Finite Group Databasebeta

← #14959808

Subgroups — #14959808

Order 2816.

2006 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077002C212yesmaximal, complemented
2#13076997C214yesmaximal, complemented
3#13076992C211yesmaximal, characteristic, complemented
4#13076976C211yesmaximal, characteristic, complemented
5#13076967C212yesmaximal
6#13076951C214yesmaximal
7#13076927C211yesmaximal, characteristic
8#13076921C211yesmaximal, characteristic
9C4×#66941C212yesmaximal, complemented
10C4×#66923C211yesmaximal, characteristic, complemented
11C4×#66949C214yesmaximal
12#13071092C214yesmaximal, complemented
13#13071012C212yesmaximal
14C43×D11C211yesmaximal, characteristic
15C4×C11×#125C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×#66949C2214yes—
18C2×#66941C2212yes—
19C2×C42×D11C2212yes—
20C2×C42×D11C2211yescharacteristic
21C2×C42×D11C2212yes—
22C2×C42×D11C2211yescharacteristic
23C2×C42×D11C2211yescharacteristic
24C2×#66923C2211yescharacteristic
25C2×C4×Dic22C2214yes—
26C11×#389C2212yes—
27C11×#387C2214yes—
28C11×#382C2211yescharacteristic
29C4×C11×C4⋊C4C2214yes—
30C4×C11×C4⋊C4C2212yes—
31C43×C11C2211yescharacteristic
32#10622602C2214yes—
33#10622600C2212yes—
34#10622600C2212yes—
35#10622598C2212yes—
36#10622594C2214yes—
37#10622591C2214yes—
38#10622591C2214yes—
39#10622590C2212yes—
40#10622590C2212yes—
41#10622589C2212yes—
42#10622586C2212yes—
43#10622585C2214yes—
44#10622585C2214yes—
45#10622585C2214yes—
46C4×(C2×D11)⋊C4C2214yes—
47#10622549C2211yescharacteristic
48C4×C4⋊Dic11C2212yes—
49#10622546C2214yes—
50#10622545C2214yes—
51C4×Dic11⋊C4C2214yes—
52C4×Dic11⋊C4C2214yes—
53C42×Dic11C2211yescharacteristic
54C42×Dic11C2212yes—
55C42×Dic11C2211yescharacteristic
56C42×Dic11C2211yescharacteristic
57C42×Dic11C2212yes—
58#10622541C2212yes—
59#10622281C2214yes—
60#10622280C2214yes—
61#10622277C2214yes—
62#10622266C2214yes—
63#10622266C2214yes—
64#10622265C2214yes—
65#10622264C2214yes—
66#10622260C2214yes—
67#10622259C2214yes—
68#10622259C2214yes—
69#10622259C2214yes—
70#10622259C2214yes—
71C22×C4×D11C2312yes—
72C22×C4×D11C2311yescharacteristic
73C22×C4×D11C2311yescharacteristic
74C22×C4×D11C2311yescharacteristic
75C22×C4×D11C2312yes—
76C22×Dic22C2314yes—
77C11×#125—24no—
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C4⋊C4C2312yes—
82C2×C42×C11C2314yes—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2312yes—
85C2×C42×C11C2312yes—
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×(C2×D11)⋊C4C2314yes—
89C2×(C2×D11)⋊C4C2314yes—
90C2×C4⋊Dic11C2314yes—
91C2×C4⋊Dic11C2312yes—
92C2×C4⋊Dic11C2312yes—
93C2×Dic11⋊C4C2314yes—
94C2×Dic11⋊C4C2314yes—
95C2×Dic11⋊C4C2314yes—
96C2×Dic11⋊C4C2314yes—
97C2×Dic11⋊C4C2314yes—
98C2×Dic11⋊C4C2314yes—
99C2×C4×Dic11C2314yes—
100C2×C4×Dic11C2312yes—
101C2×C4×Dic11C2312yes—
102C2×C4×Dic11C2312yes—
103C2×C4×Dic11C2312yes—
104C2×C4×Dic11C2312yes—
105C2×C4×Dic11C2312yes—
106C2×C4×Dic11C2312yes—
107C2×C4×Dic11C2311yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C2×C4×Dic11C2311yescharacteristic
110C2×C4×Dic11C2311yescharacteristic
111C2×C4×Dic11C2312yes—
112C2×C4×Dic11C2311yescharacteristic
113#66949—216no—
114#66941—28no—
115C42×D11—28no—
116C42×D11—24no—
117C42×D11—28no—
118C42×D11—24no—
119C42×D11Q818yescomplemented
120#66923—24no—
121C4×Dic22—216no—
122C11×#95C2314yes—
123C11×#95C2314yes—
124C11×#95C2314yes—
125C11⋊#95C2314yes—
126C11⋊#95C2314yes—
127C11⋊#95C2314yes—
128C11⋊#95C2314yes—
129C11⋊#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136#36635—111nomaximal, Sylow
137C23×D11C2411yescharacteristic
138C22×C4×C11C2414yes—
139C22×C4×C11C2414yes—
140C22×C4×C11C2411yescharacteristic
141C22×C4×C11C2412yes—
142C22×C4×C11C2412yes—
143C22×C4×C11C2411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11C2414yes—
146C22×Dic11C2414yes—
147C22×Dic11C2411yescharacteristic
148C22×Dic11C2411yescharacteristic
149C22×Dic11C2411yescharacteristic
150C22×Dic11C2412yes—
151C22×Dic11C2412yes—
152C2×C4×D11—24no—
153C2×C4×D11—24no—
154C2×C4×D11—24no—
155C2×C4×D11—24no—
156C2×C4×D11—24no—
157C2×C4×D11—24no—
158C2×C4×D11—22no—
159C2×C4×D11—24no—
160C2×C4×D11—22no—
161C2×C4×D11C2×Q814yes—
162C2×C4×D11C2×Q814yes—
163C2×C4×D11C2×Q814yes—
164C2×C4×D11#4118yes—
165C2×Dic22—28no—
166C2×Dic22—28no—
167C2×Dic22—28no—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—28no—
170C11×C4⋊C4—28no—
171C11×C4⋊C4—24no—
172C42×C11—28no—
173C42×C11—24no—
174C42×C11—24no—
175C42×C11—22no—
176C42×C11C2×Q814yes—
177C42×C11#4114yes—
178(C2×D11)⋊C4—28no—
179(C2×D11)⋊C4—28no—
180C4⋊Dic11—28no—
181C4⋊Dic11—24no—
182C4⋊Dic11—24no—
183Dic11⋊C4—28no—
184Dic11⋊C4—28no—
185Dic11⋊C4—28no—
186Dic11⋊C4—28no—
187Dic11⋊C4—28no—
188Dic11⋊C4—28no—
189C4×Dic11—24no—
190C4×Dic11—24no—
191C4×Dic11—24no—
192C4×Dic11—24no—
193C4×Dic11—24no—
194C4×Dic11—28no—
195C4×Dic11—24no—
196C4×Dic11—22no—
197C4×Dic11—24no—
198C4×Dic11C2×Q814yes—
199C4×Dic11C2×Q814yes—
200C4×Dic11C2×Q814yes—
201C4×Dic11#4118yes—
202C4×Dic11#4114yes—
203#2864—112no—
204#2863—114no—
205#2862—111no—
206#2859—111no—
207#2857—112no—
208#2855—114no—
209#2851—111no—
210#2851—111no—
211C4×C4⋊Q8—112no—
212C4×#125—111no—
213C4×#125D1111yescharacteristic, complemented
214C4×C22⋊Q8—114no—
215#2295—114no—
216#2283—112no—
217C2×C43—111no—
218C23×C11C2511yescharacteristic
219C22×D11—21no—
220C22×D11—21no—
221C22×D11—22no—
222C22×D11C22×Q812yes—
223C22×D11C2×#4114yes—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11C22×Q812yes—
236C2×C4×C11C22×Q812yes—
237C2×C4×C11C22×Q812yes—
238C2×C4×C11C2×#4114yes—
239C2×C4×C11C2×#4112yes—
240C2×C4×C11C2×#4114yes—
241C2×C4×C11C2×#4114yes—
242C2×C4×C11C2×#4112yes—
243C2×Dic11—21no—
244C2×Dic11—22no—
245C2×Dic11—21no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11C22×Q812yes—
256C2×Dic11C22×Q812yes—
257C2×Dic11C22×Q812yes—
258C2×Dic11C2×#4114yes—
259C2×Dic11C2×#4114yes—
260C2×Dic11C2×#4114yes—
261C2×Dic11C2×#4114yes—
262C4×D11—216no—
263C4×D11—28no—
264C4×D11—28no—
265C4×D11—28no—
266C4×D11—216no—
267Dic22—416no—
268C2×C4⋊Q8—112no—
269C2×#125—111no—
270C2×#125C2×D1111yescharacteristic
271C2×C22⋊Q8—114no—
272C2×C4×Q8—114no—
273C22×C42—111no—
274C22×C42—111no—
275C22×C42—112no—
276C22×C42—111no—
277C22×C42—112no—
278#391—114no—
279#391—114no—
280#391—114no—
281#391—114no—
282#389—112no—
283#389—112no—
284#389—114no—
285#389—114no—
286#389—114no—
287#389—112no—
288#389—114no—
289#389C2×D1112yes—
290#387—114no—
291#387—114no—
292#387—114no—
293#387—114no—
294#387—114no—
295#387—114no—
296#387—114no—
297#387C2×D1114yes—
298#385—114no—
299#385—114no—
300#384—112no—
301#383—114no—
302#382—112no—
303#382—112no—
304#382—111no—
305#382C2×D1111yescharacteristic
306#381—114no—
307#380—112no—
308#380—112no—
309#380—114no—
310C4×C4⋊C4—112no—
311C4×C4⋊C4—114no—
312C4×C4⋊C4—114no—
313C4×C4⋊C4C2×D1112yes—
314C4×C4⋊C4C2×D1114yes—
315C4×C22⋊C4—114no—
316#376—114no—
317C43—111no—
318C43—111no—
319C43—112no—
320C43—111no—
321C43—112no—
322C43C2×D1111yescharacteristic
323C22×C11C23×Q811yescharacteristic
324C22×C11C22×#4111yescharacteristic
325C22×C11C22×#4111yescharacteristic
326C22×C11C22×#4112yes—
327C22×C11C22×#4112yes—
328C2×D11—24no—
329C2×D11—22no—
330C2×D11—22no—
331C2×D11—24no—
332C2×D11#53314yes—
333C4×C11—24no—
334C4×C11—22no—
335C4×C11—24no—
336C4×C11—44no—
337C4×C11—44no—
338C4×C11#53314yes—
339C4×C11#53314yes—
340Dic11—22no—
341Dic11—22no—
342Dic11—22no—
343Dic11—24no—
344Dic11—44no—
345Dic11—44no—
346Dic11#52918yes—
347C22×Q8—114no—
348C23×C4—112no—
349C23×C4—111no—
350C23×C4—111no—
351C23×C4—111no—
352C23×C4—112no—
353C4⋊Q8—228no—
354#125—24no—
355#125—224no—
356C22⋊Q8—2216no—
357C4×Q8—2216no—
358C2×C4⋊C4—114no—
359C2×C4⋊C4—114no—
360C2×C4⋊C4—114no—
361C2×C4⋊C4—114no—
362C2×C4⋊C4—114no—
363C2×C4⋊C4—112no—
364C2×C4⋊C4—114no—
365C2×C4⋊C4—112no—
366C2×C4⋊C4—114no—
367C2×C4⋊C4C22×D1114yes—
368C2×C4⋊C4C22×D1112yes—
369C2×C4⋊C4C22×D1114yes—
370C2×C4⋊C4C22×D1112yes—
371C2×C22⋊C4—114no—
372C2×C22⋊C4—114no—
373C2×C42—111no—
374C2×C42—111no—
375C2×C42—111no—
376C2×C42—112no—
377C2×C42—111no—
378C2×C42—118no—
379C2×C42—112no—
380C2×C42—112no—
381C2×C42—112no—
382C2×C42—111no—
383C2×C42—112no—
384C2×C42—112no—
385C2×C42—112no—
386C2×C42—112no—
387C2×C42—114no—
388C2×C42—228no—
389C2×C42—224no—
390C2×C42—228no—
391C2×C42—224no—
392C2×C42C22×D1112yes—
393C2×C42C22×D1111yescharacteristic
394C2×C42C22×D1114yes—
395C2×C42C22×D1112yes—
396C2×C42C22×D1111yescharacteristic
397C2×C42C22×D1111yescharacteristic
398#95—114no—
399#95—114no—
400#95—114no—
401#95—114no—
402#95—114no—
403#95—114no—
404#95—114no—
405#95—114no—
406#95—114no—
407#95—114no—
408#95—114no—
409#95C22×D1114yes—
410#95C22×D1114yes—
411#95C22×D1114yes—
412C2×C11C2×#52912yes—
413C2×C11C2×#53311yescharacteristic
414C2×C11C2×#53311yescharacteristic
415C2×C11C2×#53311yescharacteristic
416C2×C11#344412yes—
417D11—24no—
418C24—111no—
419C2×Q8—228no—
420C2×Q8—228no—
421C2×Q8—228no—
422C22×C4—112no—
423C22×C4—111no—
424C22×C4—111no—
425C22×C4—111no—
426C22×C4—112no—
427C22×C4—114no—
428C22×C4—114no—
429C22×C4—114no—
430C22×C4—118no—
431C22×C4—114no—
432C22×C4—114no—
433C22×C4—224no—
434C22×C4—224no—
435C22×C4—224no—
436C22×C4—224no—
437C22×C4—224no—
438C22×C4—224no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—224no—
442C22×C4C23×D1114yes—
443C22×C4C23×D1114yes—
444C22×C4C23×D1112yes—
445C22×C4C23×D1111yescharacteristic
446C22×C4C23×D1112yes—
447C22×C4C23×D1111yescharacteristic
448C22×C4C23×D1111yescharacteristic
449C4⋊C4—28no—
450C4⋊C4—24no—
451C4⋊C4—28no—
452C4⋊C4—24no—
453C4⋊C4—228no—
454C4⋊C4—228no—
455C4⋊C4—228no—
456C4⋊C4—228no—
457C4⋊C4—228no—
458C4⋊C4—228no—
459C4⋊C4—224no—
460C4⋊C4—228no—
461C4⋊C4—224no—
462C22⋊C4—228no—
463C22⋊C4—228no—
464C42—24no—
465C42—22no—
466C42—24no—
467C42—28no—
468C42—114no—
469C42—114no—
470C42—114no—
471C42—118no—
472C42—114no—
473C42—224no—
474C42—224no—
475C42—224no—
476C42—224no—
477C42—224no—
478C42—224no—
479C42—222no—
480C42—224no—
481C42—228no—
482C42#433914yes—
483C42Q8×D1114yes—
484C11#3663511yescharacteristic, complemented, Sylow
485C23—112no—
486C23—114no—
487C23—221no—
488C23—221no—
489C23—222no—
490C23C24×D1111yescharacteristic
491Q8—4416no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—114no—
504C2×C4—114no—
505C2×C4—114no—
506C2×C4—112no—
507C2×C4—112no—
508C2×C4—112no—
509C2×C4—114no—
510C2×C4—2216no—
511C2×C4—228no—
512C2×C4—2216no—
513C2×C4—221no—
514C2×C4—222no—
515C2×C4—222no—
516C2×C4—221no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—228no—
520C2×C4—228no—
521C2×C4—224no—
522C2×C4—224no—
523C2×C4—224no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—224no—
527C2×C4C2×#433914yes—
528C2×C4C2×#433912yes—
529C2×C4C2×Q8×D1112yes—
530C2×C4C2×Q8×D1112yes—
531C2×C4C2×Q8×D1112yes—
532C2×C4#41×D1114yes—
533C2×C4#41×D1112yes—
534C2×C4#41×D1114yes—
535C22—114no—
536C22—224no—
537C22—222no—
538C22—222no—
539C22—224no—
540C22C22×#433911yescharacteristic
541C22C22×Q8×D1111yescharacteristic
542C22C2×#41×D1111yescharacteristic
543C22C2×#41×D1112yes—
544C22C2×#41×D1112yes—
545C4—24no—
546C4—22no—
547C4—24no—
548C4—44no—
549C4—44no—
550C4—118no—
551C4—222no—
552C4—222no—
553C4—222no—
554C4—224no—
555C4—444no—
556C4—444no—
557C4#1062310914yes—
558C4#1062321914yes—
559C2—224no—
560C2D11×#52912yes—
561C2D11×#53311yescharacteristic
562C2C2×#1062310911yescharacteristic
563C2C2×#1062321911yescharacteristic
564C2#1308190912yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC4×C11×#125C2
prime radicalC23×D11C24
hypercenterC4×#125D11
hypocenterC11#36635
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
1. #13077002C2semidirect
2. #13076997C2semidirect
3. #13076992C2semidirect
4. #13076976C2semidirect
9. C4×#66941C2semidirect
10. C4×#66923C2semidirect
12. #13071092C2semidirect
15. C4×C11×#125C2semidirect
119. C42×D11Q8semidirect
213. C4×#125D11semidirect
484. C11#36635semidirect

Maximal subgroups

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

subgroupindex
#130770022
#130769972
#130769922
#130769762
#130769672
#130769512
#130769272
#130769212
C4×#669412
C4×#669232
C4×#669492
#130710922
#130710122
C43×D112
C4×C11×#1252
#3663511