Finite Group Databasebeta

← #14676355

Subgroups — #14676355

Order 2816.

1846 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66925C211yesmaximal, characteristic
2C2×#10622591C212yesmaximal, complemented
3#13066882C212yesmaximal, complemented
4#13066858C212yesmaximal
5#13066852C212yesmaximal
6#13066843C211yesmaximal, characteristic, complemented
7#13066841C211yesmaximal, characteristic, complemented
8(C2×D11)⋊#95C211yesmaximal, characteristic
9(C2×D11)⋊#95C211yesmaximal, characteristic
10#95×Dic11C211yesmaximal, characteristic, complemented
11C11×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C11×C4⋊C4C2212yes—
14C22×C42×C11C2211yescharacteristic
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×Dic11⋊C4C2211yescharacteristic
20C22×Dic11⋊C4C2211yescharacteristic
21C22×C4×Dic11C2212yes—
22C22×C4×Dic11C2211yescharacteristic
23C2×#66925—28no—
24C2×#66925C418yescomplemented
25C2×C11×#95C2211yescharacteristic
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37#10622591—28no—
38C24×D11C2311yescharacteristic
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×Dic11C2312yes—
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C22×C4×D11—24no—
50C22×C4×D11—22no—
51C22×C4×D11—22no—
52C22×C4×D11—24no—
53C22×C4×D11C2×C414yes—
54C2×C11×C4⋊C4—24no—
55C2×C11×C4⋊C4—24no—
56C2×C11×C4⋊C4—42no—
57C2×C42×C11—24no—
58C2×C42×C11C2×C414yes—
59C2×(C2×D11)⋊C4—24no—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—24no—
62C2×(C2×D11)⋊C4—24no—
63C2×(C2×D11)⋊C4—24no—
64C2×(C2×D11)⋊C4—24no—
65C2×(C2×D11)⋊C4—42no—
66C2×(C2×D11)⋊C4—42no—
67C2×(C2×D11)⋊C4C2×C414yes—
68C2×(C2×D11)⋊C4C2×C414yes—
69C2×Dic11⋊C4—24no—
70C2×Dic11⋊C4C2×C414yes—
71C2×Dic11⋊C4C2×C414yes—
72C2×Dic11⋊C4D418yes—
73C2×C4×Dic11—24no—
74C2×C4×Dic11—24no—
75C2×C4×Dic11—24no—
76C2×C4×Dic11—42no—
77C2×C4×Dic11C2×C414yes—
78#66925—232no—
79C11×#95—22no—
80C11×#95—22no—
81C11×#95—42no—
82C11⋊#95—24no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C11⋊#95—24no—
86C11⋊#95—24no—
87C11⋊#95—24no—
88C11⋊#95—24no—
89C11⋊#95—24no—
90C11⋊#95—42no—
91#13944—111nomaximal, Sylow
92C24×C11C2411yescharacteristic
93C23×D11—22no—
94C23×D11—22no—
95C23×D11—22no—
96C23×D11—21no—
97C23×D11—21no—
98C23×D11—21no—
99C23×D11—21no—
100C23×D11—21no—
101C23×D11—21no—
102C23×D11C22×C412yes—
103C23×D11#4114yes—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—22no—
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×C11C22×C412yes—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C22×C412yes—
129C22×C4×C11C2×D414yes—
130C22×C4×C11#4114yes—
131C22×C4×C11#4112yes—
132C22×C4×C11#4112yes—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—21no—
138C22×Dic11—21no—
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—21no—
149C22×Dic11—21no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11C22×C412yes—
157C22×Dic11C22×C412yes—
158C22×Dic11C22×C412yes—
159C22×Dic11C2×D414yes—
160C22×Dic11C2×D414yes—
161C22×Dic11#4114yes—
162C2×C4×D11—216no—
163C2×C4×D11—216no—
164C2×C4×D11—28no—
165C2×C4×D11—28no—
166C2×C4×D11—28no—
167C11×C4⋊C4—48no—
168C42×C11—28no—
169(C2×D11)⋊C4—28no—
170(C2×D11)⋊C4—28no—
171(C2×D11)⋊C4—48no—
172(C2×D11)⋊C4—48no—
173Dic11⋊C4—28no—
174Dic11⋊C4C22⋊C4116yescomplemented
175C4×Dic11—28no—
176C4×Dic11—48no—
177C22×#117—111no—
178C2×#387—112no—
179#1445—112no—
180#1439—112no—
181#1437—112no—
182C4⋊#95D1111yescharacteristic, complemented
183#1434—111no—
184#1434—111no—
185C22⋊#95—111no—
186C22⋊#95—111no—
187C4×#95—111no—
188C23×C11C23×C411yescharacteristic
189C23×C11C22×D412yes—
190C23×C11C2×#4112yes—
191C23×C11C2×#4111yescharacteristic
192C23×C11C2×#4111yescharacteristic
193C23×C11C2×#4112yes—
194C23×C11C2×#4112yes—
195C23×C11H(5,𝔽2)11yescharacteristic
196C23×C11H(5,𝔽2)11yescharacteristic
197C23×C112−1+411yescharacteristic
198C23×C112−1+411yescharacteristic
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—24no—
206C22×D11—24no—
207C22×D11—24no—
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11#11714yes—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
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—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11C2×C22⋊C414yes—
250C2×C4×C11#11714yes—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—42no—
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×Dic11C2×C22⋊C414yes—
279C2×Dic11C2×C22⋊C414yes—
280C4×D11—232no—
281C24×C4—111no—
282C2×#117—118no—
283C2×#117—228no—
284C22×C4⋊C4—111no—
285C22×C4⋊C4—111no—
286C22×C4⋊C4C2×D1112yes—
287C22×C22⋊C4—111no—
288C22×C22⋊C4—111no—
289C22×C22⋊C4—112no—
290C22×C22⋊C4—112no—
291C22×C42—111no—
292C22×C42—112no—
293C22×C42C2×D1111yescharacteristic
294#387—228no—
295C2×#95—111no—
296C2×#95—112no—
297C2×#95—111no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95—112no—
301C2×#95—112no—
302C2×#95—112no—
303C2×#95—112no—
304C2×#95C2×D1111yescharacteristic
305C2×#95C2×D1111yescharacteristic
306C2×#95C2×D1112yes—
307C22×C11C22×C22⋊C411yescharacteristic
308C22×C11C2×#11711yescharacteristic
309C22×C11C2×#11711yescharacteristic
310C22×C11C4×#4111yescharacteristic
311C22×C11C4×#4111yescharacteristic
312C22×C11#52011yescharacteristic
313C22×C11#52011yescharacteristic
314C22×C11#52512yes—
315C22×C11#52512yes—
316C22×C11#52912yes—
317C22×C11#52912yes—
318C22×C11#54011yescharacteristic
319C22×C11#54111yescharacteristic
320C22×C11#54211yescharacteristic
321C22×C11#54211yescharacteristic
322C22×C11#54612yes—
323C22×C11#54712yes—
324C22×C11#54812yes—
325C22×C11#55012yes—
326C22×C11#55112yes—
327C22×C11#55112yes—
328C22×C11#55212yes—
329C22×C11#55212yes—
330C2×D11—24no—
331C2×D11—24no—
332C2×D11—24no—
333C2×D11—42no—
334C2×D11—42no—
335C2×D11—42no—
336C2×D11—44no—
337C2×D11—44no—
338C2×D11—44no—
339C2×D11—44no—
340C2×D11—42no—
341C4×C11—24no—
342C4×C11—24no—
343C4×C11—42no—
344C4×C11—44no—
345C4×C11—82no—
346Dic11—24no—
347Dic11—24no—
348Dic11—42no—
349Dic11—44no—
350Dic11—82no—
351C25—111no—
352C23×C4—111no—
353C23×C4—111no—
354C23×C4—111no—
355C23×C4—112no—
356C23×C4—114no—
357C23×C4—112no—
358C23×C4—224no—
359C23×C4—224no—
360C23×C4—222no—
361C23×C4—222no—
362C23×C4C22×D1112yes—
363C23×C4C22×D1111yescharacteristic
364C23×C4C22×D1112yes—
365C23×C4C22×D1111yescharacteristic
366C23×C4C22×D1111yescharacteristic
367#117—2232no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—114no—
372C2×C4⋊C4—118no—
373C2×C4⋊C4—114no—
374C2×C4⋊C4—224no—
375C2×C22⋊C4—114no—
376C2×C22⋊C4—114no—
377C2×C22⋊C4—224no—
378C2×C22⋊C4—224no—
379C2×C22⋊C4—224no—
380C2×C22⋊C4—224no—
381C2×C22⋊C4—224no—
382C2×C22⋊C4—224no—
383C2×C22⋊C4—442no—
384C2×C22⋊C4—442no—
385C2×C42—24no—
386C2×C42—114no—
387C2×C42—224no—
388C2×C42—224no—
389C2×C42—224no—
390C2×C42—442no—
391C2×C42C4×D1114yes—
392#95—22no—
393#95—22no—
394#95—42no—
395#95—224no—
396#95—224no—
397#95—224no—
398#95—224no—
399#95—224no—
400#95—224no—
401#95—222no—
402#95—222no—
403#95—442no—
404C2×C11#228011yescharacteristic
405C2×C11#229811yescharacteristic
406C2×C11#231411yescharacteristic
407C2×C11#233911yescharacteristic
408C2×C11#234111yescharacteristic
409C2×C11#234311yescharacteristic
410C2×C11#234311yescharacteristic
411C2×C11#247112yes—
412C2×C11#247512yes—
413C2×C11#247712yes—
414C2×C11#247912yes—
415D11—44no—
416C24—112no—
417C24—114no—
418C24—222no—
419C24—222no—
420C24—221no—
421C24—221no—
422C24—221no—
423C24—221no—
424C24—221no—
425C24—221no—
426C24—222no—
427C24C23×D1111yescharacteristic
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—112no—
451C22×C4—112no—
452C22×C4—114no—
453C22×C4—114no—
454C22×C4—112no—
455C22×C4—114no—
456C22×C4—228no—
457C22×C4—228no—
458C22×C4—2216no—
459C22×C4—2216no—
460C22×C4—222no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—222no—
466C22×C4—228no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—221no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—221no—
474C22×C4—222no—
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×C4C2×C4×D1112yes—
485C22×C4C2×C4×D1112yes—
486C22×C4C2×C4×D1112yes—
487C22×C4#433914yes—
488C22×C4D4×D1114yes—
489C22×C4#434112yes—
490C22×C4#434312yes—
491C4⋊C4—48no—
492C4⋊C4—1116no—
493C4⋊C4—228no—
494C22⋊C4—228no—
495C22⋊C4—228no—
496C22⋊C4—448no—
497C22⋊C4—448no—
498C42—28no—
499C42—228no—
500C42—448no—
501C11#1394411yescharacteristic, complemented, Sylow
502C23—114no—
503C23—222no—
504C23—222no—
505C23—222no—
506C23—222no—
507C23—222no—
508C23—222no—
509C23—224no—
510C23—224no—
511C23—224no—
512C23—224no—
513C23—224no—
514C23—224no—
515C23—441no—
516C23—441no—
517C23—441no—
518C23—441no—
519C23—442no—
520C23—442no—
521C23—442no—
522C23—442no—
523C23—442no—
524C23—442no—
525C23C22×C4×D1111yescharacteristic
526C23C2×#433912yes—
527C23C2×D4×D1112yes—
528C23C2×#434111yescharacteristic
529C23#6703711yescharacteristic
530C23#6703711yescharacteristic
531C23C2×#434311yescharacteristic
532C23#6704011yescharacteristic
533C23#6704011yescharacteristic
534C23#41×D1112yes—
535C23#41×D1112yes—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—114no—
564C2×C4—114no—
565C2×C4—2232no—
566C2×C4—222no—
567C2×C4—224no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—224no—
571C2×C4—222no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—224no—
578C2×C4—224no—
579C2×C4—224no—
580C2×C4—442no—
581C2×C4—442no—
582C2×C4—442no—
583C2×C4—442no—
584C2×C4—442no—
585C2×C4—442no—
586C2×C4—442no—
587C2×C4—442no—
588C2×C4—442no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4—442no—
592C2×C4—442no—
593C2×C4C22⋊C4×D1114yes—
594C2×C4#6694514yes—
595C22—224no—
596C22—224no—
597C22—224no—
598C22—442no—
599C22—442no—
600C22—444no—
601C22—442no—
602C22—442no—
603C22—444no—
604C22—444no—
605C22—444no—
606C22C4×#433911yescharacteristic
607C22C2×C22⋊C4×D1111yescharacteristic
608C22#1062302112yes—
609C22C2×#6694511yescharacteristic
610C22#1062303511yescharacteristic
611C22#1062303511yescharacteristic
612C22#1062303812yes—
613C22D11×#11711yescharacteristic
614C22#1062305311yescharacteristic
615C22#1062306912yes—
616C22#1062308712yes—
617C22#1062311112yes—
618C22#1062311212yes—
619C22#1062313012yes—
620C22#1062313712yes—
621C22#1062315812yes—
622C22#1062316412yes—
623C22#1062321012yes—
624C22#1062322412yes—
625C22#1062325011yescharacteristic
626C22#1062326211yescharacteristic
627C22#1062326411yescharacteristic
628C22#1062326411yescharacteristic
629C4—24no—
630C4—24no—
631C4—44no—
632C4—42no—
633C4—82no—
634C4—224no—
635C4—224no—
636C4—442no—
637C4—444no—
638C4—882no—
639C2—444no—
640C2#1307099811yescharacteristic
641C2#1307110911yescharacteristic
642C2#1307122411yescharacteristic
643C2#1307144311yescharacteristic
644C2#1307145311yescharacteristic
645C2#1307146911yescharacteristic
646C2#1307147911yescharacteristic
647C2#1307273212yes—
648C2#1307279212yes—
649C2#1307282412yes—
650C2#1307285412yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC4⋊#95D11
hypocenterC11#13944
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622591C2semidirect
3. #13066882C2semidirect
6. #13066843C2semidirect
7. #13066841C2semidirect
10. #95×Dic11C2semidirect
11. C11×C4⋊#95C2semidirect
24. C2×#66925C4semidirect
174. Dic11⋊C4C22⋊C4semidirect
182. C4⋊#95D11semidirect
501. C11#13944semidirect

Maximal subgroups

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

subgroupindex
C22×#669252
C2×#106225912
#130668822
#130668582
#130668522
#130668432
#130668412
(C2×D11)⋊#952
#95×Dic112
C11×C4⋊#952
#1394411