Finite Group Databasebeta

← #14719987

Subgroups — #14719987

Order 2816.

1008 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623061C211yesmaximal, characteristic
2#13077274C211yesmaximal, characteristic, complemented
3#13066986C212yesmaximal, complemented
4#13066983C212yesmaximal, complemented
5#13066977C211yesmaximal, characteristic, complemented
6#13066975C211yesmaximal, characteristic, complemented
7#13066956C212yesmaximal, complemented
8#13066952C211yesmaximal, characteristic, complemented
9#13066936C212yesmaximal, complemented
10#13066932C211yesmaximal, characteristic, complemented
11C11×#2924C211yesmaximal, characteristic, complemented
12C2×C11×#117C2211yescharacteristic
13C2×#66983C2211yescharacteristic
14C2×C4×C22⋊D11C2211yescharacteristic
15#10623061—21no—
16#10623061—21no—
17#10623061—22no—
18#10623061—21no—
19#10623061—21no—
20#10623061—22no—
21C2×#66948C411yescharacteristic
22C2×#66946C411yescharacteristic
23C2×C4⋊C4×D11C411yescharacteristic
24C2×#66943C411yescharacteristic
25C2×#66937C412yes—
26C2×#66936C412yes—
27C2×#66929C2212yes—
28C2×C4×D44C2212yes—
29C11×#433—22no—
30C11×#432C2212yes—
31C11×#431C2212yes—
32C11×#424—21no—
33C11×#407C2211yescharacteristic
34C2×C11×C22⋊C8C2211yescharacteristic
35C11×#405—21no—
36#10622820C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38#10622613—22no—
39#10622612—21no—
40#10622610—21no—
41#10622539C2212yes—
42#10622538C2212yes—
43#10622107C2211yescharacteristic
44#10622107C2211yescharacteristic
45#10622107C2212yes—
46#10622106C2211yescharacteristic
47#10622106C2211yescharacteristic
48#10622106C2212yes—
49#10622106C2212yes—
50#10622106C2212yes—
51#10622106C2212yes—
52#10622106C2212yes—
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11C2×C411yescharacteristic
55C22×C22⋊D11C2×C412yes—
56C22×D44C2×C412yes—
57C22×D44C2×C411yescharacteristic
58C22×C4×D11C2×C411yescharacteristic
59C22×C4×D11C2×C412yes—
60C22×C4×D11C2×C412yes—
61C2×C11×M16—21no—
62C22×C8×C11—21no—
63C11×#117D411yescharacteristic
64C11×#117D411yescharacteristic
65C11×#117D412yes—
66C11×#117D411yescharacteristic
67C11×#117D411yescharacteristic
68C11×#117D412yes—
69C2×C11×C4⋊C4C2×C411yescharacteristic
70C2×C11×C4⋊C4C2×C411yescharacteristic
71C2×C11×C22⋊C4C2×C412yes—
72C2×C42×C11C2312yes—
73C2×C22⋊Dic11C2×C411yescharacteristic
74#66983—21no—
75#66983—21no—
76#66983—21no—
77#66983—21no—
78C4×C22⋊D11—21no—
79C4×C22⋊D11—21no—
80C4×C22⋊D11—21no—
81C4×C22⋊D11—21no—
82C2×(C2×D11)⋊C4C2×C412yes—
83C2×(C2×D11)⋊C4C2×C412yes—
84C2×(C2×D11)⋊C4C2311yescharacteristic
85C2×(C2×D11)⋊C4C2312yes—
86C2×C4⋊Dic11C2×C412yes—
87C2×C4⋊Dic11C2×C411yescharacteristic
88C2×Dic11⋊C4C2×C412yes—
89C2×Dic11⋊C4C2×C412yes—
90C2×Dic11⋊C4C2311yescharacteristic
91C2×C4×Dic11C2×C411yescharacteristic
92C2×#4318—21no—
93C22×C11⋊C8—21no—
94#66948—22no—
95#66948—21no—
96#66948—21no—
97#66946—22no—
98#66946—21no—
99#66946—21no—
100C4⋊C4×D11—22no—
101C4⋊C4×D11—21no—
102C4⋊C4×D11—21no—
103#66943—22no—
104#66943—21no—
105#66943—21no—
106#66937—22no—
107#66937—22no—
108#66937—22no—
109#66937—22no—
110#66936—22no—
111#66936—22no—
112#66936—22no—
113#66936—22no—
114#66929—22no—
115#66929—22no—
116#66929—22no—
117#66929—22no—
118C4×D44—22no—
119C4×D44—22no—
120C4×D44—22no—
121C4×D44—22no—
122C11×C4⋊C8—22no—
123C11×C4⋊C8—22no—
124C11×C22⋊C8—21no—
125C11×C22⋊C8—21no—
126C11×C22⋊C8C2311yescharacteristic
127C11×C22⋊C8C2311yescharacteristic
128C11×C22⋊C8C2312yes—
129C11×#97—22no—
130C4×C8×C11—22no—
131C22⋊(C11⋊C8)—21no—
132C22⋊(C11⋊C8)—21no—
133C22⋊(C11⋊C8)C2311yescharacteristic
134C22⋊(C11⋊C8)C2312yes—
135C22⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)—22no—
137C4⋊(C11⋊C8)—22no—
138#66867—22no—
139C4×C11⋊C8—22no—
140#17415—111nomaximal, Sylow
141C24×C11C22×C411yescharacteristic
142C23×D11C22×C412yes—
143C23×D11C22×C411yescharacteristic
144C22×C4×C11—42no—
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C22×C412yes—
147C22×C4×C11C22×C412yes—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—21no—
154C2×C22⋊D11—21no—
155C2×C22⋊D11—22no—
156C2×C22⋊D11—22no—
157C2×C22⋊D11—22no—
158C2×C22⋊D11—41no—
159C2×C22⋊D11—82no—
160C22×Dic11C22×C411yescharacteristic
161C22×Dic11C22×C411yescharacteristic
162C22×Dic11C22×C411yescharacteristic
163C22×Dic11C22×C412yes—
164C2×D44—24no—
165C2×D44—22no—
166C2×D44—22no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—42no—
170C2×D44—42no—
171C2×C4×D11—21no—
172C2×C4×D11—21no—
173C2×C4×D11—22no—
174C2×C4×D11—22no—
175C2×C4×D11—22no—
176C2×C4×D11—22no—
177C2×C4×D11—42no—
178C2×C4×D11—82no—
179C2×C4×D11—82no—
180C11×M16—42no—
181C2×C8×C11—21no—
182C2×C8×C11—22no—
183C2×C8×C11—21no—
184C2×C8×C11—42no—
185C11×C4⋊C4C22⋊C412yes—
186C11×C4⋊C4C22⋊C411yescharacteristic
187C11×C4⋊C4C22⋊C411yescharacteristic
188C11×C4⋊C4C22⋊C412yes—
189C11×C4⋊C4C22⋊C411yescharacteristic
190C11×C4⋊C4C22⋊C411yescharacteristic
191C11×C22⋊C4C22⋊C412yes—
192C11×C22⋊C4C22⋊C412yes—
193C11×C22⋊C4C22⋊C412yes—
194C11×C22⋊C4C22⋊C412yes—
195C42×C11C2×D412yes—
196C42×C11C2×D412yes—
197C42×C11C2×D412yes—
198C42×C11C2×D412yes—
199C22⋊Dic11—21no—
200C22⋊Dic11—21no—
201(C2×D11)⋊C4—22no—
202(C2×D11)⋊C4—22no—
203(C2×D11)⋊C4—22no—
204(C2×D11)⋊C4—22no—
205(C2×D11)⋊C4—21no—
206(C2×D11)⋊C4—21no—
207(C2×D11)⋊C4—22no—
208(C2×D11)⋊C4—22no—
209C4⋊Dic11—22no—
210C4⋊Dic11—22no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213Dic11⋊C4—22no—
214Dic11⋊C4—22no—
215Dic11⋊C4—22no—
216Dic11⋊C4—22no—
217Dic11⋊C4—21no—
218Dic11⋊C4—21no—
219C4×Dic11—21no—
220C4×Dic11—21no—
221#4318—42no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—22no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—42no—
226C2×#553—111no—
227#2924—111no—
228#2924D1111yescharacteristic, complemented
229#1473—112no—
230#1473—112no—
231#1471—111no—
232#1471—111no—
233#1466—112no—
234#1465—111no—
235#1460—112no—
236#1459—111no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11C2×C22⋊C411yescharacteristic
242C23×C11C2×C22⋊C411yescharacteristic
243C23×C11C23×C411yescharacteristic
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—22no—
247C22×D11—22no—
248C22×D11—22no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—42no—
252C22×D11—42no—
253C22×D11#13112yes—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—42no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11C2×C22⋊C411yescharacteristic
264C2×C4×C11C2×C22⋊C412yes—
265C2×C4×C11C2×C22⋊C412yes—
266C2×C4×C11C2×C22⋊C412yes—
267C2×C4×C11C2×C22⋊C412yes—
268C2×C4×C11C2×C22⋊C411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C22⋊D11—42no—
272C22⋊D11—42no—
273C22⋊D11—82no—
274C22⋊D11—82no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—22no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—42no—
284D44—44no—
285D44—44no—
286D44—42no—
287D44—42no—
288C4×D11—42no—
289C4×D11—42no—
290C4×D11—82no—
291C4×D11—82no—
292C4×D11—82no—
293C4×D11—82no—
294C8×C11—41no—
295C8×C11—41no—
296C8×C11—42no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C11⋊C8—42no—
300#553—221no—
301#553—221no—
302#553—222no—
303#553—221no—
304#553—221no—
305#553—222no—
306C2×#126—112no—
307C2×#125—111no—
308C2×#123—112no—
309C2×#121—111no—
310C2×#121—111no—
311C2×#121—112no—
312C2×C4×D4—111no—
313C2×C4×D4—111no—
314C2×C4×D4—112no—
315C2×#117C2×D1111yescharacteristic
316C22×C4⋊C4—111no—
317#433—22no—
318#433—222no—
319#432—112no—
320#432C2×D1112yes—
321#431—112no—
322#431C2×D1112yes—
323#424—21no—
324#424—221no—
325#407—111no—
326#407C2×D1111yescharacteristic
327C2×C22⋊C8—111no—
328C2×C22⋊C8C2×D1111yescharacteristic
329#405—21no—
330#405—221no—
331#324—111no—
332#324—111no—
333#324—112no—
334#323—111no—
335#323—111no—
336#323—112no—
337#323—112no—
338#323—112no—
339#323—112no—
340#323—112no—
341C22×C11—21no—
342C22×C11—21no—
343C22×C11—21no—
344C22×C11—21no—
345C22×C11—21no—
346C22×C11—21no—
347C22×C11—21no—
348C22×C11—21no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11C22×C22⋊C411yescharacteristic
352C22×C11C2×#13111yescharacteristic
353C22×C11#56811yescharacteristic
354C2×D11—22no—
355C2×D11—42no—
356C2×D11—41no—
357C2×D11—41no—
358C2×D11—42no—
359C2×D11—42no—
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—82no—
363C2×D11—82no—
364C4×C11—22no—
365C4×C11—22no—
366C4×C11—21no—
367C4×C11—21no—
368C4×C11—21no—
369C4×C11—22no—
370C4×C11—22no—
371C4×C11#41012yes—
372Dic11—41no—
373Dic11—41no—
374Dic11—41no—
375Dic11—42no—
376C22×D4—111no—
377C22×D4—112no—
378C22×D4—112no—
379C22×D4—111no—
380C23×C4—111no—
381C23×C4—112no—
382C23×C4—112no—
383C23×C4C22×D1111yescharacteristic
384C2×M16—21no—
385C2×M16—221no—
386C22×C8—21no—
387C22×C8—221no—
388#126—222no—
389#126—222no—
390#126—222no—
391#126—222no—
392#125—222no—
393#125—221no—
394#125—221no—
395#123—222no—
396#123—222no—
397#123—222no—
398#123—222no—
399#121—221no—
400#121—221no—
401#121—221no—
402#121—221no—
403#121—222no—
404#121—221no—
405#121—221no—
406#121—222no—
407#121—222no—
408#121—222no—
409#121—222no—
410C4×D4—221no—
411C4×D4—221no—
412C4×D4—221no—
413C4×D4—221no—
414C4×D4—222no—
415C4×D4—221no—
416C4×D4—221no—
417C4×D4—222no—
418C4×D4—222no—
419C4×D4—222no—
420C4×D4—222no—
421#117D4411yescharacteristic
422#117D4411yescharacteristic
423#117D4412yes—
424#117C22⋊D1111yescharacteristic
425#117C22⋊D1111yescharacteristic
426#117C22⋊D1112yes—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—112no—
429C2×C4⋊C4—112no—
430C2×C4⋊C4—112no—
431C2×C4⋊C4—111no—
432C2×C4⋊C4—222no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4C4×D1111yescharacteristic
436C2×C4⋊C4C4×D1111yescharacteristic
437C2×C22⋊C4—111no—
438C2×C22⋊C4—112no—
439C2×C22⋊C4—112no—
440C2×C22⋊C4—111no—
441C2×C22⋊C4—112no—
442C2×C22⋊C4C4×D1112yes—
443C2×C42—111no—
444C2×C42C22×D1112yes—
445C4⋊C8—22no—
446C4⋊C8—22no—
447C4⋊C8—222no—
448C4⋊C8—222no—
449C22⋊C8—21no—
450C22⋊C8—21no—
451C22⋊C8—111no—
452C22⋊C8—111no—
453C22⋊C8—112no—
454C22⋊C8—221no—
455C22⋊C8—221no—
456C22⋊C8C22×D1111yescharacteristic
457C22⋊C8C22×D1111yescharacteristic
458C22⋊C8C22×D1112yes—
459#97—22no—
460#97—222no—
461C4×C8—22no—
462C4×C8—222no—
463C2×C11—21no—
464C2×C11—21no—
465C2×C11—41no—
466C2×C11—41no—
467C2×C11#288011yescharacteristic
468C2×C11C2×#41011yescharacteristic
469C2×C11#288811yescharacteristic
470D11—42no—
471D11—82no—
472C24—111no—
473C24—112no—
474C24C2×C4×D1111yescharacteristic
475C2×D4—224no—
476C2×D4—222no—
477C2×D4—221no—
478C2×D4—221no—
479C2×D4—222no—
480C2×D4—222no—
481C2×D4—221no—
482C2×D4—222no—
483C2×D4—222no—
484C2×D4—221no—
485C2×D4—442no—
486C2×D4—442no—
487C2×D4—441no—
488C2×D4—882no—
489C22×C4—42no—
490C22×C4—111no—
491C22×C4—111no—
492C22×C4—111no—
493C22×C4—112no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—442no—
501C22×C4—882no—
502C22×C4—882no—
503C22×C4C2×C4×D1111yescharacteristic
504C22×C4C2×C4×D1112yes—
505C22×C4C2×C4×D1112yes—
506C22×C4C2×D4411yescharacteristic
507C22×C4C2×D4411yescharacteristic
508C22×C4C2×C22⋊D1111yescharacteristic
509C22×C4C2×C22⋊D1111yescharacteristic
510C22×C4C23×D1111yescharacteristic
511M16—42no—
512M16—442no—
513C2×C8—21no—
514C2×C8—22no—
515C2×C8—21no—
516C2×C8—42no—
517C2×C8—221no—
518C2×C8—222no—
519C2×C8—221no—
520C2×C8—442no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—222no—
524C4⋊C4—222no—
525C4⋊C4—222no—
526C4⋊C4—222no—
527C4⋊C4—222no—
528C4⋊C4—222no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4(C2×D11)⋊C412yes—
532C4⋊C4(C2×D11)⋊C411yescharacteristic
533C4⋊C4(C2×D11)⋊C411yescharacteristic
534C4⋊C4(C2×D11)⋊C412yes—
535C4⋊C4(C2×D11)⋊C411yescharacteristic
536C4⋊C4(C2×D11)⋊C411yescharacteristic
537C22⋊C4—221no—
538C22⋊C4—221no—
539C22⋊C4—222no—
540C22⋊C4—222no—
541C22⋊C4—222no—
542C22⋊C4—222no—
543C22⋊C4—221no—
544C22⋊C4—222no—
545C22⋊C4—221no—
546C22⋊C4—222no—
547C22⋊C4(C2×D11)⋊C412yes—
548C22⋊C4(C2×D11)⋊C412yes—
549C22⋊C4(C2×D11)⋊C412yes—
550C22⋊C4(C2×D11)⋊C412yes—
551C42—221no—
552C42—221no—
553C42C2×D4412yes—
554C42C2×D4412yes—
555C42C2×C22⋊D1112yes—
556C42C2×C22⋊D1112yes—
557C11#1741511yescharacteristic, complemented, Sylow
558C23—21no—
559C23—21no—
560C23—41no—
561C23—41no—
562C23—112no—
563C23—221no—
564C23—221no—
565C23—222no—
566C23—222no—
567C23—222no—
568C23—441no—
569C23—441no—
570C23—442no—
571C23—442no—
572C23C2×(C2×D11)⋊C411yescharacteristic
573C23C2×(C2×D11)⋊C411yescharacteristic
574C23C22×C4×D1111yescharacteristic
575D4—444no—
576D4—444no—
577D4—442no—
578D4—442no—
579D4—442no—
580D4—442no—
581D4—882no—
582D4—882no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—222no—
598C2×C4—442no—
599C2×C4—442no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—442no—
603C2×C4—882no—
604C2×C4—882no—
605C2×C4—882no—
606C2×C4—882no—
607C2×C4C2×(C2×D11)⋊C411yescharacteristic
608C2×C4C2×(C2×D11)⋊C412yes—
609C2×C4C2×(C2×D11)⋊C412yes—
610C2×C4C2×(C2×D11)⋊C412yes—
611C2×C4C2×(C2×D11)⋊C412yes—
612C2×C4C2×(C2×D11)⋊C411yescharacteristic
613C2×C4C22×D4411yescharacteristic
614C2×C4C22×C22⋊D1111yescharacteristic
615C8—41no—
616C8—41no—
617C8—42no—
618C8—441no—
619C8—441no—
620C8—442no—
621C22—21no—
622C22—21no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—81no—
630C22—81no—
631C22—222no—
632C22—442no—
633C22—442no—
634C22—441no—
635C22—441no—
636C22—442no—
637C22—442no—
638C22—442no—
639C22—882no—
640C22—882no—
641C22D11×#13111yescharacteristic
642C22#1062328111yescharacteristic
643C22C22×(C2×D11)⋊C411yescharacteristic
644C4—22no—
645C4—22no—
646C4—21no—
647C4—21no—
648C4—21no—
649C4—22no—
650C4—22no—
651C4—441no—
652C4—441no—
653C4—441no—
654C4—442no—
655C4#1062261912yes—
656C2—21no—
657C2—21no—
658C2—41no—
659C2—41no—
660C2—442no—
661C2—882no—
662C2#1307706311yescharacteristic
663C2C2×#1062261911yescharacteristic
664C2#1307709411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2924C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623061C2
cosocleC22×C4×C11C24
hypercenter#2924D11
hypocenterC11#17415
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #13077274C2semidirect
3. #13066986C2semidirect
4. #13066983C2semidirect
5. #13066977C2semidirect
6. #13066975C2semidirect
7. #13066956C2semidirect
8. #13066952C2semidirect
9. #13066936C2semidirect
10. #13066932C2semidirect
11. C11×#2924C2semidirect
228. #2924D11semidirect
557. C11#17415semidirect

Maximal subgroups

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

subgroupindex
C2×#106230612
#130772742
#130669862
#130669832
#130669772
#130669752
#130669562
#130669522
#130669362
#130669322
C11×#29242
#1741511