Finite Group Databasebeta

← #14676385

Subgroups — #14676385

Order 2816.

1486 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13066878C212yesmaximal, complemented
2#13066865C212yesmaximal
3#13066853C212yesmaximal
4#13066843C211yesmaximal, characteristic, complemented
5#13066843C211yesmaximal, characteristic, complemented
6#13066843C211yesmaximal, characteristic, complemented
7#13066841C212yesmaximal, complemented
8#13066839C211yesmaximal, characteristic
9#13066839C211yesmaximal, characteristic
10C4×C11⋊#95C211yesmaximal, characteristic, complemented
11C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C4×Dic11C2212yes—
20C4×C11×C22⋊C4C418yescomplemented
21C2×C11×#95C2211yescharacteristic
22C2×C11×#95C2211yescharacteristic
23C2×C11⋊#95C2211yescharacteristic
24C2×C11⋊#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C25×C11C2311yescharacteristic
37C23×C4×C11—22no—
38C23×C4×C11—22no—
39C23×C4×C11—42no—
40C23×C4×C11—42no—
41C23×C4×C11C2×C414yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2312yes—
50C23×Dic11C2312yes—
51C23×Dic11C2312yes—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4—22no—
56C2×C11×C22⋊C4C2×C414yes—
57C2×C11×C22⋊C4C2×C414yes—
58C2×C42×C11—42no—
59C2×C42×C11—42no—
60C2×C42×C11C2×C414yes—
61C2×C42×C11C2×C414yes—
62C2×C22⋊Dic11—24no—
63C2×C22⋊Dic11—24no—
64C2×C22⋊Dic11—24no—
65C2×C22⋊Dic11—24no—
66C2×C22⋊Dic11—42no—
67C2×C22⋊Dic11—42no—
68C2×C4×Dic11—24no—
69C2×C4×Dic11—24no—
70C2×C4×Dic11—42no—
71C11×#95C2×C414yes—
72C11×#95C2×C414yes—
73C11⋊#95—22no—
74C11⋊#95—22no—
75C11⋊#95—24no—
76C11⋊#95—22no—
77C11⋊#95—22no—
78C11⋊#95—24no—
79C11⋊#95—24no—
80C11⋊#95—24no—
81C11⋊#95—42no—
82C11⋊#95—42no—
83C11⋊#95—42no—
84C11⋊#95—42no—
85C11⋊#95—42no—
86#13947—111nomaximal, Sylow
87C24×C11—22no—
88C24×C11—22no—
89C24×C11—21no—
90C24×C11—21no—
91C24×C11—21no—
92C24×C11—21no—
93C24×C11—22no—
94C24×C11—22no—
95C24×C11C22×C412yes—
96C24×C11#4112yes—
97C24×C11#4112yes—
98C24×C11C2411yescharacteristic
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—28no—
120C22×C4×C11—44no—
121C22×C4×C11—44no—
122C22×C4×C11—48no—
123C22×C4×C11—48no—
124C22×C4×C11C22×C412yes—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C22×C412yes—
129C22×C4×C11C22×C412yes—
130C22×C4×C11#4112yes—
131C22×C4×C11#4112yes—
132C22×C4×C11#4112yes—
133C22×C4×C11#4112yes—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
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—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11#4114yes—
161C22×Dic11#4114yes—
162C11×C22⋊C4—28no—
163C11×C22⋊C4—28no—
164C42×C11—44no—
165C42×C11—44no—
166C22⋊Dic11—48no—
167C22⋊Dic11—48no—
168C4×Dic11—48no—
169C2×C4×C22⋊C4D1111yescharacteristic
170#1443—112no—
171#1440—112no—
172#1437—112no—
173#1434—111no—
174#1434—111no—
175#1434—111no—
176#1434—112no—
177C22⋊#95—111no—
178C22⋊#95—111no—
179C4×#95—111no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—24no—
191C23×C11—24no—
192C23×C11—24no—
193C23×C11—24no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11—42no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11#11714yes—
203C23×C11C23×C411yescharacteristic
204C23×C11C2×#4111yescharacteristic
205C23×C11C2×#4111yescharacteristic
206C23×C11C2×#4111yescharacteristic
207C23×C11C2×#4111yescharacteristic
208C23×C11C2×#4111yescharacteristic
209C23×C11C2×#4111yescharacteristic
210C23×C11C2×#4112yes—
211C23×C11C2×#4112yes—
212C23×C11H(5,𝔽2)12yes—
213C23×C11H(5,𝔽2)12yes—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—416no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11#11714yes—
244C2×C4×C11#11714yes—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C24×C4C2×D1111yescharacteristic
274C22×C22⋊C4—112no—
275C22×C22⋊C4—112no—
276C22×C22⋊C4C2×D1111yescharacteristic
277C22×C22⋊C4C2×D1111yescharacteristic
278C22×C42—112no—
279C22×C42C2×D1111yescharacteristic
280C22×C42C2×D1111yescharacteristic
281C4×C22⋊C4Dic1118yescomplemented
282C2×#95—111no—
283C2×#95—111no—
284C2×#95—112no—
285C2×#95—111no—
286C2×#95—111no—
287C2×#95—112no—
288C2×#95—112no—
289C2×#95—112no—
290C2×#95—112no—
291C2×#95—112no—
292C2×#95—112no—
293C2×#95—112no—
294C2×#95—112no—
295C2×#95C2×D1111yescharacteristic
296C2×#95C2×D1111yescharacteristic
297C22×C11—24no—
298C22×C11—24no—
299C22×C11—24no—
300C22×C11—42no—
301C22×C11—44no—
302C22×C11—44no—
303C22×C11—44no—
304C22×C11—44no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11C2×#11711yescharacteristic
309C22×C11C2×#11711yescharacteristic
310C22×C11C2×#11711yescharacteristic
311C22×C11C4×#4111yescharacteristic
312C22×C11C4×#4111yescharacteristic
313C22×C11#51811yescharacteristic
314C22×C11#51811yescharacteristic
315C22×C11#52911yescharacteristic
316C22×C11#52911yescharacteristic
317C22×C11#52911yescharacteristic
318C22×C11#52911yescharacteristic
319C22×C11#52912yes—
320C22×C11#52912yes—
321C22×C11#53812yes—
322C22×C11#53812yes—
323C22×C11#55112yes—
324C22×C11#55112yes—
325C22×C11#55112yes—
326C22×C11#55312yes—
327C22×C11#55312yes—
328C22×C11#55312yes—
329C22×C11#55312yes—
330C22×C11#55912yes—
331C4×C11—24no—
332C4×C11—24no—
333C4×C11—42no—
334C4×C11—42no—
335C4×C11—42no—
336C4×C11—42no—
337Dic11—44no—
338Dic11—44no—
339Dic11—82no—
340Dic11—82no—
341C25C22×D1111yescharacteristic
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—42no—
345C23×C4—42no—
346C23×C4—112no—
347C23×C4—112no—
348C23×C4—112no—
349C23×C4—112no—
350C23×C4C2×Dic1114yes—
351C23×C4C22×D1111yescharacteristic
352C23×C4C22×D1111yescharacteristic
353C23×C4C22×D1111yescharacteristic
354C23×C4C22×D1111yescharacteristic
355C23×C4C22×D1111yescharacteristic
356C23×C4C22×D1111yescharacteristic
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—224no—
362C2×C22⋊C4—224no—
363C2×C22⋊C4—224no—
364C2×C22⋊C4—224no—
365C2×C22⋊C4—442no—
366C2×C22⋊C4—442no—
367C2×C22⋊C4C2×Dic1114yes—
368C2×C22⋊C4C2×Dic1114yes—
369C2×C42—42no—
370C2×C42—42no—
371C2×C42—224no—
372C2×C42—224no—
373C2×C42—442no—
374C2×C42C2×Dic1114yes—
375C2×C42C2×Dic1114yes—
376#95—224no—
377#95—224no—
378#95—224no—
379#95—222no—
380#95—222no—
381#95—224no—
382#95—222no—
383#95—222no—
384#95—442no—
385#95—442no—
386#95—442no—
387#95—442no—
388#95—442no—
389#95C2×Dic1114yes—
390#95C2×Dic1114yes—
391C2×C11—44no—
392C2×C11#228311yescharacteristic
393C2×C11#229811yescharacteristic
394C2×C11#231211yescharacteristic
395C2×C11#235311yescharacteristic
396C2×C11#235311yescharacteristic
397C2×C11#235311yescharacteristic
398C2×C11#235711yescharacteristic
399C2×C11#257612yes—
400C2×C11#257812yes—
401C2×C11#259512yes—
402C2×C11#259712yes—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24#433912yes—
412C24#433912yes—
413C24C22×Dic1112yes—
414C24C23×D1111yescharacteristic
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—28no—
436C22×C4—44no—
437C22×C4—44no—
438C22×C4—48no—
439C22×C4—48no—
440C22×C4—114no—
441C22×C4—114no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4#433912yes—
469C22×C4#433912yes—
470C22×C4#433912yes—
471C22×C4#433912yes—
472C22×C4C22×Dic1112yes—
473C22×C4C22×Dic1112yes—
474C22×C4C22×Dic1112yes—
475C22×C4C22×Dic1112yes—
476C22×C4C22×Dic1112yes—
477C22×C4C22×Dic1112yes—
478C22⋊C4—28no—
479C22⋊C4—28no—
480C22⋊C4—448no—
481C22⋊C4—448no—
482C42—44no—
483C42—44no—
484C42—448no—
485C11#1394711yescharacteristic, complemented, Sylow
486C23—22no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—24no—
494C23—22no—
495C23—22no—
496C23—24no—
497C23—24no—
498C23—22no—
499C23—22no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23#6697914yes—
509C23C2×#433911yescharacteristic
510C23C2×#433911yescharacteristic
511C23C2×#433911yescharacteristic
512C23C2×#433911yescharacteristic
513C23C2×#433911yescharacteristic
514C23C2×#433911yescharacteristic
515C23#6703712yes—
516C23#6703712yes—
517C23#41×D1112yes—
518C23#41×D1112yes—
519C23C23×Dic1111yescharacteristic
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—416no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—224no—
550C2×C4—224no—
551C2×C4—224no—
552C2×C4—224no—
553C2×C4—224no—
554C2×C4—224no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—442no—
559C2×C4—442no—
560C2×C4—442no—
561C2×C4—442no—
562C2×C4—442no—
563C2×C4—442no—
564C2×C4—442no—
565C2×C4—442no—
566C2×C4—442no—
567C2×C4—442no—
568C2×C4—442no—
569C2×C4—442no—
570C2×C4—442no—
571C2×C4—442no—
572C2×C4—442no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—442no—
576C2×C4—442no—
577C2×C4#6697914yes—
578C2×C4#6697914yes—
579C22—24no—
580C22—24no—
581C22—24no—
582C22—42no—
583C22—44no—
584C22—42no—
585C22—42no—
586C22—44no—
587C22—42no—
588C22—44no—
589C22—44no—
590C22#1062301011yescharacteristic
591C22#1062301011yescharacteristic
592C22#1062301011yescharacteristic
593C22#1062301011yescharacteristic
594C22#1062302512yes—
595C22#1062302512yes—
596C22#1062305912yes—
597C22#1062305912yes—
598C22#1062307112yes—
599C22#1062307112yes—
600C22#1062307112yes—
601C22#1062308712yes—
602C22#1062308712yes—
603C22#1062308712yes—
604C22#1062308912yes—
605C22#1062309012yes—
606C22C2×#6697911yescharacteristic
607C22C2×#6697911yescharacteristic
608C22C2×#6697911yescharacteristic
609C22#1062332911yescharacteristic
610C22#1062332911yescharacteristic
611C22#41×Dic1111yescharacteristic
612C22#41×Dic1111yescharacteristic
613C4—24no—
614C4—24no—
615C4—42no—
616C4—42no—
617C4—42no—
618C4—42no—
619C4—444no—
620C4—444no—
621C4—882no—
622C4—882no—
623C2—44no—
624C2#1307101411yescharacteristic
625C2#1307111411yescharacteristic
626C2#1307121411yescharacteristic
627C2#1307155611yescharacteristic
628C2#1307155611yescharacteristic
629C2#1307155611yescharacteristic
630C2#1307158911yescharacteristic
631C2#1307391412yes—
632C2#1307394412yes—
633C2#1307413112yes—
634C2#1307416112yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#13947
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #13066878C2semidirect
4. #13066843C2semidirect
5. #13066843C2semidirect
6. #13066843C2semidirect
7. #13066841C2semidirect
10. C4×C11⋊#95C2semidirect
20. C4×C11×C22⋊C4C4semidirect
281. C4×C22⋊C4Dic11semidirect
485. C11#13947semidirect

Maximal subgroups

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

subgroupindex
#130668782
#130668652
#130668532
#130668432
#130668412
#130668392
C4×C11⋊#952
C2×C4×C11×C22⋊C42
#1394711