Finite Group Databasebeta

← #14914404

Subgroups — #14914404

Order 2816.

2186 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623111C211yesmaximal, characteristic
2#13071748C214yesmaximal, complemented
3#13071729C214yesmaximal, complemented
4#13071591C212yesmaximal, complemented
5#13071549C212yesmaximal, complemented
6#13071504C212yesmaximal, complemented
7#13071469C212yesmaximal, complemented
8#13071307C212yesmaximal
9#13071301C212yesmaximal, complemented
10#13071260C211yesmaximal, characteristic, complemented
11#13071175C212yesmaximal, complemented
12#13071159C212yesmaximal, complemented
13#13071012C211yesmaximal, characteristic, complemented
14#13070981C211yesmaximal, characteristic, complemented
15#13070976C211yesmaximal, characteristic, complemented
16#13070955C211yesmaximal, characteristic, complemented
17C11×#2320C211yesmaximal, characteristic, complemented
18C2×C4×Q8×C11C2211yescharacteristic
19C2×#67000C2211yescharacteristic
20C2×#66999C2211yescharacteristic
21C2×Q8×Dic11C2212yes—
22#10623111C4116yescomplemented
23C2×#66951C2212yes—
24C2×#66948C2211yescharacteristic
25C2×#66947C2212yes—
26C2×#66946C2212yes—
27C2×#66943C2211yescharacteristic
28C2×C4×D44C2211yescharacteristic
29C2×C4×D44C2212yes—
30C2×#66925C2212yes—
31C2×#66925C2212yes—
32C2×C42×D11C2211yescharacteristic
33C11×#391C2212yes—
34C11×#389C2212yes—
35C11×#387C2214yes—
36C11×#383C2212yes—
37C11×#382C2212yes—
38C4×C11×C4⋊C4C2211yescharacteristic
39C11×#376C2211yescharacteristic
40#10622602C2214yes—
41#10622601C2214yes—
42#10622600C2212yes—
43#10622591C2214yes—
44#10622590C2212yes—
45C4⋊C4×Dic11C2214yes—
46C4⋊C4×Dic11C2212yes—
47C4⋊C4×Dic11C2212yes—
48C4⋊C4×Dic11C2214yes—
49#10622552C2212yes—
50C4×(C2×D11)⋊C4C2214yes—
51C4×(C2×D11)⋊C4C2212yes—
52C4×C4⋊Dic11C2212yes—
53C4×C4⋊Dic11C2211yescharacteristic
54#10622545C2211yescharacteristic
55#10622545C2212yes—
56#10622545C2212yes—
57C42×Dic11C2212yes—
58#10622541C2212yes—
59#10622283C2214yes—
60#10622283C2214yes—
61#10622283C2214yes—
62#10622282C2214yes—
63#10622282C2214yes—
64#10622282C2214yes—
65#10622280C2212yes—
66#10622279C2214yes—
67#10622279C2214yes—
68#10622279C2212yes—
69#10622279C2211yescharacteristic
70#10622279C2211yescharacteristic
71#10622279C2212yes—
72#10622278C2214yes—
73#10622277C2212yes—
74#10622277C2212yes—
75D11×#95C2212yes—
76#10622266C2214yes—
77#10622265C2214yes—
78#10622264C2212yes—
79#10622262C2214yes—
80#10622262C2211yescharacteristic
81#10622262C2212yes—
82#10622262C2211yescharacteristic
83#10622260C2214yes—
84C22×Q8×C11C2311yescharacteristic
85C22×D44C2311yescharacteristic
86C22×D44C2312yes—
87C22×C4×D11C2311yescharacteristic
88C22×C4×D11C2314yes—
89C22×C4×D11C2311yescharacteristic
90C22×C4×D11C2311yescharacteristic
91C22×C4×D11C2312yes—
92C4×Q8×C11C2×C418yescomplemented
93C2×C11×C4⋊C4C2312yes—
94C2×C11×C4⋊C4C2314yes—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2312yes—
97C2×C42×C11C2312yes—
98C2×C42×C11C2312yes—
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2312yes—
101#67000C2×C418yes—
102#66999C2×C418yescomplemented
103Q8×Dic11—28no—
104C2×(C2×D11)⋊C4C2312yes—
105C2×(C2×D11)⋊C4C2312yes—
106C2×(C2×D11)⋊C4C2314yes—
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—
114C2×(C2×D11)⋊C4C2312yes—
115C2×C4⋊Dic11C2314yes—
116C2×C4⋊Dic11C2312yes—
117C2×C4⋊Dic11C2312yes—
118C2×C4⋊Dic11C2311yescharacteristic
119C2×Dic11⋊C4C2312yes—
120C2×Dic11⋊C4C2312yes—
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2312yes—
123C2×Dic11⋊C4C2312yes—
124C2×C4×Dic11C2314yes—
125C2×C4×Dic11C2314yes—
126C2×C4×Dic11C2312yes—
127C2×C4×Dic11C2312yes—
128C2×C4×Dic11C2312yes—
129C2×C4×Dic11C2312yes—
130C2×C4×Dic11C2314yes—
131C2×C4×Dic11C2312yes—
132C2×C4×Dic11C2311yescharacteristic
133C2×C4×Dic11C2311yescharacteristic
134C2×C4×Dic11C2311yescharacteristic
135C2×C4×Dic11C2312yes—
136#66951C2×C4116yescomplemented
137#66948C2×C418yes—
138#66947C2×C4116yescomplemented
139#66946—28no—
140#66943C2×C418yescomplemented
141C4×D44C2×C418yes—
142C4×D44C2×C4116yescomplemented
143#66925—28no—
144#66925C2×C4116yescomplemented
145C42×D11C2×C418yescomplemented
146C11×#95C2314yes—
147C11×#95C2314yes—
148C11×#95C2311yescharacteristic
149C11×#95C2311yescharacteristic
150C11×#95C2312yes—
151C11×#95C2312yes—
152C11×#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2311yescharacteristic
156C11⋊#95C2311yescharacteristic
157C11⋊#95C2312yes—
158C11⋊#95C2312yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163#34227—111nomaximal, Sylow
164C23×D11C2411yescharacteristic
165C23×D11C2412yes—
166C2×Q8×C11—24no—
167C2×Q8×C11C22×C414yes—
168C22×C4×C11C2414yes—
169C22×C4×C11C2412yes—
170C22×C4×C11C2412yes—
171C22×C4×C11C2411yescharacteristic
172C22×C4×C11C2411yescharacteristic
173C22×C4×C11C2412yes—
174C22×C4×C11C2412yes—
175C22×C4×C11C2411yescharacteristic
176C22×Dic11C2414yes—
177C22×Dic11C2411yescharacteristic
178C22×Dic11C2411yescharacteristic
179C22×Dic11C2411yescharacteristic
180C22×Dic11C2412yes—
181C22×Dic11C2412yes—
182C22×Dic11C2412yes—
183C2×D44—24no—
184C2×D44—42no—
185C2×D44—42no—
186C2×D44C22×C414yes—
187C2×D44C22×C418yes—
188C2×C4×D11—28no—
189C2×C4×D11—24no—
190C2×C4×D11—41no—
191C2×C4×D11—41no—
192C2×C4×D11—42no—
193C2×C4×D11—44no—
194C2×C4×D11—44no—
195C2×C4×D11—44no—
196C2×C4×D11C22×C414yes—
197C2×C4×D11C22×C414yes—
198C2×C4×D11C22×C414yes—
199C2×C4×D11C22×C418yes—
200C11×C4⋊C4—24no—
201C11×C4⋊C4—44no—
202C11×C4⋊C4C22×C414yes—
203C11×C4⋊C4C22×C418yes—
204C42×C11—24no—
205C42×C11—42no—
206C42×C11C22×C414yes—
207C42×C11C22×C418yes—
208(C2×D11)⋊C4—24no—
209(C2×D11)⋊C4—24no—
210(C2×D11)⋊C4—28no—
211(C2×D11)⋊C4—44no—
212(C2×D11)⋊C4—44no—
213(C2×D11)⋊C4—44no—
214(C2×D11)⋊C4C22×C418yes—
215(C2×D11)⋊C4C22×C418yes—
216(C2×D11)⋊C4C22×C418yes—
217(C2×D11)⋊C4C22×C418yes—
218(C2×D11)⋊C4C22×C418yes—
219C4⋊Dic11—28no—
220C4⋊Dic11—24no—
221C4⋊Dic11C22×C414yes—
222C4⋊Dic11C22×C418yes—
223Dic11⋊C4—24no—
224Dic11⋊C4—24no—
225Dic11⋊C4—44no—
226Dic11⋊C4C22×C418yes—
227Dic11⋊C4C22×C418yes—
228C4×Dic11—28no—
229C4×Dic11—42no—
230C4×Dic11—44no—
231C4×Dic11—42no—
232C4×Dic11—42no—
233C4×Dic11—42no—
234C4×Dic11—44no—
235C4×Dic11—42no—
236C4×Dic11C22×C414yes—
237C4×Dic11C22×C414yes—
238C4×Dic11C22×C414yes—
239C4×Dic11#4118yes—
240C2×#529—111no—
241#2374—114no—
242#2373—114no—
243#2357—112no—
244#2353—112no—
245#2347—112no—
246#2343—112no—
247#2324—112no—
248#2323—112no—
249#2320D1111yescharacteristic, complemented
250#2319—111no—
251C4×#125—112no—
252C4×#124—112no—
253#2283—111no—
254#2276—111no—
255#2275—111no—
256C4×#117—111no—
257C23×C11C2511yescharacteristic
258C22×D11—22no—
259C22×D11—24no—
260C22×D11—22no—
261C22×D11—22no—
262C22×D11—24no—
263C22×D11—22no—
264C22×D11—21no—
265C22×D11—21no—
266C22×D11C23×C414yes—
267C22×D11C23×C412yes—
268Q8×C11—28no—
269C2×C4×C11—24no—
270C2×C4×C11—21no—
271C2×C4×C11—22no—
272C2×C4×C11—21no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—24no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—24no—
282C2×C4×C11—22no—
283C2×C4×C11—24no—
284C2×C4×C11C23×C412yes—
285C2×C4×C11C23×C412yes—
286C2×C4×C11C23×C414yes—
287C2×C4×C11C23×C414yes—
288C2×C4×C11C23×C412yes—
289C2×C4×C11C2×#4114yes—
290C2×Dic11—22no—
291C2×Dic11—22no—
292C2×Dic11—22no—
293C2×Dic11—21no—
294C2×Dic11—22no—
295C2×Dic11—21no—
296C2×Dic11—24no—
297C2×Dic11—22no—
298C2×Dic11—22no—
299C2×Dic11—24no—
300C2×Dic11—24no—
301C2×Dic11—24no—
302C2×Dic11C23×C412yes—
303C2×Dic11C23×C412yes—
304C2×Dic11C23×C412yes—
305C2×Dic11C23×C414yes—
306C2×Dic11C2×#4114yes—
307C2×Dic11C2×#4114yes—
308D44—28no—
309D44—48no—
310C4×D11—28no—
311C4×D11—44no—
312C4×D11—44no—
313C4×D11—48no—
314C4×D11—88no—
315#529—1116no—
316C2×#126—112no—
317C2×#125—111no—
318C2×#124—111no—
319C2×#123—112no—
320C2×C22⋊Q8—111no—
321C2×#121—111no—
322C2×C4×Q8—112no—
323C2×C4×Q8C2×D1111yescharacteristic
324C2×C4×D4—112no—
325C2×C4×D4—111no—
326C2×C4×D4—112no—
327C2×#117—112no—
328C2×#117—112no—
329C22×C42—111no—
330#391C2×D1112yes—
331#390—114no—
332#390—112no—
333#389—112no—
334#389—114no—
335#389C2×D1112yes—
336#388—114no—
337#388—114no—
338#388—114no—
339#388—114no—
340#388—114no—
341#388—114no—
342#387—114no—
343#387—114no—
344#387—114no—
345#387C2×D1114yes—
346#386—114no—
347#385—114no—
348#383—112no—
349#383C2×D1112yes—
350#382—112no—
351#382C2×D1112yes—
352#381—112no—
353#381—112no—
354#380—112no—
355#380—112no—
356C4×C4⋊C4—112no—
357C4×C4⋊C4—112no—
358C4×C4⋊C4—114no—
359C4×C4⋊C4—114no—
360C4×C4⋊C4—111no—
361C4×C4⋊C4—112no—
362C4×C4⋊C4—114no—
363C4×C4⋊C4—111no—
364C4×C4⋊C4—111no—
365C4×C4⋊C4—112no—
366C4×C4⋊C4C2×D1111yescharacteristic
367C4×C22⋊C4—114no—
368C4×C22⋊C4—112no—
369C4×C22⋊C4—114no—
370C4×C22⋊C4—112no—
371C4×C22⋊C4—111no—
372C4×C22⋊C4—114no—
373C4×C22⋊C4—111no—
374C4×C22⋊C4—112no—
375#376—112no—
376#376—112no—
377#376—111no—
378#376C2×D1111yescharacteristic
379C2×#95—112no—
380C43—112no—
381C22×C11C24×C411yescharacteristic
382C22×C11C22×#4112yes—
383C22×C11#58511yescharacteristic
384C22×C11#58512yes—
385C22×C11#58511yescharacteristic
386C2×D11—22no—
387C2×D11—24no—
388C2×D11—22no—
389C2×D11—24no—
390C2×D11—22no—
391C2×D11—24no—
392C2×D11—42no—
393C2×D11—44no—
394C2×D11—42no—
395C2×D11—44no—
396C4×C11—24no—
397C4×C11—22no—
398C4×C11—22no—
399C4×C11—24no—
400C4×C11—42no—
401C4×C11—44no—
402C4×C11—42no—
403C4×C11C4×#4114yes—
404Dic11—22no—
405Dic11—22no—
406Dic11—22no—
407Dic11—24no—
408Dic11—24no—
409Dic11—24no—
410Dic11—44no—
411C22×Q8C22×D1111yescharacteristic
412C22×D4—111no—
413C22×D4—112no—
414C23×C4—111no—
415C23×C4—112no—
416C23×C4—111no—
417C23×C4—111no—
418C23×C4—114no—
419#126—1116no—
420#125—118no—
421#124—118no—
422#123—1116no—
423C22⋊Q8—118no—
424#121—118no—
425C4×Q8—228no—
426C4×Q8C4×D1118yescomplemented
427C4×D4—118no—
428C4×D4—1116no—
429C4×D4—228no—
430#117—1116no—
431#117—228no—
432C2×C4⋊C4—112no—
433C2×C4⋊C4—112no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—112no—
436C2×C4⋊C4—112no—
437C2×C4⋊C4—112no—
438C2×C4⋊C4—112no—
439C2×C4⋊C4—114no—
440C2×C4⋊C4—114no—
441C2×C4⋊C4C22×D1112yes—
442C2×C4⋊C4C22×D1114yes—
443C2×C4⋊C4C22×D1111yescharacteristic
444C2×C4⋊C4C22×D1112yes—
445C2×C22⋊C4—112no—
446C2×C22⋊C4—112no—
447C2×C22⋊C4—112no—
448C2×C22⋊C4—112no—
449C2×C22⋊C4—112no—
450C2×C22⋊C4—112no—
451C2×C22⋊C4—112no—
452C2×C22⋊C4—114no—
453C2×C22⋊C4—114no—
454C2×C22⋊C4—114no—
455C2×C22⋊C4—114no—
456C2×C42—111no—
457C2×C42—112no—
458C2×C42—111no—
459C2×C42—111no—
460C2×C42—118no—
461C2×C42—114no—
462C2×C42—112no—
463C2×C42—112no—
464C2×C42—112no—
465C2×C42—112no—
466C2×C42—112no—
467C2×C42—114no—
468C2×C42—114no—
469C2×C42C22×D1112yes—
470C2×C42C22×D1112yes—
471C2×C42C22×D1112yes—
472C2×C42C22×D1111yescharacteristic
473#95—111no—
474#95—114no—
475#95—112no—
476#95—111no—
477#95—114no—
478#95—112no—
479#95—114no—
480#95—114no—
481#95—114no—
482#95—114no—
483#95C22×D1112yes—
484#95C22×D1111yescharacteristic
485#95C22×D1111yescharacteristic
486#95C22×D1112yes—
487#95C22×D1114yes—
488#95C22×D1114yes—
489#95C22×D1114yes—
490C2×C11C2×C4×#4111yescharacteristic
491C2×C11#342811yescharacteristic
492C2×C11#342811yescharacteristic
493C2×C11#351012yes—
494C2×C11#351212yes—
495D11—42no—
496D11—44no—
497C24—112no—
498C24—111no—
499C2×Q8—24no—
500C2×Q8C2×C4×D1114yes—
501C2×D4—114no—
502C2×D4—118no—
503C2×D4—224no—
504C2×D4—442no—
505C2×D4—442no—
506C22×C4—112no—
507C22×C4—111no—
508C22×C4—111no—
509C22×C4—111no—
510C22×C4—112no—
511C22×C4—112no—
512C22×C4—114no—
513C22×C4—114no—
514C22×C4—114no—
515C22×C4—118no—
516C22×C4—114no—
517C22×C4—228no—
518C22×C4—224no—
519C22×C4—441no—
520C22×C4—441no—
521C22×C4—442no—
522C22×C4—444no—
523C22×C4—444no—
524C22×C4—444no—
525C22×C4C23×D1114yes—
526C22×C4C23×D1112yes—
527C22×C4C23×D1112yes—
528C22×C4C23×D1111yescharacteristic
529C22×C4C23×D1111yescharacteristic
530C22×C4C23×D1112yes—
531C22×C4C23×D1112yes—
532C22×C4C23×D1111yescharacteristic
533C4⋊C4—24no—
534C4⋊C4—44no—
535C4⋊C4—118no—
536C4⋊C4—118no—
537C4⋊C4—114no—
538C4⋊C4—118no—
539C4⋊C4—224no—
540C4⋊C4—224no—
541C4⋊C4—228no—
542C4⋊C4—224no—
543C4⋊C4—444no—
544C4⋊C4C2×C4×D1114yes—
545C4⋊C4C2×C4×D1118yes—
546C22⋊C4—118no—
547C22⋊C4—118no—
548C22⋊C4—118no—
549C22⋊C4—118no—
550C22⋊C4—118no—
551C22⋊C4—224no—
552C22⋊C4—224no—
553C22⋊C4—228no—
554C22⋊C4—444no—
555C22⋊C4—444no—
556C22⋊C4—444no—
557C42—24no—
558C42—42no—
559C42—114no—
560C42—114no—
561C42—114no—
562C42—118no—
563C42—228no—
564C42—442no—
565C42—444no—
566C42—442no—
567C42—442no—
568C42—442no—
569C42—444no—
570C42—442no—
571C42C2×C4×D1114yes—
572C42C2×C4×D1118yes—
573C11#3422711yescharacteristic, complemented, Sylow
574C23—114no—
575C23—112no—
576C23—222no—
577C23—224no—
578C23—222no—
579C23—221no—
580C23—222no—
581C23—222no—
582C23—224no—
583C23—221no—
584C23C24×D1111yescharacteristic
585Q8—28no—
586D4—228no—
587D4—448no—
588C2×C4—24no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—24no—
602C2×C4—22no—
603C2×C4—112no—
604C2×C4—112no—
605C2×C4—112no—
606C2×C4—114no—
607C2×C4—114no—
608C2×C4—114no—
609C2×C4—222no—
610C2×C4—221no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—221no—
615C2×C4—222no—
616C2×C4—224no—
617C2×C4—222no—
618C2×C4—228no—
619C2×C4—224no—
620C2×C4—224no—
621C2×C4—224no—
622C2×C4—444no—
623C2×C4—444no—
624C2×C4—448no—
625C2×C4—888no—
626C2×C4C22×C4×D1112yes—
627C2×C4C22×C4×D1112yes—
628C2×C4C22×C4×D1114yes—
629C2×C4C22×C4×D1114yes—
630C2×C4C22×C4×D1112yes—
631C2×C4#41×D1114yes—
632C22—222no—
633C22—224no—
634C22—222no—
635C22—224no—
636C22—224no—
637C22—222no—
638C22—444no—
639C22—442no—
640C22—442no—
641C22—444no—
642C22C23×C4×D1111yescharacteristic
643C22C2×#41×D1112yes—
644C22#1062345511yescharacteristic
645C22#1062345712yes—
646C22#1062345711yescharacteristic
647C4—24no—
648C4—22no—
649C4—24no—
650C4—22no—
651C4—44no—
652C4—42no—
653C4—42no—
654C4—224no—
655C4—224no—
656C4—222no—
657C4—222no—
658C4—222no—
659C4—224no—
660C4—444no—
661C4#1062305314yes—
662C2—442no—
663C2—444no—
664C2C2×#1062305311yescharacteristic
665C2#1308181611yescharacteristic
666C2#1308181811yescharacteristic
667C2#1308250812yes—
668C2#1308253912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2320C2
socle, cosocleC23×C11C25
prime radicalC2×#66948C22
hypercenter#2320D11
hypocenterC11#34227
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2320

Complements

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

NH ≅ G/Ntype
2. #13071748C2semidirect
3. #13071729C2semidirect
4. #13071591C2semidirect
5. #13071549C2semidirect
6. #13071504C2semidirect
7. #13071469C2semidirect
9. #13071301C2semidirect
10. #13071260C2semidirect
11. #13071175C2semidirect
12. #13071159C2semidirect
13. #13071012C2semidirect
14. #13070981C2semidirect
15. #13070976C2semidirect
16. #13070955C2semidirect
17. C11×#2320C2semidirect
22. #10623111C4semidirect
92. C4×Q8×C11C2×C4semidirect
102. #66999C2×C4semidirect
136. #66951C2×C4semidirect
138. #66947C2×C4semidirect
140. #66943C2×C4semidirect
142. C4×D44C2×C4semidirect
144. #66925C2×C4semidirect
145. C42×D11C2×C4semidirect
249. #2320D11semidirect
426. C4×Q8C4×D11semidirect
573. C11#34227semidirect

Maximal subgroups

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

subgroupindex
C2×#106231112
#130717482
#130717292
#130715912
#130715492
#130715042
#130714692
#130713072
#130713012
#130712602
#130711752
#130711592
#130710122
#130709812
#130709762
#130709552
C11×#23202
#3422711