Finite Group Databasebeta

← #14722171

Subgroups — #14722171

Order 2816.

1252 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623256C211yesmaximal, characteristic
2#13077248C211yesmaximal, characteristic, complemented
3D11×#431C211yesmaximal, characteristic, complemented
4#13067310C214yesmaximal, complemented
5#13067297C211yesmaximal, characteristic, complemented
6#13067285C211yesmaximal, characteristic, complemented
7#13067283C211yesmaximal, characteristic, complemented
8#13067277C214yesmaximal, complemented
9C11×#1548C211yesmaximal, characteristic, complemented
10C22×#4343C412yes—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#67000C412yes—
13#10623256—21no—
14#10623256—21no—
15#10623256—21no—
16#10623256—21no—
17#10623256C412yes—
18#10623256C412yes—
19#10623256C2212yes—
20#10623256C2212yes—
21C2×#66948—21no—
22C2×#66948—21no—
23C2×#66946—21no—
24C2×#66946—21no—
25C2×#66927C2211yescharacteristic
26C2×C42×D11C2211yescharacteristic
27C11×#431C2211yescharacteristic
28C11×#423C2211yescharacteristic
29#10622739—21no—
30M16×Dic11—21no—
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622448—21no—
34#10622448C2212yescomplemented
35#10622446—21no—
36#10622446C2212yescomplemented
37#10622446C2212yescomplemented
38D11×C4⋊C8C2212yescomplemented
39D11×C22⋊C8—21no—
40#10622331—21no—
41#10622298—21no—
42C4×C8×D11—21no—
43C11×#333C2214yescomplemented
44#10622184C2214yescomplemented
45#10622123C2214yescomplemented
46#10622123C2214yescomplemented
47C22×Q8×C11C2×C412yes—
48C2×#4343—22no—
49C2×#4343—22no—
50C2×#4343—48no—
51C2×#4343C2×C414yes—
52C2×#4343C2×C414yes—
53C22×D44—22no—
54C22×D44—21no—
55C22×D44—21no—
56C22×D44C2×C412yes—
57C22×C4×D11—22no—
58C22×C4×D11C2×C411yescharacteristic
59C22×C4×D11D411yescharacteristic
60C22×C4×D11D411yescharacteristic
61C2×C11×M16—21no—
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8C2×C412yes—
65C11×C4⋊Q8C2312yes—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C42×C11C2311yescharacteristic
69#67000—22no—
70#67000—22no—
71#67000C2×C414yes—
72#67000C2×C414yes—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×C4×Dic11C2×C411yescharacteristic
76C2×C4×Dic11D411yescharacteristic
77C2×C4×Dic11D411yescharacteristic
78C2×#4318—21no—
79C2×C8×D11—22no—
80#66948—22no—
81#66948—22no—
82#66948—22no—
83#66948—22no—
84#66948—22no—
85#66948—22no—
86#66948—22no—
87#66948—22no—
88#66946—22no—
89#66946—22no—
90#66946—22no—
91#66946—22no—
92#66946—22no—
93#66946—22no—
94#66946—22no—
95#66946—22no—
96#66927—21no—
97#66927—21no—
98#66927C2×C412yes—
99#66927C2312yes—
100C42×D11C2×C411yescharacteristic
101C42×D11C2×C411yescharacteristic
102C42×D11D411yescharacteristic
103C42×D11D411yescharacteristic
104C42×D11D411yescharacteristic
105C42×D11D411yescharacteristic
106C42×D11C2311yescharacteristic
107C42×D11C2311yescharacteristic
108C11×C4⋊C8—21no—
109C11×C4⋊C8C2312yes—
110C11×C4⋊C8C2312yes—
111C11×C22⋊C8—21no—
112C4×C8×C11—21no—
113C22⋊(C11⋊C8)—21no—
114(C2×D11)⋊C8—22no—
115(C2×D11)⋊C8—22no—
116(C2×D11)⋊C8—22no—
117#66879—22no—
118Dic11⋊C8—22no—
119C8×Dic11—22no—
120C8×Dic11—22no—
121C4⋊(C11⋊C8)—21no—
122C4⋊(C11⋊C8)C2312yes—
123C4⋊(C11⋊C8)C2312yes—
124C4×C11⋊C8—21no—
125#17714—111nomaximal, Sylow
126C23×D11—22no—
127C23×D11C22⋊C411yescharacteristic
128C2×Q8×C11—22no—
129C2×Q8×C11—44no—
130C2×Q8×C11C22×C414yes—
131C22×C4×C11—22no—
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×Dic11C22⋊C411yescharacteristic
136C22×Dic11C22⋊C411yescharacteristic
137C22×Dic11C22⋊C411yescharacteristic
138#4343—48no—
139#4343—48no—
140#4343—48no—
141#4343—48no—
142C2×D44—24no—
143C2×D44—24no—
144C2×D44—22no—
145C2×D44—22no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—22no—
149C2×D44—44no—
150C2×D44—44no—
151C2×D44—48no—
152C2×D44—42no—
153C2×D44—42no—
154C2×D44C22×C414yes—
155C2×C4×D11—24no—
156C2×C4×D11—24no—
157C2×C4×D11—24no—
158C2×C4×D11—22no—
159C2×C4×D11—22no—
160C2×C4×D11—42no—
161C2×C4×D11—48no—
162C2×C4×D11C22⋊C411yescharacteristic
163C2×C4×D11C22⋊C411yescharacteristic
164C2×C4×D11C22⋊C411yescharacteristic
165C2×C4×D11C22⋊C411yescharacteristic
166C2×C4×D11C22⋊C411yescharacteristic
167C2×C4×D11C22⋊C411yescharacteristic
168C2×C4×D11C22×C411yescharacteristic
169C2×C4×D11C22×C411yescharacteristic
170C2×C4×D11C2×D411yescharacteristic
171C2×C4×D11C2×D411yescharacteristic
172C2×C4×D11C2×D411yescharacteristic
173C2×C4×D11C2×D411yescharacteristic
174C11×M16—42no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C42×C11C22×C411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11C2411yescharacteristic
185(C2×D11)⋊C4—24no—
186(C2×D11)⋊C4—24no—
187(C2×D11)⋊C4—24no—
188(C2×D11)⋊C4—24no—
189C4×Dic11C22⋊C411yescharacteristic
190C4×Dic11C22⋊C411yescharacteristic
191C4×Dic11C22⋊C411yescharacteristic
192C4×Dic11C22⋊C411yescharacteristic
193C4×Dic11C22⋊C411yescharacteristic
194C4×Dic11C22⋊C411yescharacteristic
195C4×Dic11C22×C411yescharacteristic
196C4×Dic11C22×C411yescharacteristic
197C4×Dic11C2×D411yescharacteristic
198C4×Dic11C2×D411yescharacteristic
199C4×Dic11C2×D411yescharacteristic
200C4×Dic11C2×D411yescharacteristic
201#4318—42no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204C8×D11—44no—
205C2×#532—111no—
206#2920—111no—
207C2×#431—111no—
208#1551—114no—
209#1548—111no—
210#1548D1111yescharacteristic, complemented
211#1545—111no—
212#1545—111no—
213#1543—114no—
214C23×C11C2×C22⋊C411yescharacteristic
215C22×D11—22no—
216C22×D11—22no—
217C22×D11—24no—
218C22×D11—41no—
219C22×D11—44no—
220C22×D11—44no—
221C22×D11—44no—
222C22×D11C2×C22⋊C411yescharacteristic
223C22×D11C2×C22⋊C411yescharacteristic
224Q8×C11—44no—
225Q8×C11—44no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—44no—
230C2×C4×C11C2×C22⋊C411yescharacteristic
231C2×C4×C11C2×C22⋊C411yescharacteristic
232C2×C4×C11C2×C22⋊C411yescharacteristic
233C2×C4×C11#13512yes—
234C2×C4×C11#13512yes—
235C2×C4×C11C23×C411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—41no—
241C2×Dic11C2×C22⋊C411yescharacteristic
242C2×Dic11C2×C22⋊C411yescharacteristic
243C2×Dic11C2×C22⋊C411yescharacteristic
244C2×Dic11C2×C22⋊C411yescharacteristic
245C2×Dic11C2×C22⋊C411yescharacteristic
246C2×Dic11C2×C22⋊C411yescharacteristic
247D44—44no—
248D44—44no—
249D44—48no—
250D44—48no—
251D44—42no—
252D44—42no—
253D44—44no—
254D44—44no—
255D44—44no—
256C4×D11—22no—
257C4×D11—21no—
258C4×D11—21no—
259C4×D11—21no—
260C4×D11—21no—
261C4×D11—22no—
262C4×D11—22no—
263C4×D11—22no—
264C4×D11—22no—
265C4×D11—22no—
266C4×D11—22no—
267C4×D11—41no—
268C4×D11—41no—
269C4×D11—48no—
270C4×D11—48no—
271C4×D11#10014yes—
272C8×C11—42no—
273C8×C11—42no—
274C11⋊C8—42no—
275C11⋊C8—42no—
276C22×#41—112no—
277#532—112no—
278#532—112no—
279#532—112no—
280#532—112no—
281#532—221no—
282#532—221no—
283#532—221no—
284#532—221no—
285C2×C4⋊Q8C2×D1111yescharacteristic
286C2×#127—111no—
287C2×#124—112no—
288C2×#121—221no—
289C2×#121—221no—
290C2×C4×D4—221no—
291C2×C4×D4—221no—
292C22×C42—111no—
293#432—112no—
294#432—221no—
295#431—111no—
296#431—112no—
297#431—112no—
298#431—221no—
299#431—221no—
300#431—221no—
301#431C2×D1111yescharacteristic
302#423—111no—
303#423C2×D1111yescharacteristic
304C2×C4⋊C8—112no—
305#407—221no—
306C2×C22⋊C8—221no—
307C4×M16—221no—
308C2×C4×C8—221no—
309#333—114no—
310#333C2×D1114yescomplemented
311#331—114no—
312#331—114no—
313C22×C11—21no—
314C22×C11—21no—
315C22×C11#41612yes—
316C22×C11C22×C22⋊C411yescharacteristic
317C2×D11—21no—
318C2×D11—21no—
319C2×D11—21no—
320C2×D11—21no—
321C2×D11—21no—
322C2×D11—44no—
323C2×D11—44no—
324C2×D11—44no—
325C2×D11—44no—
326C2×D11—88no—
327C2×D11C2×#10012yes—
328C4×C11—21no—
329C4×C11—21no—
330C4×C11—44no—
331C4×C11C2×#10012yes—
332C4×C11#41612yes—
333C4×C11C2×#13511yescharacteristic
334C4×C11C2×#13511yescharacteristic
335C4×C11#57512yes—
336Dic11—21no—
337Dic11—21no—
338Dic11—21no—
339Dic11—21no—
340Dic11—21no—
341Dic11C2×#10012yes—
342C2×#41—114no—
343C2×#41—114no—
344C2×#41—222no—
345C2×#41—222no—
346C2×#41—448no—
347C22×Q8C4×D1112yes—
348C22×D4—112no—
349C22×D4—222no—
350C22×D4—221no—
351C22×D4—221no—
352C23×C4—111no—
353C23×C4—111no—
354C23×C4—111no—
355C23×C4—222no—
356C2×M16—21no—
357C2×M16—221no—
358C22×C8—222no—
359C4⋊Q8—21no—
360C4⋊Q8—21no—
361C4⋊Q8C4×D1112yes—
362C4⋊Q8C22×D1112yes—
363#127—112no—
364#127—112no—
365#127—221no—
366#127—221no—
367#124—114no—
368#124—114no—
369#124—222no—
370#124—222no—
371#121—222no—
372#121—222no—
373#121—222no—
374#121—222no—
375#121—222no—
376#121—222no—
377#121—222no—
378#121—222no—
379C4×D4—222no—
380C4×D4—222no—
381C4×D4—222no—
382C4×D4—222no—
383C4×D4—222no—
384C4×D4—222no—
385C4×D4—222no—
386C4×D4—222no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C22⋊C4—222no—
390C2×C22⋊C4—222no—
391C2×C42—111no—
392C2×C42—111no—
393C2×C42—111no—
394C2×C42—111no—
395C2×C42—111no—
396C2×C42—111no—
397C2×C42—111no—
398C2×C42—111no—
399C2×C42—111no—
400C2×C42—111no—
401C2×C42—111no—
402C2×C42C22×D1111yescharacteristic
403C4⋊C8—21no—
404C4⋊C8—112no—
405C4⋊C8—112no—
406C4⋊C8—222no—
407C4⋊C8—221no—
408C4⋊C8C22×D1112yes—
409C4⋊C8C22×D1112yes—
410C22⋊C8—21no—
411C22⋊C8—222no—
412C22⋊C8—222no—
413C22⋊C8—222no—
414C22⋊C8—221no—
415#97—222no—
416C4×C8—21no—
417C4×C8—222no—
418C4×C8—222no—
419C4×C8—221no—
420C2×C11—22no—
421C2×C11C22×#10011yescharacteristic
422C2×C11C2×#41611yescharacteristic
423C2×C11#289611yescharacteristic
424D11—22no—
425D11—41no—
426D11—84no—
427C24—111no—
428C24—222no—
429#41—448no—
430#41—448no—
431#41—448no—
432#41—448no—
433C2×Q8—22no—
434C2×Q8—44no—
435C2×Q8C2×C4×D1114yes—
436C2×D4—114no—
437C2×D4—224no—
438C2×D4—224no—
439C2×D4—222no—
440C2×D4—222no—
441C2×D4—222no—
442C2×D4—222no—
443C2×D4—222no—
444C2×D4—444no—
445C2×D4—444no—
446C2×D4—448no—
447C2×D4—442no—
448C2×D4—442no—
449C22×C4—22no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—111no—
459C22×C4—111no—
460C22×C4—111no—
461C22×C4—111no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—224no—
466C22×C4—224no—
467C22×C4—224no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—442no—
471C22×C4—448no—
472C22×C4C2×C4×D1111yescharacteristic
473C22×C4D4×D1111yescharacteristic
474C22×C4D4×D1111yescharacteristic
475M16—42no—
476M16—442no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—222no—
480C2×C8—222no—
481C2×C8—444no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C22⋊C4—224no—
487C22⋊C4—224no—
488C22⋊C4—224no—
489C22⋊C4—224no—
490C42—111no—
491C42—111no—
492C42—111no—
493C42—111no—
494C42—111no—
495C42—111no—
496C42—111no—
497C42—111no—
498C42—111no—
499C42—111no—
500C42—111no—
501C42—111no—
502C42C2×C4×D1111yescharacteristic
503C42D4×D1111yescharacteristic
504C42D4×D1111yescharacteristic
505C42C23×D1111yescharacteristic
506C11#1771411yescharacteristic, complemented, Sylow
507C23—111no—
508C23—111no—
509C23—222no—
510C23—222no—
511C23—224no—
512C23—441no—
513C23—444no—
514C23—444no—
515C23—444no—
516C23C22⋊C4×D1111yescharacteristic
517Q8—44no—
518Q8—44no—
519D4—444no—
520D4—444no—
521D4—448no—
522D4—448no—
523D4—442no—
524D4—442no—
525D4—444no—
526D4—444no—
527D4—444no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—24no—
531C2×C4—44no—
532C2×C4—111no—
533C2×C4—114no—
534C2×C4—111no—
535C2×C4—111no—
536C2×C4—111no—
537C2×C4—111no—
538C2×C4—111no—
539C2×C4—222no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—222no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—222no—
548C2×C4—222no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—222no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—448no—
555C2×C4—448no—
556C2×C4—441no—
557C2×C4C22⋊C4×D1111yescharacteristic
558C2×C4C22⋊C4×D1111yescharacteristic
559C2×C4C22⋊C4×D1111yescharacteristic
560C2×C4#6696912yes—
561C2×C4#6697212yes—
562C2×C4C22×C4×D1111yescharacteristic
563C2×C4C2×D4×D1111yescharacteristic
564C2×C4C2×D4×D1111yescharacteristic
565C8—42no—
566C8—42no—
567C8—442no—
568C8—442no—
569C22—21no—
570C22—21no—
571C22—112no—
572C22—221no—
573C22—221no—
574C22—221no—
575C22—221no—
576C22—221no—
577C22—444no—
578C22—444no—
579C22—444no—
580C22—444no—
581C22—888no—
582C22#1062241712yes—
583C22C2×C22⋊C4×D1111yescharacteristic
584C4—21no—
585C4—21no—
586C4—44no—
587C4—112no—
588C4—221no—
589C4—221no—
590C4—221no—
591C4—221no—
592C4—221no—
593C4D11×#10012yes—
594C4#1062241712yes—
595C4C2×#6696911yescharacteristic
596C4C2×#6697211yescharacteristic
597C4#1062330812yes—
598C2—22no—
599C2—222no—
600C2—441no—
601C2—884no—
602C2C2×D11×#10011yescharacteristic
603C2C2×#1062241711yescharacteristic
604C2#1307713411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1548C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623256C2
cosocleC42×C11C24
hypercenter#1548D11
hypocenterC11#17714
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. #13077248C2semidirect
3. D11×#431C2semidirect
4. #13067310C2semidirect
5. #13067297C2semidirect
6. #13067285C2semidirect
7. #13067283C2semidirect
8. #13067277C2semidirect
9. C11×#1548C2semidirect
34. #10622448C22semidirect
36. #10622446C22semidirect
37. #10622446C22semidirect
38. D11×C4⋊C8C22semidirect
43. C11×#333C22semidirect
44. #10622184C22semidirect
45. #10622123C22semidirect
46. #10622123C22semidirect
210. #1548D11semidirect
310. #333C2×D11semidirect
506. C11#17714semidirect

Maximal subgroups

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

subgroupindex
C2×#106232562
#130772482
D11×#4312
#130673102
#130672972
#130672852
#130672832
#130672772
C11×#15482
#1771411