Finite Group Databasebeta

← #14722224

Subgroups — #14722224

Order 2816.

1172 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082399C211yesmaximal, characteristic
2#13077724C211yesmaximal, characteristic, complemented
3#13077185C211yesmaximal, characteristic, complemented
4#13067294C211yesmaximal, characteristic, complemented
5#13067292C212yesmaximal, complemented
6#13067286C212yesmaximal, complemented
7#13067264C212yesmaximal, complemented
8#13067263C211yesmaximal, characteristic, complemented
9C2×#10622185C211yesmaximal, characteristic, complemented
10D11×#332C212yesmaximal, complemented
11C11×#1546C211yesmaximal, characteristic, complemented
12C2×#67040—21no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14#10623347—21no—
15C2×#66960—21no—
16#10623258—21no—
17#10623258C412yes—
18#10623257—21no—
19#10623257C412yes—
20#10623256C2212yes—
21#10623255—22no—
22D11×C4⋊Q8C2212yes—
23#10623038—22no—
24#10623038C414yes—
25#10623008C2211yescharacteristic
26C4×#4339C2211yescharacteristic
27C11×#431C2211yescharacteristic
28C11×#423C2211yescharacteristic
29#10622732—21no—
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32#10622452—22no—
33#10622450C2212yes—
34#10622446C2212yes—
35D11×C4⋊C8C2212yes—
36D11×C4⋊C8C2212yes—
37(C22⋊D11)⋊C8—22no—
38C8×D44—21no—
39C8×Dic22—21no—
40C11×#332C2212yes—
41C11×#332C2212yes—
42#10622185C2212yes—
43#10622185C2212yes—
44#10622124C2211yescharacteristic
45#10622124C2211yescharacteristic
46#10622123C2211yescharacteristic
47#10622123C2212yes—
48#10622123C2211yescharacteristic
49#10622120C2212yes—
50C22×Q8×C11—21no—
51#67040—44no—
52#67040—44no—
53C2×#4343—22no—
54C2×#4343—22no—
55C2×Q8×D11—22no—
56C2×Q8×D11—22no—
57C2×#4339—21no—
58C2×#4339—24no—
59C2×#4339D411yescharacteristic
60C2×C11×M16—21no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8C2×C412yes—
64C11×C4⋊Q8C2312yes—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2×C412yes—
67C2×C42×C11C2311yescharacteristic
68#67000—22no—
69#66999—22no—
70#66999—22no—
71#66997—22no—
72#66983—21no—
73#66983C2×C412yes—
74#66982—24no—
75C4×C22⋊D11C2×C412yes—
76C4×C22⋊D11D412yes—
77#66979D411yescharacteristic
78C22×C11⋊C8—21no—
79C22×C11⋊C8—21no—
80#66960—44no—
81C2×#4313—22no—
82C2×C8×D11—22no—
83C2×C8×D11—22no—
84#66949—24no—
85#66949—24no—
86#66948—22no—
87#66948C2×C414yes—
88#66947—24no—
89#66947—24no—
90#66946—22no—
91#66946C2×C414yes—
92C4⋊C4×D11—22no—
93C4⋊C4×D11C2×C414yes—
94#66941—22no—
95#66941C2×C414yes—
96#66928—21no—
97#66927C2311yescharacteristic
98C4×D44—21no—
99C4×D44C2×C411yescharacteristic
100C4×D44C2×C412yes—
101C4×D44D411yescharacteristic
102#66925D412yes—
103C42×D11C2312yes—
104#66922C2311yescharacteristic
105C4×Dic22C2×C411yescharacteristic
106C4×Dic22D411yescharacteristic
107C11×C4⋊C8—21no—
108C11×C4⋊C8C2312yes—
109C11×C4⋊C8C2311yescharacteristic
110C11×C4⋊C8C2311yescharacteristic
111C11×C22⋊C8—21no—
112C4×C8×C11—21no—
113(C2×D11)⋊C8—22no—
114Dic11⋊C8—22no—
115Dic11⋊C8—22no—
116Dic11⋊C8—22no—
117C8×Dic11—22no—
118C4⋊(C11⋊C8)—21no—
119C4⋊(C11⋊C8)—21no—
120C4⋊(C11⋊C8)C2312yes—
121C4⋊(C11⋊C8)C2311yescharacteristic
122C4⋊(C11⋊C8)C2311yescharacteristic
123#17721—111nomaximal, Sylow
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—42no—
127C2×Q8×C11—42no—
128C22×C4×C11—22no—
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C2×C22⋊D11—22no—
133C2×C22⋊D11C22⋊C412yes—
134#4343—48no—
135#4343—44no—
136#4343—44no—
137Q8×D11—44no—
138Q8×D11—44no—
139Q8×D11—48no—
140#4339—416no—
141#4339—42no—
142#4339—42no—
143#4339D814yes—
144#4339SD1614yes—
145C2×D44—24no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44C22⋊C411yescharacteristic
149C2×D44C22×C412yes—
150C2×C4×D11—24no—
151C2×C4×D11—24no—
152C2×C4×D11—22no—
153C2×C4×D11C22×C412yes—
154C2×C4×D11C2×D412yes—
155C2×C4×D11C2×D412yes—
156C2×Dic22—24no—
157C2×Dic22—21no—
158C2×Dic22C22⋊C411yescharacteristic
159C11×M16—42no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4C22×C414yes—
167C42×C11C22×C411yescharacteristic
168C42×C11C2×D411yescharacteristic
169C42×C11C2×D411yescharacteristic
170C42×C11C2411yescharacteristic
171C22⋊Dic11C22⋊C412yes—
172(C2×D11)⋊C4—24no—
173(C2×D11)⋊C4—24no—
174(C2×D11)⋊C4—22no—
175(C2×D11)⋊C4—22no—
176(C2×D11)⋊C4C22⋊C412yes—
177(C2×D11)⋊C4C22⋊C412yes—
178C4⋊Dic11—21no—
179C4⋊Dic11C22⋊C411yescharacteristic
180C4⋊Dic11C22⋊C411yescharacteristic
181C4⋊Dic11C22×C412yes—
182Dic11⋊C4—24no—
183Dic11⋊C4—24no—
184Dic11⋊C4C22⋊C412yes—
185Dic11⋊C4C22⋊C412yes—
186C4×Dic11C22×C412yes—
187C4×Dic11C2×D412yes—
188C4×Dic11C2×D412yes—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—42no—
193C2×C11⋊C8—81no—
194#4313—44no—
195C8×D11—44no—
196C8×D11—82no—
197#3499—111no—
198#2988—111no—
199#2906—111no—
200#1547—111no—
201#1547—112no—
202#1546—112no—
203#1546D1111yescharacteristic, complemented
204#1540—111no—
205#1540—112no—
206C2×#332—112no—
207C2×#332—111no—
208C23×C11C2×C22⋊C411yescharacteristic
209C22×D11—22no—
210C22×D11C2×C22⋊C412yes—
211Q8×C11—42no—
212Q8×C11—42no—
213Q8×C11—44no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—24no—
217C2×C4×C11—41no—
218C2×C4×C11—44no—
219C2×C4×C11C2×C22⋊C411yescharacteristic
220C2×C4×C11C2×C22⋊C411yescharacteristic
221C2×C4×C11C2×C22⋊C411yescharacteristic
222C2×C4×C11C2×D812yes—
223C2×C4×C11C2×SD1612yes—
224C2×C4×C11C23×C411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C22⋊D11—44no—
228C22⋊D11#10218yes—
229C2×Dic11—22no—
230C2×Dic11C2×C22⋊C412yes—
231C2×Dic11C2×C22⋊C412yes—
232C2×Dic11C2×C22⋊C412yes—
233D44—42no—
234D44—48no—
235D44—41no—
236D44—41no—
237D44—41no—
238D44—41no—
239D44#10214yes—
240C4×D11—22no—
241C4×D11—22no—
242C4×D11—42no—
243C4×D11—48no—
244C4×D11—44no—
245C4×D11—48no—
246C4×D11C2×D814yes—
247C4×D11C2×SD1614yes—
248Dic22—41no—
249Dic22—41no—
250Dic22—48no—
251Dic22#10214yes—
252C8×C11—42no—
253C8×C11—41no—
254C8×C11—41no—
255C11⋊C8—41no—
256C11⋊C8—41no—
257C11⋊C8—42no—
258C2×2−1+4—221no—
259C2×#131—221no—
260D4×Q8—112no—
261D4×Q8—221no—
262#547—112no—
263#547—114no—
264#547—222no—
265#547—221no—
266#536—222no—
267#536—221no—
268#532—112no—
269#532—111no—
270C2×C4⋊Q8—112no—
271C2×C4⋊Q8C2×D1111yescharacteristic
272C4×#41—111no—
273C8×Q8—221no—
274C8×D4—221no—
275C8×D4—222no—
276#431—112no—
277#431C2×D1111yescharacteristic
278#424—222no—
279#424—221no—
280#423—112no—
281#423C2×D1111yescharacteristic
282C2×C4⋊C8—111no—
283C2×C4⋊C8—111no—
284C2×C4⋊C8—112no—
285C2×C4⋊C8—112no—
286#332—112no—
287#332—112no—
288#332—111no—
289#332—112no—
290#332—111no—
291#332C2×D1112yes—
292#332C2×D1112yes—
293#331—111no—
294#331—112no—
295#331—111no—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11C2×#10212yes—
299C22×C11C22×C22⋊C411yescharacteristic
300C2×D11—22no—
301C2×D11—22no—
302C2×D11—42no—
303C2×D11—42no—
304C2×D11—42no—
305C2×D11C2×#10214yes—
306C4×C11—21no—
307C4×C11—21no—
308C4×C11—21no—
309C4×C11—44no—
310C4×C11C2×#10212yes—
311C4×C11C22×D811yescharacteristic
312C4×C11C22×SD1611yescharacteristic
313C4×C11#57711yescharacteristic
314C4×C11#57811yescharacteristic
315Dic11—22no—
316Dic11—22no—
317Dic11—42no—
318Dic11C2×#10214yes—
3192−1+4—444no—
3202−1+4—444no—
321C2×#41—111no—
322C2×#41—224no—
323C2×#41—222no—
324C2×#41—222no—
325C2×#41—221no—
326C22×Q8—21no—
327C22×Q8—222no—
328C22×Q8—222no—
329#131—444no—
330C2×M16—21no—
331C2×M16—222no—
332C22×C8—222no—
333C22×C8—222no—
334C22×C8—221no—
335C22×C8—221no—
336C4⋊Q8—21no—
337C4⋊Q8—21no—
338C4⋊Q8—114no—
339C4⋊Q8—111no—
340C4⋊Q8—222no—
341C4⋊Q8—222no—
342C4⋊Q8C4×D1112yes—
343C4⋊Q8C22×D1112yes—
344#127—111no—
345#124—222no—
346#124—221no—
347#123—224no—
348#123—224no—
349#123—224no—
350C22⋊Q8—224no—
351C22⋊Q8—224no—
352C22⋊Q8—222no—
353C22⋊Q8—222no—
354#121—112no—
355#121—114no—
356#121—222no—
357#121—221no—
358C4×Q8—111no—
359C4×Q8—111no—
360C4×D4—112no—
361C4×D4—112no—
362C4×D4—114no—
363C4×D4—111no—
364C4×D4—112no—
365C4×D4—111no—
366C4×D4—222no—
367C4×D4—221no—
368#117—111no—
369#117—112no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—114no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4C4×D1112yes—
374C2×C42—112no—
375C2×C42C22×D1111yescharacteristic
376C4⋊C8—21no—
377C4⋊C8—111no—
378C4⋊C8—112no—
379C4⋊C8—111no—
380C4⋊C8—222no—
381C4⋊C8—222no—
382C4⋊C8—222no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8C22×D1111yescharacteristic
386C4⋊C8C22×D1112yes—
387C4⋊C8C22×D1111yescharacteristic
388C22⋊C8—21no—
389C22⋊C8—222no—
390C4×C8—21no—
391C4×C8—222no—
392C2×C11—22no—
393C2×C11#288911yescharacteristic
394C2×C11C22×#10211yescharacteristic
395C2×C11#289811yescharacteristic
396D11—24no—
397D11—82no—
398#41—114no—
399#41—114no—
400#41—4416no—
401#41—444no—
402#41—444no—
403#41—448no—
404#41—442no—
405#41—442no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—42no—
409C2×Q8—42no—
410C2×Q8—111no—
411C2×Q8—224no—
412C2×Q8—221no—
413C2×Q8—444no—
414C2×Q8—444no—
415C2×Q8—448no—
416C2×D4—112no—
417C2×D4—111no—
418C2×D4—112no—
419C2×D4—224no—
420C2×D4—222no—
421C2×D4—221no—
422C2×D4—221no—
423C22×C4—22no—
424C22×C4—112no—
425C22×C4—112no—
426C22×C4—112no—
427C22×C4—224no—
428C22×C4—224no—
429C22×C4—222no—
430C22×C4C2×C4×D1111yescharacteristic
431C22×C4D4×D1111yescharacteristic
432C22×C4D4×D1111yescharacteristic
433M16—42no—
434M16—444no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—22no—
438C2×C8—222no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—444no—
442C2×C8—442no—
443C2×C8—882no—
444C2×C8—881no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—112no—
449C4⋊C4—112no—
450C4⋊C4—111no—
451C4⋊C4—111no—
452C4⋊C4—112no—
453C4⋊C4—224no—
454C4⋊C4—224no—
455C4⋊C4—221no—
456C4⋊C4C2×C4×D1114yes—
457C22⋊C4—112no—
458C22⋊C4—112no—
459C22⋊C4—112no—
460C22⋊C4—224no—
461C22⋊C4—224no—
462C22⋊C4—222no—
463C22⋊C4—222no—
464C42—112no—
465C42—112no—
466C42—112no—
467C42C2×C4×D1111yescharacteristic
468C42D4×D1111yescharacteristic
469C42D4×D1111yescharacteristic
470C42C23×D1111yescharacteristic
471C11#1772111yescharacteristic, complemented, Sylow
472C23—112no—
473C23—222no—
474C23C22⋊C4×D1111yescharacteristic
475Q8—42no—
476Q8—42no—
477Q8—44no—
478Q8—114no—
479Q8—448no—
480Q8—441no—
481Q8—441no—
482D4—118no—
483D4—114no—
484D4—442no—
485D4—448no—
486D4—444no—
487D4—441no—
488D4—441no—
489D4—441no—
490D4—441no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—24no—
494C2×C4—41no—
495C2×C4—44no—
496C2×C4—112no—
497C2×C4—114no—
498C2×C4—114no—
499C2×C4—112no—
500C2×C4—112no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—442no—
505C2×C4—448no—
506C2×C4—448no—
507C2×C4—444no—
508C2×C4C22⋊C4×D1111yescharacteristic
509C2×C4C22⋊C4×D1111yescharacteristic
510C2×C4C22⋊C4×D1111yescharacteristic
511C2×C4D8×D1112yes—
512C2×C4SD16×D1112yes—
513C2×C4C22×C4×D1111yescharacteristic
514C2×C4C2×D4×D1111yescharacteristic
515C2×C4C2×D4×D1111yescharacteristic
516C8—42no—
517C8—41no—
518C8—41no—
519C8—441no—
520C8—441no—
521C8—442no—
522C22—21no—
523C22—21no—
524C22—114no—
525C22—222no—
526C22—222no—
527C22—442no—
528C22—442no—
529C22—442no—
530C22D11×#10212yes—
531C22C2×C22⋊C4×D1111yescharacteristic
532C4—21no—
533C4—21no—
534C4—21no—
535C4—44no—
536C4—114no—
537C4—222no—
538C4—222no—
539C4—442no—
540C4D11×#10212yes—
541C4C2×D8×D1111yescharacteristic
542C4C2×SD16×D1111yescharacteristic
543C4#1062330911yescharacteristic
544C4#1062331011yescharacteristic
545C2—22no—
546C2—224no—
547C2—882no—
548C2#1307709611yescharacteristic
549C2C2×D11×#10211yescharacteristic
550C2#1307714811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1546C2
socleC22×C11C22×C22⋊C4
prime radical#13082399C2
cosocleC42×C11C24
hypercenter#1546D11
hypocenterC11#17721
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
2. #13077724C2semidirect
3. #13077185C2semidirect
4. #13067294C2semidirect
5. #13067292C2semidirect
6. #13067286C2semidirect
7. #13067264C2semidirect
8. #13067263C2semidirect
9. C2×#10622185C2semidirect
10. D11×#332C2semidirect
11. C11×#1546C2semidirect
203. #1546D11semidirect
471. C11#17721semidirect

Maximal subgroups

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

subgroupindex
#130823992
#130777242
#130771852
#130672942
#130672922
#130672862
#130672642
#130672632
C2×#106221852
D11×#3322
C11×#15462
#1772111