Finite Group Databasebeta

← #14813697

Subgroups — #14813697

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×#10622494C211yesmaximal, characteristic, complemented
3#13072048C211yesmaximal, characteristic
4#13071548C211yesmaximal, characteristic
5#13070164C211yesmaximal, characteristic, complemented
6#13070099C211yesmaximal, characteristic, complemented
7#13070048C211yesmaximal, characteristic, complemented
8#13069811C211yesmaximal, characteristic, complemented
9#13069201C211yesmaximal, characteristic, complemented
10#13069046C211yesmaximal, characteristic, complemented
11#13068920C211yesmaximal, characteristic, complemented
12#13068912C211yesmaximal, characteristic
13#13068818C211yesmaximal, characteristic, complemented
14#13068812C211yesmaximal, characteristic, complemented
15C11×#1928C211yesmaximal, characteristic, complemented
16C2×#66999C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C22×#4313C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35#10622600C2211yescharacteristic
36#10622600C2211yescharacteristic
37#10622600C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622553—21no—
42C4×(C2×D11)⋊C4—21no—
43#10622549C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622494—24no—
46#10622427—24no—
47#10622288—21no—
48#10622285—21no—
49#10622282—21no—
50#10622278—21no—
51#10622266—21no—
52#10622260—21no—
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D44D411yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11C2311yescharacteristic
65C22×C4×D11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C42×C11—21no—
72C2×C42×C11C2311yescharacteristic
73#66999—22no—
74#66999—22no—
75#66999—22no—
76#66999—41no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4D411yescharacteristic
85C2×(C2×D11)⋊C4D411yescharacteristic
86C2×C4⋊Dic11D411yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C2×#4313—22no—
100C2×#4313—22no—
101C2×#4313—22no—
102#66945—22no—
103#66945—22no—
104#66945—41no—
105#66945—41no—
106C4⋊C4×D11—22no—
107C4⋊C4×D11—41no—
108C4×D44—22no—
109C4×D44—22no—
110C11×#107—22no—
111C11×#103—22no—
112C11×#103—22no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95—21no—
116#66899—22no—
117#66899—41no—
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(C2×D11)⋊C8—22no—
127#66882—22no—
128#66881—22no—
129#66872—41no—
130#66872D414yescomplemented
131#66871—22no—
132#26154—111nomaximal, Sylow
133C23×D11C2×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×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C2×D44—22no—
155C2×D44—41no—
156C2×D44—41no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11—81no—
170C2×C4×D11#4112yes—
171C2×C4×D11#4112yes—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11#4112yes—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4C2×D412yes—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—81no—
187(C2×D11)⋊C4—22no—
188(C2×D11)⋊C4—22no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—81no—
196C4⋊Dic11—22no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11C2×D412yes—
205Dic11⋊C4—42no—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208Dic11⋊C4—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⋊C8C2×D412yes—
217#4313—28no—
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#1928D1111yescharacteristic, complemented
227#1920—111no—
228#1894—111no—
229#1872—111no—
230#1870—111no—
231#1854—111no—
232#1854—111no—
233C23×C11C22×D411yescharacteristic
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11#12312yes—
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—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
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×C11C22×D411yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C2×C4×C112−1+411yescharacteristic
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—22no—
281C2×Dic11—21no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11#12312yes—
294D44—44no—
295C4×D11—22no—
296C4×D11—22no—
297C4×D11—22no—
298C4×D11—22no—
299C4×D11—41no—
300C4×D11—41no—
301C4×D11—41no—
302C4×D11—41no—
303C4×D11—84no—
304C8×C11—22no—
305C8×C11—41no—
306C11⋊C8—22no—
307C11⋊C8—41no—
308C22×M16—111no—
309C2×C22⋊Q8—111no—
310C2×C22⋊Q8—111no—
311C2×C4×D4—111no—
312C2×#117—111no—
313C2×#117—111no—
314C22×C4⋊C4—111no—
315#485—224no—
316#428—224no—
317C2×#107—111no—
318C2×#107—111no—
319C2×#107C2×D1111yescharacteristic
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⋊C8—111no—
330#397—221no—
331#394—221no—
332#391C2×D1111yescharacteristic
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⋊C4C2×D1111yescharacteristic
344C4×C22⋊C4—221no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340C2×D1111yescharacteristic
351#336—111no—
352#336C2×D1111yescharacteristic
353C22×C11C2×#12311yescharacteristic
354C22×C11D4211yescharacteristic
355C22×C11#54711yescharacteristic
356C22×C11#57511yescharacteristic
357C22×C11#57511yescharacteristic
358C22×C11#57711yescharacteristic
359C22×C11#57811yescharacteristic
360C2×D11—22no—
361C2×D11—22no—
362C2×D11—22no—
363C2×D11—41no—
364C2×D11—41no—
365C2×D11—41no—
366C2×D11—41no—
367C2×D11—41no—
368C2×D11—41no—
369C2×D11—41no—
370C2×D11—41no—
371C2×D11—41no—
372C2×D11—41no—
373C2×D11—41no—
374C4×C11—41no—
375C4×C11—41no—
376C4×C11—42no—
377C4×C11—81no—
378C4×C11—81no—
379C4×C11—81no—
380C4×C11#52511yescharacteristic
381C4×C11#53911yescharacteristic
382C4×C11#54811yescharacteristic
383C4×C11#55311yescharacteristic
384Dic11—22no—
385Dic11—41no—
386Dic11—42no—
387Dic11—81no—
388Dic11—81no—
389Dic11—81no—
390C22×Q8C22×D1111yescharacteristic
391C22×D4—111no—
392C23×C4—111no—
393C23×C4—111no—
394C23×C4—221no—
395C2×M16—222no—
396C2×M16—222no—
397C2×M16—222no—
398C22×C8—111no—
399C22×C8—111no—
400C22×C8C22×D1111yescharacteristic
401C22×C8C22×D1111yescharacteristic
402C22⋊Q8—222no—
403C22⋊Q8—222no—
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—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—222no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—441no—
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C4⋊C4C22×D1111yescharacteristic
425C2×C4⋊C4C22×D1111yescharacteristic
426C2×C22⋊C4—111no—
427C2×C22⋊C4—111no—
428C2×C22⋊C4—221no—
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—21no—
436C2×C42—221no—
437C2×C42—221no—
438C2×C42C22×D1111yescharacteristic
439#107—22no—
440#107—222no—
441#107—222no—
442#106—114no—
443#106—222no—
444#106—441no—
445#103—22no—
446#103—22no—
447#103—222no—
448#103—441no—
449C22⋊C8—222no—
450C22⋊C8—222no—
451C22⋊C8—222no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461C2×C11#244311yescharacteristic
462C2×C11#309311yescharacteristic
463C2×C11#309711yescharacteristic
464C2×C11#326911yescharacteristic
465C2×C11#327511yescharacteristic
466C2×C11#335011yescharacteristic
467C2×C11#335211yescharacteristic
468D11—42no—
469D11—81no—
470C24—111no—
471C24—111no—
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—111no—
486C22×C4—112no—
487C22×C4—112no—
488C22×C4—111no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
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—442no—
504C22×C4—442no—
505C22×C4—881no—
506C22×C4D4×D1111yescharacteristic
507C22×C4D4×D1111yescharacteristic
508C22×C4C23×D1111yescharacteristic
509M16—228no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—112no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8#433912yes—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—112no—
528C4⋊C4—222no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—442no—
537C4⋊C4—442no—
538C4⋊C4—442no—
539C4⋊C4—442no—
540C4⋊C4D4×D1112yes—
541C22⋊C4—222no—
542C22⋊C4—222no—
543C22⋊C4—442no—
544C22⋊C4—442no—
545C22⋊C4—442no—
546C22⋊C4—442no—
547C22⋊C4—442no—
548C22⋊C4—442no—
549C22⋊C4—881no—
550C42—21no—
551C42—21no—
552C42—81no—
553C42—442no—
554C42—442no—
555C11#2615411yescharacteristic, complemented, Sylow
556C23—112no—
557C23—221no—
558C23—221no—
559C23—221no—
560C23—221no—
561C23—221no—
562C23—221no—
563C23—221no—
564C23—221no—
565C23—221no—
566C23—221no—
567C23—221no—
568C23—221no—
569C23—221no—
570C23C2×D4×D1111yescharacteristic
571Q8—41no—
572Q8—41no—
573Q8—41no—
574Q8—41no—
575D4—444no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—21no—
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—112no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—222no—
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—884no—
621C2×C4C2×#433911yescharacteristic
622C2×C4C2×D4×D1111yescharacteristic
623C2×C4#41×D1111yescharacteristic
624C2×C4#41×D1111yescharacteristic
625C2×C4#6704211yescharacteristic
626C2×C4#6704311yescharacteristic
627C8—22no—
628C8—41no—
629C8—222no—
630C8—441no—
631C22—222no—
632C22—222no—
633C22—222no—
634C22—441no—
635C22—441no—
636C22—441no—
637C22—441no—
638C22—441no—
639C22—441no—
640C22—441no—
641C22—441no—
642C22—441no—
643C22—441no—
644C22—441no—
645C22#1062308211yescharacteristic
646C22#1062314011yescharacteristic
647C22D11×#12311yescharacteristic
648C22#1062329711yescharacteristic
649C22#1062329911yescharacteristic
650C22#1062330611yescharacteristic
651C22#1062330811yescharacteristic
652C4—41no—
653C4—41no—
654C4—42no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4—222no—
659C4—442no—
660C4—441no—
661C4—881no—
662C4—881no—
663C4—881no—
664C4#1062306111yescharacteristic
665C4#1062307811yescharacteristic
666C4#1062320811yescharacteristic
667C4#1062323811yescharacteristic
668C2—442no—
669C2—881no—
670C2#1307235811yescharacteristic
671C2#1307854811yescharacteristic
672C2#1307858411yescharacteristic
673C2#1308016611yescharacteristic
674C2#1308025311yescharacteristic
675C2#1308116611yescharacteristic
676C2#1308119211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1928C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenter#1928D11
hypocenterC11#26154
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1928

Complements

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

NH ≅ G/Ntype
1. C2×#10622427C2semidirect
2. C2×#10622494C2semidirect
5. #13070164C2semidirect
6. #13070099C2semidirect
7. #13070048C2semidirect
8. #13069811C2semidirect
9. #13069201C2semidirect
10. #13069046C2semidirect
11. #13068920C2semidirect
13. #13068818C2semidirect
14. #13068812C2semidirect
15. C11×#1928C2semidirect
130. #66872D4semidirect
226. #1928D11semidirect
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×#106224942
#130720482
#130715482
#130701642
#130700992
#130700482
#130698112
#130692012
#130690462
#130689202
#130689122
#130688182
#130688122
C11×#19282
#2615411