Finite Group Databasebeta

← #14680689

Subgroups — #14680689

Order 2816.

1614 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622606C211yesmaximal, characteristic
2C2×#10622598C211yesmaximal, characteristic, complemented
3C2×#10622281C212yesmaximal
4C2×#10622279C211yesmaximal, characteristic
5#13066880C211yesmaximal, characteristic, complemented
6#13066874C212yesmaximal, complemented
7#13066864C212yesmaximal
8#13066862C211yesmaximal, characteristic
9#13066850C212yesmaximal, complemented
10#13066841C211yesmaximal, characteristic, complemented
11C11×#1445C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×(C2×D11)⋊C4C2211yescharacteristic
15C22×(C2×D11)⋊C4C2211yescharacteristic
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×C4⋊Dic11C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35#10622606C418yescomplemented
36#10622598—24no—
37#10622281—28no—
38#10622279—24no—
39C24×D11C2311yescharacteristic
40C23×C4×C11C2312yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×Dic11C2312yes—
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C22×C4×D11—22no—
51C22×C4×D11—22no—
52C22×C4×D11—42no—
53C22×C4×D11—42no—
54C22×C4×D11D414yes—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4C2×C414yescomplemented
58C2×(C2×D11)⋊C4—24no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—24no—
66C2×(C2×D11)⋊C4—42no—
67C2×(C2×D11)⋊C4—42no—
68C2×(C2×D11)⋊C4C2×C418yes—
69C2×(C2×D11)⋊C4C2×C414yes—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—24no—
72C2×C4⋊Dic11—24no—
73C2×C4⋊Dic11—24no—
74C2×C4⋊Dic11—42no—
75C2×Dic11⋊C4—24no—
76C2×Dic11⋊C4—42no—
77C2×Dic11⋊C4—42no—
78C2×C4×Dic11—22no—
79C2×C4×Dic11—42no—
80C2×C4×Dic11—42no—
81C2×C4×Dic11D414yes—
82C11×#95—22no—
83C11×#95—24no—
84C11×#95—24no—
85C11×#95—22no—
86C11⋊#95—22no—
87C11⋊#95—24no—
88C11⋊#95—24no—
89C11⋊#95—42no—
90C11⋊#95—42no—
91C11⋊#95—42no—
92C11⋊#95C2×C418yescomplemented
93C11⋊#95C2×C414yescomplemented
94#14313—111nomaximal, Sylow
95C24×C11C2411yescharacteristic
96C23×D11—21no—
97C23×D11—21no—
98C23×D11—21no—
99C23×D11—21no—
100C23×D11—22no—
101C23×D11—22no—
102C23×D11—22no—
103C23×D11—22no—
104C23×D11C22×C412yes—
105C23×D11C2×D412yes—
106C23×D11#4112yes—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11C22×C414yes—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11#4112yes—
135C22×C4×C11#4112yes—
136C22×Dic11—21no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143C22×Dic11—21no—
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×Dic11C22×C412yes—
160C22×Dic11C22×C414yes—
161C22×Dic11C2×D412yes—
162C22×Dic11C2×D412yes—
163C22×Dic11C2×D412yes—
164C22×Dic11#4112yes—
165C2×C4×D11—28no—
166C2×C4×D11—48no—
167C2×C4×D11—44no—
168C2×C4×D11—44no—
169C2×C4×D11—48no—
170C11×C4⋊C4—28no—
171(C2×D11)⋊C4—28no—
172(C2×D11)⋊C4—216no—
173(C2×D11)⋊C4—28no—
174(C2×D11)⋊C4—48no—
175C4⋊Dic11—44no—
176C4⋊Dic11—48no—
177Dic11⋊C4—48no—
178C4×Dic11—44no—
179C4×Dic11—44no—
180C2×#397—111no—
181C2×#389—111no—
182C2×#385—112no—
183C2×C4×C22⋊C4—111no—
184#1445D1111yescharacteristic, complemented
185#1444—111no—
186#1442—112no—
187#1440—112no—
188#1439—111no—
189#1436—112no—
190#1434—111no—
191C23×C11C23×C411yescharacteristic
192C23×C11C22×D411yescharacteristic
193C23×C11C22×D411yescharacteristic
194C23×C11C2×#4111yescharacteristic
195C23×C11C2×#4111yescharacteristic
196C23×C11C2×#4111yescharacteristic
197C23×C11C2×#4111yescharacteristic
198C23×C11H(5,𝔽2)12yes—
199C23×C11H(5,𝔽2)12yes—
200C23×C112−1+412yes—
201C23×C112−1+412yes—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—24no—
205C22×D11—24no—
206C22×D11—22no—
207C22×D11—22no—
208C22×D11—22no—
209C22×D11—22no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11—24no—
213C22×D11—24no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11C4×D414yes—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
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×C11C4×D414yes—
254C2×Dic11—22no—
255C2×Dic11—24no—
256C2×Dic11—22no—
257C2×Dic11—24no—
258C2×Dic11—22no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—42no—
267C2×Dic11—41no—
268C2×Dic11—41no—
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×Dic11#12114yes—
283C4×D11—416no—
284C24×C4—111no—
285C22×C4⋊C4—112no—
286C22×C4⋊C4—112no—
287C22×C4⋊C4—111no—
288C22×C4⋊C4C2×D1111yescharacteristic
289C22×C22⋊C4—111no—
290C22×C22⋊C4—112no—
291C22×C22⋊C4—111no—
292C22×C22⋊C4—112no—
293C22×C42—111no—
294C22×C42—111no—
295#397—118no—
296#389—224no—
297#385—228no—
298C4×C22⋊C4—224no—
299C2×#95—111no—
300C2×#95—112no—
301C2×#95—112no—
302C2×#95—112no—
303C2×#95—111no—
304C2×#95—112no—
305C2×#95—112no—
306C2×#95—112no—
307C2×#95C2×D1111yescharacteristic
308C2×#95C2×D1112yes—
309C2×#95C2×D1112yes—
310C2×#95C2×D1111yescharacteristic
311C22×C11C2×C4×D411yescharacteristic
312C22×C11C2×C4×D411yescharacteristic
313C22×C11C4×#4111yescharacteristic
314C22×C11#52012yes—
315C22×C11#52012yes—
316C22×C11C2×#12111yescharacteristic
317C22×C11#52511yescharacteristic
318C22×C11#52911yescharacteristic
319C22×C11#53211yescharacteristic
320C22×C11#53411yescharacteristic
321C22×C11#53412yes—
322C22×C11#53511yescharacteristic
323C22×C11#53611yescharacteristic
324C22×C11#53612yes—
325C22×C11#53611yescharacteristic
326C22×C11#53812yes—
327C22×C11#53912yes—
328C22×C11#53912yes—
329C22×C11#53912yes—
330C22×C11#53912yes—
331C22×C11#54112yes—
332C22×C11#54212yes—
333C22×C11#54212yes—
334C2×D11—28no—
335C2×D11—24no—
336C2×D11—42no—
337C2×D11—42no—
338C2×D11—44no—
339C2×D11—42no—
340C2×D11—42no—
341C2×D11—42no—
342C2×D11—42no—
343C2×D11—44no—
344C2×D11—44no—
345C4×C11—24no—
346C4×C11—42no—
347C4×C11—42no—
348C4×C11—44no—
349C4×C11—82no—
350Dic11—24no—
351Dic11—44no—
352Dic11—42no—
353Dic11—42no—
354Dic11—82no—
355C25—111no—
356C23×C4—111no—
357C23×C4—112no—
358C23×C4—111no—
359C23×C4—111no—
360C23×C4—114no—
361C23×C4—112no—
362C23×C4—222no—
363C23×C4—222no—
364C23×C4—442no—
365C23×C4—442no—
366C23×C4C22×D1112yes—
367C23×C4C22×D1112yes—
368C23×C4C22×D1111yescharacteristic
369C23×C4C22×D1111yescharacteristic
370C23×C4C22×D1111yescharacteristic
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—224no—
374C2×C4⋊C4—224no—
375C2×C4⋊C4—224no—
376C2×C4⋊C4—224no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—442no—
379C2×C4⋊C4—442no—
380C2×C4⋊C4—442no—
381C2×C4⋊C4C4×D1114yescomplemented
382C2×C22⋊C4—118no—
383C2×C22⋊C4—114no—
384C2×C22⋊C4—222no—
385C2×C22⋊C4—224no—
386C2×C22⋊C4—224no—
387C2×C22⋊C4—222no—
388C2×C22⋊C4—222no—
389C2×C22⋊C4—222no—
390C2×C22⋊C4—222no—
391C2×C22⋊C4—224no—
392C2×C22⋊C4—442no—
393C2×C22⋊C4—442no—
394C2×C42—114no—
395C2×C42—222no—
396C2×C42—442no—
397C2×C42—442no—
398#95—22no—
399#95—24no—
400#95—24no—
401#95—22no—
402#95—118no—
403#95—114no—
404#95—222no—
405#95—224no—
406#95—224no—
407#95—442no—
408#95—442no—
409#95—442no—
410C2×C11C4×#12111yescharacteristic
411C2×C11#232211yescharacteristic
412C2×C11#232212yes—
413C2×C11#232611yescharacteristic
414C2×C11#233412yes—
415C2×C11#261711yescharacteristic
416C2×C11#262111yescharacteristic
417C2×C11#263311yescharacteristic
418C2×C11#263811yescharacteristic
419C2×C11#265212yes—
420C2×C11#266312yes—
421D11—44no—
422C24—112no—
423C24—112no—
424C24—112no—
425C24—221no—
426C24—221no—
427C24—221no—
428C24—222no—
429C24—221no—
430C24—222no—
431C24—222no—
432C24—222no—
433C24C23×D1111yescharacteristic
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—112no—
458C22×C4—112no—
459C22×C4—112no—
460C22×C4—112no—
461C22×C4—114no—
462C22×C4—112no—
463C22×C4—228no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—221no—
467C22×C4—222no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—221no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—448no—
488C22×C4—448no—
489C22×C4—444no—
490C22×C4—444no—
491C22×C4C2×C4×D1114yes—
492C22×C4C2×C4×D1112yes—
493C22×C4D4×D1112yes—
494C22×C4D4×D1112yes—
495C22×C4#434112yes—
496C22×C4#434112yes—
497C4⋊C4—28no—
498C4⋊C4—448no—
499C4⋊C4—444no—
500C4⋊C4—448no—
501C22⋊C4—2216no—
502C22⋊C4—228no—
503C22⋊C4—228no—
504C22⋊C4—448no—
505C42—444no—
506C42—444no—
507C11#1431311yescharacteristic, complemented, Sylow
508C23—114no—
509C23—224no—
510C23—222no—
511C23—222no—
512C23—224no—
513C23—222no—
514C23—224no—
515C23—222no—
516C23—222no—
517C23—224no—
518C23—224no—
519C23—222no—
520C23—224no—
521C23—442no—
522C23—441no—
523C23—442no—
524C23—442no—
525C23—441no—
526C23—441no—
527C23—442no—
528C23—442no—
529C23—441no—
530C23—442no—
531C23C22×C4×D1111yescharacteristic
532C23C2×D4×D1111yescharacteristic
533C23C2×D4×D1111yescharacteristic
534C23C2×#434111yescharacteristic
535C23C2×#434111yescharacteristic
536C23#6704012yes—
537C23#41×D1111yescharacteristic
538C23#41×D1111yescharacteristic
539C23#6704212yes—
540C23#6704212yes—
541C23#6704312yes—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—114no—
571C2×C4—224no—
572C2×C4—222no—
573C2×C4—224no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—224no—
578C2×C4—224no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—222no—
582C2×C4—222no—
583C2×C4—4416no—
584C2×C4—442no—
585C2×C4—441no—
586C2×C4—442no—
587C2×C4—442no—
588C2×C4—442no—
589C2×C4—442no—
590C2×C4—441no—
591C2×C4—442no—
592C2×C4—442no—
593C2×C4—442no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—442no—
598C2×C4—442no—
599C2×C4—442no—
600C2×C4(C22⋊D11)⋊C414yes—
601C22—224no—
602C22—228no—
603C22—444no—
604C22—442no—
605C22—444no—
606C22—442no—
607C22—442no—
608C22—442no—
609C22—442no—
610C22—442no—
611C22—444no—
612C22C2×(C22⋊D11)⋊C411yescharacteristic
613C22#1062305412yes—
614C22C4×#434111yescharacteristic
615C22C4×D4×D1111yescharacteristic
616C22#1062310512yes—
617C22D11×#12111yescharacteristic
618C22#1062313711yescharacteristic
619C22#1062315912yes—
620C22#1062317412yes—
621C22#1062317412yes—
622C22#1062317911yescharacteristic
623C22#1062318412yes—
624C22#1062318411yescharacteristic
625C22#1062319612yes—
626C22#1062319612yes—
627C22#1062320511yescharacteristic
628C22#1062321111yescharacteristic
629C22#1062322312yes—
630C22#1062322712yes—
631C22#1062323512yes—
632C22#1062323812yes—
633C22#1062324711yescharacteristic
634C22#1062325511yescharacteristic
635C4—24no—
636C4—44no—
637C4—42no—
638C4—42no—
639C4—82no—
640C4—224no—
641C4—442no—
642C4—444no—
643C4—442no—
644C4—882no—
645C2—444no—
646C2#1307113211yescharacteristic
647C2#1307128211yescharacteristic
648C2#1307128912yes—
649C2#1307133011yescharacteristic
650C2#1307139612yes—
651C2#1307435111yescharacteristic
652C2#1307438411yescharacteristic
653C2#1307448911yescharacteristic
654C2#1307454111yescharacteristic
655C2#1307466112yes—
656C2#1307476912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1445C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1445D11
hypocenterC11#14313
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
2. C2×#10622598C2semidirect
5. #13066880C2semidirect
6. #13066874C2semidirect
9. #13066850C2semidirect
10. #13066841C2semidirect
11. C11×#1445C2semidirect
35. #10622606C4semidirect
57. C2×C11×C4⋊C4C2×C4semidirect
92. C11⋊#95C2×C4semidirect
93. C11⋊#95C2×C4semidirect
184. #1445D11semidirect
381. C2×C4⋊C4C4×D11semidirect
507. C11#14313semidirect

Maximal subgroups

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

subgroupindex
C2×#106226062
C2×#106225982
C2×#106222812
C2×#106222792
#130668802
#130668742
#130668642
#130668622
#130668502
#130668412
C11×#14452
#1431311