Finite Group Databasebeta

← #14822158

Subgroups — #14822158

Order 2816.

854 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072979C211yesmaximal, characteristic, complemented
2#13069926C211yesmaximal, characteristic, complemented
3#13069802C211yesmaximal, characteristic, complemented
4#13069752C211yesmaximal, characteristic, complemented
5#13069612C211yesmaximal, characteristic
6#13069568C211yesmaximal, characteristic, complemented
7#13069312C211yesmaximal, characteristic, complemented
8#13069243C211yesmaximal, characteristic, complemented
9#13069231C211yesmaximal, characteristic, complemented
10#13069191C211yesmaximal, characteristic, complemented
11#13068964C211yesmaximal, characteristic, complemented
12#13068938C211yesmaximal, characteristic, complemented
13#13068711C211yesmaximal, characteristic, complemented
14#13068441C211yesmaximal, characteristic, complemented
15C11×#2363C211yesmaximal, characteristic, complemented
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×#4323C2211yescharacteristic
20C2×#66983C2211yescharacteristic
21C2×#66938—21no—
22C2×#66922C2211yescharacteristic
23C11×#390—21no—
24C11×#390C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#388—21no—
27C11×#386—21no—
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C22⋊C4—21no—
30C4×C11×C22⋊C4C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34#10622825C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41#10622574—21no—
42#10622552C2211yescharacteristic
43#10622552C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47#10622286—21no—
48#10622283—21no—
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C22×D44C2311yescharacteristic
65C22×Dic22—21no—
66C11×#121—22no—
67C11×#121—22no—
68C4×D4×C11—22no—
69C4×D4×C11—41no—
70C11×#117—22no—
71C11×#117—41no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11—21no—
88C2×#4323—22no—
89C2×#4323—41no—
90C2×#4323—41no—
91#66983—22no—
92#66983—41no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4×Dic11—21no—
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107#66938—44no—
108#66922—22no—
109#66922—41no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95D411yescharacteristic
113C11×#95D411yescharacteristic
114#66896—22no—
115#66896—22no—
116#66896—41no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C22⋊(C11⋊C8)—41no—
120C22⋊(C11⋊C8)—41no—
121#66873—22no—
122#66873—22no—
123#66873—41no—
124#66872—22no—
125C4⋊(C11⋊C8)—41no—
126#66867—41no—
127#26744—111nomaximal, Sylow
128C24×C11—21no—
129C24×C11C2×D411yescharacteristic
130C23×D11—21no—
131C2×D4×C11—24no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—81no—
138C2×D4×C11—81no—
139C2×D4×C11#4112yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—81no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C2×C22⋊D11—42no—
159C2×C22⋊D11—42no—
160C2×C22⋊D11—81no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—21no—
170C2×Dic22—42no—
171C2×Dic22—42no—
172C2×Dic22—81no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—81no—
178C11×C4⋊C4#4112yes—
179C11×C4⋊C4#4112yes—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—41no—
183C11×C22⋊C4—42no—
184C11×C22⋊C4—42no—
185C11×C22⋊C4—42no—
186C11×C22⋊C4—81no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—42no—
192C42×C11—81no—
193C22⋊Dic11—42no—
194#4323—44no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—42no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—81no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—42no—
206C4⋊Dic11#4112yes—
207C4×Dic11—42no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220#2491—111no—
221#2363D1111yescharacteristic, complemented
222#2054—111no—
223#2034—111no—
224#2023—111no—
225#1999—111no—
226#1988—111no—
227#1936—111no—
228#1926—111no—
229#1924—111no—
230#1919—111no—
231#1879—111no—
232#1875—111no—
233#1825—111no—
234#1762—111no—
235C23×C11—22no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11C22×D411yescharacteristic
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11—41no—
257D4×C11—22no—
258D4×C11—22no—
259D4×C11—41no—
260D4×C11—41no—
261D4×C11—84no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—22no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—22no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—84no—
290C2×C4×C11AGL(1,ℤ/8)12yes—
291C2×C4×C11C2×#4111yescharacteristic
292C2×C4×C11C2×#4111yescharacteristic
293C2×C4×C11C2×#4111yescharacteristic
294C2×C4×C11C2×#4111yescharacteristic
295C2×C4×C11H(5,𝔽2)11yescharacteristic
296C2×C4×C11H(5,𝔽2)11yescharacteristic
297C22⋊D11—84no—
298C2×Dic11—22no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307D44—41no—
308D44—41no—
309D44—41no—
310D44—41no—
311Dic22—84no—
312C11⋊C8—41no—
313C11⋊C8—41no—
314C11⋊C8—41no—
315C11⋊C8—41no—
316C22×D8—111no—
317C2×C4⋊Q8—111no—
318C2×#124—221no—
319C2×#121—111no—
320C2×#121C2×D1111yescharacteristic
321C2×C4×D4C2×D1111yescharacteristic
322C2×#117C2×D1111yescharacteristic
323C2×#106—111no—
324C2×C4⋊C8—111no—
325C2×#102—111no—
326C2×#102—111no—
327C2×#102—111no—
328C2×#102—111no—
329C2×#102—111no—
330C2×#102—111no—
331C2×C22⋊C8—111no—
332C2×C22⋊C8—111no—
333C2×#97—111no—
334#394—221no—
335#393—221no—
336#390—21no—
337#390—111no—
338#390—111no—
339#390C2×D1111yescharacteristic
340#389C2×D1111yescharacteristic
341#388—21no—
342#388—221no—
343#386—21no—
344#380—111no—
345C4×C4⋊C4—111no—
346C4×C4⋊C4C2×D1111yescharacteristic
347C4×C22⋊C4—21no—
348C4×C22⋊C4C2×D1111yescharacteristic
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#340—111no—
357#336—111no—
358#336—111no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—42no—
362C22×C11—41no—
363C22×C11—42no—
364C22×C11—41no—
365C22×C11—42no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11—81no—
370C22×C11—81no—
371C22×C11—81no—
372C22×C11—81no—
373C22×C11#52511yescharacteristic
374C22×C11#54611yescharacteristic
375C22×C11#54611yescharacteristic
376C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
377C22×C11#57511yescharacteristic
378C22×C11#57611yescharacteristic
379C22×C11#57711yescharacteristic
380C2×D11—81no—
381C2×D11—81no—
382C2×D11—81no—
383C2×D11—81no—
384C2×D11—81no—
385C2×D11—81no—
386C2×D11—81no—
387C4×C11—22no—
388C4×C11—41no—
389C4×C11—42no—
390C4×C11—41no—
391C4×C11—41no—
392C4×C11—42no—
393C4×C11—41no—
394C4×C11—81no—
395C4×C11#52911yescharacteristic
396C4×C11#53811yescharacteristic
397C4×C11#55511yescharacteristic
398C4×C11#55911yescharacteristic
399Dic11—42no—
400Dic11—81no—
401Dic11—81no—
402C22×Q8—221no—
403C22×D4—21no—
404C22×D4—111no—
405C22×D4—221no—
406C22×D4C22×D1111yescharacteristic
407C23×C4—21no—
408C23×C4C22×D1111yescharacteristic
409C2×D8—222no—
410C2×D8—441no—
411C2×D8—441no—
412C22×C8—111no—
413C22×C8—111no—
414C22×C8—111no—
415C22×C8—111no—
416C4⋊Q8—222no—
417C4⋊Q8—441no—
418#124—444no—
419#121—22no—
420#121—22no—
421#121—222no—
422#121—441no—
423C4×D4—22no—
424C4×D4—41no—
425#117—22no—
426#117—41no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4C22⋊D1111yescharacteristic
447C2×C22⋊C4C22⋊D1111yescharacteristic
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—221no—
451C2×C42C22×D1111yescharacteristic
452C2×C42C22×D1111yescharacteristic
453#106—222no—
454C4⋊C8—441no—
455#102—222no—
456#102—222no—
457#102—222no—
458#102—222no—
459#102—441no—
460#102—441no—
461C22⋊C8—441no—
462C22⋊C8—441no—
463#97—441no—
464#95—21no—
465#95—21no—
466#95—221no—
467#95—221no—
468#95C22⋊D1111yescharacteristic
469#95C22⋊D1111yescharacteristic
470C2×C11—81no—
471C2×C11—82no—
472C2×C11#245911yescharacteristic
473C2×C11#311511yescharacteristic
474C2×C11#311811yescharacteristic
475C2×C11#331811yescharacteristic
476C2×C11#331911yescharacteristic
477C2×C11#332111yescharacteristic
478C2×C11#333211yescharacteristic
479D11—161no—
480C24—21no—
481C24—221no—
482C24C2×C22⋊D1111yescharacteristic
483C2×Q8—442no—
484C2×Q8—442no—
485C2×Q8—881no—
486C2×D4—24no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—81no—
493C2×D4—81no—
494C2×D4—221no—
495C2×D4—221no—
496C2×D4—221no—
497C2×D4—221no—
498C2×D4—221no—
499C2×D4—221no—
500C2×D4—442no—
501C2×D4—442no—
502C2×D4—881no—
503C2×D4#433912yes—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—81no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4C2×C22⋊D1111yescharacteristic
520C22×C4C2×C22⋊D1111yescharacteristic
521C22×C4C2×C22⋊D1111yescharacteristic
522C22×C4C2×C22⋊D1111yescharacteristic
523C22×C4C2×C22⋊D1111yescharacteristic
524C22×C4C23×D1111yescharacteristic
525D8—444no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8—221no—
536C2×C8—221no—
537C2×C8—221no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—81no—
543C4⋊C4—112no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—442no—
550C4⋊C4#433912yes—
551C4⋊C4#434112yes—
552C22⋊C4—24no—
553C22⋊C4—22no—
554C22⋊C4—41no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—81no—
559C22⋊C4—442no—
560C22⋊C4—442no—
561C22⋊C4—442no—
562C22⋊C4—442no—
563C22⋊C4—442no—
564C22⋊C4—881no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—42no—
570C42—81no—
571C42—442no—
572C11#2674411yescharacteristic, complemented, Sylow
573C23—22no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—441no—
588C23—441no—
589C23—441no—
590C23—441no—
591C23—441no—
592C23—441no—
593C23—441no—
594C23C22×C22⋊D1111yescharacteristic
595Q8—884no—
596D4—22no—
597D4—22no—
598D4—41no—
599D4—41no—
600D4—84no—
601D4—441no—
602D4—441no—
603D4—441no—
604D4—441no—
605D4—884no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—84no—
634C2×C4—222no—
635C2×C4—441no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4—441no—
641C2×C4—441no—
642C2×C4—441no—
643C2×C4#6700212yes—
644C2×C4C2×#433911yescharacteristic
645C2×C4C2×#433911yescharacteristic
646C2×C4C2×#434111yescharacteristic
647C2×C4#6703711yescharacteristic
648C2×C4#41×D1111yescharacteristic
649C2×C4#6704211yescharacteristic
650C8—441no—
651C8—441no—
652C8—441no—
653C8—441no—
654C22—41no—
655C22—42no—
656C22—41no—
657C22—41no—
658C22—42no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—41no—
663C22—42no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—881no—
669C22—881no—
670C22—881no—
671C22—881no—
672C22—881no—
673C22—881no—
674C22—881no—
675C22#1062332211yescharacteristic
676C22#1062333711yescharacteristic
677C22C2×#6700211yescharacteristic
678C22#1062335311yescharacteristic
679C22#1062336011yescharacteristic
680C22#1062336611yescharacteristic
681C22#1062336711yescharacteristic
682C4—22no—
683C4—42no—
684C4—41no—
685C4—41no—
686C4—41no—
687C4—42no—
688C4—41no—
689C4—81no—
690C4—442no—
691C4—881no—
692C4—881no—
693C4#1062306911yescharacteristic
694C4#1062309011yescharacteristic
695C4#1062309111yescharacteristic
696C4#1062309411yescharacteristic
697C2—81no—
698C2—82no—
699C2—1761no—
700C2#1307254711yescharacteristic
701C2#1307876711yescharacteristic
702C2#1307880011yescharacteristic
703C2#1308075111yescharacteristic
704C2#1308077211yescharacteristic
705C2#1308079611yescharacteristic
706C2#1308094311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2363C2
socleC23×C11C22×D4
prime radical#13069612C2
hypercenter#2363D11
hypocenterC11#26744
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
1. #13072979C2semidirect
2. #13069926C2semidirect
3. #13069802C2semidirect
4. #13069752C2semidirect
6. #13069568C2semidirect
7. #13069312C2semidirect
8. #13069243C2semidirect
9. #13069231C2semidirect
10. #13069191C2semidirect
11. #13068964C2semidirect
12. #13068938C2semidirect
13. #13068711C2semidirect
14. #13068441C2semidirect
15. C11×#2363C2semidirect
221. #2363D11semidirect
572. C11#26744semidirect

Maximal subgroups

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

subgroupindex
#130729792
#130699262
#130698022
#130697522
#130696122
#130695682
#130693122
#130692432
#130692312
#130691912
#130689642
#130689382
#130687112
#130684412
C11×#23632
#2674411