Finite Group Databasebeta

← #14821842

Subgroups — #14821842

Order 2816.

874 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#13072964C211yesmaximal, characteristic, complemented
2#13071636C211yesmaximal, characteristic, complemented
3#13069925C211yesmaximal, characteristic, complemented
4#13069760C211yesmaximal, characteristic, complemented
5#13069612C211yesmaximal, characteristic
6#13069570C211yesmaximal, characteristic, complemented
7#13069300C211yesmaximal, characteristic, complemented
8#13069242C211yesmaximal, characteristic, complemented
9#13069225C211yesmaximal, characteristic, complemented
10#13069196C211yesmaximal, characteristic, complemented
11#13068962C211yesmaximal, characteristic, complemented
12#13068931C211yesmaximal, characteristic, complemented
13#13068704C211yesmaximal, characteristic, complemented
14#102×Dic11C211yesmaximal, characteristic, complemented
15C11×#2034C211yesmaximal, characteristic, complemented
16C2×C11×#121C2211yescharacteristic
17C2×D4×Dic11—21no—
18C2×D4×Dic11C2211yescharacteristic
19C22×#4323C2211yescharacteristic
20C2×#66983C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C2×#66943C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27C11×#380C2211yescharacteristic
28#10622834C2211yescharacteristic
29#10622833—21no—
30C2×#66896C2211yescharacteristic
31C4×C22⋊Dic11C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622601C2211yescharacteristic
38#10622601C2211yescharacteristic
39#10622598C2211yescharacteristic
40C4⋊C4×Dic11C2211yescharacteristic
41C4⋊C4×Dic11C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43#10622574—21no—
44#10622570—21no—
45#10622564—21no—
46#10622563—21no—
47#10622288—21no—
48#10622283—21no—
49C11×#340C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C23×Dic11—21no—
64C23×Dic11—21no—
65C22×D44C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×#121—22no—
69C11×#121—22no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11D411yescharacteristic
79C2×C22⋊Dic11D411yescharacteristic
80D4×Dic11—22no—
81D4×Dic11—41no—
82D4×Dic11—44no—
83C2×#4323—22no—
84C2×#4323—41no—
85C2×#4323—41no—
86#66983—22no—
87#66983—41no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—41no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11C2311yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108#66943—22no—
109#66943—41no—
110C11×#106—22no—
111C11×#102—22no—
112C11×#102—41no—
113C11×C22⋊C8—41no—
114C11×#95—21no—
115#66896—22no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95D411yescharacteristic
120C11⋊#95D411yescharacteristic
121C22⋊(C11⋊C8)—41no—
122#66885—22no—
123#66885—41no—
124Dic11⋊C8—41no—
125C8×Dic11—41no—
126#66873—22no—
127#26723—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—42no—
138C2×D4×C11—42no—
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×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—42no—
152C2×C22⋊D11—42no—
153C2×C22⋊D11—81no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—42no—
158C22×Dic11—42no—
159C22×Dic11—42no—
160C22×Dic11—42no—
161C22×Dic11—81no—
162C22×Dic11—81no—
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—21no—
170C2×D44—21no—
171C2×D44—21no—
172C2×D44—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4#4112yes—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—81no—
187C22⋊Dic11—22no—
188C22⋊Dic11—22no—
189C22⋊Dic11—42no—
190C22⋊Dic11—42no—
191C22⋊Dic11—81no—
192#4323—44no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—81no—
196(C2×D11)⋊C4—81no—
197(C2×D11)⋊C4—81no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—42no—
203C4⋊Dic11—42no—
204C4⋊Dic11—42no—
205C4⋊Dic11#4112yes—
206C4⋊Dic11#4112yes—
207Dic11⋊C4—42no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—21no—
212C4×Dic11—42no—
213C4×Dic11—81no—
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#2490—111no—
221#2361—111no—
222#2054—111no—
223#2034D1111yescharacteristic, complemented
224#2025—111no—
225#1999—111no—
226#1989—111no—
227#1934—111no—
228#1926—111no—
229#1923—111no—
230#1919—111no—
231#1879—111no—
232#1874—111no—
233#1824—111no—
234C4×#102—111no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—22no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11#13512yes—
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—48no—
260D4×C11—41no—
261D4×C11—41no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11H(5,𝔽2)11yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C22⋊D11—84no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—22no—
291C2×Dic11—22no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—21no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—84no—
306C2×Dic11—84no—
307C2×Dic11AGL(1,ℤ/8)12yes—
308D44—41no—
309D44—41no—
310D44—41no—
311D44—41no—
312C8×C11—41no—
313C8×C11—41no—
314C11⋊C8—41no—
315C11⋊C8—41no—
316C22×D8—111no—
317C2×#125—111no—
318C2×#121—111no—
319C2×#121C2×D1111yescharacteristic
320C2×C4×D4—111no—
321C2×C4×D4—221no—
322C22×C4⋊C4—111no—
323C2×#106C2×D1111yescharacteristic
324C2×C4⋊C8—111no—
325C2×#102—111no—
326C2×#102—111no—
327C2×#102—111no—
328C2×#102—111no—
329C2×#102C2×D1111yescharacteristic
330C2×#102C2×D1111yescharacteristic
331C2×C22⋊C8—111no—
332C2×C22⋊C8C2×D1111yescharacteristic
333C2×C4×C8—111no—
334#397—221no—
335#394—221no—
336#390—111no—
337#390—111no—
338#390—111no—
339#390—221no—
340#389—111no—
341#388—221no—
342#388—221no—
343#386—221no—
344#385—221no—
345#380C2×D1111yescharacteristic
346C4×C4⋊C4—111no—
347C4×C4⋊C4—111no—
348C4×C22⋊C4—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#340C2×D1111yescharacteristic
357#336—111no—
358#336—111no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—42no—
367C22×C11—42no—
368C22×C11—42no—
369C22×C11—81no—
370C22×C11—81no—
371C22×C11—81no—
372C22×C11—81no—
373C22×C11#52511yescharacteristic
374C22×C11#54611yescharacteristic
375C22×C11#54611yescharacteristic
376C22×C11C2×#13511yescharacteristic
377C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
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—42no—
388C4×C11—41no—
389C4×C11—81no—
390C4×C11—81no—
391C4×C11#52911yescharacteristic
392C4×C11#53811yescharacteristic
393C4×C11#55511yescharacteristic
394C4×C11#55911yescharacteristic
395Dic11—22no—
396Dic11—41no—
397Dic11—41no—
398Dic11—42no—
399Dic11—41no—
400Dic11—42no—
401Dic11—81no—
402C22×D4—21no—
403C22×D4—111no—
404C22×D4—221no—
405C22×D4C22×D1111yescharacteristic
406C23×C4—221no—
407C23×C4—221no—
408C23×C4C22×D1111yescharacteristic
409C2×D8—222no—
410C2×D8—441no—
411C2×D8—441no—
412C22×C8—111no—
413C22×C8—111no—
414C22×C8C22×D1111yescharacteristic
415C22×C8C22×D1111yescharacteristic
416#125—222no—
417#125—441no—
418#121—22no—
419#121—22no—
420#121—222no—
421#121—441no—
422C4×D4—222no—
423C4×D4—441no—
424C4×D4—444no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—222no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—441no—
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—111no—
440C2×C22⋊C4—111no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C22⋊C4—221no—
449C2×C42—111no—
450C2×C42—111no—
451C2×C42—221no—
452C2×C42—221no—
453#106—22no—
454C4⋊C8—441no—
455#102—22no—
456#102—41no—
457#102—222no—
458#102—222no—
459#102—222no—
460#102—441no—
461C22⋊C8—41no—
462C22⋊C8—441no—
463C4×C8—441no—
464#95—21no—
465#95—111no—
466#95—111no—
467#95—221no—
468#95—221no—
469#95—221no—
470C2×C11—42no—
471C2×C11—82no—
472C2×C11#245911yescharacteristic
473C2×C11#310511yescharacteristic
474C2×C11#311911yescharacteristic
475C2×C11#329711yescharacteristic
476C2×C11#330111yescharacteristic
477C2×C11#331811yescharacteristic
478C2×C11#333211yescharacteristic
479D11—161no—
480C24—21no—
481C24—221no—
482C24D4×D1111yescharacteristic
483C2×D4—24no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—221no—
492C2×D4—221no—
493C2×D4—221no—
494C2×D4—221no—
495C2×D4—221no—
496C2×D4—221no—
497C2×D4—442no—
498C2×D4—442no—
499C2×D4—881no—
500C2×D4#434112yes—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—111no—
511C22×C4—111no—
512C22×C4—111no—
513C22×C4—111no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—442no—
518C22×C4—442no—
519C22×C4—442no—
520C22×C4—442no—
521C22×C4—881no—
522C22×C4—881no—
523C22×C4D4×D1111yescharacteristic
524C22×C4C23×D1111yescharacteristic
525D8—444no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
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—21no—
543C4⋊C4—112no—
544C4⋊C4—112no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—442no—
550C4⋊C4—442no—
551C4⋊C4—442no—
552C4⋊C4—442no—
553C4⋊C4#434112yes—
554C22⋊C4—24no—
555C22⋊C4—81no—
556C22⋊C4—222no—
557C22⋊C4—222no—
558C22⋊C4—442no—
559C22⋊C4—442no—
560C22⋊C4—442no—
561C22⋊C4—442no—
562C22⋊C4—881no—
563C22⋊C4—881no—
564C22⋊C4—881no—
565C22⋊C4—881no—
566C42—221no—
567C42—221no—
568C42—221no—
569C42—221no—
570C42—442no—
571C42—881no—
572C11#2672311yescharacteristic, complemented, Sylow
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—22no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—441no—
587C23—441no—
588C23—441no—
589C23—441no—
590C23—441no—
591C23—441no—
592C23—441no—
593C23#6696912yes—
594C23C2×D4×D1111yescharacteristic
595D4—22no—
596D4—22no—
597D4—48no—
598D4—41no—
599D4—41no—
600D4—441no—
601D4—441no—
602D4—441no—
603D4—441no—
604D4—884no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—112no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—221no—
626C2×C4—221no—
627C2×C4—221no—
628C2×C4—221no—
629C2×C4—221no—
630C2×C4—221no—
631C2×C4—221no—
632C2×C4—222no—
633C2×C4—221no—
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—884no—
643C2×C4—884no—
644C2×C4C2×#434111yescharacteristic
645C2×C4C2×#434111yescharacteristic
646C2×C4#6703711yescharacteristic
647C2×C4#41×D1111yescharacteristic
648C2×C4#41×D1111yescharacteristic
649C2×C4#6704211yescharacteristic
650C8—41no—
651C8—41no—
652C8—441no—
653C8—441no—
654C22—22no—
655C22—22no—
656C22—22no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—42no—
662C22—42no—
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#1062311711yescharacteristic
676C22#1062314111yescharacteristic
677C22#1062318511yescharacteristic
678C22C2×#6696911yescharacteristic
679C22#1062330011yescharacteristic
680C22D11×AGL(1,ℤ/8)11yescharacteristic
681C22#1062330611yescharacteristic
682C4—42no—
683C4—41no—
684C4—81no—
685C4—81no—
686C4—222no—
687C4—441no—
688C4—441no—
689C4—442no—
690C4—442no—
691C4—441no—
692C4—881no—
693C4#1062314711yescharacteristic
694C4#1062314811yescharacteristic
695C4#1062318011yescharacteristic
696C4#1062321211yescharacteristic
697C2—42no—
698C2—82no—
699C2—1761no—
700C2#1307254611yescharacteristic
701C2#1307866411yescharacteristic
702C2#1307880811yescharacteristic
703C2#1308047211yescharacteristic
704C2#1308051611yescharacteristic
705C2#1308076011yescharacteristic
706C2#1308093811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2034C2
socleC23×C11C22×D4
prime radical#13069612C2
hypercenter#2034D11
hypocenterC11#26723
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2034

Complements

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

NH ≅ G/Ntype
1. #13072964C2semidirect
2. #13071636C2semidirect
3. #13069925C2semidirect
4. #13069760C2semidirect
6. #13069570C2semidirect
7. #13069300C2semidirect
8. #13069242C2semidirect
9. #13069225C2semidirect
10. #13069196C2semidirect
11. #13068962C2semidirect
12. #13068931C2semidirect
13. #13068704C2semidirect
14. #102×Dic11C2semidirect
15. C11×#2034C2semidirect
223. #2034D11semidirect
572. C11#26723semidirect

Maximal subgroups

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

subgroupindex
#130729642
#130716362
#130699252
#130697602
#130696122
#130695702
#130693002
#130692422
#130692252
#130691962
#130689622
#130689312
#130687042
#102×Dic112
C11×#20342
#2672311