Finite Group Databasebeta

← #14676304

Subgroups — #14676304

Order 2816.

1862 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66930C211yesmaximal, characteristic
2C2×#10622555C211yesmaximal, characteristic
3C2×C22⋊C4×Dic11C211yesmaximal, characteristic
4#13066865C211yesmaximal, characteristic
5#13066863C211yesmaximal, characteristic
6#13066863C211yesmaximal, characteristic
7Dic11⋊#95C212yesmaximal, complemented
8Dic11⋊#95C212yesmaximal, complemented
9#13066842C212yesmaximal, complemented
10#13066841C212yesmaximal, complemented
11C11×#1440C211yesmaximal, characteristic
12C24×Dic11C2211yescharacteristic
13C22×C11×C22⋊C4C2211yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C22⋊Dic11C2211yescharacteristic
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4C2212yes—
20C22×Dic11⋊C4C2211yescharacteristic
21C22×Dic11⋊C4C2211yescharacteristic
22C22×C4×Dic11C2212yes—
23C22×C4×Dic11C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C2×#66930—24no—
26C2×#66930—24no—
27C2×#66930C418yescomplemented
28C2×C11×#95C2212yes—
29C2×C11×#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622555—24no—
39C22⋊C4×Dic11—24no—
40C25×C11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×Dic11—24no—
46C23×Dic11—24no—
47C23×Dic11C2×C414yes—
48C23×Dic11D414yes—
49C23×Dic11D414yes—
50C23×Dic11C2312yes—
51C23×Dic11C2311yescharacteristic
52C23×Dic11C2311yescharacteristic
53C23×Dic11C2312yes—
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2311yescharacteristic
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4—22no—
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—24no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—42no—
62C2×C11×C22⋊C4C2×C414yes—
63C2×C22⋊Dic11—22no—
64C2×C22⋊Dic11—22no—
65C2×C22⋊Dic11—22no—
66C2×C22⋊Dic11—24no—
67C2×C22⋊Dic11—22no—
68C2×C22⋊Dic11—42no—
69C2×C22⋊Dic11C2×C414yes—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—24no—
75C2×Dic11⋊C4—24no—
76C2×Dic11⋊C4—24no—
77C2×Dic11⋊C4C2×C414yes—
78C2×Dic11⋊C4C2×C414yes—
79C2×C4×Dic11—22no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11—22no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11—24no—
84C2×C4×Dic11—24no—
85C2×C4×Dic11—24no—
86C2×C4×Dic11C2×C414yes—
87C2×C4×Dic11C2×C414yes—
88#66930—232no—
89C11×#95—24no—
90C11×#95—42no—
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#13939—111nomaximal, Sylow
100C24×C11—22no—
101C24×C11—22no—
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—22no—
105C24×C11—22no—
106C24×C11C22×C412yes—
107C24×C11C2×D412yes—
108C24×C11C2×D412yes—
109C24×C11C2411yescharacteristic
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
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—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×C11C22×C412yes—
132C22×C4×C11C22×C412yes—
133C22×C4×C11#4114yes—
134C22×Dic11—28no—
135C22×Dic11—28no—
136C22×Dic11—216no—
137C22×Dic11—216no—
138C22×Dic11—22no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—22no—
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×Dic11C22⋊C4116yes—
162C22×Dic11C22×C412yes—
163C22×Dic11C22×C412yes—
164C22×Dic11C22×C412yes—
165C22×Dic11C22×C412yes—
166C22×Dic11C2×D412yes—
167C22×Dic11C2×D412yes—
168C22×Dic11C2×D412yes—
169C22×Dic11C2×D412yes—
170C22×Dic11#4114yes—
171C22×Dic11#4114yes—
172C22×Dic11#4114yes—
173C11×C22⋊C4—28no—
174C11×C22⋊C4—28no—
175C11×C22⋊C4—44no—
176C22⋊Dic11—28no—
177C22⋊Dic11—28no—
178C22⋊Dic11—44no—
179Dic11⋊C4—28no—
180Dic11⋊C4—28no—
181Dic11⋊C4—48no—
182C4×Dic11—28no—
183C4×Dic11—28no—
184C4×Dic11—48no—
185C22×#117—111no—
186C2×#380—111no—
187C2×C4×C22⋊C4—111no—
188#1440—111no—
189#1440—111no—
190#1440—111no—
191#1440D1111yescharacteristic
192C4⋊#95—112no—
193C4⋊#95—112no—
194#1434—112no—
195#1434—112no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—24no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—24no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11C2×C22⋊C414yes—
217C23×C11C23×C411yescharacteristic
218C23×C11C22×D411yescharacteristic
219C23×C11C22×D411yescharacteristic
220C23×C11C2×#4112yes—
221C23×C11C2×#4112yes—
222C23×C11C2×#4112yes—
223C23×C11C2×#4112yes—
224C23×C11H(5,𝔽2)12yes—
225C23×C112−1+412yes—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—42no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—42no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
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×C11—42no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—232no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—42no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—42no—
266C2×Dic11—41no—
267C2×Dic11—41no—
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×Dic11—42no—
279C2×Dic11C2×C22⋊C414yes—
280C2×Dic11C2×C22⋊C414yes—
281C2×Dic11#11714yes—
282C2×Dic11#11714yes—
283C2×Dic11#12318yes—
284C2×Dic11#12318yes—
285C24×C4—111no—
286C2×#117—118no—
287C2×#117—224no—
288C2×#117—224no—
289C22×C4⋊C4—111no—
290C22×C4⋊C4—111no—
291C22×C4⋊C4—112no—
292C22×C22⋊C4—111no—
293C22×C22⋊C4—111no—
294C22×C22⋊C4—111no—
295C22×C22⋊C4C2×D1111yescharacteristic
296C22×C22⋊C4C2×D1111yescharacteristic
297C22×C22⋊C4C2×D1111yescharacteristic
298C22×C42—111no—
299C22×C42—111no—
300C22×C42—112no—
301#380—224no—
302C4×C22⋊C4—224no—
303C2×#95—112no—
304C2×#95—112no—
305C2×#95—112no—
306C2×#95—112no—
307C2×#95—112no—
308C2×#95—112no—
309C2×#95—112no—
310C2×#95—112no—
311C2×#95C2×D1112yes—
312C2×#95C2×D1112yes—
313C22×C11—24no—
314C22×C11—24no—
315C22×C11—24no—
316C22×C11—44no—
317C22×C11—44no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—44no—
321C22×C11—44no—
322C22×C11C22×C22⋊C411yescharacteristic
323C22×C11C2×#11711yescharacteristic
324C22×C11C2×#11711yescharacteristic
325C22×C11C4×#4112yes—
326C22×C11#52012yes—
327C22×C11C2×#12312yes—
328C22×C11C2×#12312yes—
329C22×C11#52511yescharacteristic
330C22×C11#52511yescharacteristic
331C22×C11#53212yes—
332C22×C11#53511yescharacteristic
333C22×C11#53611yescharacteristic
334C22×C11#53712yes—
335C22×C11#55212yes—
336C22×C11#55212yes—
337C22×C11#55312yes—
338C22×C11#55312yes—
339C22×C11#55512yes—
340C22×C11#55512yes—
341C22×C11#55612yes—
342C22×C11#55612yes—
343C4×C11—42no—
344C4×C11—44no—
345C4×C11—42no—
346C4×C11—82no—
347Dic11—24no—
348Dic11—42no—
349Dic11—44no—
350Dic11—42no—
351Dic11—82no—
352Dic11#38118yes—
353C25C22×D1111yescharacteristic
354C23×C4—111no—
355C23×C4—114no—
356C23×C4—114no—
357C23×C4—114no—
358C23×C4—111no—
359C23×C4—111no—
360C23×C4—111no—
361C23×C4—112no—
362C23×C4—112no—
363C23×C4—224no—
364C23×C4—224no—
365C23×C4C22×D1112yes—
366C23×C4C22×D1111yescharacteristic
367C23×C4C22×D1111yescharacteristic
368C23×C4C22×D1112yes—
369#117—2232no—
370C2×C4⋊C4—114no—
371C2×C4⋊C4—114no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4—222no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4—222no—
376C2×C4⋊C4—224no—
377C2×C4⋊C4—224no—
378C2×C4⋊C4—224no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—114no—
386C2×C22⋊C4—224no—
387C2×C22⋊C4—222no—
388C2×C22⋊C4—222no—
389C2×C22⋊C4—222no—
390C2×C22⋊C4—222no—
391C2×C22⋊C4—442no—
392C2×C22⋊C4C4×D1114yes—
393C2×C42—114no—
394C2×C42—114no—
395C2×C42—222no—
396C2×C42—222no—
397C2×C42—222no—
398C2×C42—222no—
399C2×C42—224no—
400C2×C42—224no—
401C2×C42—224no—
402#95—24no—
403#95—42no—
404#95—224no—
405#95—224no—
406#95—224no—
407#95—224no—
408#95—224no—
409#95—442no—
410#95—442no—
411#95—442no—
412C2×C11—44no—
413C2×C11C2×#38111yescharacteristic
414C2×C11#229711yescharacteristic
415C2×C11#231111yescharacteristic
416C2×C11#234612yes—
417C2×C11#234712yes—
418C2×C11#248512yes—
419C2×C11#248512yes—
420C2×C11#249912yes—
421C2×C11#250012yes—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24C2×C4×D1112yes—
429C24D4×D1112yes—
430C24D4×D1112yes—
431C24C23×D1111yescharacteristic
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
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—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—112no—
454C22×C4—112no—
455C22×C4—112no—
456C22×C4—114no—
457C22×C4—114no—
458C22×C4—1116no—
459C22×C4—112no—
460C22×C4—112no—
461C22×C4—112no—
462C22×C4—112no—
463C22×C4—112no—
464C22×C4—114no—
465C22×C4—228no—
466C22×C4—228no—
467C22×C4—2216no—
468C22×C4—2216no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
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×C4—222no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4C2×C4×D1112yes—
493C22×C4C2×C4×D1112yes—
494C22×C4#434114yes—
495C4⋊C4—228no—
496C4⋊C4—228no—
497C4⋊C4—448no—
498C22⋊C4—28no—
499C22⋊C4—28no—
500C22⋊C4—44no—
501C22⋊C4—228no—
502C22⋊C4—228no—
503C22⋊C4—444no—
504C42—228no—
505C42—228no—
506C42—448no—
507C11#1393911yescharacteristic, complemented, Sylow
508C23—22no—
509C23—22no—
510C23—24no—
511C23—24no—
512C23—22no—
513C23—22no—
514C23—24no—
515C23—24no—
516C23—22no—
517C23—24no—
518C23—24no—
519C23—22no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—42no—
527C23—42no—
528C23C22⋊C4×D1114yes—
529C23C22×C4×D1111yescharacteristic
530C23C2×D4×D1111yescharacteristic
531C23C2×D4×D1111yescharacteristic
532C23C2×#434112yes—
533C23#6703712yes—
534C23#41×D1112yes—
535C23#41×D1112yes—
536C23#41×D1112yes—
537C23#6704312yes—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—41no—
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—114no—
563C2×C4—114no—
564C2×C4—114no—
565C2×C4—118no—
566C2×C4—118no—
567C2×C4—114no—
568C2×C4—2232no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—224no—
579C2×C4—224no—
580C2×C4—442no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—442no—
584C2×C4—442no—
585C2×C4—442no—
586C2×C4—441no—
587C2×C4—442no—
588C2×C4—441no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4—442no—
592C2×C4—442no—
593C2×C4—442no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—442no—
597C22—24no—
598C22—24no—
599C22—24no—
600C22—44no—
601C22—44no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—44no—
606C22C2×C22⋊C4×D1111yescharacteristic
607C22D11×#11711yescharacteristic
608C22D11×#11711yescharacteristic
609C22C4×#434112yes—
610C22#1062307712yes—
611C22#1062311711yescharacteristic
612C22#1062312311yescharacteristic
613C22#1062312712yes—
614C22#1062312812yes—
615C22#1062313212yes—
616C22#1062314712yes—
617C22#1062317911yescharacteristic
618C22#1062318112yes—
619C22D11×#12312yes—
620C22D11×#12312yes—
621C22#1062318711yescharacteristic
622C22#1062319212yes—
623C22#1062320112yes—
624C22#1062320212yes—
625C22#1062323312yes—
626C22#1062323912yes—
627C4—44no—
628C4—42no—
629C4—42no—
630C4—82no—
631C4—118no—
632C4—224no—
633C4—444no—
634C4—442no—
635C4—442no—
636C4—882no—
637C2—44no—
638C2D11×#38111yescharacteristic
639C2#1307110111yescharacteristic
640C2#1307120311yescharacteristic
641C2#1307149812yes—
642C2#1307150612yes—
643C2#1307290612yes—
644C2#1307290812yes—
645C2#1307306412yes—
646C2#1307307312yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1440C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1440D11
hypocenterC11#13939
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
7. Dic11⋊#95C2semidirect
8. Dic11⋊#95C2semidirect
9. #13066842C2semidirect
10. #13066841C2semidirect
27. C2×#66930C4semidirect
507. C11#13939semidirect

Maximal subgroups

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

subgroupindex
C22×#669302
C2×#106225552
C2×C22⋊C4×Dic112
#130668652
#130668632
Dic11⋊#952
#130668422
#130668412
C11×#14402
#1393911