Finite Group Databasebeta

← #14680755

Subgroups — #14680755

Order 2816.

1622 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622560C211yesmaximal, characteristic
2C2×#10622542C211yesmaximal, characteristic, complemented
3#13066886C211yesmaximal, characteristic, complemented
4#13066880C211yesmaximal, characteristic, complemented
5#13066877C212yesmaximal, complemented
6#13066861C211yesmaximal, characteristic
7#13066859C212yesmaximal
8#13066849C212yesmaximal, complemented
9#13066843C211yesmaximal, characteristic, complemented
10#13066839C212yesmaximal
11C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
12C24×C4×C11C2211yescharacteristic
13C23×Dic22C2211yescharacteristic
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2212yes—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×Dic11⋊C4C2212yes—
22C4×C11×C22⋊C4—24no—
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2212yes—
36#10622560C418yescomplemented
37#10622542—24no—
38C25×C11C2311yescharacteristic
39C23×C4×C11—22no—
40C23×C4×C11—22no—
41C23×C4×C11—42no—
42C23×C4×C11—42no—
43C23×C4×C11Q814yescomplemented
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×Dic11C2312yes—
51C23×Dic11C2312yes—
52C23×Dic11C2312yes—
53C23×Dic11C2312yes—
54C22×Dic22—22no—
55C22×Dic22—22no—
56C22×Dic22—42no—
57C22×Dic22—42no—
58C22×Dic22C2×C414yescomplemented
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4C2×C414yes—
65C2×C42×C11—22no—
66C2×C42×C11—42no—
67C2×C42×C11—42no—
68C2×C42×C11D414yes—
69C2×C22⋊Dic11—24no—
70C2×C22⋊Dic11—42no—
71C2×C22⋊Dic11—42no—
72C2×C22⋊Dic11—42no—
73C2×C22⋊Dic11—42no—
74C2×C22⋊Dic11C2×C418yes—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—42no—
77C2×Dic11⋊C4—24no—
78C2×Dic11⋊C4—42no—
79C2×Dic11⋊C4—42no—
80C11×#95—22no—
81C11×#95—22no—
82C11⋊#95—24no—
83C11⋊#95—24no—
84C11⋊#95—24no—
85C11⋊#95—22no—
86C11⋊#95—42no—
87C11⋊#95—42no—
88C11⋊#95—42no—
89C11⋊#95—42no—
90C11⋊#95—42no—
91C11⋊#95C2×C414yescomplemented
92C11⋊#95C2×C418yescomplemented
93#14319—111nomaximal, Sylow
94C24×C11—21no—
95C24×C11—21no—
96C24×C11—21no—
97C24×C11—21no—
98C24×C11—22no—
99C24×C11—22no—
100C24×C11—22no—
101C24×C11—22no—
102C24×C11C22×C412yes—
103C24×C11C2×Q812yes—
104C24×C11#4112yes—
105C24×C11C2411yescharacteristic
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
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—28no—
127C22×C4×C11—48no—
128C22×C4×C11—44no—
129C22×C4×C11—44no—
130C22×C4×C11—48no—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×Q812yes—
137C22×C4×C11C2×Q812yes—
138C22×C4×C11#4112yes—
139C22×C4×C11#4112yes—
140C22×C4×C11#4112yes—
141C22×Dic11—22no—
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×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11C22×C414yes—
168C22×Dic11C22×C414yes—
169C2×Dic22—28no—
170C2×Dic22—48no—
171C2×Dic22—44no—
172C2×Dic22—44no—
173C2×Dic22—48no—
174C11×C22⋊C4—28no—
175C11×C22⋊C4—28no—
176C42×C11—44no—
177C42×C11—44no—
178C22⋊Dic11—48no—
179C22⋊Dic11—48no—
180C4⋊Dic11—44no—
181Dic11⋊C4—48no—
182C2×#393—111no—
183C2×#391—111no—
184C2×C4×C22⋊C4D1111yescharacteristic
185#1446—111no—
186#1444—111no—
187#1443—112no—
188#1439—112no—
189#1439—111no—
190#1436—112no—
191#1434—111no—
192C22⋊#95—112no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—24no—
196C23×C11—24no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—24no—
202C23×C11—24no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11C4×Q814yes—
216C23×C11C23×C411yescharacteristic
217C23×C11C22×D411yescharacteristic
218C23×C11C22×Q811yescharacteristic
219C23×C11C2×#4111yescharacteristic
220C23×C11C2×#4111yescharacteristic
221C23×C11C2×#4111yescharacteristic
222C23×C11C2×#4111yescharacteristic
223C23×C11H(5,𝔽2)12yes—
224C23×C11H(5,𝔽2)12yes—
225C23×C11H(5,𝔽2)12yes—
226C23×C112−1+412yes—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—416no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11C4×D414yes—
257C2×C4×C11C22⋊Q814yes—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
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×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11—42no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286Dic22—416no—
287C23×Q8—111no—
288C24×C4C2×D1111yescharacteristic
289C22×C4⋊C4—112no—
290C22×C4⋊C4—111no—
291C22×C22⋊C4—112no—
292C22×C22⋊C4—112no—
293C22×C22⋊C4C2×D1111yescharacteristic
294C22×C22⋊C4C2×D1111yescharacteristic
295C22×C42C2×D1111yescharacteristic
296C22×C42C2×D1111yescharacteristic
297#393—118no—
298#391—224no—
299C4×C22⋊C4—24no—
300C2×#95—111no—
301C2×#95—112no—
302C2×#95—112no—
303C2×#95—112no—
304C2×#95—111no—
305C2×#95—112no—
306C2×#95—112no—
307C2×#95—112no—
308C2×#95—112no—
309C2×#95—112no—
310C2×#95—112no—
311C2×#95C2×D1111yescharacteristic
312C2×#95C2×D1111yescharacteristic
313C22×C11—28no—
314C22×C11—24no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—44no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—44no—
323C22×C11—44no—
324C22×C11C2×C4×D411yescharacteristic
325C22×C11C2×C4×Q811yescharacteristic
326C22×C11C4×#4111yescharacteristic
327C22×C11#51812yes—
328C22×C11#52012yes—
329C22×C11C2×C22⋊Q811yescharacteristic
330C22×C11#52511yescharacteristic
331C22×C11#52911yescharacteristic
332C22×C11#53311yescharacteristic
333C22×C11#53411yescharacteristic
334C22×C11#53511yescharacteristic
335C22×C11#53511yescharacteristic
336C22×C11#53611yescharacteristic
337C22×C11#53812yes—
338C22×C11#53812yes—
339C22×C11#53812yes—
340C22×C11#53812yes—
341C22×C11#53912yes—
342C22×C11#54212yes—
343C22×C11#54212yes—
344C22×C11#54212yes—
345C22×C11#54312yes—
346C22×C11#54412yes—
347C4×C11—24no—
348C4×C11—24no—
349C4×C11—42no—
350C4×C11—42no—
351C4×C11—42no—
352C4×C11—42no—
353Dic11—44no—
354Dic11—44no—
355Dic11—82no—
356Dic11—82no—
357C25C22×D1111yescharacteristic
358C22×Q8—114no—
359C22×Q8—222no—
360C22×Q8—222no—
361C22×Q8—442no—
362C22×Q8—442no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—42no—
366C23×C4—42no—
367C23×C4—112no—
368C23×C4—112no—
369C23×C4—112no—
370C23×C4—112no—
371C23×C4Dic2214yescomplemented
372C23×C4C22×D1111yescharacteristic
373C23×C4C22×D1111yescharacteristic
374C23×C4C22×D1111yescharacteristic
375C23×C4C22×D1111yescharacteristic
376C23×C4C22×D1111yescharacteristic
377C23×C4C22×D1111yescharacteristic
378C2×C4⋊C4—224no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—442no—
381C2×C4⋊C4—442no—
382C2×C4⋊C4—442no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—118no—
389C2×C22⋊C4—224no—
390C2×C22⋊C4—442no—
391C2×C22⋊C4—442no—
392C2×C22⋊C4—442no—
393C2×C22⋊C4—442no—
394C2×C22⋊C4C4×D1114yes—
395C2×C42—22no—
396C2×C42—42no—
397C2×C42—42no—
398C2×C42C22⋊D1114yes—
399#95—22no—
400#95—22no—
401#95—114no—
402#95—118no—
403#95—224no—
404#95—222no—
405#95—224no—
406#95—224no—
407#95—442no—
408#95—442no—
409#95—442no—
410#95—442no—
411#95—442no—
412C2×C11—44no—
413C2×C11C4×C22⋊Q811yescharacteristic
414C2×C11#232111yescharacteristic
415C2×C11#232611yescharacteristic
416C2×C11#232912yes—
417C2×C11#233712yes—
418C2×C11#262611yescharacteristic
419C2×C11#262811yescharacteristic
420C2×C11#263111yescharacteristic
421C2×C11#263811yescharacteristic
422C2×C11#265312yes—
423C2×C11#266512yes—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—21no—
432C24C2×Dic2212yes—
433C24C2×C4×D1112yes—
434C24#433912yes—
435C24C23×D1111yescharacteristic
436C2×Q8—228no—
437C2×Q8—448no—
438C2×Q8—444no—
439C2×Q8—448no—
440C2×Q8—444no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—28no—
462C22×C4—48no—
463C22×C4—48no—
464C22×C4—44no—
465C22×C4—44no—
466C22×C4—114no—
467C22×C4—114no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—222no—
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×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4C2×Dic2212yes—
495C22×C4C2×Dic2212yes—
496C22×C4C2×C4×D1112yes—
497C22×C4C2×C4×D1112yes—
498C22×C4#433912yes—
499C22×C4#433912yes—
500C22×C4#433912yes—
501C22×C4C2×C22⋊D1112yes—
502C22×C4C2×C22⋊D1112yes—
503C22×C4C2×C22⋊D1112yes—
504C4⋊C4—448no—
505C4⋊C4—444no—
506C22⋊C4—28no—
507C22⋊C4—28no—
508C22⋊C4—448no—
509C22⋊C4—448no—
510C42—44no—
511C42—44no—
512C11#1431911yescharacteristic, complemented, Sylow
513C23—22no—
514C23—22no—
515C23—22no—
516C23—24no—
517C23—24no—
518C23—22no—
519C23—22no—
520C23—22no—
521C23—24no—
522C23—24no—
523C23—24no—
524C23—24no—
525C23—42no—
526C23—42no—
527C23—41no—
528C23—41no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—41no—
534C23—41no—
535C23C4×Dic2214yes—
536C23C22×Dic2211yescharacteristic
537C23C22×C4×D1111yescharacteristic
538C23C2×#433911yescharacteristic
539C23C2×#433911yescharacteristic
540C23C2×#433911yescharacteristic
541C23C2×#433911yescharacteristic
542C23#6703712yes—
543C23#6703712yes—
544C23#6704212yes—
545C23#6704312yes—
546C23C22×C22⋊D1111yescharacteristic
547Q8—4416no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—24no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—416no—
566C2×C4—42no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—224no—
578C2×C4—224no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—224no—
583C2×C4—442no—
584C2×C4—442no—
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—442no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—442no—
598C2×C4—442no—
599C2×C4—442no—
600C2×C4—442no—
601C2×C4—442no—
602C2×C4—442no—
603C2×C4—442no—
604C2×C4—442no—
605C2×C4#6697714yes—
606C2×C4C4×C22⋊D1114yes—
607C22—24no—
608C22—28no—
609C22—42no—
610C22—42no—
611C22—44no—
612C22—44no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—44no—
617C22—42no—
618C22C2×C4×Dic2211yescharacteristic
619C22#1062300111yescharacteristic
620C22C4×#433911yescharacteristic
621C22#1062301011yescharacteristic
622C22#1062301412yes—
623C22#1062302512yes—
624C22#1062305012yes—
625C22#1062306512yes—
626C22#1062307612yes—
627C22#1062307712yes—
628C22#1062309112yes—
629C22#1062309112yes—
630C22#1062309112yes—
631C22#1062309212yes—
632C22#1062309212yes—
633C22#1062309512yes—
634C22C2×#6697711yescharacteristic
635C22C2×C4×C22⋊D1111yescharacteristic
636C22#1062332211yescharacteristic
637C22#1062333511yescharacteristic
638C22#1062333611yescharacteristic
639C22#1062335611yescharacteristic
640C22#1062336111yescharacteristic
641C4—24no—
642C4—24no—
643C4—42no—
644C4—42no—
645C4—42no—
646C4—42no—
647C4—444no—
648C4—444no—
649C4—882no—
650C4—882no—
651C2—44no—
652C2C4×#6697711yescharacteristic
653C2#1307127011yescharacteristic
654C2#1307132811yescharacteristic
655C2#1307134412yes—
656C2#1307142412yes—
657C2#1307442111yescharacteristic
658C2#1307443711yescharacteristic
659C2#1307446811yescharacteristic
660C2#1307453311yescharacteristic
661C2#1307467312yes—
662C2#1307478612yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#14319
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622542C2semidirect
3. #13066886C2semidirect
4. #13066880C2semidirect
5. #13066877C2semidirect
8. #13066849C2semidirect
9. #13066843C2semidirect
36. #10622560C4semidirect
43. C23×C4×C11Q8semidirect
58. C22×Dic22C2×C4semidirect
91. C11⋊#95C2×C4semidirect
92. C11⋊#95C2×C4semidirect
371. C23×C4Dic22semidirect
512. C11#14319semidirect

Maximal subgroups

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

subgroupindex
C2×#106225602
C2×#106225422
#130668862
#130668802
#130668772
#130668612
#130668592
#130668492
#130668432
#130668392
C2×C4×C11×C22⋊C42
#1431911