Finite Group Databasebeta

← #14723839

Subgroups — #14723839

Order 2816.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078659C211yesmaximal, characteristic
2#13077765C211yesmaximal, characteristic, complemented
3#13077639C211yesmaximal, characteristic, complemented
4#13067483C211yesmaximal, characteristic, complemented
5#13067476C211yesmaximal, characteristic, complemented
6#13067455C211yesmaximal, characteristic, complemented
7#13067448C211yesmaximal, characteristic, complemented
8#13067437C211yesmaximal, characteristic, complemented
9#13067431C211yesmaximal, characteristic, complemented
10#13067413C211yesmaximal, characteristic, complemented
11#13067408C211yesmaximal, characteristic, complemented
12#13067404C211yesmaximal, characteristic, complemented
13#13067042C211yesmaximal, characteristic, complemented
14#13066916C211yesmaximal, characteristic, complemented
15C11×#1482C211yesmaximal, characteristic, complemented
16C11×#529C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C11×#431C2211yescharacteristic
20#10622679C411yescharacteristic
21#10622679C411yescharacteristic
22#10622670C411yescharacteristic
23#10622670C411yescharacteristic
24#10622659C411yescharacteristic
25#10622657C411yescharacteristic
26#10622649C411yescharacteristic
27#10622647C411yescharacteristic
28C4×#4325C2211yescharacteristic
29C4×#4325C2211yescharacteristic
30#10622637C2211yescharacteristic, complemented
31Q8×C11⋊C8C2211yescharacteristic, complemented
32C4×#4323C2211yescharacteristic
33C4×#4323C2211yescharacteristic
34#10622625—21no—
35#10622625C2211yescharacteristic, complemented
36#10622624—21no—
37D4×C11⋊C8C2211yescharacteristic, complemented
38#10622613—21no—
39#10622612—21no—
40#10622538C2211yescharacteristic
41#10622538C2211yescharacteristic
42#10622537C2211yescharacteristic
43#10622447C2211yescharacteristic
44#10622447C2211yescharacteristic
45#10622447C2211yescharacteristic
46#10622447C2211yescharacteristic
47D11×C22⋊C8—21no—
48D11×C22⋊C8—21no—
49C8×D44—21no—
50C8×D44—21no—
51C11×Q8⋊C8C2211yescharacteristic, complemented
52C11×Q8⋊C8C2211yescharacteristic, complemented
53C11×D4⋊C8C2211yescharacteristic, complemented
54C11×D4⋊C8C2211yescharacteristic, complemented
55#10622118C2211yescharacteristic, complemented
56#10622118C2211yescharacteristic, complemented
57#10622117C2211yescharacteristic, complemented
58#10622117C2211yescharacteristic, complemented
59#10622097C2211yescharacteristic
60#10622097C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic
63#10622093C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65#10622092C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C22×D44C2×C411yescharacteristic
68C22×C4×D11—21no—
69C11×#126—21no—
70C11×#125C2×C411yescharacteristic
71C11×#124C2×C411yescharacteristic
72C11×#123—21no—
73C11×C22⋊Q8C2×C411yescharacteristic
74C11×#121C2×C411yescharacteristic
75C4×Q8×C11C2311yescharacteristic
76C4×D4×C11—21no—
77C4×D4×C11C2311yescharacteristic
78C11×#117—21no—
79C2×C42×C11C2311yescharacteristic
80C2×#4325C2×C411yescharacteristic
81C2×#4325C2×C411yescharacteristic
82C2×#4323C2×C411yescharacteristic
83C2×#4323C2×C411yescharacteristic
84C2×(C2×D11)⋊C4—21no—
85C2×C4⋊Dic11C2×C411yescharacteristic
86C2×#4318—21no—
87C2×#4318—21no—
88C22×C11⋊C8—21no—
89C2×C8×D11—21no—
90C2×C8×D11—21no—
91C2×C8×D11—21no—
92C2×C8×D11—21no—
93C4×D44—21no—
94C4×D44—21no—
95C4×D44C2×C411yescharacteristic
96C4×D44C2×C411yescharacteristic
97C4×D44C2311yescharacteristic
98C4×D44C2311yescharacteristic
99C11×C4⋊C8—21no—
100C11×C4⋊C8C2311yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×C22⋊C8—21no—
103C11×C22⋊C8—21no—
104C4×C8×C11—21no—
105C4×C8×C11C2311yescharacteristic
106C4×C8×C11C2311yescharacteristic
107#66899C2×C411yescharacteristic
108#66899C2×C411yescharacteristic
109#66896C2×C411yescharacteristic
110#66896C2×C411yescharacteristic
111C22⋊(C11⋊C8)—21no—
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)C2×C411yescharacteristic
114C22⋊(C11⋊C8)C2×C411yescharacteristic
115C22⋊(C11⋊C8)D411yescharacteristic
116C22⋊(C11⋊C8)D411yescharacteristic
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121#66873C2×C411yescharacteristic
122#66873C2×C411yescharacteristic
123#66873C2×C411yescharacteristic
124#66873C2×C411yescharacteristic
125#66872C2×C411yescharacteristic
126#66872C2×C411yescharacteristic
127#66871C2×C411yescharacteristic
128#66871C2×C411yescharacteristic
129C4⋊(C11⋊C8)—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)—21no—
132C4⋊(C11⋊C8)C2×C411yescharacteristic
133C4⋊(C11⋊C8)C2×C411yescharacteristic
134C4⋊(C11⋊C8)D411yescharacteristic
135C4⋊(C11⋊C8)D411yescharacteristic
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138#66867—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#17918—111nomaximal, Sylow
145C23×D11—21no—
146C2×Q8×C11C22×C411yescharacteristic
147C2×D4×C11—21no—
148C2×D4×C11C22×C411yescharacteristic
149C22×C4×C11—21no—
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11#4111yescharacteristic
153C22×Dic11—21no—
154C2×D44—22no—
155C2×D44—22no—
156C2×D44—21no—
157C2×D44C22×C411yescharacteristic
158C2×D44C22×C411yescharacteristic
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—81no—
164C2×C4×D11—81no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4C22×C411yescharacteristic
174C11×C4⋊C4C22×C411yescharacteristic
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C42×C11—21no—
181C42×C11C22×C411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11#4111yescharacteristic
184C42×C11C2411yescharacteristic
185#4325—22no—
186#4325—22no—
187#4323—22no—
188#4323—22no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191(C2×D11)⋊C4—21no—
192(C2×D11)⋊C4—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11C22×C411yescharacteristic
195C4⋊Dic11C22×C411yescharacteristic
196#4318—81no—
197#4318—81no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—81no—
201C2×C11⋊C8C22×C411yescharacteristic
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C8×D11—81no—
210C8×D11—81no—
211C8×D11—81no—
212C8×D11—81no—
213#3105—111no—
214#2993—111no—
215#2972—111no—
216#1586—111no—
217#1585—111no—
218#1582—111no—
219#1581—111no—
220#1580—111no—
221SD16⋊C8—111no—
222C8×SD16—111no—
223C8×D8—111no—
224#1574—111no—
225#1486—111no—
226#1482D1111yescharacteristic, complemented
227#1454—111no—
228C23×C11—21no—
229C23×C11C4×D411yescharacteristic
230C22×D11—21no—
231C22×D11—21no—
232C22×D11—24no—
233C22×D11—81no—
234C22×D11—81no—
235Q8×C11—21no—
236Q8×C11—21no—
237D4×C11—21no—
238D4×C11—21no—
239D4×C11—81no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11C4×D411yescharacteristic
251C2×C4×C11C4×D411yescharacteristic
252C2×C4×C11C4×D411yescharacteristic
253C2×C4×C11C23×C411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—81no—
259D44—24no—
260D44—21no—
261D44—21no—
262D44#13112yes—
263D44#13112yes—
264C4×D11—41no—
265C4×D11—41no—
266C4×D11—41no—
267C4×D11—41no—
268C4×D11—81no—
269C4×D11—81no—
270C8×C11—41no—
271C8×C11—41no—
272C8×C11—41no—
273C8×C11—41no—
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—21no—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284#529C2×D1111yescharacteristic
285C2×C4×D4—111no—
286#484—111no—
287#481—111no—
288#478—111no—
289#478—111no—
290#463—111no—
291#463—111no—
292#450—111no—
293#447—111no—
294#446—111no—
295C8×Q8—111no—
296C4×SD16—111no—
297C4×SD16—111no—
298C4×D8—111no—
299C4×D8—111no—
300#436—111no—
301#436—221no—
302#435—221no—
303C8×D4—111no—
304C8×D4—111no—
305C8×D4—111no—
306C8×D4—111no—
307C8×D4—111no—
308C8×D4—221no—
309C8×D4—221no—
310#433—221no—
311#431—111no—
312#431—111no—
313#431C2×D1111yescharacteristic
314#431C2×D1111yescharacteristic
315#424—221no—
316#423—111no—
317C2×C22⋊C8—221no—
318C2×C22⋊C8—221no—
319#335—111no—
320#335—111no—
321#334—111no—
322#334—111no—
323Q8⋊C8C2×D1111yescharacteristic, complemented
324Q8⋊C8C2×D1111yescharacteristic, complemented
325D4⋊C8—111no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8C2×D1111yescharacteristic, complemented
330D4⋊C8C2×D1111yescharacteristic, complemented
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×C11C2×C4×D411yescharacteristic
342C2×D11—22no—
343C2×D11—22no—
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—84no—
349C4×C11—21no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11C2×#13111yescharacteristic
357C4×C11C2×#13111yescharacteristic
358C4×C11#57611yescharacteristic
359C4×C11#57711yescharacteristic
360Dic11—41no—
361Dic11—41no—
362C22×D4—111no—
363C23×C4—221no—
364C2×SD16—111no—
365C2×SD16—111no—
366C2×D8—111no—
367C2×D8—111no—
368C2×M16—221no—
369C2×M16—221no—
370C22×C8—221no—
371C22×C8—221no—
372C22×C8—221no—
373C22×C8—221no—
374C22×C8—221no—
375#126—21no—
376#125C4×D1111yescharacteristic
377#124C4×D1111yescharacteristic
378#123—21no—
379C22⋊Q8C4×D1111yescharacteristic
380#121C4×D1111yescharacteristic
381C4×Q8C22×D1111yescharacteristic
382C4×D4—21no—
383C4×D4—111no—
384C4×D4—111no—
385C4×D4—111no—
386C4×D4—111no—
387C4×D4—221no—
388C4×D4—221no—
389C4×D4C22×D1111yescharacteristic
390#117—21no—
391C2×C4⋊C4—111no—
392C2×C22⋊C4—221no—
393C2×C42C22×D1111yescharacteristic
394#107—111no—
395#107—111no—
396#106—111no—
397#106—111no—
398C4⋊C8—21no—
399C4⋊C8—111no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—111no—
404C4⋊C8—111no—
405C4⋊C8—221no—
406C4⋊C8—221no—
407C4⋊C8—221no—
408C4⋊C8C22×D1111yescharacteristic
409C4⋊C8C22×D1111yescharacteristic
410#103—111no—
411#103—111no—
412#102—111no—
413#102—111no—
414#102—111no—
415#102—111no—
416#102—111no—
417#102—111no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—111no—
421C22⋊C8—111no—
422C22⋊C8—111no—
423C22⋊C8—111no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428C22⋊C8—221no—
429C22⋊C8—221no—
430#97—221no—
431C4×C8—21no—
432C4×C8—111no—
433C4×C8—111no—
434C4×C8—111no—
435C4×C8—111no—
436C4×C8—221no—
437C4×C8C22×D1111yescharacteristic
438C4×C8C22×D1111yescharacteristic
439C2×C11—41no—
440C2×C11—81no—
441C2×C11#292911yescharacteristic
442C2×C11#294611yescharacteristic
443C2×C11#295711yescharacteristic
444D11—42no—
445D11—42no—
446C24—221no—
447C2×Q8C2×C4×D1111yescharacteristic
448C2×D4—21no—
449C2×D4—111no—
450C2×D4—111no—
451C2×D4—222no—
452C2×D4—222no—
453C2×D4—221no—
454C2×D4C2×C4×D1111yescharacteristic
455C22×C4—21no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—881no—
462C22×C4—881no—
463C22×C4C2×C4×D1111yescharacteristic
464C22×C4D4×D1111yescharacteristic
465C22×C4#434111yescharacteristic
466SD16—222no—
467SD16—222no—
468D8—222no—
469D8—222no—
470M16—881no—
471M16—881no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—111no—
477C2×C8—111no—
478C2×C8—111no—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—111no—
482C2×C8—111no—
483C2×C8—111no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—881no—
487C2×C8—881no—
488C2×C8—881no—
489C2×C8—881no—
490C2×C8—881no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—111no—
496C4⋊C4—111no—
497C4⋊C4—221no—
498C4⋊C4C2×C4×D1111yescharacteristic
499C4⋊C4C2×C4×D1111yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—221no—
506C22⋊C4—221no—
507C22⋊C4—221no—
508C22⋊C4—221no—
509C42—21no—
510C42C2×C4×D1111yescharacteristic
511C42D4×D1111yescharacteristic
512C42#434111yescharacteristic
513C42C23×D1111yescharacteristic
514C11#1791811yescharacteristic, complemented, Sylow
515C23—21no—
516C23—224no—
517C23—221no—
518C23—221no—
519C23—881no—
520C23—881no—
521C23(C22⋊D11)⋊C411yescharacteristic
522Q8—21no—
523Q8—21no—
524D4—21no—
525D4—21no—
526D4—81no—
527D4—112no—
528D4—112no—
529D4—224no—
530D4—221no—
531D4—221no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—881no—
549C2×C4—881no—
550C2×C4—881no—
551C2×C4(C22⋊D11)⋊C411yescharacteristic
552C2×C4(C22⋊D11)⋊C411yescharacteristic
553C2×C4(C22⋊D11)⋊C411yescharacteristic
554C2×C4C22×C4×D1111yescharacteristic
555C2×C4C2×D4×D1111yescharacteristic
556C2×C4C2×#434111yescharacteristic
557C8—41no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—221no—
562C8—221no—
563C8—221no—
564C8—221no—
565C8—221no—
566C8—221no—
567C8—221no—
568C8—221no—
569C8—441no—
570C8—441no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—222no—
578C22—222no—
579C22—441no—
580C22—441no—
581C22—441no—
582C22—441no—
583C22—884no—
584C22C2×(C22⋊D11)⋊C411yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—441no—
593C4—441no—
594C4D11×#13111yescharacteristic
595C4D11×#13111yescharacteristic
596C4#1062330011yescharacteristic
597C4#1062330111yescharacteristic
598C2—41no—
599C2—81no—
600C2—442no—
601C2—442no—
602C2#1307731311yescharacteristic
603C2#1307745111yescharacteristic
604C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1482C2
socleC22×C11C2×C4×D4
prime radical#10622649C4
cosocleC42×C11C24
hypercenter#1482D11
hypocenterC11#17918
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1482

Complements

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

NH ≅ G/Ntype
2. #13077765C2semidirect
3. #13077639C2semidirect
4. #13067483C2semidirect
5. #13067476C2semidirect
6. #13067455C2semidirect
7. #13067448C2semidirect
8. #13067437C2semidirect
9. #13067431C2semidirect
10. #13067413C2semidirect
11. #13067408C2semidirect
12. #13067404C2semidirect
13. #13067042C2semidirect
14. #13066916C2semidirect
15. C11×#1482C2semidirect
30. #10622637C22semidirect
31. Q8×C11⋊C8C22semidirect
35. #10622625C22semidirect
37. D4×C11⋊C8C22semidirect
51. C11×Q8⋊C8C22semidirect
52. C11×Q8⋊C8C22semidirect
53. C11×D4⋊C8C22semidirect
54. C11×D4⋊C8C22semidirect
55. #10622118C22semidirect
56. #10622118C22semidirect
57. #10622117C22semidirect
58. #10622117C22semidirect
63. #10622093C22semidirect
64. #10622092C22semidirect
65. #10622092C22semidirect
66. C8×C11⋊C8C22semidirect
226. #1482D11semidirect
323. Q8⋊C8C2×D11semidirect
324. Q8⋊C8C2×D11semidirect
329. D4⋊C8C2×D11semidirect
330. D4⋊C8C2×D11semidirect
514. C11#17918semidirect

Maximal subgroups

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

subgroupindex
#130786592
#130777652
#130776392
#130674832
#130674762
#130674552
#130674482
#130674372
#130674312
#130674132
#130674082
#130674042
#130670422
#130669162
C11×#14822
#1791811