441no—
462Q8—1761no—
463D4—21no—
464D4—41no—
465D4—41no—
466D4—41no—
467D4—221no—
468D4—441no—
469D4—441no—
470D4—441no—
471D4—441no—
472D4—1761no—
473C2×C4—21no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—111no—
477C2×C4—221no—
478C2×C4—221no—
479C2×C4—221no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—441no—
485C2×C4—441no—
486C2×C4—1761no—
487C2×C4C2×D4×D1111yescharacteristic
488C8—41no—
489C8—221no—
490C8—221no—
491C8—441no—
492C8#6696411yescharacteristic
493C8#6696411yescharacteristic
494C8C2×#434111yescharacteristic
495C8#41×D1111yescharacteristic
496C22—41no—
497C22—81no—
498C22—81no—
499C22—81no—
500C22—221no—
501C22—441no—
502C22—441no—
503C22—882no—
504C22D11×AGL(1,ℤ/8)11yescharacteristic
505C4—41no—
506C4—41no—
507C4—81no—
508C4—221no—
509C4—441no—
510C4—441no—
511C4—881no—
512C4—881no—
513C4#1062313711yescharacteristic
514C4C2×#6696411yescharacteristic
515C2—21no—
516C2—81no—
517C2—161no—
518C2—441no—
519C2—881no—
520C2#1307870611yescharacteristic
subgroupG/H
centerC2#13078706
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2212C2
socleC2×C11#3109
prime radical#13070560C2
hypercenter#2212D11
hypocenterC11#33691
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2212

Complements

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

NH ≅ G/Ntype
1. #13079230C2semidirect
2. #13077514C2semidirect
3. #13070834C2semidirect
4. #13070829C2semidirect
5. #13070788C2semidirect
6. #13070787C2semidirect
7. #13070682C2semidirect
8. #13070565C2semidirect
10. #13070517C2semidirect
11. #13070515C2semidirect
12. #13070510C2semidirect
13. #13070508C2semidirect
14. #13070431C2semidirect
15. C11×#2212C2semidirect
21. C11×#495C22semidirect
25. #10622797C22semidirect
30. #10622765C22semidirect
40. #10622293C22semidirect
41. C11×#364C22semidirect
42. C11×#362C22semidirect
43. C11×#361C22semidirect
46. #10622203C22semidirect
47. #10622201C22semidirect
52. #10622151C22semidirect
53. #10622151C22semidirect
54. #10622150C22semidirect
55. #10622150C22semidirect
56. #10622132C22semidirect
57. #10622132C22semidirect
58. #10622101C22semidirect
201. #2212D11semidirect
259. #495C2×D11semidirect
281. #364C2×D11semidirect
283. #362C2×D11semidirect
285. #361C2×D11semidirect
453. C11#33691semidirect

Maximal subgroups

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

subgroupindex
#130792302
#130775142
#130708342
#130708292
#130707882
#130707872
#130706822
#130705652
#130705602
#130705172
#130705152
#130705102
#130705082
#130704312
C11×#22122
#3369111