Finite Group Databasebeta

← #14722708

Subgroups — #14722708

Order 2816.

1112 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082399C211yesmaximal, characteristic
2#13077742C211yesmaximal, characteristic, complemented
3#13077737C211yesmaximal, characteristic, complemented
4#13067349C211yesmaximal, characteristic, complemented
5#13067340C212yesmaximal, complemented
6#13067310C212yesmaximal, complemented
7#13067310C212yesmaximal, complemented
8#13067297C211yesmaximal, characteristic, complemented
9#13067276C211yesmaximal, characteristic, complemented
10D11×#333C212yesmaximal, complemented
11C11×#1548C211yesmaximal, characteristic, complemented
12C2×#67040C412yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14#10623347C412yes—
15#10623258—21no—
16#10623258—21no—
17#10623257—21no—
18#10623257—21no—
19#10623256C2212yes—
20#10623255C414yes—
21D11×C4⋊Q8C2212yes—
22#10623038—22no—
23#10623038—22no—
24#10623008C2211yescharacteristic
25C4×#4339C2211yescharacteristic
26C11×#431C2211yescharacteristic
27C11×#423C2211yescharacteristic
28#10622740—22no—
29#10622538C2211yescharacteristic
30#10622537C2211yescharacteristic
31#10622448C2212yes—
32#10622448C2212yes—
33#10622447—21no—
34D11×C4⋊C8C2212yes—
35D11×C4⋊C8C2212yes—
36#10622444—21no—
37#10622341—22no—
38C8×D44—21no—
39#10622292—21no—
40C11×#333C2212yes—
41C11×#333C2212yes—
42#10622184C2212yes—
43#10622184C2212yes—
44#10622123C2211yescharacteristic
45#10622123C2211yescharacteristic
46#10622123C2212yes—
47#10622119C2211yescharacteristic
48#10622119C2212yes—
49#10622119C2211yescharacteristic
50C22×Q8×C11C2×C412yes—
51#67040—48no—
52C2×#4343—22no—
53C2×#4343C2×C414yes—
54C2×Q8×D11—22no—
55C2×Q8×D11C2×C414yes—
56C2×#4339—24no—
57C2×#4339C2×C411yescharacteristic
58C2×#4339C2×C412yes—
59C2×C11×M16—21no—
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8C2×C412yes—
63C11×C4⋊Q8C2312yes—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C42×C11C2311yescharacteristic
67#67000C2×C414yes—
68#66999—22no—
69#66999—22no—
70#66997C2×C414yes—
71#66983—21no—
72#66983—21no—
73#66982—24no—
74C4×C22⋊D11D412yes—
75C4×C22⋊D11D412yes—
76#66979C2×C411yescharacteristic
77C2×#4318—21no—
78C2×C8×D11—22no—
79C2×C8×D11—22no—
80#66949—24no—
81#66949—24no—
82#66948—22no—
83#66948—22no—
84#66947—24no—
85#66947—24no—
86#66946—22no—
87#66946—22no—
88C4⋊C4×D11—22no—
89C4⋊C4×D11—22no—
90#66941—22no—
91#66941—22no—
92#66928C2×C412yes—
93#66927C2311yescharacteristic
94C4×D44—21no—
95C4×D44—21no—
96C4×D44D411yescharacteristic
97C4×D44D411yescharacteristic
98#66925C2×C412yes—
99C42×D11C2312yes—
100#66922C2311yescharacteristic
101C4×Dic22D411yescharacteristic
102C4×Dic22D411yescharacteristic
103C11×C4⋊C8—21no—
104C11×C4⋊C8C2312yes—
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×C22⋊C8—21no—
108C4×C8×C11—21no—
109C22⋊(C11⋊C8)—21no—
110(C2×D11)⋊C8—22no—
111(C2×D11)⋊C8—22no—
112#66879—22no—
113#66879—22no—
114Dic11⋊C8—22no—
115Dic11⋊C8—22no—
116C4⋊(C11⋊C8)—21no—
117C4⋊(C11⋊C8)C2312yes—
118C4⋊(C11⋊C8)C2311yescharacteristic
119C4⋊(C11⋊C8)C2311yescharacteristic
120C4×C11⋊C8—21no—
121#17779—111nomaximal, Sylow
122C2×Q8×C11—22no—
123C2×Q8×C11—44no—
124C2×Q8×C11C22×C414yes—
125C22×C4×C11—22no—
126C22×C4×C11C22×C411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C2×C22⋊D11—22no—
130C2×C22⋊D11C22⋊C412yes—
131#4343—48no—
132#4343—48no—
133Q8×D11—48no—
134Q8×D11—48no—
135#4339—24no—
136#4339—44no—
137#4339—416no—
138C2×D44—24no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44C22⋊C411yescharacteristic
142C2×D44C22×C412yes—
143C2×C4×D11—24no—
144C2×C4×D11—24no—
145C2×C4×D11—22no—
146C2×C4×D11C22×C412yes—
147C2×C4×D11C2×D412yes—
148C2×C4×D11C2×D412yes—
149C2×Dic22—24no—
150C2×Dic22C22⋊C411yescharacteristic
151C2×Dic22C22×C412yes—
152C11×M16—81no—
153C2×C8×C11—21no—
154C2×C8×C11—22no—
155C2×C8×C11—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C42×C11C22×C411yescharacteristic
161C42×C11C2×D411yescharacteristic
162C42×C11C2×D411yescharacteristic
163C42×C11C2411yescharacteristic
164C22⋊Dic11C22⋊C412yes—
165(C2×D11)⋊C4—24no—
166(C2×D11)⋊C4—24no—
167(C2×D11)⋊C4—22no—
168(C2×D11)⋊C4—22no—
169(C2×D11)⋊C4C22⋊C412yes—
170(C2×D11)⋊C4C22⋊C412yes—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11C22⋊C411yescharacteristic
174C4⋊Dic11C22⋊C411yescharacteristic
175Dic11⋊C4—24no—
176Dic11⋊C4—24no—
177Dic11⋊C4C22⋊C412yes—
178Dic11⋊C4C22⋊C412yes—
179C4×Dic11C22×C412yes—
180C4×Dic11C2×D412yes—
181C4×Dic11C2×D412yes—
182#4318—81no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—22no—
186C8×D11—82no—
187C8×D11—82no—
188#3499—111no—
189#2990—111no—
190#2990—111no—
191#1560—111no—
192#1558—112no—
193#1551—112no—
194#1551—112no—
195#1548—111no—
196#1548D1111yescharacteristic, complemented
197#1543—111no—
198C2×#333—112no—
199C23×C11C2×C22⋊C411yescharacteristic
200C22×D11—22no—
201C22×D11C2×C22⋊C412yes—
202Q8×C11—44no—
203Q8×C11—44no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—22no—
209C2×C4×C11—24no—
210C2×C4×C11—44no—
211C2×C4×C11C2×C22⋊C411yescharacteristic
212C2×C4×C11C2×C22⋊C411yescharacteristic
213C2×C4×C11C2×C22⋊C411yescharacteristic
214C2×C4×C11C23×C411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C22⋊D11—24no—
218C22⋊D11—44no—
219C2×Dic11—22no—
220C2×Dic11C2×C22⋊C412yes—
221C2×Dic11C2×C22⋊C412yes—
222C2×Dic11C2×C22⋊C412yes—
223D44—42no—
224D44—48no—
225D44—41no—
226D44—41no—
227D44—41no—
228D44—41no—
229D44#10014yes—
230C4×D11—24no—
231C4×D11—22no—
232C4×D11—22no—
233C4×D11—22no—
234C4×D11—22no—
235C4×D11—48no—
236C4×D11—48no—
237C4×D11—44no—
238Dic22—22no—
239Dic22—48no—
240Dic22—42no—
241C8×C11—41no—
242C8×C11—42no—
243C8×C11—41no—
244C11⋊C8—41no—
245C11⋊C8—42no—
246C11⋊C8—41no—
247C2×2−1+4—112no—
248D4×Q8—221no—
249D4×Q8—221no—
250#547—222no—
251#547—222no—
252#547—221no—
253#547—221no—
254#536—112no—
255#536—114no—
256#532—112no—
257#532—111no—
258C2×C4⋊Q8—112no—
259C2×C4⋊Q8C2×D1111yescharacteristic
260C4×#41—111no—
261#446—221no—
262#446—221no—
263#435—222no—
264#435—222no—
265C8×D4—221no—
266C8×D4—221no—
267#432—112no—
268#432—112no—
269#431—111no—
270#431C2×D1111yescharacteristic
271#423—111no—
272#423C2×D1111yescharacteristic
273C2×C4⋊C8—112no—
274C2×C4⋊C8—112no—
275#333—112no—
276#333—112no—
277#333—111no—
278#333—112no—
279#333—111no—
280#333C2×D1112yes—
281#333C2×D1112yes—
282#331—111no—
283#331—111no—
284#331—112no—
285C22×C11—21no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11C22×C22⋊C411yescharacteristic
289C2×D11—22no—
290C2×D11—22no—
291C2×D11—42no—
292C2×D11—42no—
293C2×D11—42no—
294C2×D11C2×#10014yes—
295C4×C11—21no—
296C4×C11—21no—
297C4×C11—21no—
298C4×C11—44no—
299C4×C11C2×#10012yes—
300C4×C11#57711yescharacteristic
301C4×C11#57711yescharacteristic
302C4×C11#57811yescharacteristic
303C4×C11#57811yescharacteristic
304Dic11—22no—
305Dic11—22no—
306Dic11—22no—
307Dic11—42no—
3082−1+4—448no—
309C2×#41—111no—
310C2×#41—114no—
311C2×#41—112no—
312C2×#41—224no—
313C2×#41—222no—
314C22×Q8—114no—
315C22×Q8—222no—
316C22×Q8C4×D1112yes—
317C2×M16—21no—
318C2×M16—221no—
319C22×C8—222no—
320C22×C8—222no—
321C4⋊Q8—21no—
322C4⋊Q8—21no—
323C4⋊Q8—114no—
324C4⋊Q8—111no—
325C4⋊Q8—222no—
326C4⋊Q8—222no—
327C4⋊Q8C4×D1112yes—
328C4⋊Q8C22×D1112yes—
329#127—111no—
330#124—114no—
331#124—112no—
332#123—224no—
333#123—224no—
334#123—224no—
335C22⋊Q8—224no—
336C22⋊Q8—224no—
337C22⋊Q8—222no—
338C22⋊Q8—222no—
339#121—222no—
340#121—222no—
341#121—221no—
342#121—221no—
343C4×Q8—111no—
344C4×Q8—111no—
345C4×D4—112no—
346C4×D4—112no—
347C4×D4—111no—
348C4×D4—111no—
349C4×D4—222no—
350C4×D4—222no—
351C4×D4—221no—
352C4×D4—221no—
353#117—111no—
354#117—112no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—222no—
359C2×C42—112no—
360C2×C42C22×D1111yescharacteristic
361C4⋊C8—21no—
362C4⋊C8—111no—
363C4⋊C8—112no—
364C4⋊C8—111no—
365C4⋊C8—222no—
366C4⋊C8—222no—
367C4⋊C8—221no—
368C4⋊C8C22×D1111yescharacteristic
369C4⋊C8C22×D1112yes—
370C4⋊C8C22×D1111yescharacteristic
371C22⋊C8—21no—
372C22⋊C8—222no—
373C22⋊C8—222no—
374C22⋊C8—221no—
375#97—222no—
376#97—222no—
377C4×C8—21no—
378C4×C8—221no—
379C2×C11—41no—
380C2×C11C22×#10011yescharacteristic
381C2×C11#289811yescharacteristic
382C2×C11#289811yescharacteristic
383D11—24no—
384D11—82no—
385#41—224no—
386#41—444no—
387#41—4416no—
388#41—448no—
389#41—448no—
390C2×Q8—22no—
391C2×Q8—44no—
392C2×Q8—111no—
393C2×Q8—112no—
394C2×Q8—224no—
395C2×Q8—448no—
396C2×Q8—448no—
397C2×Q8C2×C4×D1114yes—
398C2×D4—112no—
399C2×D4—111no—
400C2×D4—112no—
401C2×D4—224no—
402C2×D4—222no—
403C2×D4—221no—
404C2×D4—221no—
405C22×C4—22no—
406C22×C4—112no—
407C22×C4—112no—
408C22×C4—112no—
409C22×C4—224no—
410C22×C4—224no—
411C22×C4—222no—
412C22×C4C2×C4×D1111yescharacteristic
413C22×C4D4×D1111yescharacteristic
414C22×C4D4×D1111yescharacteristic
415M16—81no—
416M16—881no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—22no—
420C2×C8—221no—
421C2×C8—221no—
422C2×C8—222no—
423C2×C8—882no—
424C2×C8—882no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—112no—
430C4⋊C4—112no—
431C4⋊C4—111no—
432C4⋊C4—111no—
433C4⋊C4—224no—
434C4⋊C4—224no—
435C4⋊C4—221no—
436C4⋊C4—221no—
437C22⋊C4—112no—
438C22⋊C4—112no—
439C22⋊C4—112no—
440C22⋊C4—224no—
441C22⋊C4—224no—
442C22⋊C4—222no—
443C22⋊C4—222no—
444C42—112no—
445C42—112no—
446C42—112no—
447C42C2×C4×D1111yescharacteristic
448C42D4×D1111yescharacteristic
449C42D4×D1111yescharacteristic
450C42C23×D1111yescharacteristic
451C11#1777911yescharacteristic, complemented, Sylow
452C23—112no—
453C23—222no—
454C23C22⋊C4×D1111yescharacteristic
455Q8—44no—
456Q8—44no—
457Q8—222no—
458Q8—442no—
459Q8—448no—
460D4—114no—
461D4—224no—
462D4—442no—
463D4—448no—
464D4—444no—
465D4—441no—
466D4—441no—
467D4—441no—
468D4—441no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—44no—
476C2×C4—112no—
477C2×C4—112no—
478C2×C4—112no—
479C2×C4—224no—
480C2×C4—222no—
481C2×C4—222no—
482C2×C4—222no—
483C2×C4—222no—
484C2×C4—222no—
485C2×C4—448no—
486C2×C4—448no—
487C2×C4—444no—
488C2×C4C22⋊C4×D1111yescharacteristic
489C2×C4C22⋊C4×D1111yescharacteristic
490C2×C4C22⋊C4×D1111yescharacteristic
491C2×C4C22×C4×D1111yescharacteristic
492C2×C4C2×D4×D1111yescharacteristic
493C2×C4C2×D4×D1111yescharacteristic
494C8—42no—
495C8—41no—
496C8—41no—
497C8—441no—
498C8—441no—
499C8—442no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—114no—
504C22—222no—
505C22—222no—
506C22—442no—
507C22—442no—
508C22—442no—
509C22C2×C22⋊C4×D1111yescharacteristic
510C4—21no—
511C4—21no—
512C4—21no—
513C4—44no—
514C4—222no—
515C4—222no—
516C4—222no—
517C4—442no—
518C4D11×#10012yes—
519C4#1062329311yescharacteristic
520C4#1062329711yescharacteristic
521C4#1062330911yescharacteristic
522C4#1062331011yescharacteristic
523C2—41no—
524C2—224no—
525C2—882no—
526C2C2×D11×#10011yescharacteristic
527C2#1307714411yescharacteristic
528C2#1307714811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1548C2
socleC22×C11C22×C22⋊C4
prime radical#13082399C2
cosocleC42×C11C24
hypercenter#1548D11
hypocenterC11#17779
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
2. #13077742C2semidirect
3. #13077737C2semidirect
4. #13067349C2semidirect
5. #13067340C2semidirect
6. #13067310C2semidirect
7. #13067310C2semidirect
8. #13067297C2semidirect
9. #13067276C2semidirect
10. D11×#333C2semidirect
11. C11×#1548C2semidirect
196. #1548D11semidirect
451. C11#17779semidirect

Maximal subgroups

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

subgroupindex
#130823992
#130777422
#130777372
#130673492
#130673402
#130673102
#130672972
#130672762
D11×#3332
C11×#15482
#1777911