Finite Group Databasebeta

← #14926327

Subgroups — #14926327

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
2C22×C22⋊C4×D11C211yesmaximal, characteristic
3#13076902C214yesmaximal, complemented
4#13074427C214yesmaximal, complemented
5#13072284C218yesmaximal, complemented
6#13072281C218yesmaximal, complemented
7#13071228C211yesmaximal, characteristic, complemented
8#13071228C211yesmaximal, characteristic, complemented
9C2×#10622568C211yesmaximal, characteristic
10C2×#10622568C211yesmaximal, characteristic
11C11×#2315C211yesmaximal, characteristic, complemented
12C25×D11C2211yescharacteristic
13C23×C4×D11C2212yes—
14C22×C11×C22⋊C4C2211yescharacteristic
15C22×C11×C22⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C22⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2214yes—
22C22×(C2×D11)⋊C4C2214yes—
23C2×#66977C2214yescomplemented
24C2×#66949C2218yescomplemented
25C2×C22⋊C4×D11—28no—
26C2×C22⋊C4×D11C2214yes—
27C2×C22⋊C4×D11C2214yes—
28#10623014—28no—
29C2×#66931C2214yescomplemented
30C2×#66931C2214yescomplemented
31C11×#385C2214yescomplemented
32C11×#385C2214yescomplemented
33C11×#380C2214yescomplemented
34#10622823C2214yescomplemented
35#10622823C2214yescomplemented
36#10622607C2218yescomplemented
37#10622605C2218yescomplemented
38#10622602C2218yescomplemented
39#10622568C2214yes—
40#10622568C2214yes—
41#10622568C2212yes—
42#10622568C2212yes—
43#10622568C2212yes—
44#10622568C2212yes—
45#10622559C2214yescomplemented
46#10622559C2214yescomplemented
47#10622555C2214yescomplemented
48#10622555C2214yescomplemented
49#10622289C2218yescomplemented
50#10622286C2218yescomplemented
51#10622281C2218yescomplemented
52#10622280C2218yescomplemented
53C25×C11C2311yescharacteristic
54C24×D11—24no—
55C24×D11—24no—
56C24×D11—48no—
57C24×D11Q818yescomplemented
58C24×D11C2311yescharacteristic
59C24×D11C2312yes—
60C24×D11C2312yes—
61C24×D11C2311yescharacteristic
62C23×C4×C11C2312yes—
63C23×C4×C11C2312yes—
64C23×C4×C11C2312yes—
65C23×Dic11C2312yes—
66C23×Dic11C2312yes—
67C23×Dic11C2312yes—
68C22×C4×D11—28no—
69C22×C4×D11—48no—
70C22×C4×D11C2318yes—
71C22×Dic22C2314yescomplemented
72C2×C11×C4⋊C4C2318yescomplemented
73C2×C11×C22⋊C4—24no—
74C2×C11×C22⋊C4—24no—
75C2×C11×C22⋊C4—24no—
76C2×C11×C22⋊C4C2312yes—
77C2×C11×C22⋊C4C2312yes—
78C2×C11×C22⋊C4C2312yes—
79C2×C11×C22⋊C4C2312yes—
80C2×C11×C22⋊C4C2312yes—
81C2×C11×C22⋊C4C2312yes—
82C2×C22⋊Dic11—24no—
83C2×C22⋊Dic11—24no—
84C2×C22⋊Dic11D418yes—
85C2×C22⋊Dic11C2312yes—
86C2×C22⋊Dic11C2312yes—
87C2×C22⋊Dic11C2312yes—
88C2×C22⋊Dic11C2312yes—
89C2×C22⋊Dic11C2312yes—
90C2×C22⋊Dic11C2312yes—
91C2×(C2×D11)⋊C4—28no—
92C2×(C2×D11)⋊C4—48no—
93C2×(C2×D11)⋊C4—48no—
94C2×(C2×D11)⋊C4C2318yes—
95C2×(C2×D11)⋊C4C2318yes—
96C2×(C2×D11)⋊C4C2318yes—
97C2×(C2×D11)⋊C4C2318yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×C4⋊Dic11C2314yescomplemented
100#66977—216no—
101C2×Dic11⋊C4C2314yescomplemented
102C2×Dic11⋊C4C2314yescomplemented
103C2×Dic11⋊C4C2318yescomplemented
104C2×Dic11⋊C4C2318yescomplemented
105#66949—416no—
106C22⋊C4×D11—216no—
107C22⋊C4×D11—216no—
108#66931—216no—
109#66931—216no—
110C11×#95C2318yescomplemented
111C11⋊#95C2318yescomplemented
112C11⋊#95C2318yescomplemented
113#34982—111nomaximal, Sylow
114C24×C11—44no—
115C24×C11C2×D414yes—
116C24×C11C2×Q814yes—
117C24×C11#4114yes—
118C24×C11C2411yescharacteristic
119C24×C11C2411yescharacteristic
120C24×C11C2411yescharacteristic
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—28no—
124C23×D11—232no—
125C23×D11—24no—
126C23×D11—24no—
127C23×D11—22no—
128C23×D11—24no—
129C23×D11—24no—
130C23×D11—22no—
131C23×D11—28no—
132C23×D11—28no—
133C23×D11—432no—
134C23×D11—44no—
135C23×D11—44no—
136C23×D11—44no—
137C23×D11—432no—
138C23×D11—432no—
139C23×D11C2×Q814yes—
140C23×D11C2×Q818yes—
141C23×D11C2×Q818yes—
142C23×D11C2×Q814yes—
143C23×D11C2412yes—
144C23×D11C2412yes—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—44no—
149C22×C4×C11—44no—
150C22×C4×C11—44no—
151C22×C4×C11C2414yes—
152C22×C4×C11C2414yes—
153C22×C4×C11C2414yes—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—44no—
157C22×Dic11—44no—
158C22×Dic11—44no—
159C22×Dic11C2×D418yes—
160C22×Dic11C2414yes—
161C22×Dic11C2414yes—
162C22×Dic11C2414yes—
163C2×C4×D11—216no—
164C2×C4×D11—216no—
165C2×C4×D11—48no—
166C2×C4×D11—432no—
167C2×Dic22—28no—
168C2×Dic22—48no—
169C11×C4⋊C4—48no—
170C11×C22⋊C4—24no—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—24no—
174C11×C22⋊C4—24no—
175C11×C22⋊C4—24no—
176C22⋊Dic11—24no—
177C22⋊Dic11—24no—
178C22⋊Dic11—24no—
179C22⋊Dic11—24no—
180C22⋊Dic11C2×D418yes—
181C22⋊Dic11C2×D418yes—
182(C2×D11)⋊C4—216no—
183(C2×D11)⋊C4—216no—
184(C2×D11)⋊C4—216no—
185(C2×D11)⋊C4—48no—
186(C2×D11)⋊C4—48no—
187C4⋊Dic11—28no—
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#2315D1111yescharacteristic, complemented
201C2×#379—111no—
202C2×#379—111no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—48no—
207C23×C11—48no—
208C23×C11—48no—
209C23×C11C22⋊Q8116yescomplemented
210C23×C11C22×D412yes—
211C23×C11C22×D412yes—
212C23×C11C22×D412yes—
213C23×C11C22×Q812yes—
214C23×C11C22×Q812yes—
215C23×C11C22×Q812yes—
216C23×C11C2×#4112yes—
217C23×C11C2×#4112yes—
218C23×C11C2×#4112yes—
219C23×C11C2511yescharacteristic
220C22×D11—216no—
221C22×D11—216no—
222C22×D11—28no—
223C22×D11—22no—
224C22×D11—22no—
225C22×D11—24no—
226C22×D11—216no—
227C22×D11—216no—
228C22×D11—216no—
229C22×D11—28no—
230C22×D11—22no—
231C22×D11—22no—
232C22×D11—24no—
233C22×D11—24no—
234C22×D11—216no—
235C22×D11—216no—
236C22×D11—48no—
237C22×D11—48no—
238C22×D11—48no—
239C22×D11—416no—
240C22×D11—416no—
241C22×D11—416no—
242C22×D11—416no—
243C22×D11—4128no—
244C22×D11—48no—
245C22×D11—48no—
246C22×D11C22×Q814yes—
247C22×D11C22×Q814yes—
248C22×D11H(5,𝔽2)18yes—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—28no—
253C2×C4×C11—28no—
254C2×C4×C11—28no—
255C2×C4×C11—48no—
256C2×C4×C11—84no—
257C2×C4×C11—84no—
258C2×Dic11—28no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—28no—
262C2×Dic11—28no—
263C2×Dic11—48no—
264C2×Dic11—84no—
265C2×Dic11—84no—
266C2×Dic11C22×D418yes—
267C4×D11—432no—
268Dic22—88no—
269C26—111no—
270C24×C4—112no—
271#543—228no—
272C2×C22⋊Q8—114no—
273C2×C22⋊Q8—118no—
274C2×C22⋊Q8—114no—
275C2×C22⋊Q8—114no—
276C22×C22⋊C4—111no—
277C22×C22⋊C4—111no—
278C22×C22⋊C4—111no—
279C22×C22⋊C4—112no—
280C22×C22⋊C4—114no—
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×D1111yescharacteristic
288#399—118no—
289#396—118no—
290#396—118no—
291#393—118no—
292#385—114no—
293#385—114no—
294#385—118no—
295#385—114no—
296#385—114no—
297#385—118no—
298#385C2×D1114yescomplemented
299#385C2×D1114yescomplemented
300#380—114no—
301#380—114no—
302#380—118no—
303#380C2×D1114yescomplemented
304#379—112no—
305#379—112no—
306#379—112no—
307#379—112no—
308#379—114no—
309#379—114no—
310C22×C11—24no—
311C22×C11—24no—
312C22×C11—24no—
313C22×C11—24no—
314C22×C11—24no—
315C22×C11—24no—
316C22×C11—24no—
317C22×C11—24no—
318C22×C11—24no—
319C22×C11—416no—
320C22×C11C2×C22⋊Q814yes—
321C22×C11C2×C22⋊Q814yes—
322C22×C11C2×C22⋊Q814yes—
323C22×C11C23×D411yescharacteristic
324C22×C11C23×Q811yescharacteristic
325C22×C11C22×#4111yescharacteristic
326C22×C11C2×H(5,𝔽2)14yes—
327C2×D11—232no—
328C2×D11—24no—
329C2×D11—24no—
330C2×D11—28no—
331C2×D11—28no—
332C2×D11—24no—
333C2×D11—24no—
334C2×D11—24no—
335C2×D11—432no—
336C2×D11—432no—
337C2×D11—416no—
338C2×D11—44no—
339C2×D11—44no—
340C2×D11#54318yescomplemented
341C4×C11—44no—
342C4×C11—44no—
343C4×C11—44no—
344Dic11—28no—
345Dic11—44no—
346Dic11—44no—
347C25—111no—
348C25—112no—
349C25—112no—
350C25—118no—
351C25—111no—
352C25—224no—
353C25—224no—
354C25—448no—
355C25C22×D1111yescharacteristic
356C22×Q8—114no—
357C23×C4—112no—
358C23×C4—112no—
359C23×C4—112no—
360C23×C4—118no—
361C23×C4—228no—
362C23×C4—448no—
363C23×C4C22×D1112yes—
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⋊C4C22×D1118yescomplemented
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—118no—
380C2×C22⋊C4—112no—
381C2×C22⋊C4—112no—
382C2×C22⋊C4—112no—
383C2×C22⋊C4—112no—
384C2×C22⋊C4—112no—
385C2×C22⋊C4—112no—
386C2×C22⋊C4—118no—
387C2×C22⋊C4—118no—
388C2×C22⋊C4—118no—
389C2×C22⋊C4—118no—
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—448no—
397C2×C22⋊C4—448no—
398C2×C22⋊C4C22×D1112yes—
399C2×C22⋊C4C22×D1112yes—
400C2×C22⋊C4C22×D1112yes—
401C2×C22⋊C4C22×D1112yes—
402C2×C22⋊C4C22×D1112yes—
403C2×C22⋊C4C22×D1112yes—
404#95—118no—
405#95—118no—
406#95C22×D1118yescomplemented
407C2×C11—24no—
408C2×C11—24no—
409C2×C11—24no—
410C2×C11C22×C22⋊Q811yescharacteristic
411C2×C11C2×#54312yes—
412C2×C11#348412yes—
413C2×C11#349012yes—
414D11—28no—
415D11—44no—
416C24—44no—
417C24—112no—
418C24—114no—
419C24—112no—
420C24—118no—
421C24—118no—
422C24—114no—
423C24—228no—
424C24—228no—
425C24—228no—
426C24—222no—
427C24—222no—
428C24—2232no—
429C24—224no—
430C24—224no—
431C24—222no—
432C24—224no—
433C24—224no—
434C24—222no—
435C24—444no—
436C24—444no—
437C24—444no—
438C24—4432no—
439C24—4432no—
440C24—4432no—
441C24#433914yes—
442C24D4×D1114yes—
443C24Q8×D1114yes—
444C24C23×D1111yescharacteristic
445C24C23×D1111yescharacteristic
446C24C23×D1111yescharacteristic
447C2×Q8—228no—
448C2×Q8—448no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—44no—
453C22×C4—44no—
454C22×C4—44no—
455C22×C4—114no—
456C22×C4—118no—
457C22×C4—114no—
458C22×C4—114no—
459C22×C4—2216no—
460C22×C4—2216no—
461C22×C4—224no—
462C22×C4—224no—
463C22×C4—448no—
464C22×C4—4432no—
465C22×C4—444no—
466C22×C4—444no—
467C22×C4—444no—
468C22×C4C23×D1114yes—
469C22×C4C23×D1114yes—
470C22×C4C23×D1114yes—
471C4⋊C4—48no—
472C4⋊C4—228no—
473C4⋊C4—228no—
474C4⋊C4—228no—
475C4⋊C4—448no—
476C4⋊C4—448no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—24no—
482C22⋊C4—24no—
483C22⋊C4—118no—
484C22⋊C4—118no—
485C22⋊C4—2216no—
486C22⋊C4—2216no—
487C22⋊C4—2216no—
488C22⋊C4—224no—
489C22⋊C4—224no—
490C22⋊C4—224no—
491C22⋊C4—224no—
492C22⋊C4—448no—
493C22⋊C4—448no—
494C11#3498211yescharacteristic, complemented, Sylow
495C23—24no—
496C23—24no—
497C23—24no—
498C23—48no—
499C23—48no—
500C23—48no—
501C23—114no—
502C23—118no—
503C23—114no—
504C23—2216no—
505C23—2216no—
506C23—2216no—
507C23—2216no—
508C23—2216no—
509C23—228no—
510C23—222no—
511C23—222no—
512C23—224no—
513C23—2216no—
514C23—2216no—
515C23—228no—
516C23—222no—
517C23—222no—
518C23—224no—
519C23—224no—
520C23—448no—
521C23—448no—
522C23—448no—
523C23—4416no—
524C23—4416no—
525C23—4416no—
526C23—4416no—
527C23—448no—
528C23—448no—
529C23—44128no—
530C23#66949116yescomplemented
531C23C2×#433912yes—
532C23C2×#433912yes—
533C23C2×#433912yes—
534C23C2×D4×D1112yes—
535C23C2×D4×D1112yes—
536C23C2×D4×D1112yes—
537C23C2×Q8×D1112yes—
538C23C2×Q8×D1112yes—
539C23C2×Q8×D1112yes—
540C23C24×D1111yescharacteristic
541Q8—888no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—28no—
546C2×C4—28no—
547C2×C4—28no—
548C2×C4—48no—
549C2×C4—84no—
550C2×C4—84no—
551C2×C4—118no—
552C2×C4—228no—
553C2×C4—224no—
554C2×C4—224no—
555C2×C4—228no—
556C2×C4—228no—
557C2×C4—4432no—
558C2×C4—448no—
559C2×C4—884no—
560C2×C4—884no—
561C22—24no—
562C22—24no—
563C22—24no—
564C22—24no—
565C22—24no—
566C22—24no—
567C22—24no—
568C22—24no—
569C22—24no—
570C22—416no—
571C22—118no—
572C22—2232no—
573C22—228no—
574C22—224no—
575C22—228no—
576C22—224no—
577C22—224no—
578C22—224no—
579C22—224no—
580C22—4432no—
581C22—4432no—
582C22—4416no—
583C22—444no—
584C22—444no—
585C22C2×#6694914yes—
586C22C2×#6694914yes—
587C22C2×#6694914yes—
588C22C22×#433911yescharacteristic
589C22C22×D4×D1111yescharacteristic
590C22C22×Q8×D1111yescharacteristic
591C22D11×H(5,𝔽2)14yes—
592C4—44no—
593C4—44no—
594C4—44no—
595C4—228no—
596C4—444no—
597C4—444no—
598C2—24no—
599C2—24no—
600C2—24no—
601C2—228no—
602C2—444no—
603C2C22×#6694911yescharacteristic
604C2D11×#54312yes—
605C2#1308224812yes—
606C2#1308230112yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2315C2
prime radicalC25×D11C22
hypercenter#2315D11
hypocenterC11#34982
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2315

Complements

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

NH ≅ G/Ntype
1. C2×#10623014C2semidirect
3. #13076902C2semidirect
4. #13074427C2semidirect
5. #13072284C2semidirect
6. #13072281C2semidirect
7. #13071228C2semidirect
8. #13071228C2semidirect
11. C11×#2315C2semidirect
23. C2×#66977C22semidirect
24. C2×#66949C22semidirect
29. C2×#66931C22semidirect
30. C2×#66931C22semidirect
31. C11×#385C22semidirect
32. C11×#385C22semidirect
33. C11×#380C22semidirect
34. #10622823C22semidirect
35. #10622823C22semidirect
36. #10622607C22semidirect
37. #10622605C22semidirect
38. #10622602C22semidirect
45. #10622559C22semidirect
46. #10622559C22semidirect
47. #10622555C22semidirect
48. #10622555C22semidirect
49. #10622289C22semidirect
50. #10622286C22semidirect
51. #10622281C22semidirect
52. #10622280C22semidirect
57. C24×D11Q8semidirect
71. C22×Dic22C23semidirect
72. C2×C11×C4⋊C4C23semidirect
99. C2×C4⋊Dic11C23semidirect
101. C2×Dic11⋊C4C23semidirect
102. C2×Dic11⋊C4C23semidirect
103. C2×Dic11⋊C4C23semidirect
104. C2×Dic11⋊C4C23semidirect
110. C11×#95C23semidirect
111. C11⋊#95C23semidirect
112. C11⋊#95C23semidirect
200. #2315D11semidirect
209. C23×C11C22⋊Q8semidirect
298. #385C2×D11semidirect
299. #385C2×D11semidirect
303. #380C2×D11semidirect
340. C2×D11#543semidirect
375. C2×C4⋊C4C22×D11semidirect
406. #95C22×D11semidirect
494. C11#34982semidirect
530. C23#66949semidirect

Maximal subgroups

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

subgroupindex
C2×#106230142
C22×C22⋊C4×D112
#130769022
#130744272
#130722842
#130722812
#130712282
C2×#106225682
C11×#23152
#3498211