Finite Group Databasebeta

← #14760445

Subgroups — #14760445

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622425C211yesmaximal, characteristic
2C2×C4×#4325C211yesmaximal, characteristic, complemented
3C2×#10622321C211yesmaximal, characteristic, complemented
4#13071310C211yesmaximal, characteristic
5#13071292C211yesmaximal, characteristic, complemented
6#13069494C211yesmaximal, characteristic, complemented
7#13069353C211yesmaximal, characteristic, complemented
8#13069297C211yesmaximal, characteristic, complemented
9#13069294C211yesmaximal, characteristic, complemented
10#13069043C211yesmaximal, characteristic
11#13069036C211yesmaximal, characteristic, complemented
12#13068648C211yesmaximal, characteristic, complemented
13C4×#66871C211yesmaximal, characteristic, complemented
14#13068442C211yesmaximal, characteristic, complemented
15C11×#1763C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C22×#4325C2211yescharacteristic
19C22×#4313C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21C2×#66948C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×#66925C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#97C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28#10622843C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66879C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34C4×#4325—24no—
35#10622603—21no—
36#10622601C2211yescharacteristic
37#10622600C2211yescharacteristic
38#10622600C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622586C2211yescharacteristic
41#10622585—21no—
42C2×#66873C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622553—21no—
47#10622553—21no—
48#10622552—21no—
49C4×C4⋊Dic11C2211yescharacteristic
50#10622546—21no—
51C2×C4×C11⋊C8C2211yescharacteristic
52#10622425C418yescomplemented
53#10622321—24no—
54#10622281—21no—
55#10622278—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D44—21no—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×C4×D11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C42×C11—21no—
76C2×C42×C11—21no—
77C2×C42×C11C2311yescharacteristic
78#66999—22no—
79#66999C2×C414yescomplemented
80C2×#4325—22no—
81C2×#4325—22no—
82C2×#4325C2×C414yes—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4D411yescharacteristic
91C2×(C2×D11)⋊C4D411yescharacteristic
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4D411yescharacteristic
99C2×Dic11⋊C4D411yescharacteristic
100C2×C4×Dic11—21no—
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C2×#4313—22no—
105C2×#4313—22no—
106C2×#4313C2×C414yescomplemented
107C2×C8×D11—22no—
108C2×C8×D11—22no—
109C2×C8×D11—22no—
110#66948—22no—
111#66948C2×C414yes—
112C4×D44—22no—
113C4×D44—22no—
114#66925—22no—
115#66925—22no—
116C11×#103—22no—
117C11×#103C2×C414yescomplemented
118C11×#97—22no—
119C11×#95—21no—
120#66899—22no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128#66885—22no—
129#66885C2×C414yes—
130#66879—22no—
131C8×Dic11—22no—
132#66873—22no—
133#66872—22no—
134#66871—22no—
135#66871C2×C414yescomplemented
136C4×C11⋊C8D414yescomplemented
137#21535—111nomaximal, Sylow
138C23×D11—21no—
139C23×D11C2×D411yescharacteristic
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11C22×C412yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C2×D44—24no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—81no—
166C2×D44—81no—
167C2×D44C22×C412yes—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11—42no—
173C2×C4×D11—81no—
174C2×C4×D11—81no—
175C2×C4×D11C22×C412yes—
176C2×C4×D11#4112yes—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11C22×C412yes—
182C2×C8×C11#4112yes—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—42no—
189C11×C4⋊C4C22×C412yes—
190C42×C11—42no—
191C42×C11—81no—
192C42×C11C2×D412yes—
193C42×C11#4112yes—
194#4325—28no—
195(C2×D11)⋊C4—24no—
196(C2×D11)⋊C4—24no—
197(C2×D11)⋊C4—22no—
198(C2×D11)⋊C4—22no—
199(C2×D11)⋊C4—42no—
200(C2×D11)⋊C4—81no—
201(C2×D11)⋊C4—81no—
202(C2×D11)⋊C4—81no—
203(C2×D11)⋊C4—81no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—81no—
210C4⋊Dic11C22×C412yes—
211Dic11⋊C4—24no—
212Dic11⋊C4—22no—
213Dic11⋊C4—22no—
214Dic11⋊C4—81no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—81no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8C22×C412yes—
221C2×C11⋊C8C2×D412yes—
222C2×C11⋊C8C2×D412yes—
223C2×C11⋊C8#4112yes—
224#4313—28no—
225C8×D11—28no—
226C2×#468—111no—
227C2×C4×SD16—111no—
228C2×#405—111no—
229#2324—111no—
230#2323—111no—
231#1973—111no—
232#1943—111no—
233#1934—111no—
234#1933—111no—
235#1893—111no—
236#1892—111no—
237#1809—111no—
238C4×#107—111no—
239#1763D1111yescharacteristic, complemented
240#1762—111no—
241C23×C11C22×D411yescharacteristic
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—22no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11C4×D412yes—
256Q8×C11—22no—
257Q8×C11—22no—
258Q8×C11—41no—
259Q8×C11—41no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
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×C11#12112yes—
277C2×C4×C11#12112yes—
278C2×C4×C11C23×C411yescharacteristic
279C2×C4×C11C22×D411yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—22no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
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×Dic11C4×D412yes—
302D44—22no—
303D44—22no—
304D44—41no—
305D44—41no—
306D44—84no—
307C4×D11—22no—
308C4×D11—22no—
309C4×D11—22no—
310C4×D11—22no—
311C4×D11—84no—
312C8×C11—22no—
313C8×C11—22no—
314C11⋊C8—22no—
315C11⋊C8C4×D414yes—
316C22×SD16—111no—
317C22×M16—111no—
318C23×C8—111no—
319C2×C22⋊Q8—111no—
320C2×#121—111no—
321C2×C4×Q8C2×D1111yescharacteristic
322C2×C4×D4—111no—
323C2×#117—111no—
324#468—118no—
325C4×SD16—224no—
326C2×#107—111no—
327C2×#107—111no—
328C2×#106—111no—
329C2×#103—111no—
330C2×#103C2×D1111yescharacteristic
331C2×#103C2×D1111yescharacteristic
332C2×#102—111no—
333C2×#102—111no—
334C2×#102—111no—
335#405—224no—
336C2×#97—111no—
337C2×#97C2×D1111yescharacteristic
338C2×C4×C8—111no—
339C2×C4×C8—111no—
340#391—111no—
341#390—111no—
342#390—221no—
343#389—111no—
344#389—111no—
345#389—221no—
346#388—221no—
347#388—221no—
348#388—221no—
349#387—221no—
350#386—221no—
351#385—221no—
352#380—111no—
353#380—111no—
354C4×C4⋊C4—111no—
355C4×C4⋊C4C2×D1111yescharacteristic
356#340—111no—
357#340—111no—
358#340—111no—
359#340—111no—
360#340C2×D1111yescharacteristic
361#340C2×D1111yescharacteristic
362C22×C11C2×C4×D411yescharacteristic
363C22×C11C2×#12111yescharacteristic
364C22×C11#53211yescharacteristic
365C22×C11#57611yescharacteristic
366C22×C11#57711yescharacteristic
367C22×C11#57711yescharacteristic
368C22×C11#57811yescharacteristic
369C2×D11—22no—
370C2×D11—22no—
371C2×D11—22no—
372C2×D11—41no—
373C2×D11—41no—
374C2×D11—41no—
375C2×D11—41no—
376C2×D11—42no—
377C2×D11—42no—
378C2×D11—42no—
379C2×D11—81no—
380C2×D11—81no—
381C2×D11—81no—
382C2×D11—81no—
383C4×C11—22no—
384C4×C11—22no—
385C4×C11—42no—
386C4×C11—42no—
387C4×C11—81no—
388C4×C11—81no—
389C4×C11C2×C4×D411yescharacteristic
390C4×C11C4×#4111yescharacteristic
391C4×C11#52511yescharacteristic
392C4×C11#52911yescharacteristic
393Dic11—22no—
394Dic11—42no—
395Dic11—41no—
396Dic11—41no—
397Dic11—81no—
398Dic11—81no—
399C22×Q8C22×D1111yescharacteristic
400C22×D4—111no—
401C22×D4—221no—
402C23×C4—111no—
403C23×C4—221no—
404C2×SD16—114no—
405C2×SD16—222no—
406C2×SD16—222no—
407C2×M16—114no—
408C2×M16—222no—
409C2×M16—222no—
410C22×C8—111no—
411C22×C8—111no—
412C22×C8—222no—
413C22×C8—222no—
414C22×C8—222no—
415C22×C8C22×D1111yescharacteristic
416C22×C8C22×D1111yescharacteristic
417C22⋊Q8—114no—
418C22⋊Q8—222no—
419#121—114no—
420#121—222no—
421C4×Q8—22no—
422C4×Q8—22no—
423C4×D4—222no—
424C4×D4—222no—
425#117—222no—
426#117—222no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—111no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C4⋊C4C22×D1111yescharacteristic
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C22⋊C4—111no—
440C2×C22⋊C4—111no—
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×C22⋊C4—221no—
448C2×C42—21no—
449C2×C42—21no—
450C2×C42—111no—
451C2×C42—221no—
452C2×C42C22×D1111yescharacteristic
453#107—114no—
454#107—222no—
455#106—222no—
456#103—22no—
457#103—222no—
458#103C4×D1114yescomplemented
459#102—114no—
460#102—222no—
461#102—222no—
462#97—22no—
463#97—222no—
464C4×C8—114no—
465C4×C8—222no—
466#95—21no—
467#95—221no—
468#95—221no—
469#95—221no—
470#95—221no—
471#95—221no—
472#95—221no—
473#95—221no—
474C2×C11C4×#12111yescharacteristic
475C2×C11#294611yescharacteristic
476C2×C11#294711yescharacteristic
477C2×C11#305711yescharacteristic
478C2×C11#306111yescharacteristic
479C2×C11#317811yescharacteristic
480C2×C11#317911yescharacteristic
481D11—42no—
482D11—82no—
483C24—111no—
484C24—221no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8C2×C4×D1112yes—
491C2×D4—112no—
492C2×D4—224no—
493C2×D4—221no—
494C2×D4—221no—
495C2×D4—221no—
496C2×D4—221no—
497C2×D4—221no—
498C2×D4—881no—
499C2×D4—881no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—111no—
505C22×C4—112no—
506C22×C4—112no—
507C22×C4—111no—
508C22×C4—111no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—442no—
517C22×C4—881no—
518C22×C4—881no—
519C22×C4D4×D1111yescharacteristic
520C22×C4D4×D1111yescharacteristic
521C22×C4C23×D1111yescharacteristic
522SD16—228no—
523M16—228no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—112no—
529C2×C8—112no—
530C2×C8—112no—
531C2×C8—112no—
532C2×C8—228no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8C2×C4×D1112yes—
536C2×C8#433912yes—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—42no—
543C4⋊C4—112no—
544C4⋊C4—224no—
545C4⋊C4—222no—
546C4⋊C4—222no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—881no—
553C4⋊C4—881no—
554C4⋊C4C2×C4×D1112yes—
555C22⋊C4—224no—
556C22⋊C4—224no—
557C22⋊C4—222no—
558C22⋊C4—222no—
559C22⋊C4—442no—
560C22⋊C4—881no—
561C22⋊C4—881no—
562C22⋊C4—881no—
563C22⋊C4—881no—
564C42—42no—
565C42—81no—
566C42—221no—
567C42—221no—
568C42—881no—
569C42#433912yes—
570C42D4×D1112yes—
571C11#2153511yescharacteristic, complemented, Sylow
572C23—112no—
573C23—221no—
574C23—221no—
575C23—221no—
576C23—221no—
577C23—221no—
578C23—221no—
579C23—222no—
580C23—441no—
581C23—441no—
582C23—441no—
583C23—441no—
584C23—441no—
585C23—441no—
586C23C2×D4×D1111yescharacteristic
587Q8—22no—
588Q8—22no—
589Q8—41no—
590Q8—41no—
591D4—222no—
592D4—222no—
593D4—441no—
594D4—441no—
595D4—884no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—22no—
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—112no—
613C2×C4—221no—
614C2×C4—221no—
615C2×C4—222no—
616C2×C4—222no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—222no—
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—884no—
635C2×C4#6693712yes—
636C2×C4#6693712yes—
637C2×C4C22×C4×D1111yescharacteristic
638C2×C4C2×#433911yescharacteristic
639C2×C4C2×#433911yescharacteristic
640C2×C4C2×D4×D1111yescharacteristic
641C2×C4#41×D1111yescharacteristic
642C2×C4#41×D1111yescharacteristic
643C8—22no—
644C8—22no—
645C8—114no—
646C8—222no—
647C22—222no—
648C22—222no—
649C22—222no—
650C22—441no—
651C22—441no—
652C22—441no—
653C22—441no—
654C22—442no—
655C22—442no—
656C22—442no—
657C22—881no—
658C22—881no—
659C22—881no—
660C22—881no—
661C22C2×#6693711yescharacteristic
662C22C4×D4×D1111yescharacteristic
663C22#1062307911yescharacteristic
664C22#1062330511yescharacteristic
665C22#1062330911yescharacteristic
666C22#1062330911yescharacteristic
667C22#1062331011yescharacteristic
668C4—22no—
669C4—22no—
670C4—42no—
671C4—42no—
672C4—81no—
673C4—81no—
674C4—222no—
675C4—441no—
676C4—442no—
677C4—441no—
678C4—881no—
679C4—881no—
680C4C4×#433911yescharacteristic
681C4#1062305911yescharacteristic
682C4C4×D4×D1111yescharacteristic
683C4#1062307811yescharacteristic
684C2—442no—
685C2—882no—
686C2C4×#6693711yescharacteristic
687C2#1307744711yescharacteristic
688C2#1307745811yescharacteristic
689C2#1307825811yescharacteristic
690C2#1307828511yescharacteristic
691C2#1307929011yescharacteristic
692C2#1307929711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1763C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
cosocleC22×C4×C11C24
hypercenter#1763D11
hypocenterC11#21535
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4325C2semidirect
3. C2×#10622321C2semidirect
5. #13071292C2semidirect
6. #13069494C2semidirect
7. #13069353C2semidirect
8. #13069297C2semidirect
9. #13069294C2semidirect
11. #13069036C2semidirect
12. #13068648C2semidirect
13. C4×#66871C2semidirect
14. #13068442C2semidirect
15. C11×#1763C2semidirect
52. #10622425C4semidirect
79. #66999C2×C4semidirect
106. C2×#4313C2×C4semidirect
117. C11×#103C2×C4semidirect
135. #66871C2×C4semidirect
136. C4×C11⋊C8D4semidirect
239. #1763D11semidirect
458. #103C4×D11semidirect
571. C11#21535semidirect

Maximal subgroups

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

subgroupindex
C2×#106224252
C2×C4×#43252
C2×#106223212
#130713102
#130712922
#130694942
#130693532
#130692972
#130692942
#130690432
#130690362
#130686482
C4×#668712
#130684422
C11×#17632
#2153511