Finite Group Databasebeta

← #14721618

Subgroups — #14721618

Order 2816.

1010 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
1#13077645C211yesmaximal, characteristic, complemented
2#13071556C211yesmaximal, characteristic, complemented
3#13067172C212yesmaximal, complemented
4#13067167C211yesmaximal, characteristic, complemented
5#13067163C211yesmaximal, characteristic, complemented
6#13067159C212yesmaximal, complemented
7#13067128C211yesmaximal, characteristic, complemented
8#13067124C211yesmaximal, characteristic, complemented
9#13067120C212yesmaximal, complemented
10#13067107C212yesmaximal, complemented
11C11×#3506C211yesmaximal, characteristic
12C11×#559—22no—
13C11×#556C412yescomplemented
14C11×#555C412yescomplemented
15C11×#553—22no—
16C11×#550C412yescomplemented
17C11×#547C412yescomplemented
18C11×#538—21no—
19C11×#538—21no—
20C11×#535—21no—
21C11×#533C2211yescharacteristic
22C11×#532C2211yescharacteristic
23C11×#525C2212yes—
24C11×#525C2212yes—
25C11×#520—21no—
26C2×C4×D4×C11C2211yescharacteristic
27#10622833—21no—
28#10622825C2211yescharacteristic
29#10622824C2211yescharacteristic
30C4×C22⋊Dic11C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32#10622820C2212yes—
33C2×C22⋊(C11⋊C8)C2212yes—
34#10622624—22no—
35#10622624—22no—
36#10622594—21no—
37#10622564—21no—
38C22⋊C4×Dic11—21no—
39#10622550C2211yescharacteristic
40#10622545C2211yescharacteristic
41#10622539C2211yescharacteristic
42#10622539C2211yescharacteristic
43#10622176C2212yes—
44#10622176C2212yes—
45#10622176C2212yes—
46#10622176C2212yes—
47#10622175C2212yes—
48#10622175C2212yes—
49#10622175C2212yes—
50#10622175C2212yes—
51C2×C11×#41—21no—
52C2×C11×#41C2×C412yes—
53C2×C11×#41C2×C412yescomplemented
54C22×D4×C11D411yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×Dic11—21no—
58C11×C4⋊Q8C2×C411yescharacteristic, complemented
59C11×C4⋊Q8C2×C411yescharacteristic, complemented
60C11×C4⋊Q8C2×C411yescharacteristic, complemented
61C11×#127—22no—
62C11×#127C2×C411yescharacteristic, complemented
63C11×#126—22no—
64C11×#126—22no—
65C11×#125—21no—
66C11×#124—22no—
67C11×#124—22no—
68C11×#124—22no—
69C11×#124—21no—
70C11×#123—22no—
71C11×#123—22no—
72C11×#123—22no—
73C11×#123—22no—
74C11×C22⋊Q8—21no—
75C11×C22⋊Q8C2×C412yes—
76C11×C22⋊Q8C2×C412yescomplemented
77C11×C22⋊Q8C2312yes—
78C11×#121—22no—
79C11×#121—22no—
80C11×#121—21no—
81C11×#121—22no—
82C11×#121—22no—
83C11×#121C2×C412yes—
84C11×#121C2×C412yescomplemented
85C11×#121C2312yes—
86C11×#120—22no—
87C11×#120—22no—
88C4×Q8×C11—22no—
89C4×Q8×C11—21no—
90C4×Q8×C11C2×C412yescomplemented
91C4×D4×C11—22no—
92C4×D4×C11—22no—
93C4×D4×C11—22no—
94C4×D4×C11—22no—
95C4×D4×C11—22no—
96C4×D4×C11—21no—
97C4×D4×C11C2×C412yes—
98C4×D4×C11C2×C412yes—
99C4×D4×C11C2×C412yescomplemented
100C4×D4×C11D412yes—
101C4×D4×C11D412yes—
102C11×#117—21no—
103C11×#117—22no—
104C11×#117C2×C412yes—
105C11×#117C2×C412yescomplemented
106C2×C11×C4⋊C4—22no—
107C2×C11×C4⋊C4D411yescharacteristic
108C2×C11×C22⋊C4D411yescharacteristic
109C2×C11×C22⋊C4D411yescharacteristic
110C2×C42×C11C2311yescharacteristic
111C2×C22⋊Dic11—21no—
112C2×C22⋊Dic11—21no—
113C2×C22⋊Dic11—21no—
114C2×C4⋊Dic11—21no—
115C2×C4×Dic11—21no—
116C2×C4×Dic11—21no—
117C2×#4318—22no—
118C22×C11⋊C8—22no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95C2311yescharacteristic
125C11⋊#95C2311yescharacteristic
126C11⋊#95C2311yescharacteristic
127C11⋊#95C2311yescharacteristic
128C22⋊(C11⋊C8)—22no—
129C22⋊(C11⋊C8)—22no—
130C22⋊(C11⋊C8)C2312yes—
131C22⋊(C11⋊C8)C2312yes—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)—21no—
134#66867—21no—
135#66867—21no—
136#17629—111nomaximal, Sylow
137C24×C11C2×D411yescharacteristic
138C24×C11C2×D411yescharacteristic
139C11×#41—42no—
140C11×#41—42no—
141C11×#41—82no—
142C11×#41—82no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11C22×C412yes—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—41no—
154C2×D4×C11—41no—
155C2×D4×C11C22⋊C412yes—
156C2×D4×C11C22⋊C412yes—
157C2×D4×C11C22×C412yes—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—81no—
162C22×C4×C11—81no—
163C22×C4×C11C22×C412yes—
164C22×C4×C11C22×C412yes—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D412yes—
170C22×C4×C11C2×D412yes—
171C22×C4×C11C2411yescharacteristic
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—42no—
177C22×Dic11—42no—
178C22×Dic11—81no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4C22⋊C412yes—
188C11×C4⋊C4C22⋊C412yes—
189C11×C4⋊C4C22×C412yes—
190C11×C4⋊C4C22×C412yes—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—22no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—22no—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C11×C22⋊C4—22no—
198C11×C22⋊C4—22no—
199C11×C22⋊C4—22no—
200C11×C22⋊C4C22⋊C412yes—
201C11×C22⋊C4C22⋊C412yes—
202C11×C22⋊C4C22⋊C412yes—
203C11×C22⋊C4C22⋊C412yes—
204C42×C11—22no—
205C42×C11—22no—
206C42×C11—22no—
207C42×C11C22×C411yescharacteristic
208C42×C11C22×C411yescharacteristic
209C42×C11C2×D411yescharacteristic
210C42×C11C2×D411yescharacteristic
211C22⋊Dic11—42no—
212C22⋊Dic11—42no—
213C22⋊Dic11—81no—
214C4⋊Dic11—81no—
215C4×Dic11—42no—
216C4×Dic11—81no—
217#4318—82no—
218C2×C11⋊C8—22no—
219C2×C11⋊C8—22no—
220C2×C11⋊C8—82no—
221#3506D1111yescharacteristic
222#2973—111no—
223#2353—111no—
224#1516—112no—
225#1515—111no—
226#1514—111no—
227#1513—112no—
228#1506—111no—
229#1505—111no—
230#1504—112no—
231#1501—112no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—22no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11C2×C22⋊C412yes—
242C23×C11C2×C22⋊C412yes—
243C23×C11C22×D411yescharacteristic
244Q8×C11—42no—
245Q8×C11—42no—
246Q8×C11—81no—
247D4×C11—42no—
248D4×C11—42no—
249D4×C11—42no—
250D4×C11—42no—
251D4×C11—42no—
252D4×C11—42no—
253D4×C11—81no—
254D4×C11—82no—
255D4×C11—82no—
256D4×C11—82no—
257D4×C11—82no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—44no—
272C2×C4×C11—82no—
273C2×C4×C11—82no—
274C2×C4×C11C2×C22⋊C411yescharacteristic
275C2×C4×C11C2×C22⋊C412yes—
276C2×C4×C11C2×C22⋊C412yes—
277C2×C4×C11C2×C22⋊C411yescharacteristic
278C2×C4×C11C2×C22⋊C411yescharacteristic
279C2×C4×C11C2×C22⋊C411yescharacteristic
280C2×C4×C11C23×C411yescharacteristic
281C2×C4×C11C22×D411yescharacteristic
282C2×Dic11—22no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—84no—
295C11⋊C8—42no—
296C11⋊C8—42no—
297#559—22no—
298#556Dic1112yescomplemented
299#555Dic1112yescomplemented
300#553—22no—
301#550Dic1112yescomplemented
302#547Dic1112yescomplemented
303#538—21no—
304#538—21no—
305#535—21no—
306#533C2×D1111yescharacteristic
307#532C2×D1111yescharacteristic
308#525C2×D1112yes—
309#525C2×D1112yes—
310#520—21no—
311C2×C4×D4C2×D1111yescharacteristic
312#435—222no—
313#435—222no—
314#432—111no—
315#432—111no—
316#407—112no—
317C2×C22⋊C8—112no—
318#388—221no—
319#387—221no—
320#386—221no—
321#383—111no—
322#381—111no—
323#380—111no—
324C4×C22⋊C4—111no—
325C4×C22⋊C4—221no—
326#376—111no—
327C2×#95—111no—
328#328—112no—
329#328—112no—
330#328—112no—
331#328—112no—
332#327—112no—
333#327—112no—
334#327—112no—
335#327—112no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—22no—
339C22×C11—22no—
340C22×C11—22no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11C22×C22⋊C411yescharacteristic
352C22×C11#57511yescharacteristic
353C22×C11#57511yescharacteristic
354C4×C11—21no—
355C4×C11—21no—
356C4×C11—22no—
357C4×C11—22no—
358C4×C11—21no—
359C4×C11—21no—
360C4×C11—21no—
361C4×C11—21no—
362C4×C11—42no—
363C4×C11—42no—
364C4×C11—42no—
365Dic11—42no—
366Dic11—81no—
367Dic11—81no—
368Dic11—81no—
369C2×#41—21no—
370C2×#41C2×Dic1112yes—
371C2×#41C2×Dic1112yescomplemented
372C22×D4C22⋊D1111yescharacteristic
373C23×C4—221no—
374C23×C4C22×D1111yescharacteristic
375C23×C4C22×D1111yescharacteristic
376C2×M16—222no—
377C22×C8—222no—
378C4⋊Q8C2×Dic1111yescharacteristic, complemented
379C4⋊Q8C2×Dic1111yescharacteristic, complemented
380C4⋊Q8C2×Dic1111yescharacteristic, complemented
381#127—22no—
382#127C2×Dic1111yescharacteristic, complemented
383#126—22no—
384#126—22no—
385#125—21no—
386#124—22no—
387#124—22no—
388#124—22no—
389#124—21no—
390#123—22no—
391#123—22no—
392#123—22no—
393#123—22no—
394C22⋊Q8—21no—
395C22⋊Q8C2×Dic1112yes—
396C22⋊Q8C2×Dic1112yescomplemented
397C22⋊Q8C22×D1112yes—
398#121—22no—
399#121—22no—
400#121—21no—
401#121—22no—
402#121—22no—
403#121C2×Dic1112yes—
404#121C2×Dic1112yescomplemented
405#121C22×D1112yes—
406#120—22no—
407#120—22no—
408C4×Q8—22no—
409C4×Q8—21no—
410C4×Q8C2×Dic1112yescomplemented
411C4×D4—22no—
412C4×D4—22no—
413C4×D4—22no—
414C4×D4—22no—
415C4×D4—22no—
416C4×D4—21no—
417C4×D4C2×Dic1112yes—
418C4×D4C2×Dic1112yes—
419C4×D4C2×Dic1112yescomplemented
420C4×D4C22⋊D1112yes—
421C4×D4C22⋊D1112yes—
422#117—21no—
423#117—22no—
424#117C2×Dic1112yes—
425#117C2×Dic1112yescomplemented
426C2×C4⋊C4—22no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4C22⋊D1111yescharacteristic
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4C22⋊D1111yescharacteristic
433C2×C22⋊C4C22⋊D1111yescharacteristic
434C2×C42—221no—
435C2×C42—221no—
436C2×C42C22×D1111yescharacteristic
437C4⋊C8—221no—
438C4⋊C8—221no—
439C22⋊C8—112no—
440C22⋊C8—112no—
441C22⋊C8—222no—
442C22⋊C8—222no—
443#97—221no—
444#97—221no—
445#95—111no—
446#95—111no—
447#95—111no—
448#95—111no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95—221no—
454C2×C11—21no—
455C2×C11—21no—
456C2×C11—42no—
457C2×C11—42no—
458C2×C11—82no—
459C2×C11#288311yescharacteristic
460C2×C11#289611yescharacteristic
461C2×C11#290111yescharacteristic
462C24C2×C22⋊D1111yescharacteristic
463C24C2×C22⋊D1111yescharacteristic
464#41—42no—
465#41—42no—
466#41—82no—
467#41—82no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8C22×Dic1112yes—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—41no—
479C2×D4—41no—
480C2×D4C22⋊Dic1112yes—
481C2×D4C22⋊Dic1112yes—
482C2×D4C22×Dic1112yes—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—81no—
487C22×C4—81no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—442no—
493C22×C4—442no—
494C22×C4—881no—
495C22×C4C22×Dic1112yes—
496C22×C4C22×Dic1112yes—
497C22×C4C2×C22⋊D1111yescharacteristic
498C22×C4C2×C22⋊D1111yescharacteristic
499C22×C4C2×C22⋊D1111yescharacteristic
500C22×C4C2×C22⋊D1111yescharacteristic
501C22×C4C2×C22⋊D1112yes—
502C22×C4C2×C22⋊D1112yes—
503C22×C4C23×D1111yescharacteristic
504M16—882no—
505C2×C8—222no—
506C2×C8—222no—
507C2×C8—882no—
508C4⋊C4—21no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—881no—
517C4⋊C4C22⋊Dic1112yes—
518C4⋊C4C22⋊Dic1112yes—
519C4⋊C4C22×Dic1112yes—
520C4⋊C4C22×Dic1112yes—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—442no—
531C22⋊C4—442no—
532C22⋊C4—881no—
533C22⋊C4C22⋊Dic1112yes—
534C22⋊C4C22⋊Dic1112yes—
535C22⋊C4C22⋊Dic1112yes—
536C22⋊C4C22⋊Dic1112yes—
537C42—22no—
538C42—22no—
539C42—22no—
540C42—442no—
541C42—881no—
542C42C22×Dic1111yescharacteristic
543C42C22×Dic1111yescharacteristic
544C42C2×C22⋊D1111yescharacteristic
545C42C2×C22⋊D1111yescharacteristic
546C11#1762911yescharacteristic, complemented, Sylow
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—22no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23C2×C22⋊Dic1112yes—
557C23C2×C22⋊Dic1112yes—
558C23C22×C22⋊D1111yescharacteristic
559Q8—42no—
560Q8—42no—
561Q8—81no—
562D4—42no—
563D4—42no—
564D4—42no—
565D4—42no—
566D4—42no—
567D4—42no—
568D4—81no—
569D4—82no—
570D4—82no—
571D4—82no—
572D4—82no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—44no—
587C2×C4—82no—
588C2×C4—82no—
589C2×C4—222no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—884no—
602C2×C4C2×C22⋊Dic1111yescharacteristic
603C2×C4C2×C22⋊Dic1112yes—
604C2×C4C2×C22⋊Dic1112yes—
605C2×C4C2×C22⋊Dic1111yescharacteristic
606C2×C4C2×C22⋊Dic1111yescharacteristic
607C2×C4C2×C22⋊Dic1111yescharacteristic
608C2×C4C23×Dic1111yescharacteristic
609C2×C4C22×C22⋊D1111yescharacteristic
610C8—442no—
611C8—442no—
612C22—21no—
613C22—21no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—42no—
625C22—81no—
626C22—81no—
627C22#1062335311yescharacteristic
628C22#1062335311yescharacteristic
629C22C22×C22⋊Dic1111yescharacteristic
630C4—21no—
631C4—21no—
632C4—22no—
633C4—22no—
634C4—21no—
635C4—21no—
636C4—21no—
637C4—21no—
638C4—42no—
639C4—42no—
640C4—42no—
641C4—442no—
642C4—881no—
643C4—881no—
644C4—881no—
645C2—21no—
646C2—21no—
647C2—42no—
648C2—42no—
649C2—82no—
650C2#1307707711yescharacteristic
651C2#1307713511yescharacteristic
652C2#1307716311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3506C2
socleC22×C11C22×C22⋊C4
cosocleC22×C4×C11C24
hypercenter#3506D11
hypocenterC11#17629
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. #13077645C2semidirect
2. #13071556C2semidirect
3. #13067172C2semidirect
4. #13067167C2semidirect
5. #13067163C2semidirect
6. #13067159C2semidirect
7. #13067128C2semidirect
8. #13067124C2semidirect
9. #13067120C2semidirect
10. #13067107C2semidirect
13. C11×#556C4semidirect
14. C11×#555C4semidirect
16. C11×#550C4semidirect
17. C11×#547C4semidirect
53. C2×C11×#41C2×C4semidirect
58. C11×C4⋊Q8C2×C4semidirect
59. C11×C4⋊Q8C2×C4semidirect
60. C11×C4⋊Q8C2×C4semidirect
62. C11×#127C2×C4semidirect
76. C11×C22⋊Q8C2×C4semidirect
84. C11×#121C2×C4semidirect
90. C4×Q8×C11C2×C4semidirect
99. C4×D4×C11C2×C4semidirect
105. C11×#117C2×C4semidirect
298. #556Dic11semidirect
299. #555Dic11semidirect
301. #550Dic11semidirect
302. #547Dic11semidirect
371. C2×#41C2×Dic11semidirect
378. C4⋊Q8C2×Dic11semidirect
379. C4⋊Q8C2×Dic11semidirect
380. C4⋊Q8C2×Dic11semidirect
382. #127C2×Dic11semidirect
396. C22⋊Q8C2×Dic11semidirect
404. #121C2×Dic11semidirect
410. C4×Q8C2×Dic11semidirect
419. C4×D4C2×Dic11semidirect
425. #117C2×Dic11semidirect
546. C11#17629semidirect

Maximal subgroups

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

subgroupindex
#130776452
#130715562
#130671722
#130671672
#130671632
#130671592
#130671282
#130671242
#130671202
#130671072
C11×#35062
#1762911