Finite Group Databasebeta

← #14801997

Subgroups — #14801997

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622616C211yesmaximal, characteristic
2C2×#10622661C211yesmaximal, characteristic
3#13071652C211yesmaximal, characteristic
4#13070093C211yesmaximal, characteristic, complemented
5#13070030C211yesmaximal, characteristic, complemented
6#13070011C211yesmaximal, characteristic, complemented
7#13069931C211yesmaximal, characteristic, complemented
8#13069382C211yesmaximal, characteristic, complemented
9#13069247C211yesmaximal, characteristic, complemented
10#13068953C211yesmaximal, characteristic, complemented
11#13068929C211yesmaximal, characteristic, complemented
12#13068796C211yesmaximal, characteristic, complemented
13#13068613C211yesmaximal, characteristic, complemented
14#13068332C211yesmaximal, characteristic, complemented
15C11×#2499C211yesmaximal, characteristic, complemented
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×#4325C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C23×C11⋊C8C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C11×#397—21no—
24C11×#397—21no—
25C11×#391C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C11×#387—21no—
28C11×#387—21no—
29C11×#384C2211yescharacteristic
30C11×#382C2211yescharacteristic
31C4×C11×C22⋊C4C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36#10622661—24no—
37#10622616—24no—
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622570—21no—
45#10622569—21no—
46#10622552C2211yescharacteristic
47C4×C4⋊Dic11C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622282—21no—
52#10622279—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8—22no—
68C11×#117—22no—
69C11×#117—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
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⋊C4D411yescharacteristic
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C22⋊Dic11—21no—
84C2×#4325—22no—
85C2×#4325—22no—
86C2×#4325—41no—
87#66983—22no—
88#66983D414yes—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93#66979—22no—
94#66979—41no—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C22×C11⋊C8—22no—
102C22×C11⋊C8—22no—
103C22×C11⋊C8—41no—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C4×D44—22no—
109C4×D44—41no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95D411yescharacteristic
117C11×#95D411yescharacteristic
118#66899—22no—
119#66899—22no—
120#66899—41no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C22⋊(C11⋊C8)—22no—
124#66873—22no—
125#66873—22no—
126#66873—22no—
127#66872—22no—
128#66872—22no—
129#66871—22no—
130C4⋊(C11⋊C8)—22no—
131C4⋊(C11⋊C8)—41no—
132#25205—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C23×D11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×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×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11#4112yes—
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—24no—
158C2×C22⋊D11—81no—
159C2×C22⋊D11—81no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44C2×D412yes—
169C2×C4×D11—42no—
170C2×C4×D11—42no—
171C2×C4×D11—81no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—42no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4—42no—
181C11×C22⋊C4—22no—
182C11×C22⋊C4—41no—
183C11×C22⋊C4—42no—
184C11×C22⋊C4—42no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—42no—
190C22⋊Dic11—42no—
191#4325—44no—
192(C2×D11)⋊C4—24no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—81no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11C2×D412yes—
201C4⋊Dic11#4112yes—
202Dic11⋊C4—81no—
203C4×Dic11—42no—
204C4×Dic11—81no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
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—44no—
217C2×C11⋊C8#4112yes—
218C2×#482—111no—
219C2×#465—111no—
220#2499D1111yescharacteristic, complemented
221#2363—111no—
222#2084—111no—
223#2073—111no—
224#2068—111no—
225#2055—111no—
226#1949—111no—
227#1927—111no—
228#1877—111no—
229#1873—111no—
230#1850—111no—
231#1802—111no—
232#1735—111no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11#12112yes—
240C23×C11C22×D411yescharacteristic
241C22×D11—22no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—41no—
248Q8×C11—41no—
249Q8×C11—41no—
250Q8×C11—41no—
251Q8×C11—41no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
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×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11#12112yes—
282C2×C4×C11#13512yes—
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11C2×#4111yescharacteristic
287C2×C4×C11H(5,𝔽2)11yescharacteristic
288C2×C4×C112−1+411yescharacteristic
289C22⋊D11—84no—
290C2×Dic11—22no—
291C2×Dic11—22no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299D44—22no—
300D44—22no—
301D44—41no—
302D44—41no—
303C4×D11—84no—
304C11⋊C8—22no—
305C11⋊C8—41no—
306C11⋊C8—41no—
307C11⋊C8—41no—
308C22×SD16—111no—
309C23×C8—111no—
310C2×C22⋊Q8C2×D1111yescharacteristic
311C2×#121—111no—
312C2×C4×D4—111no—
313C2×#117—111no—
314C2×#117C2×D1111yescharacteristic
315#482—224no—
316#465—224no—
317C2×#107—111no—
318C2×#106—111no—
319C2×#106—111no—
320C2×C4⋊C8—111no—
321C2×C4⋊C8—111no—
322C2×#103—111no—
323C2×#103—111no—
324C2×#103—111no—
325C2×#102—111no—
326C2×#102—111no—
327C2×#102—111no—
328C2×C22⋊C8—111no—
329#397—21no—
330#397—21no—
331#391C2×D1111yescharacteristic
332#391C2×D1111yescharacteristic
333#390—111no—
334#390—221no—
335#389—111no—
336#388—221no—
337#387—21no—
338#387—21no—
339#386—221no—
340#384C2×D1111yescharacteristic
341#382C2×D1111yescharacteristic
342C4×C4⋊C4—111no—
343C4×C22⋊C4—221no—
344C4×C22⋊C4C2×D1111yescharacteristic
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#336—111no—
352#336—111no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11C2×#12111yescharacteristic
361C22×C11#54611yescharacteristic
362C22×C11#54711yescharacteristic
363C22×C11C2×#13511yescharacteristic
364C22×C11#57511yescharacteristic
365C22×C11#57711yescharacteristic
366C22×C11#57711yescharacteristic
367C2×D11—42no—
368C2×D11—42no—
369C2×D11—42no—
370C2×D11—81no—
371C2×D11—81no—
372C2×D11—81no—
373C2×D11—81no—
374C4×C11—22no—
375C4×C11—22no—
376C4×C11—41no—
377C4×C11—41no—
378C4×C11—41no—
379C4×C11—81no—
380C4×C11—81no—
381C4×C11—81no—
382C4×C11—81no—
383C4×C11#52911yescharacteristic
384C4×C11#53911yescharacteristic
385C4×C11#54611yescharacteristic
386C4×C11#54711yescharacteristic
387Dic11—42no—
388Dic11—42no—
389Dic11—81no—
390C22×Q8C22×D1111yescharacteristic
391C22×D4—111no—
392C22×D4—221no—
393C23×C4—221no—
394C23×C4C22×D1111yescharacteristic
395C2×SD16—222no—
396C2×SD16—222no—
397C2×SD16—441no—
398C22×C8—111no—
399C22×C8—111no—
400C22×C8—111no—
401C22×C8—111no—
402C22×C8—222no—
403C22×C8—222no—
404C22×C8—441no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407#121—114no—
408#121—222no—
409C4×D4—222no—
410C4×D4—441no—
411#117—22no—
412#117—22no—
413#117—222no—
414#117—441no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C4⋊C4C22×D1111yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4C22⋊D1111yescharacteristic
433C2×C22⋊C4C22⋊D1111yescharacteristic
434C2×C42—21no—
435C2×C42—221no—
436C2×C42—221no—
437C2×C42C22×D1111yescharacteristic
438C2×C42C22×D1111yescharacteristic
439#107—222no—
440#106—222no—
441#106—222no—
442C4⋊C8—222no—
443C4⋊C8—441no—
444#103—222no—
445#103—222no—
446#103—441no—
447#102—222no—
448#102—222no—
449#102—222no—
450C22⋊C8—222no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—221no—
458#95—221no—
459#95C22⋊D1111yescharacteristic
460#95C22⋊D1111yescharacteristic
461C2×C11—42no—
462C2×C11#242511yescharacteristic
463C2×C11#303511yescharacteristic
464C2×C11#304211yescharacteristic
465C2×C11#329611yescharacteristic
466C2×C11#331711yescharacteristic
467C2×C11#334011yescharacteristic
468C2×C11#335011yescharacteristic
469D11—82no—
470C24—221no—
471C24C2×C22⋊D1111yescharacteristic
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×D4—112no—
479C2×D4—224no—
480C2×D4—221no—
481C2×D4—221no—
482C2×D4—221no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—881no—
486C2×D4—881no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—442no—
499C22×C4—442no—
500C22×C4—881no—
501C22×C4D4×D1112yes—
502C22×C4#434112yes—
503C22×C4C2×C22⋊D1111yescharacteristic
504C22×C4C2×C22⋊D1111yescharacteristic
505C22×C4C2×C22⋊D1111yescharacteristic
506C22×C4C2×C22⋊D1111yescharacteristic
507C22×C4C2×C22⋊D1111yescharacteristic
508C22×C4C23×D1111yescharacteristic
509SD16—444no—
510C2×C8—112no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—444no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—42no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—112no—
533C4⋊C4—112no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—881no—
539C22⋊C4—22no—
540C22⋊C4—41no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—224no—
544C22⋊C4—442no—
545C22⋊C4—442no—
546C22⋊C4—442no—
547C22⋊C4—881no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—42no—
553C42—442no—
554C42—881no—
555C11#2520511yescharacteristic, complemented, Sylow
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—222no—
563C23—441no—
564C23—441no—
565C23—441no—
566C23—441no—
567C23—441no—
568C23—441no—
569C23#6699112yes—
570C23C22×C22⋊D1111yescharacteristic
571Q8—41no—
572Q8—41no—
573Q8—41no—
574Q8—41no—
575D4—222no—
576D4—222no—
577D4—441no—
578D4—441no—
579D4—884no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—884no—
619C2×C4#6699112yes—
620C2×C4#6700312yes—
621C2×C4C2×D4×D1111yescharacteristic
622C2×C4C2×#434111yescharacteristic
623C2×C4#41×D1111yescharacteristic
624C2×C4#41×D1111yescharacteristic
625C2×C4#6704211yescharacteristic
626C2×C4#6704311yescharacteristic
627C8—222no—
628C8—441no—
629C8—441no—
630C8—441no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—442no—
639C22—442no—
640C22—442no—
641C22—881no—
642C22—881no—
643C22—881no—
644C22—881no—
645C22C2×#6699111yescharacteristic
646C22C2×#6700311yescharacteristic
647C22#1062335311yescharacteristic
648C22#1062335511yescharacteristic
649C22#1062336011yescharacteristic
650C22#1062336811yescharacteristic
651C22#1062336811yescharacteristic
652C4—22no—
653C4—22no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—81no—
658C4—81no—
659C4—81no—
660C4—81no—
661C4—442no—
662C4—442no—
663C4—881no—
664C4#1062318011yescharacteristic
665C4#1062318511yescharacteristic
666C4#1062318611yescharacteristic
667C4#1062319611yescharacteristic
668C2—42no—
669C2—882no—
670C2#1307216311yescharacteristic
671C2#1307806511yescharacteristic
672C2#1307812411yescharacteristic
673C2#1308044511yescharacteristic
674C2#1308073611yescharacteristic
675C2#1308102311yescharacteristic
676C2#1308116111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2499C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#2499D11
hypocenterC11#25205
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2499

Complements

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

NH ≅ G/Ntype
4. #13070093C2semidirect
5. #13070030C2semidirect
6. #13070011C2semidirect
7. #13069931C2semidirect
8. #13069382C2semidirect
9. #13069247C2semidirect
10. #13068953C2semidirect
11. #13068929C2semidirect
12. #13068796C2semidirect
13. #13068613C2semidirect
14. #13068332C2semidirect
15. C11×#2499C2semidirect
220. #2499D11semidirect
555. C11#25205semidirect

Maximal subgroups

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

subgroupindex
C2×#106226162
C2×#106226612
#130716522
#130700932
#130700302
#130700112
#130699312
#130693822
#130692472
#130689532
#130689292
#130687962
#130686132
#130683322
C11×#24992
#2520511