Finite Group Databasebeta

← #14914402

Subgroups — #14914402

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×#10623088C211yesmaximal, characteristic
2#13071750C214yesmaximal, complemented
3#13071737C214yesmaximal, complemented
4#13071590C212yesmaximal, complemented
5#13071552C212yesmaximal, complemented
6#13071507C212yesmaximal, complemented
7#13071472C212yesmaximal, complemented
8#13071303C212yesmaximal
9#13071299C212yesmaximal, complemented
10#13071262C211yesmaximal, characteristic, complemented
11#13071259C211yesmaximal, characteristic, complemented
12C4×#66943C212yesmaximal, complemented
13C4×#66989C212yesmaximal, complemented
14#13071012C211yesmaximal, characteristic, complemented
15#13070979C211yesmaximal, characteristic, complemented
16#13070955C211yesmaximal, characteristic, complemented
17C11×#2275C211yesmaximal, characteristic, complemented
18C2×C4×D4×C11C2212yes—
19C2×C4×D4×C11C2211yescharacteristic
20C2×#66991C2211yescharacteristic
21C2×#66989C2211yescharacteristic
22C2×C4×C22⋊D11C2212yes—
23C2×#66979C2212yes—
24#10623088C4116yescomplemented
25C2×#66950C2211yescharacteristic
26C2×#66943C2211yescharacteristic
27C2×#66936C2212yes—
28C2×#66932C2212yes—
29C2×#66925C2212yes—
30C2×C42×D11C2211yescharacteristic
31C2×C4×Dic22C2212yes—
32C2×C4×Dic22C2211yescharacteristic
33C4×C11×C4⋊C4C2212yes—
34C4×C11×C4⋊C4C2211yescharacteristic
35C4×C11×C22⋊C4C2214yes—
36C4×C11×C22⋊C4C2212yes—
37C11×#376C2211yescharacteristic
38C2×C11×#95C2212yes—
39#10622834C2212yes—
40#10622826C2214yes—
41#10622825C2212yes—
42#10622824C2212yes—
43#10622823C2214yes—
44C4×C22⋊Dic11C2214yes—
45C4×C22⋊Dic11C2214yes—
46#10622600C2212yes—
47#10622598C2212yes—
48#10622590C2212yes—
49#10622587C2212yes—
50#10622586C2212yes—
51#10622570C2214yes—
52#10622564C2214yes—
53#10622558C2214yes—
54#10622558C2214yes—
55#10622558C2214yes—
56#10622553C2214yes—
57C4×(C2×D11)⋊C4C2212yes—
58C4×C4⋊Dic11C2212yes—
59C4×C4⋊Dic11C2214yes—
60C4×C4⋊Dic11C2211yescharacteristic
61#10622546C2214yes—
62#10622545C2211yescharacteristic
63#10622545C2212yes—
64C4×Dic11⋊C4C2214yes—
65C42×Dic11C2212yes—
66#10622541C2214yes—
67#10622283C2214yes—
68#10622279C2212yes—
69#10622279C2211yescharacteristic
70#10622279C2211yescharacteristic
71#10622277C2212yes—
72#10622268C2214yes—
73#10622267C2214yes—
74#10622266C2214yes—
75#10622264C2212yes—
76#10622264C2212yes—
77#10622263C2212yes—
78#10622262C2211yescharacteristic
79#10622262C2212yes—
80#10622262C2211yescharacteristic
81#10622262C2214yes—
82#10622262C2212yes—
83#10622261C2212yes—
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11C2314yes—
86C23×C4×C11C2312yes—
87C22×C22⋊D11C2312yes—
88C22×C4×D11C2311yescharacteristic
89C22×C4×D11C2311yescharacteristic
90C22×C4×D11C2311yescharacteristic
91C22×Dic22C2311yescharacteristic
92C4×D4×C11—28no—
93C4×D4×C11C2×C418yes—
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C22⋊C4C2314yes—
97C2×C11×C22⋊C4C2312yes—
98C2×C42×C11C2314yes—
99C2×C42×C11C2312yes—
100C2×C42×C11C2311yescharacteristic
101C2×C42×C11C2312yes—
102C2×C22⋊Dic11C2314yes—
103C2×C22⋊Dic11C2314yes—
104C2×C22⋊Dic11C2312yes—
105C2×C22⋊Dic11C2312yes—
106C2×C22⋊Dic11C2312yes—
107#66991C2×C418yes—
108#66989C2×C418yes—
109C4×C22⋊D11C2×C4116yescomplemented
110C2×(C2×D11)⋊C4C2312yes—
111C2×(C2×D11)⋊C4C2312yes—
112C2×(C2×D11)⋊C4C2314yes—
113C2×(C2×D11)⋊C4C2312yes—
114#66979C2×C4116yescomplemented
115C2×C4⋊Dic11C2312yes—
116C2×C4⋊Dic11C2314yes—
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2312yes—
119C2×C4⋊Dic11C2312yes—
120C2×Dic11⋊C4C2314yes—
121C2×Dic11⋊C4C2312yes—
122C2×Dic11⋊C4C2312yes—
123C2×Dic11⋊C4C2314yes—
124C2×Dic11⋊C4C2312yes—
125C2×Dic11⋊C4C2312yes—
126C2×C4×Dic11C2314yes—
127C2×C4×Dic11C2312yes—
128C2×C4×Dic11C2314yes—
129C2×C4×Dic11C2312yes—
130C2×C4×Dic11C2312yes—
131C2×C4×Dic11C2312yes—
132C2×C4×Dic11C2312yes—
133C2×C4×Dic11C2312yes—
134C2×C4×Dic11C2312yes—
135C2×C4×Dic11C2311yescharacteristic
136C2×C4×Dic11C2311yescharacteristic
137C2×C4×Dic11C2311yescharacteristic
138#66950C2×C418yescomplemented
139#66943C2×C418yescomplemented
140#66936C2×C4116yescomplemented
141#66932C2×C4116yescomplemented
142#66925—28no—
143C42×D11C2×C418yescomplemented
144C4×Dic22—28no—
145C4×Dic22C2×C418yescomplemented
146C11×#95C2311yescharacteristic
147C11×#95C2311yescharacteristic
148C11×#95C2312yes—
149C11×#95C2312yes—
150C11×#95C2314yes—
151C11⋊#95C2312yes—
152C11⋊#95C2314yes—
153C11⋊#95C2311yescharacteristic
154C11⋊#95C2311yescharacteristic
155C11⋊#95C2312yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163#34227—111nomaximal, Sylow
164C24×C11C2412yes—
165C23×D11C2411yescharacteristic
166C2×D4×C11—24no—
167C2×D4×C11C22×C414yes—
168C22×C4×C11—28no—
169C22×C4×C11—44no—
170C22×C4×C11—44no—
171C22×C4×C11—44no—
172C22×C4×C11C22×C418yes—
173C22×C4×C11C2414yes—
174C22×C4×C11C2411yescharacteristic
175C22×C4×C11C2411yescharacteristic
176C22×C4×C11C2412yes—
177C22×C4×C11C2412yes—
178C22×C4×C11C2412yes—
179C22×C4×C11C2411yescharacteristic
180C2×C22⋊D11—42no—
181C2×C22⋊D11—42no—
182C2×C22⋊D11C22×C418yes—
183C22×Dic11C2412yes—
184C22×Dic11C2414yes—
185C22×Dic11C2412yes—
186C22×Dic11C2411yescharacteristic
187C22×Dic11C2411yescharacteristic
188C22×Dic11C2412yes—
189C22×Dic11C2412yes—
190C22×Dic11C2411yescharacteristic
191C2×C4×D11—24no—
192C2×C4×D11—41no—
193C2×C4×D11—41no—
194C2×C4×D11—42no—
195C2×C4×D11C22×C414yes—
196C2×C4×D11C22×C414yes—
197C2×C4×D11C22×C414yes—
198C2×Dic22—24no—
199C2×Dic22C22×C414yes—
200C11×C4⋊C4—24no—
201C11×C4⋊C4C22×C414yes—
202C11×C22⋊C4—28no—
203C11×C22⋊C4C22×C418yes—
204C42×C11—44no—
205C42×C11—42no—
206C42×C11C22×C414yes—
207C42×C11#4118yes—
208C22⋊Dic11—44no—
209C22⋊Dic11—44no—
210C22⋊Dic11C22×C418yes—
211C22⋊Dic11C22×C418yes—
212C22⋊Dic11C22×C418yes—
213(C2×D11)⋊C4—24no—
214(C2×D11)⋊C4—24no—
215(C2×D11)⋊C4—44no—
216(C2×D11)⋊C4C22×C418yes—
217C4⋊Dic11—24no—
218C4⋊Dic11—44no—
219C4⋊Dic11C22×C414yes—
220C4⋊Dic11C22×C418yes—
221C4⋊Dic11C22×C418yes—
222Dic11⋊C4—28no—
223Dic11⋊C4—24no—
224Dic11⋊C4—24no—
225Dic11⋊C4—44no—
226Dic11⋊C4C22×C418yes—
227Dic11⋊C4C22×C418yes—
228C4×Dic11—28no—
229C4×Dic11—24no—
230C4×Dic11—42no—
231C4×Dic11—44no—
232C4×Dic11—42no—
233C4×Dic11—42no—
234C4×Dic11—42no—
235C4×Dic11—42no—
236C4×Dic11C22×C418yes—
237C4×Dic11C22×C414yes—
238C4×Dic11C22×C414yes—
239C4×Dic11C22×C414yes—
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#2320—111no—
250#2319—111no—
251C4×#125—112no—
252C4×#124—112no—
253#2283—111no—
254#2276—111no—
255#2275D1111yescharacteristic, complemented
256C4×#117—111no—
257C23×C11—24no—
258C23×C11—22no—
259C23×C11—24no—
260C23×C11—22no—
261C23×C11C23×C414yes—
262C23×C11C2511yescharacteristic
263C22×D11—22no—
264C22×D11—22no—
265C22×D11—21no—
266C22×D11—21no—
267C22×D11C23×C412yes—
268D4×C11—28no—
269C2×C4×C11—22no—
270C2×C4×C11—21no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—24no—
275C2×C4×C11—21no—
276C2×C4×C11—22no—
277C2×C4×C11—24no—
278C2×C4×C11—24no—
279C2×C4×C11—24no—
280C2×C4×C11—48no—
281C2×C4×C11—88no—
282C2×C4×C11C23×C412yes—
283C2×C4×C11C23×C412yes—
284C2×C4×C11C23×C414yes—
285C2×C4×C11C23×C412yes—
286C2×C4×C11C2×#4114yes—
287C2×C4×C11C2×#4114yes—
288C2×C4×C11C2×#4114yes—
289C22⋊D11—48no—
290C2×Dic11—24no—
291C2×Dic11—22no—
292C2×Dic11—21no—
293C2×Dic11—22no—
294C2×Dic11—21no—
295C2×Dic11—22no—
296C2×Dic11—22no—
297C2×Dic11—24no—
298C2×Dic11—22no—
299C2×Dic11—22no—
300C2×Dic11—24no—
301C2×Dic11—22no—
302C2×Dic11—22no—
303C2×Dic11—22no—
304C2×Dic11—22no—
305C2×Dic11—24no—
306C2×Dic11C23×C412yes—
307C2×Dic11C23×C412yes—
308C2×Dic11C23×C412yes—
309C2×Dic11C23×C414yes—
310C2×Dic11C23×C414yes—
311C4×D11—28no—
312C4×D11—44no—
313C4×D11—44no—
314Dic22—28no—
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—111no—
323C2×C4×Q8—112no—
324C2×C4×D4—112no—
325C2×C4×D4C2×D1112yes—
326C2×C4×D4C2×D1111yescharacteristic
327C2×#117—112no—
328C2×#117—112no—
329C22×C42—111no—
330#391—112no—
331#390—112no—
332#390—114no—
333#389—112no—
334#389—112no—
335#389—114no—
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#387—114no—
346#386—114no—
347#385—114no—
348#383—112no—
349#383—112no—
350#382—112no—
351#382—112no—
352#381—112no—
353#381—112no—
354#380—112no—
355#380—112no—
356C4×C4⋊C4—112no—
357C4×C4⋊C4—114no—
358C4×C4⋊C4—114no—
359C4×C4⋊C4—111no—
360C4×C4⋊C4—111no—
361C4×C4⋊C4—111no—
362C4×C4⋊C4—112no—
363C4×C4⋊C4—112no—
364C4×C4⋊C4—114no—
365C4×C4⋊C4C2×D1112yes—
366C4×C4⋊C4C2×D1111yescharacteristic
367C4×C22⋊C4—114no—
368C4×C22⋊C4—114no—
369C4×C22⋊C4—112no—
370C4×C22⋊C4—111no—
371C4×C22⋊C4—111no—
372C4×C22⋊C4—112no—
373C4×C22⋊C4C2×D1112yes—
374C4×C22⋊C4C2×D1114yes—
375#376—111no—
376#376—112no—
377#376—112no—
378#376C2×D1111yescharacteristic
379C2×#95C2×D1112yes—
380C43—112no—
381C22×C11—24no—
382C22×C11—24no—
383C22×C11—24no—
384C22×C11—44no—
385C22×C11—44no—
386C22×C11C24×C411yescharacteristic
387C22×C11C22×#4112yes—
388C22×C11#58511yescharacteristic
389C22×C11#58512yes—
390C22×C11#58511yescharacteristic
391C2×D11—22no—
392C2×D11—22no—
393C2×D11—22no—
394C2×D11—42no—
395C2×D11—42no—
396C4×C11—22no—
397C4×C11—24no—
398C4×C11—22no—
399C4×C11—24no—
400C4×C11—24no—
401C4×C11—44no—
402C4×C11C4×#4114yes—
403Dic11—24no—
404Dic11—22no—
405Dic11—22no—
406Dic11—22no—
407Dic11—24no—
408Dic11—42no—
409Dic11—44no—
410Dic11—42no—
411C22×Q8—111no—
412C22×D4—112no—
413C22×D4C22×D1111yescharacteristic
414C23×C4—111no—
415C23×C4—111no—
416C23×C4—111no—
417C23×C4C22×D1114yes—
418C23×C4C22×D1112yes—
419#126—1116no—
420#125—118no—
421#124—118no—
422#123—1116no—
423C22⋊Q8—118no—
424#121—118no—
425C4×Q8—118no—
426C4×Q8—228no—
427C4×D4—28no—
428C4×D4—1116no—
429C4×D4C4×D1118yes—
430#117—1116no—
431#117—228no—
432C2×C4⋊C4—112no—
433C2×C4⋊C4—112no—
434C2×C4⋊C4—112no—
435C2×C4⋊C4—111no—
436C2×C4⋊C4—112no—
437C2×C4⋊C4—112no—
438C2×C4⋊C4—112no—
439C2×C4⋊C4—112no—
440C2×C4⋊C4—114no—
441C2×C4⋊C4—114no—
442C2×C4⋊C4—114no—
443C2×C4⋊C4C22×D1112yes—
444C2×C4⋊C4C22×D1111yescharacteristic
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—114no—
452C2×C22⋊C4—114no—
453C2×C22⋊C4—114no—
454C2×C22⋊C4C22×D1114yes—
455C2×C22⋊C4C22×D1112yes—
456C2×C42—111no—
457C2×C42—112no—
458C2×C42—111no—
459C2×C42—111no—
460C2×C42—118no—
461C2×C42—112no—
462C2×C42—114no—
463C2×C42—112no—
464C2×C42—112no—
465C2×C42—112no—
466C2×C42—112no—
467C2×C42—112no—
468C2×C42—114no—
469C2×C42C22×D1112yes—
470C2×C42C22×D1114yes—
471C2×C42C22×D1111yescharacteristic
472C2×C42C22×D1112yes—
473#95—111no—
474#95—111no—
475#95—114no—
476#95—112no—
477#95—112no—
478#95—114no—
479#95—114no—
480#95—114no—
481#95—114no—
482#95—114no—
483#95—114no—
484#95—114no—
485#95C22×D1111yescharacteristic
486#95C22×D1112yes—
487#95C22×D1114yes—
488#95C22×D1111yescharacteristic
489#95C22×D1112yes—
490C2×C11—44no—
491C2×C11C2×C4×#4111yescharacteristic
492C2×C11#342811yescharacteristic
493C2×C11#342811yescharacteristic
494C2×C11#351012yes—
495C2×C11#351212yes—
496D11—42no—
497C24—111no—
498C24C23×D1112yes—
499C2×Q8—114no—
500C2×Q8—224no—
501C2×D4—24no—
502C2×D4—118no—
503C2×D4—442no—
504C2×D4—442no—
505C2×D4C2×C4×D1114yes—
506C22×C4—28no—
507C22×C4—44no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—111no—
511C22×C4—111no—
512C22×C4—112no—
513C22×C4—112no—
514C22×C4—111no—
515C22×C4—114no—
516C22×C4—114no—
517C22×C4—114no—
518C22×C4—112no—
519C22×C4—112no—
520C22×C4—114no—
521C22×C4—224no—
522C22×C4—441no—
523C22×C4—442no—
524C22×C4—441no—
525C22×C4C2×C4×D1118yes—
526C22×C4C23×D1114yes—
527C22×C4C23×D1111yescharacteristic
528C22×C4C23×D1111yescharacteristic
529C22×C4C23×D1112yes—
530C22×C4C23×D1112yes—
531C22×C4C23×D1112yes—
532C22×C4C23×D1111yescharacteristic
533C4⋊C4—24no—
534C4⋊C4—118no—
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⋊C4—444no—
545C4⋊C4C2×C4×D1114yes—
546C22⋊C4—28no—
547C22⋊C4—118no—
548C22⋊C4—118no—
549C22⋊C4—118no—
550C22⋊C4—118no—
551C22⋊C4—224no—
552C22⋊C4—224no—
553C22⋊C4—444no—
554C22⋊C4—444no—
555C22⋊C4—444no—
556C22⋊C4C2×C4×D1118yes—
557C42—44no—
558C42—42no—
559C42—114no—
560C42—114no—
561C42—114no—
562C42—118no—
563C42—224no—
564C42—228no—
565C42—442no—
566C42—442no—
567C42—442no—
568C42—442no—
569C42—444no—
570C42—442no—
571C42C2×C4×D1114yes—
572C42#433918yes—
573C11#3422711yescharacteristic, complemented, Sylow
574C23—24no—
575C23—24no—
576C23—22no—
577C23—22no—
578C23—112no—
579C23—222no—
580C23—222no—
581C23—221no—
582C23—221no—
583C23C22×C4×D1114yes—
584C23C24×D1111yescharacteristic
585Q8—228no—
586D4—28no—
587D4—448no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—24no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—48no—
600C2×C4—88no—
601C2×C4—112no—
602C2×C4—112no—
603C2×C4—112no—
604C2×C4—114no—
605C2×C4—114no—
606C2×C4—224no—
607C2×C4—222no—
608C2×C4—222no—
609C2×C4—221no—
610C2×C4—222no—
611C2×C4—221no—
612C2×C4—222no—
613C2×C4—228no—
614C2×C4—222no—
615C2×C4—222no—
616C2×C4—224no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—222no—
620C2×C4—224no—
621C2×C4—224no—
622C2×C4—222no—
623C2×C4—444no—
624C2×C4—444no—
625C2×C4C22×C4×D1112yes—
626C2×C4C22×C4×D1112yes—
627C2×C4C22×C4×D1114yes—
628C2×C4C22×C4×D1112yes—
629C2×C4C2×#433914yes—
630C2×C4C2×#433914yes—
631C2×C4C2×#433914yes—
632C22—24no—
633C22—24no—
634C22—24no—
635C22—44no—
636C22—44no—
637C22—222no—
638C22—222no—
639C22—222no—
640C22—442no—
641C22—442no—
642C22C23×C4×D1111yescharacteristic
643C22C22×#433912yes—
644C22#1062345511yescharacteristic
645C22#1062345512yes—
646C22#1062345711yescharacteristic
647C4—24no—
648C4—24no—
649C4—22no—
650C4—24no—
651C4—22no—
652C4—44no—
653C4—222no—
654C4—224no—
655C4—222no—
656C4—222no—
657C4—224no—
658C4—442no—
659C4—442no—
660C4—444no—
661C4C4×#433914yes—
662C2—44no—
663C2—442no—
664C2C2×C4×#433911yescharacteristic
665C2#1308181411yescharacteristic
666C2#1308181611yescharacteristic
667C2#1308250712yes—
668C2#1308253312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2275C2
socle, cosocleC23×C11C25
prime radicalC2×#66991C22
hypercenter#2275D11
hypocenterC11#34227
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2275

Complements

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

NH ≅ G/Ntype
2. #13071750C2semidirect
3. #13071737C2semidirect
4. #13071590C2semidirect
5. #13071552C2semidirect
6. #13071507C2semidirect
7. #13071472C2semidirect
9. #13071299C2semidirect
10. #13071262C2semidirect
11. #13071259C2semidirect
12. C4×#66943C2semidirect
13. C4×#66989C2semidirect
14. #13071012C2semidirect
15. #13070979C2semidirect
16. #13070955C2semidirect
17. C11×#2275C2semidirect
24. #10623088C4semidirect
109. C4×C22⋊D11C2×C4semidirect
114. #66979C2×C4semidirect
138. #66950C2×C4semidirect
139. #66943C2×C4semidirect
140. #66936C2×C4semidirect
141. #66932C2×C4semidirect
143. C42×D11C2×C4semidirect
145. C4×Dic22C2×C4semidirect
255. #2275D11semidirect
573. C11#34227semidirect

Maximal subgroups

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

subgroupindex
C2×#106230882
#130717502
#130717372
#130715902
#130715522
#130715072
#130714722
#130713032
#130712992
#130712622
#130712592
C4×#669432
C4×#669892
#130710122
#130709792
#130709552
C11×#22752
#3422711