Finite Group Databasebeta

← #14916530

Subgroups — #14916530

Order 2816.

2406 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66999C211yesmaximal, characteristic
2#13071777C214yesmaximal, complemented
3#13071695C214yesmaximal, complemented
4#13071486C212yesmaximal, complemented
5#13071480C212yesmaximal, complemented
6#13071466C212yesmaximal
7#13071458C212yesmaximal
8#13071371C214yesmaximal, complemented
9#13071348C214yesmaximal, complemented
10#13071217C211yesmaximal, characteristic, complemented
11#13071217C211yesmaximal, characteristic, complemented
12#13071202C211yesmaximal, characteristic, complemented
13#13070996C211yesmaximal, characteristic
14D11×#381C211yesmaximal, characteristic
15C11×#2310C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C2×C11×#117C2212yes—
19C2×#66999C4116yescomplemented
20C2×#66999C2212yes—
21C2×#66999C2212yes—
22C2×#66999C2212yes—
23C2×#66999C2212yes—
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C2×#66979C2212yes—
27C22×C4⋊Dic11C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C2×C22⋊C4×D11C2212yes—
31C2×#66930C2212yes—
32C11×#391C2214yescomplemented
33C11×#391C2214yescomplemented
34C11×#381C2212yes—
35C11×#381C2211yescharacteristic
36C11×#381C2211yescharacteristic
37#10622843C2214yescomplemented
38#10622843C2214yescomplemented
39#10622824C2212yes—
40#10622824C2211yescharacteristic
41#10622824C2211yescharacteristic
42#10622603C2214yes—
43#10622602C2214yes—
44#10622591C2214yescomplemented
45#10622585C2214yescomplemented
46#10622568C2212yes—
47#10622556C2212yes—
48#10622555C2212yes—
49#10622555C2212yes—
50C22⋊C4×Dic11C2212yes—
51C22⋊C4×Dic11C2212yes—
52#10622553C2214yes—
53C4×(C2×D11)⋊C4C2214yes—
54#10622546C2214yescomplemented
55C4×Dic11⋊C4C2214yescomplemented
56#10622283C2214yes—
57#10622282C2214yes—
58#10622281C2214yes—
59#10622280C2212yes—
60#10622280C2212yes—
61#10622279C2212yes—
62#10622279C2212yes—
63#10622279C2214yes—
64#10622277C2212yes—
65#10622277C2212yes—
66D11×#95C2212yes—
67D11×#95C2212yes—
68#10622268C2214yescomplemented
69#10622267C2214yescomplemented
70#10622267C2214yescomplemented
71#10622266C2214yescomplemented
72#10622266C2214yescomplemented
73#10622265C2214yescomplemented
74#10622262C2214yescomplemented
75#10622260C2214yescomplemented
76C24×D11C2311yescharacteristic
77C22×Q8×C11—44no—
78C22×Q8×C11C2×C418yescomplemented
79C22×Q8×C11C2312yes—
80C22×Q8×C11C2312yes—
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C22×C4×D11—44no—
88C22×C4×D11C2×C418yes—
89C22×C4×D11C2314yes—
90C22×C4×D11C2311yescharacteristic
91C22×C4×D11C2311yescharacteristic
92C22×C4×D11C2311yescharacteristic
93C22×C4×D11C2311yescharacteristic
94C11×#117—44no—
95C2×C11×C4⋊C4C2314yes—
96C2×C11×C22⋊C4C2312yes—
97C2×C11×C22⋊C4C2312yes—
98C2×C42×C11C2314yes—
99C2×C22⋊Dic11C2312yes—
100C2×C22⋊Dic11C2312yes—
101#66999C2×C4116yes—
102#66999C2×C4116yes—
103#66999C2×C4116yescomplemented
104#66999C2×C4116yescomplemented
105C2×(C2×D11)⋊C4C2×C418yes—
106C2×(C2×D11)⋊C4C2×C418yes—
107C2×(C2×D11)⋊C4C2314yes—
108C2×(C2×D11)⋊C4C2314yes—
109C2×(C2×D11)⋊C4C2314yes—
110C2×(C2×D11)⋊C4C2312yes—
111C2×(C2×D11)⋊C4C2312yes—
112C2×(C2×D11)⋊C4C2312yes—
113C2×(C2×D11)⋊C4C2312yes—
114#66979—44no—
115C2×C4⋊Dic11C2×C418yescomplemented
116C2×C4⋊Dic11C2314yes—
117C2×C4⋊Dic11C2312yes—
118C2×C4⋊Dic11C2312yes—
119C2×Dic11⋊C4C2×C418yescomplemented
120C2×Dic11⋊C4C2×C418yescomplemented
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2314yes—
123C2×Dic11⋊C4C2314yes—
124C2×Dic11⋊C4C2312yes—
125C2×Dic11⋊C4C2312yes—
126C2×Dic11⋊C4C2312yes—
127C2×Dic11⋊C4C2312yes—
128C2×C4×Dic11C2314yes—
129C2×C4×Dic11C2314yes—
130C2×C4×Dic11C2314yes—
131C2×C4×Dic11C2314yes—
132C22⋊C4×D11—44no—
133#66930—44no—
134C11×#95C2314yes—
135C11×#95C2314yes—
136C11×#95C2312yes—
137C11×#95C2312yes—
138C11×#95C2312yes—
139C11×#95C2312yes—
140C11⋊#95C2314yes—
141C11⋊#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2312yes—
145C11⋊#95C2312yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2312yes—
149C11⋊#95C2312yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152#34359—111nomaximal, Sylow
153C24×C11C2411yescharacteristic
154C23×D11—24no—
155C23×D11—24no—
156C23×D11—42no—
157C23×D11C22×C414yes—
158C23×D11C2411yescharacteristic
159C23×D11C2411yescharacteristic
160C2×Q8×C11—416no—
161C2×Q8×C11—42no—
162C2×Q8×C11—42no—
163C2×Q8×C11—42no—
164C2×Q8×C11—42no—
165C2×Q8×C11C22×C418yes—
166C2×Q8×C11C22×C418yes—
167C22×C4×C11—24no—
168C22×C4×C11—24no—
169C22×C4×C11—24no—
170C22×C4×C11C22×C414yes—
171C22×C4×C11C22×C414yes—
172C22×C4×C11C22×C414yes—
173C22×C4×C11C2414yes—
174C22×C4×C11C2414yes—
175C22×C4×C11C2411yescharacteristic
176C22×C4×C11C2411yescharacteristic
177C22×C4×C11C2412yes—
178C22×C4×C11C2412yes—
179C22×Dic11—24no—
180C22×Dic11—42no—
181C22×Dic11—42no—
182C22×Dic11C22×C414yes—
183C22×Dic11C22×C414yes—
184C22×Dic11C22×C414yes—
185C22×Dic11C2414yes—
186C22×Dic11C2414yes—
187C22×Dic11C2411yescharacteristic
188C22×Dic11C2412yes—
189C22×Dic11C2412yes—
190C22×Dic11C2411yescharacteristic
191C2×C4×D11—28no—
192C2×C4×D11—416no—
193C2×C4×D11—42no—
194C2×C4×D11—42no—
195C2×C4×D11—42no—
196C2×C4×D11—42no—
197C2×C4×D11—44no—
198C2×C4×D11—44no—
199C2×C4×D11C22×C414yes—
200C2×C4×D11C22×C414yes—
201C2×C4×D11C22×C414yes—
202C2×C4×D11C22×C414yes—
203C11×C4⋊C4—44no—
204C11×C22⋊C4—24no—
205C11×C22⋊C4—24no—
206C42×C11—44no—
207C22⋊Dic11—24no—
208C22⋊Dic11—24no—
209(C2×D11)⋊C4—28no—
210(C2×D11)⋊C4—44no—
211(C2×D11)⋊C4—44no—
212(C2×D11)⋊C4C22×C418yes—
213(C2×D11)⋊C4C22×C418yes—
214(C2×D11)⋊C4C22×C418yes—
215(C2×D11)⋊C4C22×C418yes—
216C4⋊Dic11—44no—
217C4⋊Dic11C22×C418yes—
218C4⋊Dic11C22×C418yes—
219Dic11⋊C4—44no—
220Dic11⋊C4—44no—
221Dic11⋊C4—44no—
222Dic11⋊C4C22×C418yes—
223Dic11⋊C4C22×C418yes—
224Dic11⋊C4C22×C418yes—
225Dic11⋊C4C22×C418yes—
226C4×Dic11—44no—
227C4×Dic11—44no—
228C4×Dic11—44no—
229C4×Dic11—44no—
230C22×C22⋊Q8—111no—
231#2378—114no—
232#2368—114no—
233#2344—112no—
234#2344—112no—
235#2342—112no—
236#2342—112no—
237#2332—114no—
238#2329—114no—
239#2313—111no—
240#2313—111no—
241#2310—111no—
242#2310D1111yescharacteristic, complemented
243#2280—111no—
244C2×#381—111no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11C23×C412yes—
248C23×C11H(5,𝔽2)14yes—
249C23×C11C2511yescharacteristic
250C22×D11—22no—
251C22×D11—22no—
252C22×D11—28no—
253C22×D11—22no—
254C22×D11—22no—
255C22×D11—22no—
256C22×D11—28no—
257C22×D11—44no—
258C22×D11—416no—
259C22×D11C23×C412yes—
260C22×D11C23×C412yes—
261C22×D112−1+414yes—
262Q8×C11—48no—
263Q8×C11—48no—
264C2×C4×C11—28no—
265C2×C4×C11—28no—
266C2×C4×C11—28no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—24no—
274C2×C4×C11—24no—
275C2×C4×C11—24no—
276C2×C4×C11—24no—
277C2×C4×C11—24no—
278C2×C4×C11—24no—
279C2×C4×C11C23×C414yes—
280C2×C4×C11C23×C414yes—
281C2×C4×C11C23×C412yes—
282C2×C4×C11C23×C412yes—
283C2×Dic11—28no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—24no—
287C2×Dic11—24no—
288C2×Dic11—24no—
289C2×Dic11—24no—
290C2×Dic11—24no—
291C2×Dic11—24no—
292C2×Dic11—24no—
293C2×Dic11—24no—
294C2×Dic11—44no—
295C2×Dic11—44no—
296C2×Dic11C23×C412yes—
297C2×Dic11C23×C412yes—
298C2×Dic11C23×C414yes—
299C2×Dic11C23×C414yes—
300C4×D11—44no—
301C4×D11—44no—
302C4×D11—44no—
303C4×D11—44no—
304C4×D11—88no—
305C23×Q8C2×D1111yescharacteristic
306C24×C4—111no—
307C2×C22⋊Q8—112no—
308C2×C22⋊Q8—112no—
309C2×C22⋊Q8—112no—
310C2×C22⋊Q8—112no—
311C2×C22⋊Q8—1116no—
312C2×#117—112no—
313C2×#117—112no—
314C2×#117C2×D1112yes—
315C22×C4⋊C4—111no—
316C22×C4⋊C4—111no—
317C22×C4⋊C4—111no—
318C22×C22⋊C4—111no—
319C22×C22⋊C4—111no—
320C22×C22⋊C4—112no—
321#391—114no—
322#391—114no—
323#391C2×D1114yescomplemented
324#391C2×D1114yescomplemented
325#389—114no—
326#389—114no—
327#388—114no—
328#388—114no—
329#388—114no—
330#388—114no—
331#387—114no—
332#387—114no—
333#387—114no—
334#387—114no—
335#387—114no—
336#387—114no—
337#387—114no—
338#387—114no—
339#385—114no—
340#385—114no—
341#381—111no—
342#381—111no—
343#381—112no—
344#381—112no—
345#381—112no—
346#381—112no—
347#381C2×D1111yescharacteristic
348#381C2×D1111yescharacteristic
349#381C2×D1112yes—
350#380—112no—
351#380—112no—
352#380—112no—
353#380—112no—
354#379—112no—
355C4×C4⋊C4—114no—
356C4×C4⋊C4—114no—
357C4×C22⋊C4—112no—
358C4×C22⋊C4—112no—
359C4×C22⋊C4—114no—
360C4×C22⋊C4—114no—
361C4×C22⋊C4—112no—
362C4×C22⋊C4—112no—
363C2×#95—112no—
364C2×#95—112no—
365C22×C11—22no—
366C22×C11—22no—
367C22×C11—28no—
368C22×C11#51814yes—
369C22×C11C24×C411yescharacteristic
370C22×C11C2×H(5,𝔽2)12yes—
371C22×C11C2×2−1+412yes—
372C22×C11#58512yes—
373C2×D11—22no—
374C2×D11—22no—
375C2×D11—28no—
376C2×D11—22no—
377C2×D11—22no—
378C2×D11—22no—
379C2×D11—416no—
380C2×D11—44no—
381C2×D11#51914yes—
382C4×C11—24no—
383C4×C11—24no—
384C4×C11—22no—
385C4×C11—22no—
386C4×C11—44no—
387C4×C11—44no—
388Dic11—22no—
389Dic11—22no—
390Dic11—24no—
391Dic11—24no—
392Dic11—44no—
393Dic11—44no—
394C25—111no—
395C22×Q8—44no—
396C22×Q8C4×D1118yescomplemented
397C22×Q8C22×D1112yes—
398C22×Q8C22×D1112yes—
399C23×C4—111no—
400C23×C4—111no—
401C23×C4—111no—
402C23×C4—118no—
403C23×C4—111no—
404C23×C4—111no—
405C23×C4—111no—
406C23×C4—111no—
407C23×C4—114no—
408C23×C4—444no—
409C23×C4C22×D1111yescharacteristic
410C23×C4C22×D1111yescharacteristic
411C23×C4C22×D1111yescharacteristic
412C22⋊Q8—1116no—
413C22⋊Q8—1116no—
414C22⋊Q8—1116no—
415C22⋊Q8—1116no—
416#117—44no—
417#117—444no—
418#117—444no—
419C2×C4⋊C4—118no—
420C2×C4⋊C4—118no—
421C2×C4⋊C4—118no—
422C2×C4⋊C4—112no—
423C2×C4⋊C4—112no—
424C2×C4⋊C4—112no—
425C2×C4⋊C4—112no—
426C2×C4⋊C4—112no—
427C2×C4⋊C4—112no—
428C2×C4⋊C4—114no—
429C2×C4⋊C4—114no—
430C2×C4⋊C4—114no—
431C2×C4⋊C4—114no—
432C2×C4⋊C4C22×D1114yes—
433C2×C22⋊C4—118no—
434C2×C22⋊C4—118no—
435C2×C22⋊C4—112no—
436C2×C22⋊C4—112no—
437C2×C22⋊C4—112no—
438C2×C22⋊C4—112no—
439C2×C22⋊C4—112no—
440C2×C22⋊C4—112no—
441C2×C22⋊C4—114no—
442C2×C22⋊C4—114no—
443C2×C22⋊C4—114no—
444C2×C22⋊C4—444no—
445C2×C22⋊C4C22×D1112yes—
446C2×C22⋊C4C22×D1112yes—
447C2×C42—114no—
448C2×C42—114no—
449C2×C42—114no—
450C2×C42—114no—
451C2×C42C22×D1114yes—
452#95—114no—
453#95—114no—
454#95—112no—
455#95—112no—
456#95—112no—
457#95—112no—
458#95—114no—
459#95—114no—
460#95—114no—
461#95—114no—
462#95—114no—
463#95—114no—
464#95C22×D1112yes—
465#95C22×D1112yes—
466#95C22×D1112yes—
467#95C22×D1112yes—
468#95C22×D1114yes—
469#95C22×D1114yes—
470C2×C11—24no—
471C2×C11C2×#51811yescharacteristic
472C2×C11C2×#51911yescharacteristic
473C2×C11#342811yescharacteristic
474C2×C11#353514yes—
475D11—24no—
476D11—42no—
477C24—111no—
478C24—111no—
479C24—114no—
480C24—224no—
481C24—224no—
482C24—442no—
483C24C23×D1111yescharacteristic
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8—42no—
487C2×Q8—42no—
488C2×Q8—416no—
489C2×Q8C2×C4×D1118yes—
490C2×Q8C2×C4×D1118yes—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—114no—
495C22×C4—111no—
496C22×C4—112no—
497C22×C4—112no—
498C22×C4—111no—
499C22×C4—114no—
500C22×C4—114no—
501C22×C4—114no—
502C22×C4—114no—
503C22×C4—114no—
504C22×C4—114no—
505C22×C4—114no—
506C22×C4—114no—
507C22×C4—228no—
508C22×C4—224no—
509C22×C4—4416no—
510C22×C4—442no—
511C22×C4—442no—
512C22×C4—442no—
513C22×C4—442no—
514C22×C4—444no—
515C22×C4—444no—
516C22×C4—442no—
517C22×C4—442no—
518C22×C4C2×C4×D1114yes—
519C22×C4C2×C4×D1114yes—
520C22×C4C2×C4×D1114yes—
521C22×C4C23×D1114yes—
522C22×C4C23×D1114yes—
523C22×C4C23×D1111yescharacteristic
524C22×C4C23×D1111yescharacteristic
525C22×C4C23×D1112yes—
526C22×C4C23×D1112yes—
527C4⋊C4—44no—
528C4⋊C4—118no—
529C4⋊C4—118no—
530C4⋊C4—118no—
531C4⋊C4—118no—
532C4⋊C4—118no—
533C4⋊C4—118no—
534C4⋊C4—444no—
535C4⋊C4—444no—
536C4⋊C4—444no—
537C4⋊C4—444no—
538C22⋊C4—24no—
539C22⋊C4—24no—
540C22⋊C4—118no—
541C22⋊C4—118no—
542C22⋊C4—118no—
543C22⋊C4—118no—
544C22⋊C4—228no—
545C22⋊C4—224no—
546C22⋊C4—224no—
547C22⋊C4—444no—
548C22⋊C4—444no—
549C42—44no—
550C42—444no—
551C42—444no—
552C42—444no—
553C42—444no—
554C11#3435911yescharacteristic, complemented, Sylow
555C23—22no—
556C23—22no—
557C23—112no—
558C23—114no—
559C23—112no—
560C23—228no—
561C23—222no—
562C23—222no—
563C23—228no—
564C23—222no—
565C23—222no—
566C23—222no—
567C23—444no—
568C23—4416no—
569C23C22×C4×D1112yes—
570C23#6703714yes—
571C23C24×D1111yescharacteristic
572Q8—48no—
573Q8—48no—
574C2×C4—28no—
575C2×C4—28no—
576C2×C4—28no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—114no—
590C2×C4—114no—
591C2×C4—112no—
592C2×C4—112no—
593C2×C4—228no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—224no—
597C2×C4—224no—
598C2×C4—224no—
599C2×C4—224no—
600C2×C4—224no—
601C2×C4—224no—
602C2×C4—224no—
603C2×C4—224no—
604C2×C4—444no—
605C2×C4—444no—
606C2×C4—444no—
607C2×C4—444no—
608C2×C4—444no—
609C2×C4—444no—
610C2×C4—888no—
611C2×C4C22×C4×D1114yes—
612C2×C4C22×C4×D1114yes—
613C2×C4C22×C4×D1112yes—
614C2×C4C22×C4×D1112yes—
615C22—28no—
616C22—22no—
617C22—22no—
618C22—114no—
619C22—228no—
620C22—222no—
621C22—222no—
622C22—222no—
623C22—222no—
624C22—222no—
625C22—4416no—
626C22—444no—
627C22#1062301714yes—
628C22C23×C4×D1111yescharacteristic
629C22C2×#6703712yes—
630C22D11×2−1+412yes—
631C22#1062345712yes—
632C4—22no—
633C4—22no—
634C4—24no—
635C4—24no—
636C4—44no—
637C4—44no—
638C4—222no—
639C4—222no—
640C4—224no—
641C4—224no—
642C4—444no—
643C4—444no—
644C2—24no—
645C2—224no—
646C2—442no—
647C2C2×#1062301711yescharacteristic
648C2D11×#51911yescharacteristic
649C2#1308181811yescharacteristic
650C2#1308281514yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2310C2
socle, cosocleC23×C11C25
prime radicalC24×D11C23
hypercenter#2310D11
hypocenterC11#34359
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2310

Complements

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

NH ≅ G/Ntype
2. #13071777C2semidirect
3. #13071695C2semidirect
4. #13071486C2semidirect
5. #13071480C2semidirect
8. #13071371C2semidirect
9. #13071348C2semidirect
10. #13071217C2semidirect
11. #13071217C2semidirect
12. #13071202C2semidirect
15. C11×#2310C2semidirect
19. C2×#66999C4semidirect
32. C11×#391C22semidirect
33. C11×#391C22semidirect
37. #10622843C22semidirect
38. #10622843C22semidirect
44. #10622591C22semidirect
45. #10622585C22semidirect
54. #10622546C22semidirect
55. C4×Dic11⋊C4C22semidirect
68. #10622268C22semidirect
69. #10622267C22semidirect
70. #10622267C22semidirect
71. #10622266C22semidirect
72. #10622266C22semidirect
73. #10622265C22semidirect
74. #10622262C22semidirect
75. #10622260C22semidirect
78. C22×Q8×C11C2×C4semidirect
103. #66999C2×C4semidirect
104. #66999C2×C4semidirect
115. C2×C4⋊Dic11C2×C4semidirect
119. C2×Dic11⋊C4C2×C4semidirect
120. C2×Dic11⋊C4C2×C4semidirect
242. #2310D11semidirect
323. #391C2×D11semidirect
324. #391C2×D11semidirect
396. C22×Q8C4×D11semidirect
554. C11#34359semidirect

Maximal subgroups

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

subgroupindex
C22×#669992
#130717772
#130716952
#130714862
#130714802
#130714662
#130714582
#130713712
#130713482
#130712172
#130712022
#130709962
D11×#3812
C11×#23102
#3435911