Finite Group Databasebeta

← #14675729

Subgroups — #14675729

Order 2816.

4046 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊Dic11C211yesmaximal, characteristic
2C2×#10622823C212yesmaximal, complemented
3C2×#10622555C212yesmaximal, complemented
4C2×#10622860C211yesmaximal, characteristic
5#13066859C214yesmaximal, complemented
6#13066839C212yesmaximal, complemented
7#13066838C212yesmaximal, complemented
8C23×C11×C22⋊C4C211yesmaximal, characteristic
9C26×C11C2211yescharacteristic
10C24×C4×C11C2212yes—
11C24×Dic11C2212yes—
12C22×C11×C22⋊C4—24no—
13C22×C11×C22⋊C4—28no—
14C22×C11×C22⋊C4C2212yes—
15C22×C11×C22⋊C4C2212yes—
16C22×C22⋊Dic11—28no—
17C22×C22⋊Dic11C418yescomplemented
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2211yescharacteristic
25C22×Dic11⋊C4C2214yescomplemented
26#10622860—24no—
27#10622823—28no—
28C2×C11⋊#95C2214yescomplemented
29C2×C11⋊#95C2214yescomplemented
30C2×C11⋊#95C2214yescomplemented
31#10622555—28no—
32C25×C11—24no—
33C25×C11—24no—
34C25×C11—24no—
35C25×C11—24no—
36C25×C11—44no—
37C25×C11C2×C414yes—
38C25×C11D414yes—
39C25×C11Q814yes—
40C25×C11C2311yescharacteristic
41C25×C11C2311yescharacteristic
42C25×C11C2311yescharacteristic
43C23×C4×C11—24no—
44C23×C4×C11—28no—
45C23×C4×C11—24no—
46C23×C4×C11—24no—
47C23×C4×C11—44no—
48C23×C4×C11C2314yes—
49C23×Dic11—24no—
50C23×Dic11—24no—
51C23×Dic11—28no—
52C23×Dic11—44no—
53C23×Dic11C2×C418yescomplemented
54C23×Dic11C2312yes—
55C23×Dic11C2312yes—
56C23×Dic11C2312yes—
57C23×Dic11C2312yes—
58C2×C11×C22⋊C4—232no—
59C2×C11×C22⋊C4—24no—
60C2×C11×C22⋊C4—24no—
61C2×C11×C22⋊C4—24no—
62C2×C11×C22⋊C4—28no—
63C2×C11×C22⋊C4D418yes—
64C2×C22⋊Dic11—24no—
65C2×C22⋊Dic11—28no—
66C2×C22⋊Dic11—232no—
67C2×C22⋊Dic11—24no—
68C2×C22⋊Dic11—24no—
69C2×C22⋊Dic11—24no—
70C2×C22⋊Dic11—22no—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—22no—
73C2×C22⋊Dic11—24no—
74C2×C22⋊Dic11—24no—
75C2×C22⋊Dic11—44no—
76C2×C22⋊Dic11C2×C414yes—
77C2×C22⋊Dic11C2×C414yes—
78C2×C22⋊Dic11C2×C418yescomplemented
79C2×C22⋊Dic11D418yes—
80C2×Dic11⋊C4—28no—
81C2×Dic11⋊C4—28no—
82C2×Dic11⋊C4—44no—
83C11⋊#95—28no—
84C11⋊#95—28no—
85C11⋊#95—44no—
86#13877—111nomaximal, Sylow
87C24×C11—22no—
88C24×C11—22no—
89C24×C11—22no—
90C24×C11—22no—
91C24×C11—24no—
92C24×C11—24no—
93C24×C11—28no—
94C24×C11—28no—
95C24×C11—216no—
96C24×C11—28no—
97C24×C11—216no—
98C24×C11—216no—
99C24×C11—216no—
100C24×C11—28no—
101C24×C11—22no—
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—22no—
105C24×C11—24no—
106C24×C11—48no—
107C24×C11—48no—
108C24×C11—48no—
109C24×C11—416no—
110C24×C11—416no—
111C24×C11—416no—
112C24×C11—416no—
113C24×C11C4⋊C4116yescomplemented
114C24×C11C22×C412yes—
115C24×C11C22×C412yes—
116C24×C11C22×C412yes—
117C24×C11C2×D412yes—
118C24×C11C2×D414yes—
119C24×C11C2×D412yes—
120C24×C11C2×D412yes—
121C24×C11C2×D414yes—
122C24×C11C2×Q812yes—
123C24×C11C2×Q812yes—
124C24×C11C2×Q812yes—
125C24×C11#4114yes—
126C24×C11#4114yes—
127C24×C11C2411yescharacteristic
128C22×C4×C11—216no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—416no—
136C22×C4×C11—416no—
137C22×C4×C11—48no—
138C22×C4×C11—48no—
139C22×C4×C11C2×D418yes—
140C22×Dic11—216no—
141C22×Dic11—216no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—24no—
145C22×Dic11—22no—
146C22×Dic11—24no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—24no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—48no—
160C22×Dic11—416no—
161C22×Dic11—416no—
162C22×Dic11C22×C414yes—
163C22×Dic11C22×C414yes—
164C22×Dic11C2×D418yes—
165C11×C22⋊C4—216no—
166C11×C22⋊C4—216no—
167C22⋊Dic11—216no—
168C22⋊Dic11—28no—
169C22⋊Dic11—48no—
170C22⋊Dic11—44no—
171C22⋊Dic11—48no—
172C22⋊Dic11—44no—
173C22⋊Dic11C22⋊C4116yescomplemented
174Dic11⋊C4—416no—
175C23×C22⋊C4—111no—
176C23×C22⋊C4D1111yescharacteristic
177C2×#385—112no—
178C2×#380—112no—
179C2×#379—111no—
180#1439—114no—
181C22⋊#95—112no—
182C22⋊#95—112no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—24no—
186C23×C11—24no—
187C23×C11—24no—
188C23×C11—22no—
189C23×C11—24no—
190C23×C11—24no—
191C23×C11—24no—
192C23×C11—22no—
193C23×C11—24no—
194C23×C11—24no—
195C23×C11—24no—
196C23×C11—24no—
197C23×C11—28no—
198C23×C11—28no—
199C23×C11—28no—
200C23×C11—28no—
201C23×C11—28no—
202C23×C11—28no—
203C23×C11—28no—
204C23×C11—28no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—24no—
208C23×C11—24no—
209C23×C11—22no—
210C23×C11—24no—
211C23×C11—24no—
212C23×C11—24no—
213C23×C11—22no—
214C23×C11—24no—
215C23×C11—24no—
216C23×C11—232no—
217C23×C11—232no—
218C23×C11—416no—
219C23×C11—432no—
220C23×C11—432no—
221C23×C11—432no—
222C23×C11—432no—
223C23×C11—464no—
224C23×C11—44no—
225C23×C11—44no—
226C23×C11—44no—
227C23×C11—44no—
228C23×C11C2×C22⋊C414yes—
229C23×C11C2×C4⋊C414yes—
230C23×C11C2×C4⋊C414yes—
231C23×C11C2×C4⋊C414yes—
232C23×C11#11714yes—
233C23×C11C4×D418yes—
234C23×C11#12014yes—
235C23×C11#12118yes—
236C23×C11C22⋊Q818yes—
237C23×C11C22⋊Q818yes—
238C23×C11#12314yes—
239C23×C11C23×C411yescharacteristic
240C23×C11C22×D412yes—
241C23×C11C22×D411yescharacteristic
242C23×C11C22×D412yes—
243C23×C11C22×Q811yescharacteristic
244C23×C11C2×#4112yes—
245C23×C11C2×#4112yes—
246C23×C11H(5,𝔽2)14yes—
247C2×C4×C11—28no—
248C2×C4×C11—28no—
249C2×C4×C11—28no—
250C2×C4×C11—432no—
251C2×C4×C11—44no—
252C2×C4×C11—44no—
253C2×C4×C11—44no—
254C2×C4×C11—44no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—28no—
258C2×Dic11—28no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—432no—
263C2×Dic11—44no—
264C2×Dic11—44no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—44no—
272C2×Dic11—44no—
273C2×Dic11—44no—
274C2×Dic11—44no—
275C2×Dic11C2×C22⋊C418yescomplemented
276C26C2×D1111yescharacteristic
277C24×C4—112no—
278C24×C4C2×D1112yes—
279C22×C4⋊C4—114no—
280C22×C22⋊C4—24no—
281C22×C22⋊C4—28no—
282C22×C22⋊C4—111no—
283C22×C22⋊C4—111no—
284C22×C22⋊C4—112no—
285C22×C22⋊C4—118no—
286C22×C22⋊C4—111no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4—111no—
289C22×C22⋊C4—112no—
290C22×C22⋊C4—228no—
291C22×C22⋊C4C2×D1112yes—
292C22×C22⋊C4C2×D1112yes—
293#385—228no—
294#380—228no—
295#379—224no—
296C2×#95—114no—
297C2×#95—114no—
298C2×#95—114no—
299C22×C11—24no—
300C22×C11—24no—
301C22×C11—28no—
302C22×C11—28no—
303C22×C11—28no—
304C22×C11—28no—
305C22×C11—28no—
306C22×C11—28no—
307C22×C11—28no—
308C22×C11—28no—
309C22×C11—216no—
310C22×C11—216no—
311C22×C11—24no—
312C22×C11—24no—
313C22×C11—24no—
314C22×C11—24no—
315C22×C11—24no—
316C22×C11—464no—
317C22×C11—44no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—44no—
321C22×C11—48no—
322C22×C11#38018yescomplemented
323C22×C11#38518yescomplemented
324C22×C11C22×C22⋊C411yescharacteristic
325C22×C11C22×C4⋊C411yescharacteristic
326C22×C11C2×#11711yescharacteristic
327C22×C11C2×C4×D412yes—
328C22×C11#51812yes—
329C22×C11C2×#12011yescharacteristic
330C22×C11C2×#12112yes—
331C22×C11C2×C22⋊Q812yes—
332C22×C11C2×C22⋊Q812yes—
333C22×C11C2×#12311yescharacteristic
334C22×C11#53412yes—
335C22×C11#54312yes—
336C22×C11D4214yes—
337C22×C11#54614yes—
338C22×C11#54614yes—
339C22×C11#55114yes—
340C4×C11—48no—
341Dic11—28no—
342Dic11—44no—
343Dic11—82no—
344Dic11—82no—
345C25—24no—
346C25—24no—
347C25—24no—
348C25—24no—
349C25—44no—
350C25Dic2214yes—
351C25C4×D1114yes—
352C25C22⋊D1114yes—
353C25C22×D1111yescharacteristic
354C25C22×D1111yescharacteristic
355C25C22×D1111yescharacteristic
356C23×C4—24no—
357C23×C4—28no—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—44no—
361C23×C4—112no—
362C23×C4—112no—
363C23×C4—118no—
364C23×C4—112no—
365C23×C4—112no—
366C23×C4—228no—
367C23×C4—224no—
368C23×C4—224no—
369C23×C4—444no—
370C23×C4C22×D1114yes—
371C2×C4⋊C4—228no—
372C2×C4⋊C4—228no—
373C2×C4⋊C4—444no—
374C2×C22⋊C4—232no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—114no—
380C2×C22⋊C4—118no—
381C2×C22⋊C4—114no—
382C2×C22⋊C4—118no—
383C2×C22⋊C4—2232no—
384C2×C22⋊C4—228no—
385C2×C22⋊C4—224no—
386C2×C22⋊C4—224no—
387C2×C22⋊C4—224no—
388C2×C22⋊C4—224no—
389C2×C22⋊C4—224no—
390C2×C22⋊C4—222no—
391C2×C22⋊C4—224no—
392C2×C22⋊C4—222no—
393C2×C22⋊C4—224no—
394C2×C22⋊C4—444no—
395C2×C22⋊C4C22⋊D1118yes—
396#95—228no—
397#95—228no—
398#95—444no—
399C2×C11—28no—
400C2×C11—28no—
401C2×C11—44no—
402C2×C11C2×#38011yescharacteristic
403C2×C11C2×#38511yescharacteristic
404C2×C11#231511yescharacteristic
405C2×C11D4×C22⋊C412yes—
406C2×C11#234212yes—
407C2×C11#241012yes—
408C2×C11#241212yes—
409C2×C11#243714yes—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—24no—
414C24—24no—
415C24—22no—
416C24—28no—
417C24—216no—
418C24—28no—
419C24—216no—
420C24—216no—
421C24—28no—
422C24—216no—
423C24—28no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—24no—
428C24—22no—
429C24—48no—
430C24—48no—
431C24—48no—
432C24—416no—
433C24—416no—
434C24—416no—
435C24—416no—
436C24Dic11⋊C4116yescomplemented
437C24C2×Dic2212yes—
438C24C2×Dic2212yes—
439C24C2×Dic2212yes—
440C24C2×C4×D1112yes—
441C24C2×C4×D1112yes—
442C24C2×C4×D1112yes—
443C24#433914yes—
444C24D4×D1114yes—
445C24#434114yes—
446C24C2×C22⋊D1112yes—
447C24C2×C22⋊D1112yes—
448C24C2×C22⋊D1112yes—
449C24C2×C22⋊D1114yes—
450C24C23×D1111yescharacteristic
451C22×C4—216no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—416no—
459C22×C4—416no—
460C22×C4—48no—
461C22×C4—48no—
462C22×C4—114no—
463C22×C4—118no—
464C22×C4—114no—
465C22×C4—2216no—
466C22×C4—222no—
467C22×C4—224no—
468C22×C4—222no—
469C22×C4—2216no—
470C22×C4—222no—
471C22×C4—224no—
472C22×C4—224no—
473C22×C4—222no—
474C22×C4—224no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—224no—
480C22×C4—224no—
481C22×C4—224no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—448no—
485C22×C4—4416no—
486C22×C4—4416no—
487C22×C4C2×C22⋊D1118yes—
488C4⋊C4—4416no—
489C22⋊C4—216no—
490C22⋊C4—216no—
491C22⋊C4—1116no—
492C22⋊C4—2216no—
493C22⋊C4—228no—
494C22⋊C4—448no—
495C22⋊C4—444no—
496C22⋊C4—448no—
497C22⋊C4—444no—
498C11#1387711yescharacteristic, complemented, Sylow
499C23—22no—
500C23—24no—
501C23—24no—
502C23—24no—
503C23—22no—
504C23—24no—
505C23—24no—
506C23—28no—
507C23—28no—
508C23—28no—
509C23—28no—
510C23—24no—
511C23—24no—
512C23—22no—
513C23—28no—
514C23—28no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—28no—
519C23—28no—
520C23—22no—
521C23—22no—
522C23—24no—
523C23—24no—
524C23—22no—
525C23—24no—
526C23—24no—
527C23—24no—
528C23—22no—
529C23—232no—
530C23—24no—
531C23—232no—
532C23—24no—
533C23—22no—
534C23—416no—
535C23—432no—
536C23—432no—
537C23—432no—
538C23—432no—
539C23—464no—
540C23—44no—
541C23—44no—
542C23—44no—
543C23—44no—
544C23#6693014yes—
545C23#6693118yes—
546C23C22⋊C4×D1114yes—
547C23C2×Dic11⋊C414yes—
548C23C2×Dic11⋊C414yes—
549C23C2×Dic11⋊C414yes—
550C23#6697718yes—
551C23C4×C22⋊D1118yes—
552C23#6698214yes—
553C23#6699218yes—
554C23#6700614yes—
555C23C22×Dic2211yescharacteristic
556C23C22×C4×D1111yescharacteristic
557C23C2×#433912yes—
558C23C2×D4×D1112yes—
559C23C2×#434112yes—
560C23#6703714yes—
561C23C22×C22⋊D1111yescharacteristic
562C23C22×C22⋊D1112yes—
563C2×C4—28no—
564C2×C4—28no—
565C2×C4—28no—
566C2×C4—432no—
567C2×C4—44no—
568C2×C4—44no—
569C2×C4—44no—
570C2×C4—44no—
571C2×C4—118no—
572C2×C4—224no—
573C2×C4—228no—
574C2×C4—224no—
575C2×C4—228no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—224no—
579C2×C4—4432no—
580C2×C4—444no—
581C2×C4—444no—
582C2×C4—444no—
583C2×C4—444no—
584C2×C4—442no—
585C2×C4—444no—
586C2×C4—442no—
587C2×C4—442no—
588C2×C4—442no—
589C2×C4—442no—
590C2×C4—444no—
591C2×C4—442no—
592C22—28no—
593C22—28no—
594C22—28no—
595C22—28no—
596C22—28no—
597C22—28no—
598C22—24no—
599C22—24no—
600C22—24no—
601C22—28no—
602C22—28no—
603C22—216no—
604C22—216no—
605C22—24no—
606C22—24no—
607C22—24no—
608C22—24no—
609C22—464no—
610C22—44no—
611C22—44no—
612C22—44no—
613C22—44no—
614C22—48no—
615C22#1062255518yescomplemented
616C22#1062282318yescomplemented
617C22C2×#6693011yescharacteristic
618C22C2×#6693112yes—
619C22#1062301412yes—
620C22C2×C22⋊C4×D1111yescharacteristic
621C22#1062301712yes—
622C22#1062302114yes—
623C22#1062302614yes—
624C22C22×Dic11⋊C411yescharacteristic
625C22C2×#6697712yes—
626C22C2×C4×C22⋊D1112yes—
627C22C2×#6698211yescharacteristic
628C22D4×C22⋊D1114yes—
629C22C2×#6699212yes—
630C22#1062333512yes—
631C22#1062333714yes—
632C22C2×#6700611yescharacteristic
633C4—48no—
634C4—228no—
635C4—444no—
636C4—882no—
637C4—882no—
638C2—28no—
639C2—28no—
640C2—44no—
641C2C2×#1062255511yescharacteristic
642C2C2×#1062282311yescharacteristic
643C2#1307122811yescharacteristic
644C2C22⋊C4×C22⋊D1112yes—
645C2#1307146112yes—
646C2#1307199012yes—
647C2#1307201212yes—
648C2#1307227714yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC23×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC26×C11C22
hypercenterC23×C22⋊C4D11
hypocenterC11#13877
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622823C2semidirect
3. C2×#10622555C2semidirect
5. #13066859C2semidirect
6. #13066839C2semidirect
7. #13066838C2semidirect
17. C22×C22⋊Dic11C4semidirect
25. C22×Dic11⋊C4C22semidirect
28. C2×C11⋊#95C22semidirect
29. C2×C11⋊#95C22semidirect
30. C2×C11⋊#95C22semidirect
53. C23×Dic11C2×C4semidirect
78. C2×C22⋊Dic11C2×C4semidirect
113. C24×C11C4⋊C4semidirect
173. C22⋊Dic11C22⋊C4semidirect
275. C2×Dic11C2×C22⋊C4semidirect
322. C22×C11#380semidirect
323. C22×C11#385semidirect
436. C24Dic11⋊C4semidirect
498. C11#13877semidirect
615. C22#10622555semidirect
616. C22#10622823semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊Dic112
C2×#106228232
C2×#106225552
C2×#106228602
#130668592
#130668392
#130668382
C23×C11×C22⋊C42
#1387711