Finite Group Databasebeta

← #14675356

Subgroups — #14675356

Order 2816.

1906 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622282C212yesmaximal
2C2×#10622262C211yesmaximal, characteristic, complemented
3C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
4C2×#10622279C211yesmaximal, characteristic
5#13066852C212yesmaximal
6#13066847C212yesmaximal, complemented
7#13066840C211yesmaximal, characteristic, complemented
8(C2×D11)⋊#95C211yesmaximal, characteristic
9C4×C11⋊#95C211yesmaximal, characteristic, complemented
10#95×Dic11C212yesmaximal, complemented
11C11×#1434C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2211yescharacteristic
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×Dic11⋊C4C2212yes—
19C22×C4×Dic11C2212yes—
20C22×C4×Dic11C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2212yes—
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2211yescharacteristic
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C4×(C2×D11)⋊C4C418yescomplemented
36#10622282C4116yescomplemented
37#10622279—24no—
38#10622262—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—24no—
53C22×C4×D11—42no—
54C22×C4×D11C2×C414yes—
55C2×C42×C11—42no—
56C2×C42×C11C2×C414yes—
57C2×(C2×D11)⋊C4—24no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—42no—
62C2×(C2×D11)⋊C4—42no—
63C2×(C2×D11)⋊C4C2×C418yes—
64C2×(C2×D11)⋊C4C2×C414yes—
65C2×(C2×D11)⋊C4C2×C418yes—
66C2×(C2×D11)⋊C4C2×C418yes—
67C2×(C2×D11)⋊C4C2×C414yes—
68C2×Dic11⋊C4—24no—
69C2×Dic11⋊C4—24no—
70C2×Dic11⋊C4C2×C418yescomplemented
71C2×C4×Dic11—22no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11—24no—
74C2×C4×Dic11—24no—
75C2×C4×Dic11—24no—
76C2×C4×Dic11—24no—
77C2×C4×Dic11—42no—
78C2×C4×Dic11—42no—
79C2×C4×Dic11—42no—
80C2×C4×Dic11—42no—
81C2×C4×Dic11C2×C414yes—
82C2×C4×Dic11C2×C418yescomplemented
83C11×#95—22no—
84C11×#95—22no—
85C11×#95—42no—
86C11×#95C2×C418yescomplemented
87C11⋊#95—22no—
88C11⋊#95—24no—
89C11⋊#95—24no—
90C11⋊#95—24no—
91C11⋊#95C2×C414yes—
92C11⋊#95C2×C414yes—
93C11⋊#95C2×C418yescomplemented
94C11⋊#95D414yes—
95#13822—111nomaximal, Sylow
96C24×C11C2411yescharacteristic
97C23×D11—21no—
98C23×D11—21no—
99C23×D11—21no—
100C23×D11—22no—
101C23×D11—22no—
102C23×D11—21no—
103C23×D11—21no—
104C23×D11—22no—
105C23×D11—21no—
106C23×D11C22×C414yes—
107C23×D11C22×C412yes—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
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×C11C22×C412yes—
130C22×C4×C11C22×C414yes—
131C22×C4×C11C22×C414yes—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C22×C414yes—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11#4112yes—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—21no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—21no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—21no—
157C22×Dic11C22×C414yes—
158C22×Dic11C22×C412yes—
159C22×Dic11C22×C414yes—
160C22×Dic11C22×C412yes—
161C22×Dic11C22×C412yes—
162C22×Dic11C22×C414yes—
163C22×Dic11C2×D414yes—
164C22×Dic11#4112yes—
165C22×Dic11#4114yes—
166C22×Dic11#4112yes—
167C22×Dic11#4114yes—
168C2×C4×D11—28no—
169C2×C4×D11—28no—
170C2×C4×D11—44no—
171C2×C4×D11—48no—
172C2×C4×D11—48no—
173C42×C11—44no—
174(C2×D11)⋊C4—28no—
175(C2×D11)⋊C4—216no—
176(C2×D11)⋊C4—48no—
177(C2×D11)⋊C4C42116yescomplemented
178Dic11⋊C4—216no—
179C4×Dic11—28no—
180C4×Dic11—48no—
181C4×Dic11—48no—
182C4×Dic11—48no—
183C2×#388—112no—
184C2×C4×C4⋊C4—111no—
185C2×C4×C22⋊C4—111no—
186C2×C4×C22⋊C4—111no—
187#1437—112no—
188#1436—112no—
189#1434—111no—
190#1434D1111yescharacteristic, complemented
191C22⋊#95—111no—
192C4×#95—111no—
193C4×#95—112no—
194C23×C11C23×C411yescharacteristic
195C23×C11C23×C412yes—
196C23×C11C22×D411yescharacteristic
197C23×C11C2×#4111yescharacteristic
198C23×C11C2×#4112yes—
199C23×C11C2×#4111yescharacteristic
200C23×C11C2×#4111yescharacteristic
201C23×C11C2×#4112yes—
202C23×C11H(5,𝔽2)12yes—
203C23×C11H(5,𝔽2)11yescharacteristic
204C23×C112−1+411yescharacteristic
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—24no—
208C22×D11—22no—
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—22no—
212C22×D11—24no—
213C22×D11—24no—
214C22×D11—22no—
215C22×D11—22no—
216C22×D11—24no—
217C22×D11—42no—
218C22×D11—41no—
219C22×D11—41no—
220C22×D11—42no—
221C22×D11—41no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11—41no—
225C22×D11—42no—
226C22×D11—42no—
227C22×D11C2×C4214yes—
228C2×C4×C11—22no—
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—22no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
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×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11C2×C4214yes—
256C2×C4×C11C4×D414yes—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—24no—
260C2×Dic11—22no—
261C2×Dic11—24no—
262C2×Dic11—22no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—22no—
272C2×Dic11—24no—
273C2×Dic11—22no—
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—24no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11C2×C4214yes—
285C2×Dic11#11714yes—
286C2×Dic11#11714yes—
287C2×Dic11C4×D418yes—
288C4×D11—416no—
289C24×C4—111no—
290C22×C4⋊C4—112no—
291C22×C22⋊C4—111no—
292C22×C22⋊C4—111no—
293C22×C22⋊C4—112no—
294C22×C22⋊C4—112no—
295C22×C42—111no—
296C22×C42—112no—
297C22×C42—112no—
298C22×C42—112no—
299C22×C42C2×D1111yescharacteristic
300#388—1116no—
301C4×C4⋊C4—224no—
302C4×C22⋊C4—118no—
303C4×C22⋊C4—224no—
304C2×#95—111no—
305C2×#95—111no—
306C2×#95—112no—
307C2×#95—111no—
308C2×#95—111no—
309C2×#95—112no—
310C2×#95—112no—
311C2×#95—112no—
312C2×#95C2×D1111yescharacteristic
313C2×#95C2×D1111yescharacteristic
314C2×#95C2×D1112yes—
315C2×#95C2×D1112yes—
316C22×C11C22×C4211yescharacteristic
317C22×C11C2×#11711yescharacteristic
318C22×C11C2×#11711yescharacteristic
319C22×C11C2×C4×D411yescharacteristic
320C22×C11C2×C4×D412yes—
321C22×C11C4×#4111yescharacteristic
322C22×C11C4×#4112yes—
323C22×C11C4×#4112yes—
324C22×C11C4×#4112yes—
325C22×C11#51811yescharacteristic
326C22×C11#51812yes—
327C22×C11#52011yescharacteristic
328C22×C11#52012yes—
329C22×C11#54612yes—
330C22×C11#54611yescharacteristic
331C22×C11#54811yescharacteristic
332C22×C11#55112yes—
333C22×C11#55211yescharacteristic
334C22×C11#55312yes—
335C22×C11#55312yes—
336C22×C11#55311yescharacteristic
337C22×C11#55612yes—
338C22×C11#55912yes—
339C2×D11—24no—
340C2×D11—24no—
341C2×D11—24no—
342C2×D11—42no—
343C2×D11—42no—
344C2×D11—42no—
345C2×D11—42no—
346C2×D11—44no—
347C2×D11—44no—
348C2×D11—44no—
349C2×D11—44no—
350C4×C11—24no—
351C4×C11—24no—
352C4×C11—42no—
353C4×C11—44no—
354C4×C11—44no—
355Dic11—24no—
356Dic11—24no—
357Dic11—28no—
358Dic11—24no—
359Dic11—44no—
360C25—111no—
361C23×C4—111no—
362C23×C4—112no—
363C23×C4—111no—
364C23×C4—111no—
365C23×C4—112no—
366C23×C4—114no—
367C23×C4—224no—
368C23×C4—222no—
369C23×C4—222no—
370C23×C4—442no—
371C23×C4C22×D1112yes—
372C23×C4C22×D1111yescharacteristic
373C23×C4C22×D1112yes—
374C23×C4C22×D1111yescharacteristic
375C23×C4C22×D1111yescharacteristic
376C2×C4⋊C4—118no—
377C2×C4⋊C4—224no—
378C2×C4⋊C4—224no—
379C2×C22⋊C4—114no—
380C2×C22⋊C4—118no—
381C2×C22⋊C4—114no—
382C2×C22⋊C4—118no—
383C2×C22⋊C4—118no—
384C2×C22⋊C4—224no—
385C2×C22⋊C4—222no—
386C2×C22⋊C4—224no—
387C2×C22⋊C4—222no—
388C2×C22⋊C4—442no—
389C2×C22⋊C4—442no—
390C2×C42—42no—
391C2×C42—114no—
392C2×C42—118no—
393C2×C42—222no—
394C2×C42—222no—
395C2×C42—224no—
396C2×C42—224no—
397C2×C42—224no—
398C2×C42—224no—
399C2×C42—442no—
400C2×C42—442no—
401C2×C42—442no—
402C2×C42—442no—
403C2×C42C4×D1114yes—
404#95—22no—
405#95—22no—
406#95—42no—
407#95—114no—
408#95—114no—
409#95—118no—
410#95—114no—
411#95—224no—
412#95—224no—
413#95—224no—
414#95—222no—
415#95C4×D1118yescomplemented
416C2×C11C4×#11711yescharacteristic
417C2×C11C42×D411yescharacteristic
418C2×C11#227511yescharacteristic
419C2×C11#234211yescharacteristic
420C2×C11#234711yescharacteristic
421C2×C11#235211yescharacteristic
422C2×C11#235711yescharacteristic
423C2×C11#236412yes—
424C2×C11#236712yes—
425C2×C11#237312yes—
426C2×C11#237412yes—
427D11—44no—
428C24—114no—
429C24—112no—
430C24—221no—
431C24—222no—
432C24—221no—
433C24—221no—
434C24—221no—
435C24—222no—
436C24—222no—
437C24—221no—
438C24—221no—
439C24C23×D1111yescharacteristic
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
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—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—112no—
462C22×C4—112no—
463C22×C4—112no—
464C22×C4—114no—
465C22×C4—114no—
466C22×C4—114no—
467C22×C4—112no—
468C22×C4—114no—
469C22×C4—114no—
470C22×C4—112no—
471C22×C4—114no—
472C22×C4—228no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—228no—
494C22×C4—444no—
495C22×C4—448no—
496C22×C4—448no—
497C22×C4C2×C4×D1114yes—
498C22×C4C2×C4×D1112yes—
499C22×C4C2×C4×D1114yes—
500C22×C4C2×C4×D1112yes—
501C22×C4C2×C4×D1114yes—
502C22×C4C2×C4×D1112yes—
503C22×C4D4×D1112yes—
504C22×C4#434312yes—
505C4⋊C4—2216no—
506C22⋊C4—1116no—
507C22⋊C4—228no—
508C22⋊C4—2216no—
509C22⋊C4—448no—
510C42—44no—
511C42—228no—
512C42—448no—
513C42—448no—
514C42—448no—
515C11#1382211yescharacteristic, complemented, Sylow
516C23—114no—
517C23—222no—
518C23—222no—
519C23—222no—
520C23—222no—
521C23—224no—
522C23—224no—
523C23—222no—
524C23—222no—
525C23—224no—
526C23—224no—
527C23—224no—
528C23—224no—
529C23—442no—
530C23—442no—
531C23—442no—
532C23—442no—
533C23—442no—
534C23—442no—
535C23—441no—
536C23—441no—
537C23—441no—
538C23—441no—
539C23C22×C4×D1111yescharacteristic
540C23C22×C4×D1112yes—
541C23C2×D4×D1111yescharacteristic
542C23#6703712yes—
543C23C2×#434311yescharacteristic
544C23#41×D1112yes—
545C23#41×D1112yes—
546C23#41×D1111yescharacteristic
547C23#41×D1111yescharacteristic
548C23#6704211yescharacteristic
549C23#6704311yescharacteristic
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—114no—
578C2×C4—114no—
579C2×C4—114no—
580C2×C4—118no—
581C2×C4—224no—
582C2×C4—222no—
583C2×C4—222no—
584C2×C4—222no—
585C2×C4—222no—
586C2×C4—224no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—224no—
590C2×C4—224no—
591C2×C4—224no—
592C2×C4—224no—
593C2×C4—224no—
594C2×C4—224no—
595C2×C4—224no—
596C2×C4—222no—
597C2×C4—224no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—224no—
602C2×C4—224no—
603C2×C4—224no—
604C2×C4—4416no—
605C2×C4—442no—
606C2×C4—442no—
607C2×C4—442no—
608C2×C4—442no—
609C2×C4C42×D1114yes—
610C2×C4#6694614yes—
611C22—224no—
612C22—224no—
613C22—224no—
614C22—444no—
615C22—444no—
616C22—442no—
617C22—444no—
618C22—444no—
619C22—442no—
620C22—442no—
621C22—442no—
622C22C2×C42×D1111yescharacteristic
623C22#1062301711yescharacteristic
624C22C2×#6694611yescharacteristic
625C22D11×#11711yescharacteristic
626C22D11×#11711yescharacteristic
627C22#1062305312yes—
628C22#1062305312yes—
629C22#1062305311yescharacteristic
630C22#1062305411yescharacteristic
631C22C4×D4×D1112yes—
632C22#1062307612yes—
633C22#1062307712yes—
634C22C4×#434312yes—
635C22#1062314112yes—
636C22#1062316812yes—
637C22#1062319212yes—
638C22#1062319512yes—
639C22#1062320711yescharacteristic
640C22#1062320811yescharacteristic
641C22#1062322511yescharacteristic
642C22#1062322611yescharacteristic
643C22#1062323312yes—
644C22#1062324012yes—
645C4—24no—
646C4—24no—
647C4—44no—
648C4—44no—
649C4—42no—
650C4—228no—
651C4—224no—
652C4—224no—
653C4—224no—
654C4—444no—
655C2—444no—
656C2#1307095511yescharacteristic
657C2C4×#6694611yescharacteristic
658C2#1307097511yescharacteristic
659C2#1307146211yescharacteristic
660C2#1307150411yescharacteristic
661C2#1307154211yescharacteristic
662C2#1307158411yescharacteristic
663C2#1307166012yes—
664C2#1307168212yes—
665C2#1307174212yes—
666C2#1307174812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1434D11
hypocenterC11#13822
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C2×#10622262C2semidirect
6. #13066847C2semidirect
7. #13066840C2semidirect
9. C4×C11⋊#95C2semidirect
10. #95×Dic11C2semidirect
11. C11×#1434C2semidirect
35. C4×(C2×D11)⋊C4C4semidirect
36. #10622282C4semidirect
70. C2×Dic11⋊C4C2×C4semidirect
82. C2×C4×Dic11C2×C4semidirect
86. C11×#95C2×C4semidirect
93. C11⋊#95C2×C4semidirect
177. (C2×D11)⋊C4C42semidirect
190. #1434D11semidirect
415. #95C4×D11semidirect
515. C11#13822semidirect

Maximal subgroups

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

subgroupindex
C2×#106222822
C2×#106222622
C2×C4×(C2×D11)⋊C42
C2×#106222792
#130668522
#130668472
#130668402
(C2×D11)⋊#952
C4×C11⋊#952
#95×Dic112
C11×#14342
#1382211