Finite Group Databasebeta

← #14914227

Subgroups — #14914227

Order 2816.

2110 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623219C211yesmaximal, characteristic
2#13071700C214yesmaximal
3#13071693C214yesmaximal
4#13071570C214yesmaximal, complemented
5#13071569C214yesmaximal, complemented
6#13071363C212yesmaximal, complemented
7#13071360C212yesmaximal, complemented
8#13071238C212yesmaximal
9#125×Dic11C211yesmaximal, characteristic, complemented
10C4×#66923C211yesmaximal, characteristic, complemented
11#13071171C211yesmaximal, characteristic, complemented
12D11×#382C211yesmaximal, characteristic
13#13070970C212yesmaximal
14C4×#66925C211yesmaximal, characteristic
15C4×C11×#125C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17#10623219C4116yescomplemented
18C2×#66949C2214yes—
19C2×#66945C2212yes—
20C2×C4⋊C4×D11C2212yes—
21C2×#66941C2212yes—
22C2×#66940C2214yes—
23C2×#66925C2211yescharacteristic
24C2×#66925C2211yescharacteristic
25C2×C42×D11C2211yescharacteristic
26C2×#66923C2211yescharacteristic
27C11×#389C2212yes—
28C11×#387C2214yes—
29C11×#382C2211yescharacteristic
30C4×C11×C4⋊C4C2212yes—
31C4×C11×C4⋊C4C2214yes—
32C43×C11C2211yescharacteristic
33#10622602C2214yes—
34#10622598C2212yes—
35#10622594C2214yes—
36#10622591C2214yes—
37#10622590C2212yes—
38#10622589C2214yes—
39C4⋊C4×Dic11C2212yes—
40C4⋊C4×Dic11C2212yes—
41C4⋊C4×Dic11C2214yes—
42#10622587C2214yes—
43#10622586C2212yes—
44C4×(C2×D11)⋊C4C2212yes—
45C4×(C2×D11)⋊C4C2212yes—
46C4×(C2×D11)⋊C4C2214yes—
47#10622549C2211yescharacteristic
48C4×C4⋊Dic11C2212yes—
49#10622546C2214yes—
50#10622546C2214yes—
51#10622545C2211yescharacteristic
52#10622545C2211yescharacteristic
53C4×Dic11⋊C4C2214yes—
54C4×Dic11⋊C4C2212yes—
55C4×Dic11⋊C4C2212yes—
56C4×Dic11⋊C4C2214yes—
57C42×Dic11C2211yescharacteristic
58#10622542C2214yes—
59#10622541C2212yes—
60#10622281C2214yes—
61#10622279C2214yes—
62D11×#95C2214yes—
63#10622268C2214yes—
64#10622265C2214yes—
65#10622265C2214yes—
66#10622263C2214yes—
67#10622263C2214yes—
68#10622262C2214yes—
69#10622262C2214yes—
70#10622259C2214yes—
71#10622259C2214yes—
72C22×C4×D11C2314yes—
73C22×C4×D11C2312yes—
74C22×C4×D11C2311yescharacteristic
75C22×Dic22C2314yes—
76C11×#125C2×C418yescomplemented
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2312yes—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2314yes—
83C2×C42×C11C2312yes—
84C2×C42×C11C2312yes—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×(C2×D11)⋊C4C2312yes—
88C2×(C2×D11)⋊C4C2314yes—
89C2×(C2×D11)⋊C4C2311yescharacteristic
90C2×(C2×D11)⋊C4C2311yescharacteristic
91C2×C4⋊Dic11C2312yes—
92C2×C4⋊Dic11C2314yes—
93C2×C4⋊Dic11C2312yes—
94C2×Dic11⋊C4C2312yes—
95C2×Dic11⋊C4C2314yes—
96C2×Dic11⋊C4C2314yes—
97C2×Dic11⋊C4C2314yes—
98C2×Dic11⋊C4C2314yes—
99C2×Dic11⋊C4C2314yes—
100C2×Dic11⋊C4C2311yescharacteristic
101C2×Dic11⋊C4C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2314yes—
104C2×C4×Dic11C2314yes—
105C2×C4×Dic11C2312yes—
106C2×C4×Dic11C2312yes—
107C2×C4×Dic11C2314yes—
108C2×C4×Dic11C2312yes—
109C2×C4×Dic11C2311yescharacteristic
110C2×C4×Dic11C2314yes—
111C2×C4×Dic11C2311yescharacteristic
112#66949C2×C4132yes—
113#66945C2×C4116yes—
114C4⋊C4×D11—28no—
115#66941C2×C4116yescomplemented
116#66940C2×C4132yescomplemented
117#66925—24no—
118#66925Q818yescomplemented
119C42×D11C2×C418yes—
120#66923C2×C418yescomplemented
121C11×#95C2314yes—
122C11×#95C2314yes—
123C11×#95C2314yes—
124C11⋊#95C2312yes—
125C11⋊#95C2312yes—
126C11⋊#95C2314yes—
127C11⋊#95C2314yes—
128C11⋊#95C2314yes—
129C11⋊#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2312yes—
135C11⋊#95C2312yes—
136C11⋊#95C2314yes—
137#34215—111nomaximal, Sylow
138C23×D11C2411yescharacteristic
139C22×C4×C11C2414yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2412yes—
142C22×C4×C11C2414yes—
143C22×C4×C11C2411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C22×Dic11C2414yes—
147C22×Dic11C2412yes—
148C22×Dic11C2412yes—
149C22×Dic11C2414yes—
150C22×Dic11C2411yescharacteristic
151C22×Dic11C2411yescharacteristic
152C22×Dic11C2411yescharacteristic
153C2×C4×D11—28no—
154C2×C4×D11—42no—
155C2×C4×D11—42no—
156C2×C4×D11—44no—
157C2×C4×D11—44no—
158C2×C4×D11C22×C418yes—
159C2×C4×D11C22×C414yes—
160C2×C4×D11C2×Q814yes—
161C2×C4×D11#4114yes—
162C2×Dic22—44no—
163C2×Dic22—44no—
164C2×Dic22C22×C4116yes—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—44no—
167C11×C4⋊C4C22×C4116yes—
168C11×C4⋊C4C22×C418yes—
169C42×C11—22no—
170C42×C11—42no—
171C42×C11—44no—
172C42×C11—42no—
173C42×C11C22×C414yes—
174C42×C11C2×Q814yes—
175(C2×D11)⋊C4—24no—
176(C2×D11)⋊C4C22×C4116yes—
177(C2×D11)⋊C4C2×Q814yes—
178(C2×D11)⋊C4C2×Q814yes—
179C4⋊Dic11—24no—
180C4⋊Dic11—44no—
181C4⋊Dic11C22×C418yes—
182Dic11⋊C4—24no—
183Dic11⋊C4—28no—
184Dic11⋊C4—44no—
185Dic11⋊C4—44no—
186Dic11⋊C4C22×C4116yes—
187Dic11⋊C4C22×C4116yes—
188Dic11⋊C4C2×Q814yes—
189Dic11⋊C4C2×Q814yes—
190C4×Dic11—22no—
191C4×Dic11—44no—
192C4×Dic11—44no—
193C4×Dic11—42no—
194C4×Dic11—42no—
195C4×Dic11—44no—
196C4×Dic11C22×C418yes—
197C4×Dic11C22×C414yes—
198C4×Dic11C22×C4116yes—
199C4×Dic11C2×Q814yes—
200C2×#533—111no—
201#2368—114no—
202#2368—114no—
203#2355—114no—
204#2355—114no—
205#2331—112no—
206#2331—112no—
207#2317—112no—
208C4×#125—111no—
209C4×#125—111no—
210C4×#125—111no—
211C4×#125D1111yescharacteristic, complemented
212C2×#382—111no—
213#2274—112no—
214C4×#117—111no—
215C23×C11C2511yescharacteristic
216C22×D11—22no—
217C22×D11—22no—
218C22×D11C23×C412yes—
219C22×D11C22×Q812yes—
220C22×D11C2×#4112yes—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11C23×C414yes—
234C2×C4×C11C23×C418yes—
235C2×C4×C11C23×C412yes—
236C2×C4×C11C22×Q812yes—
237C2×C4×C11C22×Q812yes—
238C2×C4×C11C22×Q812yes—
239C2×C4×C11C2×#4112yes—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—24no—
248C2×Dic11—22no—
249C2×Dic11—24no—
250C2×Dic11—22no—
251C2×Dic11—24no—
252C2×Dic11C23×C414yes—
253C2×Dic11C23×C418yes—
254C2×Dic11C23×C412yes—
255C2×Dic11C22×Q812yes—
256C2×Dic11C22×Q812yes—
257C2×Dic11C22×Q812yes—
258C2×Dic11C2×#4112yes—
259C4×D11—48no—
260C4×D11—88no—
261C4×D11C4×Q8116yes—
262Dic22—416no—
263#533—1116no—
264C2×C4⋊Q8—112no—
265C2×#125—111no—
266C2×#125C2×D1111yescharacteristic
267C2×C22⋊Q8—114no—
268C2×C4×Q8—114no—
269C2×#117—112no—
270C2×#117—111no—
271C2×#117—111no—
272C22×C4⋊C4—112no—
273C22×C42—111no—
274#391—114no—
275#391—114no—
276#391—114no—
277#391—114no—
278#389—112no—
279#389—112no—
280#389—112no—
281#389C2×D1112yes—
282#387—114no—
283#387—114no—
284#387—114no—
285#387—114no—
286#387—114no—
287#387—114no—
288#387—114no—
289#387C2×D1114yes—
290#385—114no—
291#385—114no—
292#384—114no—
293#382—112no—
294#382—111no—
295#382—114no—
296#382—114no—
297#382C2×D1111yescharacteristic
298C4×C4⋊C4—112no—
299C4×C4⋊C4—112no—
300C4×C4⋊C4—114no—
301C4×C4⋊C4—112no—
302C4×C4⋊C4—114no—
303C4×C4⋊C4—112no—
304C4×C4⋊C4—112no—
305C4×C4⋊C4—114no—
306C4×C4⋊C4—114no—
307C4×C4⋊C4—114no—
308C4×C4⋊C4C2×D1112yes—
309C4×C4⋊C4C2×D1114yes—
310C4×C22⋊C4—112no—
311C4×C22⋊C4—112no—
312C4×C22⋊C4—114no—
313C4×C22⋊C4—114no—
314#376—111no—
315#376—111no—
316C2×#95—114no—
317C43—111no—
318C43C2×D1111yescharacteristic
319C22×C11C24×C411yescharacteristic
320C22×C11C23×Q811yescharacteristic
321C22×C11C22×#4111yescharacteristic
322C22×C11#58512yes—
323C22×C11#58512yes—
324C2×D11—24no—
325C2×D11—22no—
326C2×D11—22no—
327C2×D11—24no—
328C2×D11C2×C4×Q814yes—
329C4×C11—28no—
330C4×C11—24no—
331C4×C11—22no—
332C4×C11—22no—
333C4×C11—42no—
334C4×C11—44no—
335C4×C11C2×C4×Q814yes—
336Dic11—24no—
337Dic11—28no—
338Dic11—22no—
339Dic11—22no—
340Dic11—44no—
341Dic11—42no—
342Dic11C2×C4×Q814yes—
343C22×Q8—114no—
344C23×C4—111no—
345C23×C4—112no—
346C23×C4—114no—
347C4⋊Q8—1116no—
348#125—118no—
349#125C4×D1118yescomplemented
350C22⋊Q8—1132no—
351C4×Q8—1132no—
352#117—1116no—
353#117—118no—
354#117—224no—
355C2×C4⋊C4—112no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—114no—
359C2×C4⋊C4—114no—
360C2×C4⋊C4—114no—
361C2×C4⋊C4—112no—
362C2×C4⋊C4—112no—
363C2×C4⋊C4—114no—
364C2×C4⋊C4—114no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—228no—
367C2×C4⋊C4C22×D1112yes—
368C2×C4⋊C4C22×D1114yes—
369C2×C4⋊C4C22×D1112yes—
370C2×C4⋊C4C22×D1114yes—
371C2×C22⋊C4—114no—
372C2×C22⋊C4—111no—
373C2×C22⋊C4—111no—
374C2×C22⋊C4—112no—
375C2×C42—114no—
376C2×C42—111no—
377C2×C42—112no—
378C2×C42—111no—
379C2×C42—118no—
380C2×C42—111no—
381C2×C42—112no—
382C2×C42—112no—
383C2×C42—114no—
384C2×C42—114no—
385C2×C42—114no—
386C2×C42C22×D1111yescharacteristic
387C2×C42C22×D1112yes—
388C2×C42C22×D1112yes—
389C2×C42C22×D1114yes—
390C2×C42C22×D1111yescharacteristic
391C2×C42C22×D1111yescharacteristic
392#95—114no—
393#95—114no—
394#95—114no—
395#95—112no—
396#95—112no—
397#95—112no—
398#95—112no—
399#95—114no—
400#95—114no—
401#95—114no—
402#95—114no—
403#95—114no—
404#95—114no—
405#95C22×D1114yes—
406#95C22×D1114yes—
407#95C22×D1114yes—
408C2×C11C22×C4×Q811yescharacteristic
409C2×C11#342812yes—
410C2×C11#350411yescharacteristic
411C2×C11#350411yescharacteristic
412C2×C11#351012yes—
413D11—24no—
414C24—111no—
415C2×Q8—1116no—
416C2×Q8—444no—
417C2×Q8—444no—
418C22×C4—111no—
419C22×C4—114no—
420C22×C4—114no—
421C22×C4—114no—
422C22×C4—112no—
423C22×C4—111no—
424C22×C4—111no—
425C22×C4—114no—
426C22×C4—118no—
427C22×C4—114no—
428C22×C4—112no—
429C22×C4—228no—
430C22×C4—442no—
431C22×C4—442no—
432C22×C4—444no—
433C22×C4—444no—
434C22×C4C23×D1114yes—
435C22×C4C23×D1112yes—
436C22×C4C23×D1112yes—
437C22×C4C23×D1114yes—
438C22×C4C23×D1111yescharacteristic
439C22×C4C23×D1111yescharacteristic
440C22×C4C23×D1111yescharacteristic
441C4⋊C4—24no—
442C4⋊C4—44no—
443C4⋊C4—118no—
444C4⋊C4—1116no—
445C4⋊C4—1116no—
446C4⋊C4—114no—
447C4⋊C4—114no—
448C4⋊C4—228no—
449C4⋊C4—224no—
450C4⋊C4—224no—
451C4⋊C4—444no—
452C4⋊C4—444no—
453C4⋊C4—444no—
454C4⋊C4C2×C4×D1118yes—
455C4⋊C4C2×C4×D11116yes—
456C22⋊C4—1116no—
457C22⋊C4—114no—
458C22⋊C4—114no—
459C22⋊C4—224no—
460C42—22no—
461C42—42no—
462C42—44no—
463C42—42no—
464C42—118no—
465C42—114no—
466C42—1116no—
467C42—114no—
468C42—222no—
469C42—444no—
470C42—442no—
471C42—442no—
472C42—444no—
473C42—444no—
474C42C2×C4×D1114yes—
475C42Q8×D1114yes—
476C11#3421511yescharacteristic, complemented, Sylow
477C23—112no—
478C23—112no—
479C23—112no—
480C23—222no—
481C23—222no—
482C23C24×D1111yescharacteristic
483Q8—4416no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—112no—
497C2×C4—112no—
498C2×C4—112no—
499C2×C4—1116no—
500C2×C4—114no—
501C2×C4—118no—
502C2×C4—112no—
503C2×C4—112no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—224no—
507C2×C4—224no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—224no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—448no—
517C2×C4—888no—
518C2×C4C22×C4×D1114yes—
519C2×C4C22×C4×D1118yes—
520C2×C4C22×C4×D1112yes—
521C2×C4C2×Q8×D1112yes—
522C2×C4C2×Q8×D1112yes—
523C2×C4C2×Q8×D1112yes—
524C2×C4#41×D1112yes—
525C22—114no—
526C22—222no—
527C22—222no—
528C22—224no—
529C22—224no—
530C22C23×C4×D1111yescharacteristic
531C22C22×Q8×D1111yescharacteristic
532C22C2×#41×D1111yescharacteristic
533C22#1062345312yes—
534C22#1062345312yes—
535C4—22no—
536C4—22no—
537C4—24no—
538C4—28no—
539C4—44no—
540C4—42no—
541C4—114no—
542C4—222no—
543C4—222no—
544C4—224no—
545C4—228no—
546C4—444no—
547C4—442no—
548C4C4×Q8×D1114yes—
549C2—224no—
550C2C2×C4×Q8×D1111yescharacteristic
551C2#1308181512yes—
552C2#1308243711yescharacteristic
553C2#1308244011yescharacteristic
554C2#1308250512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC4×C11×#125C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenterC4×#125D11
hypocenterC11#34215
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
4. #13071570C2semidirect
5. #13071569C2semidirect
6. #13071363C2semidirect
7. #13071360C2semidirect
9. #125×Dic11C2semidirect
10. C4×#66923C2semidirect
11. #13071171C2semidirect
15. C4×C11×#125C2semidirect
17. #10623219C4semidirect
76. C11×#125C2×C4semidirect
115. #66941C2×C4semidirect
116. #66940C2×C4semidirect
118. #66925Q8semidirect
120. #66923C2×C4semidirect
211. C4×#125D11semidirect
349. #125C4×D11semidirect
476. C11#34215semidirect

Maximal subgroups

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

subgroupindex
C2×#106232192
#130717002
#130716932
#130715702
#130715692
#130713632
#130713602
#130712382
#125×Dic112
C4×#669232
#130711712
D11×#3822
#130709702
C4×#669252
C4×C11×#1252
#3421511