Finite Group Databasebeta

← #14676424

Subgroups — #14676424

Order 2816.

2006 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66925C211yesmaximal, characteristic
2C2×#10622585C212yesmaximal, complemented
3C2×#10622280C211yesmaximal, characteristic
4C2×#10622279C211yesmaximal, characteristic
5#13066860C212yesmaximal
6#13066858C212yesmaximal
7Dic11⋊#95C212yesmaximal, complemented
8Dic11⋊#95C211yesmaximal, characteristic, complemented
9#13066843C211yesmaximal, characteristic, complemented
10#13066842C211yesmaximal, characteristic, complemented
11C11×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C11×C4⋊C4C2212yes—
14C22×C42×C11C2211yescharacteristic
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2212yes—
19C22×Dic11⋊C4C2212yes—
20C22×Dic11⋊C4C2212yes—
21C22×Dic11⋊C4C2211yescharacteristic
22C22×Dic11⋊C4C2211yescharacteristic
23C22×C4×Dic11C2212yes—
24C22×C4×Dic11C2211yescharacteristic
25C2×#66925—28no—
26C2×#66925C418yescomplemented
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37#10622585—28no—
38#10622280—24no—
39#10622279—24no—
40C24×D11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C22×C4×D11—24no—
52C22×C4×D11—24no—
53C22×C4×D11C2×C414yes—
54C22×C4×D11D414yes—
55C22×C4×D11Q814yes—
56C2×C11×C4⋊C4—24no—
57C2×C11×C4⋊C4—24no—
58C2×C11×C4⋊C4—42no—
59C2×C42×C11—24no—
60C2×C42×C11C2×C414yes—
61C2×(C2×D11)⋊C4—24no—
62C2×(C2×D11)⋊C4—24no—
63C2×(C2×D11)⋊C4—24no—
64C2×(C2×D11)⋊C4—24no—
65C2×(C2×D11)⋊C4—24no—
66C2×(C2×D11)⋊C4—24no—
67C2×(C2×D11)⋊C4—42no—
68C2×(C2×D11)⋊C4—42no—
69C2×(C2×D11)⋊C4C2×C414yes—
70C2×(C2×D11)⋊C4C2×C414yes—
71C2×Dic11⋊C4—24no—
72C2×Dic11⋊C4—24no—
73C2×Dic11⋊C4—24no—
74C2×Dic11⋊C4—24no—
75C2×Dic11⋊C4—24no—
76C2×Dic11⋊C4—24no—
77C2×Dic11⋊C4—42no—
78C2×Dic11⋊C4C2×C414yes—
79C2×Dic11⋊C4C2×C414yes—
80C2×Dic11⋊C4D418yes—
81C2×C4×Dic11—24no—
82C2×C4×Dic11—24no—
83C2×C4×Dic11—24no—
84C2×C4×Dic11—24no—
85C2×C4×Dic11C2×C414yes—
86#66925—232no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95—42no—
90C11⋊#95—22no—
91C11⋊#95—22no—
92C11⋊#95—24no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96C11⋊#95—42no—
97#13951—111nomaximal, Sylow
98C24×C11C2411yescharacteristic
99C23×D11—22no—
100C23×D11—22no—
101C23×D11—22no—
102C23×D11—22no—
103C23×D11—21no—
104C23×D11—21no—
105C23×D11—21no—
106C23×D11—21no—
107C23×D11C22×C412yes—
108C23×D11C2×D412yes—
109C23×D11C2×Q812yes—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C2×D414yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×Q812yes—
138C22×C4×C11#4114yes—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—21no—
156C22×Dic11—22no—
157C22×Dic11—21no—
158C22×Dic11—22no—
159C22×Dic11C22×C412yes—
160C22×Dic11C22×C412yes—
161C22×Dic11C22×C412yes—
162C22×Dic11C2×D414yes—
163C22×Dic11C2×D414yes—
164C22×Dic11C2×D412yes—
165C22×Dic11C2×Q812yes—
166C22×Dic11#4114yes—
167C22×Dic11#4114yes—
168C2×C4×D11—28no—
169C2×C4×D11—28no—
170C2×C4×D11—216no—
171C2×C4×D11—216no—
172C2×C4×D11C4⋊C4116yescomplemented
173C11×C4⋊C4—48no—
174C42×C11—28no—
175(C2×D11)⋊C4—216no—
176(C2×D11)⋊C4—28no—
177(C2×D11)⋊C4—28no—
178(C2×D11)⋊C4—48no—
179Dic11⋊C4—28no—
180Dic11⋊C4—48no—
181Dic11⋊C4—48no—
182Dic11⋊C4C22⋊C4116yescomplemented
183C4×Dic11—28no—
184C4×Dic11—48no—
185C22×#117—111no—
186C2×#389—112no—
187C2×#380—111no—
188C2×C4×C22⋊C4—111no—
189#1439—112no—
190#1439—112no—
191C4⋊#95—112no—
192C4⋊#95—111no—
193C4⋊#95D1111yescharacteristic, complemented
194#1434—111no—
195#1434—111no—
196C23×C11C23×C411yescharacteristic
197C23×C11C22×D412yes—
198C23×C11C22×D411yescharacteristic
199C23×C11C22×Q811yescharacteristic
200C23×C11C2×#4112yes—
201C23×C11C2×#4112yes—
202C23×C11C2×#4112yes—
203C23×C11H(5,𝔽2)11yescharacteristic
204C23×C11H(5,𝔽2)11yescharacteristic
205C23×C112−1+411yescharacteristic
206C23×C112−1+411yescharacteristic
207C22×D11—22no—
208C22×D11—22no—
209C22×D11—22no—
210C22×D11—22no—
211C22×D11—22no—
212C22×D11—22no—
213C22×D11—24no—
214C22×D11—24no—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—42no—
227C22×D11—42no—
228C22×D11—42no—
229C22×D11C2×C4⋊C414yes—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11C2×C22⋊C414yes—
258C2×C4×C11C2×C4⋊C414yes—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11C2×C22⋊C414yes—
283C2×Dic11C2×C22⋊C414yes—
284C2×Dic11C2×C4⋊C414yes—
285C2×Dic11#11714yes—
286C2×Dic11#12118yes—
287C2×Dic11C22⋊Q818yes—
288C4×D11—232no—
289C24×C4—111no—
290C2×#117—118no—
291C2×#117—228no—
292C22×C4⋊C4—111no—
293C22×C4⋊C4—111no—
294C22×C4⋊C4—112no—
295C22×C4⋊C4—112no—
296C22×C4⋊C4C2×D1112yes—
297C22×C22⋊C4—111no—
298C22×C22⋊C4—111no—
299C22×C22⋊C4—112no—
300C22×C22⋊C4—112no—
301C22×C42—111no—
302C22×C42—112no—
303C22×C42C2×D1111yescharacteristic
304#389—228no—
305#380—224no—
306C4×C22⋊C4—224no—
307C2×#95—111no—
308C2×#95—112no—
309C2×#95—112no—
310C2×#95—111no—
311C2×#95—112no—
312C2×#95—112no—
313C2×#95—112no—
314C2×#95C2×D1111yescharacteristic
315C2×#95C2×D1111yescharacteristic
316C2×#95C2×D1112yes—
317C22×C11C22×C22⋊C411yescharacteristic
318C22×C11C22×C4⋊C411yescharacteristic
319C22×C11C2×#11711yescharacteristic
320C22×C11C4×#4111yescharacteristic
321C22×C11C4×#4111yescharacteristic
322C22×C11#52011yescharacteristic
323C22×C11#52011yescharacteristic
324C22×C11C2×#12112yes—
325C22×C11C2×C22⋊Q812yes—
326C22×C11#52512yes—
327C22×C11#53312yes—
328C22×C11#53511yescharacteristic
329C22×C11#53611yescharacteristic
330C22×C11#54411yescharacteristic
331C22×C11#54411yescharacteristic
332C22×C11#54612yes—
333C22×C11#54712yes—
334C22×C11#54812yes—
335C22×C11#55012yes—
336C22×C11#55212yes—
337C22×C11#55312yes—
338C22×C11#55512yes—
339C22×C11#55612yes—
340C2×D11—24no—
341C2×D11—24no—
342C2×D11—24no—
343C2×D11—42no—
344C2×D11—42no—
345C2×D11—42no—
346C2×D11—42no—
347C2×D11—44no—
348C2×D11—44no—
349C2×D11—44no—
350C2×D11—44no—
351C4×C11—24no—
352C4×C11—24no—
353C4×C11—42no—
354C4×C11—44no—
355C4×C11—82no—
356Dic11—24no—
357Dic11—42no—
358Dic11—44no—
359Dic11—82no—
360Dic11#38018yes—
361C25—111no—
362C23×C4—111no—
363C23×C4—111no—
364C23×C4—114no—
365C23×C4—114no—
366C23×C4—114no—
367C23×C4—111no—
368C23×C4—112no—
369C23×C4—112no—
370C23×C4—224no—
371C23×C4—224no—
372C23×C4C22×D1112yes—
373C23×C4C22×D1111yescharacteristic
374C23×C4C22×D1112yes—
375C23×C4C22×D1111yescharacteristic
376C23×C4C22×D1111yescharacteristic
377#117—2232no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—42no—
381C2×C4⋊C4—114no—
382C2×C4⋊C4—118no—
383C2×C4⋊C4—114no—
384C2×C4⋊C4—224no—
385C2×C4⋊C4—224no—
386C2×C4⋊C4—224no—
387C2×C4⋊C4—224no—
388C2×C4⋊C4—224no—
389C2×C4⋊C4—224no—
390C2×C4⋊C4—442no—
391C2×C22⋊C4—114no—
392C2×C22⋊C4—114no—
393C2×C22⋊C4—224no—
394C2×C22⋊C4—224no—
395C2×C22⋊C4—224no—
396C2×C22⋊C4—224no—
397C2×C22⋊C4—224no—
398C2×C22⋊C4—224no—
399C2×C22⋊C4—442no—
400C2×C22⋊C4—442no—
401C2×C42—24no—
402C2×C42—114no—
403C2×C42—224no—
404C2×C42—224no—
405C2×C42—224no—
406C2×C42—224no—
407C2×C42C4×D1114yes—
408#95—22no—
409#95—22no—
410#95—42no—
411#95—224no—
412#95—224no—
413#95—224no—
414#95—222no—
415#95—222no—
416#95—224no—
417#95—442no—
418C2×C11C2×#38011yescharacteristic
419C2×C11#229611yescharacteristic
420C2×C11#231711yescharacteristic
421C2×C11#233911yescharacteristic
422C2×C11#234111yescharacteristic
423C2×C11#234611yescharacteristic
424C2×C11#234711yescharacteristic
425C2×C11#241412yes—
426C2×C11#241512yes—
427C2×C11#243912yes—
428C2×C11#244112yes—
429D11—44no—
430C24—112no—
431C24—112no—
432C24—112no—
433C24—222no—
434C24—222no—
435C24—221no—
436C24—221no—
437C24—221no—
438C24—221no—
439C24—222no—
440C24—222no—
441C24C23×D1111yescharacteristic
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—112no—
465C22×C4—112no—
466C22×C4—114no—
467C22×C4—112no—
468C22×C4—114no—
469C22×C4—112no—
470C22×C4—114no—
471C22×C4—1116no—
472C22×C4—112no—
473C22×C4—114no—
474C22×C4—228no—
475C22×C4—228no—
476C22×C4—2216no—
477C22×C4—2216no—
478C22×C4—222no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4C2×C4×D1112yes—
499C22×C4C2×C4×D1112yes—
500C22×C4C2×C4×D1112yes—
501C22×C4#433914yes—
502C22×C4D4×D1114yes—
503C22×C4D4×D1112yes—
504C22×C4Q8×D1112yes—
505C4⋊C4—48no—
506C4⋊C4—1116no—
507C4⋊C4—228no—
508C4⋊C4—448no—
509C4⋊C4—448no—
510C22⋊C4—228no—
511C22⋊C4—2216no—
512C22⋊C4—228no—
513C22⋊C4—448no—
514C42—28no—
515C42—228no—
516C42—448no—
517C11#1395111yescharacteristic, complemented, Sylow
518C23—114no—
519C23—222no—
520C23—222no—
521C23—222no—
522C23—222no—
523C23—222no—
524C23—222no—
525C23—222no—
526C23—222no—
527C23—222no—
528C23—222no—
529C23—224no—
530C23—224no—
531C23—224no—
532C23—224no—
533C23—442no—
534C23—442no—
535C23—442no—
536C23—442no—
537C23—442no—
538C23—442no—
539C23—442no—
540C23—442no—
541C23C22×C4×D1111yescharacteristic
542C23C2×#433912yes—
543C23C2×D4×D1111yescharacteristic
544C23C2×D4×D1112yes—
545C23#6703711yescharacteristic
546C23#6703711yescharacteristic
547C23C2×Q8×D1111yescharacteristic
548C23#6704011yescharacteristic
549C23#6704011yescharacteristic
550C23#41×D1112yes—
551C23#41×D1112yes—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—114no—
580C2×C4—114no—
581C2×C4—114no—
582C2×C4—118no—
583C2×C4—118no—
584C2×C4—114no—
585C2×C4—2232no—
586C2×C4—222no—
587C2×C4—224no—
588C2×C4—222no—
589C2×C4—224no—
590C2×C4—222no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—224no—
594C2×C4—224no—
595C2×C4—224no—
596C2×C4—442no—
597C2×C4—442no—
598C2×C4—442no—
599C2×C4—442no—
600C2×C4—442no—
601C2×C4—442no—
602C2×C4—442no—
603C2×C4—442no—
604C2×C4—442no—
605C2×C4—442no—
606C2×C4—442no—
607C2×C4—442no—
608C2×C4—442no—
609C2×C4C22⋊C4×D1114yes—
610C2×C4C4⋊C4×D1114yes—
611C22—224no—
612C22—224no—
613C22—224no—
614C22—442no—
615C22—442no—
616C22—442no—
617C22—442no—
618C22—444no—
619C22—444no—
620C22—444no—
621C22—444no—
622C22C4×#433911yescharacteristic
623C22C2×C22⋊C4×D1111yescharacteristic
624C22#1062302112yes—
625C22C2×C4⋊C4×D1111yescharacteristic
626C22#1062303511yescharacteristic
627C22#1062303511yescharacteristic
628C22#1062303812yes—
629C22D11×#11711yescharacteristic
630C22#1062305311yescharacteristic
631C22#1062307112yes—
632C22#1062307812yes—
633C22#1062309912yes—
634C22#1062310912yes—
635C22#1062313012yes—
636C22D11×#12112yes—
637C22D11×C22⋊Q812yes—
638C22#1062316412yes—
639C22#1062320112yes—
640C22#1062322412yes—
641C22#1062324611yescharacteristic
642C22#1062325511yescharacteristic
643C22#1062326011yescharacteristic
644C22#1062326011yescharacteristic
645C4—24no—
646C4—24no—
647C4—42no—
648C4—44no—
649C4—82no—
650C4—118no—
651C4—224no—
652C4—442no—
653C4—444no—
654C4—882no—
655C2—444no—
656C2D11×#38011yescharacteristic
657C2#1307109611yescharacteristic
658C2#1307123711yescharacteristic
659C2#1307144311yescharacteristic
660C2#1307145311yescharacteristic
661C2#1307149611yescharacteristic
662C2#1307151011yescharacteristic
663C2#1307203112yes—
664C2#1307204412yes—
665C2#1307230412yes—
666C2#1307232612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC4⋊#95D11
hypocenterC11#13951
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622585C2semidirect
7. Dic11⋊#95C2semidirect
8. Dic11⋊#95C2semidirect
9. #13066843C2semidirect
10. #13066842C2semidirect
11. C11×C4⋊#95C2semidirect
26. C2×#66925C4semidirect
172. C2×C4×D11C4⋊C4semidirect
182. Dic11⋊C4C22⋊C4semidirect
193. C4⋊#95D11semidirect
517. C11#13951semidirect

Maximal subgroups

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

subgroupindex
C22×#669252
C2×#106225852
C2×#106222802
C2×#106222792
#130668602
#130668582
Dic11⋊#952
#130668432
#130668422
C11×C4⋊#952
#1395111