Finite Group Databasebeta

← #14722108

Subgroups — #14722108

Order 2816.

1298 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623256C211yesmaximal, characteristic
2D11×#431C211yesmaximal, characteristic, complemented
3D11×#423C211yesmaximal, characteristic, complemented
4#13067292C214yesmaximal, complemented
5#13067288C211yesmaximal, characteristic, complemented
6#13067285C211yesmaximal, characteristic, complemented
7#13067283C211yesmaximal, characteristic, complemented
8#13067264C214yesmaximal, complemented
9C11×#1546C211yesmaximal, characteristic, complemented
10C22×#4343—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#67000—21no—
13C2×M16×D11—21no—
14#10623256—21no—
15#10623256—21no—
16#10623256—21no—
17#10623256—21no—
18#10623256C412yes—
19#10623256C412yes—
20#10623256C2212yes—
21#10623256C2212yes—
22C2×#66948—21no—
23C2×#66948C412yes—
24C2×#66946—21no—
25C2×#66946C412yes—
26C2×#66927C2211yescharacteristic
27C2×C42×D11C2211yescharacteristic
28C11×#431C2211yescharacteristic
29C11×#423C2211yescharacteristic
30#10622731—21no—
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622450—21no—
34#10622450C2212yescomplemented
35#10622446C2212yescomplemented
36D11×C4⋊C8—21no—
37D11×C4⋊C8C2212yescomplemented
38D11×C4⋊C8C2212yescomplemented
39D11×C22⋊C8—21no—
40#10622331—21no—
41#10622298—21no—
42C4×C8×D11—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—44no—
53C2×#4343—44no—
54C22×D44—22no—
55C22×D44—21no—
56C22×D44—21no—
57C22×D44C2×C412yes—
58C22×C4×D11—22no—
59C22×C4×D11C2×C411yescharacteristic
60C22×C4×D11D411yescharacteristic
61C22×C4×D11D411yescharacteristic
62C2×C11×M16—21no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8C2×C412yes—
66C11×C4⋊Q8C2312yes—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2×C412yes—
69C2×C42×C11C2311yescharacteristic
70#67000—22no—
71#67000—22no—
72#67000—22no—
73#67000—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
76C2×C4×Dic11C2×C411yescharacteristic
77C2×C4×Dic11D411yescharacteristic
78C2×C4×Dic11D411yescharacteristic
79C2×#4318—21no—
80M16×D11—44no—
81C2×#4313—22no—
82C2×C8×D11—22no—
83C2×C8×D11—22no—
84#66948—22no—
85#66948—22no—
86#66948—22no—
87#66948—22no—
88#66948—22no—
89#66948—22no—
90#66948C2×C414yes—
91#66948C2×C414yes—
92#66946—22no—
93#66946—22no—
94#66946—22no—
95#66946—22no—
96#66946—22no—
97#66946—22no—
98#66946C2×C414yes—
99#66946C2×C414yes—
100#66927—21no—
101#66927—21no—
102#66927C2×C412yes—
103#66927C2312yes—
104C42×D11C2×C411yescharacteristic
105C42×D11C2×C411yescharacteristic
106C42×D11D411yescharacteristic
107C42×D11D411yescharacteristic
108C42×D11D411yescharacteristic
109C42×D11D411yescharacteristic
110C42×D11C2311yescharacteristic
111C42×D11C2311yescharacteristic
112C11×C4⋊C8—21no—
113C11×C4⋊C8C2312yes—
114C11×C4⋊C8C2312yes—
115C11×C22⋊C8—21no—
116C4×C8×C11—21no—
117C22⋊(C11⋊C8)—21no—
118(C2×D11)⋊C8—22no—
119Dic11⋊C8—22no—
120Dic11⋊C8—22no—
121Dic11⋊C8—22no—
122C8×Dic11—22no—
123C4⋊(C11⋊C8)—21no—
124C4⋊(C11⋊C8)C2312yes—
125C4⋊(C11⋊C8)C2312yes—
126C4×C11⋊C8—21no—
127#17704—111nomaximal, Sylow
128C23×D11—22no—
129C23×D11C22⋊C411yescharacteristic
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11—42no—
133C2×Q8×C11—42no—
134C22×C4×C11—22no—
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×Dic11C22⋊C411yescharacteristic
139C22×Dic11C22⋊C411yescharacteristic
140C22×Dic11C22⋊C411yescharacteristic
141#4343—48no—
142#4343—48no—
143#4343—44no—
144#4343—44no—
145#4343—44no—
146#4343—44no—
147C2×D44—24no—
148C2×D44—24no—
149C2×D44—22no—
150C2×D44—22no—
151C2×D44—22no—
152C2×D44—22no—
153C2×D44—22no—
154C2×D44—44no—
155C2×D44—44no—
156C2×D44—48no—
157C2×D44—42no—
158C2×D44—42no—
159C2×D44C22×C414yes—
160C2×C4×D11—24no—
161C2×C4×D11—24no—
162C2×C4×D11—42no—
163C2×C4×D11—42no—
164C2×C4×D11—48no—
165C2×C4×D11C22⋊C411yescharacteristic
166C2×C4×D11C22⋊C411yescharacteristic
167C2×C4×D11C22⋊C411yescharacteristic
168C2×C4×D11C22⋊C411yescharacteristic
169C2×C4×D11C22⋊C411yescharacteristic
170C2×C4×D11C22⋊C411yescharacteristic
171C2×C4×D11D814yes—
172C2×C4×D11SD1614yes—
173C2×C4×D11C22×C411yescharacteristic
174C2×C4×D11C22×C411yescharacteristic
175C2×C4×D11C2×D411yescharacteristic
176C2×C4×D11C2×D411yescharacteristic
177C2×C4×D11C2×D411yescharacteristic
178C2×C4×D11C2×D411yescharacteristic
179C11×M16—42no—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4C22×C414yes—
186C42×C11C22×C411yescharacteristic
187C42×C11C2×D411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11C2411yescharacteristic
190(C2×D11)⋊C4—24no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—24no—
193(C2×D11)⋊C4—24no—
194C4×Dic11C22⋊C411yescharacteristic
195C4×Dic11C22⋊C411yescharacteristic
196C4×Dic11C22⋊C411yescharacteristic
197C4×Dic11C22⋊C411yescharacteristic
198C4×Dic11C22⋊C411yescharacteristic
199C4×Dic11C22⋊C411yescharacteristic
200C4×Dic11C22×C411yescharacteristic
201C4×Dic11C22×C411yescharacteristic
202C4×Dic11C2×D411yescharacteristic
203C4×Dic11C2×D411yescharacteristic
204C4×Dic11C2×D411yescharacteristic
205C4×Dic11C2×D411yescharacteristic
206#4318—42no—
207C2×C11⋊C8—22no—
208C2×C11⋊C8—22no—
209#4313—44no—
210C8×D11—44no—
211C8×D11—44no—
212C2×#532—111no—
213C2×#431—111no—
214C2×#423—111no—
215#1547—114no—
216#1546—111no—
217#1546D1111yescharacteristic, complemented
218#1545—111no—
219#1545—111no—
220#1540—114no—
221C23×C11C2×C22⋊C411yescharacteristic
222C22×D11—24no—
223C22×D11—41no—
224C22×D11—41no—
225C22×D11—44no—
226C22×D11—44no—
227C22×D11—44no—
228C22×D11#10214yes—
229C22×D11C2×C22⋊C411yescharacteristic
230C22×D11C2×C22⋊C411yescharacteristic
231Q8×C11—42no—
232Q8×C11—42no—
233Q8×C11—44no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—44no—
238C2×C4×C11C2×C22⋊C411yescharacteristic
239C2×C4×C11C2×C22⋊C411yescharacteristic
240C2×C4×C11C2×C22⋊C411yescharacteristic
241C2×C4×C11C2×D812yes—
242C2×C4×C11C2×SD1612yes—
243C2×C4×C11C23×C411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11#10214yes—
249C2×Dic11C2×C22⋊C411yescharacteristic
250C2×Dic11C2×C22⋊C411yescharacteristic
251C2×Dic11C2×C22⋊C411yescharacteristic
252C2×Dic11C2×C22⋊C411yescharacteristic
253C2×Dic11C2×C22⋊C411yescharacteristic
254C2×Dic11C2×C22⋊C411yescharacteristic
255D44—44no—
256D44—44no—
257D44—48no—
258D44—48no—
259D44—42no—
260D44—42no—
261D44—44no—
262D44—44no—
263D44—44no—
264C4×D11—22no—
265C4×D11—22no—
266C4×D11—22no—
267C4×D11—22no—
268C4×D11—41no—
269C4×D11—41no—
270C4×D11—41no—
271C4×D11—41no—
272C4×D11—48no—
273C4×D11—48no—
274C4×D11#10214yes—
275C4×D11#10214yes—
276C4×D11C2×D812yes—
277C4×D11C2×D812yes—
278C4×D11C2×SD1612yes—
279C4×D11C2×SD1612yes—
280C8×C11—42no—
281C8×C11—42no—
282C11⋊C8—42no—
283C11⋊C8—42no—
284C22×#41—221no—
285C22×M16—221no—
286#532—112no—
287#532—112no—
288#532—112no—
289#532—112no—
290#532—221no—
291#532—221no—
292#532—221no—
293#532—221no—
294C2×C4⋊Q8C2×D1111yescharacteristic
295C2×#127—111no—
296C2×#124—221no—
297C2×#121—112no—
298C2×#121—221no—
299C2×C4×D4—112no—
300C2×C4×D4—221no—
301C22×C42—111no—
302#431—111no—
303#431—112no—
304#431—221no—
305#431—221no—
306#431C2×D1111yescharacteristic
307#423—111no—
308#423—112no—
309#423—221no—
310#423—221no—
311#423C2×D1111yescharacteristic
312C2×C4⋊C8—112no—
313C2×C4⋊C8—112no—
314C2×C4⋊C8—221no—
315C2×C22⋊C8—221no—
316C2×C4×C8—221no—
317#332—114no—
318#332C2×D1114yescomplemented
319#331—114no—
320#331—114no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11C2×#10212yes—
324C22×C11C22×C22⋊C411yescharacteristic
325C2×D11—21no—
326C2×D11—21no—
327C2×D11—21no—
328C2×D11—21no—
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—88no—
334C2×D11C2×#10212yes—
335C2×D11C2×#10212yes—
336C4×C11—21no—
337C4×C11—21no—
338C4×C11—44no—
339C4×C11#41312yes—
340C4×C11C2×#10212yes—
341C4×C11C22×D811yescharacteristic
342C4×C11C22×SD1611yescharacteristic
343C4×C11#57512yes—
344Dic11—21no—
345Dic11—21no—
346Dic11—21no—
347Dic11—21no—
348Dic11C2×#10212yes—
349Dic11C2×#10212yes—
350C2×#41—222no—
351C2×#41—222no—
352C2×#41—222no—
353C2×#41—222no—
354C2×#41—444no—
355C2×#41—444no—
356C22×Q8—21no—
357C22×D4—112no—
358C22×D4—222no—
359C22×D4—221no—
360C22×D4—221no—
361C23×C4—111no—
362C23×C4—111no—
363C23×C4—111no—
364C23×C4—222no—
365C2×M16—21no—
366C2×M16—222no—
367C2×M16—221no—
368C2×M16—444no—
369C22×C8—222no—
370C22×C8—222no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8C4×D1112yes—
374C4⋊Q8C22×D1112yes—
375#127—112no—
376#127—112no—
377#127—221no—
378#127—221no—
379#124—222no—
380#124—222no—
381#124—222no—
382#124—222no—
383#121—114no—
384#121—114no—
385#121—222no—
386#121—222no—
387#121—222no—
388#121—222no—
389#121—222no—
390#121—222no—
391C4×D4—114no—
392C4×D4—114no—
393C4×D4—222no—
394C4×D4—222no—
395C4×D4—222no—
396C4×D4—222no—
397C4×D4—222no—
398C4×D4—222no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4C4×D1112yes—
401C2×C22⋊C4—222no—
402C2×C22⋊C4—222no—
403C2×C42—111no—
404C2×C42—111no—
405C2×C42—111no—
406C2×C42—111no—
407C2×C42—111no—
408C2×C42—111no—
409C2×C42—111no—
410C2×C42—111no—
411C2×C42—111no—
412C2×C42—111no—
413C2×C42—111no—
414C2×C42C22×D1111yescharacteristic
415C4⋊C8—21no—
416C4⋊C8—112no—
417C4⋊C8—112no—
418C4⋊C8—222no—
419C4⋊C8—222no—
420C4⋊C8—222no—
421C4⋊C8—221no—
422C4⋊C8C22×D1112yes—
423C4⋊C8C22×D1112yes—
424C22⋊C8—21no—
425C22⋊C8—222no—
426C22⋊C8—221no—
427C4×C8—21no—
428C4×C8—222no—
429C4×C8—221no—
430C2×C11—22no—
431C2×C11C2×#41311yescharacteristic
432C2×C11C22×#10211yescharacteristic
433C2×C11#289611yescharacteristic
434D11—22no—
435D11—22no—
436D11—84no—
437C24—111no—
438C24—222no—
439#41—444no—
440#41—444no—
441#41—444no—
442#41—444no—
443#41—448no—
444#41—448no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—42no—
448C2×Q8—42no—
449C2×D4—114no—
450C2×D4—224no—
451C2×D4—224no—
452C2×D4—222no—
453C2×D4—222no—
454C2×D4—222no—
455C2×D4—222no—
456C2×D4—222no—
457C2×D4—444no—
458C2×D4—444no—
459C2×D4—448no—
460C2×D4—442no—
461C2×D4—442no—
462C22×C4—22no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—114no—
467C22×C4—114no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—224no—
481C22×C4—224no—
482C22×C4—442no—
483C22×C4—442no—
484C22×C4—448no—
485C22×C4C2×C4×D1111yescharacteristic
486C22×C4D4×D1111yescharacteristic
487C22×C4D4×D1111yescharacteristic
488M16—42no—
489M16—444no—
490M16—442no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—222no—
494C2×C8—222no—
495C2×C8—444no—
496C2×C8—444no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4C2×C4×D1114yes—
501C22⋊C4—224no—
502C22⋊C4—224no—
503C22⋊C4—224no—
504C22⋊C4—224no—
505C42—111no—
506C42—111no—
507C42—111no—
508C42—111no—
509C42—111no—
510C42—111no—
511C42—111no—
512C42—111no—
513C42—111no—
514C42—111no—
515C42—111no—
516C42—111no—
517C42C2×C4×D1111yescharacteristic
518C42D4×D1111yescharacteristic
519C42D4×D1111yescharacteristic
520C42C23×D1111yescharacteristic
521C11#1770411yescharacteristic, complemented, Sylow
522C23—111no—
523C23—111no—
524C23—114no—
525C23—224no—
526C23—441no—
527C23—441no—
528C23—444no—
529C23—444no—
530C23—444no—
531C23C22⋊C4×D1111yescharacteristic
532Q8—42no—
533Q8—42no—
534Q8—44no—
535D4—444no—
536D4—444no—
537D4—448no—
538D4—448no—
539D4—442no—
540D4—442no—
541D4—444no—
542D4—444no—
543D4—444no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—44no—
548C2×C4—111no—
549C2×C4—111no—
550C2×C4—114no—
551C2×C4—112no—
552C2×C4—112no—
553C2×C4—112no—
554C2×C4—112no—
555C2×C4—114no—
556C2×C4—114no—
557C2×C4—111no—
558C2×C4—111no—
559C2×C4—111no—
560C2×C4—111no—
561C2×C4—222no—
562C2×C4—222no—
563C2×C4—222no—
564C2×C4—222no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—448no—
570C2×C4—448no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4C22⋊C4×D1111yescharacteristic
574C2×C4C22⋊C4×D1111yescharacteristic
575C2×C4C22⋊C4×D1111yescharacteristic
576C2×C4D8×D1112yes—
577C2×C4SD16×D1112yes—
578C2×C4C22×C4×D1111yescharacteristic
579C2×C4C2×D4×D1111yescharacteristic
580C2×C4C2×D4×D1111yescharacteristic
581C8—42no—
582C8—42no—
583C8—442no—
584C8—442no—
585C22—21no—
586C22—21no—
587C22—112no—
588C22—112no—
589C22—221no—
590C22—221no—
591C22—221no—
592C22—221no—
593C22—444no—
594C22—444no—
595C22—444no—
596C22—444no—
597C22—888no—
598C22D11×#10212yes—
599C22C2×C22⋊C4×D1111yescharacteristic
600C4—21no—
601C4—21no—
602C4—44no—
603C4—112no—
604C4—112no—
605C4—221no—
606C4—221no—
607C4—221no—
608C4—221no—
609C4#1062236412yes—
610C4D11×#10212yes—
611C4C2×D8×D1111yescharacteristic
612C4C2×SD16×D1111yescharacteristic
613C4#1062330812yes—
614C2—22no—
615C2—222no—
616C2—222no—
617C2—884no—
618C2C2×#1062236411yescharacteristic
619C2C2×D11×#10211yescharacteristic
620C2#1307713411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1546C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623256C2
cosocleC42×C11C24
hypercenter#1546D11
hypocenterC11#17704
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. D11×#431C2semidirect
3. D11×#423C2semidirect
4. #13067292C2semidirect
5. #13067288C2semidirect
6. #13067285C2semidirect
7. #13067283C2semidirect
8. #13067264C2semidirect
9. C11×#1546C2semidirect
34. #10622450C22semidirect
35. #10622446C22semidirect
37. D11×C4⋊C8C22semidirect
38. D11×C4⋊C8C22semidirect
43. C11×#332C22semidirect
44. #10622185C22semidirect
45. #10622123C22semidirect
46. #10622123C22semidirect
217. #1546D11semidirect
318. #332C2×D11semidirect
521. C11#17704semidirect

Maximal subgroups

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

subgroupindex
C2×#106232562
D11×#4312
D11×#4232
#130672922
#130672882
#130672852
#130672832
#130672642
C11×#15462
#1770411