Finite Group Databasebeta

← #14925799

Subgroups — #14925799

Order 2816.

1778 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073858C211yesmaximal, characteristic, complemented
2#13073855C211yesmaximal, characteristic, complemented
3#13073852C212yesmaximal, complemented
4#13073846C212yesmaximal, complemented
5#13073834C214yesmaximal
6#13073647C211yesmaximal, characteristic, complemented
7#13072338C212yesmaximal
8#13072336C212yesmaximal
9#13071920C214yesmaximal, complemented
10#125×Dic11C212yesmaximal, complemented
11#13071175C212yesmaximal, complemented
12#13071097C212yesmaximal
13#13071021C212yesmaximal
14#13071021C211yesmaximal, characteristic
15C4×#66945C211yesmaximal, characteristic
16C4×C4⋊C4×D11C211yesmaximal, characteristic
17C11×#2552C211yesmaximal, characteristic, complemented
18C2×C11×#125C2212yes—
19C2×#66945C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×#66945C2212yes—
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C4⋊C4×D11C2211yescharacteristic
24C2×#66943C2212yes—
25C2×C42×D11C2212yes—
26C2×C42×D11C2211yescharacteristic
27C11×#398C2214yes—
28C11×#389C2212yes—
29C11×#389C2212yes—
30C11×#384C2212yes—
31C11×#384C2211yescharacteristic
32C4×C11×C4⋊C4C2211yescharacteristic
33C4×C11×C4⋊C4C2211yescharacteristic
34#10622602C2214yes—
35#10622600C2212yes—
36#10622600C2214yes—
37#10622600C2214yes—
38#10622600C2212yes—
39#10622599C2214yes—
40#10622598C2212yes—
41#10622598C2212yes—
42#10622598C2212yes—
43#10622597C2214yes—
44#10622596C2214yes—
45#10622595C2214yes—
46#10622594C2214yes—
47#10622594C2214yes—
48#10622591C2214yes—
49#10622590C2212yes—
50#10622590C2212yes—
51#10622590C2212yes—
52#10622590C2212yes—
53C4⋊C4×Dic11C2212yes—
54C4⋊C4×Dic11C2214yes—
55C4⋊C4×Dic11C2214yes—
56C4⋊C4×Dic11C2214yes—
57C4⋊C4×Dic11C2211yescharacteristic
58C4⋊C4×Dic11C2212yes—
59C4⋊C4×Dic11C2211yescharacteristic
60C4⋊C4×Dic11C2211yescharacteristic
61C4⋊C4×Dic11C2211yescharacteristic
62#10622586C2212yes—
63C4×(C2×D11)⋊C4C2212yes—
64#10622549C2212yes—
65#10622548C2212yes—
66#10622548C2211yescharacteristic
67C4×C4⋊Dic11C2211yescharacteristic
68C4×C4⋊Dic11C2211yescharacteristic
69C4×Dic11⋊C4C2212yes—
70C42×Dic11C2212yes—
71#10622541C2212yes—
72#10622541C2212yes—
73#10622281C2214yes—
74#10622279C2212yes—
75D11×#95C2212yes—
76#10622274C2214yes—
77#10622273C2214yes—
78#10622272C2214yes—
79#10622266C2214yes—
80#10622262C2212yes—
81#10622262C2214yes—
82#10622261C2212yes—
83C22×C4×D11C2312yes—
84C22×C4×D11C2312yes—
85C22×C4×D11C2311yescharacteristic
86C22×C4×D11C2311yescharacteristic
87C22×C4×D11C2311yescharacteristic
88C11×#125—28no—
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C4⋊C4C2312yes—
93C2×C11×C4⋊C4C2314yes—
94C2×C11×C4⋊C4C2314yes—
95C2×C11×C4⋊C4C2314yes—
96C2×C11×C4⋊C4C2312yes—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C42×C11C2312yes—
100C2×C42×C11C2312yes—
101C2×C42×C11C2311yescharacteristic
102C2×(C2×D11)⋊C4C2312yes—
103C2×(C2×D11)⋊C4C2312yes—
104C2×(C2×D11)⋊C4C2314yes—
105C2×C4⋊Dic11C2314yes—
106C2×C4⋊Dic11C2312yes—
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4⋊Dic11C2312yes—
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2312yes—
113C2×C4⋊Dic11C2314yes—
114C2×C4⋊Dic11C2314yes—
115C2×Dic11⋊C4C2314yes—
116C2×Dic11⋊C4C2312yes—
117C2×Dic11⋊C4C2312yes—
118C2×Dic11⋊C4C2314yes—
119C2×C4×Dic11C2312yes—
120C2×C4×Dic11C2312yes—
121C2×C4×Dic11C2312yes—
122C2×C4×Dic11C2312yes—
123C2×C4×Dic11C2312yes—
124C2×C4×Dic11C2314yes—
125C2×C4×Dic11C2312yes—
126C2×C4×Dic11C2312yes—
127C2×C4×Dic11C2312yes—
128C2×C4×Dic11C2311yescharacteristic
129C2×C4×Dic11C2311yescharacteristic
130C2×C4×Dic11C2311yescharacteristic
131#66945—24no—
132#66945—24no—
133#66945—28no—
134C4⋊C4×D11—24no—
135C4⋊C4×D11—24no—
136#66943—28no—
137C42×D11—28no—
138C42×D11Q818yes—
139C11×#95C2312yes—
140C11×#95C2314yes—
141C11×#95C2312yes—
142C11⋊#95C2312yes—
143C11⋊#95C2312yes—
144C11⋊#95C2312yes—
145C11⋊#95C2312yes—
146C11⋊#95C2314yes—
147C11⋊#95C2312yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2312yes—
157#34948—111nomaximal, Sylow
158C23×D11C2411yescharacteristic
159C22×C4×C11C2412yes—
160C22×C4×C11C2414yes—
161C22×C4×C11C2412yes—
162C22×C4×C11C2411yescharacteristic
163C22×C4×C11C2412yes—
164C22×C4×C11C2412yes—
165C22×C4×C11C2411yescharacteristic
166C22×C4×C11C2411yescharacteristic
167C22×Dic11C2412yes—
168C22×Dic11C2412yes—
169C22×Dic11C2412yes—
170C22×Dic11C2412yes—
171C22×Dic11C2414yes—
172C22×Dic11C2411yescharacteristic
173C22×Dic11C2411yescharacteristic
174C22×Dic11C2411yescharacteristic
175C2×C4×D11—24no—
176C2×C4×D11—24no—
177C2×C4×D11—22no—
178C2×C4×D11—22no—
179C2×C4×D11—24no—
180C2×C4×D11—24no—
181C2×C4×D11—41no—
182C2×C4×D11—42no—
183C2×C4×D11—41no—
184C2×C4×D11—42no—
185C2×C4×D11C2×Q814yes—
186C2×C4×D11C2×Q814yes—
187C2×C4×D11C2×Q814yes—
188C2×C4×D11#4114yes—
189C2×C4×D11#4114yes—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—24no—
193C11×C4⋊C4—28no—
194C11×C4⋊C4—28no—
195C11×C4⋊C4—24no—
196C11×C4⋊C4—44no—
197C11×C4⋊C4—42no—
198C11×C4⋊C4#4114yes—
199C11×C4⋊C4#4114yes—
200C42×C11—24no—
201C42×C11—24no—
202C42×C11C2×Q814yes—
203(C2×D11)⋊C4—24no—
204(C2×D11)⋊C4—28no—
205(C2×D11)⋊C4—24no—
206C4⋊Dic11—28no—
207C4⋊Dic11—24no—
208C4⋊Dic11—22no—
209C4⋊Dic11—22no—
210C4⋊Dic11—22no—
211C4⋊Dic11—24no—
212C4⋊Dic11—22no—
213C4⋊Dic11—44no—
214C4⋊Dic11—42no—
215C4⋊Dic11—44no—
216Dic11⋊C4—28no—
217Dic11⋊C4—24no—
218Dic11⋊C4—24no—
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—42no—
228C4×Dic11—42no—
229C4×Dic11C2×Q814yes—
230C4×Dic11C2×Q814yes—
231C4×Dic11C2×Q814yes—
232#2571—111no—
233#2571—111no—
234#2570—112no—
235#2570—112no—
236#2569—114no—
237#2552—111no—
238#2552D1111yescharacteristic, complemented
239#2442—112no—
240#2442—112no—
241#2402—114no—
242C4×#125—112no—
243C4×#125—112no—
244#2296—112no—
245#2285—112no—
246#2285—111no—
247C4×#117—111no—
248C2×C4×C4⋊C4—111no—
249C23×C11C2511yescharacteristic
250C22×D11—21no—
251C22×D11—21no—
252C22×D11—21no—
253C22×D11—21no—
254C22×D11C22×Q812yes—
255C22×D11C2×#4112yes—
256C22×D11C2×#4112yes—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—24no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—24no—
269C2×C4×C11—22no—
270C2×C4×C11—22no—
271C2×C4×C11—24no—
272C2×C4×C11C22×Q812yes—
273C2×C4×C11C22×Q812yes—
274C2×C4×C11C22×Q812yes—
275C2×C4×C11C2×#4114yes—
276C2×C4×C11C2×#4112yes—
277C2×C4×C11C2×#4114yes—
278C2×C4×C11C2×#4112yes—
279C2×C4×C11C2×#4112yes—
280C2×C4×C11C2×#4112yes—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—22no—
291C2×Dic11—24no—
292C2×Dic11—24no—
293C2×Dic11—22no—
294C2×Dic11—22no—
295C2×Dic11—22no—
296C2×Dic11—22no—
297C2×Dic11—22no—
298C2×Dic11—24no—
299C2×Dic11—22no—
300C2×Dic11C22×Q812yes—
301C2×Dic11C22×Q812yes—
302C2×Dic11C22×Q812yes—
303C2×Dic11C2×#4112yes—
304C2×Dic11C2×#4112yes—
305C4×D11—28no—
306C4×D11—44no—
307C4×D11—48no—
308C4×D11—48no—
309C4×D11#125116yescomplemented
310C2×#125—112no—
311C2×#125C2×D1112yes—
312C2×#117—111no—
313C2×#117—111no—
314C2×#117—112no—
315C22×C4⋊C4—111no—
316C22×C4⋊C4—111no—
317C22×C42—111no—
318C22×C42—112no—
319#400—114no—
320#400—114no—
321#400—114no—
322#400—114no—
323#398—114no—
324#398—114no—
325#398—114no—
326#398C2×D1114yes—
327#389—112no—
328#389—112no—
329#389—112no—
330#389—112no—
331#389—112no—
332#389—112no—
333#389C2×D1112yes—
334#389C2×D1112yes—
335#387—114no—
336#387—114no—
337#387—114no—
338#387—114no—
339#385—114no—
340#385—114no—
341#384—112no—
342#384—111no—
343#384C2×D1112yes—
344#384C2×D1111yescharacteristic
345#382—112no—
346#382—112no—
347#382—112no—
348#382—112no—
349#382—112no—
350#380—112no—
351#380—114no—
352#380—114no—
353#380—112no—
354C4×C4⋊C4—111no—
355C4×C4⋊C4—111no—
356C4×C4⋊C4—112no—
357C4×C4⋊C4—114no—
358C4×C4⋊C4—114no—
359C4×C4⋊C4—114no—
360C4×C4⋊C4—111no—
361C4×C4⋊C4—111no—
362C4×C4⋊C4—112no—
363C4×C4⋊C4—112no—
364C4×C4⋊C4—111no—
365C4×C4⋊C4—111no—
366C4×C4⋊C4—114no—
367C4×C4⋊C4—112no—
368C4×C4⋊C4C2×D1111yescharacteristic
369C4×C4⋊C4C2×D1111yescharacteristic
370C4×C22⋊C4—112no—
371C4×C22⋊C4—112no—
372#376—112no—
373C2×#95—112no—
374C43—112no—
375C22×C11C23×Q811yescharacteristic
376C22×C11C22×#4111yescharacteristic
377C22×C11C22×#4111yescharacteristic
378C22×C11C22×#4111yescharacteristic
379C22×C11C22×#4111yescharacteristic
380C22×C11#58511yescharacteristic
381C22×C11#58511yescharacteristic
382C2×D11—22no—
383C2×D11—22no—
384C2×D11—22no—
385C2×D11—22no—
386C2×D11—22no—
387C2×D11—22no—
388C2×D11C2×#12514yes—
389C4×C11—22no—
390C4×C11—24no—
391C4×C11—24no—
392C4×C11—42no—
393C4×C11—42no—
394C4×C11—44no—
395C4×C11C2×#12514yes—
396C4×C11#53314yes—
397Dic11—22no—
398Dic11—22no—
399Dic11—42no—
400Dic11—42no—
401Dic11—42no—
402Dic11—42no—
403Dic11—44no—
404Dic11C2×#12514yes—
405C23×C4—111no—
406C23×C4—111no—
407C23×C4—111no—
408C23×C4—112no—
409C23×C4—112no—
410#125—28no—
411#125—228no—
412#117—224no—
413#117—224no—
414#117—228no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—112no—
418C2×C4⋊C4—112no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—112no—
422C2×C4⋊C4—112no—
423C2×C4⋊C4—114no—
424C2×C4⋊C4—114no—
425C2×C4⋊C4—114no—
426C2×C4⋊C4—112no—
427C2×C4⋊C4—114no—
428C2×C4⋊C4—114no—
429C2×C4⋊C4—224no—
430C2×C4⋊C4—224no—
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C4⋊C4C22×D1112yes—
434C2×C4⋊C4C22×D1112yes—
435C2×C4⋊C4C22×D1114yes—
436C2×C4⋊C4C22×D1114yes—
437C2×C4⋊C4C22×D1114yes—
438C2×C4⋊C4C22×D1112yes—
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C22⋊C4—112no—
442C2×C22⋊C4—112no—
443C2×C22⋊C4—114no—
444C2×C42—111no—
445C2×C42—111no—
446C2×C42—111no—
447C2×C42—118no—
448C2×C42—112no—
449C2×C42—112no—
450C2×C42—114no—
451C2×C42—112no—
452C2×C42—112no—
453C2×C42—112no—
454C2×C42—112no—
455C2×C42—112no—
456C2×C42—112no—
457C2×C42—228no—
458C2×C42C22×D1112yes—
459C2×C42C22×D1112yes—
460C2×C42C22×D1111yescharacteristic
461#95—112no—
462#95—112no—
463#95—112no—
464#95—112no—
465#95—112no—
466#95—112no—
467#95—114no—
468#95—114no—
469#95—114no—
470#95—114no—
471#95—114no—
472#95—114no—
473#95—114no—
474#95—114no—
475#95—114no—
476#95C22×D1112yes—
477#95C22×D1112yes—
478#95C22×D1114yes—
479C2×C11C22×#12511yescharacteristic
480C2×C11C2×#53311yescharacteristic
481C2×C11#345811yescharacteristic
482C2×C11#347511yescharacteristic
483C2×C11#347511yescharacteristic
484C2×C11#348011yescharacteristic
485C2×C11#348011yescharacteristic
486D11—24no—
487C24—111no—
488C22×C4—111no—
489C22×C4—114no—
490C22×C4—114no—
491C22×C4—114no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—114no—
495C22×C4—114no—
496C22×C4—112no—
497C22×C4—112no—
498C22×C4—112no—
499C22×C4—112no—
500C22×C4—114no—
501C22×C4—224no—
502C22×C4—224no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—224no—
506C22×C4—224no—
507C22×C4—441no—
508C22×C4—442no—
509C22×C4—441no—
510C22×C4—442no—
511C22×C4C23×D1112yes—
512C22×C4C23×D1114yes—
513C22×C4C23×D1112yes—
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—44no—
526C4⋊C4—42no—
527C4⋊C4—224no—
528C4⋊C4—222no—
529C4⋊C4—224no—
530C4⋊C4—222no—
531C4⋊C4—228no—
532C4⋊C4—228no—
533C4⋊C4—224no—
534C4⋊C4—222no—
535C4⋊C4—222no—
536C4⋊C4—224no—
537C4⋊C4—444no—
538C4⋊C4—444no—
539C4⋊C4—442no—
540C4⋊C4—444no—
541C4⋊C4#434114yes—
542C4⋊C4#434314yes—
543C22⋊C4—224no—
544C22⋊C4—228no—
545C22⋊C4—224no—
546C42—24no—
547C42—24no—
548C42—114no—
549C42—114no—
550C42—114no—
551C42—224no—
552C42—224no—
553C42—224no—
554C42—224no—
555C42—228no—
556C42—224no—
557C42—224no—
558C42—442no—
559C42—442no—
560C42Q8×D1114yes—
561C11#3494811yescharacteristic, complemented, Sylow
562C23—112no—
563C23—112no—
564C23—112no—
565C23—221no—
566C23—221no—
567C23—221no—
568C23—221no—
569C23C24×D1111yescharacteristic
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—22no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—112no—
586C2×C4—112no—
587C2×C4—112no—
588C2×C4—1116no—
589C2×C4—112no—
590C2×C4—112no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—228no—
596C2×C4—222no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—224no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—224no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—222no—
609C2×C4—224no—
610C2×C4—222no—
611C2×C4—444no—
612C2×C4—448no—
613C2×C4—448no—
614C2×C4C2×#434114yes—
615C2×C4C2×#434112yes—
616C2×C4C2×Q8×D1112yes—
617C2×C4C2×Q8×D1112yes—
618C2×C4C2×Q8×D1112yes—
619C2×C4C2×#434314yes—
620C2×C4C2×#434312yes—
621C2×C4#41×D1112yes—
622C2×C4#41×D1112yes—
623C22—114no—
624C22—222no—
625C22—222no—
626C22—222no—
627C22—222no—
628C22—222no—
629C22—222no—
630C22C22×#434111yescharacteristic
631C22C22×Q8×D1111yescharacteristic
632C22C22×#434311yescharacteristic
633C22C2×#41×D1111yescharacteristic
634C22C2×#41×D1111yescharacteristic
635C22#1062345511yescharacteristic
636C22#1062345711yescharacteristic
637C4—24no—
638C4—24no—
639C4—22no—
640C4—42no—
641C4—42no—
642C4—44no—
643C4—114no—
644C4—222no—
645C4—222no—
646C4—442no—
647C4—442no—
648C4—442no—
649C4—442no—
650C4—444no—
651C4D11×#12514yes—
652C4#1062325914yes—
653C2—224no—
654C2C2×D11×#12511yescharacteristic
655C2C2×#1062325911yescharacteristic
656C2#1308202011yescharacteristic
657C2#1308217911yescharacteristic
658C2#1308218211yescharacteristic
659C2#1308221511yescharacteristic
660C2#1308221611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2552C2
prime radicalC23×D11C24
hypercenter#2552D11
hypocenterC11#34948
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2552

Complements

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

NH ≅ G/Ntype
1. #13073858C2semidirect
2. #13073855C2semidirect
3. #13073852C2semidirect
4. #13073846C2semidirect
6. #13073647C2semidirect
9. #13071920C2semidirect
10. #125×Dic11C2semidirect
11. #13071175C2semidirect
17. C11×#2552C2semidirect
238. #2552D11semidirect
309. C4×D11#125semidirect
561. C11#34948semidirect

Maximal subgroups

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

subgroupindex
#130738582
#130738552
#130738522
#130738462
#130738342
#130736472
#130723382
#130723362
#130719202
#125×Dic112
#130711752
#130710972
#130710212
C4×#669452
C4×C4⋊C4×D112
C11×#25522
#3494811