Finite Group Databasebeta

← #14676457

Subgroups — #14676457

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×#4341C211yesmaximal, characteristic
2C2×#10622569C214yesmaximal, complemented
3C2×#10622277C211yesmaximal, characteristic, complemented
4C2×D11×#95C211yesmaximal, characteristic, complemented
5#13066886C211yesmaximal, characteristic, complemented
6#13066886C211yesmaximal, characteristic, complemented
7#13066857C211yesmaximal, characteristic, complemented
8#13066838C214yesmaximal, complemented
9C11×#1438C211yesmaximal, characteristic, complemented
10C23×D4×C11C2211yescharacteristic
11C23×C22⋊D11C2212yes—
12C24×Dic11C2212yes—
13C22×#4341—216no—
14C22×#4341—24no—
15C22×#4341—24no—
16C22×#4341C418yescomplemented
17C23×C4×D11C2212yes—
18C23×C4×D11C2211yescharacteristic
19C23×Dic22C2211yescharacteristic
20C22×C11×C22⋊C4C2214yes—
21C22×C22⋊Dic11C2214yes—
22C22×(C2×D11)⋊C4C2212yes—
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31#10622569—216no—
32#10622277—24no—
33D11×#95—24no—
34C25×C11C2312yes—
35C24×D11C2311yescharacteristic
36C22×D4×C11—28no—
37C22×D4×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11C2×C414yescomplemented
40C23×C4×C11C2312yes—
41C23×C4×C11C2312yes—
42C23×C4×C11C2311yescharacteristic
43C22×C22⋊D11—24no—
44C22×C22⋊D11—28no—
45C22×C22⋊D11—24no—
46C22×C22⋊D11C2×C418yes—
47C22×C22⋊D11D4116yes—
48C23×Dic11—28no—
49C23×Dic11—24no—
50C23×Dic11—24no—
51C23×Dic11—28no—
52C23×Dic11C2×C418yescomplemented
53C23×Dic11C2312yes—
54C23×Dic11C2312yes—
55C23×Dic11C2312yes—
56C23×Dic11C2311yescharacteristic
57C2×#4341—264no—
58C2×#4341—264no—
59C2×#4341—264no—
60C2×#4341—232no—
61C22×C4×D11—28no—
62C22×C4×D11—24no—
63C22×C4×D11—24no—
64C22×C4×D11—24no—
65C22×C4×D11—28no—
66C22×C4×D11—44no—
67C22×C4×D11C2×C414yes—
68C22×C4×D11D414yes—
69C22×C4×D11D414yes—
70C22×Dic22—22no—
71C22×Dic22—22no—
72C22×Dic22—28no—
73C22×Dic22C2×C414yescomplemented
74C2×C11×C22⋊C4—28no—
75C2×C11×C22⋊C4—28no—
76C2×C11×C22⋊C4—44no—
77C2×C22⋊Dic11—28no—
78C2×C22⋊Dic11—28no—
79C2×C22⋊Dic11—44no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—28no—
82C11×#95—22no—
83C11×#95—22no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95—24no—
87C11⋊#95—24no—
88C11⋊#95—28no—
89C11⋊#95—28no—
90#13956—111nomaximal, Sylow
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—24no—
94C24×C11—24no—
95C24×C11—24no—
96C24×C11—24no—
97C24×C11—24no—
98C24×C11C22×C414yes—
99C24×C11C2×D418yes—
100C24×C11C2411yescharacteristic
101C23×D11—22no—
102C23×D11—22no—
103C23×D11—22no—
104C23×D11—22no—
105C23×D11C22×C412yes—
106C23×D11C2×D412yes—
107C23×D11C2×D418yes—
108C23×D11C2×D412yes—
109C2×D4×C11—216no—
110C2×D4×C11—216no—
111C2×D4×C11—216no—
112C2×D4×C11—28no—
113C22×C4×C11—24no—
114C22×C4×C11—22no—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—24no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11C22×C412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11#4114yescomplemented
127C2×C22⋊D11—216no—
128C2×C22⋊D11—216no—
129C2×C22⋊D11—232no—
130C2×C22⋊D11—232no—
131C2×C22⋊D11C22⋊C4132yescomplemented
132C22×Dic11—232no—
133C22×Dic11—232no—
134C22×Dic11—216no—
135C22×Dic11—216no—
136C22×Dic11—216no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—24no—
140C22×Dic11—24no—
141C22×Dic11—22no—
142C22×Dic11—24no—
143C22×Dic11—22no—
144C22×Dic11—24no—
145C22×Dic11—22no—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11C22×C414yes—
151C22×Dic11C22×C412yes—
152C22×Dic11C2×D418yes—
153C22×Dic11C2×D412yes—
154C22×Dic11C2×D412yes—
155C22×Dic11#4114yescomplemented
156#4341—2256no—
157C2×C4×D11—216no—
158C2×C4×D11—216no—
159C2×C4×D11—216no—
160C2×C4×D11—216no—
161C2×C4×D11—416no—
162C2×C4×D11—416no—
163C2×C4×D11—48no—
164C2×C4×D11—48no—
165C2×C4×D11C22⋊C4116yescomplemented
166C2×Dic22—216no—
167C2×Dic22—216no—
168C2×Dic22—216no—
169C2×Dic22—28no—
170C11×C22⋊C4—416no—
171C22⋊Dic11—416no—
172(C2×D11)⋊C4—48no—
173C23×#41—111no—
174C2×#386—114no—
175C2×#381—111no—
176C22×#95—111no—
177#1446—111no—
178#1446—111no—
179#1438—111no—
180#1438D1111yescharacteristic, complemented
181C22⋊#95—114no—
182C23×C11—24no—
183C23×C11—24no—
184C23×C11—28no—
185C23×C11—28no—
186C23×C11—28no—
187C23×C11—28no—
188C23×C11—28no—
189C23×C11—28no—
190C23×C11—28no—
191C23×C11—28no—
192C23×C11—44no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—44no—
198C23×C11—44no—
199C23×C11—44no—
200C23×C11—44no—
201C23×C11—44no—
202C23×C11C2×C22⋊C418yes—
203C23×C11C23×C411yescharacteristic
204C23×C11C22×D411yescharacteristic
205C23×C11C22×D411yescharacteristic
206C23×C11C22×D414yes—
207C23×C11C2×#4112yes—
208C23×C11C2×#4112yes—
209C23×C11H(5,𝔽2)12yes—
210C23×C112−1+412yes—
211C22×D11—24no—
212C22×D11—24no—
213C22×D11—24no—
214C22×D11—22no—
215C22×D11—22no—
216C22×D11—22no—
217C22×D11—22no—
218C22×D11—24no—
219C22×D11—28no—
220C22×D11—28no—
221C22×D11—28no—
222C22×D11—28no—
223C22×D11C2×C22⋊C418yes—
224C22×D11C2×C22⋊C414yes—
225C22×D11#12018yes—
226C22×D11#12018yes—
227D4×C11—232no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—28no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—44no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—44no—
240C2×C4×C11—44no—
241C2×C4×C11C2×C22⋊C414yes—
242C22⋊D11—264no—
243C2×Dic11—264no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—28no—
248C2×Dic11—28no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—28no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—44no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—44no—
260C2×Dic11—44no—
261C2×Dic11C2×C22⋊C418yes—
262C2×Dic11C2×C22⋊C414yes—
263C4×D11—232no—
264C4×D11—432no—
265Dic22—232no—
266C22×#41—118no—
267C22×#41—224no—
268C22×#41—224no—
269C22×#41—2216no—
270C23×Q8—111no—
271C23×D4—112no—
272C23×D4C2×D1111yescharacteristic
273C24×C4—111no—
274C24×C4—112no—
275C24×C4—112no—
276C22×C22⋊C4—112no—
277C22×C22⋊C4—114no—
278C22×C22⋊C4C2×D1114yes—
279#386—2216no—
280#381—224no—
281C2×#95—112no—
282C2×#95—112no—
283C2×#95—114no—
284C2×#95—114no—
285C2×#95—111no—
286C2×#95—111no—
287C2×#95—224no—
288C2×#95C2×D1111yescharacteristic
289C2×#95C2×D1111yescharacteristic
290C22×C11—216no—
291C22×C11—28no—
292C22×C11—44no—
293C22×C11—48no—
294C22×C11—48no—
295C22×C11—48no—
296C22×C11—48no—
297C22×C11—48no—
298C22×C11—44no—
299C22×C11C22×C22⋊C411yescharacteristic
300C22×C11C22×C22⋊C412yes—
301C22×C11C4×#4112yes—
302C22×C11#52012yes—
303C22×C11C2×#12012yes—
304C22×C11C2×#12012yes—
305C22×C11#52512yes—
306C22×C11#53211yescharacteristic
307C22×C11#53211yescharacteristic
308C22×C11#53511yescharacteristic
309C22×C11#53611yescharacteristic
310C22×C11#53712yes—
311C22×C11#54614yes—
312C22×C11#54614yes—
313C22×C11#54714yes—
314C22×C11#54714yes—
315C2×D11—24no—
316C2×D11—216no—
317C2×D11—28no—
318C2×D11—28no—
319C2×D11—28no—
320C2×D11—28no—
321C2×D11—24no—
322C2×D11#37918yes—
323C4×C11—24no—
324C4×C11—44no—
325C4×C11—82no—
326Dic11—28no—
327Dic11—24no—
328Dic11—44no—
329Dic11—82no—
330C25—111no—
331C25C22×D1112yes—
332C2×#41—2232no—
333C2×#41—2264no—
334C2×#41—2264no—
335C2×#41—2264no—
336C22×Q8—114no—
337C22×Q8—228no—
338C22×Q8—222no—
339C22×Q8—222no—
340C22×D4—28no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—118no—
344C22×D4—1116no—
345C22×D4—224no—
346C22×D4—228no—
347C22×D4—224no—
348C22×D4C4×D1114yescomplemented
349C23×C4—111no—
350C23×C4—112no—
351C23×C4—114no—
352C23×C4—114no—
353C23×C4—114no—
354C23×C4—118no—
355C23×C4—112no—
356C23×C4—112no—
357C23×C4—224no—
358C23×C4—228no—
359C23×C4—224no—
360C23×C4—228no—
361C23×C4—224no—
362C23×C4—224no—
363C23×C4—228no—
364C23×C4—228no—
365C23×C4—224no—
366C23×C4—444no—
367C23×C4C22×D1112yes—
368C23×C4C22×D1112yes—
369C23×C4C22×D1111yescharacteristic
370C2×C22⋊C4—28no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—224no—
374C2×C22⋊C4—228no—
375C2×C22⋊C4—228no—
376C2×C22⋊C4—228no—
377C2×C22⋊C4—444no—
378#95—22no—
379#95—22no—
380#95—224no—
381#95—224no—
382#95—228no—
383#95—228no—
384#95—222no—
385#95—222no—
386C2×C11—48no—
387C2×C11C2×#37911yescharacteristic
388C2×C11#229711yescharacteristic
389C2×C11#231111yescharacteristic
390C2×C11#233914yes—
391C2×C11#240412yes—
392C2×C11#240612yes—
393C2×C11#243012yes—
394C2×C11#243012yes—
395D11—28no—
396C24—22no—
397C24—22no—
398C24—24no—
399C24—24no—
400C24—24no—
401C24—24no—
402C24—24no—
403C24—112no—
404C24—112no—
405C24—118no—
406C24—112no—
407C24—222no—
408C24—222no—
409C24—222no—
410C24—222no—
411C24C2×C4×D1114yes—
412C24D4×D1118yes—
413C24C23×D1111yescharacteristic
414#41—22256no—
415C2×Q8—2216no—
416C2×Q8—2216no—
417C2×Q8—2216no—
418C2×Q8—228no—
419C2×D4—216no—
420C2×D4—216no—
421C2×D4—216no—
422C2×D4—28no—
423C2×D4—1132no—
424C2×D4—2216no—
425C2×D4—2216no—
426C2×D4—2232no—
427C2×D4—2232no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—112no—
439C22×C4—114no—
440C22×C4—112no—
441C22×C4—112no—
442C22×C4—118no—
443C22×C4—1116no—
444C22×C4—114no—
445C22×C4—2216no—
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—222no—
456C22×C4—222no—
457C22×C4—224no—
458C22×C4—222no—
459C22×C4—224no—
460C22×C4—222no—
461C22×C4—224no—
462C22×C4—222no—
463C22×C4—224no—
464C22×C4—222no—
465C22×C4—224no—
466C22×C4—222no—
467C22×C4—4416no—
468C22×C4—4416no—
469C22×C4—448no—
470C22×C4—448no—
471C22×C4C2×C4×D1112yes—
472C22×C4D4×D1112yes—
473C22×C4D4×D1112yes—
474C22×C4#434114yescomplemented
475C22⋊C4—416no—
476C22⋊C4—448no—
477C22⋊C4—4416no—
478C11#1395611yescharacteristic, complemented, Sylow
479C23—24no—
480C23—24no—
481C23—28no—
482C23—28no—
483C23—28no—
484C23—28no—
485C23—28no—
486C23—28no—
487C23—28no—
488C23—28no—
489C23—42no—
490C23—42no—
491C23—44no—
492C23—44no—
493C23—44no—
494C23—44no—
495C23—44no—
496C23—44no—
497C23—42no—
498C23—42no—
499C23—114no—
500C23—118no—
501C23—118no—
502C23—118no—
503C23—222no—
504C23—222no—
505C23—224no—
506C23—224no—
507C23—228no—
508C23—224no—
509C23—224no—
510C23—228no—
511C23—228no—
512C23—228no—
513C23—222no—
514C23—222no—
515C23C22⋊C4×D1118yes—
516C23C22×C4×D1111yescharacteristic
517C23C2×D4×D1111yescharacteristic
518C23C2×D4×D1111yescharacteristic
519C23C2×D4×D1114yes—
520C23C2×#434112yes—
521C23#6703712yes—
522C23#41×D1112yes—
523C23#6704312yes—
524Q8—2232no—
525D4—232no—
526D4—2264no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—28no—
531C2×C4—24no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—44no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—44no—
538C2×C4—42no—
539C2×C4—44no—
540C2×C4—114no—
541C2×C4—118no—
542C2×C4—2232no—
543C2×C4—2264no—
544C2×C4—224no—
545C2×C4—224no—
546C2×C4—224no—
547C2×C4—224no—
548C2×C4—224no—
549C2×C4—228no—
550C2×C4—228no—
551C2×C4—224no—
552C2×C4—228no—
553C2×C4—4432no—
554C2×C4—442no—
555C2×C4—442no—
556C2×C4—444no—
557C2×C4—442no—
558C2×C4—442no—
559C2×C4—444no—
560C2×C4—444no—
561C2×C4—442no—
562C2×C4C22⋊C4×D1114yes—
563C22—216no—
564C22—28no—
565C22—48no—
566C22—48no—
567C22—48no—
568C22—48no—
569C22—48no—
570C22—44no—
571C22—44no—
572C22—118no—
573C22—228no—
574C22—228no—
575C22—2216no—
576C22—228no—
577C22—228no—
578C22—224no—
579C22—224no—
580C22C2×C22⋊C4×D1112yes—
581C22C2×C22⋊C4×D1111yescharacteristic
582C22C4×#434112yes—
583C22#1062307712yes—
584C22D11×#12012yes—
585C22D11×#12012yes—
586C22#1062312214yes—
587C22#1062313712yes—
588C22#1062313912yes—
589C22#1062314114yes—
590C22#1062314214yes—
591C22#1062318614yes—
592C22#1062319911yescharacteristic
593C22#1062320611yescharacteristic
594C22#1062324611yescharacteristic
595C22#1062324711yescharacteristic
596C4—24no—
597C4—44no—
598C4—82no—
599C4—224no—
600C4—228no—
601C4—444no—
602C4—882no—
603C2—48no—
604C2—228no—
605C2D11×#37911yescharacteristic
606C2#1307110311yescharacteristic
607C2#1307120611yescharacteristic
608C2#1307144214yes—
609C2#1307193012yes—
610C2#1307194612yes—
611C2#1307221912yes—
612C2#1307222112yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC23×#4341C2
hypercenter#1438D11
hypocenterC11#13956
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. C2×#10622569C2semidirect
3. C2×#10622277C2semidirect
4. C2×D11×#95C2semidirect
5. #13066886C2semidirect
6. #13066886C2semidirect
7. #13066857C2semidirect
8. #13066838C2semidirect
9. C11×#1438C2semidirect
16. C22×#4341C4semidirect
39. C22×D4×C11C2×C4semidirect
52. C23×Dic11C2×C4semidirect
73. C22×Dic22C2×C4semidirect
126. C22×C4×C11#41semidirect
131. C2×C22⋊D11C22⋊C4semidirect
155. C22×Dic11#41semidirect
165. C2×C4×D11C22⋊C4semidirect
180. #1438D11semidirect
348. C22×D4C4×D11semidirect
474. C22×C4#4341semidirect
478. C11#13956semidirect

Maximal subgroups

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

subgroupindex
C23×#43412
C2×#106225692
C2×#106222772
C2×D11×#952
#130668862
#130668572
#130668382
C11×#14382
#1395611