Finite Group Databasebeta

← #14814707

Subgroups — #14814707

Order 2816.

782 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072041C211yesmaximal, characteristic
2#13071546C211yesmaximal, characteristic
3#13070187C211yesmaximal, characteristic, complemented
4#13070044C211yesmaximal, characteristic, complemented
5#13070037C211yesmaximal, characteristic, complemented
6#13069809C211yesmaximal, characteristic, complemented
7#13069259C211yesmaximal, characteristic, complemented
8#13069204C211yesmaximal, characteristic, complemented
9#13069046C211yesmaximal, characteristic, complemented
10#13068920C211yesmaximal, characteristic, complemented
11#13068910C211yesmaximal, characteristic
12#13068818C211yesmaximal, characteristic, complemented
13#13068711C211yesmaximal, characteristic, complemented
14#13068334C211yesmaximal, characteristic, complemented
15C11×#1873C211yesmaximal, characteristic, complemented
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×#66999C2211yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C22×#4313C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26#10622843C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29#10622825C2211yescharacteristic
30#10622825C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34#10622606—21no—
35#10622600C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622590C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39#10622586—21no—
40C2×#66872C2211yescharacteristic
41#10622574—21no—
42#10622569—21no—
43#10622558—21no—
44#10622557—21no—
45C4×(C2×D11)⋊C4—21no—
46#10622546—21no—
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11D411yescharacteristic
62C22×C4×D11—21no—
63C22×C4×D11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8—41no—
68C11×#117—22no—
69C11×#117—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11D411yescharacteristic
80#66999—22no—
81#66999—22no—
82C4×C22⋊D11—22no—
83C4×C22⋊D11—22no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4D411yescharacteristic
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4D411yescharacteristic
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C2×#4313—22no—
102C2×#4313—41no—
103C2×#4313—41no—
104#66945—22no—
105#66945—41no—
106C4⋊C4×D11—22no—
107C4⋊C4×D11—41no—
108C11×#103—22no—
109C11×#103—41no—
110C11×C22⋊C8—41no—
111#66899—41no—
112#66899—41no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C22⋊(C11⋊C8)—41no—
123(C2×D11)⋊C8—22no—
124#66882—41no—
125#66872—22no—
126#26222—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C23×D11C2×D411yescharacteristic
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C2×C22⋊D11—22no—
148C2×C22⋊D11—41no—
149C2×C22⋊D11—41no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—42no—
162C2×C4×D11—42no—
163C2×C4×D11—81no—
164C2×C4×D11#4112yes—
165C2×C4×D11#4112yes—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—42no—
177C11×C4⋊C4#4112yes—
178C11×C4⋊C4#4112yes—
179C11×C22⋊C4—42no—
180C11×C22⋊C4—42no—
181C42×C11—42no—
182C22⋊Dic11—22no—
183C22⋊Dic11—42no—
184C22⋊Dic11—81no—
185(C2×D11)⋊C4—22no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—42no—
188(C2×D11)⋊C4—42no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—42no—
198Dic11⋊C4—22no—
199Dic11⋊C4—42no—
200Dic11⋊C4—42no—
201C4×Dic11—21no—
202C4×Dic11—21no—
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—
211#4313—44no—
212#2415—111no—
213#2352—111no—
214#2101—111no—
215#2076—111no—
216#2074—111no—
217#2035—111no—
218#1928—111no—
219#1920—111no—
220#1894—111no—
221#1873D1111yescharacteristic, complemented
222#1872—111no—
223#1870—111no—
224#1854—111no—
225#1825—111no—
226#1736—111no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11C22×D411yescharacteristic
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11#12312yes—
242Q8×C11—41no—
243Q8×C11—41no—
244Q8×C11—41no—
245Q8×C11—41no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
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—41no—
264C2×C4×C11—41no—
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11H(5,𝔽2)11yescharacteristic
270C2×C4×C11H(5,𝔽2)11yescharacteristic
271C22⋊D11—44no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11#12312yes—
293C4×D11—22no—
294C4×D11—22no—
295C4×D11—22no—
296C4×D11—22no—
297C4×D11—84no—
298C8×C11—41no—
299C8×C11—41no—
300C11⋊C8—41no—
301C11⋊C8—41no—
302C22×M16—111no—
303C2×C22⋊Q8—111no—
304C2×C22⋊Q8C2×D1111yescharacteristic
305C2×C4×D4—111no—
306C2×#117—111no—
307C2×#117C2×D1111yescharacteristic
308C22×C4⋊C4—111no—
309C2×#107—111no—
310C2×#106—111no—
311C2×#103—111no—
312C2×#103—111no—
313C2×#103C2×D1111yescharacteristic
314C2×#103C2×D1111yescharacteristic
315C2×C22⋊C8—111no—
316C2×C22⋊C8—111no—
317C2×C22⋊C8C2×D1111yescharacteristic
318#397—221no—
319#394—221no—
320#391—111no—
321#389—111no—
322#389—221no—
323#388—221no—
324#388—221no—
325#387—221no—
326#386—221no—
327#382—111no—
328#380—111no—
329#380—111no—
330#380—111no—
331C4×C4⋊C4—111no—
332C4×C22⋊C4—221no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340C2×D1111yescharacteristic
342#340C2×D1111yescharacteristic
343#336—111no—
344#336—111no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11C2×#12311yescharacteristic
353C22×C11#54611yescharacteristic
354C22×C11#54611yescharacteristic
355C22×C11#57511yescharacteristic
356C22×C11#57511yescharacteristic
357C22×C11#57711yescharacteristic
358C22×C11#57811yescharacteristic
359C2×D11—22no—
360C2×D11—22no—
361C2×D11—22no—
362C2×D11—41no—
363C2×D11—41no—
364C2×D11—41no—
365C2×D11—41no—
366C4×C11—41no—
367C4×C11—42no—
368C4×C11—42no—
369C4×C11—81no—
370C4×C11—81no—
371C4×C11#52911yescharacteristic
372C4×C11#53811yescharacteristic
373C4×C11#55311yescharacteristic
374C4×C11#55311yescharacteristic
375Dic11—22no—
376Dic11—41no—
377Dic11—41no—
378Dic11—81no—
379Dic11—81no—
380Dic11—81no—
381Dic11—81no—
382C22×Q8C22×D1111yescharacteristic
383C22×D4—111no—
384C23×C4—111no—
385C23×C4—221no—
386C23×C4C22×D1111yescharacteristic
387C2×M16—222no—
388C2×M16—441no—
389C2×M16—441no—
390C22×C8—111no—
391C22×C8—111no—
392C22×C8C22×D1111yescharacteristic
393C22×C8C22×D1111yescharacteristic
394C22⋊Q8—22no—
395C22⋊Q8—41no—
396C22⋊Q8—222no—
397C22⋊Q8—222no—
398C4×D4—222no—
399C4×D4—222no—
400#117—22no—
401#117—41no—
402#117—222no—
403#117—441no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—111no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—222no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—441no—
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—111no—
421C2×C22⋊C4—111no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C42—21no—
428C2×C42—111no—
429C2×C42—221no—
430C2×C42—221no—
431#107—441no—
432#106—222no—
433#103—22no—
434#103—41no—
435#103—441no—
436#103—441no—
437C22⋊C8—41no—
438C22⋊C8—222no—
439C22⋊C8—441no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444#95—221no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449C2×C11—81no—
450C2×C11#244411yescharacteristic
451C2×C11#309311yescharacteristic
452C2×C11#309711yescharacteristic
453C2×C11#331111yescharacteristic
454C2×C11#331511yescharacteristic
455C2×C11#332611yescharacteristic
456C2×C11#332711yescharacteristic
457D11—42no—
458C24—111no—
459C24D4×D1111yescharacteristic
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×D4—222no—
467C2×D4—441no—
468C2×D4—441no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—111no—
480C22×C4—112no—
481C22×C4—112no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—442no—
493C22×C4—442no—
494C22×C4—881no—
495C22×C4D4×D1111yescharacteristic
496C22×C4C23×D1111yescharacteristic
497M16—444no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—42no—
515C4⋊C4—222no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—221no—
524C4⋊C4—442no—
525C4⋊C4—442no—
526C4⋊C4—442no—
527C4⋊C4#433912yes—
528C4⋊C4#434112yes—
529C22⋊C4—42no—
530C22⋊C4—42no—
531C22⋊C4—222no—
532C22⋊C4—222no—
533C22⋊C4—442no—
534C22⋊C4—442no—
535C22⋊C4—442no—
536C22⋊C4—442no—
537C22⋊C4—881no—
538C42—42no—
539C42—221no—
540C42—221no—
541C42—442no—
542C42—881no—
543C11#2622211yescharacteristic, complemented, Sylow
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—112no—
552C23—221no—
553C23—221no—
554C23—221no—
555C23—221no—
556C23—221no—
557C23—221no—
558C23C2×D4×D1111yescharacteristic
559Q8—41no—
560Q8—41no—
561Q8—41no—
562Q8—41no—
563D4—444no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—112no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—222no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—884no—
609C2×C4C2×#433911yescharacteristic
610C2×C4C2×#434111yescharacteristic
611C2×C4#6703711yescharacteristic
612C2×C4#6703711yescharacteristic
613C2×C4#41×D1111yescharacteristic
614C2×C4#41×D1111yescharacteristic
615C8—41no—
616C8—41no—
617C8—441no—
618C8—441no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—222no—
627C22—222no—
628C22—222no—
629C22—441no—
630C22—441no—
631C22—441no—
632C22—441no—
633C22#1062302111yescharacteristic
634C22#1062312211yescharacteristic
635C22D11×#12311yescharacteristic
636C22#1062329911yescharacteristic
637C22#1062330211yescharacteristic
638C22#1062330811yescharacteristic
639C22#1062330911yescharacteristic
640C4—42no—
641C4—42no—
642C4—41no—
643C4—81no—
644C4—81no—
645C4—222no—
646C4—441no—
647C4—441no—
648C4—881no—
649C4—881no—
650C4—881no—
651C4—881no—
652C4#1062308811yescharacteristic
653C4#1062308911yescharacteristic
654C4#1062314411yescharacteristic
655C4#1062314511yescharacteristic
656C2—81no—
657C2—442no—
658C2#1307236311yescharacteristic
659C2#1307854811yescharacteristic
660C2#1307858011yescharacteristic
661C2#1308065611yescharacteristic
662C2#1308070811yescharacteristic
663C2#1308086511yescharacteristic
664C2#1308087711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1873C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
hypercenter#1873D11
hypocenterC11#26222
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
3. #13070187C2semidirect
4. #13070044C2semidirect
5. #13070037C2semidirect
6. #13069809C2semidirect
7. #13069259C2semidirect
8. #13069204C2semidirect
9. #13069046C2semidirect
10. #13068920C2semidirect
12. #13068818C2semidirect
13. #13068711C2semidirect
14. #13068334C2semidirect
15. C11×#1873C2semidirect
221. #1873D11semidirect
543. C11#26222semidirect

Maximal subgroups

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

subgroupindex
#130720412
#130715462
#130701872
#130700442
#130700372
#130698092
#130692592
#130692042
#130690462
#130689202
#130689102
#130688182
#130687112
#130683342
C11×#18732
#2622211