Finite Group Databasebeta

← #14675667

Subgroups — #14675667

Order 2816.

2590 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2C2×#10622825C211yesmaximal, characteristic, complemented
3C2×#10622600C212yesmaximal, complemented
4#13066863C212yesmaximal, complemented
5#13066855C212yesmaximal
6#13066854C212yesmaximal, complemented
7#13066849C212yesmaximal, complemented
8#13066845C212yesmaximal, complemented
9C22×C11×#117C211yesmaximal, characteristic, complemented
10C24×C4×C11C2211yescharacteristic
11C23×C22⋊D11C2211yescharacteristic
12C23×C4×D11C2211yescharacteristic
13C2×C11×#117—24no—
14C2×C11×#117—28no—
15C22×C11×C4⋊C4C2212yes—
16C22×C11×C22⋊C4C2212yes—
17C22×C42×C11C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C2×C4×C22⋊D11—24no—
21C2×C4×C22⋊D11—24no—
22C2×C4×C22⋊D11C418yescomplemented
23C22×(C2×D11)⋊C4C2214yes—
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×C4⋊Dic11C2212yes—
26C22×Dic11⋊C4C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28#10622825—24no—
29C2×C11⋊#95C2214yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2214yes—
32C2×C11⋊#95C2214yes—
33#10622600—28no—
34C25×C11C2311yescharacteristic
35C24×D11C2311yescharacteristic
36C23×C4×C11—24no—
37C23×C4×C11—24no—
38C23×C4×C11C2×C414yes—
39C23×C4×C11D414yes—
40C23×C4×C11D414yes—
41C23×C4×C11C2314yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11—22no—
45C22×C22⋊D11—22no—
46C22×C22⋊D11—24no—
47C22×C22⋊D11—24no—
48C22×C22⋊D11C2×C414yes—
49C23×Dic11C2314yes—
50C23×Dic11C2311yescharacteristic
51C23×Dic11C2311yescharacteristic
52C23×Dic11C2311yescharacteristic
53C22×C4×D11—22no—
54C22×C4×D11—22no—
55C22×C4×D11—24no—
56C22×C4×D11—24no—
57C22×C4×D11C2×C414yes—
58C11×#117—232no—
59C2×C11×C4⋊C4—24no—
60C2×C11×C4⋊C4—24no—
61C2×C11×C4⋊C4D418yescomplemented
62C2×C11×C22⋊C4—24no—
63C2×C11×C22⋊C4—28no—
64C2×C42×C11—28no—
65C2×C42×C11—24no—
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11—22no—
68C2×C22⋊Dic11—24no—
69C2×C22⋊Dic11—44no—
70C2×C22⋊Dic11C2×C414yes—
71C4×C22⋊D11—232no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—28no—
75C2×(C2×D11)⋊C4—28no—
76C2×(C2×D11)⋊C4—44no—
77C2×(C2×D11)⋊C4C2×C414yes—
78C2×C4⋊Dic11—24no—
79C2×C4⋊Dic11—24no—
80C2×C4⋊Dic11—24no—
81C2×Dic11⋊C4—22no—
82C2×Dic11⋊C4—22no—
83C2×Dic11⋊C4C2×C414yes—
84C2×C4×Dic11—22no—
85C2×C4×Dic11—22no—
86C2×C4×Dic11C2×C414yes—
87C11⋊#95—24no—
88C11⋊#95—28no—
89C11⋊#95—28no—
90C11⋊#95—44no—
91#13871—111nomaximal, Sylow
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—22no—
95C24×C11—22no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11C22×C412yes—
99C24×C11C2×D412yes—
100C24×C11C2×D412yes—
101C24×C11C2411yescharacteristic
102C23×D11—22no—
103C23×D11—21no—
104C23×D11—21no—
105C23×D11—22no—
106C23×D11—22no—
107C23×D11—22no—
108C23×D11—22no—
109C23×D11C22×C412yes—
110C23×D11#4114yes—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—216no—
114C22×C4×C11—28no—
115C22×C4×C11—216no—
116C22×C4×C11—28no—
117C22×C4×C11—24no—
118C22×C4×C11—24no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11C22⋊C4116yescomplemented
124C22×C4×C11C22×C412yes—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C2×D418yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D414yes—
132C22×C4×C11#4114yes—
133C2×C22⋊D11—216no—
134C2×C22⋊D11—216no—
135C2×C22⋊D11—28no—
136C2×C22⋊D11—28no—
137C2×C22⋊D11—28no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—22no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—22no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—22no—
156C22×Dic11C22×C412yes—
157C22×Dic11C22×C412yes—
158C22×Dic11C22×C412yes—
159C22×Dic11#4114yes—
160C2×C4×D11—28no—
161C2×C4×D11—216no—
162C2×C4×D11—44no—
163C2×C4×D11—48no—
164C2×C4×D11—44no—
165C11×C4⋊C4—216no—
166C11×C22⋊C4—216no—
167C42×C11—216no—
168C22⋊Dic11—28no—
169C22⋊Dic11—48no—
170(C2×D11)⋊C4—28no—
171(C2×D11)⋊C4—416no—
172C4⋊Dic11—48no—
173Dic11⋊C4—28no—
174C4×Dic11—28no—
175C22×C4×D4—111no—
176C22×#117D1111yescharacteristic, complemented
177C2×#380—111no—
178C2×#380—112no—
179#1440—112no—
180#1438—112no—
181#1437—112no—
182#1436—112no—
183C4⋊#95—112no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—24no—
187C23×C11—24no—
188C23×C11—22no—
189C23×C11—24no—
190C23×C11—22no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—24no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11C2×C22⋊C414yes—
205C23×C11C23×C411yescharacteristic
206C23×C11C22×D411yescharacteristic
207C23×C11C22×D411yescharacteristic
208C23×C11C22×D412yes—
209C23×C11C2×#4112yes—
210C23×C11C2×#4112yes—
211C23×C11C2×#4112yes—
212C23×C11H(5,𝔽2)12yes—
213C23×C112−1+412yes—
214C22×D11—22no—
215C22×D11—22no—
216C22×D11—24no—
217C22×D11—24no—
218C22×D11—24no—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11—24no—
222C22×D11—24no—
223C22×D11—24no—
224C22×D11—41no—
225C22×D11—42no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—42no—
230C22×D11—42no—
231C22×D11—42no—
232C22×D11—42no—
233C22×D11—42no—
234C22×D11#11714yescomplemented
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—232no—
240C2×C4×C11—28no—
241C2×C4×C11—28no—
242C2×C4×C11—28no—
243C2×C4×C11—44no—
244C2×C4×C11—44no—
245C2×C4×C11—44no—
246C2×C4×C11—44no—
247C2×C4×C11C2×C22⋊C414yes—
248C2×C4×C11C2×C22⋊C414yes—
249C2×C4×C11C4×D418yes—
250C2×C4×C11#12014yes—
251C2×C4×C11#12118yes—
252C2×C4×C11#12314yes—
253C22⋊D11—232no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—41no—
263C2×Dic11—42no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—42no—
268C2×Dic11—44no—
269C2×Dic11—44no—
270C2×Dic11—44no—
271C2×Dic11—44no—
272C2×Dic11—44no—
273C2×Dic11—44no—
274C2×Dic11—44no—
275C2×Dic11#11714yescomplemented
276C4×D11—416no—
277C23×D4—111no—
278C24×C4—111no—
279C24×C4C2×D1111yescharacteristic
280C2×C4×D4—118no—
281C2×C4×D4—224no—
282C2×C4×D4—224no—
283C2×#117—24no—
284C2×#117—28no—
285C22×C4⋊C4—111no—
286C22×C4⋊C4—112no—
287C22×C4⋊C4C2×D1112yes—
288C22×C22⋊C4—111no—
289C22×C22⋊C4—111no—
290C22×C22⋊C4—114no—
291C22×C22⋊C4—112no—
292C22×C22⋊C4C2×D1112yes—
293C22×C42—111no—
294C22×C42C2×D1112yes—
295#380—224no—
296#380—228no—
297C2×#95—114no—
298C2×#95—112no—
299C2×#95—114no—
300C2×#95—114no—
301C22×C11—24no—
302C22×C11—24no—
303C22×C11—24no—
304C22×C11—44no—
305C22×C11—44no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—44no—
309C22×C11—44no—
310C22×C11C22×C22⋊C411yescharacteristic
311C22×C11C2×#11711yescharacteristic
312C22×C11C2×#11711yescharacteristic
313C22×C11C2×C4×D412yes—
314C22×C11#52012yes—
315C22×C11C2×#12011yescharacteristic
316C22×C11C2×#12112yes—
317C22×C11C2×#12311yescharacteristic
318C22×C11#52512yes—
319C22×C11#52512yes—
320C22×C11#53511yescharacteristic
321C22×C11#53611yescharacteristic
322C22×C11#53712yes—
323C22×C11#54612yes—
324C22×C11#54712yes—
325C22×C11#54812yes—
326C22×C11#55012yes—
327C22×C11#55212yes—
328C22×C11#55312yes—
329C22×C11#55512yes—
330C22×C11#55612yes—
331C2×D11—28no—
332C2×D11—24no—
333C2×D11—42no—
334C2×D11—44no—
335C2×D11—44no—
336C2×D11—44no—
337C2×D11—44no—
338C2×D11—44no—
339C2×D11—42no—
340C4×C11—24no—
341C4×C11—48no—
342C4×C11#38618yes—
343Dic11—24no—
344Dic11—42no—
345Dic11—42no—
346Dic11—84no—
347C25—111no—
348C25C22×D1111yescharacteristic
349C22×D4—114no—
350C22×D4—224no—
351C22×D4—224no—
352C22×D4—222no—
353C22×D4—222no—
354C23×C4—24no—
355C23×C4—24no—
356C23×C4—111no—
357C23×C4—111no—
358C23×C4—111no—
359C23×C4—114no—
360C23×C4—114no—
361C23×C4—222no—
362C23×C4—224no—
363C23×C4—222no—
364C23×C4—224no—
365C23×C4C4×D1114yes—
366C23×C4D4414yes—
367C23×C4C22⋊D1114yes—
368C23×C4C22×D1114yes—
369C23×C4C22×D1111yescharacteristic
370C23×C4C22×D1111yescharacteristic
371C4×D4—2232no—
372#117—232no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—114no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—224no—
379C2×C4⋊C4—224no—
380C2×C4⋊C4—224no—
381C2×C4⋊C4C22⋊D1118yescomplemented
382C2×C22⋊C4—24no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—114no—
385C2×C22⋊C4—114no—
386C2×C22⋊C4—222no—
387C2×C22⋊C4—222no—
388C2×C22⋊C4—222no—
389C2×C22⋊C4—222no—
390C2×C22⋊C4—228no—
391C2×C22⋊C4—224no—
392C2×C22⋊C4—228no—
393C2×C22⋊C4—444no—
394C2×C22⋊C4—444no—
395C2×C42—28no—
396C2×C42—24no—
397C2×C42—114no—
398C2×C42—222no—
399C2×C42—222no—
400#95—228no—
401#95—224no—
402#95—228no—
403#95—444no—
404C2×C11—44no—
405C2×C11#228011yescharacteristic
406C2×C11C2×#38611yescharacteristic
407C2×C11#231111yescharacteristic
408C2×C11#235212yes—
409C2×C11#235412yes—
410C2×C11#240712yes—
411C2×C11#241412yes—
412C2×C11#241512yes—
413C2×C11#248512yes—
414D11—44no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—112no—
422C24—114no—
423C24—221no—
424C24—222no—
425C24—222no—
426C24—222no—
427C24—222no—
428C24—222no—
429C24—221no—
430C24C2×C4×D1112yes—
431C24C2×D4412yes—
432C24C2×C22⋊D1112yes—
433C24C23×D1111yescharacteristic
434C2×D4—228no—
435C2×D4—228no—
436C2×D4—2216no—
437C2×D4—2216no—
438C2×D4—228no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—216no—
442C22×C4—28no—
443C22×C4—216no—
444C22×C4—28no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—112no—
452C22×C4—114no—
453C22×C4—112no—
454C22×C4—112no—
455C22×C4—221no—
456C22×C4—222no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—228no—
467C22×C4—2216no—
468C22×C4—224no—
469C22×C4—224no—
470C22×C4—224no—
471C22×C4—224no—
472C22×C4—224no—
473C22×C4—224no—
474C22×C4—224no—
475C22×C4—444no—
476C22×C4—448no—
477C22×C4—444no—
478C22×C4(C2×D11)⋊C4116yescomplemented
479C22×C4C2×C4×D1112yes—
480C22×C4C2×C4×D1112yes—
481C22×C4C2×D4412yes—
482C22×C4C2×D4412yes—
483C22×C4#433914yes—
484C22×C4C2×C22⋊D1118yes—
485C22×C4C2×C22⋊D1112yes—
486C22×C4C2×C22⋊D1112yes—
487C22×C4C2×C22⋊D1114yes—
488C4⋊C4—216no—
489C4⋊C4—228no—
490C4⋊C4—448no—
491C22⋊C4—216no—
492C22⋊C4—228no—
493C22⋊C4—228no—
494C22⋊C4—4416no—
495C22⋊C4—448no—
496C42—216no—
497C42—228no—
498C11#1387111yescharacteristic, complemented, Sylow
499C23—22no—
500C23—22no—
501C23—24no—
502C23—24no—
503C23—22no—
504C23—22no—
505C23—24no—
506C23—22no—
507C23—24no—
508C23—24no—
509C23—24no—
510C23—22no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—114no—
520C23—222no—
521C23—224no—
522C23—224no—
523C23—224no—
524C23—224no—
525C23—222no—
526C23—224no—
527C23—224no—
528C23—224no—
529C23—224no—
530C23—441no—
531C23—441no—
532C23—442no—
533C23—442no—
534C23—441no—
535C23—442no—
536C23—442no—
537C23—442no—
538C23—442no—
539C23—441no—
540C23C2×(C2×D11)⋊C414yes—
541C23C22×C4×D1111yescharacteristic
542C23C22×D4411yescharacteristic
543C23C2×#433912yes—
544C23#41×D1112yes—
545C23#41×D1112yes—
546C23#6704212yes—
547C23#6704312yes—
548C23C22×C22⋊D1111yescharacteristic
549C23C22×C22⋊D1112yes—
550D4—2232no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—22no—
555C2×C4—232no—
556C2×C4—28no—
557C2×C4—28no—
558C2×C4—28no—
559C2×C4—44no—
560C2×C4—44no—
561C2×C4—44no—
562C2×C4—44no—
563C2×C4—114no—
564C2×C4—222no—
565C2×C4—224no—
566C2×C4—222no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—224no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—442no—
576C2×C4—442no—
577C2×C4—441no—
578C2×C4—4416no—
579C2×C4—444no—
580C2×C4—444no—
581C2×C4—444no—
582C2×C4—444no—
583C2×C4—444no—
584C2×C4—444no—
585C2×C4—444no—
586C2×C4C2×(C2×D11)⋊C414yes—
587C2×C4C2×(C2×D11)⋊C414yes—
588C2×C4C4×C22⋊D1118yes—
589C2×C4#6698214yes—
590C2×C4#6698318yes—
591C2×C4#6700614yes—
592C22—24no—
593C22—24no—
594C22—24no—
595C22—44no—
596C22—44no—
597C22—44no—
598C22—44no—
599C22—44no—
600C22—44no—
601C22—224no—
602C22—228no—
603C22—444no—
604C22—444no—
605C22—442no—
606C22—444no—
607C22—444no—
608C22—442no—
609C22—444no—
610C22D11×#11711yescharacteristic
611C22D11×#11711yescharacteristic
612C22#1062305412yes—
613C22#1062305512yes—
614C22#1062305611yescharacteristic
615C22#1062305711yescharacteristic
616C22#1062306012yes—
617C22#1062306112yes—
618C22#1062306312yes—
619C22#1062306412yes—
620C22C22×(C2×D11)⋊C411yescharacteristic
621C22C2×C4×C22⋊D1112yes—
622C22C2×#6698211yescharacteristic
623C22C2×#6698312yes—
624C22#1062335512yes—
625C22#1062335912yes—
626C22#1062336012yes—
627C22#1062336212yes—
628C22#1062336412yes—
629C22#1062336512yes—
630C22C2×#6700611yescharacteristic
631C4—24no—
632C4—48no—
633C4—224no—
634C4—442no—
635C4—442no—
636C4—884no—
637C4#1062282618yes—
638C2—44no—
639C2—444no—
640C2#1307099511yescharacteristic
641C2C2×#1062282611yescharacteristic
642C2#1307120411yescharacteristic
643C2#1307154612yes—
644C2#1307156612yes—
645C2#1307195512yes—
646C2#1307202812yes—
647C2#1307203912yes—
648C2#1307290712yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×#117C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22×#117D11
hypocenterC11#13871
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
2. C2×#10622825C2semidirect
3. C2×#10622600C2semidirect
4. #13066863C2semidirect
6. #13066854C2semidirect
7. #13066849C2semidirect
8. #13066845C2semidirect
9. C22×C11×#117C2semidirect
22. C2×C4×C22⋊D11C4semidirect
61. C2×C11×C4⋊C4D4semidirect
123. C22×C4×C11C22⋊C4semidirect
176. C22×#117D11semidirect
234. C22×D11#117semidirect
275. C2×Dic11#117semidirect
381. C2×C4⋊C4C22⋊D11semidirect
478. C22×C4(C2×D11)⋊C4semidirect
498. C11#13871semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C2×#106228252
C2×#106226002
#130668632
#130668552
#130668542
#130668492
#130668452
C22×C11×#1172
#1387111