Finite Group Databasebeta

← #14926326

Subgroups — #14926326

Order 2816.

4046 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623014C211yesmaximal, characteristic, complemented
2C23×C22⋊Dic11C211yesmaximal, characteristic
3#13076901C214yesmaximal, complemented
4#13074425C214yesmaximal, complemented
5#13072282C218yesmaximal, complemented
6#13072277C218yesmaximal, complemented
7#13071230C211yesmaximal, characteristic, complemented
8#13071228C211yesmaximal, characteristic, complemented
9#13071228C211yesmaximal, characteristic, complemented
10C2×#10622860C211yesmaximal, characteristic
11C2×C11×#379C211yesmaximal, characteristic
12C26×C11C2211yescharacteristic
13C24×Dic11C2212yes—
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2214yes—
17C22×C22⋊Dic11—28no—
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2214yes—
22C22×C22⋊Dic11C2214yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2214yes—
25C22×C22⋊Dic11C2211yescharacteristic
26C2×#66977C2214yescomplemented
27#10623014—28no—
28C2×#66931C2214yescomplemented
29C2×#66931C2214yescomplemented
30C2×#66931C2218yescomplemented
31C11×#379C2214yes—
32C11×#379C2212yes—
33C11×#379C2212yes—
34#10622860C2214yes—
35#10622860C2212yes—
36#10622860C2212yes—
37#10622825C2214yescomplemented
38#10622823C2214yescomplemented
39#10622823C2214yescomplemented
40#10622563C2214yescomplemented
41#10622563C2214yescomplemented
42#10622563C2218yescomplemented
43#10622562C2218yescomplemented
44#10622561C2218yescomplemented
45#10622561C2218yescomplemented
46#10622560C2218yescomplemented
47#10622559C2214yescomplemented
48#10622559C2214yescomplemented
49#10622559C2218yescomplemented
50#10622555C2214yescomplemented
51#10622555C2214yescomplemented
52#10622555C2218yescomplemented
53C25×C11—24no—
54C25×C11—24no—
55C25×C11—48no—
56C25×C11Q818yescomplemented
57C25×C11C2311yescharacteristic
58C25×C11C2312yes—
59C25×C11C2312yes—
60C25×C11C2311yescharacteristic
61C25×C11C2311yescharacteristic
62C23×C4×C11C2312yes—
63C23×C4×C11C2312yes—
64C23×Dic11—28no—
65C23×Dic11—48no—
66C23×Dic11C2318yes—
67C23×Dic11C2312yes—
68C23×Dic11C2312yes—
69C23×Dic11C2312yes—
70C23×Dic11C2312yes—
71C22×Dic22C2314yescomplemented
72C2×C11×C22⋊C4—24no—
73C2×C11×C22⋊C4—24no—
74C2×C11×C22⋊C4—48no—
75C2×C11×C22⋊C4C2312yes—
76C2×C11×C22⋊C4C2312yes—
77C2×C11×C22⋊C4C2318yes—
78C2×C11×C22⋊C4C2312yes—
79C2×C11×C22⋊C4C2312yes—
80C2×C11×C22⋊C4C2318yes—
81C2×C22⋊Dic11—24no—
82C2×C22⋊Dic11—24no—
83C2×C22⋊Dic11—24no—
84C2×C22⋊Dic11—28no—
85C2×C22⋊Dic11—216no—
86C2×C22⋊Dic11—216no—
87C2×C22⋊Dic11—48no—
88C2×C22⋊Dic11D418yes—
89C2×C22⋊Dic11C2312yes—
90C2×C22⋊Dic11C2318yes—
91C2×C22⋊Dic11C2312yes—
92C2×C22⋊Dic11C2312yes—
93C2×C22⋊Dic11C2312yes—
94C2×C22⋊Dic11C2318yes—
95C2×C22⋊Dic11C2312yes—
96C2×C22⋊Dic11C2312yes—
97C2×C22⋊Dic11C2318yes—
98C2×C22⋊Dic11C2312yes—
99C2×C22⋊Dic11C2312yes—
100C2×C4⋊Dic11C2314yescomplemented
101C2×C4⋊Dic11C2318yescomplemented
102#66977—216no—
103C2×Dic11⋊C4C2314yescomplemented
104C2×Dic11⋊C4C2314yescomplemented
105C2×Dic11⋊C4C2318yescomplemented
106C2×Dic11⋊C4C2318yescomplemented
107#66931—216no—
108#66931—216no—
109#66931—416no—
110C11⋊#95C2318yescomplemented
111C11⋊#95C2318yescomplemented
112C11⋊#95C2318yescomplemented
113#34982—111nomaximal, Sylow
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—28no—
117C24×C11—232no—
118C24×C11—24no—
119C24×C11—24no—
120C24×C11—22no—
121C24×C11—24no—
122C24×C11—24no—
123C24×C11—22no—
124C24×C11—28no—
125C24×C11—28no—
126C24×C11—432no—
127C24×C11—44no—
128C24×C11—44no—
129C24×C11—44no—
130C24×C11—44no—
131C24×C11—432no—
132C24×C11—432no—
133C24×C11C2×D414yes—
134C24×C11C2×Q814yes—
135C24×C11C2×Q818yes—
136C24×C11C2×Q818yes—
137C24×C11C2×Q814yes—
138C24×C11C2×Q814yes—
139C24×C11#4114yes—
140C24×C11C2412yes—
141C24×C11C2411yescharacteristic
142C24×C11C2411yescharacteristic
143C24×C11C2411yescharacteristic
144C24×C11C2412yes—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—44no—
148C22×C4×C11—44no—
149C22×C4×C11C2414yes—
150C22×C4×C11C2414yes—
151C22×Dic11—216no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—216no—
156C22×Dic11—44no—
157C22×Dic11—48no—
158C22×Dic11—44no—
159C22×Dic11—44no—
160C22×Dic11—44no—
161C22×Dic11—432no—
162C22×Dic11C2×D418yes—
163C22×Dic11C2414yes—
164C22×Dic11C2414yes—
165C22×Dic11C2414yes—
166C22×Dic11C2414yes—
167C2×Dic22—28no—
168C2×Dic22—48no—
169C11×C22⋊C4—24no—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—216no—
174C11×C22⋊C4—48no—
175C22⋊Dic11—216no—
176C22⋊Dic11—24no—
177C22⋊Dic11—24no—
178C22⋊Dic11—24no—
179C22⋊Dic11—24no—
180C22⋊Dic11—24no—
181C22⋊Dic11—24no—
182C22⋊Dic11—216no—
183C22⋊Dic11—48no—
184C22⋊Dic11C2×D418yes—
185C22⋊Dic11C2×D418yes—
186C4⋊Dic11—28no—
187C4⋊Dic11—48no—
188Dic11⋊C4—28no—
189Dic11⋊C4—28no—
190Dic11⋊C4—48no—
191Dic11⋊C4—48no—
192C2×#543—111no—
193C23×C22⋊C4—111no—
194#2848—114no—
195#2626—114no—
196#2437—118no—
197#2437—118no—
198#2315—111no—
199#2315—111no—
200#2315—111no—
201C2×#379—111no—
202C2×#379D1111yescharacteristic
203C23×C11—216no—
204C23×C11—216no—
205C23×C11—28no—
206C23×C11—216no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—24no—
212C23×C11—24no—
213C23×C11—216no—
214C23×C11—216no—
215C23×C11—28no—
216C23×C11—216no—
217C23×C11—216no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11—48no—
223C23×C11—48no—
224C23×C11—48no—
225C23×C11—48no—
226C23×C11—48no—
227C23×C11—48no—
228C23×C11—416no—
229C23×C11—416no—
230C23×C11—416no—
231C23×C11—416no—
232C23×C11—4128no—
233C23×C11—48no—
234C23×C11—48no—
235C23×C11C22⋊Q8116yescomplemented
236C23×C11C22×D412yes—
237C23×C11C22×D412yes—
238C23×C11C22×D412yes—
239C23×C11C22×Q814yes—
240C23×C11C22×Q812yes—
241C23×C11C22×Q812yes—
242C23×C11C22×Q812yes—
243C23×C11C22×Q814yes—
244C23×C11C2×#4112yes—
245C23×C11C2×#4112yes—
246C23×C11C2×#4112yes—
247C23×C11H(5,𝔽2)18yes—
248C23×C11C2511yescharacteristic
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—28no—
252C2×C4×C11—28no—
253C2×C4×C11—84no—
254C2×C4×C11—84no—
255C2×Dic11—28no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—28no—
260C2×Dic11—28no—
261C2×Dic11—28no—
262C2×Dic11—48no—
263C2×Dic11—432no—
264C2×Dic11—48no—
265C2×Dic11—84no—
266C2×Dic11—84no—
267C2×Dic11C22×D418yes—
268Dic22—88no—
269C26C2×D1111yescharacteristic
270C24×C4—112no—
271#543—228no—
272C2×C22⋊Q8—114no—
273C2×C22⋊Q8—114no—
274C2×C22⋊Q8—114no—
275C2×C22⋊Q8—118no—
276C22×C22⋊C4—111no—
277C22×C22⋊C4—111no—
278C22×C22⋊C4—111no—
279C22×C22⋊C4—111no—
280C22×C22⋊C4—112no—
281C22×C22⋊C4—114no—
282C22×C22⋊C4—114no—
283C22×C22⋊C4—114no—
284C22×C22⋊C4—228no—
285C22×C22⋊C4C2×D1111yescharacteristic
286C22×C22⋊C4C2×D1111yescharacteristic
287C22×C22⋊C4C2×D1114yes—
288#399—118no—
289#396—118no—
290#396—118no—
291#393—118no—
292#385—114no—
293#385—114no—
294#385—114no—
295#385—114no—
296#385—114no—
297#385—114no—
298#385—118no—
299#385—118no—
300#380—114no—
301#380—114no—
302#380—114no—
303#380—118no—
304#379—112no—
305#379—112no—
306#379—114no—
307#379C2×D1112yes—
308#379C2×D1112yes—
309#379C2×D1114yes—
310C22×C11—232no—
311C22×C11—24no—
312C22×C11—24no—
313C22×C11—24no—
314C22×C11—24no—
315C22×C11—24no—
316C22×C11—24no—
317C22×C11—24no—
318C22×C11—28no—
319C22×C11—24no—
320C22×C11—24no—
321C22×C11—24no—
322C22×C11—28no—
323C22×C11—24no—
324C22×C11—24no—
325C22×C11—24no—
326C22×C11—24no—
327C22×C11—416no—
328C22×C11—432no—
329C22×C11—432no—
330C22×C11—416no—
331C22×C11—44no—
332C22×C11—44no—
333C22×C11C2×C22⋊Q814yes—
334C22×C11C2×C22⋊Q814yes—
335C22×C11C2×C22⋊Q814yes—
336C22×C11#54318yescomplemented
337C22×C11C23×D411yescharacteristic
338C22×C11C23×Q811yescharacteristic
339C22×C11C22×#4111yescharacteristic
340C22×C11C2×H(5,𝔽2)14yes—
341C4×C11—44no—
342C4×C11—44no—
343Dic11—28no—
344Dic11—44no—
345Dic11—44no—
346Dic11—44no—
347C25—24no—
348C25—24no—
349C25—48no—
350C25Dic2218yescomplemented
351C25C22×D1111yescharacteristic
352C25C22×D1112yes—
353C25C22×D1112yes—
354C25C22×D1111yescharacteristic
355C25C22×D1111yescharacteristic
356C22×Q8—114no—
357C23×C4—112no—
358C23×C4—118no—
359C23×C4—112no—
360C23×C4—112no—
361C23×C4—112no—
362C23×C4—228no—
363C23×C4—448no—
364C23×C4C22×D1112yes—
365C23×C4C22×D1112yes—
366C22⋊Q8—2216no—
367C22⋊Q8—2216no—
368C22⋊Q8—2216no—
369C22⋊Q8—4416no—
370C2×C4⋊C4—114no—
371C2×C4⋊C4—114no—
372C2×C4⋊C4—114no—
373C2×C4⋊C4—118no—
374C2×C4⋊C4—118no—
375C2×C4⋊C4—118no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—48no—
379C2×C22⋊C4—118no—
380C2×C22⋊C4—112no—
381C2×C22⋊C4—112no—
382C2×C22⋊C4—112no—
383C2×C22⋊C4—112no—
384C2×C22⋊C4—118no—
385C2×C22⋊C4—112no—
386C2×C22⋊C4—112no—
387C2×C22⋊C4—118no—
388C2×C22⋊C4—112no—
389C2×C22⋊C4—112no—
390C2×C22⋊C4—118no—
391C2×C22⋊C4—2216no—
392C2×C22⋊C4—2216no—
393C2×C22⋊C4—228no—
394C2×C22⋊C4—224no—
395C2×C22⋊C4—224no—
396C2×C22⋊C4—224no—
397C2×C22⋊C4—448no—
398C2×C22⋊C4C22×D1112yes—
399C2×C22⋊C4C22×D1112yes—
400C2×C22⋊C4C22×D1118yes—
401C2×C22⋊C4C22×D1112yes—
402C2×C22⋊C4C22×D1112yes—
403C2×C22⋊C4C22×D1118yes—
404#95—118no—
405#95—118no—
406#95—118no—
407C2×C11—24no—
408C2×C11—28no—
409C2×C11—24no—
410C2×C11—24no—
411C2×C11—44no—
412C2×C11C22×C22⋊Q811yescharacteristic
413C2×C11C2×#54312yes—
414C2×C11#348412yes—
415C2×C11#349012yes—
416C24—22no—
417C24—22no—
418C24—28no—
419C24—232no—
420C24—24no—
421C24—24no—
422C24—22no—
423C24—24no—
424C24—24no—
425C24—22no—
426C24—28no—
427C24—28no—
428C24—44no—
429C24—44no—
430C24—44no—
431C24—44no—
432C24—432no—
433C24—432no—
434C24—432no—
435C24C2×Dic2214yes—
436C24C2×Dic2218yes—
437C24C2×Dic2218yes—
438C24C2×Dic2214yes—
439C24C2×Dic2214yes—
440C24D4×D1114yes—
441C24#434114yes—
442C24C23×D1112yes—
443C24C23×D1111yescharacteristic
444C24C23×D1111yescharacteristic
445C24C23×D1111yescharacteristic
446C24C23×D1112yes—
447C2×Q8—228no—
448C2×Q8—448no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—44no—
452C22×C4—44no—
453C22×C4—114no—
454C22×C4—118no—
455C22×C4—114no—
456C22×C4—114no—
457C22×C4—114no—
458C22×C4—2216no—
459C22×C4—224no—
460C22×C4—2216no—
461C22×C4—224no—
462C22×C4—224no—
463C22×C4—444no—
464C22×C4—448no—
465C22×C4—444no—
466C22×C4—444no—
467C22×C4—444no—
468C22×C4—4432no—
469C22×C4C23×D1114yes—
470C22×C4C23×D1114yes—
471C4⋊C4—228no—
472C4⋊C4—228no—
473C4⋊C4—228no—
474C4⋊C4—448no—
475C4⋊C4—448no—
476C4⋊C4—448no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—216no—
482C22⋊C4—48no—
483C22⋊C4—118no—
484C22⋊C4—118no—
485C22⋊C4—2216no—
486C22⋊C4—224no—
487C22⋊C4—224no—
488C22⋊C4—224no—
489C22⋊C4—224no—
490C22⋊C4—224no—
491C22⋊C4—224no—
492C22⋊C4—2216no—
493C22⋊C4—448no—
494C11#3498211yescharacteristic, complemented, Sylow
495C23—216no—
496C23—216no—
497C23—28no—
498C23—216no—
499C23—22no—
500C23—22no—
501C23—24no—
502C23—24no—
503C23—24no—
504C23—24no—
505C23—216no—
506C23—216no—
507C23—28no—
508C23—216no—
509C23—216no—
510C23—22no—
511C23—22no—
512C23—24no—
513C23—24no—
514C23—48no—
515C23—48no—
516C23—48no—
517C23—48no—
518C23—48no—
519C23—48no—
520C23—416no—
521C23—416no—
522C23—416no—
523C23—416no—
524C23—4128no—
525C23—48no—
526C23—48no—
527C23#66931116yescomplemented
528C23C22×Dic2214yes—
529C23C22×Dic2212yes—
530C23C22×Dic2212yes—
531C23C22×Dic2212yes—
532C23C22×Dic2214yes—
533C23C2×D4×D1112yes—
534C23C2×D4×D1112yes—
535C23C2×D4×D1112yes—
536C23C2×#434112yes—
537C23C2×#434112yes—
538C23C2×#434112yes—
539C23#6703718yes—
540C23C24×D1111yescharacteristic
541Q8—888no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—28no—
545C2×C4—28no—
546C2×C4—84no—
547C2×C4—84no—
548C2×C4—118no—
549C2×C4—228no—
550C2×C4—224no—
551C2×C4—224no—
552C2×C4—224no—
553C2×C4—228no—
554C2×C4—228no—
555C2×C4—228no—
556C2×C4—448no—
557C2×C4—4432no—
558C2×C4—448no—
559C2×C4—884no—
560C2×C4—884no—
561C22—232no—
562C22—24no—
563C22—24no—
564C22—28no—
565C22—24no—
566C22—24no—
567C22—24no—
568C22—24no—
569C22—24no—
570C22—24no—
571C22—24no—
572C22—24no—
573C22—28no—
574C22—24no—
575C22—24no—
576C22—24no—
577C22—24no—
578C22—416no—
579C22—432no—
580C22—432no—
581C22—416no—
582C22—44no—
583C22—44no—
584C22C2×#6693114yes—
585C22C2×#6693114yes—
586C22C2×#6693114yes—
587C22#1062301418yescomplemented
588C22C23×Dic2211yescharacteristic
589C22C22×D4×D1111yescharacteristic
590C22C22×#434111yescharacteristic
591C22C2×#6703714yes—
592C4—44no—
593C4—44no—
594C4—228no—
595C4—444no—
596C4—444no—
597C4—444no—
598C2—24no—
599C2—28no—
600C2—24no—
601C2—24no—
602C2—44no—
603C2C22×#6693111yescharacteristic
604C2C2×#1062301412yes—
605C2#1308224512yes—
606C2#1308230312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#379C2
prime radicalC26×C11C22
hypercenterC2×#379D11
hypocenterC11#34982
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
1. C2×#10623014C2semidirect
3. #13076901C2semidirect
4. #13074425C2semidirect
5. #13072282C2semidirect
6. #13072277C2semidirect
7. #13071230C2semidirect
8. #13071228C2semidirect
9. #13071228C2semidirect
26. C2×#66977C22semidirect
28. C2×#66931C22semidirect
29. C2×#66931C22semidirect
30. C2×#66931C22semidirect
37. #10622825C22semidirect
38. #10622823C22semidirect
39. #10622823C22semidirect
40. #10622563C22semidirect
41. #10622563C22semidirect
42. #10622563C22semidirect
43. #10622562C22semidirect
44. #10622561C22semidirect
45. #10622561C22semidirect
46. #10622560C22semidirect
47. #10622559C22semidirect
48. #10622559C22semidirect
49. #10622559C22semidirect
50. #10622555C22semidirect
51. #10622555C22semidirect
52. #10622555C22semidirect
56. C25×C11Q8semidirect
71. C22×Dic22C23semidirect
100. C2×C4⋊Dic11C23semidirect
101. C2×C4⋊Dic11C23semidirect
103. C2×Dic11⋊C4C23semidirect
104. C2×Dic11⋊C4C23semidirect
105. C2×Dic11⋊C4C23semidirect
106. C2×Dic11⋊C4C23semidirect
110. C11⋊#95C23semidirect
111. C11⋊#95C23semidirect
112. C11⋊#95C23semidirect
235. C23×C11C22⋊Q8semidirect
336. C22×C11#543semidirect
350. C25Dic22semidirect
494. C11#34982semidirect
527. C23#66931semidirect
587. C22#10623014semidirect

Maximal subgroups

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

subgroupindex
C2×#106230142
C23×C22⋊Dic112
#130769012
#130744252
#130722822
#130722772
#130712302
#130712282
C2×#106228602
C2×C11×#3792
#3498211