Finite Group Databasebeta

← #14676306

Subgroups — #14676306

Order 2816.

1862 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66925C211yesmaximal, characteristic
2C2×#10622280C211yesmaximal, characteristic
3C2×#10622279C211yesmaximal, characteristic
4#13066864C212yesmaximal
5#13066864C212yesmaximal
6Dic11⋊#95C212yesmaximal, complemented
7Dic11⋊#95C212yesmaximal, complemented
8#13066843C211yesmaximal, characteristic, complemented
9#13066840C211yesmaximal, characteristic, complemented
10#13066840C211yesmaximal, characteristic, complemented
11C11×#1434C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2211yescharacteristic
16C22×(C2×D11)⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2212yes—
18C22×Dic11⋊C4C2212yes—
19C22×Dic11⋊C4C2211yescharacteristic
20C22×Dic11⋊C4C2211yescharacteristic
21C22×C4×Dic11C2212yes—
22C22×C4×Dic11C2211yescharacteristic
23C2×#66925—24no—
24C2×#66925—24no—
25C2×#66925C418yescomplemented
26C2×C11×#95C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2212yes—
29C2×C11×#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622280—24no—
39#10622279—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—24no—
52C22×C4×D11—24no—
53C22×C4×D11C2×C414yes—
54C22×C4×D11D414yes—
55C22×C4×D11D414yes—
56C2×C42×C11—22no—
57C2×C42×C11—22no—
58C2×C42×C11C2×C414yes—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—24no—
64C2×(C2×D11)⋊C4—24no—
65C2×(C2×D11)⋊C4—24no—
66C2×(C2×D11)⋊C4—24no—
67C2×(C2×D11)⋊C4—42no—
68C2×(C2×D11)⋊C4—42no—
69C2×(C2×D11)⋊C4C2×C414yes—
70C2×(C2×D11)⋊C4C2×C414yes—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—24no—
76C2×Dic11⋊C4—24no—
77C2×Dic11⋊C4—24no—
78C2×Dic11⋊C4C2×C414yes—
79C2×Dic11⋊C4C2×C414yes—
80C2×C4×Dic11—22no—
81C2×C4×Dic11—22no—
82C2×C4×Dic11—24no—
83C2×C4×Dic11—24no—
84C2×C4×Dic11—24no—
85C2×C4×Dic11C2×C414yes—
86#66925—232no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95—24no—
90C11×#95—42no—
91C11⋊#95—22no—
92C11⋊#95—22no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96C11⋊#95—42no—
97C11⋊#95—42no—
98C11⋊#95—42no—
99#13939—111nomaximal, Sylow
100C24×C11C2411yescharacteristic
101C23×D11—22no—
102C23×D11—22no—
103C23×D11—22no—
104C23×D11—22no—
105C23×D11—21no—
106C23×D11—21no—
107C23×D11—21no—
108C23×D11—21no—
109C23×D11C22×C412yes—
110C23×D11C2×D412yes—
111C23×D11C2×D412yes—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
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—21no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11C22×C412yes—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C22×C412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11#4114yes—
143C22×Dic11—22no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
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—21no—
159C22×Dic11—21no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—21no—
164C22×Dic11—22no—
165C22×Dic11—21no—
166C22×Dic11C22×C412yes—
167C22×Dic11C22×C412yes—
168C22×Dic11C22×C412yes—
169C22×Dic11C2×D412yes—
170C22×Dic11C2×D412yes—
171C22×Dic11#4114yes—
172C22×Dic11#4114yes—
173C22×Dic11#4114yes—
174C2×C4×D11—28no—
175C2×C4×D11—28no—
176C2×C4×D11—216no—
177C2×C4×D11—216no—
178C2×C4×D11C22⋊C4116yes—
179C42×C11—28no—
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—
186Dic11⋊C4—48no—
187C4×Dic11—28no—
188C4×Dic11—48no—
189C22×#117—111no—
190C2×#380—111no—
191C2×C4×C22⋊C4—111no—
192#1440—112no—
193#1440—112no—
194C4⋊#95—112no—
195C4⋊#95—112no—
196#1434—111no—
197#1434—111no—
198#1434—111no—
199#1434D1111yescharacteristic, complemented
200C23×C11C23×C411yescharacteristic
201C23×C11C22×D411yescharacteristic
202C23×C11C22×D411yescharacteristic
203C23×C11C2×#4112yes—
204C23×C11C2×#4112yes—
205C23×C11C2×#4112yes—
206C23×C11C2×#4112yes—
207C23×C11H(5,𝔽2)11yescharacteristic
208C23×C11H(5,𝔽2)11yescharacteristic
209C23×C112−1+411yescharacteristic
210C23×C112−1+411yescharacteristic
211C22×D11—22no—
212C22×D11—22no—
213C22×D11—22no—
214C22×D11—22no—
215C22×D11—22no—
216C22×D11—22no—
217C22×D11—24no—
218C22×D11—24no—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11—22no—
222C22×D11—22no—
223C22×D11—22no—
224C22×D11—22no—
225C22×D11—42no—
226C22×D11—42no—
227C22×D11—42no—
228C22×D11—42no—
229C22×D11—42no—
230C22×D11—42no—
231C22×D11—42no—
232C22×D11—42no—
233C22×D11C2×C22⋊C414yes—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—42no—
254C2×C4×C11—41no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11C2×C22⋊C414yes—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289C2×Dic11—42no—
290C2×Dic11—42no—
291C2×Dic11C2×C22⋊C414yes—
292C2×Dic11#11714yes—
293C2×Dic11#11714yes—
294C2×Dic11#12318yes—
295C2×Dic11#12318yes—
296C4×D11—232no—
297C24×C4—111no—
298C2×#117—118no—
299C2×#117—224no—
300C2×#117—224no—
301C22×C4⋊C4—111no—
302C22×C4⋊C4—111no—
303C22×C4⋊C4—112no—
304C22×C22⋊C4—111no—
305C22×C22⋊C4—111no—
306C22×C22⋊C4—112no—
307C22×C22⋊C4—112no—
308C22×C42—111no—
309C22×C42—112no—
310C22×C42C2×D1111yescharacteristic
311#380—224no—
312C4×C22⋊C4—224no—
313C2×#95—111no—
314C2×#95—111no—
315C2×#95—112no—
316C2×#95—112no—
317C2×#95—112no—
318C2×#95—112no—
319C2×#95—112no—
320C2×#95—112no—
321C2×#95C2×D1111yescharacteristic
322C2×#95C2×D1111yescharacteristic
323C2×#95C2×D1112yes—
324C2×#95C2×D1112yes—
325C22×C11C22×C22⋊C411yescharacteristic
326C22×C11C2×#11711yescharacteristic
327C22×C11C2×#11711yescharacteristic
328C22×C11C4×#4111yescharacteristic
329C22×C11C4×#4111yescharacteristic
330C22×C11#52011yescharacteristic
331C22×C11#52011yescharacteristic
332C22×C11C2×#12312yes—
333C22×C11C2×#12312yes—
334C22×C11#52512yes—
335C22×C11#53212yes—
336C22×C11#53511yescharacteristic
337C22×C11#53611yescharacteristic
338C22×C11#53711yescharacteristic
339C22×C11#53711yescharacteristic
340C22×C11#55212yes—
341C22×C11#55212yes—
342C22×C11#55312yes—
343C22×C11#55312yes—
344C22×C11#55512yes—
345C22×C11#55512yes—
346C22×C11#55612yes—
347C22×C11#55612yes—
348C2×D11—24no—
349C2×D11—24no—
350C2×D11—24no—
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—44no—
356C2×D11—44no—
357C2×D11—44no—
358C2×D11—44no—
359C4×C11—24no—
360C4×C11—42no—
361C4×C11—44no—
362C4×C11—42no—
363C4×C11—82no—
364Dic11—42no—
365Dic11—44no—
366Dic11—42no—
367Dic11—82no—
368Dic11#38118yes—
369C25—111no—
370C23×C4—111no—
371C23×C4—114no—
372C23×C4—114no—
373C23×C4—114no—
374C23×C4—111no—
375C23×C4—111no—
376C23×C4—112no—
377C23×C4—112no—
378C23×C4—224no—
379C23×C4—224no—
380C23×C4C22×D1112yes—
381C23×C4C22×D1111yescharacteristic
382C23×C4C22×D1111yescharacteristic
383C23×C4C22×D1112yes—
384C23×C4C22×D1111yescharacteristic
385#117—2232no—
386C2×C4⋊C4—114no—
387C2×C4⋊C4—114no—
388C2×C4⋊C4—222no—
389C2×C4⋊C4—222no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—222no—
392C2×C4⋊C4—224no—
393C2×C4⋊C4—224no—
394C2×C4⋊C4—224no—
395C2×C22⋊C4—114no—
396C2×C22⋊C4—114no—
397C2×C22⋊C4—224no—
398C2×C22⋊C4—222no—
399C2×C22⋊C4—222no—
400C2×C22⋊C4—222no—
401C2×C22⋊C4—222no—
402C2×C22⋊C4—224no—
403C2×C22⋊C4—224no—
404C2×C22⋊C4—224no—
405C2×C22⋊C4—442no—
406C2×C22⋊C4—442no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—114no—
410C2×C42—222no—
411C2×C42—222no—
412C2×C42—224no—
413C2×C42—224no—
414C2×C42—224no—
415C2×C42C4×D1114yes—
416#95—24no—
417#95—22no—
418#95—22no—
419#95—42no—
420#95—224no—
421#95—224no—
422#95—224no—
423#95—222no—
424#95—222no—
425#95—442no—
426#95—442no—
427#95—442no—
428C2×C11C2×#38111yescharacteristic
429C2×C11#229711yescharacteristic
430C2×C11#231111yescharacteristic
431C2×C11#234611yescharacteristic
432C2×C11#234611yescharacteristic
433C2×C11#234711yescharacteristic
434C2×C11#234711yescharacteristic
435C2×C11#248512yes—
436C2×C11#248512yes—
437C2×C11#249912yes—
438C2×C11#250012yes—
439D11—44no—
440C24—112no—
441C24—112no—
442C24—112no—
443C24—222no—
444C24—221no—
445C24—221no—
446C24—222no—
447C24—222no—
448C24—222no—
449C24—221no—
450C24—221no—
451C24C23×D1111yescharacteristic
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—112no—
478C22×C4—112no—
479C22×C4—112no—
480C22×C4—114no—
481C22×C4—114no—
482C22×C4—1116no—
483C22×C4—112no—
484C22×C4—112no—
485C22×C4—114no—
486C22×C4—228no—
487C22×C4—228no—
488C22×C4—2216no—
489C22×C4—2216no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—222no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—222no—
507C22×C4—222no—
508C22×C4—222no—
509C22×C4—222no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—222no—
513C22×C4C2×C4×D1112yes—
514C22×C4C2×C4×D1112yes—
515C22×C4C2×C4×D1112yes—
516C22×C4#433914yes—
517C22×C4D4×D1112yes—
518C22×C4D4×D1112yes—
519C4⋊C4—228no—
520C4⋊C4—228no—
521C4⋊C4—448no—
522C22⋊C4—228no—
523C22⋊C4—228no—
524C22⋊C4—2216no—
525C22⋊C4—448no—
526C42—28no—
527C42—228no—
528C42—448no—
529C11#1393911yescharacteristic, complemented, Sylow
530C23—114no—
531C23—222no—
532C23—222no—
533C23—222no—
534C23—222no—
535C23—222no—
536C23—222no—
537C23—224no—
538C23—224no—
539C23—222no—
540C23—222no—
541C23—222no—
542C23—222no—
543C23—224no—
544C23—224no—
545C23—442no—
546C23—442no—
547C23—442no—
548C23—442no—
549C23—442no—
550C23—442no—
551C23—442no—
552C23—442no—
553C23C22×C4×D1111yescharacteristic
554C23C2×#433912yes—
555C23C2×D4×D1111yescharacteristic
556C23C2×D4×D1111yescharacteristic
557C23#6703711yescharacteristic
558C23#6704011yescharacteristic
559C23#41×D1112yes—
560C23#41×D1112yes—
561C23#41×D1112yes—
562C23#6704211yescharacteristic
563C23#6704311yescharacteristic
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—114no—
595C2×C4—114no—
596C2×C4—114no—
597C2×C4—118no—
598C2×C4—118no—
599C2×C4—2232no—
600C2×C4—224no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—224no—
608C2×C4—224no—
609C2×C4—442no—
610C2×C4—442no—
611C2×C4—442no—
612C2×C4—442no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—442no—
617C2×C4—441no—
618C2×C4—442no—
619C2×C4—442no—
620C2×C4—442no—
621C2×C4—442no—
622C2×C4—442no—
623C2×C4—442no—
624C2×C4—442no—
625C2×C4—442no—
626C2×C4C22⋊C4×D1114yes—
627C22—224no—
628C22—224no—
629C22—224no—
630C22—444no—
631C22—444no—
632C22—442no—
633C22—442no—
634C22—442no—
635C22—442no—
636C22—444no—
637C22—444no—
638C22C4×#433911yescharacteristic
639C22C2×C22⋊C4×D1111yescharacteristic
640C22#1062303511yescharacteristic
641C22D11×#11711yescharacteristic
642C22D11×#11711yescharacteristic
643C22#1062305311yescharacteristic
644C22#1062305411yescharacteristic
645C22#1062306212yes—
646C22#1062306312yes—
647C22#1062307112yes—
648C22#1062307812yes—
649C22#1062307912yes—
650C22#1062309912yes—
651C22#1062313811yescharacteristic
652C22#1062313911yescharacteristic
653C22#1062315911yescharacteristic
654C22#1062316011yescharacteristic
655C22D11×#12312yes—
656C22D11×#12312yes—
657C22#1062320112yes—
658C22#1062322412yes—
659C22#1062323312yes—
660C22#1062324012yes—
661C4—24no—
662C4—44no—
663C4—42no—
664C4—42no—
665C4—82no—
666C4—118no—
667C4—444no—
668C4—442no—
669C4—442no—
670C4—882no—
671C2—444no—
672C2D11×#38111yescharacteristic
673C2#1307110211yescharacteristic
674C2#1307120511yescharacteristic
675C2#1307149611yescharacteristic
676C2#1307150211yescharacteristic
677C2#1307150411yescharacteristic
678C2#1307151011yescharacteristic
679C2#1307291012yes—
680C2#1307291212yes—
681C2#1307306712yes—
682C2#1307307612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1434D11
hypocenterC11#13939
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
6. Dic11⋊#95C2semidirect
7. Dic11⋊#95C2semidirect
8. #13066843C2semidirect
9. #13066840C2semidirect
10. #13066840C2semidirect
11. C11×#1434C2semidirect
25. C2×#66925C4semidirect
199. #1434D11semidirect
529. C11#13939semidirect

Maximal subgroups

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

subgroupindex
C22×#669252
C2×#106222802
C2×#106222792
#130668642
Dic11⋊#952
#130668432
#130668402
C11×#14342
#1393911