Finite Group Databasebeta

← #14814512

Subgroups — #14814512

Order 2816.

830 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072030C211yesmaximal, characteristic
2#13071566C211yesmaximal, characteristic, complemented
3#13070177C211yesmaximal, characteristic, complemented
4#13070049C211yesmaximal, characteristic, complemented
5#13070022C211yesmaximal, characteristic, complemented
6#13069795C211yesmaximal, characteristic, complemented
7#13069245C211yesmaximal, characteristic, complemented
8#13069211C211yesmaximal, characteristic, complemented
9#13069041C211yesmaximal, characteristic, complemented
10#13068935C211yesmaximal, characteristic, complemented
11#13068905C211yesmaximal, characteristic, complemented
12#13068816C211yesmaximal, characteristic, complemented
13#13068711C211yesmaximal, characteristic, complemented
14#13068331C211yesmaximal, characteristic, complemented
15C11×#1875C211yesmaximal, characteristic, complemented
16C2×C11×#121C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×#66991C2211yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C2×#66945C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26#10622836—21no—
27#10622834—21no—
28#10622834C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31#10622825C2211yescharacteristic
32#10622825C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36#10622600C2211yescharacteristic
37#10622598C2211yescharacteristic
38#10622589C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622574—21no—
42#10622570—21no—
43#10622557—21no—
44#10622557—21no—
45#10622553—21no—
46C4×Dic11⋊C4—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×D4×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C22×C22⋊D11D411yescharacteristic
64C22×C4×D11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×#121—22no—
68C11×#121—41no—
69C11×#117—22no—
70C11×#117—41no—
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⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11D411yescharacteristic
83#66991—22no—
84#66991—22no—
85C4×C22⋊D11—22no—
86C4×C22⋊D11—22no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4D411yescharacteristic
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4D411yescharacteristic
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C2×C8×D11—22no—
106C2×C8×D11—41no—
107C2×C8×D11—41no—
108#66945—22no—
109#66945—22no—
110#66945—41no—
111#66945—41no—
112C11×#102—22no—
113C11×#102—41no—
114C11×C22⋊C8—41no—
115#66896—41no—
116#66896—41no—
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#66881—41no—
125#66871—22no—
126#26209—111nomaximal, Sylow
127C24×C11—21no—
128C24×C11C2×D411yescharacteristic
129C23×D11C2×D411yescharacteristic
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11—81no—
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×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C2×C22⋊D11—22no—
151C2×C22⋊D11—22no—
152C2×C22⋊D11—41no—
153C2×C22⋊D11—42no—
154C2×C22⋊D11—81no—
155C2×C22⋊D11—81no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11#4112yes—
168C2×C4×D11#4112yes—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4#4112yes—
180C11×C4⋊C4#4112yes—
181C11×C22⋊C4—42no—
182C11×C22⋊C4—42no—
183C42×C11—42no—
184C22⋊Dic11—22no—
185C22⋊Dic11—42no—
186C22⋊Dic11—42no—
187C22⋊Dic11—81no—
188C22⋊Dic11—81no—
189C22⋊Dic11—81no—
190(C2×D11)⋊C4—22no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—81no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—81no—
203Dic11⋊C4—22no—
204Dic11⋊C4—42no—
205Dic11⋊C4—81no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—42no—
209C4×Dic11—42no—
210C4×Dic11—42no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C8×D11—44no—
218#2414—111no—
219#2354—111no—
220#2099—111no—
221#2077—111no—
222#2071—111no—
223#2033—111no—
224#1926—111no—
225#1921—111no—
226#1893—111no—
227#1875—111no—
228#1875D1111yescharacteristic, complemented
229#1869—111no—
230#1854—111no—
231#1825—111no—
232#1735—111no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11C22×D411yescharacteristic
248C22×D11—21no—
249C22×D11—21no—
250C22×D11—21no—
251C22×D11—21no—
252C22×D11—21no—
253C22×D11—21no—
254C22×D11#12312yes—
255D4×C11—41no—
256D4×C11—41no—
257D4×C11—41no—
258D4×C11—41no—
259D4×C11—84no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—41no—
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×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11H(5,𝔽2)11yescharacteristic
281C2×C4×C11H(5,𝔽2)11yescharacteristic
282C22⋊D11—44no—
283C22⋊D11—84no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11#12312yes—
304C2×Dic11#13512yes—
305C4×D11—22no—
306C4×D11—22no—
307C4×D11—22no—
308C4×D11—22no—
309C8×C11—41no—
310C8×C11—41no—
311C11⋊C8—41no—
312C11⋊C8—41no—
313C23×C8—111no—
314C2×#121—111no—
315C2×#121C2×D1111yescharacteristic
316C2×C4×D4—111no—
317C2×#117—111no—
318C2×#117—111no—
319C2×#117C2×D1111yescharacteristic
320C2×#107—111no—
321C2×#106—111no—
322C2×#102—111no—
323C2×#102—111no—
324C2×#102C2×D1111yescharacteristic
325C2×#102C2×D1111yescharacteristic
326C2×C22⋊C8—111no—
327C2×C22⋊C8—111no—
328C2×C22⋊C8C2×D1111yescharacteristic
329#394—221no—
330#392—221no—
331#390—111no—
332#390—221no—
333#390—221no—
334#389—111no—
335#388—221no—
336#388—221no—
337#388—221no—
338#384—111no—
339#380—111no—
340#380—111no—
341#380—111no—
342C4×C4⋊C4—111no—
343C4×C4⋊C4—221no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340C2×D1111yescharacteristic
353#340C2×D1111yescharacteristic
354#336—111no—
355#336—111no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11C2×#12311yescharacteristic
371C22×C11#54611yescharacteristic
372C22×C11#54611yescharacteristic
373C22×C11C2×#13511yescharacteristic
374C22×C11#57511yescharacteristic
375C22×C11#57611yescharacteristic
376C22×C11#57711yescharacteristic
377C2×D11—22no—
378C2×D11—22no—
379C2×D11—22no—
380C2×D11—41no—
381C2×D11—41no—
382C2×D11—41no—
383C2×D11—41no—
384C4×C11—41no—
385C4×C11—42no—
386C4×C11—42no—
387C4×C11—81no—
388C4×C11#52911yescharacteristic
389C4×C11#53811yescharacteristic
390C4×C11#55311yescharacteristic
391C4×C11#55311yescharacteristic
392Dic11—22no—
393Dic11—22no—
394Dic11—41no—
395Dic11—81no—
396Dic11—81no—
397Dic11—81no—
398Dic11—81no—
399C22×D4—21no—
400C22×D4—111no—
401C22×D4—221no—
402C22×D4C22×D1111yescharacteristic
403C23×C4—111no—
404C23×C4C22×D1111yescharacteristic
405C22×C8—111no—
406C22×C8—111no—
407C22×C8—222no—
408C22×C8—441no—
409C22×C8—441no—
410C22×C8C22×D1111yescharacteristic
411C22×C8C22×D1111yescharacteristic
412#121—22no—
413#121—41no—
414#121—222no—
415#121—222no—
416C4×D4—222no—
417C4×D4—222no—
418#117—22no—
419#117—41no—
420#117—222no—
421#117—222no—
422#117—441no—
423#117—441no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
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—111no—
438C2×C22⋊C4—111no—
439C2×C22⋊C4—221no—
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⋊C4—221no—
447C2×C42—21no—
448C2×C42—111no—
449C2×C42—221no—
450C2×C42—221no—
451C2×C42—221no—
452#107—222no—
453#106—441no—
454#102—22no—
455#102—41no—
456#102—441no—
457#102—441no—
458C22⋊C8—41no—
459C22⋊C8—222no—
460C22⋊C8—441no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466C2×C11—81no—
467C2×C11—161no—
468C2×C11#244411yescharacteristic
469C2×C11#309111yescharacteristic
470C2×C11#309611yescharacteristic
471C2×C11#330411yescharacteristic
472C2×C11#330511yescharacteristic
473C2×C11#330711yescharacteristic
474C2×C11#331911yescharacteristic
475D11—42no—
476C24—21no—
477C24—111no—
478C24D4×D1111yescharacteristic
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—81no—
488C2×D4—222no—
489C2×D4—222no—
490C2×D4—441no—
491C2×D4—442no—
492C2×D4—881no—
493C2×D4—881no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—111no—
504C22×C4—111no—
505C22×C4—112no—
506C22×C4—112no—
507C22×C4—111no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4D4×D1111yescharacteristic
517C22×C4C23×D1111yescharacteristic
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8—444no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—222no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—442no—
545C4⋊C4—881no—
546C4⋊C4—881no—
547C4⋊C4#433912yes—
548C4⋊C4#434112yes—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—222no—
552C22⋊C4—222no—
553C22⋊C4—442no—
554C22⋊C4—442no—
555C22⋊C4—442no—
556C22⋊C4—442no—
557C22⋊C4—881no—
558C22⋊C4—881no—
559C22⋊C4—881no—
560C22⋊C4—881no—
561C42—42no—
562C42—221no—
563C42—221no—
564C42—442no—
565C42—442no—
566C42—442no—
567C11#2620911yescharacteristic, complemented, Sylow
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—112no—
583C23—221no—
584C23—221no—
585C23—221no—
586C23—221no—
587C23—221no—
588C23—221no—
589C23C2×D4×D1111yescharacteristic
590D4—41no—
591D4—41no—
592D4—41no—
593D4—41no—
594D4—84no—
595D4—444no—
596D4—884no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—112no—
614C2×C4—112no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—222no—
622C2×C4—222no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—221no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4C2×#433911yescharacteristic
639C2×C4C2×#434111yescharacteristic
640C2×C4#6703711yescharacteristic
641C2×C4#6703711yescharacteristic
642C2×C4#41×D1111yescharacteristic
643C2×C4#41×D1111yescharacteristic
644C8—41no—
645C8—41no—
646C8—441no—
647C8—441no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22—222no—
663C22—222no—
664C22—222no—
665C22—441no—
666C22—441no—
667C22—441no—
668C22—441no—
669C22#1062302111yescharacteristic
670C22#1062312211yescharacteristic
671C22D11×#12311yescharacteristic
672C22D11×#13511yescharacteristic
673C22#1062330111yescharacteristic
674C22#1062330411yescharacteristic
675C22#1062330511yescharacteristic
676C4—42no—
677C4—42no—
678C4—41no—
679C4—81no—
680C4—222no—
681C4—222no—
682C4—441no—
683C4—881no—
684C4—881no—
685C4—881no—
686C4—881no—
687C4#1062308811yescharacteristic
688C4#1062308911yescharacteristic
689C4#1062314411yescharacteristic
690C4#1062314511yescharacteristic
691C2—81no—
692C2—161no—
693C2—442no—
694C2#1307236311yescharacteristic
695C2#1307852811yescharacteristic
696C2#1307856911yescharacteristic
697C2#1308055111yescharacteristic
698C2#1308055911yescharacteristic
699C2#1308058511yescharacteristic
700C2#1308077311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1875C2
socleC23×C11C22×D4
prime radical#13072030C2
hypercenter#1875D11
hypocenterC11#26209
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1875

Complements

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

NH ≅ G/Ntype
2. #13071566C2semidirect
3. #13070177C2semidirect
4. #13070049C2semidirect
5. #13070022C2semidirect
6. #13069795C2semidirect
7. #13069245C2semidirect
8. #13069211C2semidirect
9. #13069041C2semidirect
10. #13068935C2semidirect
11. #13068905C2semidirect
12. #13068816C2semidirect
13. #13068711C2semidirect
14. #13068331C2semidirect
15. C11×#1875C2semidirect
228. #1875D11semidirect
567. C11#26209semidirect

Maximal subgroups

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

subgroupindex
#130720302
#130715662
#130701772
#130700492
#130700222
#130697952
#130692452
#130692112
#130690412
#130689352
#130689052
#130688162
#130687112
#130683312
C11×#18752
#2620911