Finite Group Databasebeta

← #14724189

Subgroups — #14724189

Order 2816.

608 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077733C211yesmaximal, characteristic, complemented
2#13077692C211yesmaximal, characteristic, complemented
3#13067530C211yesmaximal, characteristic, complemented
4#13067519C211yesmaximal, characteristic, complemented
5#13067507C211yesmaximal, characteristic, complemented
6#13067501C211yesmaximal, characteristic, complemented
7#13067481C211yesmaximal, characteristic, complemented
8#13067474C211yesmaximal, characteristic, complemented
9#13067453C211yesmaximal, characteristic, complemented
10#13067446C211yesmaximal, characteristic, complemented
11#13067401C211yesmaximal, characteristic, complemented
12#13067050C211yesmaximal, characteristic, complemented
13#13067015C211yesmaximal, characteristic, complemented
14#13066916C211yesmaximal, characteristic, complemented
15C11×#3106C211yesmaximal, characteristic
16C11×#532C2211yescharacteristic
17C4×C11×#41C2211yescharacteristic
18C11×#482C411yescharacteristic
19C11×#482C411yescharacteristic
20C11×#477C411yescharacteristic
21C11×#476C411yescharacteristic
22C11×#460C411yescharacteristic
23C11×#459C411yescharacteristic
24C11×#449C411yescharacteristic
25C11×#449C411yescharacteristic
26C4×C11×SD16C2211yescharacteristic
27C4×C11×SD16C2211yescharacteristic
28C4×C11×D8C2211yescharacteristic
29C4×C11×D8C2211yescharacteristic
30C11×#431C2211yescharacteristic
31#10622847—21no—
32#10622847—21no—
33#10622637C2211yescharacteristic
34#10622637C2211yescharacteristic
35#10622625C2211yescharacteristic
36#10622625C2211yescharacteristic
37#10622625C2211yescharacteristic
38#10622625C2211yescharacteristic
39#10622624—21no—
40#10622624—21no—
41#10622624—21no—
42#10622624—21no—
43D4×C11⋊C8C2211yescharacteristic
44D4×C11⋊C8C2211yescharacteristic
45#10622539—21no—
46#10622539C2211yescharacteristic
47#10622538C2211yescharacteristic
48#10622538C2211yescharacteristic
49#10622537—21no—
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51Q8⋊(C11⋊C8)C2211yescharacteristic
52Q8⋊(C11⋊C8)C2211yescharacteristic
53D4⋊(C11⋊C8)C2211yescharacteristic
54D4⋊(C11⋊C8)C2211yescharacteristic
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57D4⋊(C11⋊C8)C2211yescharacteristic
58D4⋊(C11⋊C8)C2211yescharacteristic
59#10622096C2211yescharacteristic
60#10622096C2211yescharacteristic
61#10622095C2211yescharacteristic
62#10622095C2211yescharacteristic
63#10622093C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×C11×#41—21no—
68C2×C11×#41C2×C411yescharacteristic
69C2×C11×SD16C2×C411yescharacteristic
70C2×C11×SD16C2×C411yescharacteristic
71C2×C11×D8C2×C411yescharacteristic
72C2×C11×D8C2×C411yescharacteristic
73C11×C4⋊Q8C2×C411yescharacteristic
74C11×#127C2×C411yescharacteristic
75C11×#124—21no—
76C11×#121—21no—
77C11×#121C2×C411yescharacteristic
78C11×#121C2×C411yescharacteristic
79C4×Q8×C11C2×C411yescharacteristic
80C4×Q8×C11C2311yescharacteristic
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C4×D4×C11—21no—
84C4×D4×C11C2×C411yescharacteristic
85C4×D4×C11C2311yescharacteristic
86C4×D4×C11C2311yescharacteristic
87C4×D4×C11C2311yescharacteristic
88C11×#117—21no—
89C11×#117C2×C411yescharacteristic
90C2×C42×C11—21no—
91C2×C42×C11C2311yescharacteristic
92C2×#4318—21no—
93C2×#4318—21no—
94C2×#4318—21no—
95C2×#4318—21no—
96C22×C11⋊C8—21no—
97C22×C11⋊C8—21no—
98C22×C11⋊C8—21no—
99C11×#107C2×C411yescharacteristic
100C11×#107C2×C411yescharacteristic
101C11×#106C2×C411yescharacteristic
102C11×#106C2×C411yescharacteristic
103C11×C4⋊C8C2×C411yescharacteristic
104C11×C4⋊C8C2×C411yescharacteristic
105C11×#103C2×C411yescharacteristic
106C11×#103C2×C411yescharacteristic
107C11×#102C2×C411yescharacteristic
108C11×#102C2×C411yescharacteristic
109C11×#102C2×C411yescharacteristic
110C11×#102C2×C411yescharacteristic
111C11×#102C2×C411yescharacteristic
112C11×#102C2×C411yescharacteristic
113C11×C22⋊C8C2×C411yescharacteristic
114C11×C22⋊C8C2×C411yescharacteristic
115C4×C8×C11C2311yescharacteristic
116C4×C8×C11C2311yescharacteristic
117C22⋊(C11⋊C8)—21no—
118C22⋊(C11⋊C8)—21no—
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121C22⋊(C11⋊C8)—21no—
122C22⋊(C11⋊C8)—21no—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)—21no—
125C22⋊(C11⋊C8)D411yescharacteristic
126C22⋊(C11⋊C8)D411yescharacteristic
127C4⋊(C11⋊C8)—21no—
128C4⋊(C11⋊C8)—21no—
129C4⋊(C11⋊C8)—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)D411yescharacteristic
132C4⋊(C11⋊C8)D411yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135C4⋊(C11⋊C8)C2311yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137#66867—21no—
138#66867—21no—
139#66867—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17948—111nomaximal, Sylow
145C11×#41—41no—
146C11×#41—41no—
147C11×#41—81no—
148C11×#41—81no—
149C2×Q8×C11—21no—
150C2×Q8×C11C22×C411yescharacteristic
151C2×D4×C11—21no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11C22×C411yescharacteristic
157C2×D4×C11C22×C411yescharacteristic
158C2×D4×C11C22×C411yescharacteristic
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11C22×C411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11#4111yescharacteristic
167C11×SD16—41no—
168C11×SD16—41no—
169C11×D8—41no—
170C11×D8—41no—
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C22×C411yescharacteristic
173C2×C8×C11C22×C411yescharacteristic
174C2×C8×C11C22×C411yescharacteristic
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C22×C411yescharacteristic
179C11×C4⋊C4C22×C411yescharacteristic
180C11×C4⋊C4C22×C411yescharacteristic
181C11×C4⋊C4C22×C411yescharacteristic
182C11×C22⋊C4—21no—
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C11×C22⋊C4—21no—
188C11×C22⋊C4—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11C22×C411yescharacteristic
193C42×C11C2×D411yescharacteristic
194C42×C11#4111yescharacteristic
195C42×C11C2411yescharacteristic
196#4318—81no—
197#4318—81no—
198#4318—81no—
199#4318—81no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—81no—
207C2×C11⋊C8—81no—
208C2×C11⋊C8—81no—
209C2×C11⋊C8C2×D411yescharacteristic
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213#3106D1111yescharacteristic
214#2989—111no—
215#2981—111no—
216#1594—111no—
217#1592—111no—
218#1590—111no—
219#1589—111no—
220#1586—111no—
221#1585—111no—
222#1582—111no—
223#1581—111no—
224#1573—111no—
225#1488—111no—
226#1480—111no—
227#1454—111no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11C4×D411yescharacteristic
232Q8×C11—21no—
233Q8×C11—21no—
234Q8×C11—81no—
235D4×C11—21no—
236D4×C11—21no—
237D4×C11—21no—
238D4×C11—21no—
239D4×C11—21no—
240D4×C11—21no—
241D4×C11—42no—
242D4×C11—81no—
243D4×C11—81no—
244D4×C11—81no—
245D4×C11—81no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—41no—
256C2×C4×C11—42no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—81no—
264C2×C4×C11C4×D411yescharacteristic
265C2×C4×C11C4×D411yescharacteristic
266C2×C4×C11C4×D411yescharacteristic
267C2×C4×C11C23×C411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C8×C11—21no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—21no—
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—21no—
278C11⋊C8—41no—
279C11⋊C8—41no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284#532C2×D1111yescharacteristic
285C4×#41C2×D1111yescharacteristic
286#482Dic1111yescharacteristic
287#482Dic1111yescharacteristic
288#477Dic1111yescharacteristic
289#476Dic1111yescharacteristic
290#460Dic1111yescharacteristic
291#459Dic1111yescharacteristic
292#449Dic1111yescharacteristic
293#449Dic1111yescharacteristic
294#446—111no—
295#446—111no—
296C4×SD16C2×D1111yescharacteristic
297C4×SD16C2×D1111yescharacteristic
298C4×D8C2×D1111yescharacteristic
299C4×D8C2×D1111yescharacteristic
300#436—111no—
301#436—111no—
302#436—111no—
303#436—111no—
304#435—221no—
305#435—221no—
306#435—221no—
307#435—221no—
308C8×D4—111no—
309C8×D4—111no—
310#432—111no—
311#432—221no—
312#431—111no—
313#431—111no—
314#431C2×D1111yescharacteristic
315#423—221no—
316C2×C4⋊C8—111no—
317#408—221no—
318#408—221no—
319#335—111no—
320#335—111no—
321#334—111no—
322#334—111no—
323Q8⋊C8—111no—
324Q8⋊C8—111no—
325D4⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331#322—111no—
332#322—111no—
333#322—111no—
334C82—111no—
335C22×C11—21no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11C2×C4×D411yescharacteristic
348C4×C11—21no—
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11#56811yescharacteristic
358C4×C11#56811yescharacteristic
359C4×C11#57611yescharacteristic
360C4×C11#57711yescharacteristic
361C2×#41—21no—
362C2×#41C2×Dic1111yescharacteristic
363C2×SD16C2×Dic1111yescharacteristic
364C2×SD16C2×Dic1111yescharacteristic
365C2×D8C2×Dic1111yescharacteristic
366C2×D8C2×Dic1111yescharacteristic
367C2×M16—221no—
368C2×M16—221no—
369C2×M16—221no—
370C2×M16—221no—
371C22×C8—221no—
372C22×C8—221no—
373C22×C8—221no—
374C4⋊Q8C2×Dic1111yescharacteristic
375#127C2×Dic1111yescharacteristic
376#124—21no—
377#121—21no—
378#121C2×Dic1111yescharacteristic
379#121C2×Dic1111yescharacteristic
380C4×Q8C2×Dic1111yescharacteristic
381C4×Q8C22×D1111yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4C2×Dic1111yescharacteristic
386C4×D4C22×D1111yescharacteristic
387C4×D4C22×D1111yescharacteristic
388C4×D4C22×D1111yescharacteristic
389#117—21no—
390#117C2×Dic1111yescharacteristic
391C2×C42—21no—
392C2×C42C22×D1111yescharacteristic
393#107C2×Dic1111yescharacteristic
394#107C2×Dic1111yescharacteristic
395#106C2×Dic1111yescharacteristic
396#106C2×Dic1111yescharacteristic
397C4⋊C8—111no—
398C4⋊C8—111no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—221no—
404C4⋊C8—221no—
405C4⋊C8—221no—
406C4⋊C8—221no—
407C4⋊C8C2×Dic1111yescharacteristic
408C4⋊C8C2×Dic1111yescharacteristic
409#103C2×Dic1111yescharacteristic
410#103C2×Dic1111yescharacteristic
411#102C2×Dic1111yescharacteristic
412#102C2×Dic1111yescharacteristic
413#102C2×Dic1111yescharacteristic
414#102C2×Dic1111yescharacteristic
415#102C2×Dic1111yescharacteristic
416#102C2×Dic1111yescharacteristic
417C22⋊C8—111no—
418C22⋊C8—111no—
419C22⋊C8—221no—
420C22⋊C8—221no—
421C22⋊C8—221no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8C2×Dic1111yescharacteristic
428C22⋊C8C2×Dic1111yescharacteristic
429#97—221no—
430#97—221no—
431#97—221no—
432C4×C8—111no—
433C4×C8—111no—
434C4×C8—111no—
435C4×C8—111no—
436C4×C8C22×D1111yescharacteristic
437C4×C8C22×D1111yescharacteristic
438C2×C11—41no—
439C2×C11—81no—
440C2×C11—81no—
441C2×C11—81no—
442C2×C11#293011yescharacteristic
443C2×C11#294611yescharacteristic
444C2×C11#295711yescharacteristic
445#41—41no—
446#41—41no—
447#41—81no—
448#41—81no—
449C2×Q8—21no—
450C2×Q8C22×Dic1111yescharacteristic
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4C22×Dic1111yescharacteristic
457C2×D4C22×Dic1111yescharacteristic
458C2×D4C22×Dic1111yescharacteristic
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4D4×D1111yescharacteristic
465C22×C4#434111yescharacteristic
466C22×C4C22×Dic1111yescharacteristic
467SD16—41no—
468SD16—41no—
469D8—41no—
470D8—41no—
471M16—881no—
472M16—881no—
473M16—881no—
474M16—881no—
475C2×C8—111no—
476C2×C8—111no—
477C2×C8—111no—
478C2×C8—111no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—881no—
486C2×C8—881no—
487C2×C8—881no—
488C2×C8C22×Dic1111yescharacteristic
489C2×C8C22×Dic1111yescharacteristic
490C2×C8C22×Dic1111yescharacteristic
491C2×C8C22×Dic1111yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4C22×Dic1111yescharacteristic
496C4⋊C4C22×Dic1111yescharacteristic
497C4⋊C4C22×Dic1111yescharacteristic
498C4⋊C4C22×Dic1111yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42D4×D1111yescharacteristic
510C42#434111yescharacteristic
511C42C22×Dic1111yescharacteristic
512C42C23×D1111yescharacteristic
513C11#1794811yescharacteristic, complemented, Sylow
514C23—21no—
515C23—21no—
516C23—21no—
517C23D4×Dic1111yescharacteristic
518Q8—21no—
519Q8—21no—
520Q8—81no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—42no—
528D4—81no—
529D4—81no—
530D4—81no—
531D4—81no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—81no—
550C2×C4D4×Dic1111yescharacteristic
551C2×C4D4×Dic1111yescharacteristic
552C2×C4D4×Dic1111yescharacteristic
553C2×C4C2×D4×D1111yescharacteristic
554C2×C4C2×#434111yescharacteristic
555C2×C4C23×Dic1111yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—221no—
561C8—221no—
562C8—221no—
563C8—221no—
564C8—441no—
565C8—441no—
566C8—441no—
567C8—441no—
568C8—441no—
569C8—441no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22C2×D4×Dic1111yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4#1062330511yescharacteristic
593C4#1062330611yescharacteristic
594C4#1062335011yescharacteristic
595C4#1062335011yescharacteristic
596C2—41no—
597C2—81no—
598C2—81no—
599C2—81no—
600C2#1307732011yescharacteristic
601C2#1307744911yescharacteristic
602C2#1307753311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
Fitting, prime radicalC11×#3106C2
socleC22×C11C2×C4×D4
cosocleC42×C11C24
hypercenter#3106D11
hypocenterC11#17948
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. #13077733C2semidirect
2. #13077692C2semidirect
3. #13067530C2semidirect
4. #13067519C2semidirect
5. #13067507C2semidirect
6. #13067501C2semidirect
7. #13067481C2semidirect
8. #13067474C2semidirect
9. #13067453C2semidirect
10. #13067446C2semidirect
11. #13067401C2semidirect
12. #13067050C2semidirect
13. #13067015C2semidirect
14. #13066916C2semidirect
513. C11#17948semidirect

Maximal subgroups

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

subgroupindex
#130777332
#130776922
#130675302
#130675192
#130675072
#130675012
#130674812
#130674742
#130674532
#130674462
#130674012
#130670502
#130670152
#130669162
C11×#31062
#1794811