Finite Group Databasebeta

← #14760294

Subgroups — #14760294

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×#10622784C211yesmaximal, characteristic
2C2×SD16×Dic11C211yesmaximal, characteristic, complemented
3C2×#10622302C211yesmaximal, characteristic, complemented
4#13071312C211yesmaximal, characteristic
5#13071301C211yesmaximal, characteristic, complemented
6#13069344C211yesmaximal, characteristic, complemented
7#13069316C211yesmaximal, characteristic, complemented
8#13069309C211yesmaximal, characteristic, complemented
9#13069051C211yesmaximal, characteristic
10#13069046C211yesmaximal, characteristic, complemented
11#13068638C211yesmaximal, characteristic, complemented
12#106×Dic11C211yesmaximal, characteristic, complemented
13#13068448C211yesmaximal, characteristic, complemented
14#13068443C211yesmaximal, characteristic, complemented
15C11×#1968C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×#66991C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C22×#4313C2211yescharacteristic
22C22×C8×D11C2211yescharacteristic
23C2×#66925C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28C11×#391C2211yescharacteristic
29C11×#390C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34#10622784C418yescomplemented
35SD16×Dic11—24no—
36C2×#66881C2211yescharacteristic
37C2×#66881C2211yescharacteristic
38C2×#66879C2211yescharacteristic
39C2×C8×Dic11C2211yescharacteristic
40#10622600C2211yescharacteristic
41#10622600C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43C4⋊C4×Dic11C2211yescharacteristic
44#10622571—21no—
45#10622570—21no—
46#10622559—21no—
47#10622557—21no—
48#10622541C2211yescharacteristic
49#10622541C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51#10622302—24no—
52#10622283—21no—
53#10622282—21no—
54#10622265—21no—
55#10622260—21no—
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C22×C22⋊D11—21no—
65C23×Dic11—21no—
66C22×C4×D11C2311yescharacteristic
67C2×C11×SD16—22no—
68C2×C11×SD16—22no—
69C2×C11×SD16C2×C414yes—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79#66999—22no—
80#66999C2×C414yescomplemented
81Q8×Dic11—22no—
82Q8×Dic11—22no—
83#66991—22no—
84#66991C2×C414yes—
85D4×Dic11—22no—
86D4×Dic11—22no—
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×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4D411yescharacteristic
101C2×Dic11⋊C4D411yescharacteristic
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C2×#4313—22no—
109C2×#4313—22no—
110C2×#4313—22no—
111C2×C8×D11—22no—
112C2×C8×D11—22no—
113C2×C8×D11C2×C414yescomplemented
114#66925—22no—
115#66925—22no—
116C11×#106—22no—
117C11×#103—22no—
118C11×#102—22no—
119C4×C8×C11—22no—
120C11×#95—21no—
121C11×#95—21no—
122#66899—22no—
123#66899C2×C414yescomplemented
124#66896—22no—
125#66896C2×C414yes—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132#66881—22no—
133#66881C2×C414yescomplemented
134#66879—22no—
135C8×Dic11D414yescomplemented
136#66867—22no—
137#21523—111nomaximal, Sylow
138C24×C11—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—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11—21no—
151C2×D4×C11C22×C412yes—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C2×C22⋊D11—24no—
159C2×C22⋊D11—81no—
160C2×C22⋊D11—81no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—42no—
166C22×Dic11—81no—
167C22×Dic11—81no—
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D411yescharacteristic
171C2×C4×D11—21no—
172C2×C4×D11—21no—
173C2×C4×D11—21no—
174C2×C4×D11—21no—
175C2×C4×D11C22×C412yes—
176C2×C4×D11#4112yes—
177C11×SD16—28no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11C22×C412yes—
181C2×C8×C11C2×D412yes—
182C2×C8×C11#4112yes—
183C2×C8×C11#4112yes—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C22⋊C4—81no—
189C11×C22⋊C4—81no—
190C42×C11—21no—
191C42×C11—21no—
192C22⋊Dic11—24no—
193C22⋊Dic11—42no—
194(C2×D11)⋊C4—22no—
195(C2×D11)⋊C4—22no—
196(C2×D11)⋊C4—24no—
197(C2×D11)⋊C4—81no—
198(C2×D11)⋊C4—81no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—42no—
206C4⋊Dic11C22×C412yes—
207C4⋊Dic11C22×C412yes—
208Dic11⋊C4—24no—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211Dic11⋊C4—81no—
212Dic11⋊C4—81no—
213C4×Dic11—42no—
214C4×Dic11—81no—
215C4×Dic11—81no—
216C4×Dic11C2×D412yes—
217C4×Dic11#4112yes—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8C22×C412yes—
223C2×C11⋊C8C2×D412yes—
224#4313—28no—
225C8×D11—28no—
226C2×#465—111no—
227C2×C4×SD16—111no—
228C2×#405—111no—
229#2324—111no—
230#2323—111no—
231#1968D1111yescharacteristic, complemented
232#1941—111no—
233#1936—111no—
234#1935—111no—
235#1895—111no—
236#1894—111no—
237#1807—111no—
238C4×#106—111no—
239#1763—111no—
240#1762—111no—
241C23×C11—22no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11C22×D411yescharacteristic
249C22×D11—21no—
250C22×D11—21no—
251C22×D11—21no—
252C22×D11—21no—
253C22×D11—21no—
254C22×D11—21no—
255C22×D11C4×D412yes—
256Q8×C11—22no—
257Q8×C11—22no—
258Q8×C11—41no—
259Q8×C11—41no—
260D4×C11—22no—
261D4×C11—22no—
262D4×C11—41no—
263D4×C11—41no—
264C2×C4×C11—22no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
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×C11C23×C411yescharacteristic
280C2×C4×C11C22×D411yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C22⋊D11—84no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—22no—
293C2×Dic11—22no—
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—84no—
305C2×Dic11C4×D412yes—
306C2×Dic11#12112yes—
307C2×Dic11#12112yes—
308C4×D11—22no—
309C4×D11—22no—
310C4×D11—22no—
311C4×D11—22no—
312C8×C11—22no—
313C8×C11C4×D414yes—
314C11⋊C8—22no—
315C11⋊C8—22no—
316C22×SD16C2×D1111yescharacteristic
317C22×M16—111no—
318C23×C8—111no—
319C2×C22⋊Q8—111no—
320C2×#121—111no—
321C2×C4×Q8—111no—
322C2×C4×D4—111no—
323C2×#117—111no—
324#465—118no—
325C4×SD16—224no—
326C2×#106—111no—
327C2×#106—111no—
328C2×#106C2×D1111yescharacteristic
329C2×#103—111no—
330C2×#103—111no—
331C2×#103C2×D1111yescharacteristic
332C2×#102—111no—
333C2×#102—111no—
334C2×#102C2×D1111yescharacteristic
335#405—224no—
336C2×#97—111no—
337C2×#97—111no—
338C2×C4×C8—111no—
339C2×C4×C8C2×D1111yescharacteristic
340#391C2×D1111yescharacteristic
341#390—221no—
342#390C2×D1111yescharacteristic
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⋊C4—111no—
356#340—111no—
357#340—111no—
358#340—111no—
359#340—111no—
360#340—111no—
361#340—111no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11C2×C4×D411yescharacteristic
370C22×C11C2×#12111yescharacteristic
371C22×C11#53211yescharacteristic
372C22×C11#57711yescharacteristic
373C22×C11#57711yescharacteristic
374C22×C11#57711yescharacteristic
375C22×C11#57711yescharacteristic
376C2×D11—22no—
377C2×D11—22no—
378C2×D11—22no—
379C2×D11—41no—
380C2×D11—41no—
381C2×D11—41no—
382C2×D11—41no—
383C4×C11—41no—
384C4×C11—41no—
385C4×C11—42no—
386C4×C11—81no—
387C4×C11—81no—
388C4×C11C2×C4×D411yescharacteristic
389C4×C11C4×#4111yescharacteristic
390C4×C11#52511yescharacteristic
391C4×C11#52911yescharacteristic
392Dic11—22no—
393Dic11—22no—
394Dic11—22no—
395Dic11—42no—
396Dic11—42no—
397Dic11—81no—
398Dic11—81no—
399C22×Q8C22×D1111yescharacteristic
400C22×D4—221no—
401C22×D4C22×D1111yescharacteristic
402C23×C4—111no—
403C23×C4—221no—
404C2×SD16—22no—
405C2×SD16—22no—
406C2×SD16C4×D1114yes—
407C2×M16—222no—
408C2×M16—222no—
409C2×M16—222no—
410C22×C8—111no—
411C22×C8—111no—
412C22×C8—114no—
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—222no—
422C4×Q8—222no—
423C4×D4—222no—
424C4×D4—222no—
425#117—222no—
426#117—222no—
427C2×C4⋊C4—111no—
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⋊C4—221no—
437C2×C4⋊C4C22×D1111yescharacteristic
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—111no—
442C2×C22⋊C4—111no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C42—111no—
449C2×C42—221no—
450C2×C42—221no—
451C2×C42—221no—
452C2×C42C22×D1111yescharacteristic
453#106—22no—
454#106—114no—
455#106—222no—
456#103—22no—
457#103—114no—
458#103—222no—
459#102—22no—
460#102—114no—
461#102—222no—
462#97—222no—
463#97—222no—
464C4×C8—22no—
465C4×C8—114no—
466#95—21no—
467#95—21no—
468#95—221no—
469#95—221no—
470#95—221no—
471#95—221no—
472#95—221no—
473#95—221no—
474C2×C11—82no—
475C2×C11C4×#12111yescharacteristic
476C2×C11#294911yescharacteristic
477C2×C11#295211yescharacteristic
478C2×C11#305711yescharacteristic
479C2×C11#306011yescharacteristic
480C2×C11#317311yescharacteristic
481C2×C11#317411yescharacteristic
482D11—42no—
483C24—21no—
484C24—111no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8C2×C4×D1112yes—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—224no—
497C2×D4—881no—
498C2×D4—881no—
499C2×D4C2×C4×D1112yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—111no—
504C22×C4—111no—
505C22×C4—111no—
506C22×C4—112no—
507C22×C4—112no—
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×C4—442no—
517C22×C4—881no—
518C22×C4—881no—
519C22×C4D4×D1111yescharacteristic
520C22×C4D4×D1111yescharacteristic
521C22×C4C23×D1111yescharacteristic
522SD16—28no—
523M16—228no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—112no—
527C2×C8—112no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—228no—
533C2×C8C2×C4×D1112yes—
534C2×C8D4×D1112yes—
535C2×C8#434112yes—
536C2×C8#434112yes—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—112no—
542C4⋊C4—112no—
543C4⋊C4—222no—
544C4⋊C4—222no—
545C4⋊C4—224no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—442no—
553C4⋊C4—881no—
554C4⋊C4—881no—
555C22⋊C4—81no—
556C22⋊C4—81no—
557C22⋊C4—222no—
558C22⋊C4—222no—
559C22⋊C4—224no—
560C22⋊C4—224no—
561C22⋊C4—442no—
562C22⋊C4—881no—
563C22⋊C4—881no—
564C42—21no—
565C42—21no—
566C42—112no—
567C42—112no—
568C42—442no—
569C42—881no—
570C42—881no—
571C11#2152311yescharacteristic, complemented, Sylow
572C23—22no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—112no—
580C23—221no—
581C23—221no—
582C23—221no—
583C23—221no—
584C23—221no—
585C23—221no—
586C23C2×D4×D1111yescharacteristic
587Q8—22no—
588Q8—22no—
589Q8—41no—
590Q8—41no—
591D4—22no—
592D4—22no—
593D4—41no—
594D4—41no—
595D4—884no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—21no—
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—112no—
612C2×C4—112no—
613C2×C4—112no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—221no—
620C2×C4—222no—
621C2×C4—222no—
622C2×C4—222no—
623C2×C4—222no—
624C2×C4—222no—
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—441no—
635C2×C4—441no—
636C2×C4—884no—
637C2×C4C22×C4×D1111yescharacteristic
638C2×C4C2×D4×D1111yescharacteristic
639C2×C4C2×#434111yescharacteristic
640C2×C4C2×#434111yescharacteristic
641C2×C4#41×D1111yescharacteristic
642C2×C4#41×D1111yescharacteristic
643C8—22no—
644C8—222no—
645C8—222no—
646C8(C22⋊D11)⋊C414yes—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—222no—
655C22—222no—
656C22—222no—
657C22—441no—
658C22—441no—
659C22—441no—
660C22—441no—
661C22C4×D4×D1111yescharacteristic
662C22D11×#12111yescharacteristic
663C22#1062324711yescharacteristic
664C22#1062329311yescharacteristic
665C22#1062329311yescharacteristic
666C22#1062330111yescharacteristic
667C22#1062330111yescharacteristic
668C4—41no—
669C4—42no—
670C4—41no—
671C4—81no—
672C4—81no—
673C4—222no—
674C4—222no—
675C4—222no—
676C4—442no—
677C4—442no—
678C4—881no—
679C4—881no—
680C4C2×(C22⋊D11)⋊C411yescharacteristic
681C4C4×#434111yescharacteristic
682C4#1062313711yescharacteristic
683C4#1062321111yescharacteristic
684C2—82no—
685C2—442no—
686C2#1307113211yescharacteristic
687C2#1307747011yescharacteristic
688C2#1307749411yescharacteristic
689C2#1307825011yescharacteristic
690C2#1307827311yescharacteristic
691C2#1307923011yescharacteristic
692C2#1307924111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1968C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
cosocleC22×C4×C11C24
hypercenter#1968D11
hypocenterC11#21523
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1968

Complements

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

NH ≅ G/Ntype
2. C2×SD16×Dic11C2semidirect
3. C2×#10622302C2semidirect
5. #13071301C2semidirect
6. #13069344C2semidirect
7. #13069316C2semidirect
8. #13069309C2semidirect
10. #13069046C2semidirect
11. #13068638C2semidirect
12. #106×Dic11C2semidirect
13. #13068448C2semidirect
14. #13068443C2semidirect
15. C11×#1968C2semidirect
34. #10622784C4semidirect
80. #66999C2×C4semidirect
113. C2×C8×D11C2×C4semidirect
123. #66899C2×C4semidirect
133. #66881C2×C4semidirect
135. C8×Dic11D4semidirect
231. #1968D11semidirect
571. C11#21523semidirect

Maximal subgroups

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

subgroupindex
C2×#106227842
C2×SD16×Dic112
C2×#106223022
#130713122
#130713012
#130693442
#130693162
#130693092
#130690512
#130690462
#130686382
#106×Dic112
#130684482
#130684432
C11×#19682
#2152311