Finite Group Databasebeta

← #14827069

Subgroups — #14827069

Order 2816.

748 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073191C211yesmaximal, characteristic, complemented
2#13070144C211yesmaximal, characteristic
3#13069933C211yesmaximal, characteristic
4#13069852C211yesmaximal, characteristic
5#13069710C211yesmaximal, characteristic
6#13069476C211yesmaximal, characteristic, complemented
7#13069257C211yesmaximal, characteristic, complemented
8#13069254C211yesmaximal, characteristic, complemented
9#13069187C211yesmaximal, characteristic, complemented
10#13069175C211yesmaximal, characteristic, complemented
11#13068957C211yesmaximal, characteristic, complemented
12#13068950C211yesmaximal, characteristic
13#13068621C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic
15C11×#2367C211yesmaximal, characteristic
16C2×C11×#124C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C11×#391C2211yescharacteristic
22C11×#390C2211yescharacteristic
23C11×#388—21no—
24C11×#388—21no—
25C11×#385—21no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C22⋊C4—21no—
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35#10622599—21no—
36#10622594—21no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622548C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622542C2211yescharacteristic
44#10622542C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622541C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622273—21no—
50#10622267—21no—
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C22×Dic22C2311yescharacteristic
63C11×#124—22no—
64C11×#124—22no—
65C4×Q8×C11—22no—
66C4×Q8×C11—41no—
67C4×D4×C11—22no—
68C4×D4×C11—41no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×#4326—22no—
85C2×#4326—22no—
86C2×#4326—41no—
87C2×#4324—22no—
88C2×#4324—41no—
89C2×#4324—41no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95D411yescharacteristic
105C11×#95D411yescharacteristic
106#66899—22no—
107#66899—41no—
108#66899—41no—
109#66896—22no—
110#66896—22no—
111#66896—41no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120#66874—22no—
121#66874—41no—
122#66871—22no—
123#66871—41no—
124C4⋊(C11⋊C8)—41no—
125C4×C11⋊C8—41no—
126#27073—111nomaximal, Sylow
127C24×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11#4112yes—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11#4112yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—42no—
144C22×C4×C11—42no—
145C22×C4×C11—81no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4#4112yes—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—42no—
173C11×C22⋊C4—42no—
174C11×C22⋊C4—81no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—42no—
182C42×C11—81no—
183#4326—44no—
184#4324—44no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—42no—
192C4⋊Dic11—81no—
193Dic11⋊C4—81no—
194C4×Dic11—81no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
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#4112yes—
207#2511—111no—
208#2367D1111yescharacteristic
209#2093—111no—
210#2055—111no—
211#2042—111no—
212#2015—111no—
213#1969—111no—
214#1928—111no—
215#1928—111no—
216#1918—111no—
217#1916—111no—
218#1878—111no—
219#1877—111no—
220#1803—111no—
221C4×#102—111no—
222C23×C11—22no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11C22×D411yescharacteristic
230Q8×C11—22no—
231Q8×C11—22no—
232Q8×C11—41no—
233Q8×C11—41no—
234D4×C11—22no—
235D4×C11—22no—
236D4×C11—41no—
237D4×C11—41no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
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—21no—
256C2×C4×C11—41no—
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—84no—
264C2×C4×C11#13512yes—
265C2×C4×C11#13712yes—
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11H(5,𝔽2)11yescharacteristic
271C2×C4×C11H(5,𝔽2)11yescharacteristic
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284Dic22—41no—
285Dic22—41no—
286Dic22—41no—
287Dic22—41no—
288C11⋊C8—22no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C22×Q16—111no—
293C22×SD16—111no—
294C2×#124C2×D1111yescharacteristic
295C2×C4×Q8C2×D1111yescharacteristic
296C2×C4×D4C2×D1111yescharacteristic
297C2×#107—111no—
298C2×#107—111no—
299C2×C4⋊C8—111no—
300C2×#103—111no—
301C2×#103—111no—
302C2×#103—111no—
303C2×#103—111no—
304C2×#103—111no—
305C2×#102—111no—
306C2×#102—111no—
307C2×#102—111no—
308C2×C4×C8—111no—
309#400—221no—
310#400—221no—
311#391—111no—
312#391—111no—
313#391—111no—
314#391C2×D1111yescharacteristic
315#390C2×D1111yescharacteristic
316#389—111no—
317#388—21no—
318#388—21no—
319#387—221no—
320#387—221no—
321#385—21no—
322#384—111no—
323C4×C4⋊C4—111no—
324C4×C4⋊C4C2×D1111yescharacteristic
325C4×C4⋊C4C2×D1111yescharacteristic
326C4×C22⋊C4—21no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340—111no—
331#336—111no—
332#336—111no—
333#336—111no—
334#336—111no—
335C22×C11—42no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—81no—
339C22×C11—81no—
340C22×C11—81no—
341C22×C11—81no—
342C22×C11#52511yescharacteristic
343C22×C11#54611yescharacteristic
344C22×C11#55011yescharacteristic
345C22×C11C2×#13511yescharacteristic
346C22×C11C2×#13711yescharacteristic
347C22×C11#57611yescharacteristic
348C22×C11#57811yescharacteristic
349C4×C11—22no—
350C4×C11—22no—
351C4×C11—41no—
352C4×C11—41no—
353C4×C11—42no—
354C4×C11—41no—
355C4×C11—41no—
356C4×C11—42no—
357C4×C11—81no—
358C4×C11#52911yescharacteristic
359C4×C11#53811yescharacteristic
360C4×C11#55111yescharacteristic
361C4×C11#55311yescharacteristic
362Dic11—81no—
363Dic11—81no—
364Dic11—81no—
365Dic11—81no—
366C22×Q8—111no—
367C22×Q8C22×D1111yescharacteristic
368C22×D4C22×D1111yescharacteristic
369C23×C4—21no—
370C2×Q16—222no—
371C2×Q16—222no—
372C2×Q16—441no—
373C2×SD16—222no—
374C2×SD16—441no—
375C2×SD16—441no—
376C22×C8—111no—
377C22×C8—111no—
378C22×C8—111no—
379C22×C8—111no—
380#124—22no—
381#124—22no—
382C4×Q8—22no—
383C4×Q8—41no—
384C4×D4—22no—
385C4×D4—41no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4C22⋊D1111yescharacteristic
394C2×C4⋊C4C22⋊D1111yescharacteristic
395C2×C4⋊C4C22×D1111yescharacteristic
396C2×C4⋊C4C22×D1111yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—221no—
405C2×C42C22×D1111yescharacteristic
406C2×C42C22×D1111yescharacteristic
407C2×C42C22×D1111yescharacteristic
408#107—222no—
409#107—441no—
410C4⋊C8—441no—
411#103—222no—
412#103—222no—
413#103—441no—
414#103—441no—
415#103—441no—
416#102—222no—
417#102—222no—
418#102—441no—
419C4×C8—441no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95C22⋊D1111yescharacteristic
432#95C22⋊D1111yescharacteristic
433C2×C11—82no—
434C2×C11#246711yescharacteristic
435C2×C11#310711yescharacteristic
436C2×C11#312411yescharacteristic
437C2×C11#330011yescharacteristic
438C2×C11#331411yescharacteristic
439C2×C11#339611yescharacteristic
440C2×C11#339811yescharacteristic
441C24—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8—221no—
450C2×Q8—221no—
451C2×Q8—221no—
452C2×Q8—221no—
453C2×Q8#433912yes—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4#433912yes—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—81no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C2×C22⋊D1111yescharacteristic
473C22×C4C2×C22⋊D1111yescharacteristic
474C22×C4C2×C22⋊D1111yescharacteristic
475C22×C4C2×C22⋊D1111yescharacteristic
476C22×C4C23×D1111yescharacteristic
477Q16—444no—
478SD16—444no—
479C2×C8—112no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—42no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—442no—
504C4⋊C4—881no—
505C4⋊C4—881no—
506C4⋊C4#434112yes—
507C22⋊C4—24no—
508C22⋊C4—24no—
509C22⋊C4—42no—
510C22⋊C4—42no—
511C22⋊C4—81no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—21no—
518C42—42no—
519C42—81no—
520C42—881no—
521C11#2707311yescharacteristic, complemented, Sylow
522C23—22no—
523C23—41no—
524C23—41no—
525C23—41no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23C22×C22⋊D1111yescharacteristic
530Q8—22no—
531Q8—22no—
532Q8—41no—
533Q8—41no—
534Q8—441no—
535Q8—441no—
536Q8—441no—
537Q8—441no—
538D4—22no—
539D4—22no—
540D4—41no—
541D4—41no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—84no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4#6700312yes—
581C2×C4#6700412yes—
582C2×C4C2×#433911yescharacteristic
583C2×C4C2×#433911yescharacteristic
584C2×C4C2×#434111yescharacteristic
585C2×C4#6703711yescharacteristic
586C2×C4#41×D1111yescharacteristic
587C2×C4#6704211yescharacteristic
588C8—222no—
589C8—441no—
590C8—441no—
591C8—441no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22#1062332211yescharacteristic
600C22#1062333711yescharacteristic
601C22C2×#6700311yescharacteristic
602C22C2×#6700411yescharacteristic
603C22#1062336511yescharacteristic
604C22#1062336611yescharacteristic
605C22#1062336911yescharacteristic
606C4—22no—
607C4—22no—
608C4—42no—
609C4—41no—
610C4—41no—
611C4—42no—
612C4—41no—
613C4—41no—
614C4—81no—
615C4—881no—
616C4—881no—
617C4—881no—
618C4—881no—
619C4#1062306911yescharacteristic
620C4#1062308711yescharacteristic
621C4#1062309111yescharacteristic
622C4#1062309611yescharacteristic
623C2—82no—
624C2#1307266111yescharacteristic
625C2#1307868711yescharacteristic
626C2#1307887811yescharacteristic
627C2#1308050311yescharacteristic
628C2#1308069711yescharacteristic
629C2#1308162411yescharacteristic
630C2#1308164711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2367C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2367D11
hypocenterC11#27073
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2367

Complements

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

NH ≅ G/Ntype
1. #13073191C2semidirect
6. #13069476C2semidirect
7. #13069257C2semidirect
8. #13069254C2semidirect
9. #13069187C2semidirect
10. #13069175C2semidirect
11. #13068957C2semidirect
13. #13068621C2semidirect
521. C11#27073semidirect

Maximal subgroups

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

subgroupindex
#130731912
#130701442
#130699332
#130698522
#130697102
#130694762
#130692572
#130692542
#130691872
#130691752
#130689572
#130689502
#130686212
C4×#668962
C11×#23672
#2707311