Finite Group Databasebeta

← #14925758

Subgroups — #14925758

Order 2816.

1812 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073869C214yesmaximal, complemented
2#13073855C211yesmaximal, characteristic, complemented
3#13073828C211yesmaximal, characteristic, complemented
4#13073611C211yesmaximal, characteristic
5#13073534C211yesmaximal, characteristic
6#13073224C212yesmaximal, complemented
7#13073010C212yesmaximal, complemented
8#13072403C212yesmaximal
9#13072113C212yesmaximal, complemented
10#13071917C214yesmaximal, complemented
11C4×#66922C211yesmaximal, characteristic, complemented
12C4×#66928C212yesmaximal
13C4×#66999C212yesmaximal, complemented
14#13071093C212yesmaximal, complemented
15#13071012C212yesmaximal, complemented
16C42×D44C211yesmaximal, characteristic
17C42×Q8×C11C211yesmaximal, characteristic, complemented
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21C2×#66999C2212yes—
22C2×#66928C2212yes—
23C2×C4×D44C2211yescharacteristic
24C2×C4×D44C2211yescharacteristic
25C2×C4×D44C2211yescharacteristic
26C2×C42×D11C2212yes—
27C2×#66922C2211yescharacteristic
28C2×C4×Dic22C2212yes—
29C4×C11×C4⋊C4C2212yes—
30C4×C11×C4⋊C4C2212yes—
31C4×C11×C4⋊C4C2211yescharacteristic
32C4×C11×C4⋊C4C2211yescharacteristic
33C4×C11×C4⋊C4C2211yescharacteristic
34C4×C11×C4⋊C4C2212yes—
35C43×C11C2212yes—
36C43×C11C2211yescharacteristic
37#10622843C2212yes—
38#10622607C2214yes—
39#10622606C2214yes—
40#10622602C2214yes—
41#10622600C2212yes—
42#10622600C2212yes—
43#10622600C2212yes—
44#10622599C2214yes—
45#10622595C2214yes—
46#10622591C2214yes—
47#10622590C2212yes—
48#10622590C2212yes—
49#10622586C2212yes—
50#10622553C2214yes—
51#10622553C2214yes—
52#10622552C2212yes—
53C4×(C2×D11)⋊C4C2214yes—
54C4×(C2×D11)⋊C4C2212yes—
55C4×(C2×D11)⋊C4C2214yes—
56C4×(C2×D11)⋊C4C2212yes—
57C4×(C2×D11)⋊C4C2212yes—
58#10622549C2212yes—
59#10622548C2211yescharacteristic
60C4×C4⋊Dic11C2212yes—
61C4×C4⋊Dic11C2212yes—
62C4×C4⋊Dic11C2211yescharacteristic
63C4×C4⋊Dic11C2211yescharacteristic
64C4×C4⋊Dic11C2211yescharacteristic
65#10622546C2214yes—
66#10622546C2214yes—
67#10622545C2214yes—
68C4×Dic11⋊C4C2214yes—
69#10622542C2212yes—
70#10622542C2212yes—
71#10622542C2212yes—
72#10622542C2212yes—
73#10622541C2212yes—
74#10622541C2212yes—
75#10622541C2212yes—
76#10622541C2212yes—
77#10622288C2214yes—
78#10622287C2214yes—
79#10622277C2214yes—
80C11⋊#401C2214yes—
81#10622273C2214yes—
82#10622264C2214yes—
83C22×Q8×C11C2311yescharacteristic
84C22×D44C2311yescharacteristic
85C22×C4×D11C2312yes—
86C22×C4×D11C2312yes—
87C22×C4×D11C2312yes—
88C22×Dic22C2312yes—
89C4×Q8×C11—24no—
90C4×Q8×C11—24no—
91C4×Q8×C11—24no—
92C2×C11×C4⋊C4C2311yescharacteristic
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2312yes—
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2312yes—
100C2×C42×C11C2311yescharacteristic
101C2×C42×C11C2312yes—
102C2×C42×C11C2312yes—
103C2×C42×C11C2312yes—
104C2×C42×C11C2312yes—
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C42×C11C2312yes—
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2311yescharacteristic
111#66999—28no—
112C2×(C2×D11)⋊C4C2312yes—
113C2×(C2×D11)⋊C4C2312yes—
114C2×(C2×D11)⋊C4C2312yes—
115C2×(C2×D11)⋊C4C2314yes—
116C2×(C2×D11)⋊C4C2314yes—
117C2×(C2×D11)⋊C4C2314yes—
118C2×(C2×D11)⋊C4C2314yes—
119C2×C4⋊Dic11C2312yes—
120C2×C4⋊Dic11C2312yes—
121C2×C4⋊Dic11C2312yes—
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2312yes—
126C2×C4⋊Dic11C2312yes—
127C2×Dic11⋊C4C2314yes—
128C2×Dic11⋊C4C2314yes—
129C2×Dic11⋊C4C2314yes—
130C2×C4×Dic11C2314yes—
131C2×C4×Dic11C2312yes—
132C2×C4×Dic11C2312yes—
133C2×C4×Dic11C2312yes—
134#66928—28no—
135C4×D44—24no—
136C4×D44—24no—
137C4×D44—24no—
138C42×D11—28no—
139#66922—24no—
140C4×Dic22—28no—
141C11×#95C2312yes—
142C11×#95C2312yes—
143C11×#95C2312yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2312yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2312yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2312yes—
159#34945—111nomaximal, Sylow
160C23×D11C2412yes—
161C2×Q8×C11—22no—
162C2×Q8×C11—22no—
163C2×Q8×C11#4114yes—
164C22×C4×C11C2412yes—
165C22×C4×C11C2411yescharacteristic
166C22×C4×C11C2412yes—
167C22×C4×C11C2412yes—
168C22×C4×C11C2411yescharacteristic
169C22×C4×C11C2412yes—
170C22×C4×C11C2411yescharacteristic
171C22×C4×C11C2411yescharacteristic
172C22×C4×C11C2411yescharacteristic
173C22×C4×C11C2411yescharacteristic
174C22×C4×C11C2411yescharacteristic
175C22×Dic11C2412yes—
176C22×Dic11C2412yes—
177C22×Dic11C2412yes—
178C22×Dic11C2414yes—
179C22×Dic11C2414yes—
180C2×D44—22no—
181C2×D44—22no—
182C2×D44#4114yes—
183C2×C4×D11—24no—
184C2×C4×D11—24no—
185C2×C4×D11—24no—
186C2×C4×D11—24no—
187C2×C4×D11—24no—
188C2×C4×D11—24no—
189C2×C4×D11—24no—
190C2×C4×D11—24no—
191C2×C4×D11—42no—
192C2×Dic22—24no—
193C2×Dic22—24no—
194C2×Dic22—24no—
195C11×C4⋊C4—24no—
196C11×C4⋊C4—24no—
197C11×C4⋊C4—24no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—22no—
200C11×C4⋊C4—22no—
201C42×C11—22no—
202C42×C11—24no—
203C42×C11—24no—
204C42×C11—22no—
205C42×C11—24no—
206C42×C11—24no—
207C42×C11—22no—
208C42×C11—24no—
209C42×C11—41no—
210C42×C11—42no—
211C42×C11#4114yes—
212C42×C11#4114yes—
213C42×C11#4114yes—
214(C2×D11)⋊C4—24no—
215(C2×D11)⋊C4—28no—
216(C2×D11)⋊C4—28no—
217(C2×D11)⋊C4—24no—
218(C2×D11)⋊C4—24no—
219(C2×D11)⋊C4—28no—
220(C2×D11)⋊C4—44no—
221C4⋊Dic11—24no—
222C4⋊Dic11—24no—
223C4⋊Dic11—24no—
224C4⋊Dic11—22no—
225C4⋊Dic11—22no—
226C4⋊Dic11—22no—
227C4⋊Dic11—24no—
228C4⋊Dic11—42no—
229Dic11⋊C4—28no—
230Dic11⋊C4—28no—
231Dic11⋊C4—44no—
232C4×Dic11—28no—
233C4×Dic11—24no—
234C4×Dic11—24no—
235C4×Dic11—24no—
236#2573—114no—
237#2571—111no—
238#2568—111no—
239#2547—111no—
240#2538—111no—
241#2514—112no—
242#2494—112no—
243#2447—112no—
244#2421—112no—
245#2401—114no—
246C4×C4⋊Q8—111no—
247C4×#124—112no—
248C4×C22⋊Q8—112no—
249#2295—112no—
250#2283—112no—
251C42×Q8D1111yescharacteristic, complemented
252C42×D4—111no—
253C23×C11C2511yescharacteristic
254C22×D11—22no—
255C22×D11—22no—
256C22×D11—22no—
257C22×D11—22no—
258C22×D11—22no—
259C22×D11—22no—
260C22×D11C2×#4114yes—
261Q8×C11—28no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
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—22no—
271C2×C4×C11—21no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—21no—
277C2×C4×C11—22no—
278C2×C4×C11—21no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11C2×#4112yes—
283C2×C4×C11C2×#4114yes—
284C2×C4×C11C2×#4112yes—
285C2×C4×C11C2×#4112yes—
286C2×C4×C11C2×#4112yes—
287C2×C4×C11C2×#4112yes—
288C2×C4×C11C2×#4112yes—
289C2×C4×C11C2×#4112yes—
290C2×C4×C11C2×#4112yes—
291C2×C4×C11C2×#4112yes—
292C2×C4×C11C2×#4112yes—
293C2×C4×C11C2×#4112yes—
294C2×C4×C112−1+412yes—
295C2×Dic11—22no—
296C2×Dic11—22no—
297C2×Dic11—22no—
298C2×Dic11—24no—
299C2×Dic11—24no—
300C2×Dic11—22no—
301C2×Dic11—24no—
302C2×Dic11—24no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—24no—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—24no—
310D44—28no—
311C4×D11—48no—
312C4×D11—48no—
313C4×D11—48no—
314Dic22—48no—
315C2×C4⋊Q8—111no—
316C2×#124—112no—
317C2×C22⋊Q8—112no—
318C2×C4×Q8—112no—
319C2×C4×Q8C2×D1111yescharacteristic
320C2×C4×Q8C2×D1111yescharacteristic
321C2×C4×Q8C2×D1111yescharacteristic
322C2×C4×D4—111no—
323C2×C4×D4—111no—
324C2×C4×D4—111no—
325C22×C42—112no—
326#401—114no—
327#400—114no—
328#400—114no—
329#400—114no—
330#397—114no—
331#397—114no—
332#397—114no—
333#396—114no—
334#391—112no—
335#391—112no—
336#391—112no—
337#391—112no—
338#391—112no—
339#390—112no—
340#389—112no—
341#389—112no—
342#389—112no—
343#389—112no—
344#389—112no—
345#388—114no—
346#388—114no—
347#387—114no—
348#387—114no—
349#387—114no—
350#385—114no—
351#384—111no—
352#383—114no—
353#382—112no—
354#382—112no—
355#382—112no—
356#381—114no—
357#380—112no—
358#380—112no—
359#380—112no—
360C4×C4⋊C4—112no—
361C4×C4⋊C4—112no—
362C4×C4⋊C4—111no—
363C4×C4⋊C4—114no—
364C4×C4⋊C4—111no—
365C4×C4⋊C4—111no—
366C4×C4⋊C4C2×D1111yescharacteristic
367C4×C4⋊C4C2×D1112yes—
368C4×C4⋊C4C2×D1112yes—
369C4×C4⋊C4C2×D1112yes—
370C4×C4⋊C4C2×D1111yescharacteristic
371C4×C4⋊C4C2×D1111yescharacteristic
372C4×C22⋊C4—112no—
373C4×C22⋊C4—112no—
374C4×C22⋊C4—114no—
375C4×C22⋊C4—114no—
376C4×C22⋊C4—112no—
377#376—114no—
378C43C2×D1111yescharacteristic
379C43C2×D1112yes—
380C22×C11C22×#4111yescharacteristic
381C22×C11C22×#4111yescharacteristic
382C22×C11C22×#4111yescharacteristic
383C22×C11C22×#4111yescharacteristic
384C22×C11C22×#4111yescharacteristic
385C22×C11C2×2−1+411yescharacteristic
386C22×C11#58511yescharacteristic
387C2×D11—24no—
388C2×D11—24no—
389C2×D11—24no—
390C2×D11—42no—
391C2×D11—42no—
392C2×D11—42no—
393C2×D11—42no—
394C4×C11—24no—
395C4×C11—22no—
396C4×C11—22no—
397C4×C11—22no—
398C4×C11—42no—
399C4×C11—42no—
400C4×C11—41no—
401C4×C11—42no—
402C4×C11#52914yes—
403C4×C11#52914yes—
404C4×C11#55614yes—
405Dic11—44no—
406Dic11—42no—
407Dic11—42no—
408Dic11—42no—
409Dic11—44no—
410C22×Q8—112no—
411C22×Q8C22×D1111yescharacteristic
412C22×D4—111no—
413C23×C4—112no—
414C23×C4—112no—
415C23×C4—112no—
416C4⋊Q8—224no—
417#124—228no—
418C22⋊Q8—228no—
419C4×Q8—24no—
420C4×Q8—24no—
421C4×Q8—24no—
422C4×Q8—228no—
423C4×D4—224no—
424C4×D4—224no—
425C4×D4—224no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—112no—
430C2×C4⋊C4—114no—
431C2×C4⋊C4—112no—
432C2×C4⋊C4—114no—
433C2×C4⋊C4—112no—
434C2×C4⋊C4—112no—
435C2×C4⋊C4—112no—
436C2×C4⋊C4—114no—
437C2×C4⋊C4C22×D1111yescharacteristic
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C4⋊C4C22×D1112yes—
441C2×C4⋊C4C22×D1112yes—
442C2×C4⋊C4C22×D1112yes—
443C2×C22⋊C4—112no—
444C2×C22⋊C4—112no—
445C2×C22⋊C4—112no—
446C2×C22⋊C4—114no—
447C2×C22⋊C4—114no—
448C2×C22⋊C4—114no—
449C2×C22⋊C4—114no—
450C2×C42—112no—
451C2×C42—112no—
452C2×C42—114no—
453C2×C42—112no—
454C2×C42—228no—
455C2×C42C22×D1111yescharacteristic
456C2×C42C22×D1111yescharacteristic
457C2×C42C22×D1112yes—
458C2×C42C22×D1112yes—
459C2×C42C22×D1112yes—
460C2×C42C22×D1112yes—
461C2×C42C22×D1112yes—
462C2×C42C22×D1111yescharacteristic
463C2×C42C22×D1111yescharacteristic
464C2×C42C22×D1112yes—
465C2×C42C22×D1111yescharacteristic
466C2×C42C22×D1111yescharacteristic
467C2×C42C22×D1111yescharacteristic
468#95—114no—
469#95—114no—
470#95—114no—
471#95—114no—
472#95—112no—
473#95—112no—
474#95—112no—
475#95—114no—
476#95—114no—
477#95—114no—
478#95—114no—
479#95—114no—
480#95—114no—
481#95—114no—
482#95—114no—
483#95C22×D1112yes—
484#95C22×D1112yes—
485#95C22×D1112yes—
486C2×C11C2×#52911yescharacteristic
487C2×C11C2×#52911yescharacteristic
488C2×C11#346111yescharacteristic
489C2×C11C2×#55611yescharacteristic
490C2×C11#347511yescharacteristic
491C2×C11#348011yescharacteristic
492C2×C11#348211yescharacteristic
493D11—44no—
494C24—112no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—224no—
498C2×Q8—224no—
499C2×Q8—224no—
500C2×Q8#433914yes—
501C2×D4—114no—
502C2×D4—222no—
503C2×D4—222no—
504C22×C4—112no—
505C22×C4—112no—
506C22×C4—112no—
507C22×C4—114no—
508C22×C4—114no—
509C22×C4—224no—
510C22×C4—224no—
511C22×C4—224no—
512C22×C4—224no—
513C22×C4—224no—
514C22×C4—224no—
515C22×C4—224no—
516C22×C4—224no—
517C22×C4—442no—
518C22×C4C23×D1112yes—
519C22×C4C23×D1111yescharacteristic
520C22×C4C23×D1112yes—
521C22×C4C23×D1112yes—
522C22×C4C23×D1111yescharacteristic
523C22×C4C23×D1112yes—
524C22×C4C23×D1111yescharacteristic
525C22×C4C23×D1111yescharacteristic
526C22×C4C23×D1111yescharacteristic
527C22×C4C23×D1111yescharacteristic
528C22×C4C23×D1111yescharacteristic
529C4⋊C4—24no—
530C4⋊C4—24no—
531C4⋊C4—24no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—222no—
536C4⋊C4—228no—
537C4⋊C4—224no—
538C4⋊C4—224no—
539C4⋊C4—224no—
540C4⋊C4—222no—
541C4⋊C4—228no—
542C4⋊C4—224no—
543C4⋊C4—222no—
544C4⋊C4—444no—
545C4⋊C4—442no—
546C22⋊C4—224no—
547C22⋊C4—228no—
548C22⋊C4—228no—
549C22⋊C4—224no—
550C22⋊C4—228no—
551C22⋊C4—224no—
552C22⋊C4—444no—
553C42—24no—
554C42—22no—
555C42—24no—
556C42—24no—
557C42—22no—
558C42—24no—
559C42—22no—
560C42—24no—
561C42—41no—
562C42—42no—
563C42—224no—
564C42—224no—
565C42—224no—
566C42—228no—
567C42#433914yes—
568C42#433914yes—
569C42#434314yes—
570C11#3494511yescharacteristic, complemented, Sylow
571C23—114no—
572C23—222no—
573C23—222no—
574C23—222no—
575C23—222no—
576C23—222no—
577C23—222no—
578C23C24×D1111yescharacteristic
579Q8—28no—
580Q8—448no—
581D4—228no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—224no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—224no—
609C2×C4—224no—
610C2×C4—224no—
611C2×C4—222no—
612C2×C4—224no—
613C2×C4—222no—
614C2×C4—222no—
615C2×C4—224no—
616C2×C4—222no—
617C2×C4—448no—
618C2×C4—448no—
619C2×C4—448no—
620C2×C4C2×#433914yes—
621C2×C4C2×#433912yes—
622C2×C4C2×#433912yes—
623C2×C4C2×#433912yes—
624C2×C4C2×#433912yes—
625C2×C4C2×#433912yes—
626C2×C4C2×#433912yes—
627C2×C4C2×#433912yes—
628C2×C4C2×#434312yes—
629C2×C4C2×#434312yes—
630C2×C4C2×#434312yes—
631C2×C4#41×D1112yes—
632C2×C4#6704312yes—
633C22—224no—
634C22—224no—
635C22—224no—
636C22—442no—
637C22—442no—
638C22—442no—
639C22—442no—
640C22C22×#433911yescharacteristic
641C22C22×#433911yescharacteristic
642C22C22×#433911yescharacteristic
643C22C22×#434311yescharacteristic
644C22C2×#41×D1111yescharacteristic
645C22C2×#6704311yescharacteristic
646C22#1062345311yescharacteristic
647C4—24no—
648C4—22no—
649C4—22no—
650C4—22no—
651C4—42no—
652C4—41no—
653C4—42no—
654C4—42no—
655C4—442no—
656C4—444no—
657C4—442no—
658C4—442no—
659C4—444no—
660C4#1062301014yes—
661C4#1062311114yes—
662C4#1062311514yes—
663C2—444no—
664C2C2×#1062301011yescharacteristic
665C2C2×#1062311111yescharacteristic
666C2#1308204311yescharacteristic
667C2C2×#1062311511yescharacteristic
668C2#1308218011yescharacteristic
669C2#1308221111yescharacteristic
670C2#1308223811yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC42×Q8×C11C2
prime radicalC22×D44C23
hypercenterC42×Q8D11
hypocenterC11#34945
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C42×Q8

Complements

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

NH ≅ G/Ntype
1. #13073869C2semidirect
2. #13073855C2semidirect
3. #13073828C2semidirect
6. #13073224C2semidirect
7. #13073010C2semidirect
9. #13072113C2semidirect
10. #13071917C2semidirect
11. C4×#66922C2semidirect
13. C4×#66999C2semidirect
14. #13071093C2semidirect
15. #13071012C2semidirect
17. C42×Q8×C11C2semidirect
251. C42×Q8D11semidirect
570. C11#34945semidirect

Maximal subgroups

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

subgroupindex
#130738692
#130738552
#130738282
#130736112
#130735342
#130732242
#130730102
#130724032
#130721132
#130719172
C4×#669222
C4×#669282
C4×#669992
#130710932
#130710122
C42×D442
C42×Q8×C112
#3494511