Finite Group Databasebeta

← #14913881

Subgroups — #14913881

Order 2816.

3006 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623035C211yesmaximal, characteristic
2C2×#10623054C211yesmaximal, characteristic
3C2×#10623053C211yesmaximal, characteristic
4#13071535C214yesmaximal, complemented
5#13071525C214yesmaximal, complemented
6#13071522C218yesmaximal, complemented
7#13071241C212yesmaximal, complemented
8#13071239C211yesmaximal, characteristic, complemented
9#13071237C212yesmaximal, complemented
10#13071021C212yesmaximal, complemented
11#13071019C211yesmaximal, characteristic, complemented
12C2×#10622590C211yesmaximal, characteristic, complemented
13D11×#382C212yesmaximal, complemented
14C11×#2317C211yesmaximal, characteristic, complemented
15C22×#4339C2211yescharacteristic
16C2×C11×#117C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×C4×C22⋊D11C2214yes—
20C2×#66979C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23#10623054—28no—
24#10623053C4116yescomplemented
25#10623035—28no—
26C2×#66946C2212yes—
27C2×#66946C2212yes—
28C2×#66945C2212yes—
29C2×#66945C2212yes—
30C2×C4⋊C4×D11C2212yes—
31C2×C4⋊C4×D11C2212yes—
32C2×#66940C2212yes—
33C2×#66940C2212yes—
34C2×(C22⋊D11)⋊C4C2214yes—
35C2×(C22⋊D11)⋊C4C2214yes—
36C2×C4×D44C2212yes—
37C2×#66925C2212yes—
38C2×C42×D11C2212yes—
39C2×C4×Dic22C2212yes—
40C11×#389C2214yes—
41C11×#385C2214yes—
42C11×#384C2212yes—
43C11×#382C2212yes—
44C2×C11⋊#95C2214yes—
45#10622602C2218yes—
46#10622600C2218yes—
47#10622598C2214yes—
48#10622590C2212yes—
49#10622590C2211yescharacteristic
50#10622590C2212yes—
51#10622590C2214yes—
52#10622590C2211yescharacteristic
53#10622589C2211yescharacteristic
54#10622589C2211yescharacteristic
55C4⋊C4×Dic11C2218yes—
56#10622585C2218yes—
57#10622563C2214yes—
58#10622555C2214yes—
59#10622549C2212yes—
60#10622548C2212yes—
61C4×Dic11⋊C4C2214yes—
62#10622281C2218yes—
63D11×#95C2218yes—
64#10622263C2218yes—
65#10622260C2218yes—
66C23×C4×C11C2312yes—
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11C2312yes—
69C23×Dic11C2312yes—
70C23×Dic11C2312yes—
71C2×#4339C2×C418yes—
72C2×#4339D418yes—
73C2×#4339Q818yes—
74C22×D44C2311yescharacteristic
75C22×C4×D11C2314yes—
76C22×C4×D11C2314yes—
77C22×C4×D11C2314yes—
78C22×C4×D11C2312yes—
79C22×Dic22C2311yescharacteristic
80C11×#117—24no—
81C11×#117C2×C418yescomplemented
82C2×C11×C4⋊C4—24no—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2318yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C22⋊C4C2312yes—
90C2×C11×C22⋊C4C2312yes—
91C2×C42×C11C2312yes—
92C2×C42×C11C2312yes—
93C2×C22⋊Dic11C2312yes—
94C4×C22⋊D11—216no—
95C2×(C2×D11)⋊C4C2314yes—
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2314yes—
98#66979—24no—
99C2×C4⋊Dic11—24no—
100C2×C4⋊Dic11C2312yes—
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2312yes—
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2318yes—
105C2×Dic11⋊C4C2314yes—
106C2×Dic11⋊C4C2314yes—
107C2×Dic11⋊C4C2314yes—
108C2×Dic11⋊C4C2314yes—
109C2×Dic11⋊C4C2314yes—
110C2×C4×Dic11C2×C418yescomplemented
111C2×C4×Dic11C2314yes—
112C2×C4×Dic11C2314yes—
113C2×C4×Dic11C2312yes—
114C2×C4×Dic11C2311yescharacteristic
115C2×C4×Dic11C2314yes—
116C2×C4×Dic11C2311yescharacteristic
117C2×C4×Dic11C2312yes—
118#66946—28no—
119#66946C2×C4116yescomplemented
120#66945—28no—
121#66945—28no—
122C4⋊C4×D11—28no—
123C4⋊C4×D11—28no—
124#66940—28no—
125#66940C2×C4116yescomplemented
126(C22⋊D11)⋊C4—216no—
127(C22⋊D11)⋊C4C2×C4132yescomplemented
128C4×D44—28no—
129#66925C2×C4116yescomplemented
130C42×D11C2×C4116yescomplemented
131C4×Dic22—28no—
132C11×#95C2318yes—
133C11⋊#95C2318yes—
134C11⋊#95C2314yes—
135C11⋊#95C2318yes—
136C11⋊#95C2318yes—
137C11⋊#95C2314yes—
138#34184—111nomaximal, Sylow
139C24×C11C2411yescharacteristic
140C23×D11C2412yes—
141C22×C4×C11—24no—
142C22×C4×C11—44no—
143C22×C4×C11C22×C414yes—
144C22×C4×C11C2×D414yes—
145C22×C4×C11C2×Q814yes—
146C22×C4×C11C2414yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2412yes—
149C22×C4×C11C2414yes—
150C22×C4×C11C2411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C2×C22⋊D11C22×C418yes—
153C2×C22⋊D11C2×D418yes—
154C2×C22⋊D11C2×Q818yes—
155C22×Dic11—24no—
156C22×Dic11—42no—
157C22×Dic11—42no—
158C22×Dic11—44no—
159C22×Dic11C22×C418yes—
160C22×Dic11C2412yes—
161C22×Dic11C2414yes—
162C22×Dic11C2412yes—
163C22×Dic11C2412yes—
164C22×Dic11C2412yes—
165C22×Dic11C2412yes—
166#4339C4⋊C4164yescomplemented
167C2×D44C22×C414yes—
168C2×D44C2×D414yes—
169C2×D44C2×Q814yes—
170C2×C4×D11—28no—
171C2×C4×D11—28no—
172C2×C4×D11—44no—
173C2×C4×D11—44no—
174C2×C4×D11—48no—
175C2×C4×D11—48no—
176C2×C4×D11C22×C4116yes—
177C2×C4×D11C22×C418yes—
178C2×C4×D11C2×D418yes—
179C2×C4×D11C2×Q818yes—
180C2×Dic22C22×C414yes—
181C2×Dic22C2×D414yes—
182C2×Dic22C2×Q814yes—
183C11×C4⋊C4—24no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—24no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—48no—
188C11×C4⋊C4C22×C418yes—
189C11×C22⋊C4—24no—
190C11×C22⋊C4C22×C418yes—
191C42×C11—24no—
192C42×C11C22×C418yes—
193C22⋊Dic11—24no—
194(C2×D11)⋊C4—28no—
195(C2×D11)⋊C4—28no—
196(C2×D11)⋊C4C22×C4116yes—
197C4⋊Dic11—24no—
198C4⋊Dic11—22no—
199C4⋊Dic11—24no—
200C4⋊Dic11—22no—
201C4⋊Dic11—48no—
202Dic11⋊C4—28no—
203Dic11⋊C4—28no—
204Dic11⋊C4—44no—
205Dic11⋊C4—44no—
206Dic11⋊C4C22×C4116yes—
207C4×Dic11—28no—
208C4×Dic11—28no—
209C4×Dic11—24no—
210C4×Dic11C22×C414yes—
211C4×Dic11C22×C4116yes—
212C4×Dic11C22×C414yes—
213C4×Dic11C22×C418yes—
214C2×#520—111no—
215C2×#520—111no—
216C2×C4×#41—111no—
217#2351—114no—
218#2349—114no—
219#2349—118no—
220#2317—112no—
221#2317—112no—
222#2317—111no—
223#2317D1111yescharacteristic, complemented
224#2285—112no—
225#2285—111no—
226C2×#382—112no—
227C2×#382—111no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11C23×C412yes—
231C23×C11C22×D412yes—
232C23×C11C22×Q812yes—
233C23×C11C2511yescharacteristic
234C22×D11—24no—
235C22×D11—24no—
236C22×D11C23×C414yes—
237C22×D11C22×D414yes—
238C22×D11C22×Q814yes—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—28no—
247C2×C4×C11—84no—
248C2×C4×C11C2×C4⋊C4116yes—
249C2×C4×C11C23×C418yes—
250C2×C4×C11C23×C412yes—
251C2×C4×C11C23×C412yes—
252C2×C4×C11C22×D412yes—
253C2×C4×C11C22×D412yes—
254C2×C4×C11C22×Q812yes—
255C2×C4×C11C22×Q812yes—
256C22⋊D11C2×C4⋊C4132yes—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—28no—
267C2×Dic11—48no—
268C2×Dic11—84no—
269C2×Dic11C23×C414yes—
270C2×Dic11C23×C414yes—
271C2×Dic11C23×C414yes—
272C2×Dic11C22×D414yes—
273C2×Dic11C22×Q814yes—
274D44C2×C4⋊C4116yes—
275C4×D11—416no—
276C4×D11—88no—
277C4×D11—88no—
278C4×D11C2×C4⋊C4132yes—
279Dic22C2×C4⋊C4116yes—
280C22×#41—111no—
281#520—228no—
282#520—228no—
283C4×#41—1116no—
284C2×C4×Q8—112no—
285C2×C4×Q8—112no—
286C2×C4×Q8—112no—
287C2×C4×D4—114no—
288C2×C4×D4—112no—
289C2×C4×D4—112no—
290C2×C4×D4—114no—
291C2×C4×D4—114no—
292C2×C4×D4—112no—
293C2×#117—111no—
294C2×#117—112no—
295C2×#117—112no—
296C2×#117—112no—
297C2×#117C2×D1111yescharacteristic
298C2×#117C2×D1111yescharacteristic
299C22×C4⋊C4—111no—
300C22×C4⋊C4—112no—
301C22×C4⋊C4—112no—
302C22×C4⋊C4C2×D1111yescharacteristic
303C22×C42—111no—
304C22×C42—112no—
305#389—118no—
306#389—114no—
307#389—118no—
308#389C2×D1114yes—
309#385—118no—
310#385—114no—
311#385—118no—
312#385C2×D1114yes—
313#384—111no—
314#384—111no—
315#384—112no—
316#384C2×D1112yes—
317#382—112no—
318#382—114no—
319#382—111no—
320#382—112no—
321#382—111no—
322#382—112no—
323#382—118no—
324#382C2×D1112yes—
325#380—118no—
326#380—114no—
327C4×C4⋊C4—118no—
328C4×C4⋊C4—114no—
329C2×#95—114no—
330C2×#95—118no—
331C22×C11—24no—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—24no—
335C22×C11C22×C4⋊C414yes—
336C22×C11C24×C411yescharacteristic
337C22×C11C23×D411yescharacteristic
338C22×C11C23×Q811yescharacteristic
339C22×C11#58512yes—
340C22×C11#58512yes—
341C2×D11—28no—
342C2×D11—24no—
343C2×D11—24no—
344C2×D11—28no—
345C2×D11C22×C4⋊C418yes—
346C4×C11—28no—
347C4×C11—42no—
348C4×C11—44no—
349C4×C11—42no—
350C4×C11C22×C4⋊C414yes—
351C4×C11C22×C4⋊C414yes—
352Dic11—24no—
353Dic11—24no—
354Dic11—42no—
355Dic11—44no—
356Dic11—42no—
357Dic11C22×C4⋊C418yes—
358C2×#41—118no—
359C2×#41—118no—
360C2×#41—118no—
361C22×Q8—111no—
362C22×D4—112no—
363C22×D4—111no—
364C23×C4—112no—
365C23×C4—112no—
366C23×C4—114no—
367C23×C4—112no—
368C23×C4—114no—
369C23×C4—114no—
370C23×C4C22×D1112yes—
371C23×C4C22×D1111yescharacteristic
372C4×Q8—1116no—
373C4×Q8—228no—
374C4×Q8—228no—
375C4×D4—1116no—
376C4×D4—1132no—
377C4×D4—228no—
378C4×D4—2216no—
379C4×D4—228no—
380C4×D4—2216no—
381#117—24no—
382#117—1116no—
383#117—228no—
384#117—228no—
385#117—224no—
386#117C4×D1118yescomplemented
387C2×C4⋊C4—24no—
388C2×C4⋊C4—114no—
389C2×C4⋊C4—112no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—114no—
392C2×C4⋊C4—114no—
393C2×C4⋊C4—112no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—114no—
396C2×C4⋊C4—114no—
397C2×C4⋊C4—118no—
398C2×C4⋊C4—228no—
399C2×C4⋊C4—228no—
400C2×C4⋊C4—224no—
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C4⋊C4C22×D1112yes—
403C2×C4⋊C4C22×D1112yes—
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C4⋊C4C22×D1118yes—
406C2×C4⋊C4C22×D1112yes—
407C2×C22⋊C4—114no—
408C2×C22⋊C4—112no—
409C2×C22⋊C4—114no—
410C2×C22⋊C4—114no—
411C2×C22⋊C4C22×D1112yes—
412C2×C22⋊C4C22×D1112yes—
413C2×C42—118no—
414C2×C42—111no—
415C2×C42—114no—
416C2×C42—112no—
417C2×C42—111no—
418C2×C42—1116no—
419C2×C42—114no—
420C2×C42—114no—
421C2×C42—112no—
422C2×C42C22×D1112yes—
423C2×C42C22×D1112yes—
424#95—118no—
425#95—114no—
426#95—118no—
427#95—118no—
428#95—114no—
429#95C22×D1118yes—
430C2×C11—24no—
431C2×C11C23×C4⋊C411yescharacteristic
432C2×C11#342812yes—
433C2×C11#350011yescharacteristic
434C2×C11#350011yescharacteristic
435C2×C11#350412yes—
436D11—28no—
437C24—112no—
438C24C23×D1111yescharacteristic
439#41—1164no—
440C2×Q8—114no—
441C2×Q8—114no—
442C2×Q8—114no—
443C2×D4—118no—
444C2×D4—118no—
445C2×D4—118no—
446C2×D4—114no—
447C2×D4—114no—
448C2×D4—114no—
449C22×C4—24no—
450C22×C4—44no—
451C22×C4—112no—
452C22×C4—118no—
453C22×C4—118no—
454C22×C4—118no—
455C22×C4—112no—
456C22×C4—112no—
457C22×C4—118no—
458C22×C4—1116no—
459C22×C4—112no—
460C22×C4—114no—
461C22×C4—112no—
462C22×C4—228no—
463C22×C4—228no—
464C22×C4—224no—
465C22×C4—444no—
466C22×C4—444no—
467C22×C4—448no—
468C22×C4—448no—
469C22×C4—442no—
470C22×C4—442no—
471C22×C4—444no—
472C22×C4C2×C4×D1114yes—
473C22×C4D4×D1114yes—
474C22×C4Q8×D1114yes—
475C22×C4C23×D1114yes—
476C22×C4C23×D1112yes—
477C22×C4C23×D1112yes—
478C22×C4C23×D1114yes—
479C22×C4C23×D1111yescharacteristic
480C22×C4C23×D1111yescharacteristic
481C4⋊C4—24no—
482C4⋊C4—24no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—48no—
486C4⋊C4—1116no—
487C4⋊C4—228no—
488C4⋊C4—228no—
489C4⋊C4—222no—
490C4⋊C4—224no—
491C4⋊C4—224no—
492C4⋊C4—222no—
493C4⋊C4—444no—
494C4⋊C4—444no—
495C4⋊C4—448no—
496C4⋊C4C2×C4×D1118yes—
497C22⋊C4—24no—
498C22⋊C4—1116no—
499C22⋊C4—228no—
500C22⋊C4—228no—
501C22⋊C4—224no—
502C22⋊C4C2×C4×D1118yes—
503C42—24no—
504C42—114no—
505C42—114no—
506C42—1116no—
507C42—118no—
508C42—228no—
509C42—228no—
510C42—224no—
511C42C2×C4×D1118yes—
512C11#3418411yescharacteristic, complemented, Sylow
513C23—22no—
514C23—22no—
515C23—114no—
516C23—114no—
517C23—114no—
518C23—224no—
519C23—224no—
520C23C22×C4×D1112yes—
521C23C2×D4×D1112yes—
522C23C2×Q8×D1112yes—
523C23C24×D1111yescharacteristic
524Q8—1116no—
525D4—1132no—
526D4—1116no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—28no—
534C2×C4—24no—
535C2×C4—84no—
536C2×C4—114no—
537C2×C4—114no—
538C2×C4—114no—
539C2×C4—1132no—
540C2×C4—114no—
541C2×C4—114no—
542C2×C4—222no—
543C2×C4—222no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4—224no—
548C2×C4—222no—
549C2×C4—224no—
550C2×C4—224no—
551C2×C4—228no—
552C2×C4—4416no—
553C2×C4—448no—
554C2×C4—888no—
555C2×C4—888no—
556C2×C4—884no—
557C2×C4C4⋊C4×D11116yes—
558C2×C4C22×C4×D1118yes—
559C2×C4C22×C4×D1112yes—
560C2×C4C22×C4×D1112yes—
561C2×C4C2×D4×D1112yes—
562C2×C4C2×D4×D1112yes—
563C2×C4C2×Q8×D1112yes—
564C2×C4C2×Q8×D1112yes—
565C22—22no—
566C22—22no—
567C22—24no—
568C22—24no—
569C22—118no—
570C22—224no—
571C22—224no—
572C22—228no—
573C22—228no—
574C22C2×C4⋊C4×D1114yes—
575C22C23×C4×D1111yescharacteristic
576C22C22×D4×D1111yescharacteristic
577C22C22×Q8×D1111yescharacteristic
578C22#1062345512yes—
579C22#1062345712yes—
580C4—28no—
581C4—42no—
582C4—44no—
583C4—42no—
584C4—118no—
585C4—224no—
586C4—224no—
587C4—444no—
588C4—442no—
589C4—442no—
590C4C2×C4⋊C4×D1114yes—
591C4C2×C4⋊C4×D1114yes—
592C2—24no—
593C2—228no—
594C2C22×C4⋊C4×D1111yescharacteristic
595C2#1308181612yes—
596C2#1308240511yescharacteristic
597C2#1308240811yescharacteristic
598C2#1308243912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2317C2
socle, cosocleC23×C11C25
prime radicalC22×#4339C22
hypercenter#2317D11
hypocenterC11#34184
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2317

Complements

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

NH ≅ G/Ntype
4. #13071535C2semidirect
5. #13071525C2semidirect
6. #13071522C2semidirect
7. #13071241C2semidirect
8. #13071239C2semidirect
9. #13071237C2semidirect
10. #13071021C2semidirect
11. #13071019C2semidirect
12. C2×#10622590C2semidirect
13. D11×#382C2semidirect
14. C11×#2317C2semidirect
24. #10623053C4semidirect
81. C11×#117C2×C4semidirect
110. C2×C4×Dic11C2×C4semidirect
119. #66946C2×C4semidirect
125. #66940C2×C4semidirect
127. (C22⋊D11)⋊C4C2×C4semidirect
129. #66925C2×C4semidirect
130. C42×D11C2×C4semidirect
166. #4339C4⋊C4semidirect
223. #2317D11semidirect
386. #117C4×D11semidirect
512. C11#34184semidirect

Maximal subgroups

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

subgroupindex
C2×#106230352
C2×#106230542
C2×#106230532
#130715352
#130715252
#130715222
#130712412
#130712392
#130712372
#130710212
#130710192
C2×#106225902
D11×#3822
C11×#23172
#3418411