Finite Group Databasebeta

← #14912760

Subgroups — #14912760

Order 2816.

2094 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623109C211yesmaximal, characteristic
2#13071415C214yesmaximal, complemented
3#13071367C214yesmaximal
4#13071360C212yesmaximal, complemented
5#13071332C212yesmaximal, complemented
6#13071299C212yesmaximal
7#13071292C212yesmaximal
8#13071113C212yesmaximal
9#13071109C212yesmaximal
10#13071094C211yesmaximal, characteristic, complemented
11#13071093C212yesmaximal, complemented
12#13071092C212yesmaximal, complemented
13#13071090C211yesmaximal, characteristic, complemented
14#13071012C211yesmaximal, characteristic
15C42×Dic22C211yesmaximal, characteristic, complemented
16C4×#66925C211yesmaximal, characteristic
17C42×Q8×C11C211yesmaximal, characteristic, complemented
18C2×C4×Q8×C11C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×#66999C2211yescharacteristic
21C2×#66997C2211yescharacteristic
22#10623109C4116yescomplemented
23C2×#66950C2211yescharacteristic
24C2×#66949C2212yes—
25C2×#66942C2212yes—
26C2×#66941C2211yescharacteristic
27C2×#66925C2212yes—
28C2×#66925C2212yes—
29C2×C42×D11C2211yescharacteristic
30C2×C4×Dic22C2212yes—
31C2×C4×Dic22C2211yescharacteristic
32C2×C4×Dic22C2212yes—
33C4×C11×C4⋊C4C2212yes—
34C4×C11×C4⋊C4C2212yes—
35C4×C11×C4⋊C4C2214yes—
36C4×C11×C4⋊C4C2211yescharacteristic
37C43×C11C2212yes—
38C43×C11C2211yescharacteristic
39#10622843C2212yes—
40#10622603C2214yes—
41#10622600C2212yes—
42#10622598C2212yes—
43#10622594C2214yes—
44#10622591C2214yes—
45#10622591C2214yes—
46#10622590C2212yes—
47#10622587C2212yes—
48#10622586C2212yes—
49#10622585C2214yes—
50#10622553C2214yes—
51#10622553C2214yes—
52C4×(C2×D11)⋊C4C2211yescharacteristic
53C4×(C2×D11)⋊C4C2212yes—
54C4×(C2×D11)⋊C4C2212yes—
55C4×(C2×D11)⋊C4C2211yescharacteristic
56C4×C4⋊Dic11C2212yes—
57C4×C4⋊Dic11C2212yes—
58C4×C4⋊Dic11C2211yescharacteristic
59#10622546C2214yes—
60#10622546C2214yes—
61#10622546C2214yes—
62#10622546C2214yes—
63#10622545C2212yes—
64#10622545C2212yes—
65#10622545C2212yes—
66#10622545C2212yes—
67C4×Dic11⋊C4C2214yes—
68C4×Dic11⋊C4C2212yes—
69C4×Dic11⋊C4C2212yes—
70C4×Dic11⋊C4C2212yes—
71C4×Dic11⋊C4C2211yescharacteristic
72C4×Dic11⋊C4C2211yescharacteristic
73C42×Dic11C2212yes—
74C42×Dic11C2211yescharacteristic
75#10622542C2214yes—
76#10622541C2214yes—
77#10622283C2214yes—
78#10622277C2212yes—
79#10622268C2214yes—
80#10622266C2214yes—
81#10622265C2214yes—
82#10622264C2212yes—
83#10622259C2214yes—
84C22×Q8×C11C2311yescharacteristic
85C22×C4×D11C2311yescharacteristic
86C22×C4×D11C2311yescharacteristic
87C22×C4×D11C2311yescharacteristic
88C22×Dic22C2311yescharacteristic
89C22×Dic22C2312yes—
90C4×Q8×C11—28no—
91C4×Q8×C11C2×C418yes—
92C2×C11×C4⋊C4C2314yes—
93C2×C11×C4⋊C4C2312yes—
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2312yes—
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2312yes—
99C2×C42×C11C2314yes—
100C2×C42×C11C2314yes—
101C2×C42×C11C2312yes—
102C2×C42×C11C2311yescharacteristic
103C2×C42×C11C2312yes—
104C2×C42×C11C2312yes—
105#66999C2×C418yes—
106#66997C2×C418yes—
107C2×(C2×D11)⋊C4C2312yes—
108C2×(C2×D11)⋊C4C2312yes—
109C2×(C2×D11)⋊C4C2314yes—
110C2×(C2×D11)⋊C4C2312yes—
111C2×(C2×D11)⋊C4C2312yes—
112C2×C4⋊Dic11C2312yes—
113C2×C4⋊Dic11C2314yes—
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2312yes—
116C2×Dic11⋊C4C2314yes—
117C2×Dic11⋊C4C2312yes—
118C2×Dic11⋊C4C2312yes—
119C2×Dic11⋊C4C2314yes—
120C2×Dic11⋊C4C2312yes—
121C2×Dic11⋊C4C2312yes—
122C2×Dic11⋊C4C2312yes—
123C2×Dic11⋊C4C2312yes—
124C2×Dic11⋊C4C2312yes—
125C2×C4×Dic11C2314yes—
126C2×C4×Dic11C2312yes—
127C2×C4×Dic11C2311yescharacteristic
128C2×C4×Dic11C2312yes—
129C2×C4×Dic11C2311yescharacteristic
130C2×C4×Dic11C2314yes—
131C2×C4×Dic11C2312yes—
132C2×C4×Dic11C2311yescharacteristic
133C2×C4×Dic11C2312yes—
134C2×C4×Dic11C2311yescharacteristic
135C2×C4×Dic11C2311yescharacteristic
136#66950C2×C418yes—
137#66949C2×C4116yes—
138#66942C2×C4116yes—
139#66941C2×C418yes—
140#66925—28no—
141#66925C2×C4116yes—
142C42×D11C2×C418yes—
143C4×Dic22—28no—
144C4×Dic22C2×C4116yes—
145C4×Dic22C2×C418yes—
146C11×#95C2314yes—
147C11×#95C2312yes—
148C11⋊#95C2312yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2312yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2312yes—
158C11⋊#95C2312yes—
159C11⋊#95C2314yes—
160C11⋊#95C2312yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163#34085—111nomaximal, Sylow
164C23×D11C2411yescharacteristic
165C2×Q8×C11—24no—
166C2×Q8×C11C22×C414yes—
167C22×C4×C11C2414yes—
168C22×C4×C11C2412yes—
169C22×C4×C11C2411yescharacteristic
170C22×C4×C11C2412yes—
171C22×C4×C11C2412yes—
172C22×C4×C11C2412yes—
173C22×C4×C11C2411yescharacteristic
174C22×C4×C11C2411yescharacteristic
175C22×Dic11C2412yes—
176C22×Dic11C2414yes—
177C22×Dic11C2412yes—
178C22×Dic11C2411yescharacteristic
179C22×Dic11C2411yescharacteristic
180C22×Dic11C2412yes—
181C22×Dic11C2412yes—
182C22×Dic11C2411yescharacteristic
183C2×C4×D11—24no—
184C2×C4×D11—22no—
185C2×C4×D11—22no—
186C2×C4×D11—42no—
187C2×C4×D11C22×C414yes—
188C2×C4×D11C22×C414yes—
189C2×C4×D11C22×C414yes—
190C2×Dic22—24no—
191C2×Dic22—44no—
192C2×Dic22C22×C414yes—
193C2×Dic22C22×C418yes—
194C11×C4⋊C4—28no—
195C11×C4⋊C4—24no—
196C11×C4⋊C4C22×C414yes—
197C11×C4⋊C4C22×C418yes—
198C42×C11—28no—
199C42×C11—22no—
200C42×C11—22no—
201C42×C11—24no—
202C42×C11—42no—
203C42×C11—44no—
204C42×C11C22×C414yes—
205C42×C11C22×C418yes—
206C42×C11#4118yes—
207(C2×D11)⋊C4—24no—
208(C2×D11)⋊C4—24no—
209(C2×D11)⋊C4—44no—
210(C2×D11)⋊C4C22×C418yes—
211(C2×D11)⋊C4C22×C418yes—
212C4⋊Dic11—24no—
213C4⋊Dic11—44no—
214C4⋊Dic11C22×C414yes—
215C4⋊Dic11C22×C418yes—
216Dic11⋊C4—28no—
217Dic11⋊C4—24no—
218Dic11⋊C4—24no—
219Dic11⋊C4—44no—
220Dic11⋊C4C22×C418yes—
221Dic11⋊C4C22×C418yes—
222Dic11⋊C4C22×C418yes—
223Dic11⋊C4C22×C418yes—
224Dic11⋊C4C22×C418yes—
225C4×Dic11—28no—
226C4×Dic11—24no—
227C4×Dic11—24no—
228C4×Dic11—22no—
229C4×Dic11—22no—
230C4×Dic11—44no—
231C4×Dic11—42no—
232C4×Dic11C22×C414yes—
233C4×Dic11C22×C418yes—
234C4×Dic11C22×C414yes—
235C4×Dic11C22×C414yes—
236C2×#533—111no—
237#2336—114no—
238#2332—114no—
239#2331—112no—
240#2327—112no—
241#2323—112no—
242#2323—112no—
243#2298—112no—
244#2298—112no—
245#2295—111no—
246#2295—112no—
247#2295—112no—
248#2295—111no—
249#2283—111no—
250C42×Q8—111no—
251C42×Q8D1111yescharacteristic, complemented
252C4×#117—111no—
253C23×C11C2511yescharacteristic
254C22×D11—22no—
255C22×D11—21no—
256C22×D11—21no—
257C22×D11—22no—
258C22×D11C23×C412yes—
259Q8×C11—28no—
260C2×C4×C11—24no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—24no—
266C2×C4×C11—22no—
267C2×C4×C11—24no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11C23×C412yes—
271C2×C4×C11C23×C414yes—
272C2×C4×C11C23×C414yes—
273C2×C4×C11C23×C412yes—
274C2×C4×C11C23×C412yes—
275C2×C4×C11C2×#4114yes—
276C2×C4×C11C2×#4114yes—
277C2×C4×C11C2×#4114yes—
278C2×C4×C112−1+412yes—
279C2×C4×C112−1+412yes—
280C2×Dic11—24no—
281C2×Dic11—22no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—24no—
285C2×Dic11—22no—
286C2×Dic11—24no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—24no—
290C2×Dic11—22no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—22no—
294C2×Dic11—24no—
295C2×Dic11C23×C412yes—
296C2×Dic11C23×C412yes—
297C2×Dic11C23×C412yes—
298C2×Dic11C23×C414yes—
299C2×Dic11C23×C414yes—
300C4×D11—28no—
301C4×D11—28no—
302C4×D11—44no—
303Dic22—28no—
304Dic22—48no—
305#533—1116no—
306C2×C4⋊Q8—111no—
307C2×C4⋊Q8—111no—
308C2×#125—112no—
309C2×C22⋊Q8—111no—
310C2×C22⋊Q8—111no—
311C2×C22⋊Q8—112no—
312C2×C4×Q8—111no—
313C2×C4×Q8—112no—
314C2×C4×Q8—112no—
315C2×C4×Q8C2×D1112yes—
316C2×C4×Q8C2×D1111yescharacteristic
317C2×#117—112no—
318C2×#117—112no—
319C22×C42—111no—
320#391—112no—
321#391—112no—
322#391—114no—
323#391—114no—
324#389—112no—
325#389—112no—
326#389—114no—
327#389—114no—
328#388—114no—
329#388—114no—
330#388—114no—
331#388—114no—
332#387—114no—
333#387—114no—
334#387—114no—
335#387—114no—
336#387—114no—
337#387—114no—
338#387—114no—
339#387—114no—
340#387—114no—
341#387—114no—
342#383—112no—
343#382—112no—
344#381—112no—
345#380—112no—
346C4×C4⋊C4—112no—
347C4×C4⋊C4—114no—
348C4×C4⋊C4—112no—
349C4×C4⋊C4—111no—
350C4×C4⋊C4—111no—
351C4×C4⋊C4—112no—
352C4×C4⋊C4—112no—
353C4×C4⋊C4—111no—
354C4×C4⋊C4—112no—
355C4×C4⋊C4C2×D1112yes—
356C4×C4⋊C4C2×D1114yes—
357C4×C4⋊C4C2×D1111yescharacteristic
358C4×C4⋊C4C2×D1112yes—
359C4×C22⋊C4—112no—
360C4×C22⋊C4—111no—
361C4×C22⋊C4—111no—
362C4×C22⋊C4—112no—
363#376—112no—
364#376—112no—
365#376—112no—
366#376—112no—
367C43—111no—
368C43—112no—
369C43C2×D1111yescharacteristic
370C43C2×D1112yes—
371C22×C11C24×C411yescharacteristic
372C22×C11C22×#4112yes—
373C22×C11C2×2−1+411yescharacteristic
374C22×C11C2×2−1+411yescharacteristic
375C22×C11#58512yes—
376C2×D11—22no—
377C2×D11—22no—
378C2×D11—22no—
379C2×D11—42no—
380C2×D11—42no—
381C4×C11—24no—
382C4×C11—24no—
383C4×C11—22no—
384C4×C11—24no—
385C4×C11—24no—
386C4×C11—44no—
387C4×C11C4×#4114yes—
388C4×C11#51914yes—
389Dic11—24no—
390Dic11—22no—
391Dic11—22no—
392Dic11—22no—
393Dic11—24no—
394Dic11—42no—
395Dic11—44no—
396Dic11—42no—
397C22×Q8—111no—
398C22×Q8—112no—
399C22×Q8C22×D1111yescharacteristic
400C23×C4—111no—
401C23×C4—111no—
402C23×C4—111no—
403C4⋊Q8—118no—
404C4⋊Q8—118no—
405#125—1116no—
406C22⋊Q8—118no—
407C22⋊Q8—1116no—
408C22⋊Q8—118no—
409C4×Q8—28no—
410C4×Q8—1116no—
411C4×Q8—118no—
412C4×Q8—228no—
413C4×Q8C4×D1118yes—
414#117—1116no—
415#117—228no—
416C2×C4⋊C4—112no—
417C2×C4⋊C4—112no—
418C2×C4⋊C4—112no—
419C2×C4⋊C4—112no—
420C2×C4⋊C4—112no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—112no—
423C2×C4⋊C4—112no—
424C2×C4⋊C4—112no—
425C2×C4⋊C4—112no—
426C2×C4⋊C4—114no—
427C2×C4⋊C4—114no—
428C2×C4⋊C4—114no—
429C2×C4⋊C4C22×D1112yes—
430C2×C4⋊C4C22×D1114yes—
431C2×C4⋊C4C22×D1112yes—
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C22⋊C4—112no—
434C2×C22⋊C4—112no—
435C2×C22⋊C4—112no—
436C2×C22⋊C4—112no—
437C2×C22⋊C4—114no—
438C2×C42—111no—
439C2×C42—111no—
440C2×C42—112no—
441C2×C42—111no—
442C2×C42—118no—
443C2×C42—112no—
444C2×C42—114no—
445C2×C42—111no—
446C2×C42—112no—
447C2×C42—111no—
448C2×C42—112no—
449C2×C42—114no—
450C2×C42C22×D1114yes—
451C2×C42C22×D1111yescharacteristic
452C2×C42C22×D1111yescharacteristic
453C2×C42C22×D1112yes—
454C2×C42C22×D1112yes—
455C2×C42C22×D1114yes—
456C2×C42C22×D1112yes—
457C2×C42C22×D1111yescharacteristic
458C2×C42C22×D1112yes—
459#95—112no—
460#95—112no—
461#95—112no—
462#95—112no—
463#95—114no—
464#95—114no—
465#95—114no—
466#95—114no—
467#95—114no—
468#95—114no—
469#95—114no—
470#95—112no—
471#95—114no—
472#95—114no—
473#95—114no—
474#95C22×D1112yes—
475#95C22×D1114yes—
476C2×C11C2×C4×#4111yescharacteristic
477C2×C11C2×#51911yescharacteristic
478C2×C11#342811yescharacteristic
479C2×C11#346112yes—
480C2×C11#346112yes—
481D11—42no—
482C24—111no—
483C2×Q8—24no—
484C2×Q8—114no—
485C2×Q8—118no—
486C2×Q8—224no—
487C2×Q8—444no—
488C2×Q8C2×C4×D1114yes—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—112no—
492C22×C4—112no—
493C22×C4—111no—
494C22×C4—114no—
495C22×C4—114no—
496C22×C4—114no—
497C22×C4—112no—
498C22×C4—112no—
499C22×C4—114no—
500C22×C4—224no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—442no—
504C22×C4C23×D1114yes—
505C22×C4C23×D1112yes—
506C22×C4C23×D1111yescharacteristic
507C22×C4C23×D1112yes—
508C22×C4C23×D1112yes—
509C22×C4C23×D1112yes—
510C22×C4C23×D1111yescharacteristic
511C22×C4C23×D1111yescharacteristic
512C4⋊C4—28no—
513C4⋊C4—24no—
514C4⋊C4—118no—
515C4⋊C4—118no—
516C4⋊C4—118no—
517C4⋊C4—118no—
518C4⋊C4—118no—
519C4⋊C4—118no—
520C4⋊C4—114no—
521C4⋊C4—224no—
522C4⋊C4—224no—
523C4⋊C4—228no—
524C4⋊C4—224no—
525C4⋊C4—444no—
526C4⋊C4—444no—
527C4⋊C4C2×C4×D1118yes—
528C4⋊C4C2×C4×D1114yes—
529C22⋊C4—118no—
530C22⋊C4—118no—
531C22⋊C4—224no—
532C22⋊C4—224no—
533C22⋊C4—444no—
534C42—28no—
535C42—22no—
536C42—22no—
537C42—24no—
538C42—42no—
539C42—44no—
540C42—114no—
541C42—114no—
542C42—114no—
543C42—118no—
544C42—224no—
545C42—228no—
546C42—222no—
547C42—224no—
548C42—222no—
549C42—444no—
550C42—442no—
551C42C2×C4×D1114yes—
552C42C2×C4×D1118yes—
553C42#433918yes—
554C11#3408511yescharacteristic, complemented, Sylow
555C23—112no—
556C23—222no—
557C23—221no—
558C23—221no—
559C23—222no—
560C23C24×D1111yescharacteristic
561Q8—28no—
562Q8—228no—
563Q8—448no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—112no—
575C2×C4—112no—
576C2×C4—112no—
577C2×C4—114no—
578C2×C4—114no—
579C2×C4—224no—
580C2×C4—222no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—224no—
584C2×C4—222no—
585C2×C4—228no—
586C2×C4—228no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—224no—
590C2×C4—222no—
591C2×C4—224no—
592C2×C4—222no—
593C2×C4—224no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—444no—
597C2×C4C22×C4×D1112yes—
598C2×C4C22×C4×D1114yes—
599C2×C4C22×C4×D1114yes—
600C2×C4C22×C4×D1112yes—
601C2×C4C22×C4×D1112yes—
602C2×C4C2×#433914yes—
603C2×C4C2×#433914yes—
604C2×C4C2×#433914yes—
605C2×C4#6704012yes—
606C2×C4#6704312yes—
607C22—222no—
608C22—222no—
609C22—222no—
610C22—442no—
611C22—442no—
612C22C23×C4×D1111yescharacteristic
613C22C22×#433912yes—
614C22C2×#6704011yescharacteristic
615C22C2×#6704311yescharacteristic
616C22#1062345312yes—
617C4—24no—
618C4—24no—
619C4—24no—
620C4—22no—
621C4—24no—
622C4—44no—
623C4—222no—
624C4—224no—
625C4—222no—
626C4—222no—
627C4—224no—
628C4—442no—
629C4—442no—
630C4—444no—
631C4C4×#433914yes—
632C4#1062310314yes—
633C2—442no—
634C2C2×C4×#433911yescharacteristic
635C2C2×#1062310311yescharacteristic
636C2#1308181511yescharacteristic
637C2#1308204312yes—
638C2#1308204912yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC42×Q8×C11C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenterC42×Q8D11
hypocenterC11#34085
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C42×Q8

Complements

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

NH ≅ G/Ntype
2. #13071415C2semidirect
4. #13071360C2semidirect
5. #13071332C2semidirect
10. #13071094C2semidirect
11. #13071093C2semidirect
12. #13071092C2semidirect
13. #13071090C2semidirect
15. C42×Dic22C2semidirect
17. C42×Q8×C11C2semidirect
22. #10623109C4semidirect
251. C42×Q8D11semidirect
554. C11#34085semidirect

Maximal subgroups

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

subgroupindex
C2×#106231092
#130714152
#130713672
#130713602
#130713322
#130712992
#130712922
#130711132
#130711092
#130710942
#130710932
#130710922
#130710902
#130710122
C42×Dic222
C4×#669252
C42×Q8×C112
#3408511