Finite Group Databasebeta

← #14813692

Subgroups — #14813692

Order 2816.

846 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622427C211yesmaximal, characteristic, complemented
2C2×#10622577C211yesmaximal, characteristic, complemented
3#13072046C211yesmaximal, characteristic
4#13071541C211yesmaximal, characteristic
5#13070166C211yesmaximal, characteristic, complemented
6#13070103C211yesmaximal, characteristic, complemented
7#13070048C211yesmaximal, characteristic, complemented
8#13069810C211yesmaximal, characteristic, complemented
9#13069260C211yesmaximal, characteristic, complemented
10#13069199C211yesmaximal, characteristic, complemented
11#13069050C211yesmaximal, characteristic, complemented
12#13068911C211yesmaximal, characteristic
13#13068817C211yesmaximal, characteristic, complemented
14#13068816C211yesmaximal, characteristic, complemented
15C11×#1872C211yesmaximal, characteristic, complemented
16C2×C11×C22⋊Q8C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×#66999C2211yescharacteristic
19C2×C4×C22⋊D11C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C2×#66945C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26#10622843C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29#10622826—21no—
30#10622825C2211yescharacteristic
31C4×C22⋊Dic11—21no—
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36#10622603—21no—
37#10622603—21no—
38#10622600C2211yescharacteristic
39#10622600C2211yescharacteristic
40#10622591—21no—
41#10622590C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43#10622586C2211yescharacteristic
44#10622585—21no—
45#10622577—24no—
46C2×#66872C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50#10622572—21no—
51#10622565—21no—
52#10622427—24no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11D411yescharacteristic
65C22×C4×D11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×C22⋊Q8—22no—
69C11×C22⋊Q8—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—41no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11D411yescharacteristic
81#66999—22no—
82#66999—41no—
83C4×C22⋊D11—22no—
84C4×C22⋊D11—22no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4D411yescharacteristic
90#66979—22no—
91#66979—41no—
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
103C2×#4318—22no—
104C2×#4318—22no—
105C2×#4318—22no—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108#66945—22no—
109#66945—41no—
110C11×#103—22no—
111C11×#103—41no—
112C11×C22⋊C8—22no—
113#66899—22no—
114#66899—22no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124(C2×D11)⋊C8—22no—
125(C2×D11)⋊C8—22no—
126#66882—22no—
127#66881—41no—
128#66872—22no—
129#66872D414yescomplemented
130#66871—22no—
131#66871—22no—
132#26154—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C23×D11C2×D411yescharacteristic
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×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×C11—21no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—81no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11#4112yes—
154C22×C4×C11#4112yes—
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—22no—
157C2×C22⋊D11—41no—
158C2×C22⋊D11—41no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—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—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4C2×D412yes—
186C11×C22⋊C4—42no—
187C22⋊Dic11—22no—
188C22⋊Dic11—42no—
189C22⋊Dic11—42no—
190(C2×D11)⋊C4—22no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—81no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11C2×D412yes—
203Dic11⋊C4—22no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—42no—
209C4×Dic11—42no—
210C4×Dic11—81no—
211#4318—28no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8C2×D412yes—
217C2×C11⋊C8#4112yes—
218C2×#485—111no—
219C2×#428—111no—
220#2415—111no—
221#2352—111no—
222#2097—111no—
223#2085—111no—
224#2076—111no—
225#2035—111no—
226#1928—111no—
227#1920—111no—
228#1894—111no—
229#1872D1111yescharacteristic, complemented
230#1870—111no—
231#1854—111no—
232#1854—111no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11#12312yes—
240C23×C11C22×D411yescharacteristic
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248Q8×C11—41no—
249Q8×C11—41no—
250Q8×C11—41no—
251Q8×C11—41no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
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×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—84no—
271C2×C4×C11#12312yes—
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11H(5,𝔽2)11yescharacteristic
277C2×C4×C112−1+411yescharacteristic
278C22⋊D11—44no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—22no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
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—
300C4×D11—41no—
301C4×D11—41no—
302C4×D11—41no—
303C4×D11—41no—
304C8×C11—41no—
305C8×C11—41no—
306C11⋊C8—22no—
307C11⋊C8—22no—
308C22×M16—111no—
309C2×C22⋊Q8—111no—
310C2×C22⋊Q8C2×D1111yescharacteristic
311C2×C4×D4—111no—
312C2×#117—111no—
313C2×#117—111no—
314C22×C4⋊C4C2×D1111yescharacteristic
315#485—224no—
316#428—224no—
317C2×#107—111no—
318C2×#107—111no—
319C2×#107—111no—
320C2×#106—111no—
321C2×#106—111no—
322C2×#106—111no—
323C2×#103—111no—
324C2×#103—111no—
325C2×#103C2×D1111yescharacteristic
326C2×#103C2×D1111yescharacteristic
327C2×C22⋊C8—111no—
328C2×C22⋊C8—111no—
329C2×C22⋊C8C2×D1111yescharacteristic
330#397—221no—
331#394—221no—
332#391—111no—
333#389—111no—
334#389—221no—
335#388—221no—
336#388—221no—
337#387—221no—
338#386—221no—
339#382—111no—
340#380—111no—
341#380—111no—
342#380—111no—
343C4×C4⋊C4—111no—
344C4×C22⋊C4—221no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340C2×D1111yescharacteristic
350#340C2×D1111yescharacteristic
351#336—111no—
352#336—111no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11C2×#12311yescharacteristic
361C22×C11D4211yescharacteristic
362C22×C11#54711yescharacteristic
363C22×C11#57511yescharacteristic
364C22×C11#57511yescharacteristic
365C22×C11#57711yescharacteristic
366C22×C11#57811yescharacteristic
367C2×D11—41no—
368C2×D11—41no—
369C2×D11—41no—
370C2×D11—41no—
371C2×D11—41no—
372C2×D11—41no—
373C2×D11—41no—
374C4×C11—22no—
375C4×C11—42no—
376C4×C11—81no—
377C4×C11—81no—
378C4×C11—81no—
379C4×C11#52511yescharacteristic
380C4×C11#53911yescharacteristic
381C4×C11#54811yescharacteristic
382C4×C11#55311yescharacteristic
383Dic11—41no—
384Dic11—41no—
385Dic11—41no—
386Dic11—42no—
387Dic11—81no—
388Dic11—81no—
389Dic11—81no—
390C22×Q8C22×D1111yescharacteristic
391C22×D4—111no—
392C23×C4—21no—
393C23×C4—111no—
394C23×C4C22×D1111yescharacteristic
395C2×M16—222no—
396C2×M16—222no—
397C2×M16—222no—
398C22×C8—111no—
399C22×C8—111no—
400C22×C8C22×D1111yescharacteristic
401C22×C8C22×D1111yescharacteristic
402C22⋊Q8—22no—
403C22⋊Q8—22no—
404C22⋊Q8—222no—
405C22⋊Q8—441no—
406C4×D4—222no—
407C4×D4—222no—
408#117—222no—
409#117—222no—
410#117—441no—
411#117—441no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—41no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C4⋊C4C22×D1111yescharacteristic
425C2×C4⋊C4C22×D1111yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—111no—
428C2×C22⋊C4—111no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C42—111no—
436C2×C42—221no—
437C2×C42—221no—
438C2×C42—221no—
439#107—222no—
440#107—222no—
441#107—222no—
442#106—114no—
443#106—222no—
444#106—441no—
445#103—22no—
446#103—41no—
447#103—222no—
448#103—222no—
449C22⋊C8—22no—
450C22⋊C8—222no—
451C22⋊C8—222no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461C2×C11—42no—
462C2×C11#244311yescharacteristic
463C2×C11#309311yescharacteristic
464C2×C11#309711yescharacteristic
465C2×C11#326911yescharacteristic
466C2×C11#327511yescharacteristic
467C2×C11#335011yescharacteristic
468C2×C11#335211yescharacteristic
469D11—81no—
470C24—111no—
471C24D4×D1111yescharacteristic
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×D4—222no—
479C2×D4—441no—
480C2×D4—441no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—81no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4#433912yes—
506C22×C4D4×D1111yescharacteristic
507C22×C4#434112yes—
508C22×C4C23×D1111yescharacteristic
509M16—228no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—112no—
517C2×C8—112no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—42no—
528C4⋊C4—42no—
529C4⋊C4—112no—
530C4⋊C4—222no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—442no—
539C4⋊C4—442no—
540C4⋊C4D4×D1112yes—
541C22⋊C4—42no—
542C22⋊C4—222no—
543C22⋊C4—222no—
544C22⋊C4—442no—
545C22⋊C4—442no—
546C22⋊C4—442no—
547C22⋊C4—442no—
548C22⋊C4—442no—
549C22⋊C4—881no—
550C42—221no—
551C42—221no—
552C42—442no—
553C42—442no—
554C42—881no—
555C11#2615411yescharacteristic, complemented, Sylow
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—221no—
563C23—221no—
564C23—221no—
565C23—221no—
566C23—221no—
567C23—221no—
568C23—221no—
569C23#6693612yes—
570C23C2×D4×D1111yescharacteristic
571Q8—41no—
572Q8—41no—
573Q8—41no—
574Q8—41no—
575D4—444no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—84no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—222no—
604C2×C4—221no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4#6693612yes—
621C2×C4C2×#433911yescharacteristic
622C2×C4C2×D4×D1111yescharacteristic
623C2×C4C2×#434111yescharacteristic
624C2×C4#6703711yescharacteristic
625C2×C4#41×D1111yescharacteristic
626C2×C4#6704311yescharacteristic
627C8—41no—
628C8—41no—
629C8—222no—
630C8—222no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—441no—
639C22—441no—
640C22—441no—
641C22—441no—
642C22—441no—
643C22—441no—
644C22—441no—
645C22C2×#6693611yescharacteristic
646C22#1062312111yescharacteristic
647C22#1062318611yescharacteristic
648C22#1062329311yescharacteristic
649C22#1062329711yescharacteristic
650C22#1062330411yescharacteristic
651C22#1062330811yescharacteristic
652C4—22no—
653C4—42no—
654C4—81no—
655C4—81no—
656C4—81no—
657C4—441no—
658C4—441no—
659C4—442no—
660C4—441no—
661C4—881no—
662C4—881no—
663C4—881no—
664C4#1062307811yescharacteristic
665C4#1062309511yescharacteristic
666C4#1062312911yescharacteristic
667C4#1062313211yescharacteristic
668C2—42no—
669C2—881no—
670C2#1307235311yescharacteristic
671C2#1307854611yescharacteristic
672C2#1307858111yescharacteristic
673C2#1308017411yescharacteristic
674C2#1308025111yescharacteristic
675C2#1308116411yescharacteristic
676C2#1308119111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1872C2
socleC23×C11C22×D4
prime radicalC22×C22⋊D11D4
hypercenter#1872D11
hypocenterC11#26154
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
1. C2×#10622427C2semidirect
2. C2×#10622577C2semidirect
5. #13070166C2semidirect
6. #13070103C2semidirect
7. #13070048C2semidirect
8. #13069810C2semidirect
9. #13069260C2semidirect
10. #13069199C2semidirect
11. #13069050C2semidirect
13. #13068817C2semidirect
14. #13068816C2semidirect
15. C11×#1872C2semidirect
129. #66872D4semidirect
229. #1872D11semidirect
555. C11#26154semidirect

Maximal subgroups

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

subgroupindex
C2×#106224272
C2×#106225772
#130720462
#130715412
#130701662
#130701032
#130700482
#130698102
#130692602
#130691992
#130690502
#130689112
#130688172
#130688162
C11×#18722
#2615411