Finite Group Databasebeta

← #14722198

Subgroups — #14722198

Order 2816.

972 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#533C211yesmaximal, characteristic
2#13077244C211yesmaximal, characteristic
3C2×#10622446C211yesmaximal, characteristic
4#13067325C212yesmaximal, complemented
5#13067323C212yesmaximal, complemented
6#13067295C212yesmaximal, complemented
7#13067286C212yesmaximal, complemented
8#13067274C211yesmaximal, characteristic, complemented
9#13067273C211yesmaximal, characteristic, complemented
10#13067271C211yesmaximal, characteristic, complemented
11C11×#1542C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13#10623259C2211yescharacteristic
14#10623259C2211yescharacteristic
15D11×C4⋊Q8C2211yescharacteristic
16D11×C4⋊Q8C2211yescharacteristic
17#10623219—21no—
18D11×#125—21no—
19D11×C22⋊Q8—21no—
20D11×C22⋊Q8C412yes—
21#10623153—21no—
22#10623153C412yes—
23#10623109—21no—
24#10623109C412yes—
25C4×Q8×D11—21no—
26C4×Q8×D11C412yes—
27D11×#117—21no—
28#10623048—21no—
29C2×C42×D11C2211yescharacteristic
30#10623001C2211yescharacteristic
31C11×#431C2211yescharacteristic
32C2×C11×C4⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8—21no—
34C2×C8×Dic11—21no—
35#10622538C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37#10622450C2212yes—
38#10622448C2212yes—
39#10622446—21no—
40#10622446—21no—
41#10622446C2212yes—
42#10622446C2212yes—
43#10622339—21no—
44#10622332—21no—
45C4×#4313—21no—
46#10622298—21no—
47C11×#333C2212yescomplemented
48C11×#332C2212yescomplemented
49#10622185C2212yescomplemented
50#10622184C2212yescomplemented
51#10622124C2212yescomplemented
52#10622120C2212yescomplemented
53#10622119C2212yescomplemented
54#10622119C2212yescomplemented
55C2×Q8×D11—21no—
56C2×Q8×D11C2×C412yes—
57C22×C4×D11C2×C411yescharacteristic
58C22×C4×D11D411yescharacteristic
59C22×C4×D11D411yescharacteristic
60C22×C8×C11—21no—
61C11×C4⋊Q8C2311yescharacteristic
62C11×C4⋊Q8C2311yescharacteristic
63C11×#125—21no—
64C11×C22⋊Q8—21no—
65C11×C22⋊Q8C2×C412yes—
66C4×Q8×C11—21no—
67C4×Q8×C11C2×C412yes—
68C11×#117—21no—
69C2×C42×C11C2311yescharacteristic
70#66999—21no—
71#66999C2×C412yes—
72Q8×Dic11—21no—
73Q8×Dic11C2×C412yes—
74#66997—21no—
75#66997C2×C412yes—
76#66979—21no—
77#66977—21no—
78#66977C2×C412yes—
79C2×C4×Dic11C2×C411yescharacteristic
80C2×C4×Dic11D411yescharacteristic
81C2×C4×Dic11D411yescharacteristic
82C22×C11⋊C8—21no—
83C2×#4313—22no—
84#66950—21no—
85#66950C2×C412yes—
86#66949—22no—
87#66949—22no—
88#66945—21no—
89#66945—21no—
90C4⋊C4×D11—22no—
91C4⋊C4×D11—22no—
92C4⋊C4×D11—21no—
93C4⋊C4×D11—21no—
94C4⋊C4×D11—21no—
95C4⋊C4×D11C2×C412yes—
96#66943—21no—
97#66943—21no—
98#66942—22no—
99#66942—22no—
100#66941—21no—
101#66941—21no—
102#66941—21no—
103#66941C2×C412yes—
104#66940—22no—
105#66940—22no—
106#66940—21no—
107#66940C2×C412yes—
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#66923—21no—
123#66922C2311yescharacteristic
124#66922C2311yescharacteristic
125C4×Dic22—21no—
126C4×Dic22—22no—
127C4×Dic22—22no—
128C4×Dic22C2×C412yes—
129C11×C4⋊C8—21no—
130C11×C4⋊C8C2312yes—
131C11×C4⋊C8C2312yes—
132C11×C22⋊C8—21no—
133C4×C8×C11—21no—
134C22⋊(C11⋊C8)—21no—
135(C2×D11)⋊C8—22no—
136(C2×D11)⋊C8—22no—
137(C2×D11)⋊C8—22no—
138#66879—22no—
139Dic11⋊C8—22no—
140C8×Dic11—22no—
141C8×Dic11—22no—
142C4⋊(C11⋊C8)—21no—
143C4⋊(C11⋊C8)C2312yes—
144C4⋊(C11⋊C8)C2312yes—
145C4×C11⋊C8—21no—
146#17718—111nomaximal, Sylow
147C23×D11C22⋊C411yescharacteristic
148C2×Q8×C11—21no—
149C2×Q8×C11C22×C412yes—
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×Dic11C22⋊C411yescharacteristic
154C22×Dic11C22⋊C411yescharacteristic
155C22×Dic11C22⋊C411yescharacteristic
156Q8×D11—44no—
157Q8×D11—44no—
158C2×C4×D11—24no—
159C2×C4×D11—22no—
160C2×C4×D11—22no—
161C2×C4×D11—22no—
162C2×C4×D11—22no—
163C2×C4×D11—42no—
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×D11C22×C411yescharacteristic
171C2×C4×D11C22×C411yescharacteristic
172C2×C4×D11C2×D411yescharacteristic
173C2×C4×D11C2×D411yescharacteristic
174C2×C4×D11C2×D411yescharacteristic
175C2×C4×D11C2×D411yescharacteristic
176C2×Dic22—22no—
177C2×Dic22—22no—
178C2×Dic22—21no—
179C2×Dic22C22×C412yes—
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11—42no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4C22×C412yes—
189C11×C22⋊C4—22no—
190C42×C11—22no—
191C42×C11C22×C411yescharacteristic
192C42×C11C2×D411yescharacteristic
193C42×C11C2×D411yescharacteristic
194C42×C11C2411yescharacteristic
195C22⋊Dic11—22no—
196(C2×D11)⋊C4—22no—
197(C2×D11)⋊C4—22no—
198C4⋊Dic11—22no—
199C4⋊Dic11—22no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11C22×C412yes—
204Dic11⋊C4—22no—
205Dic11⋊C4—22no—
206Dic11⋊C4—22no—
207Dic11⋊C4—22no—
208Dic11⋊C4—22no—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212C4×Dic11—22no—
213C4×Dic11—22no—
214C4×Dic11—22no—
215C4×Dic11C22⋊C411yescharacteristic
216C4×Dic11C22⋊C411yescharacteristic
217C4×Dic11C22⋊C411yescharacteristic
218C4×Dic11C22⋊C411yescharacteristic
219C4×Dic11C22⋊C411yescharacteristic
220C4×Dic11C22⋊C411yescharacteristic
221C4×Dic11C22×C411yescharacteristic
222C4×Dic11C22×C411yescharacteristic
223C4×Dic11C2×D411yescharacteristic
224C4×Dic11C2×D411yescharacteristic
225C4×Dic11C2×D411yescharacteristic
226C4×Dic11C2×D411yescharacteristic
227C2×C11⋊C8—22no—
228C2×C11⋊C8—22no—
229C2×C11⋊C8—42no—
230#4313—44no—
231C2×#533—111no—
232#2920—111no—
233C2×#431—111no—
234#1554—112no—
235#1554—112no—
236#1548—112no—
237#1546—112no—
238#1542—111no—
239#1542—111no—
240#1542—111no—
241#1542D1111yescharacteristic, complemented
242C23×C11C2×C22⋊C411yescharacteristic
243C22×D11—22no—
244C22×D11—22no—
245C22×D11—41no—
246C22×D11C2×C22⋊C411yescharacteristic
247C22×D11C2×C22⋊C411yescharacteristic
248Q8×C11—42no—
249Q8×C11—42no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—41no—
254C2×C4×C11C2×C22⋊C411yescharacteristic
255C2×C4×C11C2×C22⋊C411yescharacteristic
256C2×C4×C11C2×C22⋊C411yescharacteristic
257C2×C4×C11#13712yes—
258C2×C4×C11#13712yes—
259C2×C4×C11C23×C411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11C2×C22⋊C411yescharacteristic
268C2×Dic11C2×C22⋊C411yescharacteristic
269C2×Dic11C2×C22⋊C411yescharacteristic
270C2×Dic11C2×C22⋊C411yescharacteristic
271C2×Dic11C2×C22⋊C411yescharacteristic
272C2×Dic11C2×C22⋊C411yescharacteristic
273C4×D11—22no—
274C4×D11—22no—
275C4×D11—21no—
276C4×D11—21no—
277C4×D11—21no—
278C4×D11—21no—
279C4×D11—22no—
280C4×D11—22no—
281C4×D11—22no—
282C4×D11—22no—
283C4×D11—22no—
284C4×D11—41no—
285C4×D11—41no—
286C4×D11—44no—
287C4×D11—44no—
288C4×D11#13514yes—
289Dic22—42no—
290Dic22—44no—
291Dic22—44no—
292Dic22—42no—
293C8×C11—42no—
294C8×C11—42no—
295C11⋊C8—42no—
296C11⋊C8—42no—
297#533—111no—
298#533—111no—
299#533—112no—
300#533—112no—
301#533—111no—
302#533—221no—
303#533—221no—
304#533—221no—
305#533—221no—
306#533C2×D1111yescharacteristic
307C2×C4⋊Q8—111no—
308C2×C4⋊Q8—111no—
309C2×#125—221no—
310C2×C22⋊Q8—112no—
311C2×C22⋊Q8—221no—
312C2×C4×Q8—112no—
313C2×C4×Q8—221no—
314C2×#117—221no—
315C22×C42—111no—
316#432—112no—
317#432—221no—
318#431—111no—
319#431—112no—
320#431—112no—
321#431—221no—
322#431—221no—
323#431—221no—
324#431C2×D1111yescharacteristic
325#423—112no—
326C2×C4⋊C8—111no—
327C2×C4⋊C8C2×D1111yescharacteristic
328#407—221no—
329C2×C22⋊C8—221no—
330C4×M16—221no—
331C2×C4×C8—221no—
332#333—112no—
333#333—112no—
334#333—112no—
335#333C2×D1112yescomplemented
336#332—112no—
337#332—112no—
338#332—112no—
339#332C2×D1112yescomplemented
340C22×C11—21no—
341C22×C11—21no—
342C22×C11#41912yes—
343C22×C11C22×C22⋊C411yescharacteristic
344C2×D11—21no—
345C2×D11—21no—
346C2×D11—21no—
347C2×D11—21no—
348C2×D11—21no—
349C2×D11—44no—
350C2×D11#41612yes—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—42no—
355C4×C11—42no—
356C4×C11#41912yes—
357C4×C11C2×#13512yes—
358C4×C11C2×#13711yescharacteristic
359C4×C11C2×#13711yescharacteristic
360Dic11—21no—
361Dic11—21no—
362Dic11—21no—
363Dic11—21no—
364Dic11—42no—
365Dic11—42no—
366Dic11#41312yes—
367Dic11#41612yes—
368C22×Q8—112no—
369C22×Q8—221no—
370C23×C4—111no—
371C23×C4—111no—
372C23×C4—111no—
373C2×M16—222no—
374C22×C8—21no—
375C22×C8—221no—
376C4⋊Q8—112no—
377C4⋊Q8—112no—
378C4⋊Q8—111no—
379C4⋊Q8—111no—
380C4⋊Q8—221no—
381C4⋊Q8—221no—
382C4⋊Q8—221no—
383C4⋊Q8—221no—
384C4⋊Q8C22×D1111yescharacteristic
385C4⋊Q8C22×D1111yescharacteristic
386#125—21no—
387#125—222no—
388#125—222no—
389#125—221no—
390#125—221no—
391#125—221no—
392C22⋊Q8—21no—
393C22⋊Q8—112no—
394C22⋊Q8—112no—
395C22⋊Q8—112no—
396C22⋊Q8—222no—
397C22⋊Q8—222no—
398C22⋊Q8—222no—
399C22⋊Q8—222no—
400C22⋊Q8—221no—
401C22⋊Q8—221no—
402C22⋊Q8—221no—
403C22⋊Q8C4×D1112yes—
404C4×Q8—21no—
405C4×Q8—112no—
406C4×Q8—112no—
407C4×Q8—112no—
408C4×Q8—222no—
409C4×Q8—222no—
410C4×Q8—222no—
411C4×Q8—222no—
412C4×Q8—221no—
413C4×Q8—221no—
414C4×Q8—221no—
415C4×Q8C4×D1112yes—
416#117—21no—
417#117—222no—
418#117—222no—
419#117—221no—
420#117—221no—
421#117—221no—
422C2×C4⋊C4—112no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—222no—
426C2×C4⋊C4—222no—
427C2×C4⋊C4—221no—
428C2×C22⋊C4—222no—
429C2×C42—111no—
430C2×C42—111no—
431C2×C42—111no—
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—222no—
441C2×C42C22×D1111yescharacteristic
442C4⋊C8—21no—
443C4⋊C8—112no—
444C4⋊C8—112no—
445C4⋊C8—222no—
446C4⋊C8—221no—
447C4⋊C8C22×D1112yes—
448C4⋊C8C22×D1112yes—
449C22⋊C8—21no—
450C22⋊C8—222no—
451C22⋊C8—222no—
452C22⋊C8—222no—
453C22⋊C8—221no—
454#97—222no—
455C4×C8—21no—
456C4×C8—222no—
457C4×C8—222no—
458C4×C8—221no—
459C2×C11—22no—
460C2×C11C2×#41311yescharacteristic
461C2×C11C2×#41611yescharacteristic
462C2×C11C2×#41911yescharacteristic
463D11—22no—
464D11—41no—
465C24—111no—
466C2×Q8—21no—
467C2×Q8—112no—
468C2×Q8—222no—
469C2×Q8—222no—
470C2×Q8—221no—
471C2×Q8—444no—
472C2×Q8—444no—
473C2×Q8C2×C4×D1112yes—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—111no—
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—224no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—442no—
495C22×C4C2×C4×D1111yescharacteristic
496C22×C4D4×D1111yescharacteristic
497C22×C4D4×D1111yescharacteristic
498M16—444no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—42no—
502C2×C8—222no—
503C2×C8—222no—
504C2×C8—442no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—112no—
511C4⋊C4—222no—
512C4⋊C4—222no—
513C4⋊C4—222no—
514C4⋊C4—222no—
515C4⋊C4—222no—
516C4⋊C4—222no—
517C4⋊C4—222no—
518C4⋊C4—222no—
519C4⋊C4—222no—
520C4⋊C4—222no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4C2×C4×D1112yes—
525C22⋊C4—22no—
526C22⋊C4—222no—
527C22⋊C4—222no—
528C22⋊C4—222no—
529C42—22no—
530C42—111no—
531C42—111no—
532C42—111no—
533C42—111no—
534C42—111no—
535C42—111no—
536C42—111no—
537C42—111no—
538C42—111no—
539C42—111no—
540C42—111no—
541C42—111no—
542C42—222no—
543C42—222no—
544C42—222no—
545C42C2×C4×D1111yescharacteristic
546C42D4×D1111yescharacteristic
547C42D4×D1111yescharacteristic
548C42C23×D1111yescharacteristic
549C11#1771811yescharacteristic, complemented, Sylow
550C23—111no—
551C23—111no—
552C23—222no—
553C23—222no—
554C23—441no—
555C23C22⋊C4×D1111yescharacteristic
556Q8—42no—
557Q8—42no—
558Q8—442no—
559Q8—444no—
560Q8—444no—
561Q8—442no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—41no—
566C2×C4—111no—
567C2×C4—111no—
568C2×C4—114no—
569C2×C4—111no—
570C2×C4—111no—
571C2×C4—111no—
572C2×C4—111no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—444no—
592C2×C4—444no—
593C2×C4C22⋊C4×D1111yescharacteristic
594C2×C4C22⋊C4×D1111yescharacteristic
595C2×C4C22⋊C4×D1111yescharacteristic
596C2×C4#6696812yes—
597C2×C4#6697112yes—
598C2×C4C22×C4×D1111yescharacteristic
599C2×C4C2×D4×D1111yescharacteristic
600C2×C4C2×D4×D1111yescharacteristic
601C8—42no—
602C8—42no—
603C8—442no—
604C8—442no—
605C22—21no—
606C22—21no—
607C22—112no—
608C22—221no—
609C22—221no—
610C22—221no—
611C22—221no—
612C22—221no—
613C22—444no—
614C22#1062241512yes—
615C22C2×C22⋊C4×D1111yescharacteristic
616C4—21no—
617C4—21no—
618C4—21no—
619C4—42no—
620C4—42no—
621C4—112no—
622C4—112no—
623C4—221no—
624C4—221no—
625C4—221no—
626C4—221no—
627C4—442no—
628C4—442no—
629C4#1062241512yes—
630C4C2×#6696811yescharacteristic
631C4C2×#6697111yescharacteristic
632C4D11×#13512yes—
633C2—22no—
634C2—222no—
635C2—441no—
636C2D11×#41311yescharacteristic
637C2D11×#41611yescharacteristic
638C2C2×#1062241511yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1542C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1542D11
hypocenterC11#17718
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
4. #13067325C2semidirect
5. #13067323C2semidirect
6. #13067295C2semidirect
7. #13067286C2semidirect
8. #13067274C2semidirect
9. #13067273C2semidirect
10. #13067271C2semidirect
11. C11×#1542C2semidirect
47. C11×#333C22semidirect
48. C11×#332C22semidirect
49. #10622185C22semidirect
50. #10622184C22semidirect
51. #10622124C22semidirect
52. #10622120C22semidirect
53. #10622119C22semidirect
54. #10622119C22semidirect
241. #1542D11semidirect
335. #333C2×D11semidirect
339. #332C2×D11semidirect
549. C11#17718semidirect

Maximal subgroups

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

subgroupindex
D11×#5332
#130772442
C2×#106224462
#130673252
#130673232
#130672952
#130672862
#130672742
#130672732
#130672712
C11×#15422
#1771811