Finite Group Databasebeta

← #14676459

Subgroups — #14676459

Order 2816.

4686 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4343C211yesmaximal, characteristic
2C2×#10622278C214yesmaximal, complemented
3C2×#10622277C211yesmaximal, characteristic, complemented
4C2×D11×#95C211yesmaximal, characteristic, complemented
5#13066887C211yesmaximal, characteristic, complemented
6#13066856C211yesmaximal, characteristic, complemented
7#13066856C211yesmaximal, characteristic, complemented
8(C2×D11)⋊#95C214yesmaximal, complemented
9C11×#1446C211yesmaximal, characteristic, complemented
10C23×Q8×C11C2211yescharacteristic
11C22×#4343—216no—
12C22×#4343—24no—
13C22×#4343—24no—
14C22×#4343C418yescomplemented
15C23×D44C2211yescharacteristic
16C23×D44C2212yes—
17C23×C4×D11C2212yes—
18C23×C4×D11C2212yes—
19C23×C4×D11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2214yes—
22C22×(C2×D11)⋊C4C2214yes—
23C2×C11×#95C2214yes—
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2211yescharacteristic
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31#10622278—216no—
32#10622277—24no—
33D11×#95—24no—
34C24×D11C2312yes—
35C24×D11C2311yescharacteristic
36C22×Q8×C11—28no—
37C22×Q8×C11—22no—
38C22×Q8×C11—22no—
39C22×Q8×C11C2×C414yescomplemented
40C23×C4×C11C2312yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×Dic11C2312yes—
45C23×Dic11C2312yes—
46C23×Dic11C2311yescharacteristic
47C2×#4343—264no—
48C2×#4343—264no—
49C2×#4343—264no—
50C2×#4343—232no—
51C22×D44—28no—
52C22×D44—24no—
53C22×D44—28no—
54C22×D44—24no—
55C22×D44—22no—
56C22×D44—22no—
57C22×D44C2×C418yes—
58C22×D44C2×C414yescomplemented
59C22×D44D4116yes—
60C22×C4×D11—28no—
61C22×C4×D11—28no—
62C22×C4×D11—28no—
63C22×C4×D11—24no—
64C22×C4×D11—24no—
65C22×C4×D11—24no—
66C22×C4×D11—24no—
67C22×C4×D11—24no—
68C22×C4×D11—28no—
69C22×C4×D11—44no—
70C22×C4×D11C2×C414yes—
71C22×C4×D11C2×C418yescomplemented
72C22×C4×D11D414yes—
73C22×C4×D11D414yes—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—28no—
76C2×(C2×D11)⋊C4—28no—
77C2×(C2×D11)⋊C4—28no—
78C2×(C2×D11)⋊C4—28no—
79C2×(C2×D11)⋊C4—28no—
80C2×(C2×D11)⋊C4—44no—
81C2×(C2×D11)⋊C4—44no—
82C11×#95—22no—
83C11×#95—22no—
84C11×#95—28no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95—28no—
88C11⋊#95—24no—
89C11⋊#95—24no—
90#13956—111nomaximal, Sylow
91C24×C11C2411yescharacteristic
92C23×D11—22no—
93C23×D11—22no—
94C23×D11—22no—
95C23×D11—22no—
96C23×D11—22no—
97C23×D11—22no—
98C23×D11—24no—
99C23×D11—24no—
100C23×D11—24no—
101C23×D11—24no—
102C23×D11—24no—
103C23×D11C22×C414yes—
104C23×D11C22×C412yes—
105C23×D11C2×D418yes—
106C23×D11C2×D412yes—
107C23×D11C2×D418yes—
108C23×D11C2×D412yes—
109C2×Q8×C11—216no—
110C2×Q8×C11—216no—
111C2×Q8×C11—216no—
112C2×Q8×C11—28no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—24no—
116C22×C4×C11—24no—
117C22×C4×C11—22no—
118C22×C4×C11—24no—
119C22×C4×C11—22no—
120C22×C4×C11—24no—
121C22×C4×C11—22no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C22×C414yes—
128C22×C4×C11C2×D418yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11#4114yescomplemented
132C22×Dic11—24no—
133C22×Dic11—22no—
134C22×Dic11—24no—
135C22×Dic11—22no—
136C22×Dic11—24no—
137C22×Dic11—22no—
138C22×Dic11—24no—
139C22×Dic11—24no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11C22×C412yes—
143C22×Dic11C2×D412yes—
144C22×Dic11C2×D412yes—
145C22×Dic11#4114yescomplemented
146#4343—2256no—
147C2×D44—216no—
148C2×D44—216no—
149C2×D44—216no—
150C2×D44—216no—
151C2×D44—216no—
152C2×D44—232no—
153C2×D44—232no—
154C2×D44—28no—
155C2×D44C22⋊C4132yescomplemented
156C2×C4×D11—232no—
157C2×C4×D11—232no—
158C2×C4×D11—216no—
159C2×C4×D11—216no—
160C2×C4×D11—216no—
161C2×C4×D11—216no—
162C2×C4×D11—216no—
163C2×C4×D11—216no—
164C2×C4×D11—216no—
165C2×C4×D11—416no—
166C2×C4×D11—416no—
167C2×C4×D11—48no—
168C2×C4×D11—48no—
169C2×C4×D11C22⋊C4116yescomplemented
170(C2×D11)⋊C4—416no—
171(C2×D11)⋊C4—416no—
172(C2×D11)⋊C4—48no—
173C23×#41—111no—
174C2×#386—114no—
175C2×#381—111no—
176C22×#95—111no—
177#1446—111no—
178#1446D1111yescharacteristic, complemented
179#1438—111no—
180#1438—111no—
181C22⋊#95—114no—
182C23×C11C23×C411yescharacteristic
183C23×C11C22×D411yescharacteristic
184C23×C11C22×D411yescharacteristic
185C23×C11C22×D414yes—
186C23×C11C2×#4112yes—
187C23×C11C2×#4112yes—
188C23×C11H(5,𝔽2)12yes—
189C23×C112−1+412yes—
190C22×D11—24no—
191C22×D11—24no—
192C22×D11—24no—
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—22no—
196C22×D11—22no—
197C22×D11—24no—
198C22×D11—28no—
199C22×D11—28no—
200C22×D11—28no—
201C22×D11—28no—
202C22×D11—24no—
203C22×D11—24no—
204C22×D11—28no—
205C22×D11—28no—
206C22×D11—28no—
207C22×D11—28no—
208C22×D11—28no—
209C22×D11—28no—
210C22×D11—28no—
211C22×D11—28no—
212C22×D11—44no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—44no—
218C22×D11—44no—
219C22×D11—44no—
220C22×D11—44no—
221C22×D11—44no—
222C22×D11C2×C22⋊C418yes—
223C22×D11C2×C22⋊C418yes—
224C22×D11C2×C22⋊C414yes—
225C22×D11#12018yes—
226C22×D11#12018yes—
227Q8×C11—232no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—28no—
232C2×C4×C11—24no—
233C2×C4×C11—28no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—28no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—44no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—44no—
244C2×C4×C11—44no—
245C2×C4×C11C2×C22⋊C418yes—
246C2×C4×C11C2×C22⋊C414yes—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—28no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—44no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—44no—
259C2×Dic11—44no—
260C2×Dic11C2×C22⋊C414yes—
261D44—232no—
262D44—264no—
263C4×D11—264no—
264C4×D11—232no—
265C4×D11—432no—
266C22×#41—118no—
267C22×#41—224no—
268C22×#41—224no—
269C22×#41—2216no—
270C23×Q8C2×D1111yescharacteristic
271C23×D4—112no—
272C23×D4—111no—
273C24×C4—111no—
274C24×C4—112no—
275C24×C4—112no—
276C22×C22⋊C4—112no—
277C22×C22⋊C4—114no—
278C22×C22⋊C4—114no—
279#386—2216no—
280#381—224no—
281C2×#95—112no—
282C2×#95—112no—
283C2×#95—114no—
284C2×#95—111no—
285C2×#95—111no—
286C2×#95—224no—
287C2×#95C2×D1114yes—
288C2×#95C2×D1111yescharacteristic
289C2×#95C2×D1111yescharacteristic
290C22×C11C22×C22⋊C411yescharacteristic
291C22×C11C22×C22⋊C412yes—
292C22×C11C4×#4112yes—
293C22×C11#52012yes—
294C22×C11C2×#12012yes—
295C22×C11C2×#12012yes—
296C22×C11#52512yes—
297C22×C11#53211yescharacteristic
298C22×C11#53211yescharacteristic
299C22×C11#53511yescharacteristic
300C22×C11#53611yescharacteristic
301C22×C11#53712yes—
302C22×C11#54614yes—
303C22×C11#54614yes—
304C22×C11#54714yes—
305C22×C11#54714yes—
306C2×D11—24no—
307C2×D11—216no—
308C2×D11—28no—
309C2×D11—28no—
310C2×D11—28no—
311C2×D11—28no—
312C2×D11—24no—
313C2×D11—216no—
314C2×D11—28no—
315C2×D11—44no—
316C2×D11—48no—
317C2×D11—48no—
318C2×D11—48no—
319C2×D11—48no—
320C2×D11—48no—
321C2×D11—44no—
322C2×D11#37918yes—
323C4×C11—28no—
324C4×C11—24no—
325C4×C11—44no—
326C4×C11—82no—
327Dic11—24no—
328Dic11—44no—
329Dic11—82no—
330C25—111no—
331C25—112no—
332C2×#41—2232no—
333C2×#41—2264no—
334C2×#41—2264no—
335C2×#41—2264no—
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—28no—
339C22×Q8C4×D1114yescomplemented
340C22×D4—118no—
341C22×D4—114no—
342C22×D4—1116no—
343C22×D4—224no—
344C22×D4—228no—
345C22×D4—224no—
346C22×D4—228no—
347C22×D4—222no—
348C22×D4—222no—
349C23×C4—111no—
350C23×C4—114no—
351C23×C4—114no—
352C23×C4—114no—
353C23×C4—112no—
354C23×C4—118no—
355C23×C4—112no—
356C23×C4—224no—
357C23×C4—224no—
358C23×C4—224no—
359C23×C4—228no—
360C23×C4—228no—
361C23×C4—224no—
362C23×C4—228no—
363C23×C4—228no—
364C23×C4—224no—
365C23×C4—444no—
366C23×C4C22×D1112yes—
367C23×C4C22×D1112yes—
368C23×C4C22×D1111yescharacteristic
369C23×C4C22×D1112yes—
370C2×C22⋊C4—228no—
371C2×C22⋊C4—224no—
372C2×C22⋊C4—228no—
373C2×C22⋊C4—228no—
374C2×C22⋊C4—228no—
375C2×C22⋊C4—228no—
376C2×C22⋊C4—444no—
377C2×C22⋊C4—444no—
378#95—22no—
379#95—22no—
380#95—28no—
381#95—224no—
382#95—224no—
383#95—222no—
384#95—222no—
385#95—228no—
386C2×C11C2×#37911yescharacteristic
387C2×C11#229711yescharacteristic
388C2×C11#231111yescharacteristic
389C2×C11#233914yes—
390C2×C11#240412yes—
391C2×C11#240612yes—
392C2×C11#243012yes—
393C2×C11#243012yes—
394D11—28no—
395D11—48no—
396C24—112no—
397C24—112no—
398C24—118no—
399C24—112no—
400C24—114no—
401C24—118no—
402C24—222no—
403C24—222no—
404C24—222no—
405C24—222no—
406C24—222no—
407C24—222no—
408C24—224no—
409C24—224no—
410C24—224no—
411C24—224no—
412C24—224no—
413C24C23×D1111yescharacteristic
414#41—22256no—
415C2×Q8—216no—
416C2×Q8—216no—
417C2×Q8—28no—
418C2×Q8—216no—
419C2×D4—1132no—
420C2×D4—2216no—
421C2×D4—2216no—
422C2×D4—2216no—
423C2×D4—2232no—
424C2×D4—2232no—
425C2×D4—2216no—
426C2×D4—2216no—
427C2×D4—228no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—24no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—112no—
442C22×C4—112no—
443C22×C4—112no—
444C22×C4—1116no—
445C22×C4—114no—
446C22×C4—2216no—
447C22×C4—2216no—
448C22×C4—2216no—
449C22×C4—2216no—
450C22×C4—2216no—
451C22×C4—2232no—
452C22×C4—2232no—
453C22×C4—2216no—
454C22×C4—224no—
455C22×C4—2216no—
456C22×C4—222no—
457C22×C4—224no—
458C22×C4—222no—
459C22×C4—224no—
460C22×C4—222no—
461C22×C4—224no—
462C22×C4—224no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—4416no—
466C22×C4—4416no—
467C22×C4—448no—
468C22×C4—448no—
469C22×C4C2×C4×D1112yes—
470C22×C4C2×C4×D1114yes—
471C22×C4D4×D1112yes—
472C22×C4D4×D1112yes—
473C22×C4D4×D1118yes—
474C22×C4#434314yescomplemented
475C22⋊C4—4416no—
476C22⋊C4—4416no—
477C22⋊C4—448no—
478C11#1395611yescharacteristic, complemented, Sylow
479C23—114no—
480C23—118no—
481C23—118no—
482C23—118no—
483C23—118no—
484C23—222no—
485C23—222no—
486C23—228no—
487C23—224no—
488C23—224no—
489C23—224no—
490C23—224no—
491C23—228no—
492C23—228no—
493C23—222no—
494C23—222no—
495C23—228no—
496C23—228no—
497C23—224no—
498C23—224no—
499C23—228no—
500C23—228no—
501C23—228no—
502C23—228no—
503C23—228no—
504C23—228no—
505C23—228no—
506C23—442no—
507C23—442no—
508C23—444no—
509C23—444no—
510C23—444no—
511C23—444no—
512C23—444no—
513C23—442no—
514C23—442no—
515C23—444no—
516C23C22×C4×D1111yescharacteristic
517C23C2×D4×D1111yescharacteristic
518C23C2×D4×D1111yescharacteristic
519C23C2×D4×D1114yes—
520C23C2×#434312yes—
521C23#6704012yes—
522C23#41×D1112yes—
523C23#6704212yes—
524Q8—232no—
525D4—2264no—
526D4—2232no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—28no—
532C2×C4—24no—
533C2×C4—28no—
534C2×C4—24no—
535C2×C4—28no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—44no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—44no—
542C2×C4—42no—
543C2×C4—44no—
544C2×C4—114no—
545C2×C4—2232no—
546C2×C4—2264no—
547C2×C4—224no—
548C2×C4—224no—
549C2×C4—224no—
550C2×C4—224no—
551C2×C4—228no—
552C2×C4—4432no—
553C2×C4—442no—
554C2×C4—444no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—444no—
558C2×C4—442no—
559C2×C4—442no—
560C2×C4—444no—
561C2×C4C22⋊C4×D1114yes—
562C2×C4C22⋊C4×D1118yes—
563C22—118no—
564C22—224no—
565C22—228no—
566C22—228no—
567C22—2216no—
568C22—228no—
569C22—228no—
570C22—224no—
571C22—2216no—
572C22—228no—
573C22—444no—
574C22—448no—
575C22—448no—
576C22—448no—
577C22—448no—
578C22—448no—
579C22—444no—
580C22C2×C22⋊C4×D1111yescharacteristic
581C22C2×C22⋊C4×D1112yes—
582C22C4×#434312yes—
583C22#1062310512yes—
584C22D11×#12012yes—
585C22D11×#12012yes—
586C22#1062315812yes—
587C22#1062316012yes—
588C22#1062316114yes—
589C22#1062316214yes—
590C22#1062319911yescharacteristic
591C22#1062320511yescharacteristic
592C22#1062320714yes—
593C22#1062325511yescharacteristic
594C22#1062325611yescharacteristic
595C22#1062325714yes—
596C4—24no—
597C4—28no—
598C4—44no—
599C4—82no—
600C4—224no—
601C4—444no—
602C4—882no—
603C2—228no—
604C2—448no—
605C2D11×#37911yescharacteristic
606C2#1307110511yescharacteristic
607C2#1307120711yescharacteristic
608C2#1307144514yes—
609C2#1307193612yes—
610C2#1307195212yes—
611C2#1307222712yes—
612C2#1307222912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1446C2
socle, cosocleC24×C11C24
prime radicalC23×#4343C2
hypercenter#1446D11
hypocenterC11#13956
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
2. C2×#10622278C2semidirect
3. C2×#10622277C2semidirect
4. C2×D11×#95C2semidirect
5. #13066887C2semidirect
6. #13066856C2semidirect
7. #13066856C2semidirect
8. (C2×D11)⋊#95C2semidirect
9. C11×#1446C2semidirect
14. C22×#4343C4semidirect
39. C22×Q8×C11C2×C4semidirect
58. C22×D44C2×C4semidirect
71. C22×C4×D11C2×C4semidirect
131. C22×C4×C11#41semidirect
145. C22×Dic11#41semidirect
155. C2×D44C22⋊C4semidirect
169. C2×C4×D11C22⋊C4semidirect
178. #1446D11semidirect
339. C22×Q8C4×D11semidirect
474. C22×C4#4343semidirect
478. C11#13956semidirect

Maximal subgroups

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

subgroupindex
C23×#43432
C2×#106222782
C2×#106222772
C2×D11×#952
#130668872
#130668562
(C2×D11)⋊#952
C11×#14462
#1395611