Finite Group Databasebeta

← #14722380

Subgroups — #14722380

Order 2816.

1232 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623256C211yesmaximal, characteristic
2#13077246C211yesmaximal, characteristic, complemented
3D11×#432C211yesmaximal, characteristic, complemented
4#13067333C211yesmaximal, characteristic, complemented
5#13067329C211yesmaximal, characteristic, complemented
6#13067329C211yesmaximal, characteristic, complemented
7#13067320C214yesmaximal, complemented
8#13067292C214yesmaximal, complemented
9C11×#1556C211yesmaximal, characteristic, complemented
10C22×#4343—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#67000—21no—
13#10623256—21no—
14#10623256—21no—
15#10623256—21no—
16#10623256—21no—
17#10623256C412yes—
18#10623256C412yes—
19#10623256C2212yes—
20#10623256C2212yes—
21C2×#66948—21no—
22C2×#66948C412yes—
23C2×#66946—21no—
24C2×#66946C412yes—
25C2×#66927C2211yescharacteristic
26C2×C42×D11C2211yescharacteristic
27C11×#432C2211yescharacteristic
28C11×#432C2211yescharacteristic
29#10622539C2211yescharacteristic
30#10622539C2211yescharacteristic
31#10622450C2212yescomplemented
32#10622448C2212yescomplemented
33#10622446C2212yescomplemented
34D11×C4⋊C8C2212yescomplemented
35#10622339—21no—
36D11×C22⋊C8—21no—
37#10622332—21no—
38#10622331—21no—
39#10622320—21no—
40#10622318—21no—
41#10622318—21no—
42D11×#97—21no—
43C11×#332C2214yescomplemented
44#10622185C2214yescomplemented
45#10622123C2214yescomplemented
46#10622123C2214yescomplemented
47C22×Q8×C11—21no—
48C2×#4343—22no—
49C2×#4343—22no—
50C2×#4343—22no—
51C2×#4343—22no—
52C2×#4343—48no—
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
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#67000—22no—
70#67000—22no—
71#67000—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×C4×Dic11C2×C411yescharacteristic
75C2×C4×Dic11D411yescharacteristic
76C2×C4×Dic11D411yescharacteristic
77C2×#4313—22no—
78C2×C8×D11—22no—
79#66948—22no—
80#66948—22no—
81#66948—22no—
82#66948—22no—
83#66948—22no—
84#66948—22no—
85#66948C2×C414yes—
86#66948C2×C414yes—
87#66946—22no—
88#66946—22no—
89#66946—22no—
90#66946—22no—
91#66946—22no—
92#66946—22no—
93#66946C2×C414yes—
94#66946C2×C414yes—
95#66927—21no—
96#66927—21no—
97#66927C2×C412yes—
98#66927C2312yes—
99C42×D11C2×C411yescharacteristic
100C42×D11C2×C411yescharacteristic
101C42×D11D411yescharacteristic
102C42×D11D411yescharacteristic
103C42×D11D411yescharacteristic
104C42×D11D411yescharacteristic
105C42×D11C2311yescharacteristic
106C42×D11C2311yescharacteristic
107C11×C4⋊C8C2312yes—
108C11×C4⋊C8C2312yes—
109C11×C22⋊C8—21no—
110C11×C22⋊C8—21no—
111C11×#97—21no—
112C11×#97—21no—
113C22⋊(C11⋊C8)—21no—
114C22⋊(C11⋊C8)—21no—
115(C2×D11)⋊C8—22no—
116(C2×D11)⋊C8—22no—
117#66879—22no—
118Dic11⋊C8—22no—
119Dic11⋊C8—22no—
120C8×Dic11—22no—
121C4⋊(C11⋊C8)C2312yes—
122C4⋊(C11⋊C8)C2312yes—
123#66867—21no—
124#66867—21no—
125#17744—111nomaximal, Sylow
126C23×D11—22no—
127C23×D11C22⋊C411yescharacteristic
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—44no—
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—44no—
152C2×D44—48no—
153C2×D44C22×C414yes—
154C2×C4×D11—24no—
155C2×C4×D11—24no—
156C2×C4×D11—24no—
157C2×C4×D11—42no—
158C2×C4×D11—42no—
159C2×C4×D11—48no—
160C2×C4×D11C22⋊C411yescharacteristic
161C2×C4×D11C22⋊C411yescharacteristic
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×D11C2×D411yescharacteristic
169C2×C4×D11C2×D411yescharacteristic
170C2×C4×D11C2×D411yescharacteristic
171C2×C4×D11C2×D411yescharacteristic
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4C22×C414yes—
178C42×C11C22×C411yescharacteristic
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11C2411yescharacteristic
182(C2×D11)⋊C4—24no—
183(C2×D11)⋊C4—24no—
184(C2×D11)⋊C4—24no—
185(C2×D11)⋊C4—24no—
186C4×Dic11C22⋊C411yescharacteristic
187C4×Dic11C22⋊C411yescharacteristic
188C4×Dic11C22⋊C411yescharacteristic
189C4×Dic11C22⋊C411yescharacteristic
190C4×Dic11C22⋊C411yescharacteristic
191C4×Dic11C22⋊C411yescharacteristic
192C4×Dic11C22×C411yescharacteristic
193C4×Dic11C22×C411yescharacteristic
194C4×Dic11C2×D411yescharacteristic
195C4×Dic11C2×D411yescharacteristic
196C4×Dic11C2×D411yescharacteristic
197C4×Dic11C2×D411yescharacteristic
198C2×C11⋊C8—22no—
199C2×C11⋊C8—22no—
200#4313—44no—
201C8×D11—44no—
202C2×#532—111no—
203#2920—111no—
204C2×#432—111no—
205#1556—111no—
206#1556D1111yescharacteristic, complemented
207#1555—111no—
208#1555—111no—
209#1553—114no—
210#1547—114no—
211C23×C11C2×C22⋊C411yescharacteristic
212C22×D11—22no—
213C22×D11—22no—
214C22×D11—24no—
215C22×D11—41no—
216C22×D11—44no—
217C22×D11—44no—
218C22×D11—44no—
219C22×D11C2×C22⋊C411yescharacteristic
220C22×D11C2×C22⋊C411yescharacteristic
221Q8×C11—44no—
222Q8×C11—44no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—44no—
228C2×C4×C11C2×C22⋊C411yescharacteristic
229C2×C4×C11C2×C22⋊C411yescharacteristic
230C2×C4×C11C2×C22⋊C411yescharacteristic
231C2×C4×C11C23×C411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—41no—
237C2×Dic11C2×C22⋊C411yescharacteristic
238C2×Dic11C2×C22⋊C411yescharacteristic
239C2×Dic11C2×C22⋊C411yescharacteristic
240C2×Dic11C2×C22⋊C411yescharacteristic
241C2×Dic11C2×C22⋊C411yescharacteristic
242C2×Dic11C2×C22⋊C411yescharacteristic
243D44—44no—
244D44—44no—
245D44—44no—
246D44—44no—
247D44—48no—
248D44—48no—
249D44—44no—
250D44—44no—
251C4×D11—22no—
252C4×D11—22no—
253C4×D11—22no—
254C4×D11—22no—
255C4×D11—22no—
256C4×D11—41no—
257C4×D11—41no—
258C4×D11—41no—
259C4×D11—41no—
260C4×D11—41no—
261C4×D11—41no—
262C4×D11—48no—
263C4×D11—48no—
264C4×D11AGL(1,ℤ/8)14yes—
265C8×C11—42no—
266C8×C11—42no—
267C11⋊C8—42no—
268C11⋊C8—42no—
269C22×#41—221no—
270#532—112no—
271#532—112no—
272#532—112no—
273#532—112no—
274#532—221no—
275#532—221no—
276#532—221no—
277#532—221no—
278C2×C4⋊Q8C2×D1111yescharacteristic
279C2×#127—111no—
280C2×#124—221no—
281C2×#121—112no—
282C2×#121—221no—
283C2×C4×D4—112no—
284C2×C4×D4—221no—
285C22×C42—111no—
286#432—111no—
287#432—111no—
288#432—112no—
289#432—221no—
290#432—221no—
291#432—221no—
292#432C2×D1111yescharacteristic
293#432C2×D1111yescharacteristic
294#431—112no—
295#431—221no—
296#423—112no—
297C2×C4⋊C8—112no—
298#407—221no—
299C2×C22⋊C8—221no—
300C4×M16—221no—
301C2×#97—221no—
302#332—114no—
303#332C2×D1114yescomplemented
304#331—114no—
305#331—114no—
306C22×C11—21no—
307C22×C11—21no—
308C22×C11#41312yes—
309C22×C11C22×C22⋊C411yescharacteristic
310C2×D11—21no—
311C2×D11—21no—
312C2×D11—21no—
313C2×D11—21no—
314C2×D11—21no—
315C2×D11—44no—
316C2×D11—44no—
317C2×D11—44no—
318C2×D11—44no—
319C2×D11—88no—
320C2×D11#41812yes—
321C4×C11—21no—
322C4×C11—21no—
323C4×C11—21no—
324C4×C11—21no—
325C4×C11—44no—
326C4×C11C2×AGL(1,ℤ/8)12yes—
327C4×C11#57512yes—
328Dic11—21no—
329Dic11—21no—
330Dic11—21no—
331Dic11—21no—
332Dic11—21no—
333Dic11#41812yes—
334C2×#41—222no—
335C2×#41—222no—
336C2×#41—222no—
337C2×#41—222no—
338C2×#41—448no—
339C22×Q8—21no—
340C22×D4—112no—
341C22×D4—222no—
342C22×D4—221no—
343C22×D4—221no—
344C23×C4—111no—
345C23×C4—111no—
346C23×C4—111no—
347C23×C4—222no—
348C2×M16—222no—
349C22×C8—222no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8C4×D1112yes—
353C4⋊Q8C22×D1112yes—
354#127—112no—
355#127—112no—
356#127—221no—
357#127—221no—
358#124—222no—
359#124—222no—
360#124—222no—
361#124—222no—
362#121—114no—
363#121—114no—
364#121—222no—
365#121—222no—
366#121—222no—
367#121—222no—
368#121—222no—
369#121—222no—
370C4×D4—114no—
371C4×D4—114no—
372C4×D4—222no—
373C4×D4—222no—
374C4×D4—222no—
375C4×D4—222no—
376C4×D4—222no—
377C4×D4—222no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4C4×D1112yes—
380C2×C22⋊C4—222no—
381C2×C22⋊C4—222no—
382C2×C42—111no—
383C2×C42—111no—
384C2×C42—111no—
385C2×C42—111no—
386C2×C42—111no—
387C2×C42—111no—
388C2×C42—111no—
389C2×C42—111no—
390C2×C42—111no—
391C2×C42—111no—
392C2×C42—111no—
393C2×C42C22×D1111yescharacteristic
394C4⋊C8—112no—
395C4⋊C8—112no—
396C4⋊C8—222no—
397C4⋊C8—222no—
398C4⋊C8C22×D1112yes—
399C4⋊C8C22×D1112yes—
400C22⋊C8—21no—
401C22⋊C8—21no—
402C22⋊C8—222no—
403C22⋊C8—222no—
404C22⋊C8—221no—
405C22⋊C8—221no—
406#97—21no—
407#97—21no—
408#97—222no—
409#97—221no—
410#97—221no—
411C4×C8—222no—
412C2×C11—22no—
413C2×C11C2×#41311yescharacteristic
414C2×C11C2×#41811yescharacteristic
415C2×C11#289611yescharacteristic
416D11—22no—
417D11—41no—
418D11—84no—
419C24—111no—
420C24—222no—
421#41—448no—
422#41—448no—
423#41—448no—
424#41—448no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—44no—
428C2×D4—114no—
429C2×D4—224no—
430C2×D4—224no—
431C2×D4—222no—
432C2×D4—222no—
433C2×D4—222no—
434C2×D4—222no—
435C2×D4—222no—
436C2×D4—444no—
437C2×D4—444no—
438C2×D4—444no—
439C2×D4—448no—
440C22×C4—22no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—224no—
457C22×C4—224no—
458C22×C4—224no—
459C22×C4—442no—
460C22×C4—442no—
461C22×C4—448no—
462C22×C4C2×C4×D1111yescharacteristic
463C22×C4D4×D1111yescharacteristic
464C22×C4D4×D1111yescharacteristic
465M16—444no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—222no—
469C2×C8—222no—
470C2×C8—444no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4C2×C4×D1114yes—
475C22⋊C4—224no—
476C22⋊C4—224no—
477C22⋊C4—224no—
478C22⋊C4—224no—
479C42—111no—
480C42—111no—
481C42—111no—
482C42—111no—
483C42—111no—
484C42—111no—
485C42—111no—
486C42—111no—
487C42—111no—
488C42—111no—
489C42—111no—
490C42—111no—
491C42C2×C4×D1111yescharacteristic
492C42D4×D1111yescharacteristic
493C42D4×D1111yescharacteristic
494C42C23×D1111yescharacteristic
495C11#1774411yescharacteristic, complemented, Sylow
496C23—111no—
497C23—111no—
498C23—222no—
499C23—222no—
500C23—224no—
501C23—441no—
502C23—444no—
503C23—444no—
504C23—444no—
505C23C22⋊C4×D1111yescharacteristic
506Q8—44no—
507Q8—44no—
508D4—444no—
509D4—444no—
510D4—444no—
511D4—444no—
512D4—448no—
513D4—448no—
514D4—444no—
515D4—444no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—44no—
521C2×C4—111no—
522C2×C4—114no—
523C2×C4—111no—
524C2×C4—111no—
525C2×C4—111no—
526C2×C4—111no—
527C2×C4—111no—
528C2×C4—222no—
529C2×C4—222no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—222no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—448no—
542C2×C4—448no—
543C2×C4—441no—
544C2×C4C22⋊C4×D1111yescharacteristic
545C2×C4C22⋊C4×D1111yescharacteristic
546C2×C4C22⋊C4×D1111yescharacteristic
547C2×C4C22×C4×D1111yescharacteristic
548C2×C4C2×D4×D1111yescharacteristic
549C2×C4C2×D4×D1111yescharacteristic
550C8—42no—
551C8—42no—
552C8—442no—
553C8—442no—
554C22—21no—
555C22—21no—
556C22—112no—
557C22—221no—
558C22—221no—
559C22—221no—
560C22—221no—
561C22—221no—
562C22—444no—
563C22—444no—
564C22—444no—
565C22—444no—
566C22—888no—
567C22#1062236412yes—
568C22C2×C22⋊C4×D1111yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—44no—
574C4—112no—
575C4—221no—
576C4—221no—
577C4—221no—
578C4—221no—
579C4—221no—
580C4D11×AGL(1,ℤ/8)12yes—
581C4#1062330812yes—
582C2—22no—
583C2—222no—
584C2—441no—
585C2—884no—
586C2C2×#1062236411yescharacteristic
587C2D11×#41811yescharacteristic
588C2#1307713411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1556C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623256C2
cosocleC42×C11C24
hypercenter#1556D11
hypocenterC11#17744
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1556

Complements

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

NH ≅ G/Ntype
2. #13077246C2semidirect
3. D11×#432C2semidirect
4. #13067333C2semidirect
5. #13067329C2semidirect
6. #13067329C2semidirect
7. #13067320C2semidirect
8. #13067292C2semidirect
9. C11×#1556C2semidirect
31. #10622450C22semidirect
32. #10622448C22semidirect
33. #10622446C22semidirect
34. D11×C4⋊C8C22semidirect
43. C11×#332C22semidirect
44. #10622185C22semidirect
45. #10622123C22semidirect
46. #10622123C22semidirect
206. #1556D11semidirect
303. #332C2×D11semidirect
495. C11#17744semidirect

Maximal subgroups

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

subgroupindex
C2×#106232562
#130772462
D11×#4322
#130673332
#130673292
#130673202
#130672922
C11×#15562
#1774411