Finite Group Databasebeta

← #14676470

Subgroups — #14676470

Order 2816.

1862 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66945C211yesmaximal, characteristic
2C2×#10622263C211yesmaximal, characteristic, complemented
3C2×#10622545C211yesmaximal, characteristic, complemented
4#13066868C212yesmaximal, complemented
5#13066860C212yesmaximal
6#13066854C211yesmaximal, characteristic
7#13066852C211yesmaximal, characteristic
8#13066848C211yesmaximal, characteristic, complemented
9#13066841C212yesmaximal, complemented
10(C2×D11)⋊#95C212yesmaximal
11C11×#1436C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C22×C4×Dic11C2211yescharacteristic
24C2×#66945—24no—
25C2×#66945—24no—
26C2×#66945C418yescomplemented
27C2×C11×#95C2212yes—
28C2×C11×#95C2212yes—
29C2×C11×#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622545—24no—
39#10622263—24no—
40C24×D11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C22×C4×D11—24no—
52C22×C4×D11—24no—
53C22×C4×D11—22no—
54C22×C4×D11—22no—
55C22×C4×D11C2×C414yes—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4C2×C414yes—
59C2×C42×C11—22no—
60C2×C42×C11—24no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—24no—
66C2×(C2×D11)⋊C4—24no—
67C2×(C2×D11)⋊C4—24no—
68C2×(C2×D11)⋊C4—24no—
69C2×(C2×D11)⋊C4—42no—
70C2×(C2×D11)⋊C4—42no—
71C2×(C2×D11)⋊C4C2×C414yes—
72C2×(C2×D11)⋊C4C2×C414yes—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11C2×C414yes—
76C2×Dic11⋊C4—24no—
77C2×Dic11⋊C4—42no—
78C2×Dic11⋊C4—42no—
79C2×C4×Dic11—22no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11—22no—
82C2×C4×Dic11—24no—
83C2×C4×Dic11C2×C414yes—
84C2×C4×Dic11C2×C414yes—
85C2×C4×Dic11D414yes—
86C2×C4×Dic11D414yes—
87#66945—232no—
88C11×#95—22no—
89C11×#95—24no—
90C11×#95—24no—
91C11⋊#95—22no—
92C11⋊#95—24no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97C11⋊#95—42no—
98C11⋊#95—42no—
99#13957—111nomaximal, Sylow
100C24×C11C2411yescharacteristic
101C23×D11—21no—
102C23×D11—21no—
103C23×D11—22no—
104C23×D11—22no—
105C23×D11—22no—
106C23×D11—22no—
107C23×D11—22no—
108C23×D11C22×C412yes—
109C23×D11#4114yes—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
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×C11—22no—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11#4114yes—
138C22×C4×C11#4114yes—
139C22×Dic11—22no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—22no—
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×Dic11C22×C412yes—
161C22×Dic11C22×C412yes—
162C22×Dic11C22×C412yes—
163C22×Dic11C2×D412yes—
164C22×Dic11C2×D412yes—
165C22×Dic11C2×D412yes—
166C22×Dic11C2×D412yes—
167C22×Dic11#4114yes—
168C2×C4×D11—216no—
169C2×C4×D11—216no—
170C2×C4×D11—28no—
171C2×C4×D11—28no—
172C2×C4×D11—28no—
173C11×C4⋊C4—28no—
174C42×C11—28no—
175(C2×D11)⋊C4—28no—
176(C2×D11)⋊C4—28no—
177(C2×D11)⋊C4—48no—
178(C2×D11)⋊C4—48no—
179C4⋊Dic11—28no—
180Dic11⋊C4—48no—
181C4×Dic11—28no—
182C4×Dic11—28no—
183C4×Dic11C22⋊C4116yescomplemented
184C22×#117—111no—
185C2×#382—111no—
186C2×#376—111no—
187#1441—112no—
188#1439—112no—
189#1437—111no—
190#1437—111no—
191#1436—111no—
192#1436D1111yescharacteristic, complemented
193#1434—112no—
194C22⋊#95—112no—
195C23×C11C23×C411yescharacteristic
196C23×C11C22×D411yescharacteristic
197C23×C11C22×D411yescharacteristic
198C23×C11C2×#4112yes—
199C23×C11C2×#4112yes—
200C23×C11C2×#4112yes—
201C23×C11C2×#4112yes—
202C23×C11H(5,𝔽2)12yes—
203C23×C112−1+412yes—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—24no—
207C22×D11—24no—
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11—24no—
213C22×D11—24no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—42no—
217C22×D11—41no—
218C22×D11—41no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11#11714yes—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—42no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
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×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11C2×C22⋊C414yes—
253C2×C4×C11#11714yes—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—24no—
262C2×Dic11—22no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—42no—
268C2×Dic11—41no—
269C2×Dic11—41no—
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×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11C2×C22⋊C414yes—
282C2×Dic11C2×C22⋊C414yes—
283C4×D11—232no—
284C24×C4—111no—
285C2×#117—118no—
286C2×#117—224no—
287C2×#117—224no—
288C22×C4⋊C4—111no—
289C22×C4⋊C4—112no—
290C22×C4⋊C4C2×D1111yescharacteristic
291C22×C22⋊C4—111no—
292C22×C22⋊C4—111no—
293C22×C22⋊C4—112no—
294C22×C22⋊C4—112no—
295C22×C42—111no—
296C22×C42—111no—
297C22×C42—111no—
298C22×C42C2×D1111yescharacteristic
299#382—224no—
300#376—224no—
301C2×#95—112no—
302C2×#95—112no—
303C2×#95—112no—
304C2×#95—112no—
305C2×#95—111no—
306C2×#95—112no—
307C2×#95—112no—
308C2×#95—112no—
309C2×#95C2×D1112yes—
310C2×#95C2×D1112yes—
311C2×#95C2×D1111yescharacteristic
312C22×C11C22×C22⋊C411yescharacteristic
313C22×C11C2×#11711yescharacteristic
314C22×C11C2×#11711yescharacteristic
315C22×C11C4×#4112yes—
316C22×C11#52012yes—
317C22×C11#52512yes—
318C22×C11#52512yes—
319C22×C11#52511yescharacteristic
320C22×C11#52511yescharacteristic
321C22×C11#53212yes—
322C22×C11#53511yescharacteristic
323C22×C11#53611yescharacteristic
324C22×C11#53712yes—
325C22×C11#55112yes—
326C22×C11#55112yes—
327C22×C11#55212yes—
328C22×C11#55212yes—
329C22×C11#55212yes—
330C22×C11#55212yes—
331C22×C11#55512yes—
332C22×C11#55512yes—
333C2×D11—28no—
334C2×D11—24no—
335C2×D11—42no—
336C2×D11—44no—
337C2×D11—44no—
338C2×D11—44no—
339C2×D11—44no—
340C2×D11—44no—
341C2×D11—42no—
342C4×C11—24no—
343C4×C11—24no—
344C4×C11—44no—
345C4×C11—42no—
346C4×C11—82no—
347Dic11—24no—
348Dic11—24no—
349Dic11—42no—
350Dic11—44no—
351Dic11—82no—
352C25—111no—
353C23×C4—111no—
354C23×C4—111no—
355C23×C4—111no—
356C23×C4—112no—
357C23×C4—114no—
358C23×C4—112no—
359C23×C4—222no—
360C23×C4—222no—
361C23×C4—224no—
362C23×C4—224no—
363C23×C4C22×D1112yes—
364C23×C4C22×D1111yescharacteristic
365C23×C4C22×D1112yes—
366C23×C4C22×D1111yescharacteristic
367C23×C4C22×D1111yescharacteristic
368#117—2232no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—114no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4—222no—
374C2×C4⋊C4—224no—
375C2×C4⋊C4—442no—
376C2×C4⋊C4—442no—
377C2×C4⋊C4C4×D1114yes—
378C2×C22⋊C4—114no—
379C2×C22⋊C4—114no—
380C2×C22⋊C4—222no—
381C2×C22⋊C4—222no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4—224no—
385C2×C22⋊C4—224no—
386C2×C22⋊C4—224no—
387C2×C22⋊C4—224no—
388C2×C22⋊C4—442no—
389C2×C22⋊C4—442no—
390C2×C42—22no—
391C2×C42—24no—
392C2×C42—114no—
393C2×C42—114no—
394C2×C42—114no—
395C2×C42—114no—
396C2×C42—222no—
397C2×C42—222no—
398C2×C42—224no—
399C2×C42—222no—
400#95—24no—
401#95—22no—
402#95—24no—
403#95—224no—
404#95—224no—
405#95—224no—
406#95—224no—
407#95—224no—
408#95—222no—
409#95—442no—
410#95—442no—
411C2×C11#228011yescharacteristic
412C2×C11#229711yescharacteristic
413C2×C11#231111yescharacteristic
414C2×C11#234312yes—
415C2×C11#234612yes—
416C2×C11#260912yes—
417C2×C11#260912yes—
418C2×C11#261012yes—
419C2×C11#261112yes—
420D11—44no—
421C24—112no—
422C24—114no—
423C24—222no—
424C24—221no—
425C24—221no—
426C24—222no—
427C24—222no—
428C24—222no—
429C24—222no—
430C24C23×D1111yescharacteristic
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
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—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—112no—
454C22×C4—112no—
455C22×C4—112no—
456C22×C4—112no—
457C22×C4—112no—
458C22×C4—112no—
459C22×C4—112no—
460C22×C4—114no—
461C22×C4—228no—
462C22×C4—228no—
463C22×C4—2216no—
464C22×C4—2216no—
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—228no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—221no—
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×C4—222no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4C2×C4×D1112yes—
488C22×C4C2×C4×D1112yes—
489C22×C4C2×C4×D1112yes—
490C22×C4#433914yes—
491C22×C4D4×D1112yes—
492C22×C4D4×D1112yes—
493C22×C4#434114yes—
494C4⋊C4—28no—
495C4⋊C4—228no—
496C4⋊C4—448no—
497C22⋊C4—228no—
498C22⋊C4—228no—
499C22⋊C4—448no—
500C22⋊C4—448no—
501C42—28no—
502C42—1116no—
503C42—228no—
504C42—228no—
505C11#1395711yescharacteristic, complemented, Sylow
506C23—114no—
507C23—224no—
508C23—222no—
509C23—222no—
510C23—224no—
511C23—224no—
512C23—224no—
513C23—224no—
514C23—224no—
515C23—224no—
516C23—224no—
517C23—441no—
518C23—442no—
519C23—442no—
520C23—442no—
521C23—442no—
522C23—441no—
523C23—442no—
524C23—442no—
525C23—441no—
526C23—441no—
527C23C22×C4×D1111yescharacteristic
528C23C2×#433912yes—
529C23C2×D4×D1111yescharacteristic
530C23C2×D4×D1111yescharacteristic
531C23C2×#434112yes—
532C23#6704012yes—
533C23#41×D1112yes—
534C23#41×D1112yes—
535C23#6704212yes—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—41no—
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—222no—
568C2×C4—222no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—222no—
574C2×C4—224no—
575C2×C4—222no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—224no—
579C2×C4—441no—
580C2×C4—442no—
581C2×C4—442no—
582C2×C4—442no—
583C2×C4—442no—
584C2×C4—441no—
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×C4#6692514yes—
594C2×C4C22⋊C4×D1114yes—
595C22—228no—
596C22—224no—
597C22—442no—
598C22—444no—
599C22—444no—
600C22—444no—
601C22—444no—
602C22—444no—
603C22—442no—
604C22C2×#6692511yescharacteristic
605C22C2×C22⋊C4×D1111yescharacteristic
606C22#1062304412yes—
607C22D11×#11711yescharacteristic
608C22#1062306312yes—
609C22C4×#434112yes—
610C22#1062307812yes—
611C22#1062307812yes—
612C22#1062309412yes—
613C22#1062310512yes—
614C22#1062311212yes—
615C22#1062311711yescharacteristic
616C22#1062312712yes—
617C22#1062316012yes—
618C22#1062317012yes—
619C22#1062318711yescharacteristic
620C22#1062318912yes—
621C22#1062320511yescharacteristic
622C22#1062322412yes—
623C22#1062323612yes—
624C22#1062325511yescharacteristic
625C4—24no—
626C4—24no—
627C4—44no—
628C4—42no—
629C4—82no—
630C4—224no—
631C4—224no—
632C4—442no—
633C4—444no—
634C4—882no—
635C2—444no—
636C2#1307099711yescharacteristic
637C2#1307110111yescharacteristic
638C2#1307120711yescharacteristic
639C2#1307147112yes—
640C2#1307149712yes—
641C2#1307429212yes—
642C2#1307429512yes—
643C2#1307430212yes—
644C2#1307431312yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1436D11
hypocenterC11#13957
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#10622263C2semidirect
3. C2×#10622545C2semidirect
4. #13066868C2semidirect
8. #13066848C2semidirect
9. #13066841C2semidirect
11. C11×#1436C2semidirect
26. C2×#66945C4semidirect
183. C4×Dic11C22⋊C4semidirect
192. #1436D11semidirect
505. C11#13957semidirect

Maximal subgroups

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

subgroupindex
C22×#669452
C2×#106222632
C2×#106225452
#130668682
#130668602
#130668542
#130668522
#130668482
#130668412
(C2×D11)⋊#952
C11×#14362
#1395711