Finite Group Databasebeta

← #14680455

Subgroups — #14680455

Order 2816.

1782 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66949C211yesmaximal, characteristic
2C2×#10622277C211yesmaximal, characteristic
3C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
4#13066886C212yesmaximal, complemented
5#13066882C212yesmaximal, complemented
6#13066864C212yesmaximal
7#13066864C212yesmaximal
8#13066851C211yesmaximal, characteristic, complemented
9#13066849C211yesmaximal, characteristic, complemented
10#13066848C211yesmaximal, characteristic, complemented
11C11×#1436C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C23×Dic22C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2212yes—
20C22×Dic11⋊C4C2211yescharacteristic
21C22×Dic11⋊C4C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C2×#66949—24no—
24C2×#66949—24no—
25C2×#66949C418yescomplemented
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2212yes—
28C2×C11×#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C4×(C2×D11)⋊C4—24no—
39#10622277—24no—
40C24×D11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2312yes—
50C23×Dic11C2311yescharacteristic
51C22×C4×D11—42no—
52C22×C4×D11—42no—
53C22×C4×D11C2×C414yes—
54C22×C4×D11D414yes—
55C22×C4×D11D414yes—
56C22×Dic22—22no—
57C22×Dic22—22no—
58C22×Dic22—42no—
59C22×Dic22—42no—
60C22×Dic22C2×C414yes—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4C2×C414yes—
64C2×C42×C11—22no—
65C2×C42×C11—42no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—24no—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—24no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—42no—
75C2×(C2×D11)⋊C4—42no—
76C2×(C2×D11)⋊C4C2×C414yes—
77C2×(C2×D11)⋊C4C2×C414yes—
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4—22no—
80C2×Dic11⋊C4—22no—
81C2×Dic11⋊C4—22no—
82C2×Dic11⋊C4C2×C414yes—
83C2×Dic11⋊C4C2×C414yes—
84C2×C4×Dic11—22no—
85C2×C4×Dic11—42no—
86#66949—232no—
87C11×#95—22no—
88C11×#95—24no—
89C11×#95—42no—
90C11⋊#95—22no—
91C11⋊#95—24no—
92C11⋊#95—24no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96C11⋊#95—42no—
97C11⋊#95—42no—
98C11⋊#95—42no—
99#14292—111nomaximal, Sylow
100C24×C11C2411yescharacteristic
101C23×D11—22no—
102C23×D11—22no—
103C23×D11—22no—
104C23×D11—22no—
105C23×D11—22no—
106C23×D11—22no—
107C23×D11C22×C412yes—
108C23×D11C2×D412yes—
109C23×D11C2×D412yes—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
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×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11#4114yes—
139C22×Dic11—22no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
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×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11C22×C412yes—
163C22×Dic11C22×C412yes—
164C22×Dic11C22×C412yes—
165C22×Dic11C2×D412yes—
166C22×Dic11C2×D412yes—
167C22×Dic11#4114yes—
168C2×C4×D11—48no—
169C2×C4×D11—44no—
170C2×C4×D11—44no—
171C2×C4×D11—48no—
172C2×C4×D11C22⋊C4116yes—
173C2×Dic22—28no—
174C2×Dic22—48no—
175C2×Dic22—44no—
176C2×Dic22—48no—
177C2×Dic22—44no—
178C11×C4⋊C4—28no—
179C42×C11—44no—
180(C2×D11)⋊C4—216no—
181(C2×D11)⋊C4—28no—
182(C2×D11)⋊C4—28no—
183(C2×D11)⋊C4—48no—
184Dic11⋊C4—28no—
185Dic11⋊C4—28no—
186C4×Dic11—44no—
187C22×C22⋊Q8—111no—
188C2×#381—111no—
189C2×C4×C22⋊C4—111no—
190#1446—112no—
191#1445—112no—
192#1440—112no—
193#1440—112no—
194#1436—111no—
195#1436—111no—
196#1436—111no—
197#1436D1111yescharacteristic, complemented
198C23×C11C23×C411yescharacteristic
199C23×C11C22×D411yescharacteristic
200C23×C11C22×D411yescharacteristic
201C23×C11C2×#4112yes—
202C23×C11C2×#4112yes—
203C23×C11H(5,𝔽2)12yes—
204C23×C11H(5,𝔽2)12yes—
205C23×C112−1+412yes—
206C23×C112−1+412yes—
207C22×D11—22no—
208C22×D11—22no—
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11—24no—
213C22×D11—24no—
214C22×D11—22no—
215C22×D11—22no—
216C22×D11—22no—
217C22×D11—24no—
218C22×D11—22no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—42no—
227C22×D11C2×C22⋊C414yes—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—41no—
244C2×C4×C11—42no—
245C2×C4×C11—41no—
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×C11C2×C22⋊C414yes—
257C2×Dic11—24no—
258C2×Dic11—22no—
259C2×Dic11—24no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—41no—
273C2×Dic11—42no—
274C2×Dic11—41no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11C2×C22⋊C414yes—
286C4×D11—416no—
287Dic22—416no—
288C23×Q8—111no—
289C24×C4—111no—
290C2×C22⋊Q8—118no—
291C2×C22⋊Q8—224no—
292C2×C22⋊Q8—224no—
293C22×C4⋊C4—111no—
294C22×C4⋊C4—111no—
295C22×C4⋊C4C2×D1111yescharacteristic
296C22×C22⋊C4—111no—
297C22×C22⋊C4—111no—
298C22×C22⋊C4—112no—
299C22×C22⋊C4—112no—
300C22×C42—111no—
301C22×C42C2×D1111yescharacteristic
302#381—224no—
303C4×C22⋊C4—224no—
304C2×#95—111no—
305C2×#95—112no—
306C2×#95—112no—
307C2×#95—112no—
308C2×#95—112no—
309C2×#95—112no—
310C2×#95—112no—
311C2×#95—112no—
312C2×#95—112no—
313C2×#95C2×D1111yescharacteristic
314C2×#95C2×D1112yes—
315C2×#95C2×D1112yes—
316C22×C11C22×C22⋊C411yescharacteristic
317C22×C11C4×#4111yescharacteristic
318C22×C11C4×#4111yescharacteristic
319C22×C11#51812yes—
320C22×C11#51912yes—
321C22×C11#52512yes—
322C22×C11#53212yes—
323C22×C11#53411yescharacteristic
324C22×C11#53412yes—
325C22×C11#53411yescharacteristic
326C22×C11#53611yescharacteristic
327C22×C11#53612yes—
328C22×C11#53611yescharacteristic
329C22×C11#53912yes—
330C22×C11#53912yes—
331C22×C11#53912yes—
332C22×C11#53912yes—
333C22×C11#54212yes—
334C22×C11#54212yes—
335C22×C11#54212yes—
336C22×C11#54212yes—
337C2×D11—24no—
338C2×D11—24no—
339C2×D11—24no—
340C2×D11—44no—
341C2×D11—44no—
342C2×D11—44no—
343C2×D11—44no—
344C2×D11—44no—
345C2×D11—44no—
346C4×C11—24no—
347C4×C11—42no—
348C4×C11—44no—
349C4×C11—42no—
350C4×C11—82no—
351Dic11—24no—
352Dic11—42no—
353Dic11—44no—
354Dic11—42no—
355Dic11—82no—
356C25—111no—
357C22×Q8—114no—
358C22×Q8—222no—
359C22×Q8—222no—
360C22×Q8—442no—
361C22×Q8—442no—
362C23×C4—111no—
363C23×C4—114no—
364C23×C4—114no—
365C23×C4—114no—
366C23×C4—111no—
367C23×C4—111no—
368C23×C4—112no—
369C23×C4—112no—
370C23×C4—442no—
371C23×C4—442no—
372C23×C4C22×D1112yes—
373C23×C4C22×D1111yescharacteristic
374C23×C4C22×D1111yescharacteristic
375C23×C4C22×D1112yes—
376C23×C4C22×D1111yescharacteristic
377C22⋊Q8—2232no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—114no—
381C2×C4⋊C4—114no—
382C2×C4⋊C4—222no—
383C2×C4⋊C4—222no—
384C2×C4⋊C4—222no—
385C2×C4⋊C4—222no—
386C2×C4⋊C4C4×D1114yes—
387C2×C22⋊C4—114no—
388C2×C22⋊C4—114no—
389C2×C22⋊C4—224no—
390C2×C22⋊C4—222no—
391C2×C22⋊C4—222no—
392C2×C22⋊C4—222no—
393C2×C22⋊C4—222no—
394C2×C22⋊C4—224no—
395C2×C22⋊C4—224no—
396C2×C22⋊C4—224no—
397C2×C22⋊C4—442no—
398C2×C22⋊C4—442no—
399C2×C42—22no—
400C2×C42—42no—
401C2×C42—222no—
402C2×C42—442no—
403#95—24no—
404#95—22no—
405#95—42no—
406#95—224no—
407#95—224no—
408#95—224no—
409#95—224no—
410#95—224no—
411#95—222no—
412#95—442no—
413#95—442no—
414#95—442no—
415C2×C11#229711yescharacteristic
416C2×C11#230811yescharacteristic
417C2×C11#231011yescharacteristic
418C2×C11#233212yes—
419C2×C11#233212yes—
420C2×C11#263812yes—
421C2×C11#263812yes—
422C2×C11#266312yes—
423C2×C11#266312yes—
424D11—44no—
425C24—112no—
426C24—112no—
427C24—112no—
428C24—222no—
429C24—222no—
430C24—222no—
431C24—222no—
432C24—222no—
433C24—222no—
434C24C23×D1111yescharacteristic
435C2×Q8—228no—
436C2×Q8—448no—
437C2×Q8—444no—
438C2×Q8—448no—
439C2×Q8—444no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
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—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—112no—
464C22×C4—112no—
465C22×C4—112no—
466C22×C4—1116no—
467C22×C4—112no—
468C22×C4—112no—
469C22×C4—114no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
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—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—448no—
494C22×C4—444no—
495C22×C4—448no—
496C22×C4—444no—
497C22×C4C2×C4×D1112yes—
498C22×C4C2×C4×D1112yes—
499C22×C4C2×C4×D1112yes—
500C22×C4#433914yes—
501C22×C4D4×D1112yes—
502C22×C4D4×D1112yes—
503C4⋊C4—28no—
504C4⋊C4—228no—
505C4⋊C4—228no—
506C22⋊C4—228no—
507C22⋊C4—228no—
508C22⋊C4—2216no—
509C22⋊C4—448no—
510C42—44no—
511C42—444no—
512C11#1429211yescharacteristic, complemented, Sylow
513C23—114no—
514C23—222no—
515C23—222no—
516C23—222no—
517C23—224no—
518C23—224no—
519C23—224no—
520C23—224no—
521C23—222no—
522C23—224no—
523C23—224no—
524C23—222no—
525C23—222no—
526C23—442no—
527C23—442no—
528C23—442no—
529C23—442no—
530C23—442no—
531C23—442no—
532C23—442no—
533C23—442no—
534C23C22×C4×D1111yescharacteristic
535C23C2×#433912yes—
536C23C2×D4×D1111yescharacteristic
537C23C2×D4×D1111yescharacteristic
538C23#6703712yes—
539C23#6704012yes—
540C23#41×D1112yes—
541C23#6704212yes—
542C23#6704312yes—
543Q8—4416no—
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—42no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—114no—
573C2×C4—224no—
574C2×C4—222no—
575C2×C4—224no—
576C2×C4—222no—
577C2×C4—224no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—224no—
583C2×C4—224no—
584C2×C4—224no—
585C2×C4—4416no—
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—441no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—442no—
598C2×C4—442no—
599C2×C4—442no—
600C2×C4—442no—
601C2×C4—442no—
602C2×C4C22⋊C4×D1114yes—
603C22—224no—
604C22—224no—
605C22—224no—
606C22—444no—
607C22—444no—
608C22—444no—
609C22—444no—
610C22—444no—
611C22—444no—
612C22C4×#433911yescharacteristic
613C22C2×C22⋊C4×D1111yescharacteristic
614C22#1062304612yes—
615C22#1062305311yescharacteristic
616C22#1062306512yes—
617C22#1062307612yes—
618C22#1062307812yes—
619C22#1062307912yes—
620C22#1062309512yes—
621C22#1062310312yes—
622C22#1062311312yes—
623C22#1062312011yescharacteristic
624C22#1062313612yes—
625C22#1062315912yes—
626C22#1062317112yes—
627C22#1062318411yescharacteristic
628C22#1062319312yes—
629C22#1062320611yescharacteristic
630C22#1062322312yes—
631C22#1062323812yes—
632C22#1062325511yescharacteristic
633C4—24no—
634C4—42no—
635C4—44no—
636C4—42no—
637C4—82no—
638C4—224no—
639C4—442no—
640C4—444no—
641C4—442no—
642C4—882no—
643C2—444no—
644C2#1307110211yescharacteristic
645C2#1307119011yescharacteristic
646C2#1307119911yescharacteristic
647C2#1307136712yes—
648C2#1307137012yes—
649C2#1307453712yes—
650C2#1307454012yes—
651C2#1307476812yes—
652C2#1307477012yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1436D11
hypocenterC11#14292
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. #13066886C2semidirect
5. #13066882C2semidirect
8. #13066851C2semidirect
9. #13066849C2semidirect
10. #13066848C2semidirect
11. C11×#1436C2semidirect
25. C2×#66949C4semidirect
197. #1436D11semidirect
512. C11#14292semidirect

Maximal subgroups

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

subgroupindex
C22×#669492
C2×#106222772
C2×C4×(C2×D11)⋊C42
#130668862
#130668822
#130668642
#130668512
#130668492
#130668482
C11×#14362
#1429211