Finite Group Databasebeta

← #14926284

Subgroups — #14926284

Order 2816.

1834 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074320C214yesmaximal, complemented
2#13073855C211yesmaximal, characteristic, complemented
3#13073652C211yesmaximal, characteristic, complemented
4#13073642C211yesmaximal, characteristic, complemented
5#13072332C212yesmaximal
6#13072325C212yesmaximal
7#13072309C212yesmaximal
8#13072305C212yesmaximal
9#13071893C214yesmaximal
10#13071187C212yesmaximal, complemented
11#13071183C212yesmaximal, complemented
12#125×Dic11C212yesmaximal, complemented
13#13071175C212yesmaximal, complemented
14#13071021C211yesmaximal, characteristic
15C4×#66945C211yesmaximal, characteristic
16C4×#66945C211yesmaximal, characteristic
17C11×#2552C211yesmaximal, characteristic, complemented
18C2×C11×#125C2212yes—
19C2×#66945C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C2×#66945C2211yescharacteristic
23C2×#66945C2212yes—
24C2×#66943C2212yes—
25C2×#66941C2212yes—
26C2×#66940C2214yes—
27C2×C42×D11C2211yescharacteristic
28C2×#66922C2212yes—
29C11×#398C2214yes—
30C11×#389C2212yes—
31C11×#389C2212yes—
32C11×#384C2212yes—
33C11×#384C2211yescharacteristic
34C4×C11×C4⋊C4C2211yescharacteristic
35C4×C11×C4⋊C4C2211yescharacteristic
36#10622607C2214yes—
37#10622607C2214yes—
38#10622605C2214yes—
39#10622600C2212yes—
40#10622600C2212yes—
41#10622598C2212yes—
42#10622598C2212yes—
43#10622597C2214yes—
44#10622594C2214yes—
45#10622594C2214yes—
46#10622591C2214yes—
47#10622590C2212yes—
48#10622590C2212yes—
49#10622589C2212yes—
50C4⋊C4×Dic11C2214yes—
51C4⋊C4×Dic11C2214yes—
52C4⋊C4×Dic11C2211yescharacteristic
53C4⋊C4×Dic11C2212yes—
54C4⋊C4×Dic11C2211yescharacteristic
55C4⋊C4×Dic11C2212yes—
56C4⋊C4×Dic11C2211yescharacteristic
57C4⋊C4×Dic11C2211yescharacteristic
58#10622587C2214yes—
59#10622586C2214yes—
60#10622586C2212yes—
61#10622586C2212yes—
62#10622585C2214yes—
63C4×(C2×D11)⋊C4C2212yes—
64C4×(C2×D11)⋊C4C2212yes—
65#10622549C2212yes—
66#10622548C2211yescharacteristic
67C4×C4⋊Dic11C2211yescharacteristic
68C4×C4⋊Dic11C2211yescharacteristic
69C42×Dic11C2212yes—
70C42×Dic11C2212yes—
71#10622541C2212yes—
72#10622541C2212yes—
73#10622286C2214yes—
74#10622279C2212yes—
75#10622279C2212yes—
76#10622273C2214yes—
77#10622269C2214yes—
78#10622266C2214yes—
79#10622262C2214yes—
80#10622261C2212yes—
81#10622261C2212yes—
82#10622259C2214yes—
83C22×C4×D11C2311yescharacteristic
84C22×C4×D11C2311yescharacteristic
85C22×C4×D11C2311yescharacteristic
86C22×Dic22C2314yes—
87C11×#125—28no—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2314yes—
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C4⋊C4C2314yes—
94C2×C11×C4⋊C4C2314yes—
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C42×C11C2312yes—
99C2×C42×C11C2312yes—
100C2×C42×C11C2311yescharacteristic
101C2×(C2×D11)⋊C4C2312yes—
102C2×(C2×D11)⋊C4C2312yes—
103C2×(C2×D11)⋊C4C2312yes—
104C2×(C2×D11)⋊C4C2312yes—
105C2×(C2×D11)⋊C4C2314yes—
106C2×C4⋊Dic11C2314yes—
107C2×C4⋊Dic11C2312yes—
108C2×C4⋊Dic11C2312yes—
109C2×C4⋊Dic11C2314yes—
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2312yes—
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115C2×Dic11⋊C4C2314yes—
116C2×Dic11⋊C4C2314yes—
117C2×Dic11⋊C4C2314yes—
118C2×Dic11⋊C4C2314yes—
119C2×C4×Dic11C2312yes—
120C2×C4×Dic11C2312yes—
121C2×C4×Dic11C2312yes—
122C2×C4×Dic11C2314yes—
123C2×C4×Dic11C2312yes—
124C2×C4×Dic11C2312yes—
125C2×C4×Dic11C2312yes—
126C2×C4×Dic11C2312yes—
127C2×C4×Dic11C2312yes—
128C2×C4×Dic11C2312yes—
129C2×C4×Dic11C2312yes—
130C2×C4×Dic11C2311yescharacteristic
131C2×C4×Dic11C2311yescharacteristic
132C2×C4×Dic11C2311yescharacteristic
133#66945—24no—
134#66945—24no—
135#66945—24no—
136#66945—24no—
137#66945—44no—
138#66943—28no—
139#66941—28no—
140#66940—48no—
141C42×D11Q818yescomplemented
142#66922—28no—
143C11×#95C2314yes—
144C11×#95C2312yes—
145C11×#95C2312yes—
146C11⋊#95C2312yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2312yes—
150C11⋊#95C2312yes—
151C11⋊#95C2312yes—
152C11⋊#95C2312yes—
153C11⋊#95C2312yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159#34978—111nomaximal, Sylow
160C23×D11C2411yescharacteristic
161C22×C4×C11C2412yes—
162C22×C4×C11C2412yes—
163C22×C4×C11C2414yes—
164C22×C4×C11C2411yescharacteristic
165C22×C4×C11C2412yes—
166C22×C4×C11C2412yes—
167C22×C4×C11C2411yescharacteristic
168C22×C4×C11C2411yescharacteristic
169C22×Dic11C2412yes—
170C22×Dic11C2414yes—
171C22×Dic11C2412yes—
172C22×Dic11C2411yescharacteristic
173C22×Dic11C2411yescharacteristic
174C22×Dic11C2412yes—
175C22×Dic11C2412yes—
176C22×Dic11C2411yescharacteristic
177C2×C4×D11—22no—
178C2×C4×D11—22no—
179C2×C4×D11—22no—
180C2×C4×D11—22no—
181C2×C4×D11—22no—
182C2×C4×D11—22no—
183C2×C4×D11C2×Q814yes—
184C2×C4×D11C2×Q814yes—
185C2×C4×D11C2×Q814yes—
186C2×Dic22—28no—
187C2×Dic22—28no—
188C2×Dic22—44no—
189C11×C4⋊C4—24no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—28no—
193C11×C4⋊C4—28no—
194C11×C4⋊C4—24no—
195C11×C4⋊C4—44no—
196C11×C4⋊C4—42no—
197C11×C4⋊C4#4114yes—
198C11×C4⋊C4#4114yes—
199C42×C11—24no—
200C42×C11—24no—
201C42×C11C2×Q814yes—
202(C2×D11)⋊C4—24no—
203(C2×D11)⋊C4—24no—
204(C2×D11)⋊C4—24no—
205(C2×D11)⋊C4—24no—
206(C2×D11)⋊C4—44no—
207C4⋊Dic11—28no—
208C4⋊Dic11—28no—
209C4⋊Dic11—24no—
210C4⋊Dic11—24no—
211C4⋊Dic11—22no—
212C4⋊Dic11—22no—
213C4⋊Dic11—42no—
214C4⋊Dic11#4114yes—
215C4⋊Dic11#4114yes—
216Dic11⋊C4—28no—
217Dic11⋊C4—28no—
218Dic11⋊C4—44no—
219Dic11⋊C4—44no—
220C4×Dic11—24no—
221C4×Dic11—24no—
222C4×Dic11—24no—
223C4×Dic11—24no—
224C4×Dic11—28no—
225C4×Dic11—24no—
226C4×Dic11—24no—
227C4×Dic11—24no—
228C4×Dic11—24no—
229C4×Dic11—24no—
230C4×Dic11—24no—
231C4×Dic11C2×Q814yes—
232C4×Dic11C2×Q814yes—
233C4×Dic11C2×Q814yes—
234#2612—114no—
235#2571—111no—
236#2552—111no—
237#2552D1111yescharacteristic, complemented
238#2551—111no—
239#2441—112no—
240#2441—112no—
241#2439—112no—
242#2439—112no—
243#2396—114no—
244C4×C4⋊Q8—112no—
245C4×C4⋊Q8—112no—
246C4×#125—112no—
247C4×#125—112no—
248#2285—111no—
249C4×#117—111no—
250C4×#117—111no—
251C23×C11C2511yescharacteristic
252C22×D11—21no—
253C22×D11—21no—
254C22×D11—21no—
255C22×D11—21no—
256C22×D11—21no—
257C22×D11—21no—
258C22×D11C22×Q812yes—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—21no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—24no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—24no—
271C2×C4×C11—22no—
272C2×C4×C11—24no—
273C2×C4×C11—22no—
274C2×C4×C11C22×Q812yes—
275C2×C4×C11C22×Q812yes—
276C2×C4×C11C22×Q812yes—
277C2×C4×C11C2×#4114yes—
278C2×C4×C11C2×#4112yes—
279C2×C4×C11C2×#4114yes—
280C2×C4×C11C2×#4112yes—
281C2×C4×C11C2×#4112yes—
282C2×C4×C11C2×#4112yes—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—22no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—22no—
294C2×Dic11—22no—
295C2×Dic11—24no—
296C2×Dic11—24no—
297C2×Dic11—22no—
298C2×Dic11—24no—
299C2×Dic11—22no—
300C2×Dic11C22×Q812yes—
301C2×Dic11C22×Q812yes—
302C2×Dic11C22×Q812yes—
303C2×Dic11C2×#4114yes—
304C2×Dic11C2×#4114yes—
305C2×Dic11H(5,𝔽2)12yes—
306C2×Dic112−1+412yes—
307C4×D11—28no—
308C4×D11—28no—
309C4×D11—28no—
310Dic22—416no—
311C2×C4⋊Q8—112no—
312C2×C4⋊Q8—112no—
313C2×#125—112no—
314C2×#125C2×D1112yes—
315C2×C4×Q8—114no—
316C2×#117—111no—
317C2×#117—111no—
318C2×#117—111no—
319C2×#117—111no—
320C2×#117—112no—
321C22×C42—111no—
322#400—114no—
323#399—114no—
324#398—114no—
325#398C2×D1114yes—
326#396—114no—
327#396—114no—
328#395—114no—
329#393—114no—
330#391—114no—
331#391—114no—
332#389—112no—
333#389—112no—
334#389—112no—
335#389—114no—
336#389—114no—
337#389—112no—
338#389—112no—
339#389—112no—
340#389C2×D1112yes—
341#389C2×D1112yes—
342#387—114no—
343#387—114no—
344#387—114no—
345#387—114no—
346#384—112no—
347#384—111no—
348#384C2×D1112yes—
349#384C2×D1111yescharacteristic
350#382—112no—
351#382—112no—
352#382—112no—
353#380—112no—
354#380—112no—
355C4×C4⋊C4—114no—
356C4×C4⋊C4—111no—
357C4×C4⋊C4—111no—
358C4×C4⋊C4—114no—
359C4×C4⋊C4—112no—
360C4×C4⋊C4—112no—
361C4×C4⋊C4—111no—
362C4×C4⋊C4—111no—
363C4×C4⋊C4—111no—
364C4×C4⋊C4—111no—
365C4×C4⋊C4—114no—
366C4×C4⋊C4C2×D1111yescharacteristic
367C4×C4⋊C4C2×D1111yescharacteristic
368C4×C22⋊C4—112no—
369C4×C22⋊C4—112no—
370C4×C22⋊C4—112no—
371C4×C22⋊C4—112no—
372#376—112no—
373#376—112no—
374C43—112no—
375C43—112no—
376C22×C11C23×Q811yescharacteristic
377C22×C11C22×#4111yescharacteristic
378C22×C11C22×#4111yescharacteristic
379C22×C11C22×#4111yescharacteristic
380C22×C11C22×#4111yescharacteristic
381C22×C11C2×H(5,𝔽2)11yescharacteristic
382C22×C11C2×2−1+411yescharacteristic
383C2×D11—22no—
384C2×D11—22no—
385C2×D11—22no—
386C2×D11—41no—
387C2×D11—41no—
388C2×D11—41no—
389C2×D11—41no—
390C4×C11—22no—
391C4×C11—24no—
392C4×C11—24no—
393C4×C11—42no—
394C4×C11—42no—
395C4×C11—44no—
396C4×C11#53314yes—
397C4×C11#53314yes—
398Dic11—22no—
399Dic11—22no—
400Dic11—24no—
401Dic11—24no—
402Dic11—44no—
403Dic11—42no—
404Dic11—42no—
405Dic11#54414yes—
406C22×Q8—114no—
407C23×C4—111no—
408C23×C4—111no—
409C23×C4—111no—
410C4⋊Q8—228no—
411C4⋊Q8—228no—
412#125—28no—
413#125—228no—
414C4×Q8—448no—
415#117—224no—
416#117—224no—
417#117—224no—
418#117—224no—
419#117—444no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—114no—
425C2×C4⋊C4—114no—
426C2×C4⋊C4—112no—
427C2×C4⋊C4—112no—
428C2×C4⋊C4—114no—
429C2×C4⋊C4—114no—
430C2×C4⋊C4—112no—
431C2×C4⋊C4—114no—
432C2×C4⋊C4—114no—
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C4⋊C4C22×D1112yes—
436C2×C4⋊C4C22×D1112yes—
437C2×C4⋊C4C22×D1114yes—
438C2×C4⋊C4C22×D1114yes—
439C2×C4⋊C4C22×D1112yes—
440C2×C4⋊C4C22×D1114yes—
441C2×C4⋊C4C22×D1111yescharacteristic
442C2×C4⋊C4C22×D1111yescharacteristic
443C2×C22⋊C4—112no—
444C2×C22⋊C4—112no—
445C2×C22⋊C4—112no—
446C2×C22⋊C4—112no—
447C2×C22⋊C4—114no—
448C2×C42—111no—
449C2×C42—111no—
450C2×C42—111no—
451C2×C42—118no—
452C2×C42—114no—
453C2×C42—112no—
454C2×C42—112no—
455C2×C42—112no—
456C2×C42—112no—
457C2×C42—112no—
458C2×C42—112no—
459C2×C42—112no—
460C2×C42—112no—
461C2×C42—112no—
462C2×C42—112no—
463C2×C42C22×D1112yes—
464C2×C42C22×D1112yes—
465C2×C42C22×D1111yescharacteristic
466#95—112no—
467#95—112no—
468#95—112no—
469#95—112no—
470#95—112no—
471#95—112no—
472#95—114no—
473#95—114no—
474#95—114no—
475#95—114no—
476#95—114no—
477#95—114no—
478#95—114no—
479#95C22×D1112yes—
480#95C22×D1112yes—
481#95C22×D1114yes—
482C2×C11C2×#53311yescharacteristic
483C2×C11C2×#53311yescharacteristic
484C2×C11C2×#54411yescharacteristic
485C2×C11#348111yescharacteristic
486C2×C11#348211yescharacteristic
487C2×C11#348211yescharacteristic
488C2×C11#348311yescharacteristic
489D11—42no—
490C24—111no—
491C2×Q8—228no—
492C2×Q8—228no—
493C2×Q8—444no—
494C22×C4—111no—
495C22×C4—111no—
496C22×C4—111no—
497C22×C4—112no—
498C22×C4—112no—
499C22×C4—114no—
500C22×C4—114no—
501C22×C4—114no—
502C22×C4—112no—
503C22×C4—114no—
504C22×C4—112no—
505C22×C4—222no—
506C22×C4—222no—
507C22×C4—222no—
508C22×C4—222no—
509C22×C4—222no—
510C22×C4—222no—
511C22×C4C23×D1112yes—
512C22×C4C23×D1112yes—
513C22×C4C23×D1114yes—
514C22×C4C23×D1112yes—
515C22×C4C23×D1111yescharacteristic
516C22×C4C23×D1112yes—
517C22×C4C23×D1111yescharacteristic
518C22×C4C23×D1111yescharacteristic
519C4⋊C4—28no—
520C4⋊C4—28no—
521C4⋊C4—24no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—24no—
525C4⋊C4—42no—
526C4⋊C4—44no—
527C4⋊C4—114no—
528C4⋊C4—114no—
529C4⋊C4—228no—
530C4⋊C4—228no—
531C4⋊C4—228no—
532C4⋊C4—222no—
533C4⋊C4—222no—
534C4⋊C4—228no—
535C4⋊C4—224no—
536C4⋊C4—224no—
537C4⋊C4—442no—
538C4⋊C4—444no—
539C4⋊C4—444no—
540C4⋊C4#434114yes—
541C4⋊C4#434314yes—
542C22⋊C4—224no—
543C22⋊C4—224no—
544C22⋊C4—224no—
545C22⋊C4—224no—
546C22⋊C4—444no—
547C42—24no—
548C42—24no—
549C42—114no—
550C42—114no—
551C42—114no—
552C42—224no—
553C42—224no—
554C42—228no—
555C42—224no—
556C42—224no—
557C42—224no—
558C42—224no—
559C42—224no—
560C42—224no—
561C42—224no—
562C42—224no—
563C42Q8×D1114yes—
564C11#3497811yescharacteristic, complemented, Sylow
565C23—112no—
566C23—221no—
567C23—221no—
568C23—221no—
569C23—221no—
570C23—221no—
571C23—221no—
572C23C24×D1111yescharacteristic
573Q8—4416no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—112no—
590C2×C4—112no—
591C2×C4—112no—
592C2×C4—112no—
593C2×C4—112no—
594C2×C4—114no—
595C2×C4—114no—
596C2×C4—228no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—228no—
606C2×C4—228no—
607C2×C4—222no—
608C2×C4—222no—
609C2×C4—224no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—224no—
613C2×C4—224no—
614C2×C4—222no—
615C2×C4—222no—
616C2×C4C2×#434114yes—
617C2×C4C2×#434112yes—
618C2×C4C2×Q8×D1112yes—
619C2×C4C2×Q8×D1112yes—
620C2×C4C2×Q8×D1112yes—
621C2×C4C2×#434314yes—
622C2×C4C2×#434312yes—
623C2×C4#41×D1112yes—
624C2×C4#41×D1112yes—
625C22—222no—
626C22—222no—
627C22—222no—
628C22—441no—
629C22—441no—
630C22—441no—
631C22—441no—
632C22C22×#434111yescharacteristic
633C22C22×Q8×D1111yescharacteristic
634C22C22×#434311yescharacteristic
635C22C2×#41×D1111yescharacteristic
636C22C2×#41×D1111yescharacteristic
637C22D11×H(5,𝔽2)11yescharacteristic
638C22D11×2−1+411yescharacteristic
639C4—24no—
640C4—24no—
641C4—22no—
642C4—42no—
643C4—42no—
644C4—44no—
645C4—114no—
646C4—222no—
647C4—222no—
648C4—224no—
649C4—224no—
650C4—444no—
651C4—442no—
652C4—442no—
653C4#1062321914yes—
654C4#1062325914yes—
655C2—442no—
656C2C2×#1062325911yescharacteristic
657C2C2×#1062321911yescharacteristic
658C2D11×#54411yescharacteristic
659C2#1308222711yescharacteristic
660C2#1308222811yescharacteristic
661C2#1308223611yescharacteristic
662C2#1308223911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2552C2
prime radicalC23×D11C24
hypercenter#2552D11
hypocenterC11#34978
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2552

Complements

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

NH ≅ G/Ntype
1. #13074320C2semidirect
2. #13073855C2semidirect
3. #13073652C2semidirect
4. #13073642C2semidirect
10. #13071187C2semidirect
11. #13071183C2semidirect
12. #125×Dic11C2semidirect
13. #13071175C2semidirect
17. C11×#2552C2semidirect
141. C42×D11Q8semidirect
237. #2552D11semidirect
564. C11#34978semidirect

Maximal subgroups

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

subgroupindex
#130743202
#130738552
#130736522
#130736422
#130723322
#130723252
#130723092
#130723052
#130718932
#130711872
#130711832
#125×Dic112
#130711752
#130710212
C4×#669452
C11×#25522
#3497811