Finite Group Databasebeta

← #14680147

Subgroups — #14680147

Order 2816.

2142 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66931C211yesmaximal, characteristic
2C22×#66930C211yesmaximal, characteristic
3C2×#10622259C212yesmaximal, complemented
4C2×#10622555C211yesmaximal, characteristic
5#13066868C212yesmaximal, complemented
6#13066867C212yesmaximal, complemented
7#13066865C211yesmaximal, characteristic
8#13066863C211yesmaximal, characteristic
9#13066863C211yesmaximal, characteristic
10Dic11⋊#95C212yesmaximal, complemented
11C11×#1440C211yesmaximal, characteristic
12C24×Dic11C2211yescharacteristic
13C23×Dic22C2211yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×Dic11⋊C4C2212yes—
22C22×Dic11⋊C4C2212yes—
23C22×Dic11⋊C4C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×C4×Dic11C2212yes—
26C2×#66931—24no—
27C2×#66931—24no—
28C2×#66931C418yescomplemented
29C2×#66930—24no—
30C2×#66930—28no—
31C2×C11×#95C2212yes—
32C2×C11×#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40#10622555—24no—
41#10622259—28no—
42C25×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2312yes—
47C23×Dic11—24no—
48C23×Dic11—24no—
49C23×Dic11C2×C414yes—
50C23×Dic11D414yes—
51C23×Dic11D414yes—
52C23×Dic11C2312yes—
53C23×Dic11C2311yescharacteristic
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2312yes—
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2311yescharacteristic
58C22×Dic22—22no—
59C22×Dic22—22no—
60C22×Dic22—24no—
61C22×Dic22—24no—
62C22×Dic22C2×C414yes—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—42no—
69C2×C11×C22⋊C4C2×C414yes—
70C2×C22⋊Dic11—22no—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—42no—
76C2×C22⋊Dic11C2×C414yes—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11C2×C414yes—
80C2×Dic11⋊C4—24no—
81C2×Dic11⋊C4—24no—
82C2×Dic11⋊C4—24no—
83C2×Dic11⋊C4—22no—
84C2×Dic11⋊C4—22no—
85C2×Dic11⋊C4—22no—
86C2×Dic11⋊C4—22no—
87C2×Dic11⋊C4—24no—
88C2×Dic11⋊C4—24no—
89C2×Dic11⋊C4—24no—
90C2×Dic11⋊C4C2×C414yes—
91C2×Dic11⋊C4C2×C414yes—
92C2×C4×Dic11—24no—
93C2×C4×Dic11—24no—
94C2×C4×Dic11D418yes—
95#66931—232no—
96#66930—232no—
97C11×#95—24no—
98C11×#95—42no—
99C11⋊#95—24no—
100C11⋊#95—24no—
101C11⋊#95—24no—
102C11⋊#95—24no—
103C11⋊#95—42no—
104C11⋊#95—42no—
105C11⋊#95—42no—
106#14258—111nomaximal, Sylow
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11C22×C412yes—
114C24×C11C2×D412yes—
115C24×C11C2×D412yes—
116C24×C11C2411yescharacteristic
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
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×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C22×C412yes—
140C22×C4×C11C2×D414yes—
141C22×Dic11—216no—
142C22×Dic11—28no—
143C22×Dic11—216no—
144C22×Dic11—28no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
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×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11C22⋊C4116yes—
169C22×Dic11C22×C412yes—
170C22×Dic11C22×C412yes—
171C22×Dic11C22×C412yes—
172C22×Dic11C22×C412yes—
173C22×Dic11C2×D414yes—
174C22×Dic11C2×D412yes—
175C22×Dic11C2×D412yes—
176C22×Dic11C2×D412yes—
177C22×Dic11C2×D412yes—
178C22×Dic11C2×D414yes—
179C22×Dic11#4114yes—
180C2×Dic22—28no—
181C2×Dic22—216no—
182C2×Dic22—44no—
183C2×Dic22—48no—
184C2×Dic22—44no—
185C11×C22⋊C4—28no—
186C11×C22⋊C4—28no—
187C11×C22⋊C4—44no—
188C22⋊Dic11—28no—
189C22⋊Dic11—28no—
190C22⋊Dic11—44no—
191C4⋊Dic11—28no—
192Dic11⋊C4—216no—
193Dic11⋊C4—28no—
194Dic11⋊C4—28no—
195Dic11⋊C4—48no—
196C4×Dic11—216no—
197C22×C22⋊Q8—111no—
198C22×#117—111no—
199C2×#391—112no—
200C2×#380—111no—
201#1441—112no—
202#1441—112no—
203#1440—111no—
204#1440—111no—
205#1440—111no—
206#1440D1111yescharacteristic
207C4⋊#95—112no—
208C23×C11—24no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—24no—
212C23×C11—22no—
213C23×C11—24no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—22no—
219C23×C11—24no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11C2×C22⋊C414yes—
229C23×C11C23×C411yescharacteristic
230C23×C11C22×D411yescharacteristic
231C23×C11C22×D411yescharacteristic
232C23×C11C22×D412yes—
233C23×C11C2×#4112yes—
234C23×C11H(5,𝔽2)12yes—
235C23×C112−1+412yes—
236C23×C112−1+412yes—
237C23×C112−1+412yes—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—41no—
246C2×C4×C11—42no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
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×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×Dic11—24no—
263C2×Dic11—22no—
264C2×Dic11—24no—
265C2×Dic11—22no—
266C2×Dic11—232no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—41no—
275C2×Dic11—42no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—42no—
280C2×Dic11—42no—
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×Dic11C2×C22⋊C414yes—
293C2×Dic11C4×D418yes—
294C2×Dic11#12014yes—
295C2×Dic11#12118yes—
296C2×Dic11#12314yes—
297Dic22—416no—
298C23×Q8—111no—
299C24×C4—111no—
300C2×C22⋊Q8—118no—
301C2×C22⋊Q8—224no—
302C2×C22⋊Q8—224no—
303C2×#117—228no—
304C2×#117—224no—
305C22×C4⋊C4—111no—
306C22×C4⋊C4—111no—
307C22×C4⋊C4—111no—
308C22×C4⋊C4—112no—
309C22×C4⋊C4—112no—
310C22×C22⋊C4—111no—
311C22×C22⋊C4—111no—
312C22×C22⋊C4—111no—
313C22×C22⋊C4C2×D1111yescharacteristic
314C22×C22⋊C4C2×D1111yescharacteristic
315C22×C22⋊C4C2×D1111yescharacteristic
316C22×C42—112no—
317#391—228no—
318#380—224no—
319C2×#95—112no—
320C2×#95—112no—
321C2×#95—112no—
322C2×#95—112no—
323C2×#95—112no—
324C2×#95—112no—
325C2×#95—112no—
326C2×#95C2×D1112yes—
327C2×#95C2×D1112yes—
328C22×C11—24no—
329C22×C11—24no—
330C22×C11—24no—
331C22×C11—44no—
332C22×C11—44no—
333C22×C11—44no—
334C22×C11—44no—
335C22×C11—44no—
336C22×C11—44no—
337C22×C11C22×C22⋊C411yescharacteristic
338C22×C11C2×C4×D412yes—
339C22×C11#51911yescharacteristic
340C22×C11#51911yescharacteristic
341C22×C11#52012yes—
342C22×C11C2×#12011yescharacteristic
343C22×C11C2×#12112yes—
344C22×C11C2×#12311yescharacteristic
345C22×C11#53511yescharacteristic
346C22×C11#53612yes—
347C22×C11#53612yes—
348C22×C11#53611yescharacteristic
349C22×C11#53612yes—
350C22×C11#53612yes—
351C22×C11#53712yes—
352C22×C11#53712yes—
353C22×C11#53712yes—
354C22×C11#54112yes—
355C22×C11#54112yes—
356C22×C11#54212yes—
357C22×C11#54212yes—
358C4×C11—42no—
359C4×C11—44no—
360C4×C11—42no—
361C4×C11—82no—
362Dic11—24no—
363Dic11—42no—
364Dic11—44no—
365Dic11—42no—
366Dic11—82no—
367Dic11#38618yes—
368C25C22×D1111yescharacteristic
369C22×Q8—114no—
370C22×Q8—222no—
371C22×Q8—222no—
372C22×Q8—224no—
373C22×Q8—224no—
374C23×C4—111no—
375C23×C4—114no—
376C23×C4—114no—
377C23×C4—114no—
378C23×C4—111no—
379C23×C4—111no—
380C23×C4—111no—
381C23×C4—112no—
382C23×C4—112no—
383C23×C4—224no—
384C23×C4—224no—
385C23×C4C22×D1112yes—
386C23×C4C22×D1111yescharacteristic
387C23×C4C22×D1111yescharacteristic
388C23×C4C22×D1112yes—
389C22⋊Q8—2232no—
390#117—2232no—
391C2×C4⋊C4—114no—
392C2×C4⋊C4—114no—
393C2×C4⋊C4—114no—
394C2×C4⋊C4—224no—
395C2×C4⋊C4—224no—
396C2×C4⋊C4—222no—
397C2×C4⋊C4—222no—
398C2×C4⋊C4—222no—
399C2×C4⋊C4—222no—
400C2×C4⋊C4—222no—
401C2×C4⋊C4—222no—
402C2×C4⋊C4—224no—
403C2×C4⋊C4—224no—
404C2×C4⋊C4—224no—
405C2×C4⋊C4—224no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—22no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—42no—
412C2×C22⋊C4—114no—
413C2×C22⋊C4—224no—
414C2×C22⋊C4—222no—
415C2×C22⋊C4—222no—
416C2×C22⋊C4—222no—
417C2×C22⋊C4—222no—
418C2×C22⋊C4—442no—
419C2×C22⋊C4C4×D1114yes—
420C2×C42—118no—
421C2×C42—224no—
422C2×C42—224no—
423#95—24no—
424#95—42no—
425#95—224no—
426#95—224no—
427#95—224no—
428#95—224no—
429#95—442no—
430#95—442no—
431#95—442no—
432C2×C11—44no—
433C2×C11C2×#38611yescharacteristic
434C2×C11#231011yescharacteristic
435C2×C11#231111yescharacteristic
436C2×C11#232312yes—
437C2×C11#232312yes—
438C2×C11#261612yes—
439C2×C11#262012yes—
440C2×C11#262112yes—
441C2×C11#262512yes—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24C2×C4×D1112yes—
449C24D4×D1112yes—
450C24D4×D1112yes—
451C24C23×D1111yescharacteristic
452C2×Q8—228no—
453C2×Q8—2216no—
454C2×Q8—444no—
455C2×Q8—448no—
456C2×Q8—444no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
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—22no—
478C22×C4—112no—
479C22×C4—114no—
480C22×C4—112no—
481C22×C4—112no—
482C22×C4—114no—
483C22×C4—1116no—
484C22×C4—112no—
485C22×C4—112no—
486C22×C4—112no—
487C22×C4—112no—
488C22×C4—112no—
489C22×C4—114no—
490C22×C4—228no—
491C22×C4—2216no—
492C22×C4—2216no—
493C22×C4—228no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—222no—
506C22×C4—222no—
507C22×C4—222no—
508C22×C4—222no—
509C22×C4—222no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—222no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4C2×C4×D1112yes—
518C22×C4C2×C4×D1112yes—
519C22×C4D4×D1114yes—
520C4⋊C4—228no—
521C4⋊C4—228no—
522C4⋊C4—228no—
523C4⋊C4—2216no—
524C4⋊C4—448no—
525C22⋊C4—28no—
526C22⋊C4—28no—
527C22⋊C4—44no—
528C22⋊C4—228no—
529C22⋊C4—228no—
530C22⋊C4—444no—
531C42—2216no—
532C11#1425811yescharacteristic, complemented, Sylow
533C23—22no—
534C23—22no—
535C23—24no—
536C23—24no—
537C23—22no—
538C23—22no—
539C23—24no—
540C23—24no—
541C23—24no—
542C23—24no—
543C23—22no—
544C23—22no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—42no—
552C23—42no—
553C23C22⋊C4×D1114yes—
554C23C22×C4×D1111yescharacteristic
555C23C2×D4×D1111yescharacteristic
556C23C2×D4×D1111yescharacteristic
557C23C2×D4×D1112yes—
558C23#6703712yes—
559C23#41×D1112yes—
560C23#6704312yes—
561C23#6704312yes—
562C23#6704312yes—
563Q8—4416no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—41no—
578C2×C4—42no—
579C2×C4—41no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—114no—
589C2×C4—118no—
590C2×C4—114no—
591C2×C4—118no—
592C2×C4—114no—
593C2×C4—114no—
594C2×C4—2232no—
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—224no—
605C2×C4—224no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—442no—
609C2×C4—442no—
610C2×C4—442no—
611C2×C4—442no—
612C2×C4—441no—
613C2×C4—442no—
614C2×C4—442no—
615C2×C4—441no—
616C2×C4—442no—
617C2×C4—442no—
618C2×C4—442no—
619C2×C4—442no—
620C2×C4—442no—
621C2×C4—442no—
622C2×C4—442no—
623C22—24no—
624C22—24no—
625C22—24no—
626C22—44no—
627C22—44no—
628C22—44no—
629C22—44no—
630C22—44no—
631C22—44no—
632C22C2×C22⋊C4×D1111yescharacteristic
633C22#1062304711yescharacteristic
634C22#1062304711yescharacteristic
635C22C4×D4×D1112yes—
636C22#1062307712yes—
637C22D11×#12011yescharacteristic
638C22#1062312311yescharacteristic
639C22#1062312812yes—
640C22#1062312812yes—
641C22D11×#12112yes—
642C22#1062313912yes—
643C22#1062317912yes—
644C22#1062317912yes—
645C22#1062317911yescharacteristic
646C22#1062317912yes—
647C22D11×#12311yescharacteristic
648C22#1062319312yes—
649C22#1062320012yes—
650C22#1062320612yes—
651C22#1062323212yes—
652C22#1062323212yes—
653C4—42no—
654C4—44no—
655C4—42no—
656C4—82no—
657C4—118no—
658C4—224no—
659C4—442no—
660C4—444no—
661C4—442no—
662C4—882no—
663C2—44no—
664C2D11×#38611yescharacteristic
665C2#1307120111yescharacteristic
666C2#1307120311yescharacteristic
667C2#1307129112yes—
668C2#1307129512yes—
669C2#1307434412yes—
670C2#1307437212yes—
671C2#1307438112yes—
672C2#1307441212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1440C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1440D11
hypocenterC11#14258
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
3. C2×#10622259C2semidirect
5. #13066868C2semidirect
6. #13066867C2semidirect
10. Dic11⋊#95C2semidirect
28. C2×#66931C4semidirect
532. C11#14258semidirect

Maximal subgroups

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

subgroupindex
C22×#669312
C22×#669302
C2×#106222592
C2×#106225552
#130668682
#130668672
#130668652
#130668632
Dic11⋊#952
C11×#14402
#1425811