Finite Group Databasebeta

← #14720002

Subgroups — #14720002

Order 2816.

944 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623044C211yesmaximal, characteristic
2#13077270C212yesmaximal, complemented
3#13066984C212yesmaximal, complemented
4#13066970C212yesmaximal, complemented
5#13066962C212yesmaximal
6#13066958C211yesmaximal, characteristic, complemented
7#13066949C211yesmaximal, characteristic, complemented
8#13066946C211yesmaximal, characteristic, complemented
9#13066938C211yesmaximal, characteristic, complemented
10#13066929C211yesmaximal, characteristic, complemented
11C2×C11×#324C211yesmaximal, characteristic, complemented
12C22×C11×C4⋊C4C2211yescharacteristic
13C2×#66982C411yescharacteristic
14C2×#66982C2211yescharacteristic
15C2×C4×C22⋊D11C411yescharacteristic
16C2×#66979C411yescharacteristic
17C2×#66979C2211yescharacteristic
18C2×#66977C411yescharacteristic
19#10623044—22no—
20#10623044—22no—
21#10623044—22no—
22#10623044—22no—
23C2×#66951C411yescharacteristic
24C2×#66951C2211yescharacteristic
25C2×#66950C411yescharacteristic
26C2×#66945C2211yescharacteristic
27C2×#66943C411yescharacteristic
28C2×#66942C411yescharacteristic
29C2×#66942C2211yescharacteristic
30C2×#66940C2211yescharacteristic
31C2×C11×C22⋊C8C2212yes—
32#10622820C2212yes—
33#10622715—22no—
34#10622714—22no—
35#10622333—22no—
36#10622333—22no—
37#10622332C2212yes—
38#10622332C2212yes—
39#10622331C2212yes—
40#10622331C2212yes—
41C11×#324C2211yescharacteristic
42C11×#324C2211yescharacteristic
43C11×#324C2212yes—
44#10622166C2211yescharacteristic
45#10622166C2211yescharacteristic
46#10622166C2212yes—
47#10622107C2212yes—
48#10622107C2212yes—
49#10622106C2212yes—
50#10622106C2212yes—
51C23×C4×C11C2×C411yescharacteristic
52C23×C4×C11C2×C411yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11C2×C411yescharacteristic
55C22×C4×D11C2×C411yescharacteristic
56C22×Dic22C2×C411yescharacteristic
57C22×C8×C11—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4C2×C411yescharacteristic
61C2×C11×C4⋊C4C2×C411yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C22⋊Dic11C2×C411yescharacteristic
65C2×C22⋊Dic11C2×C411yescharacteristic
66C2×C22⋊Dic11C2×C411yescharacteristic
67#66982—22no—
68#66982—22no—
69#66982—22no—
70#66982—22no—
71C4×C22⋊D11—21no—
72C4×C22⋊D11—21no—
73C4×C22⋊D11—21no—
74C4×C22⋊D11—21no—
75C2×(C2×D11)⋊C4C2×C411yescharacteristic
76C2×(C2×D11)⋊C4C2×C411yescharacteristic
77C2×(C2×D11)⋊C4C2×C411yescharacteristic
78C2×(C2×D11)⋊C4C2×C411yescharacteristic
79C2×(C2×D11)⋊C4C2311yescharacteristic
80#66979—21no—
81#66979—21no—
82#66979—21no—
83#66979—21no—
84#66979D412yes—
85#66979D412yes—
86#66979D412yes—
87#66979D412yes—
88C2×C4⋊Dic11C2×C411yescharacteristic
89C2×C4⋊Dic11C2×C411yescharacteristic
90C2×C4⋊Dic11C2×C411yescharacteristic
91C2×C4⋊Dic11C2×C411yescharacteristic
92C2×C4⋊Dic11C2×C411yescharacteristic
93#66977—22no—
94#66977—22no—
95C2×Dic11⋊C4C2×C411yescharacteristic
96C2×Dic11⋊C4C2×C411yescharacteristic
97C2×Dic11⋊C4C2×C411yescharacteristic
98C2×Dic11⋊C4C2×C411yescharacteristic
99C2×Dic11⋊C4C2×C411yescharacteristic
100C2×Dic11⋊C4C2×C411yescharacteristic
101C2×Dic11⋊C4C2311yescharacteristic
102C2×C4×Dic11C2×C411yescharacteristic
103C2×C4×Dic11C2×C411yescharacteristic
104C2×C4×Dic11C2×C411yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C2×#4318—22no—
108#66951—22no—
109#66951—22no—
110#66951—22no—
111#66951—22no—
112#66950—22no—
113#66950—22no—
114#66945—22no—
115#66945—22no—
116#66943—22no—
117#66943—22no—
118#66942—22no—
119#66942—22no—
120#66942—22no—
121#66942—22no—
122#66940—22no—
123#66940—22no—
124C11×C22⋊C8—22no—
125C11×C22⋊C8C2312yes—
126C11×C22⋊C8C2312yes—
127C22⋊(C11⋊C8)—22no—
128C22⋊(C11⋊C8)C2312yes—
129C22⋊(C11⋊C8)C2312yes—
130#66879—22no—
131#66879—22no—
132Dic11⋊C8—22no—
133Dic11⋊C8—22no—
134Dic11⋊C8—22no—
135Dic11⋊C8—22no—
136C8×Dic11—22no—
137C8×Dic11—22no—
138#17417—111nomaximal, Sylow
139C24×C11C22×C411yescharacteristic
140C23×D11C22×C411yescharacteristic
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—22no—
146C22×C4×C11—41no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C22×C411yescharacteristic
152C22×C4×C11C22×C411yescharacteristic
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—21no—
158C2×C22⋊D11—21no—
159C2×C22⋊D11—42no—
160C22×Dic11C22×C411yescharacteristic
161C22×Dic11C22×C411yescharacteristic
162C22×Dic11C22×C411yescharacteristic
163C22×Dic11C22×C411yescharacteristic
164C22×Dic11C22×C411yescharacteristic
165C22×Dic11C22×C411yescharacteristic
166C22×Dic11C22×C411yescharacteristic
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—22no—
170C2×C4×D11—41no—
171C2×Dic22—22no—
172C2×Dic22—22no—
173C2×Dic22—41no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—44no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C22⋊Dic11—21no—
182C22⋊Dic11—21no—
183C22⋊Dic11C22⋊C412yes—
184C22⋊Dic11C22⋊C412yes—
185C22⋊Dic11C22⋊C411yescharacteristic
186C22⋊Dic11C22⋊C411yescharacteristic
187C22⋊Dic11C22⋊C411yescharacteristic
188C22⋊Dic11C22⋊C411yescharacteristic
189(C2×D11)⋊C4—22no—
190(C2×D11)⋊C4—22no—
191(C2×D11)⋊C4—21no—
192(C2×D11)⋊C4—21no—
193(C2×D11)⋊C4—22no—
194(C2×D11)⋊C4—22no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—22no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11C22⋊C412yes—
201C4⋊Dic11C22⋊C412yes—
202C4⋊Dic11C22⋊C412yes—
203C4⋊Dic11C22⋊C412yes—
204Dic11⋊C4—22no—
205Dic11⋊C4—21no—
206Dic11⋊C4—21no—
207Dic11⋊C4—22no—
208Dic11⋊C4—22no—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—21no—
218C4×Dic11C2×D412yes—
219C4×Dic11C2×D412yes—
220C4×Dic11C2×D412yes—
221C4×Dic11C2×D412yes—
222#4318—44no—
223C2×C11⋊C8—22no—
224C2×C11⋊C8—22no—
225C2×#552—111no—
226#2924—112no—
227#1473—112no—
228#1470—112no—
229#1468—112no—
230#1467—111no—
231#1464—111no—
232#1463—111no—
233#1461—111no—
234#1458—111no—
235C2×#324D1111yescharacteristic, complemented
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—22no—
239C23×C11—41no—
240C23×C11C2×C22⋊C411yescharacteristic
241C23×C11C2×C22⋊C411yescharacteristic
242C23×C11C23×C411yescharacteristic
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—41no—
247C22×D11—41no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—24no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—41no—
257C2×C4×C11—42no—
258C2×C4×C11—41no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11C2×C22⋊C412yes—
266C2×C4×C11#13112yes—
267C2×C4×C11C22×D412yes—
268C22⋊D11—42no—
269C22⋊D11—42no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11C2×C22⋊C411yescharacteristic
284C2×Dic11C2×C22⋊C411yescharacteristic
285C2×Dic11C2×C22⋊C411yescharacteristic
286C2×Dic11C2×C22⋊C411yescharacteristic
287C2×Dic11C2×C22⋊C412yes—
288C2×Dic11C2×C22⋊C412yes—
289C4×D11—42no—
290C4×D11—42no—
291Dic22—44no—
292C8×C11—42no—
293C8×C11—42no—
294C11⋊C8—42no—
295C11⋊C8—42no—
296#552—222no—
297#552—222no—
298#552—222no—
299#552—222no—
300C2×#126—111no—
301C2×#126—111no—
302C2×#125—111no—
303C2×#125—111no—
304C2×#125—111no—
305C2×#123—111no—
306C2×#123—111no—
307C2×C22⋊Q8—111no—
308C2×C22⋊Q8—111no—
309C2×C4×Q8—111no—
310C2×C4×D4—111no—
311C2×#117—111no—
312C2×#117—111no—
313C2×#117—111no—
314C22×C4⋊C4C2×D1111yescharacteristic
315#433—222no—
316#433—222no—
317#432—112no—
318#432—112no—
319#431—112no—
320#431—112no—
321#424—222no—
322#407—112no—
323C2×C22⋊C8C2×D1112yes—
324#405—222no—
325#324—111no—
326#324—111no—
327#324—112no—
328#324—112no—
329#324—112no—
330#324C2×D1111yescharacteristic
331#324C2×D1111yescharacteristic
332#324C2×D1112yes—
333#323—112no—
334#323—112no—
335C22×C11—21no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—21no—
339C22×C11—21no—
340C22×C11—21no—
341C22×C11—21no—
342C22×C11—42no—
343C22×C11—42no—
344C22×C11#41012yes—
345C22×C11C22×C22⋊C411yescharacteristic
346C22×C11C2×#13111yescharacteristic
347C22×C11#56811yescharacteristic
348C2×D11—41no—
349C2×D11—41no—
350C2×D11—41no—
351C2×D11—81no—
352C2×D11—81no—
353C4×C11—22no—
354C4×C11—22no—
355C4×C11—22no—
356C4×C11—41no—
357C4×C11—41no—
358C4×C11—41no—
359Dic11—22no—
360Dic11—21no—
361Dic11—21no—
362Dic11—21no—
363Dic11—21no—
364Dic11—22no—
365Dic11—41no—
366Dic11—41no—
367Dic11—41no—
368C22×Q8—111no—
369C22×D4—111no—
370C23×C4—111no—
371C23×C4C4×D1111yescharacteristic
372C23×C4C4×D1111yescharacteristic
373C23×C4C22×D1111yescharacteristic
374C2×M16—222no—
375C22×C8—22no—
376#126—222no—
377#126—222no—
378#126—222no—
379#126—222no—
380#125—222no—
381#125—222no—
382#125—222no—
383#125—222no—
384#125—222no—
385#125—222no—
386#123—222no—
387#123—222no—
388#123—222no—
389#123—222no—
390C22⋊Q8—222no—
391C22⋊Q8—222no—
392C22⋊Q8—222no—
393C22⋊Q8—222no—
394C4×Q8—222no—
395C4×Q8—222no—
396C4×D4—221no—
397C4×D4—221no—
398C4×D4—221no—
399C4×D4—221no—
400#117—112no—
401#117—112no—
402#117—112no—
403#117—112no—
404#117—222no—
405#117—222no—
406#117—221no—
407#117—221no—
408#117—221no—
409#117—221no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4C4×D1111yescharacteristic
425C2×C4⋊C4C4×D1111yescharacteristic
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C22⋊C4—111no—
429C2×C22⋊C4—111no—
430C2×C22⋊C4—111no—
431C2×C22⋊C4—111no—
432C2×C22⋊C4—111no—
433C2×C22⋊C4—111no—
434C2×C22⋊C4—111no—
435C2×C22⋊C4—111no—
436C2×C42—111no—
437C2×C42—111no—
438C2×C42—111no—
439C2×C42—111no—
440C2×C42—111no—
441C4⋊C8—222no—
442C4⋊C8—222no—
443C4⋊C8—222no—
444C4⋊C8—222no—
445C22⋊C8—22no—
446C22⋊C8—112no—
447C22⋊C8—112no—
448C22⋊C8—222no—
449C22⋊C8C22×D1112yes—
450C22⋊C8C22×D1112yes—
451#97—222no—
452#97—222no—
453C4×C8—222no—
454C4×C8—222no—
455C2×C11—21no—
456C2×C11—21no—
457C2×C11—22no—
458C2×C11—41no—
459C2×C11#288011yescharacteristic
460C2×C11C2×#41011yescharacteristic
461C2×C11#288911yescharacteristic
462D11—81no—
463C24—111no—
464C24C2×C4×D1111yescharacteristic
465C2×Q8—222no—
466C2×Q8—222no—
467C2×Q8—441no—
468C2×D4—221no—
469C2×D4—221no—
470C2×D4—442no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—42no—
477C22×C4—41no—
478C22×C4—42no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—222no—
489C22×C4—441no—
490C22×C4C2×C4×D1111yescharacteristic
491C22×C4C2×C4×D1111yescharacteristic
492C22×C4C2×C4×D1111yescharacteristic
493C22×C4C2×C4×D1111yescharacteristic
494C22×C4C2×C4×D1111yescharacteristic
495C22×C4D4×D1112yes—
496C22×C4D4×D1112yes—
497C22×C4C23×D1111yescharacteristic
498M16—444no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—44no—
502C2×C8—222no—
503C2×C8—222no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—112no—
509C4⋊C4—112no—
510C4⋊C4—112no—
511C4⋊C4—112no—
512C4⋊C4—222no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—222no—
520C4⋊C4—222no—
521C4⋊C4—222no—
522C4⋊C4—222no—
523C4⋊C4—222no—
524C4⋊C4—222no—
525C22⋊C4—111no—
526C22⋊C4—111no—
527C22⋊C4—111no—
528C22⋊C4—111no—
529C22⋊C4—112no—
530C22⋊C4—112no—
531C22⋊C4—222no—
532C22⋊C4—221no—
533C22⋊C4—221no—
534C22⋊C4—222no—
535C22⋊C4—221no—
536C22⋊C4—221no—
537C22⋊C4—222no—
538C22⋊C4—222no—
539C42—112no—
540C42—112no—
541C42—112no—
542C42—112no—
543C42—221no—
544C42—221no—
545C42—221no—
546C42—221no—
547C42—221no—
548C42—221no—
549C11#1741711yescharacteristic, complemented, Sylow
550C23—21no—
551C23—21no—
552C23—22no—
553C23—41no—
554C23—221no—
555C23—221no—
556C23—221no—
557C23—441no—
558C23—441no—
559C23C22⋊C4×D1111yescharacteristic
560C23C22⋊C4×D1111yescharacteristic
561C23C22×C4×D1111yescharacteristic
562Q8—444no—
563D4—442no—
564D4—442no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—24no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—111no—
583C2×C4—111no—
584C2×C4—111no—
585C2×C4—111no—
586C2×C4—112no—
587C2×C4—112no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—442no—
598C2×C4—442no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4C22⋊C4×D1112yes—
604C2×C4#6695412yes—
605C2×C4C2×D4×D1112yes—
606C8—42no—
607C8—42no—
608C8—442no—
609C8—442no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—42no—
618C22—42no—
619C22—441no—
620C22—441no—
621C22—441no—
622C22—881no—
623C22—881no—
624C22#1062235312yes—
625C22C2×C22⋊C4×D1111yescharacteristic
626C22C2×#6695411yescharacteristic
627C22#1062327611yescharacteristic
628C4—22no—
629C4—22no—
630C4—22no—
631C4—41no—
632C4—41no—
633C4—41no—
634C4—221no—
635C4—221no—
636C4—222no—
637C4—221no—
638C4—221no—
639C4—222no—
640C4—441no—
641C4—441no—
642C4—441no—
643C2—21no—
644C2—21no—
645C2—22no—
646C2—41no—
647C2—881no—
648C2#1307706211yescharacteristic
649C2C2×#1062235311yescharacteristic
650C2#1307709611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#324C2
socleC22×C11C22×C22⋊C4
prime radicalC22×C22⋊D11C2×C4
cosocleC22×C4×C11C24
hypercenterC2×#324D11
hypocenterC11#17417
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #13077270C2semidirect
3. #13066984C2semidirect
4. #13066970C2semidirect
6. #13066958C2semidirect
7. #13066949C2semidirect
8. #13066946C2semidirect
9. #13066938C2semidirect
10. #13066929C2semidirect
11. C2×C11×#324C2semidirect
235. C2×#324D11semidirect
549. C11#17417semidirect

Maximal subgroups

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

subgroupindex
C2×#106230442
#130772702
#130669842
#130669702
#130669622
#130669582
#130669492
#130669462
#130669382
#130669292
C2×C11×#3242
#1741711