Finite Group Databasebeta

← #14914927

Subgroups — #14914927

Order 2816.

3586 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623336C211yesmaximal, characteristic
2C2×#10623054C211yesmaximal, characteristic, complemented
3C22×D4×Dic11C211yesmaximal, characteristic, complemented
4#13071686C214yesmaximal, complemented
5#13071677C214yesmaximal, complemented
6#13071659C214yesmaximal, complemented
7#13071637C214yesmaximal, complemented
8#13071271C214yesmaximal, complemented
9#13071115C214yesmaximal, complemented
10#13071104C211yesmaximal, characteristic, complemented
11#13071098C211yesmaximal, characteristic, complemented
12#13070972C211yesmaximal, characteristic, complemented
13C11×#2309C211yesmaximal, characteristic, complemented
14C23×D4×C11C2211yescharacteristic
15C24×Dic11C2212yes—
16C22×#4339C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×#67006C2214yes—
20C22×C22⋊Dic11C2212yes—
21#10623336C4116yescomplemented
22C2×#66993C2212yes—
23C2×#66991C2214yes—
24C2×#66989C2212yes—
25C2×D4×Dic11—28no—
26C2×D4×Dic11C2214yes—
27C2×D4×Dic11C2214yes—
28C2×#66979C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31#10623054—28no—
32C2×#66945C2212yescomplemented
33C2×C4⋊C4×D11C2212yescomplemented
34C2×(C22⋊D11)⋊C4C2214yes—
35C2×(C22⋊D11)⋊C4C2218yescomplemented
36C2×C4×D44C2212yescomplemented
37C2×C4×Dic22C2212yescomplemented
38C11×#390C2212yes—
39C11×#390C2212yes—
40C11×#390C2214yes—
41C11×#379C2214yes—
42#10622601C2212yescomplemented
43C4⋊C4×Dic11C2214yescomplemented
44#10622587C2212yescomplemented
45#10622586C2212yescomplemented
46#10622586C2212yescomplemented
47#10622571C2212yes—
48#10622571C2212yes—
49#10622571C2218yescomplemented
50#10622570C2218yescomplemented
51#10622569C2218yescomplemented
52#10622559C2212yes—
53#10622559C2212yes—
54#10622559C2218yescomplemented
55#10622558C2218yescomplemented
56#10622557C2218yescomplemented
57C22⋊C4×Dic11C2214yes—
58C22⋊C4×Dic11C2218yescomplemented
59C4×(C2×D11)⋊C4C2214yescomplemented
60C4×C4⋊Dic11C2214yescomplemented
61C4×Dic11⋊C4C2214yescomplemented
62C25×C11C2312yes—
63C22×D4×C11—24no—
64C22×D4×C11—24no—
65C22×D4×C11C2×C418yescomplemented
66C22×D4×C11C2312yes—
67C22×D4×C11C2312yes—
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11C2312yes—
70C22×C22⋊D11C2318yes—
71C23×Dic11—28no—
72C23×Dic11—48no—
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2318yes—
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2312yes—
77C2×#4339—24no—
78C2×#4339—24no—
79C2×#4339C2×C418yescomplemented
80C22×D44C2311yescharacteristic
81C22×C4×D11C2312yes—
82C22×C4×D11C2314yes—
83C22×Dic22C2311yescharacteristic
84C11×#117—24no—
85C11×#117—24no—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C4⋊C4C2311yescharacteristic
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C22⋊C4C2312yes—
90C2×C11×C22⋊C4C2312yes—
91C2×C11×C22⋊C4C2318yes—
92C2×C11×C22⋊C4C2318yes—
93C2×C42×C11C2312yes—
94C2×C42×C11C2312yes—
95#67006C2×C4132yescomplemented
96C2×C22⋊Dic11—28no—
97C2×C22⋊Dic11C2318yes—
98C2×C22⋊Dic11C2312yes—
99C2×C22⋊Dic11C2318yes—
100#66993C2×C4116yescomplemented
101#66991C2×C4132yescomplemented
102#66989C2×C4116yescomplemented
103D4×Dic11—216no—
104D4×Dic11—216no—
105C2×(C2×D11)⋊C4C2314yes—
106C2×(C2×D11)⋊C4C2314yes—
107C2×(C2×D11)⋊C4C2314yes—
108#66979C2×C418yescomplemented
109C2×C4⋊Dic11D418yescomplemented
110C2×C4⋊Dic11C2312yes—
111C2×C4⋊Dic11C2312yes—
112C2×C4⋊Dic11C2312yes—
113C2×Dic11⋊C4C2314yes—
114C2×Dic11⋊C4C2314yes—
115C2×Dic11⋊C4C2314yes—
116C2×C4×Dic11—24no—
117C2×C4×Dic11C2314yes—
118C2×C4×Dic11C2312yes—
119C2×C4×Dic11C2312yes—
120C2×C4×Dic11C2318yes—
121C2×C4×Dic11C2312yes—
122#66945—28no—
123C4⋊C4×D11—28no—
124(C22⋊D11)⋊C4—216no—
125(C22⋊D11)⋊C4—416no—
126C4×D44—28no—
127C4×Dic22—28no—
128C11⋊#95C2314yes—
129C11⋊#95C2314yes—
130C11⋊#95C2318yes—
131C11⋊#95C2314yes—
132C11⋊#95C2314yes—
133#34265—111nomaximal, Sylow
134C24×C11—24no—
135C24×C11—24no—
136C24×C11—44no—
137C24×C11—44no—
138C24×C11C22×C418yes—
139C24×C11C2414yes—
140C24×C11C2411yescharacteristic
141C23×D11C2412yes—
142C2×D4×C11—232no—
143C2×D4×C11—24no—
144C2×D4×C11—24no—
145C2×D4×C11—24no—
146C2×D4×C11—24no—
147C2×D4×C11C22×C418yes—
148C2×D4×C11C22×C418yes—
149C22×C4×C11C22×C414yes—
150C22×C4×C11C2×D414yes—
151C22×C4×C11#4114yes—
152C22×C4×C11C2414yes—
153C22×C4×C11C2412yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—24no—
158C2×C22⋊D11—24no—
159C2×C22⋊D11—48no—
160C2×C22⋊D11—48no—
161C2×C22⋊D11C22×C418yes—
162C2×C22⋊D11C22×C4132yescomplemented
163C22×Dic11—24no—
164C22×Dic11—216no—
165C22×Dic11—216no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—44no—
169C22×Dic11—48no—
170C22×Dic11—42no—
171C22×Dic11—432no—
172C22×Dic11C2×D418yes—
173C22×Dic11C2412yes—
174C22×Dic11C2414yes—
175C22×Dic11C2412yes—
176C22×Dic11C2414yes—
177C22×Dic11C2412yes—
178#4339—232no—
179C2×D44—22no—
180C2×D44—22no—
181C2×D44C22×C414yescomplemented
182C2×C4×D11—28no—
183C2×C4×D11—24no—
184C2×C4×D11—24no—
185C2×C4×D11—48no—
186C2×C4×D11C22×C418yescomplemented
187C2×Dic22—22no—
188C2×Dic22—22no—
189C2×Dic22C22×C414yescomplemented
190C11×C4⋊C4—22no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—24no—
193C11×C22⋊C4—24no—
194C11×C22⋊C4—24no—
195C11×C22⋊C4—48no—
196C11×C22⋊C4—48no—
197C42×C11—24no—
198C42×C11—24no—
199C22⋊Dic11—216no—
200C22⋊Dic11C22×C418yes—
201C22⋊Dic11C22×C4132yescomplemented
202(C2×D11)⋊C4—28no—
203(C2×D11)⋊C4—28no—
204(C2×D11)⋊C4—44no—
205C4⋊Dic11C22×C418yescomplemented
206C4⋊Dic11C2×D418yes—
207C4⋊Dic11C2×D418yes—
208Dic11⋊C4—28no—
209Dic11⋊C4—28no—
210Dic11⋊C4—44no—
211C4×Dic11—28no—
212C4×Dic11—24no—
213C4×Dic11—24no—
214C4×Dic11—48no—
215C4×Dic11C22×C418yescomplemented
216C2×#535—111no—
217C2×#520—111no—
218C22×C4×D4—111no—
219#2367—114no—
220#2366—114no—
221#2363—114no—
222#2361—114no—
223#2321—114no—
224#2309D1111yescharacteristic, complemented
225C4×#120—114no—
226#2297—111no—
227#2296—111no—
228#2274—111no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—216no—
232C23×C11—24no—
233C23×C11—24no—
234C23×C11—28no—
235C23×C11—28no—
236C23×C11—416no—
237C23×C11—48no—
238C23×C11—48no—
239C23×C11—416no—
240C23×C11C23×C418yes—
241C23×C11C23×C412yes—
242C23×C11C22×D412yes—
243C23×C11C2×#4112yes—
244C23×C11C2511yescharacteristic
245C22×D11—22no—
246C22×D11—22no—
247C22×D11—24no—
248C22×D11—24no—
249C22×D11C23×C414yes—
250D4×C11—216no—
251D4×C11—216no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—24no—
259C2×C4×C11C4×D4116yescomplemented
260C2×C4×C11C23×C412yes—
261C2×C4×C11C23×C412yes—
262C2×C4×C11C22×D412yes—
263C2×C4×C11C22×D412yes—
264C2×C4×C11C2×#4112yes—
265C2×C4×C11C2×#4112yes—
266C22⋊D11—216no—
267C22⋊D11—432no—
268C2×Dic11—28no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—24no—
273C2×Dic11—28no—
274C2×Dic11—22no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—48no—
280C2×Dic11—432no—
281C2×Dic11—44no—
282C2×Dic11C23×C418yes—
283C2×Dic11C23×C414yes—
284C2×Dic11C22×D418yes—
285C2×Dic11H(5,𝔽2)14yes—
286D44—28no—
287C4×D11—216no—
288C4×D11—88no—
289Dic22—28no—
290C22×#41—111no—
291C23×D4C2×D1111yescharacteristic
292C24×C4—112no—
293#535—1116no—
294C2×#127—112no—
295C2×#124—112no—
296C2×#121—114no—
297C2×#120—114no—
298#520—228no—
299C2×C4×Q8—112no—
300C2×C4×D4—114no—
301C2×C4×D4—114no—
302C2×C4×D4—114no—
303C2×C4×D4—118no—
304C2×C4×D4—112no—
305C2×C4×D4—228no—
306C2×#117—111no—
307C2×#117—112no—
308C2×#117C2×D1111yescharacteristic
309C2×#117C2×D1111yescharacteristic
310C22×C4⋊C4—111no—
311C22×C4⋊C4—112no—
312C22×C22⋊C4—112no—
313C22×C42—111no—
314#391—112no—
315#390—112no—
316#390—118no—
317#390C2×D1112yes—
318#390C2×D1112yes—
319#390C2×D1114yes—
320#389—112no—
321#389—112no—
322#388—118no—
323#388—118no—
324#386—112no—
325#386—118no—
326#386—118no—
327#386—112no—
328#385—112no—
329#385—118no—
330#385—112no—
331#379C2×D1114yes—
332C4×C4⋊C4—114no—
333C4×C4⋊C4—114no—
334C4×C4⋊C4—114no—
335C4×C22⋊C4—114no—
336C4×C22⋊C4—118no—
337C4×C22⋊C4—114no—
338C22×C11—24no—
339C22×C11—22no—
340C22×C11—22no—
341C22×C11—24no—
342C22×C11—28no—
343C22×C11—216no—
344C22×C11—432no—
345C22×C11—44no—
346C22×C11—44no—
347C22×C11—48no—
348C22×C11C2×C4×D414yes—
349C22×C11C24×C411yescharacteristic
350C22×C11C23×D411yescharacteristic
351C22×C11C22×#4111yescharacteristic
352C22×C11C2×H(5,𝔽2)12yes—
353C22×C11#58512yes—
354C2×D11—24no—
355C2×D11—28no—
356C2×D11—42no—
357C2×D11—42no—
358C2×D11—44no—
359C4×C11—42no—
360C4×C11—42no—
361C4×C11—44no—
362C4×C11C2×C4×D414yes—
363C4×C11C2×C4×D414yes—
364Dic11—24no—
365Dic11—28no—
366Dic11—28no—
367Dic11—24no—
368Dic11—42no—
369C25C22×D1112yes—
370C2×#41—118no—
371C2×#41—224no—
372C2×#41—224no—
373C22×Q8—111no—
374C22×D4—24no—
375C22×D4—24no—
376C22×D4—112no—
377C22×D4—118no—
378C22×D4—111no—
379C22×D4C4×D1118yescomplemented
380C22×D4C22×D1112yes—
381C22×D4C22×D1112yes—
382C23×C4—112no—
383C23×C4—112no—
384C23×C4—111no—
385C23×C4—118no—
386C23×C4—111no—
387C23×C4—114no—
388C23×C4—228no—
389C23×C4—448no—
390C23×C4C22×D1111yescharacteristic
391#127—1116no—
392#124—1116no—
393#121—1132no—
394#120—1132no—
395C4×Q8—228no—
396C4×D4—228no—
397C4×D4—2216no—
398C4×D4—2216no—
399C4×D4—2216no—
400C4×D4—4416no—
401#117—24no—
402#117—24no—
403#117—118no—
404#117—228no—
405C2×C4⋊C4—118no—
406C2×C4⋊C4—112no—
407C2×C4⋊C4—112no—
408C2×C4⋊C4—112no—
409C2×C4⋊C4—114no—
410C2×C4⋊C4—114no—
411C2×C4⋊C4—114no—
412C2×C4⋊C4—228no—
413C2×C4⋊C4C22×D1111yescharacteristic
414C2×C4⋊C4C22×D1111yescharacteristic
415C2×C4⋊C4C22×D1112yes—
416C2×C22⋊C4—112no—
417C2×C22⋊C4—118no—
418C2×C22⋊C4—118no—
419C2×C22⋊C4—114no—
420C2×C22⋊C4—114no—
421C2×C22⋊C4—114no—
422C2×C22⋊C4—228no—
423C2×C22⋊C4C22×D1112yes—
424C2×C22⋊C4C22×D1112yes—
425C2×C22⋊C4C22×D1118yes—
426C2×C22⋊C4C22×D1118yes—
427C2×C42—112no—
428C2×C42—114no—
429C2×C42—112no—
430C2×C42—112no—
431C2×C42—118no—
432C2×C42—224no—
433C2×C42C22×D1112yes—
434C2×C42C22×D1112yes—
435#95—114no—
436#95—114no—
437#95—118no—
438#95—114no—
439#95—114no—
440C2×C11—24no—
441C2×C11—48no—
442C2×C11C22×C4×D411yescharacteristic
443C2×C11C4×H(5,𝔽2)12yes—
444C2×C11#348411yescharacteristic
445C2×C11#348711yescharacteristic
446C2×C11#350612yes—
447D11—44no—
448C24—24no—
449C24—24no—
450C24—44no—
451C24—44no—
452C24—112no—
453C24C2×C4×D1118yes—
454C24C23×D1114yes—
455C24C23×D1111yescharacteristic
456#41—2232no—
457C2×Q8—114no—
458C2×Q8—222no—
459C2×Q8—222no—
460C2×D4—232no—
461C2×D4—24no—
462C2×D4—24no—
463C2×D4—24no—
464C2×D4—24no—
465C2×D4—118no—
466C2×D4—1132no—
467C2×D4—114no—
468C2×D4—224no—
469C2×D4—224no—
470C2×D4—222no—
471C2×D4—222no—
472C2×D4—448no—
473C2×D4—448no—
474C2×D4C2×C4×D1118yes—
475C2×D4C2×C4×D1118yes—
476C22×C4—114no—
477C22×C4—112no—
478C22×C4—112no—
479C22×C4—114no—
480C22×C4—118no—
481C22×C4—118no—
482C22×C4—112no—
483C22×C4—228no—
484C22×C4—224no—
485C22×C4—2216no—
486C22×C4—2216no—
487C22×C4—222no—
488C22×C4—224no—
489C22×C4—224no—
490C22×C4—222no—
491C22×C4—448no—
492C22×C4—444no—
493C22×C4—448no—
494C22×C4—442no—
495C22×C4—4432no—
496C22×C4C2×C4×D1114yes—
497C22×C4D4×D1114yes—
498C22×C4#434114yes—
499C22×C4C23×D1114yes—
500C22×C4C23×D1112yes—
501C22×C4C23×D1112yes—
502C22×C4C23×D1111yescharacteristic
503C22×C4C23×D1111yescharacteristic
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—24no—
507C4⋊C4—118no—
508C4⋊C4—118no—
509C4⋊C4—118no—
510C4⋊C4—228no—
511C4⋊C4—228no—
512C4⋊C4—444no—
513C22⋊C4—24no—
514C22⋊C4—24no—
515C22⋊C4—48no—
516C22⋊C4—48no—
517C22⋊C4—118no—
518C22⋊C4—1132no—
519C22⋊C4—228no—
520C22⋊C4—228no—
521C22⋊C4—2216no—
522C22⋊C4—444no—
523C42—24no—
524C42—24no—
525C42—118no—
526C42—228no—
527C42—224no—
528C42—224no—
529C42—448no—
530C11#3426511yescharacteristic, complemented, Sylow
531C23—22no—
532C23—22no—
533C23—216no—
534C23—24no—
535C23—24no—
536C23—28no—
537C23—28no—
538C23—416no—
539C23—48no—
540C23—416no—
541C23—48no—
542C23—114no—
543C23—222no—
544C23—222no—
545C23—224no—
546C23—224no—
547C23C22×C4×D1118yes—
548C23C22×C4×D1112yes—
549C23C2×D4×D1112yes—
550C23C2×#434112yes—
551C23C24×D1111yescharacteristic
552Q8—228no—
553D4—216no—
554D4—216no—
555D4—2216no—
556D4—228no—
557D4—4432no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—118no—
566C2×C4—114no—
567C2×C4—118no—
568C2×C4—114no—
569C2×C4—228no—
570C2×C4—222no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—224no—
574C2×C4—228no—
575C2×C4—222no—
576C2×C4—224no—
577C2×C4—2216no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—448no—
582C2×C4—4432no—
583C2×C4—444no—
584C2×C4—888no—
585C2×C4(C22⋊D11)⋊C4116yescomplemented
586C2×C4C22×C4×D1112yes—
587C2×C4C22×C4×D1112yes—
588C2×C4C2×D4×D1112yes—
589C2×C4C2×D4×D1112yes—
590C2×C4C2×#434112yes—
591C2×C4C2×#434112yes—
592C22—24no—
593C22—22no—
594C22—22no—
595C22—24no—
596C22—28no—
597C22—216no—
598C22—432no—
599C22—48no—
600C22—44no—
601C22—44no—
602C22—224no—
603C22—228no—
604C22—444no—
605C22—442no—
606C22—442no—
607C22C2×(C22⋊D11)⋊C414yes—
608C22C23×C4×D1111yescharacteristic
609C22C22×D4×D1111yescharacteristic
610C22C22×#434111yescharacteristic
611C22D11×H(5,𝔽2)12yes—
612C22#1062345512yes—
613C4—44no—
614C4—42no—
615C4—42no—
616C4—224no—
617C4—228no—
618C4—224no—
619C4—228no—
620C4—442no—
621C4C2×(C22⋊D11)⋊C414yes—
622C4C2×(C22⋊D11)⋊C414yes—
623C2—24no—
624C2—48no—
625C2—444no—
626C2C22×(C22⋊D11)⋊C411yescharacteristic
627C2#1308182012yes—
628C2#1308225011yescharacteristic
629C2#1308227211yescharacteristic
630C2#1308246712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2309C2
socle, cosocleC23×C11C25
prime radicalC2×#10623336C2
hypercenter#2309D11
hypocenterC11#34265
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2309

Complements

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

NH ≅ G/Ntype
2. C2×#10623054C2semidirect
3. C22×D4×Dic11C2semidirect
4. #13071686C2semidirect
5. #13071677C2semidirect
6. #13071659C2semidirect
7. #13071637C2semidirect
8. #13071271C2semidirect
9. #13071115C2semidirect
10. #13071104C2semidirect
11. #13071098C2semidirect
12. #13070972C2semidirect
13. C11×#2309C2semidirect
21. #10623336C4semidirect
32. C2×#66945C22semidirect
33. C2×C4⋊C4×D11C22semidirect
35. C2×(C22⋊D11)⋊C4C22semidirect
36. C2×C4×D44C22semidirect
37. C2×C4×Dic22C22semidirect
42. #10622601C22semidirect
43. C4⋊C4×Dic11C22semidirect
44. #10622587C22semidirect
45. #10622586C22semidirect
46. #10622586C22semidirect
49. #10622571C22semidirect
50. #10622570C22semidirect
51. #10622569C22semidirect
54. #10622559C22semidirect
55. #10622558C22semidirect
56. #10622557C22semidirect
58. C22⋊C4×Dic11C22semidirect
59. C4×(C2×D11)⋊C4C22semidirect
60. C4×C4⋊Dic11C22semidirect
61. C4×Dic11⋊C4C22semidirect
65. C22×D4×C11C2×C4semidirect
79. C2×#4339C2×C4semidirect
95. #67006C2×C4semidirect
100. #66993C2×C4semidirect
101. #66991C2×C4semidirect
102. #66989C2×C4semidirect
108. #66979C2×C4semidirect
109. C2×C4⋊Dic11D4semidirect
162. C2×C22⋊D11C22×C4semidirect
181. C2×D44C22×C4semidirect
186. C2×C4×D11C22×C4semidirect
189. C2×Dic22C22×C4semidirect
201. C22⋊Dic11C22×C4semidirect
205. C4⋊Dic11C22×C4semidirect
215. C4×Dic11C22×C4semidirect
224. #2309D11semidirect
259. C2×C4×C11C4×D4semidirect
379. C22×D4C4×D11semidirect
530. C11#34265semidirect
585. C2×C4(C22⋊D11)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#106233362
C2×#106230542
C22×D4×Dic112
#130716862
#130716772
#130716592
#130716372
#130712712
#130711152
#130711042
#130710982
#130709722
C11×#23092
#3426511