Finite Group Databasebeta

← #14720102

Subgroups — #14720102

Order 2816.

1016 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623090C211yesmaximal, characteristic
2#13077651C211yesmaximal, characteristic, complemented
3#13066969C211yesmaximal, characteristic, complemented
4#13066967C211yesmaximal, characteristic, complemented
5#13066965C212yesmaximal, complemented
6#13066962C212yesmaximal, complemented
7#13066959C211yesmaximal, characteristic, complemented
8#13066952C212yesmaximal, complemented
9#13066939C211yesmaximal, characteristic, complemented
10#13066932C212yesmaximal, complemented
11C11×#2974C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66993C411yescharacteristic
14C2×#66989C411yescharacteristic
15C2×#66982C2212yes—
16C2×C4×C22⋊D11C2212yes—
17#10623090—21no—
18#10623090—22no—
19#10623090—21no—
20#10623090—21no—
21#10623090—22no—
22#10623090—21no—
23C2×#66946C411yescharacteristic
24C2×#66940C411yescharacteristic
25C2×#66938C412yes—
26C2×#66936C412yes—
27C2×#66928C2211yescharacteristic
28C2×C4×Dic22C2211yescharacteristic
29C11×#436—21no—
30C11×#435—22no—
31C8×D4×C11—21no—
32C11×#432C2211yescharacteristic
33C11×#431C2211yescharacteristic
34C11×#407C2212yes—
35C2×C11×C22⋊C8C2212yes—
36#10622820C2212yes—
37C2×C22⋊(C11⋊C8)C2212yes—
38#10622625—21no—
39#10622624—22no—
40D4×C11⋊C8—21no—
41#10622539C2211yescharacteristic
42#10622538C2211yescharacteristic
43#10622107C2211yescharacteristic
44#10622107C2212yes—
45#10622107C2211yescharacteristic
46#10622107C2211yescharacteristic
47#10622107C2211yescharacteristic
48#10622107C2212yes—
49#10622106C2212yes—
50#10622106C2212yes—
51#10622106C2212yes—
52#10622106C2212yes—
53C22×D4×C11C2×C411yescharacteristic
54C23×C4×C11C2312yes—
55C22×C22⋊D11C2×C412yes—
56C22×C22⋊D11C2×C412yes—
57C22×D44C2×C411yescharacteristic
58C22×C4×D11C2×C412yes—
59C22×Dic22C2×C411yescharacteristic
60C22×Dic22C2×C411yescharacteristic
61C2×C11×M16—22no—
62C22×C8×C11—22no—
63C4×D4×C11D411yescharacteristic
64C4×D4×C11D412yes—
65C4×D4×C11D411yescharacteristic
66C4×D4×C11D411yescharacteristic
67C4×D4×C11D412yes—
68C4×D4×C11D411yescharacteristic
69C2×C11×C4⋊C4C2×C411yescharacteristic
70C2×C11×C22⋊C4C2×C412yes—
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11C2×C412yes—
73C2×C22⋊Dic11C2×C412yes—
74#66993—21no—
75#66993—21no—
76#66993—22no—
77#66989—21no—
78#66989—21no—
79#66989—22no—
80#66982—22no—
81#66982—22no—
82#66982—22no—
83#66982—22no—
84C4×C22⋊D11—22no—
85C4×C22⋊D11—22no—
86C4×C22⋊D11—22no—
87C4×C22⋊D11—22no—
88C2×(C2×D11)⋊C4C2×C412yes—
89C2×(C2×D11)⋊C4C2×C412yes—
90C2×(C2×D11)⋊C4C2312yes—
91C2×C4⋊Dic11C2×C411yescharacteristic
92C2×Dic11⋊C4C2×C412yes—
93C2×Dic11⋊C4C2311yescharacteristic
94C2×Dic11⋊C4C2311yescharacteristic
95C2×C4×Dic11C2×C411yescharacteristic
96C2×C4×Dic11C2×C411yescharacteristic
97C2×C4×Dic11C2×C412yes—
98C2×#4318—22no—
99C22×C11⋊C8—22no—
100#66946—22no—
101#66946—21no—
102#66946—21no—
103#66940—22no—
104#66940—21no—
105#66940—21no—
106#66938—22no—
107#66938—22no—
108#66938—22no—
109#66938—22no—
110#66936—22no—
111#66936—22no—
112#66936—22no—
113#66936—22no—
114#66928—21no—
115#66928—21no—
116#66928—21no—
117#66928—21no—
118C4×Dic22—21no—
119C4×Dic22—21no—
120C4×Dic22—21no—
121C4×Dic22—21no—
122C11×C4⋊C8—21no—
123C11×C4⋊C8—21no—
124C11×C22⋊C8—22no—
125C11×C22⋊C8—22no—
126C11×C22⋊C8C2311yescharacteristic
127C11×C22⋊C8C2312yes—
128C11×C22⋊C8C2311yescharacteristic
129C11×#97—21no—
130C4×C8×C11—21no—
131C22⋊(C11⋊C8)—22no—
132C22⋊(C11⋊C8)—22no—
133C22⋊(C11⋊C8)C2311yescharacteristic
134C22⋊(C11⋊C8)C2311yescharacteristic
135C22⋊(C11⋊C8)C2312yes—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)—21no—
138#66867—21no—
139C4×C11⋊C8—21no—
140#17429—111nomaximal, Sylow
141C24×C11C22×C412yes—
142C23×D11C22×C412yes—
143C2×D4×C11—42no—
144C2×D4×C11C22⋊C411yescharacteristic
145C2×D4×C11C22⋊C411yescharacteristic
146C2×D4×C11C22⋊C412yes—
147C22×C4×C11—82no—
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C22×C412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D412yes—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—24no—
157C2×C22⋊D11—22no—
158C2×C22⋊D11—22no—
159C2×C22⋊D11—22no—
160C2×C22⋊D11—22no—
161C2×C22⋊D11—42no—
162C2×C22⋊D11—82no—
163C22×Dic11C22×C411yescharacteristic
164C22×Dic11C22×C411yescharacteristic
165C22×Dic11C22×C411yescharacteristic
166C22×Dic11C22×C412yes—
167C22×Dic11C22×C411yescharacteristic
168C2×D44—21no—
169C2×D44—21no—
170C2×D44—42no—
171C2×C4×D11—22no—
172C2×C4×D11—22no—
173C2×C4×D11—82no—
174C2×Dic22—22no—
175C2×Dic22—21no—
176C2×Dic22—21no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×Dic22—41no—
180C2×Dic22—42no—
181C11×M16—82no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—22no—
185C2×C8×C11—82no—
186C11×C4⋊C4C22⋊C412yes—
187C11×C4⋊C4C22⋊C411yescharacteristic
188C11×C4⋊C4C22⋊C411yescharacteristic
189C11×C22⋊C4C22⋊C412yes—
190C11×C22⋊C4C22⋊C412yes—
191C11×C22⋊C4C22⋊C412yes—
192C11×C22⋊C4C22⋊C412yes—
193C42×C11C2×D411yescharacteristic
194C42×C11C2×D411yescharacteristic
195C42×C11C2×D411yescharacteristic
196C42×C11C2×D411yescharacteristic
197C22⋊Dic11—22no—
198C22⋊Dic11—22no—
199C22⋊Dic11—22no—
200C22⋊Dic11—22no—
201(C2×D11)⋊C4—22no—
202(C2×D11)⋊C4—22no—
203(C2×D11)⋊C4—22no—
204(C2×D11)⋊C4—22no—
205(C2×D11)⋊C4—22no—
206(C2×D11)⋊C4—22no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211Dic11⋊C4—21no—
212Dic11⋊C4—21no—
213Dic11⋊C4—21no—
214Dic11⋊C4—21no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—21no—
218C4×Dic11—21no—
219C4×Dic11—22no—
220C4×Dic11—22no—
221#4318—82no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—22no—
225C2×C11⋊C8—82no—
226C2×#559—111no—
227#2974—111no—
228#2974D1111yescharacteristic, complemented
229#1469—111no—
230#1469—111no—
231#1468—112no—
232#1468—112no—
233#1467—111no—
234#1465—112no—
235#1461—111no—
236#1459—112no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11C2×C22⋊C412yes—
242C23×C11C2×C22⋊C412yes—
243C23×C11C23×C411yescharacteristic
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—22no—
247C22×D11—42no—
248C22×D11—42no—
249D4×C11—22no—
250D4×C11—22no—
251D4×C11—42no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—41no—
261C2×C4×C11C2×C22⋊C411yescharacteristic
262C2×C4×C11C2×C22⋊C412yes—
263C2×C4×C11C2×C22⋊C412yes—
264C2×C4×C11C2×C22⋊C411yescharacteristic
265C2×C4×C11C2×C22⋊C411yescharacteristic
266C2×C4×C11C2×C22⋊C411yescharacteristic
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C22⋊D11—44no—
270C22⋊D11—44no—
271C22⋊D11—82no—
272C22⋊D11—82no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—22no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—42no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11#13112yes—
285D44—42no—
286D44—42no—
287C4×D11—82no—
288C4×D11—82no—
289Dic22—42no—
290Dic22—42no—
291Dic22—42no—
292Dic22—42no—
293C8×C11—41no—
294C8×C11—42no—
295C8×C11—41no—
296C11⋊C8—41no—
297C11⋊C8—42no—
298C11⋊C8—41no—
299#559—221no—
300#559—222no—
301#559—221no—
302#559—221no—
303#559—222no—
304#559—221no—
305C2×#127—111no—
306C2×#124—111no—
307C2×#124—112no—
308C2×#124—111no—
309C2×#123—112no—
310C2×#123—112no—
311C2×C4×Q8—111no—
312C2×C4×Q8—111no—
313C2×C4×D4—112no—
314C2×C4×D4—111no—
315C2×C4×D4C2×D1111yescharacteristic
316#436—21no—
317#436—221no—
318#435—22no—
319#435—222no—
320C8×D4—21no—
321C8×D4—221no—
322#432—111no—
323#432C2×D1111yescharacteristic
324#431—111no—
325#431C2×D1111yescharacteristic
326#407—112no—
327#407C2×D1112yes—
328C2×C22⋊C8—112no—
329C2×C22⋊C8C2×D1112yes—
330#324—111no—
331#324—112no—
332#324—111no—
333#324—111no—
334#324—111no—
335#324—112no—
336#323—112no—
337#323—112no—
338#323—112no—
339#323—112no—
340C22×C11—21no—
341C22×C11—21no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—22no—
345C22×C11—22no—
346C22×C11—22no—
347C22×C11—22no—
348C22×C11—82no—
349C22×C11—82no—
350C22×C11C22×C22⋊C411yescharacteristic
351C22×C11C2×#13111yescharacteristic
352C22×C11#56811yescharacteristic
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—42no—
356C2×D11—82no—
357C2×D11—82no—
358C4×C11—21no—
359C4×C11—21no—
360C4×C11—21no—
361C4×C11—21no—
362C4×C11—22no—
363C4×C11—22no—
364C4×C11—21no—
365C4×C11#41312yes—
366Dic11—22no—
367Dic11—41no—
368Dic11—41no—
369Dic11—41no—
370Dic11—42no—
371C22×Q8—111no—
372C22×Q8—111no—
373C22×D4—112no—
374C22×D4—112no—
375C22×D4—111no—
376C22×D4C4×D1111yescharacteristic
377C23×C4—112no—
378C23×C4C22×D1112yes—
379C2×M16—22no—
380C2×M16—222no—
381C22×C8—22no—
382C22×C8—222no—
383#127—221no—
384#127—221no—
385#127—222no—
386#124—221no—
387#124—221no—
388#124—222no—
389#124—222no—
390#124—222no—
391#124—222no—
392#124—222no—
393#124—221no—
394#124—221no—
395#124—221no—
396#124—221no—
397#123—222no—
398#123—222no—
399#123—222no—
400#123—222no—
401#123—222no—
402#123—222no—
403#123—222no—
404#123—222no—
405C4×Q8—222no—
406C4×Q8—221no—
407C4×Q8—221no—
408C4×Q8—221no—
409C4×Q8—221no—
410C4×Q8—221no—
411C4×Q8—221no—
412C4×D4—222no—
413C4×D4—222no—
414C4×D4—222no—
415C4×D4—222no—
416C4×D4—222no—
417C4×D4—221no—
418C4×D4—221no—
419C4×D4D4411yescharacteristic
420C4×D4D4412yes—
421C4×D4D4411yescharacteristic
422C4×D4C22⋊D1111yescharacteristic
423C4×D4C22⋊D1112yes—
424C4×D4C22⋊D1111yescharacteristic
425C2×C4⋊C4—112no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4C4×D1111yescharacteristic
430C2×C22⋊C4—112no—
431C2×C22⋊C4—112no—
432C2×C22⋊C4—112no—
433C2×C22⋊C4—112no—
434C2×C22⋊C4—112no—
435C2×C22⋊C4C4×D1112yes—
436C2×C42—112no—
437C2×C42—111no—
438C2×C42—111no—
439C2×C42C22×D1111yescharacteristic
440C4⋊C8—21no—
441C4⋊C8—21no—
442C4⋊C8—221no—
443C4⋊C8—221no—
444C22⋊C8—22no—
445C22⋊C8—22no—
446C22⋊C8—111no—
447C22⋊C8—112no—
448C22⋊C8—111no—
449C22⋊C8—222no—
450C22⋊C8—222no—
451C22⋊C8C22×D1111yescharacteristic
452C22⋊C8C22×D1112yes—
453C22⋊C8C22×D1111yescharacteristic
454#97—21no—
455#97—221no—
456C4×C8—21no—
457C4×C8—221no—
458C2×C11—21no—
459C2×C11—21no—
460C2×C11—42no—
461C2×C11—42no—
462C2×C11#288011yescharacteristic
463C2×C11#288311yescharacteristic
464C2×C11C2×#41311yescharacteristic
465D11—82no—
466C24—112no—
467C24C2×C4×D1112yes—
468C2×Q8—222no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×Q8—221no—
472C2×Q8—221no—
473C2×Q8—441no—
474C2×Q8—442no—
475C2×D4—42no—
476C2×D4—224no—
477C2×D4—222no—
478C2×D4—222no—
479C2×D4—222no—
480C2×D4—222no—
481C2×D4—221no—
482C2×D4—221no—
483C2×D4—442no—
484C2×D4—442no—
485C2×D4—882no—
486C2×D4(C2×D11)⋊C411yescharacteristic
487C2×D4(C2×D11)⋊C411yescharacteristic
488C2×D4(C2×D11)⋊C412yes—
489C22×C4—82no—
490C22×C4—111no—
491C22×C4—111no—
492C22×C4—112no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4—882no—
498C22×C4C2×C4×D1111yescharacteristic
499C22×C4C2×C4×D1111yescharacteristic
500C22×C4C2×C4×D1112yes—
501C22×C4C2×D4412yes—
502C22×C4C2×D4412yes—
503C22×C4C2×C22⋊D1112yes—
504C22×C4C2×C22⋊D1112yes—
505C22×C4C23×D1111yescharacteristic
506M16—82no—
507M16—882no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—22no—
511C2×C8—82no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—222no—
515C2×C8—882no—
516C4⋊C4—222no—
517C4⋊C4—222no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4(C2×D11)⋊C412yes—
525C4⋊C4(C2×D11)⋊C411yescharacteristic
526C4⋊C4(C2×D11)⋊C411yescharacteristic
527C22⋊C4—222no—
528C22⋊C4—222no—
529C22⋊C4—222no—
530C22⋊C4—222no—
531C22⋊C4—222no—
532C22⋊C4—222no—
533C22⋊C4—222no—
534C22⋊C4—222no—
535C22⋊C4—222no—
536C22⋊C4—222no—
537C22⋊C4(C2×D11)⋊C412yes—
538C22⋊C4(C2×D11)⋊C412yes—
539C22⋊C4(C2×D11)⋊C412yes—
540C22⋊C4(C2×D11)⋊C412yes—
541C42—222no—
542C42—222no—
543C42—221no—
544C42—221no—
545C42—221no—
546C42—221no—
547C42C2×D4411yescharacteristic
548C42C2×D4411yescharacteristic
549C42C2×C22⋊D1111yescharacteristic
550C42C2×C22⋊D1111yescharacteristic
551C11#1742911yescharacteristic, complemented, Sylow
552C23—22no—
553C23—22no—
554C23—42no—
555C23—42no—
556C23—222no—
557C23—222no—
558C23—222no—
559C23—442no—
560C23—442no—
561C23C2×(C2×D11)⋊C412yes—
562C23C2×(C2×D11)⋊C412yes—
563C23C22×C4×D1111yescharacteristic
564Q8—442no—
565Q8—442no—
566Q8—442no—
567Q8—442no—
568D4—22no—
569D4—22no—
570D4—42no—
571D4—442no—
572D4—444no—
573D4—444no—
574D4—442no—
575D4—882no—
576D4—882no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—112no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—222no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—442no—
598C2×C4—882no—
599C2×C4—882no—
600C2×C4C2×(C2×D11)⋊C411yescharacteristic
601C2×C4C2×(C2×D11)⋊C412yes—
602C2×C4C2×(C2×D11)⋊C412yes—
603C2×C4C2×(C2×D11)⋊C411yescharacteristic
604C2×C4C2×(C2×D11)⋊C411yescharacteristic
605C2×C4C2×(C2×D11)⋊C411yescharacteristic
606C2×C4C22×D4411yescharacteristic
607C2×C4C22×C22⋊D1111yescharacteristic
608C8—41no—
609C8—42no—
610C8—41no—
611C8—441no—
612C8—442no—
613C8—441no—
614C22—21no—
615C22—21no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—82no—
623C22—82no—
624C22—442no—
625C22—442no—
626C22—442no—
627C22—882no—
628C22—882no—
629C22D11×#13111yescharacteristic
630C22#1062328111yescharacteristic
631C22C22×(C2×D11)⋊C411yescharacteristic
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—22no—
637C4—22no—
638C4—21no—
639C4—222no—
640C4—441no—
641C4—441no—
642C4—441no—
643C4—442no—
644C4#1062274512yes—
645C2—21no—
646C2—21no—
647C2—42no—
648C2—42no—
649C2—882no—
650C2#1307706311yescharacteristic
651C2#1307707611yescharacteristic
652C2C2×#1062274511yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2974C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#66993C4
cosocleC22×C4×C11C24
hypercenter#2974D11
hypocenterC11#17429
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #13077651C2semidirect
3. #13066969C2semidirect
4. #13066967C2semidirect
5. #13066965C2semidirect
6. #13066962C2semidirect
7. #13066959C2semidirect
8. #13066952C2semidirect
9. #13066939C2semidirect
10. #13066932C2semidirect
11. C11×#2974C2semidirect
228. #2974D11semidirect
551. C11#17429semidirect

Maximal subgroups

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

subgroupindex
C2×#106230902
#130776512
#130669692
#130669672
#130669652
#130669622
#130669592
#130669522
#130669392
#130669322
C11×#29742
#1742911