Finite Group Databasebeta

← #14722176

Subgroups — #14722176

Order 2816.

972 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#533C211yesmaximal, characteristic
2#13077246C211yesmaximal, characteristic
3C2×#10622446C211yesmaximal, characteristic
4#13067317C211yesmaximal, characteristic, complemented
5#13067316C211yesmaximal, characteristic, complemented
6#13067314C211yesmaximal, characteristic, complemented
7#13067299C212yesmaximal, complemented
8#13067286C212yesmaximal, complemented
9#13067279C212yesmaximal, complemented
10#13067279C212yesmaximal, complemented
11C11×#1552C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13#10623259C2211yescharacteristic
14#10623259C2211yescharacteristic
15D11×C4⋊Q8C2211yescharacteristic
16D11×C4⋊Q8C2211yescharacteristic
17#10623219C412yes—
18D11×#125C412yes—
19D11×C22⋊Q8—21no—
20D11×C22⋊Q8—21no—
21#10623153—21no—
22#10623153—21no—
23#10623109—21no—
24#10623109—21no—
25C4×Q8×D11—21no—
26C4×Q8×D11—21no—
27D11×#117C412yes—
28#10623048C412yes—
29C2×C42×D11C2211yescharacteristic
30#10623001C2211yescharacteristic
31C11×#432C2211yescharacteristic
32C2×C11×C4⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8—21no—
34C2×C8×Dic11—21no—
35#10622539C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37#10622450C2212yes—
38#10622446—21no—
39#10622446—21no—
40#10622446C2212yes—
41#10622446C2212yes—
42#10622446C2212yes—
43#10622339—21no—
44#10622331—21no—
45#10622320—21no—
46#10622318—21no—
47C11×#332C2212yescomplemented
48C11×#332C2212yescomplemented
49#10622185C2212yescomplemented
50#10622185C2212yescomplemented
51#10622124C2212yescomplemented
52#10622124C2212yescomplemented
53#10622120C2212yescomplemented
54#10622120C2212yescomplemented
55C2×Q8×D11—21no—
56C2×Q8×D11—21no—
57C22×C4×D11C2×C411yescharacteristic
58C22×C4×D11D411yescharacteristic
59C22×C4×D11D411yescharacteristic
60C22×C8×C11—21no—
61C11×C4⋊Q8C2311yescharacteristic
62C11×C4⋊Q8C2311yescharacteristic
63C11×#125C2×C412yes—
64C11×C22⋊Q8—21no—
65C11×C22⋊Q8—21no—
66C4×Q8×C11—21no—
67C4×Q8×C11—21no—
68C11×#117C2×C412yes—
69C2×C42×C11C2311yescharacteristic
70#66999—21no—
71#66999—21no—
72Q8×Dic11—21no—
73Q8×Dic11—21no—
74#66997—21no—
75#66997—21no—
76#66979C2×C412yes—
77#66977—21no—
78#66977—21no—
79C2×C4×Dic11C2×C411yescharacteristic
80C2×C4×Dic11D411yescharacteristic
81C2×C4×Dic11D411yescharacteristic
82C22×C11⋊C8—21no—
83C2×#4313—22no—
84#66950—21no—
85#66950—21no—
86#66949—22no—
87#66949—22no—
88#66945C2×C412yes—
89#66945C2×C412yes—
90C4⋊C4×D11—22no—
91C4⋊C4×D11—22no—
92C4⋊C4×D11—21no—
93C4⋊C4×D11—21no—
94C4⋊C4×D11C2×C412yes—
95C4⋊C4×D11C2×C412yes—
96#66943C2×C412yes—
97#66943C2×C412yes—
98#66942—22no—
99#66942—22no—
100#66941—21no—
101#66941—21no—
102#66941C2×C412yes—
103#66941C2×C412yes—
104#66940—22no—
105#66940—22no—
106#66940—21no—
107#66940—21no—
108C22⋊C4×D11—22no—
109#66931—22no—
110#66931—22no—
111#66930—22no—
112#66925—22no—
113C42×D11—22no—
114C42×D11C2×C411yescharacteristic
115C42×D11C2×C411yescharacteristic
116C42×D11D411yescharacteristic
117C42×D11D411yescharacteristic
118C42×D11D411yescharacteristic
119C42×D11D411yescharacteristic
120C42×D11C2311yescharacteristic
121C42×D11C2311yescharacteristic
122#66923C2×C412yes—
123#66922C2311yescharacteristic
124#66922C2311yescharacteristic
125C4×Dic22—21no—
126C4×Dic22—21no—
127C4×Dic22—22no—
128C4×Dic22—22no—
129C11×C4⋊C8—21no—
130C11×C4⋊C8C2312yes—
131C11×C4⋊C8C2312yes—
132C11×C22⋊C8—21no—
133C11×#97—21no—
134C22⋊(C11⋊C8)—21no—
135(C2×D11)⋊C8—22no—
136(C2×D11)⋊C8—22no—
137(C2×D11)⋊C8—22no—
138Dic11⋊C8—22no—
139C8×Dic11—22no—
140C8×Dic11—22no—
141C8×Dic11—22no—
142C4⋊(C11⋊C8)—21no—
143C4⋊(C11⋊C8)C2312yes—
144C4⋊(C11⋊C8)C2312yes—
145#66867—21no—
146#17715—111nomaximal, Sylow
147C23×D11C22⋊C411yescharacteristic
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×Dic11C22⋊C411yescharacteristic
154C22×Dic11C22⋊C411yescharacteristic
155C22×Dic11C22⋊C411yescharacteristic
156Q8×D11—42no—
157Q8×D11—42no—
158Q8×D11—44no—
159C2×C4×D11—24no—
160C2×C4×D11—24no—
161C2×C4×D11—22no—
162C2×C4×D11—22no—
163C2×C4×D11—41no—
164C2×C4×D11—41no—
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×D11C22×C411yescharacteristic
172C2×C4×D11C22×C411yescharacteristic
173C2×C4×D11C2×D411yescharacteristic
174C2×C4×D11C2×D411yescharacteristic
175C2×C4×D11C2×D411yescharacteristic
176C2×C4×D11C2×D411yescharacteristic
177C2×Dic22—22no—
178C2×Dic22—22no—
179C2×Dic22—21no—
180C2×Dic22—21no—
181C2×C8×C11—22no—
182C2×C8×C11—22no—
183C2×C8×C11—42no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4C22×C412yes—
189C11×C4⋊C4C22×C412yes—
190C11×C22⋊C4—22no—
191C42×C11—22no—
192C42×C11C22×C411yescharacteristic
193C42×C11C2×D411yescharacteristic
194C42×C11C2×D411yescharacteristic
195C42×C11C2411yescharacteristic
196C22⋊Dic11—22no—
197(C2×D11)⋊C4—22no—
198(C2×D11)⋊C4—22no—
199C4⋊Dic11—22no—
200C4⋊Dic11—22no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11C22×C412yes—
204C4⋊Dic11C22×C412yes—
205Dic11⋊C4—22no—
206Dic11⋊C4—22no—
207Dic11⋊C4—22no—
208Dic11⋊C4—22no—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212Dic11⋊C4—22no—
213C4×Dic11—22no—
214C4×Dic11—22no—
215C4×Dic11—22no—
216C4×Dic11C22⋊C411yescharacteristic
217C4×Dic11C22⋊C411yescharacteristic
218C4×Dic11C22⋊C411yescharacteristic
219C4×Dic11C22⋊C411yescharacteristic
220C4×Dic11C22⋊C411yescharacteristic
221C4×Dic11C22⋊C411yescharacteristic
222C4×Dic11C22×C411yescharacteristic
223C4×Dic11C22×C411yescharacteristic
224C4×Dic11C2×D411yescharacteristic
225C4×Dic11C2×D411yescharacteristic
226C4×Dic11C2×D411yescharacteristic
227C4×Dic11C2×D411yescharacteristic
228C2×C11⋊C8—22no—
229C2×C11⋊C8—22no—
230C2×C11⋊C8—42no—
231#4313—44no—
232C2×#533—111no—
233#2920—111no—
234C2×#431—111no—
235#1552—111no—
236#1552—111no—
237#1552—111no—
238#1552D1111yescharacteristic, complemented
239#1549—112no—
240#1546—112no—
241#1544—112no—
242#1544—112no—
243C23×C11C2×C22⋊C411yescharacteristic
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—41no—
247C22×D11C2×C22⋊C411yescharacteristic
248C22×D11C2×C22⋊C411yescharacteristic
249Q8×C11—42no—
250Q8×C11—41no—
251Q8×C11—41no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11C2×C22⋊C411yescharacteristic
259C2×C4×C11C2×C22⋊C411yescharacteristic
260C2×C4×C11C2×C22⋊C411yescharacteristic
261C2×C4×C11C23×C411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—41no—
268C2×Dic11#10114yes—
269C2×Dic11C2×C22⋊C411yescharacteristic
270C2×Dic11C2×C22⋊C411yescharacteristic
271C2×Dic11C2×C22⋊C411yescharacteristic
272C2×Dic11C2×C22⋊C411yescharacteristic
273C2×Dic11C2×C22⋊C411yescharacteristic
274C2×Dic11C2×C22⋊C411yescharacteristic
275C4×D11—22no—
276C4×D11—22no—
277C4×D11—21no—
278C4×D11—21no—
279C4×D11—21no—
280C4×D11—21no—
281C4×D11—22no—
282C4×D11—22no—
283C4×D11—22no—
284C4×D11—22no—
285C4×D11—22no—
286C4×D11—41no—
287C4×D11—41no—
288C4×D11—44no—
289C4×D11—44no—
290C4×D11#13514yes—
291Dic22—44no—
292Dic22—42no—
293Dic22—41no—
294Dic22—41no—
295Dic22—44no—
296C8×C11—42no—
297C8×C11—42no—
298C11⋊C8—42no—
299C11⋊C8—42no—
300#533—111no—
301#533—111no—
302#533—112no—
303#533—112no—
304#533—111no—
305#533—221no—
306#533—221no—
307#533—221no—
308#533—221no—
309#533C2×D1111yescharacteristic
310C2×C4⋊Q8—111no—
311C2×C4⋊Q8—111no—
312C2×#125—112no—
313C2×C22⋊Q8—221no—
314C2×C22⋊Q8—221no—
315C2×C4×Q8—221no—
316C2×C4×Q8—221no—
317C2×#117—112no—
318C22×C42—111no—
319#432—111no—
320#432—221no—
321#432C2×D1111yescharacteristic
322#431—112no—
323#431—112no—
324#431—112no—
325#431—221no—
326#431—221no—
327#431—221no—
328#423—112no—
329C2×C4⋊C8—111no—
330C2×C4⋊C8C2×D1111yescharacteristic
331#407—221no—
332C2×C22⋊C8—221no—
333C4×M16—221no—
334C2×C4×C8—221no—
335#332—112no—
336#332—112no—
337#332—112no—
338#332—112no—
339#332—112no—
340#332—112no—
341#332C2×D1112yescomplemented
342#332C2×D1112yescomplemented
343C22×C11—21no—
344C22×C11—21no—
345C22×C11C2×#10112yes—
346C22×C11C22×C22⋊C411yescharacteristic
347C2×D11—21no—
348C2×D11—21no—
349C2×D11—21no—
350C2×D11—21no—
351C2×D11—21no—
352C2×D11—44no—
353C2×D11#41612yes—
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—21no—
357C4×C11—21no—
358C4×C11—42no—
359C4×C11—42no—
360C4×C11C2×#13512yes—
361C4×C11#57511yescharacteristic
362C4×C11#57511yescharacteristic
363Dic11—21no—
364Dic11—21no—
365Dic11—21no—
366Dic11—42no—
367Dic11—42no—
368Dic11C2×#10112yes—
369Dic11C2×#10112yes—
370Dic11#41612yes—
371C22×Q8—221no—
372C22×Q8—221no—
373C23×C4—111no—
374C23×C4—111no—
375C23×C4—111no—
376C2×M16—222no—
377C22×C8—21no—
378C22×C8—221no—
379C4⋊Q8—112no—
380C4⋊Q8—112no—
381C4⋊Q8—111no—
382C4⋊Q8—111no—
383C4⋊Q8—221no—
384C4⋊Q8—221no—
385C4⋊Q8—221no—
386C4⋊Q8—221no—
387C4⋊Q8C22×D1111yescharacteristic
388C4⋊Q8C22×D1111yescharacteristic
389#125—112no—
390#125—112no—
391#125—112no—
392#125—222no—
393#125—222no—
394#125C4×D1112yes—
395C22⋊Q8—21no—
396C22⋊Q8—21no—
397C22⋊Q8—222no—
398C22⋊Q8—222no—
399C22⋊Q8—222no—
400C22⋊Q8—222no—
401C22⋊Q8—221no—
402C22⋊Q8—221no—
403C22⋊Q8—221no—
404C22⋊Q8—221no—
405C22⋊Q8—221no—
406C22⋊Q8—221no—
407C4×Q8—21no—
408C4×Q8—21no—
409C4×Q8—222no—
410C4×Q8—222no—
411C4×Q8—222no—
412C4×Q8—222no—
413C4×Q8—221no—
414C4×Q8—221no—
415C4×Q8—221no—
416C4×Q8—221no—
417C4×Q8—221no—
418C4×Q8—221no—
419#117—112no—
420#117—112no—
421#117—112no—
422#117—222no—
423#117—222no—
424#117C4×D1112yes—
425C2×C4⋊C4—112no—
426C2×C4⋊C4—112no—
427C2×C4⋊C4—222no—
428C2×C4⋊C4—222no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C22⋊C4—222no—
432C2×C42—111no—
433C2×C42—111no—
434C2×C42—111no—
435C2×C42—111no—
436C2×C42—111no—
437C2×C42—111no—
438C2×C42—111no—
439C2×C42—111no—
440C2×C42—111no—
441C2×C42—111no—
442C2×C42—111no—
443C2×C42—222no—
444C2×C42C22×D1111yescharacteristic
445C4⋊C8—21no—
446C4⋊C8—112no—
447C4⋊C8—112no—
448C4⋊C8—222no—
449C4⋊C8—221no—
450C4⋊C8C22×D1112yes—
451C4⋊C8C22×D1112yes—
452C22⋊C8—21no—
453C22⋊C8—222no—
454C22⋊C8—222no—
455C22⋊C8—222no—
456C22⋊C8—221no—
457#97—21no—
458#97—221no—
459C4×C8—222no—
460C4×C8—222no—
461C4×C8—222no—
462C2×C11—22no—
463C2×C11C22×#10111yescharacteristic
464C2×C11C2×#41611yescharacteristic
465C2×C11#289611yescharacteristic
466D11—22no—
467D11—41no—
468C24—111no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—222no—
472C2×Q8—222no—
473C2×Q8—221no—
474C2×Q8—221no—
475C2×Q8—444no—
476C2×Q8—442no—
477C2×Q8—442no—
478C22×C4—111no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—111no—
487C22×C4—111no—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—111no—
492C22×C4—111no—
493C22×C4—224no—
494C22×C4—224no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4—441no—
498C22×C4—441no—
499C22×C4C2×C4×D1111yescharacteristic
500C22×C4D4×D1111yescharacteristic
501C22×C4D4×D1111yescharacteristic
502M16—444no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—42no—
506C2×C8—222no—
507C2×C8—222no—
508C2×C8—442no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—112no—
514C4⋊C4—112no—
515C4⋊C4—222no—
516C4⋊C4—222no—
517C4⋊C4—222no—
518C4⋊C4—222no—
519C4⋊C4—222no—
520C4⋊C4—222no—
521C4⋊C4—222no—
522C4⋊C4—222no—
523C4⋊C4—222no—
524C4⋊C4—222no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4C2×C4×D1112yes—
528C4⋊C4C2×C4×D1112yes—
529C22⋊C4—22no—
530C22⋊C4—222no—
531C22⋊C4—222no—
532C22⋊C4—222no—
533C42—22no—
534C42—111no—
535C42—111no—
536C42—111no—
537C42—111no—
538C42—111no—
539C42—111no—
540C42—111no—
541C42—111no—
542C42—111no—
543C42—111no—
544C42—111no—
545C42—111no—
546C42—222no—
547C42—222no—
548C42—222no—
549C42C2×C4×D1111yescharacteristic
550C42D4×D1111yescharacteristic
551C42D4×D1111yescharacteristic
552C42C23×D1111yescharacteristic
553C11#1771511yescharacteristic, complemented, Sylow
554C23—111no—
555C23—111no—
556C23—222no—
557C23—222no—
558C23—441no—
559C23C22⋊C4×D1111yescharacteristic
560Q8—42no—
561Q8—41no—
562Q8—41no—
563Q8—444no—
564Q8—444no—
565Q8—442no—
566Q8—441no—
567Q8—441no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—111no—
575C2×C4—111no—
576C2×C4—111no—
577C2×C4—114no—
578C2×C4—114no—
579C2×C4—111no—
580C2×C4—111no—
581C2×C4—111no—
582C2×C4—222no—
583C2×C4—222no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—222no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—444no—
599C2×C4—444no—
600C2×C4—441no—
601C2×C4C22⋊C4×D1111yescharacteristic
602C2×C4C22⋊C4×D1111yescharacteristic
603C2×C4C22⋊C4×D1111yescharacteristic
604C2×C4C22×C4×D1111yescharacteristic
605C2×C4C2×D4×D1111yescharacteristic
606C2×C4C2×D4×D1111yescharacteristic
607C8—42no—
608C8—42no—
609C8—442no—
610C8—442no—
611C22—21no—
612C22—21no—
613C22—112no—
614C22—221no—
615C22—221no—
616C22—221no—
617C22—221no—
618C22—221no—
619C22—444no—
620C22D11×#10112yes—
621C22C2×C22⋊C4×D1111yescharacteristic
622C4—21no—
623C4—21no—
624C4—21no—
625C4—21no—
626C4—42no—
627C4—42no—
628C4—112no—
629C4—112no—
630C4—112no—
631C4—221no—
632C4—221no—
633C4—221no—
634C4—442no—
635C4—442no—
636C4D11×#13512yes—
637C4#1062330411yescharacteristic
638C4#1062330811yescharacteristic
639C2—22no—
640C2—222no—
641C2—441no—
642C2C2×D11×#10111yescharacteristic
643C2D11×#41611yescharacteristic
644C2#1307713211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1552C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1552D11
hypocenterC11#17715
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1552

Complements

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

NH ≅ G/Ntype
4. #13067317C2semidirect
5. #13067316C2semidirect
6. #13067314C2semidirect
7. #13067299C2semidirect
8. #13067286C2semidirect
9. #13067279C2semidirect
10. #13067279C2semidirect
11. C11×#1552C2semidirect
47. C11×#332C22semidirect
48. C11×#332C22semidirect
49. #10622185C22semidirect
50. #10622185C22semidirect
51. #10622124C22semidirect
52. #10622124C22semidirect
53. #10622120C22semidirect
54. #10622120C22semidirect
238. #1552D11semidirect
341. #332C2×D11semidirect
342. #332C2×D11semidirect
553. C11#17715semidirect

Maximal subgroups

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

subgroupindex
D11×#5332
#130772462
C2×#106224462
#130673172
#130673162
#130673142
#130672992
#130672862
#130672792
C11×#15522
#1771511