Finite Group Databasebeta

← #14814513

Subgroups — #14814513

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#13072034C211yesmaximal, characteristic
2#13071565C211yesmaximal, characteristic, complemented
3#13070175C211yesmaximal, characteristic, complemented
4#13070049C211yesmaximal, characteristic, complemented
5#13070021C211yesmaximal, characteristic, complemented
6#13069799C211yesmaximal, characteristic, complemented
7#13069244C211yesmaximal, characteristic, complemented
8#13069209C211yesmaximal, characteristic, complemented
9#13069044C211yesmaximal, characteristic, complemented
10#13068936C211yesmaximal, characteristic, complemented
11#13068936C211yesmaximal, characteristic, complemented
12#13068817C211yesmaximal, characteristic, complemented
13#13068712C211yesmaximal, characteristic, complemented
14#13068333C211yesmaximal, characteristic, complemented
15C11×#1869C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66983C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26#10622836—21no—
27#10622834—21no—
28#10622825C2211yescharacteristic
29#10622825C2211yescharacteristic
30#10622825C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×#66882C2211yescharacteristic
36C2×#66881C2211yescharacteristic
37#10622603—21no—
38C4⋊C4×Dic11—21no—
39#10622572—21no—
40#10622570—21no—
41#10622564—21no—
42#10622564—21no—
43#10622552C2211yescharacteristic
44#10622548C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46#10622541C2211yescharacteristic
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C22×D4×C11D411yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C22×C22⋊D11—21no—
64C22×D44C2311yescharacteristic
65C22×C8×C11—22no—
66C22×C8×C11—41no—
67C22×C8×C11—41no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C4×D4×C11—22no—
73C4×D4×C11—22no—
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C22⋊C4D411yescharacteristic
76C2×C11×C22⋊C4D411yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84#66983—22no—
85#66983—22no—
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—
92#66979—22no—
93#66979—22no—
94#66979—22no—
95#66979—41no—
96#66979—41no—
97#66979—41no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C2×Dic11⋊C4—21no—
108C2×C4×Dic11—21no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11—21no—
112C11×C22⋊C8—22no—
113C11×C22⋊C8—41no—
114C11×C22⋊C8—41no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120#66885—22no—
121#66885—41no—
122#66885—41no—
123#66885—41no—
124#66882—22no—
125#66881—41no—
126#26209—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C24×C11C2×D411yescharacteristic
129C23×D11—21no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—41no—
133C22×C4×C11—21no—
134C22×C4×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×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4112yes—
148C22×C4×C11#4112yes—
149C22×C4×C11C2411yescharacteristic
150C2×C22⋊D11—42no—
151C2×C22⋊D11—42no—
152C2×C22⋊D11—42no—
153C2×C22⋊D11—81no—
154C2×C22⋊D11—81no—
155C2×C22⋊D11—81no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
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×D44—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—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—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—44no—
182C11×C4⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C42×C11—21no—
186C42×C11—21no—
187C22⋊Dic11—42no—
188C22⋊Dic11—42no—
189C22⋊Dic11—42no—
190C22⋊Dic11—81no—
191C22⋊Dic11—81no—
192C22⋊Dic11—81no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—81no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—42no—
210C4⋊Dic11—81no—
211C4⋊Dic11#4112yes—
212C4⋊Dic11#4112yes—
213Dic11⋊C4—81no—
214C4×Dic11—42no—
215C4×Dic11—42no—
216C4×Dic11—42no—
217C4×Dic11—42no—
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#1875—111no—
229#1869D1111yescharacteristic, complemented
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—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11#12312yes—
247C23×C11C22×D411yescharacteristic
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—41no—
255D4×C11—44no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11#12312yes—
275C2×C4×C11#13512yes—
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—84no—
283C22⋊D11—84no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
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—41no—
304C2×Dic11—41no—
305D44—41no—
306D44—41no—
307D44—41no—
308D44—41no—
309C8×C11—41no—
310C8×C11—41no—
311C8×C11—41no—
312C8×C11—41no—
313C23×C8C2×D1111yescharacteristic
314C2×#121—111no—
315C2×#121—111no—
316C2×C4×D4C2×D1111yescharacteristic
317C2×#117—111no—
318C2×#117—111no—
319C2×#117—111no—
320C2×#107—111no—
321C2×#106—111no—
322C2×#102—111no—
323C2×#102—111no—
324C2×#102—111no—
325C2×#102—111no—
326C2×C22⋊C8C2×D1111yescharacteristic
327C2×C22⋊C8C2×D1111yescharacteristic
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#340—111no—
353#340—111no—
354#336C2×D1111yescharacteristic
355#336C2×D1111yescharacteristic
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11C2×#12311yescharacteristic
371C22×C11#54611yescharacteristic
372C22×C11#54611yescharacteristic
373C22×C11C2×#13511yescharacteristic
374C22×C11#57511yescharacteristic
375C22×C11#57611yescharacteristic
376C22×C11#57711yescharacteristic
377C2×D11—81no—
378C2×D11—81no—
379C2×D11—81no—
380C2×D11—81no—
381C2×D11—81no—
382C2×D11—81no—
383C2×D11—81no—
384C4×C11—22no—
385C4×C11—22no—
386C4×C11—41no—
387C4×C11—41no—
388C4×C11#52911yescharacteristic
389C4×C11#53811yescharacteristic
390C4×C11#55311yescharacteristic
391C4×C11#55311yescharacteristic
392Dic11—42no—
393Dic11—42no—
394Dic11—81no—
395Dic11—81no—
396Dic11—81no—
397Dic11—81no—
398Dic11—81no—
399C22×D4—111no—
400C22×D4—221no—
401C22×D4—221no—
402C22×D4D4411yescharacteristic
403C23×C4C22×D1111yescharacteristic
404C23×C4C22×D1111yescharacteristic
405C22×C8—22no—
406C22×C8—41no—
407C22×C8—41no—
408C22×C8C22×D1111yescharacteristic
409C22×C8C22×D1111yescharacteristic
410C22×C8C22×D1111yescharacteristic
411C22×C8C22×D1111yescharacteristic
412#121—222no—
413#121—222no—
414#121—222no—
415#121—441no—
416C4×D4—22no—
417C4×D4—22no—
418#117—222no—
419#117—222no—
420#117—222no—
421#117—441no—
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—111no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4D4411yescharacteristic
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
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⋊C4D4411yescharacteristic
446C2×C22⋊C4D4411yescharacteristic
447C2×C42—221no—
448C2×C42—221no—
449C2×C42—221no—
450C2×C42—221no—
451C2×C42C22×D1111yescharacteristic
452#107—222no—
453#106—441no—
454#102—222no—
455#102—441no—
456#102—441no—
457#102—441no—
458C22⋊C8—22no—
459C22⋊C8—41no—
460C22⋊C8—41no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466C2×C11—42no—
467C2×C11—81no—
468C2×C11#244411yescharacteristic
469C2×C11#309111yescharacteristic
470C2×C11#309611yescharacteristic
471C2×C11#330411yescharacteristic
472C2×C11#330511yescharacteristic
473C2×C11#330711yescharacteristic
474C2×C11#331911yescharacteristic
475D11—161no—
476C24—221no—
477C24C2×D4411yescharacteristic
478C24C2×D4411yescharacteristic
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—41no—
482C2×D4—221no—
483C2×D4—221no—
484C2×D4—221no—
485C2×D4—221no—
486C2×D4—221no—
487C2×D4—221no—
488C2×D4—442no—
489C2×D4—442no—
490C2×D4—442no—
491C2×D4—881no—
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—21no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4C2×D4411yescharacteristic
512C22×C4C2×D4411yescharacteristic
513C22×C4C2×D4411yescharacteristic
514C22×C4C2×D4411yescharacteristic
515C22×C4#434112yes—
516C22×C4#434112yes—
517C22×C4C23×D1111yescharacteristic
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—44no—
531C4⋊C4—22no—
532C4⋊C4—112no—
533C4⋊C4—112no—
534C4⋊C4—221no—
535C4⋊C4—221no—
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—221no—
545C4⋊C4—221no—
546C4⋊C4—442no—
547C4⋊C4—881no—
548C4⋊C4—881no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—442no—
552C22⋊C4—442no—
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—21no—
562C42—21no—
563C42—442no—
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—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—441no—
582C23—441no—
583C23—441no—
584C23—441no—
585C23—441no—
586C23—441no—
587C23—441no—
588C23#6693912yes—
589C23C22×D4411yescharacteristic
590D4—44no—
591D4—441no—
592D4—441no—
593D4—441no—
594D4—441no—
595D4—884no—
596D4—884no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—222no—
616C2×C4—222no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
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#6693912yes—
637C2×C4#6695712yes—
638C2×C4C2×#434111yescharacteristic
639C2×C4C2×#434111yescharacteristic
640C2×C4#6703711yescharacteristic
641C2×C4#6703711yescharacteristic
642C2×C4#41×D1111yescharacteristic
643C2×C4#41×D1111yescharacteristic
644C8—41no—
645C8—41no—
646C8—41no—
647C8—41no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—881no—
663C22—881no—
664C22—881no—
665C22—881no—
666C22—881no—
667C22—881no—
668C22—881no—
669C22C2×#6693911yescharacteristic
670C22#1062308511yescharacteristic
671C22#1062308511yescharacteristic
672C22C2×#6695711yescharacteristic
673C22#1062327911yescharacteristic
674C22#1062328211yescharacteristic
675C22#1062328311yescharacteristic
676C4—22no—
677C4—22no—
678C4—41no—
679C4—41no—
680C4—442no—
681C4—442no—
682C4—881no—
683C4—881no—
684C4—881no—
685C4—881no—
686C4—881no—
687C4#1062312411yescharacteristic
688C4#1062313211yescharacteristic
689C4#1062313211yescharacteristic
690C4#1062318011yescharacteristic
691C2—42no—
692C2—81no—
693C2—1761no—
694C2#1307236411yescharacteristic
695C2#1307853111yescharacteristic
696C2#1307857511yescharacteristic
697C2#1308055611yescharacteristic
698C2#1308056711yescharacteristic
699C2#1308059411yescharacteristic
700C2#1308077411yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1869C2
socleC23×C11C22×D4
prime radical#13072034C2
hypercenter#1869D11
hypocenterC11#26209
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1869

Complements

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

NH ≅ G/Ntype
2. #13071565C2semidirect
3. #13070175C2semidirect
4. #13070049C2semidirect
5. #13070021C2semidirect
6. #13069799C2semidirect
7. #13069244C2semidirect
8. #13069209C2semidirect
9. #13069044C2semidirect
10. #13068936C2semidirect
11. #13068936C2semidirect
12. #13068817C2semidirect
13. #13068712C2semidirect
14. #13068333C2semidirect
15. C11×#1869C2semidirect
229. #1869D11semidirect
567. C11#26209semidirect

Maximal subgroups

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

subgroupindex
#130720342
#130715652
#130701752
#130700492
#130700212
#130697992
#130692442
#130692092
#130690442
#130689362
#130688172
#130687122
#130683332
C11×#18692
#2620911