Finite Group Databasebeta

← #14914010

Subgroups — #14914010

Order 2816.

2350 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
1C2×C4×Q8×D11C211yesmaximal, characteristic
2#13071572C212yesmaximal, complemented
3#13071570C214yesmaximal, complemented
4#13071530C212yesmaximal, complemented
5#13071484C212yesmaximal
6#13071482C214yesmaximal
7#13071450C212yesmaximal
8#13071267C211yesmaximal, characteristic, complemented
9#13071266C212yesmaximal, complemented
10#13071264C212yesmaximal, complemented
11#13071022C212yesmaximal
12#13071020C211yesmaximal, characteristic
13#13071013C212yesmaximal
14#13071008C211yesmaximal, characteristic
15#13070980C211yesmaximal, characteristic, complemented
16#13070979C211yesmaximal, characteristic, complemented
17C11×#2320C211yesmaximal, characteristic, complemented
18C22×Q8×D11C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C4×Q8×D11C4116yescomplemented
22C2×#66945C2214yes—
23C2×C4⋊C4×D11C2212yes—
24C2×C4⋊C4×D11C2211yescharacteristic
25C2×#66940C2212yes—
26C2×#66940C2211yescharacteristic
27C2×#66940C2212yes—
28C2×#66925C2212yes—
29C2×C42×D11C2211yescharacteristic
30C2×C42×D11C2212yes—
31C2×C4×Dic22C2212yes—
32C2×C4×Dic22C2211yescharacteristic
33C2×C4×Dic22C2212yes—
34C11×#391C2212yes—
35C11×#389C2212yes—
36C11×#387C2214yes—
37C11×#383C2212yes—
38C11×#382C2212yes—
39C4×C11×C4⋊C4C2211yescharacteristic
40C11×#376C2211yescharacteristic
41#10622843C2212yes—
42#10622600C2212yes—
43#10622598C2212yes—
44#10622594C2214yes—
45#10622591C2214yes—
46#10622589C2212yes—
47#10622589C2214yes—
48C4⋊C4×Dic11C2212yes—
49#10622585C2214yes—
50C4×(C2×D11)⋊C4C2212yes—
51#10622550C2212yes—
52#10622549C2212yes—
53C4×C4⋊Dic11C2212yes—
54C4×C4⋊Dic11C2211yescharacteristic
55#10622545C2211yescharacteristic
56C4×Dic11⋊C4C2214yes—
57C4×Dic11⋊C4C2212yes—
58C4×Dic11⋊C4C2212yes—
59#10622280C2214yes—
60#10622280C2211yescharacteristic
61#10622280C2211yescharacteristic
62#10622280C2212yes—
63#10622279C2214yes—
64#10622277C2212yes—
65#10622277C2214yes—
66#10622268C2214yes—
67#10622267C2214yes—
68#10622266C2214yes—
69#10622264C2211yescharacteristic
70#10622264C2211yescharacteristic
71#10622263C2212yes—
72#10622263C2212yes—
73#10622263C2214yes—
74#10622262C2214yes—
75#10622262C2212yes—
76#10622262C2212yes—
77#10622262C2214yes—
78#10622262C2214yes—
79#10622261C2212yes—
80#10622261C2212yes—
81#10622260C2214yes—
82#10622259C2214yes—
83#10622259C2214yes—
84C22×Q8×C11C2311yescharacteristic
85C2×Q8×D11—28no—
86C2×Q8×D11C2×C418yes—
87C22×C4×D11C2311yescharacteristic
88C22×C4×D11C2311yescharacteristic
89C22×C4×D11C2312yes—
90C22×C4×D11C2312yes—
91C22×C4×D11C2311yescharacteristic
92C22×Dic22C2312yes—
93C22×Dic22C2311yescharacteristic
94C4×Q8×C11C2×C418yes—
95C2×C11×C4⋊C4C2312yes—
96C2×C11×C4⋊C4C2314yes—
97C2×C11×C4⋊C4C2312yes—
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C42×C11C2312yes—
100C2×C42×C11C2312yes—
101C2×C42×C11C2311yescharacteristic
102C2×C42×C11C2312yes—
103Q8×Dic11C2×C418yes—
104C2×(C2×D11)⋊C4C2314yes—
105C2×(C2×D11)⋊C4C2312yes—
106C2×(C2×D11)⋊C4C2312yes—
107C2×C4⋊Dic11C2312yes—
108C2×C4⋊Dic11C2314yes—
109C2×C4⋊Dic11C2312yes—
110C2×C4⋊Dic11C2311yescharacteristic
111C2×Dic11⋊C4C2314yes—
112C2×Dic11⋊C4C2314yes—
113C2×Dic11⋊C4C2312yes—
114C2×Dic11⋊C4C2314yes—
115C2×Dic11⋊C4C2312yes—
116C2×Dic11⋊C4C2314yes—
117C2×Dic11⋊C4C2312yes—
118C2×Dic11⋊C4C2312yes—
119C2×Dic11⋊C4C2312yes—
120C2×C4×Dic11C2314yes—
121C2×C4×Dic11C2314yes—
122C2×C4×Dic11C2312yes—
123C2×C4×Dic11C2312yes—
124C2×C4×Dic11C2314yes—
125C2×C4×Dic11C2314yes—
126C2×C4×Dic11C2312yes—
127C2×C4×Dic11C2311yescharacteristic
128C2×C4×Dic11C2312yes—
129C2×C4×Dic11C2311yescharacteristic
130C2×C4×Dic11C2312yes—
131C2×C4×Dic11C2311yescharacteristic
132#66945—48no—
133C4⋊C4×D11C2×C4116yes—
134C4⋊C4×D11C2×C418yes—
135#66940—28no—
136#66940C2×C4116yes—
137#66940C2×C418yes—
138#66925—44no—
139C42×D11C2×C418yes—
140C42×D11C2×C4116yes—
141C4×Dic22—28no—
142C4×Dic22C2×C4116yes—
143C4×Dic22C2×C418yes—
144C11×#95C2314yes—
145C11×#95C2314yes—
146C11×#95C2314yes—
147C11×#95C2311yescharacteristic
148C11×#95C2312yes—
149C11×#95C2312yes—
150C11×#95C2311yescharacteristic
151C11⋊#95C2312yes—
152C11⋊#95C2312yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2312yes—
157C11⋊#95C2311yescharacteristic
158C11⋊#95C2314yes—
159C11⋊#95C2312yes—
160C11⋊#95C2314yes—
161C11⋊#95C2311yescharacteristic
162C11⋊#95C2314yes—
163C11⋊#95C2312yes—
164C11⋊#95C2312yes—
165#34196—111nomaximal, Sylow
166C23×D11C2411yescharacteristic
167C2×Q8×C11—24no—
168C2×Q8×C11C22×C414yes—
169C22×C4×C11C2412yes—
170C22×C4×C11C2414yes—
171C22×C4×C11C2412yes—
172C22×C4×C11C2411yescharacteristic
173C22×C4×C11C2412yes—
174C22×C4×C11C2411yescharacteristic
175C22×C4×C11C2412yes—
176C22×C4×C11C2411yescharacteristic
177C22×Dic11C2412yes—
178C22×Dic11C2412yes—
179C22×Dic11C2414yes—
180C22×Dic11C2411yescharacteristic
181C22×Dic11C2412yes—
182C22×Dic11C2411yescharacteristic
183C22×Dic11C2412yes—
184C22×Dic11C2411yescharacteristic
185Q8×D11—232no—
186C2×C4×D11—28no—
187C2×C4×D11—24no—
188C2×C4×D11—22no—
189C2×C4×D11—24no—
190C2×C4×D11—22no—
191C2×C4×D11—24no—
192C2×C4×D11—24no—
193C2×C4×D11C22×C414yes—
194C2×C4×D11C22×C414yes—
195C2×C4×D11C22×C418yes—
196C2×C4×D11C22×C418yes—
197C2×C4×D11C22×C414yes—
198C2×Dic22—28no—
199C2×Dic22C22×C418yes—
200C2×Dic22C22×C414yes—
201C2×Dic22#4118yes—
202C11×C4⋊C4—24no—
203C11×C4⋊C4—44no—
204C11×C4⋊C4C22×C418yes—
205C11×C4⋊C4C22×C414yes—
206C42×C11—24no—
207C42×C11—42no—
208C42×C11C22×C418yes—
209C42×C11C22×C414yes—
210(C2×D11)⋊C4—28no—
211(C2×D11)⋊C4—24no—
212(C2×D11)⋊C4—24no—
213C4⋊Dic11—24no—
214C4⋊Dic11—44no—
215C4⋊Dic11C22×C418yes—
216C4⋊Dic11C22×C414yes—
217Dic11⋊C4—28no—
218Dic11⋊C4—28no—
219Dic11⋊C4—24no—
220Dic11⋊C4—28no—
221Dic11⋊C4—24no—
222Dic11⋊C4—44no—
223Dic11⋊C4C22×C418yes—
224Dic11⋊C4C22×C418yes—
225Dic11⋊C4C22×C418yes—
226C4×Dic11—28no—
227C4×Dic11—28no—
228C4×Dic11—24no—
229C4×Dic11—42no—
230C4×Dic11—44no—
231C4×Dic11—44no—
232C4×Dic11C22×C414yes—
233C4×Dic11C22×C418yes—
234C4×Dic11C22×C414yes—
235C4×Dic11C22×C418yes—
236C4×Dic11C22×C418yes—
237C4×Dic11C22×C414yes—
238C22×C4×Q8—111no—
239#2355—112no—
240#2355—114no—
241Q8×C4⋊C4—112no—
242#2344—112no—
243#2344—114no—
244Q8×C22⋊C4—112no—
245#2320—112no—
246#2320—112no—
247#2320—111no—
248#2320D1111yescharacteristic, complemented
249#2285—112no—
250#2285—111no—
251#2283—112no—
252#2283—111no—
253#2276—111no—
254#2276—111no—
255C23×C11C2511yescharacteristic
256C22×D11—22no—
257C22×D11—22no—
258C22×D11C23×C412yes—
259C22×D11H(5,𝔽2)12yes—
260C22×D112−1+412yes—
261Q8×C11—28no—
262C2×C4×C11—24no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—21no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—24no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—24no—
273C2×C4×C11—24no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11C23×C412yes—
278C2×C4×C11C23×C412yes—
279C2×C4×C11C23×C414yes—
280C2×C4×C11C23×C414yes—
281C2×C4×C11C23×C412yes—
282C2×C4×C11C2×#4114yes—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—21no—
286C2×Dic11—22no—
287C2×Dic11—21no—
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—24no—
291C2×Dic11—24no—
292C2×Dic11—22no—
293C2×Dic11—22no—
294C2×Dic11—24no—
295C2×Dic11—22no—
296C2×Dic11—22no—
297C2×Dic11C23×C414yes—
298C2×Dic11C23×C412yes—
299C2×Dic11C23×C412yes—
300C2×Dic11C23×C414yes—
301C2×Dic11C23×C412yes—
302C2×Dic11C2×#4118yes—
303C2×Dic112−1+414yes—
304C4×D11—28no—
305C4×D11—216no—
306C4×D11—28no—
307C4×D11—216no—
308C4×D11—28no—
309Dic22—216no—
310Dic22#117116yescomplemented
311C23×Q8—111no—
312C2×C4×Q8—111no—
313C2×C4×Q8—1116no—
314C2×C4×Q8—111no—
315C2×C4×Q8—112no—
316C2×C4×Q8—112no—
317C2×C4×Q8—112no—
318C2×C4×Q8—111no—
319C2×C4×Q8—112no—
320C2×C4×Q8C2×D1111yescharacteristic
321C2×#117—114no—
322C2×#117—112no—
323C22×C4⋊C4—112no—
324C22×C4⋊C4—111no—
325C22×C42—112no—
326C22×C42—111no—
327#391—112no—
328#391—114no—
329#391—114no—
330#391C2×D1112yes—
331#389—114no—
332#389—112no—
333#389—114no—
334#389C2×D1112yes—
335#387—114no—
336#387—114no—
337#387—114no—
338#387—114no—
339#387—114no—
340#387C2×D1114yes—
341#384—114no—
342#384—112no—
343#383—112no—
344#383—111no—
345#383—111no—
346#383C2×D1112yes—
347#382—112no—
348#382—112no—
349#382—114no—
350#382—112no—
351#382C2×D1112yes—
352#381—114no—
353#381—112no—
354#380—112no—
355#380—114no—
356#380—111no—
357#380—112no—
358#380—111no—
359C4×C4⋊C4—112no—
360C4×C4⋊C4—111no—
361C4×C4⋊C4—114no—
362C4×C4⋊C4—112no—
363C4×C4⋊C4—112no—
364C4×C4⋊C4—112no—
365C4×C4⋊C4—112no—
366C4×C4⋊C4—112no—
367C4×C4⋊C4—114no—
368C4×C4⋊C4—114no—
369C4×C4⋊C4—114no—
370C4×C4⋊C4C2×D1111yescharacteristic
371C4×C22⋊C4—112no—
372C4×C22⋊C4—114no—
373#376—111no—
374#376—112no—
375#376—112no—
376#376C2×D1111yescharacteristic
377C22×C11C24×C411yescharacteristic
378C22×C11C22×#4112yes—
379C22×C11C2×H(5,𝔽2)11yescharacteristic
380C22×C11C2×2−1+412yes—
381C22×C11C2×2−1+411yescharacteristic
382C2×D11—22no—
383C2×D11—22no—
384C2×D11—24no—
385C2×D11—24no—
386C2×D11#52014yes—
387C4×C11—24no—
388C4×C11—22no—
389C4×C11—22no—
390C4×C11—24no—
391C4×C11—44no—
392C4×C11—42no—
393C4×C11—42no—
394C4×C11C2×#11714yes—
395Dic11—22no—
396Dic11—24no—
397Dic11—22no—
398Dic11—42no—
399Dic11—44no—
400Dic11—42no—
401Dic11C2×#11718yes—
402Dic11#51914yes—
403C22×Q8—118no—
404C22×Q8—111no—
405C22×Q8—112no—
406C22×Q8—228no—
407C22×Q8C22×D1111yescharacteristic
408C23×C4—112no—
409C23×C4—111no—
410C23×C4—112no—
411C23×C4—111no—
412C23×C4—111no—
413C4×Q8—118no—
414C4×Q8—118no—
415C4×Q8—1116no—
416C4×Q8—118no—
417C4×Q8—1116no—
418C4×Q8—228no—
419C4×Q8—228no—
420C4×Q8C4×D1118yes—
421#117—444no—
422#117—448no—
423C2×C4⋊C4—112no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—112no—
426C2×C4⋊C4—112no—
427C2×C4⋊C4—112no—
428C2×C4⋊C4—1116no—
429C2×C4⋊C4—118no—
430C2×C4⋊C4—114no—
431C2×C4⋊C4—114no—
432C2×C4⋊C4—112no—
433C2×C4⋊C4—112no—
434C2×C4⋊C4—112no—
435C2×C4⋊C4—114no—
436C2×C4⋊C4—114no—
437C2×C4⋊C4—114no—
438C2×C4⋊C4C22×D1112yes—
439C2×C4⋊C4C22×D1114yes—
440C2×C4⋊C4C22×D1112yes—
441C2×C4⋊C4C22×D1111yescharacteristic
442C2×C22⋊C4—112no—
443C2×C22⋊C4—114no—
444C2×C22⋊C4—112no—
445C2×C42—112no—
446C2×C42—111no—
447C2×C42—112no—
448C2×C42—112no—
449C2×C42—111no—
450C2×C42—111no—
451C2×C42—1116no—
452C2×C42—118no—
453C2×C42—114no—
454C2×C42—114no—
455C2×C42—112no—
456C2×C42—114no—
457C2×C42—114no—
458C2×C42—112no—
459C2×C42C22×D1112yes—
460C2×C42C22×D1112yes—
461C2×C42C22×D1111yescharacteristic
462C2×C42C22×D1112yes—
463#95—111no—
464#95—112no—
465#95—111no—
466#95—114no—
467#95—114no—
468#95—112no—
469#95—112no—
470#95—112no—
471#95—114no—
472#95—114no—
473#95—114no—
474#95—112no—
475#95—112no—
476#95—114no—
477#95C22×D1111yescharacteristic
478#95C22×D1112yes—
479#95C22×D1111yescharacteristic
480#95C22×D1112yes—
481#95C22×D1114yes—
482#95C22×D1114yes—
483#95C22×D1114yes—
484C2×C11C22×#11711yescharacteristic
485C2×C11C2×#51911yescharacteristic
486C2×C11C2×#52011yescharacteristic
487C2×C11#352212yes—
488C2×C11#352312yes—
489D11—24no—
490C24—111no—
491C2×Q8—24no—
492C2×Q8—114no—
493C2×Q8—118no—
494C2×Q8—118no—
495C2×Q8—228no—
496C2×Q8—2232no—
497C2×Q8C2×C4×D1114yes—
498C22×C4—111no—
499C22×C4—112no—
500C22×C4—111no—
501C22×C4—112no—
502C22×C4—111no—
503C22×C4—114no—
504C22×C4—118no—
505C22×C4—114no—
506C22×C4—118no—
507C22×C4—114no—
508C22×C4—112no—
509C22×C4—112no—
510C22×C4—114no—
511C22×C4—228no—
512C22×C4—224no—
513C22×C4—222no—
514C22×C4—224no—
515C22×C4—222no—
516C22×C4—224no—
517C22×C4—224no—
518C22×C4C23×D1112yes—
519C22×C4C23×D1112yes—
520C22×C4C23×D1114yes—
521C22×C4C23×D1111yescharacteristic
522C22×C4C23×D1112yes—
523C22×C4C23×D1111yescharacteristic
524C22×C4C23×D1112yes—
525C22×C4C23×D1111yescharacteristic
526C4⋊C4—24no—
527C4⋊C4—44no—
528C4⋊C4—118no—
529C4⋊C4—118no—
530C4⋊C4—118no—
531C4⋊C4—118no—
532C4⋊C4—114no—
533C4⋊C4—228no—
534C4⋊C4—228no—
535C4⋊C4—224no—
536C4⋊C4—224no—
537C4⋊C4—228no—
538C4⋊C4—224no—
539C4⋊C4—444no—
540C4⋊C4—444no—
541C4⋊C4C2×C4×D1118yes—
542C4⋊C4C2×C4×D1114yes—
543C22⋊C4—228no—
544C22⋊C4—224no—
545C22⋊C4—224no—
546C42—24no—
547C42—42no—
548C42—118no—
549C42—118no—
550C42—114no—
551C42—114no—
552C42—118no—
553C42—114no—
554C42—228no—
555C42—228no—
556C42—224no—
557C42—442no—
558C42—444no—
559C42—444no—
560C42C2×C4×D1118yes—
561C42C2×C4×D1114yes—
562C11#3419611yescharacteristic, complemented, Sylow
563C23—112no—
564C23—112no—
565C23—112no—
566C23—222no—
567C23—222no—
568C23C24×D1111yescharacteristic
569Q8—28no—
570Q8—1116no—
571Q8—2216no—
572C2×C4—24no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—112no—
588C2×C4—114no—
589C2×C4—118no—
590C2×C4—114no—
591C2×C4—114no—
592C2×C4—112no—
593C2×C4—112no—
594C2×C4—2216no—
595C2×C4—228no—
596C2×C4—228no—
597C2×C4—2216no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—221no—
601C2×C4—222no—
602C2×C4—221no—
603C2×C4—228no—
604C2×C4—222no—
605C2×C4—224no—
606C2×C4—222no—
607C2×C4—224no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—224no—
612C2×C4—222no—
613C2×C4C22×C4×D1112yes—
614C2×C4C22×C4×D1112yes—
615C2×C4C22×C4×D1114yes—
616C2×C4C22×C4×D1114yes—
617C2×C4C22×C4×D1112yes—
618C2×C4#41×D1114yes—
619C22—114no—
620C22—224no—
621C22—224no—
622C22—222no—
623C22—222no—
624C22C23×C4×D1111yescharacteristic
625C22C2×#41×D1112yes—
626C22D11×H(5,𝔽2)11yescharacteristic
627C22D11×2−1+412yes—
628C22D11×2−1+411yescharacteristic
629C4—24no—
630C4—22no—
631C4—22no—
632C4—24no—
633C4—42no—
634C4—44no—
635C4—42no—
636C4—118no—
637C4—114no—
638C4—222no—
639C4—224no—
640C4—222no—
641C4—444no—
642C4—442no—
643C4—442no—
644C4D11×#11714yes—
645C2—224no—
646C2C2×D11×#11711yescharacteristic
647C2D11×#51911yescharacteristic
648C2D11×#52011yescharacteristic
649C2#1308269712yes—
650C2#1308270812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2320C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2320D11
hypocenterC11#34196
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2320

Complements

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

NH ≅ G/Ntype
2. #13071572C2semidirect
3. #13071570C2semidirect
4. #13071530C2semidirect
8. #13071267C2semidirect
9. #13071266C2semidirect
10. #13071264C2semidirect
15. #13070980C2semidirect
16. #13070979C2semidirect
17. C11×#2320C2semidirect
21. C4×Q8×D11C4semidirect
248. #2320D11semidirect
310. Dic22#117semidirect
562. C11#34196semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D112
#130715722
#130715702
#130715302
#130714842
#130714822
#130714502
#130712672
#130712662
#130712642
#130710222
#130710202
#130710132
#130710082
#130709802
#130709792
C11×#23202
#3419611