Finite Group Databasebeta

← #14909635

Subgroups — #14909635

Order 2816.

564 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078286C211yesmaximal, characteristic
2#13078271C211yesmaximal, characteristic, complemented
3#13070825C211yesmaximal, characteristic, complemented
4#13070819C211yesmaximal, characteristic, complemented
5#13070814C211yesmaximal, characteristic, complemented
6#13070808C211yesmaximal, characteristic, complemented
7#13070729C211yesmaximal, characteristic, complemented
8#13070724C211yesmaximal, characteristic, complemented
9#13070712C211yesmaximal, characteristic, complemented
10#13070707C211yesmaximal, characteristic, complemented
11#13070558C211yesmaximal, characteristic, complemented
12#13070558C211yesmaximal, characteristic, complemented
13#13070552C211yesmaximal, characteristic, complemented
14#13070535C211yesmaximal, characteristic, complemented
15C11×#2113C211yesmaximal, characteristic, complemented
16C2×C11×#131C2211yescharacteristic
17#10623364—21no—
18#10623356—21no—
19C22×Dic44C2211yescharacteristic
20C2×#66957C2211yescharacteristic
21C2×C11×M32C2211yescharacteristic
22C22×C11×C16C2211yescharacteristic
23#10622750—21no—
24#10622750—21no—
25#10622747—21no—
26#10622747—21no—
27#10622746—21no—
28#10622733—21no—
29#10622729C2211yescharacteristic
30#10622729C2211yescharacteristic
31#10622729C2211yescharacteristic
32#10622729C2211yescharacteristic
33#10622729C2211yescharacteristic
34#10622729C2211yescharacteristic
35#10622728C2211yescharacteristic
36#10622728C2211yescharacteristic
37#10622719C2211yescharacteristic
38C2×#66882C2211yescharacteristic
39C2×Dic88C2211yescharacteristic
40C2×Dic88C2211yescharacteristic
41C2×#66864C2211yescharacteristic
42C2×#66864C2211yescharacteristic
43C11×C22⋊C16C2211yescharacteristic
44C11×C22⋊C16C2211yescharacteristic
45C11×C22⋊C16C2211yescharacteristic
46C11×C22⋊C16C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622143C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622142C2211yescharacteristic
52#10622142C2211yescharacteristic
53#10622141C2211yescharacteristic
54#10622141C2211yescharacteristic
55#10622141C2211yescharacteristic
56#10622141C2211yescharacteristic
57#10622141C2211yescharacteristic
58#10622141C2211yescharacteristic
59C2×C11×#41D411yescharacteristic
60C2×#4339—21no—
61C22×Dic22—21no—
62C11×#131—41no—
63C11×#131—41no—
64C2×C11×M16D411yescharacteristic
65C2×C11×M16D411yescharacteristic
66C2×C11×M16D411yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70#66999—41no—
71#66997—41no—
72#66992—41no—
73#66992—41no—
74#66991—41no—
75#66989—41no—
76#66988—41no—
77#66988—41no—
78#66983—21no—
79#66983—21no—
80#66979—21no—
81C2×C4⋊Dic11—21no—
82#66977—21no—
83#66977—21no—
84#66977—21no—
85#66977—21no—
86#66977—21no—
87#66977—21no—
88C2×Dic44—21no—
89C2×Dic44—41no—
90C2×Dic44—41no—
91C2×Dic44C2311yescharacteristic
92C2×Dic44C2311yescharacteristic
93C2×Dic44C2311yescharacteristic
94#66957—41no—
95#66957—41no—
96C2×D88C2311yescharacteristic
97C2×#4314—21no—
98C11×M32—41no—
99C2×C11×C16—41no—
100C2×C11×C16C2311yescharacteristic
101C2×C11×C16C2311yescharacteristic
102C2×C11×C16C2311yescharacteristic
103C2×C11×C16C2311yescharacteristic
104#66885—21no—
105#66885—21no—
106#66882—21no—
107#66882C2311yescharacteristic
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
110#66882C2311yescharacteristic
111#66881—21no—
112#66880—21no—
113#66880—21no—
114#66880—21no—
115#66880—21no—
116#66880—21no—
117#66880—21no—
118Dic88—41no—
119Dic88—41no—
120#66864—41no—
121#66864—41no—
122#33767—111nomaximal, Sylow
123C11×#41—41no—
124C11×#41—41no—
125C2×Q8×C11D811yescharacteristic
126C2×D4×C11D811yescharacteristic
127C2×D4×C11D811yescharacteristic
128C2×D4×C11D811yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C2×C22⋊D11—41no—
133C2×C22⋊D11—41no—
134C2×C22⋊D11—41no—
135C22×Dic11—41no—
136C22×Dic11—41no—
137#4339—42no—
138#4339—42no—
139C2×D44—21no—
140C2×C4×D11—41no—
141C2×Dic22—21no—
142C2×Dic22—21no—
143C2×Dic22—21no—
144C2×Dic22—42no—
145C2×Dic22—42no—
146C2×Dic22—41no—
147C11×M16—41no—
148C11×M16—41no—
149C11×M16—41no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11C2×D411yescharacteristic
157C2×C8×C11C2×D411yescharacteristic
158C2×C8×C11C2×D411yescharacteristic
159C2×C8×C11C2411yescharacteristic
160C22⋊Dic11—41no—
161C22⋊Dic11—41no—
162C22⋊Dic11—41no—
163C22⋊Dic11—41no—
164C22⋊Dic11—41no—
165C22⋊Dic11—41no—
166C22⋊Dic11—41no—
167(C2×D11)⋊C4—41no—
168(C2×D11)⋊C4—41no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—41no—
174Dic11⋊C4—41no—
175Dic11⋊C4—41no—
176Dic11⋊C4—41no—
177Dic11⋊C4—41no—
178Dic11⋊C4—41no—
179Dic11⋊C4—41no—
180C4×Dic11—41no—
181Dic44—21no—
182Dic44—21no—
183Dic44—21no—
184Dic44—21no—
185Dic44—21no—
186Dic44—21no—
187Dic44—42no—
188D88—21no—
189D88—21no—
190#4314—42no—
191C11×C16—21no—
192C11×C16—21no—
193C11×C16—21no—
194C11×C16—21no—
195#3061—111no—
196#3059—111no—
197#2237—111no—
198#2236—111no—
199#2235—111no—
200#2234—111no—
201#2220—111no—
202#2219—111no—
203#2217—111no—
204#2216—111no—
205#2189—111no—
206#2189—111no—
207#2188—111no—
208#2185—111no—
209#2113D1111yescharacteristic, complemented
210C23×C11C2×D811yescharacteristic
211C23×C11C2×D811yescharacteristic
212C23×C11C2×D811yescharacteristic
213C22×D11—41no—
214Q8×C11—41no—
215D4×C11—41no—
216D4×C11—41no—
217D4×C11—41no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11C2×D811yescharacteristic
225C2×C4×C11C2×D811yescharacteristic
226C2×C4×C11C2×D811yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C22⋊D11—82no—
229C22⋊D11—161no—
230C22⋊D11—161no—
231C2×Dic11—41no—
232C2×Dic11—41no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—82no—
239C2×Dic11—161no—
240D44—41no—
241D44—41no—
242C4×D11—82no—
243Dic22—41no—
244Dic22—41no—
245Dic22—41no—
246Dic22—41no—
247Dic22—41no—
248Dic22—41no—
249Dic22—82no—
250C8×C11—21no—
251C8×C11—21no—
252C8×C11—21no—
253C8×C11H(5,𝔽2)11yescharacteristic
254C8×C11H(5,𝔽2)11yescharacteristic
255C2×#135—111no—
256C22×Q16—111no—
257C2×#131C2×D1111yescharacteristic
258#537—221no—
259#536—221no—
260C2×Q32—111no—
261C2×Q32—111no—
262C2×SD32—111no—
263C2×SD32—111no—
264C2×M32C2×D1111yescharacteristic
265C22×C16C2×D1111yescharacteristic
266#470—221no—
267#470—221no—
268#468—221no—
269#468—221no—
270#467—111no—
271#467—111no—
272#467—111no—
273#467—111no—
274#467—111no—
275#467—111no—
276#466—111no—
277#466—111no—
278#427—111no—
279C2×#107—111no—
280#419—221no—
281#417—221no—
282#367—111no—
283#367—111no—
284#366—111no—
285#366—111no—
286#358—111no—
287#358—111no—
288#358—111no—
289#358—111no—
290#358—111no—
291#358—111no—
292#357—111no—
293#357—111no—
294C22⋊C16C2×D1111yescharacteristic
295C22⋊C16C2×D1111yescharacteristic
296C22⋊C16C2×D1111yescharacteristic
297C22⋊C16C2×D1111yescharacteristic
298C22×C11—21no—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11C22×D811yescharacteristic
308C2×D11—81no—
309C2×D11—81no—
310C2×D11—81no—
311C4×C11—21no—
312C4×C11—21no—
313C4×C11—21no—
314C4×C11#53411yescharacteristic
315C4×C11#57511yescharacteristic
316Dic11—81no—
317Dic11—81no—
318Dic11—81no—
319Dic11—81no—
320Dic11—81no—
321Dic11—81no—
322Dic11—81no—
323C2×#41—221no—
324C2×#41D4411yescharacteristic
325C22×Q8—221no—
326#135—441no—
327#135—441no—
328C2×Q16—111no—
329C2×Q16—111no—
330C2×Q16—111no—
331C2×Q16—221no—
332C2×Q16—441no—
333C2×Q16—441no—
334C2×SD16—221no—
335C2×D8—111no—
336#131—41no—
337#131—41no—
338C2×M16D4411yescharacteristic
339C2×M16D4411yescharacteristic
340C2×M16D4411yescharacteristic
341C22×C8C22×D1111yescharacteristic
342C22×C8C22×D1111yescharacteristic
343C22×C8C22×D1111yescharacteristic
344C4⋊Q8—441no—
345#124—441no—
346#123—441no—
347#123—441no—
348C22⋊Q8—221no—
349C22⋊Q8—221no—
350C22⋊Q8—221no—
351C22⋊Q8—221no—
352C22⋊Q8—221no—
353C22⋊Q8—221no—
354C22⋊Q8—441no—
355#121—221no—
356#121—221no—
357#121—441no—
358#121—441no—
359#121—441no—
360#117—221no—
361C2×C4⋊C4—221no—
362Q32—441no—
363Q32—441no—
364SD32—441no—
365SD32—441no—
366M32—41no—
367C2×C16—41no—
368C2×C16C22×D1111yescharacteristic
369C2×C16C22×D1111yescharacteristic
370C2×C16C22×D1111yescharacteristic
371C2×C16C22×D1111yescharacteristic
372#107—111no—
373#107—111no—
374#107—111no—
375#107—111no—
376#107—221no—
377#106—221no—
378#103—221no—
379#103—221no—
380#103—221no—
381#103—221no—
382#103—221no—
383#103—221no—
384#102—221no—
385#102—221no—
386C2×C11—41no—
387C2×C11—41no—
388C2×C11—41no—
389C2×C11#318611yescharacteristic
390C2×C11#341611yescharacteristic
391C2×C11#341711yescharacteristic
392D11—161no—
393#41—41no—
394#41—41no—
395#41—442no—
396#41—442no—
397C2×Q8—221no—
398C2×Q8—221no—
399C2×Q8—221no—
400C2×Q8—442no—
401C2×Q8—442no—
402C2×Q8—441no—
403C2×Q8D8811yescharacteristic
404C2×D4—221no—
405C2×D4—441no—
406C2×D4—441no—
407C2×D4—441no—
408C2×D4D8811yescharacteristic
409C2×D4D8811yescharacteristic
410C2×D4D8811yescharacteristic
411C22×C4—441no—
412C22×C4—441no—
413C22×C4—441no—
414C22×C4C2×D4411yescharacteristic
415C22×C4C2×D4411yescharacteristic
416C22×C4C2×D4411yescharacteristic
417Q16—221no—
418Q16—221no—
419Q16—221no—
420Q16—221no—
421Q16—221no—
422Q16—221no—
423Q16—442no—
424SD16—442no—
425D8—221no—
426D8—221no—
427M16—41no—
428M16—41no—
429M16—41no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8C2×D4411yescharacteristic
437C2×C8C2×D4411yescharacteristic
438C2×C8C2×D4411yescharacteristic
439C2×C8C23×D1111yescharacteristic
440C4⋊C4—221no—
441C4⋊C4—221no—
442C4⋊C4—221no—
443C4⋊C4—221no—
444C4⋊C4—441no—
445C4⋊C4—441no—
446C4⋊C4—441no—
447C4⋊C4—441no—
448C4⋊C4—441no—
449C4⋊C4—441no—
450C4⋊C4—441no—
451C22⋊C4—441no—
452C22⋊C4—441no—
453C22⋊C4—441no—
454C22⋊C4—441no—
455C22⋊C4—441no—
456C22⋊C4—441no—
457C22⋊C4—441no—
458C22⋊C4—441no—
459C22⋊C4—441no—
460C42—441no—
461C16—21no—
462C16—21no—
463C16—21no—
464C16—21no—
465C11#3376711yescharacteristic, complemented, Sylow
466C23—441no—
467C23C2×D8811yescharacteristic
468C23C2×D8811yescharacteristic
469C23C2×D8811yescharacteristic
470Q8—41no—
471Q8—441no—
472Q8—441no—
473Q8—441no—
474Q8—441no—
475Q8—441no—
476Q8—441no—
477Q8—882no—
478D4—41no—
479D4—41no—
480D4—41no—
481D4—441no—
482D4—441no—
483D4—882no—
484D4—1761no—
485D4—1761no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—441no—
493C2×C4—441no—
494C2×C4—441no—
495C2×C4—441no—
496C2×C4—441no—
497C2×C4—441no—
498C2×C4—441no—
499C2×C4—882no—
500C2×C4—882no—
501C2×C4—1761no—
502C2×C4C2×D8811yescharacteristic
503C2×C4C2×D8811yescharacteristic
504C2×C4C2×D8811yescharacteristic
505C2×C4C22×D4411yescharacteristic
506C8—21no—
507C8—21no—
508C8—21no—
509C8#6703711yescharacteristic
510C8#6703711yescharacteristic
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—881no—
521C22—881no—
522C22—881no—
523C22C22×D8811yescharacteristic
524C4—21no—
525C4—21no—
526C4—21no—
527C4—881no—
528C4—881no—
529C4—881no—
530C4—881no—
531C4—881no—
532C4—881no—
533C4—881no—
534C4#1062302411yescharacteristic
535C4#1062327911yescharacteristic
536C2—41no—
537C2—41no—
538C2—41no—
539C2—1761no—
540C2#1307936711yescharacteristic
541C2#1308176411yescharacteristic
542C2#1308176911yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2113C2
socleC22×C11C22×D8
prime radical#13078286C2
hypercenter#2113D11
hypocenterC11#33767
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ #2113

Complements

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

NH ≅ G/Ntype
2. #13078271C2semidirect
3. #13070825C2semidirect
4. #13070819C2semidirect
5. #13070814C2semidirect
6. #13070808C2semidirect
7. #13070729C2semidirect
8. #13070724C2semidirect
9. #13070712C2semidirect
10. #13070707C2semidirect
11. #13070558C2semidirect
12. #13070558C2semidirect
13. #13070552C2semidirect
14. #13070535C2semidirect
15. C11×#2113C2semidirect
209. #2113D11semidirect
465. C11#33767semidirect

Maximal subgroups

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

subgroupindex
#130782862
#130782712
#130708252
#130708192
#130708142
#130708082
#130707292
#130707242
#130707122
#130707072
#130705582
#130705522
#130705352
C11×#21132
#3376711