Finite Group Databasebeta

← #14724935

Subgroups — #14724935

Order 2816.

650 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078659C211yesmaximal, characteristic
2#13077776C211yesmaximal, characteristic, complemented
3#13077653C211yesmaximal, characteristic, complemented
4#13067503C211yesmaximal, characteristic, complemented
5#13067498C211yesmaximal, characteristic, complemented
6#13067491C211yesmaximal, characteristic, complemented
7#13067483C211yesmaximal, characteristic, complemented
8#13067477C211yesmaximal, characteristic, complemented
9#13067476C211yesmaximal, characteristic, complemented
10#13067413C211yesmaximal, characteristic, complemented
11#13067408C211yesmaximal, characteristic, complemented
12#13067402C211yesmaximal, characteristic, complemented
13C2×#10622097C211yesmaximal, characteristic, complemented
14#13066899C211yesmaximal, characteristic, complemented
15C11×#1494C211yesmaximal, characteristic, complemented
16C11×#529C2211yescharacteristic
17C2×C4×D44C2211yescharacteristic
18C11×#432C2211yescharacteristic
19C2×C4×C8×C11C2211yescharacteristic
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#10622625C2211yescharacteristic, complemented
35#10622624—21no—
36D4×C11⋊C8—21no—
37D4×C11⋊C8C2211yescharacteristic, complemented
38#10622613—21no—
39#10622612—21no—
40#10622538C2211yescharacteristic
41#10622538C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43#10622451C2211yescharacteristic
44#10622451C2211yescharacteristic
45#10622447C2211yescharacteristic
46#10622447C2211yescharacteristic
47#10622339—21no—
48D11×C22⋊C8—21no—
49#10622319—21no—
50#10622319—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#10622093C2211yescharacteristic, complemented
65C8×C11⋊C8C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, complemented
67C22×D44C2×C411yescharacteristic
68C22×C4×D11—21no—
69C22×C8×C11—21no—
70C11×#126—21no—
71C11×#125C2×C411yescharacteristic
72C11×#124C2×C411yescharacteristic
73C11×#123—21no—
74C11×C22⋊Q8C2×C411yescharacteristic
75C11×#121C2×C411yescharacteristic
76C4×Q8×C11C2311yescharacteristic
77C4×D4×C11—21no—
78C4×D4×C11C2311yescharacteristic
79C11×#117—21no—
80C2×C42×C11C2311yescharacteristic
81C2×#4325C2×C411yescharacteristic
82C2×#4325C2×C411yescharacteristic
83C2×#4323C2×C411yescharacteristic
84C2×#4323C2×C411yescharacteristic
85C2×(C2×D11)⋊C4—21no—
86C2×C4⋊Dic11C2×C411yescharacteristic
87C2×#4318—21no—
88C22×C11⋊C8—21no—
89C22×C11⋊C8—21no—
90C2×#4313—21no—
91C2×#4313—21no—
92C2×C8×D11—21no—
93C2×C8×D11—21no—
94C4×D44—21no—
95C4×D44—21no—
96C4×D44C2×C411yescharacteristic
97C4×D44C2×C411yescharacteristic
98C4×D44C2311yescharacteristic
99C4×D44C2311yescharacteristic
100C11×C4⋊C8C2311yescharacteristic
101C11×C4⋊C8C2311yescharacteristic
102C11×C22⋊C8—21no—
103C11×#97—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#18014—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—21no—
156C2×D44—41no—
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—24no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4C22×C411yescharacteristic
175C11×C4⋊C4C22×C411yescharacteristic
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C42×C11—21no—
182C42×C11C22×C411yescharacteristic
183C42×C11C2×D411yescharacteristic
184C42×C11#4111yescharacteristic
185C42×C11C2411yescharacteristic
186#4325—22no—
187#4325—41no—
188#4323—22no—
189#4323—41no—
190(C2×D11)⋊C4—21no—
191(C2×D11)⋊C4—21no—
192(C2×D11)⋊C4—21no—
193(C2×D11)⋊C4—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11C22×C411yescharacteristic
196C4⋊Dic11C22×C411yescharacteristic
197#4318—81no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—81no—
201C2×C11⋊C8—81no—
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C22×C411yescharacteristic
205C2×C11⋊C8C22×C411yescharacteristic
206C2×C11⋊C8C2×D411yescharacteristic
207C2×C11⋊C8C2×D411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210#4313—81no—
211#4313—81no—
212C8×D11—81no—
213C8×D11—81no—
214#3105—111no—
215#2994—111no—
216#2974—111no—
217#1590—111no—
218#1589—111no—
219#1588—111no—
220#1586—111no—
221#1586—111no—
222#1585—111no—
223C8×SD16—111no—
224C8×D8—111no—
225#1573—111no—
226#1494D1111yescharacteristic, complemented
227C2×D4⋊C8—111no—
228#1450—111no—
229C23×C11—21no—
230C23×C11C4×D411yescharacteristic
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—42no—
234C22×D11—42no—
235C22×D11—81no—
236Q8×C11—21no—
237Q8×C11—21no—
238D4×C11—21no—
239D4×C11—21no—
240D4×C11—42no—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11C4×D411yescharacteristic
252C2×C4×C11C4×D411yescharacteristic
253C2×C4×C11C4×D411yescharacteristic
254C2×C4×C11C23×C411yescharacteristic
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—81no—
260D44—21no—
261D44—21no—
262D44—21no—
263D44—42no—
264D44#13112yes—
265C4×D11—41no—
266C4×D11—41no—
267C4×D11—41no—
268C4×D11—41no—
269C4×D11—81no—
270C4×D11—81no—
271C8×C11—22no—
272C8×C11—22no—
273C8×C11—41no—
274C8×C11—41no—
275C11⋊C8—21no—
276C11⋊C8—21no—
277C11⋊C8—21no—
278C11⋊C8—21no—
279C11⋊C8—21no—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—21no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285#529C2×D1111yescharacteristic
286C2×C4×D4—111no—
287#484—111no—
288#481—111no—
289#478—111no—
290#478—111no—
291#463—111no—
292#463—111no—
293#450—111no—
294#447—111no—
295#446—111no—
296C8×Q8—111no—
297C4×SD16—111no—
298C4×SD16—111no—
299C4×D8—111no—
300C4×D8—111no—
301#436—111no—
302#436—111no—
303#436—111no—
304#435—221no—
305#435—221no—
306#435—221no—
307C8×D4—111no—
308C8×D4—111no—
309C8×D4—111no—
310C8×D4—221no—
311#433—221no—
312#432C2×D1111yescharacteristic
313#431—111no—
314#431—111no—
315#424—221no—
316C2×C4⋊C8—111no—
317#407—221no—
318C2×C22⋊C8—221no—
319C2×C4×C8C2×D1111yescharacteristic
320#335—111no—
321#335—111no—
322#334—111no—
323#334—111no—
324Q8⋊C8C2×D1111yescharacteristic, complemented
325Q8⋊C8C2×D1111yescharacteristic, complemented
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8C2×D1111yescharacteristic, complemented
331D4⋊C8C2×D1111yescharacteristic, complemented
332#322—111no—
333#322—111no—
334C82—111no—
335C82—111no—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11#44312yes—
342C22×C11C2×C4×D411yescharacteristic
343C2×D11—22no—
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—84no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—41no—
357C4×C11C2×#13111yescharacteristic
358C4×C11#56811yescharacteristic
359C4×C11#57611yescharacteristic
360C4×C11#57711yescharacteristic
361Dic11—41no—
362Dic11—41no—
363C22×D4—111no—
364C23×C4—221no—
365C2×SD16—111no—
366C2×SD16—111no—
367C2×D8—111no—
368C2×D8—111no—
369C2×M16—221no—
370C2×M16—221no—
371C2×M16—221no—
372C22×C8—21no—
373C22×C8—221no—
374C22×C8—221no—
375C22×C8—221no—
376C22×C8—221no—
377#126—21no—
378#125C4×D1111yescharacteristic
379#124C4×D1111yescharacteristic
380#123—21no—
381C22⋊Q8C4×D1111yescharacteristic
382#121C4×D1111yescharacteristic
383C4×Q8C22×D1111yescharacteristic
384C4×D4—21no—
385C4×D4—111no—
386C4×D4—111no—
387C4×D4—111no—
388C4×D4—111no—
389C4×D4—221no—
390C4×D4—221no—
391C4×D4C22×D1111yescharacteristic
392#117—21no—
393C2×C4⋊C4—111no—
394C2×C22⋊C4—221no—
395C2×C42C22×D1111yescharacteristic
396#107—111no—
397#107—111no—
398#106—111no—
399#106—111no—
400C4⋊C8—111no—
401C4⋊C8—111no—
402C4⋊C8—111no—
403C4⋊C8—111no—
404C4⋊C8—111no—
405C4⋊C8—111no—
406C4⋊C8—221no—
407C4⋊C8—221no—
408C4⋊C8—221no—
409C4⋊C8C22×D1111yescharacteristic
410C4⋊C8C22×D1111yescharacteristic
411#103—111no—
412#103—111no—
413#102—111no—
414#102—111no—
415#102—111no—
416#102—111no—
417#102—111no—
418#102—111no—
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—21no—
431#97—221no—
432C4×C8—21no—
433C4×C8—111no—
434C4×C8—111no—
435C4×C8—111no—
436C4×C8—111no—
437C4×C8—221no—
438C4×C8C22×D1111yescharacteristic
439C4×C8C22×D1111yescharacteristic
440C2×C11—22no—
441C2×C11—81no—
442C2×C11#293311yescharacteristic
443C2×C11#294611yescharacteristic
444C2×C11C2×#44311yescharacteristic
445D11—42no—
446D11—81no—
447C24—221no—
448C2×Q8C2×C4×D1111yescharacteristic
449C2×D4—21no—
450C2×D4—111no—
451C2×D4—111no—
452C2×D4—222no—
453C2×D4—221no—
454C2×D4—441no—
455C2×D4C2×C4×D1111yescharacteristic
456C22×C4—21no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—881no—
463C22×C4—881no—
464C22×C4C2×C4×D1111yescharacteristic
465C22×C4D4×D1111yescharacteristic
466C22×C4#434111yescharacteristic
467SD16—222no—
468SD16—441no—
469D8—222no—
470D8—441no—
471M16—881no—
472M16—881no—
473M16—881no—
474C2×C8—24no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—111no—
482C2×C8—111no—
483C2×C8—111no—
484C2×C8—111no—
485C2×C8—111no—
486C2×C8—111no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—881no—
490C2×C8—881no—
491C2×C8—881no—
492C2×C8—881no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—111no—
498C4⋊C4—111no—
499C4⋊C4—221no—
500C4⋊C4C2×C4×D1111yescharacteristic
501C4⋊C4C2×C4×D1111yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—221no—
508C22⋊C4—221no—
509C22⋊C4—221no—
510C22⋊C4—221no—
511C42—21no—
512C42C2×C4×D1111yescharacteristic
513C42D4×D1111yescharacteristic
514C42#434111yescharacteristic
515C42C23×D1111yescharacteristic
516C11#1801411yescharacteristic, complemented, Sylow
517C23—21no—
518C23—221no—
519C23—221no—
520C23—442no—
521C23—442no—
522C23—881no—
523C23(C22⋊D11)⋊C411yescharacteristic
524Q8—21no—
525Q8—21no—
526D4—21no—
527D4—21no—
528D4—42no—
529D4—112no—
530D4—221no—
531D4—221no—
532D4—221no—
533D4—442no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—881no—
551C2×C4—881no—
552C2×C4—881no—
553C2×C4(C22⋊D11)⋊C411yescharacteristic
554C2×C4(C22⋊D11)⋊C411yescharacteristic
555C2×C4(C22⋊D11)⋊C411yescharacteristic
556C2×C4C22×C4×D1111yescharacteristic
557C2×C4C2×D4×D1111yescharacteristic
558C2×C4C2×#434111yescharacteristic
559C8—22no—
560C8—22no—
561C8—41no—
562C8—41no—
563C8—221no—
564C8—221no—
565C8—221no—
566C8—221no—
567C8—221no—
568C8—221no—
569C8—221no—
570C8—221no—
571C8—441no—
572C8—441no—
573C22—21no—
574C22—21no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—222no—
579C22—441no—
580C22—441no—
581C22—441no—
582C22—441no—
583C22—441no—
584C22—884no—
585C22#1062243712yes—
586C22C2×(C22⋊D11)⋊C411yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—441no—
595C4—441no—
596C4D11×#13111yescharacteristic
597C4#1062328111yescharacteristic
598C4#1062330011yescharacteristic
599C4#1062330111yescharacteristic
600C2—22no—
601C2—81no—
602C2—442no—
603C2—881no—
604C2#1307734611yescharacteristic
605C2#1307745111yescharacteristic
606C2C2×#1062243711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1494C2
socleC22×C11C2×C4×D4
prime radical#10622649C4
cosocleC42×C11C24
hypercenter#1494D11
hypocenterC11#18014
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
2. #13077776C2semidirect
3. #13077653C2semidirect
4. #13067503C2semidirect
5. #13067498C2semidirect
6. #13067491C2semidirect
7. #13067483C2semidirect
8. #13067477C2semidirect
9. #13067476C2semidirect
10. #13067413C2semidirect
11. #13067408C2semidirect
12. #13067402C2semidirect
13. C2×#10622097C2semidirect
14. #13066899C2semidirect
15. C11×#1494C2semidirect
30. #10622637C22semidirect
31. Q8×C11⋊C8C22semidirect
34. #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. #10622093C22semidirect
65. C8×C11⋊C8C22semidirect
66. C8×C11⋊C8C22semidirect
226. #1494D11semidirect
324. Q8⋊C8C2×D11semidirect
325. Q8⋊C8C2×D11semidirect
330. D4⋊C8C2×D11semidirect
331. D4⋊C8C2×D11semidirect
516. C11#18014semidirect

Maximal subgroups

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

subgroupindex
#130786592
#130777762
#130776532
#130675032
#130674982
#130674912
#130674832
#130674772
#130674762
#130674132
#130674082
#130674022
C2×#106220972
#130668992
C11×#14942
#1801411