Finite Group Databasebeta

← #14912923

Subgroups — #14912923

Order 2816.

2070 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×#10623262C211yesmaximal, characteristic
2#13071421C214yesmaximal, complemented
3#13071396C214yesmaximal
4#13071357C211yesmaximal, characteristic, complemented
5#13071292C212yesmaximal
6#13071261C212yesmaximal, complemented
7#13071226C211yesmaximal, characteristic
8C4⋊Q8×Dic11C211yesmaximal, characteristic, complemented
9#13071173C214yesmaximal, complemented
10#13071171C211yesmaximal, characteristic, complemented
11#13071166C214yesmaximal
12#13071154C212yesmaximal
13C4×Q8×Dic11C212yesmaximal, complemented
14#13070955C211yesmaximal, characteristic
15C11×#2327C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2212yes—
18C2×#66999C2212yes—
19C2×Q8×Dic11C2212yes—
20C2×Q8×Dic11C2212yes—
21#10623262C4116yescomplemented
22C2×#66951C2214yes—
23C2×#66942C2214yes—
24C2×#66925C2211yescharacteristic
25C2×#66925C2211yescharacteristic
26C2×C42×D11C2211yescharacteristic
27C2×#66923C2211yescharacteristic
28C11×#391C2212yes—
29C11×#387C2214yes—
30C11×#387C2214yes—
31C11×#382C2211yescharacteristic
32C11×#376C2211yescharacteristic
33#10622843C2212yes—
34#10622603C2214yes—
35#10622600C2212yes—
36#10622598C2214yes—
37C4⋊C4×Dic11C2214yes—
38C4⋊C4×Dic11C2212yes—
39C4⋊C4×Dic11C2214yes—
40C4⋊C4×Dic11C2214yes—
41C4⋊C4×Dic11C2212yes—
42#10622586C2212yes—
43#10622585C2214yes—
44#10622553C2214yes—
45#10622548C2211yescharacteristic
46C4×C4⋊Dic11C2214yes—
47C4×C4⋊Dic11C2212yes—
48#10622546C2214yes—
49#10622545C2211yescharacteristic
50C42×Dic11C2214yes—
51C42×Dic11C2211yescharacteristic
52C42×Dic11C2211yescharacteristic
53#10622541C2212yes—
54#10622283C2214yes—
55#10622281C2214yes—
56#10622279C2212yes—
57#10622279C2214yes—
58#10622279C2212yes—
59#10622268C2214yes—
60#10622268C2214yes—
61#10622268C2214yes—
62#10622267C2214yes—
63#10622266C2214yes—
64#10622265C2214yes—
65#10622264C2214yes—
66#10622263C2214yes—
67#10622262C2214yes—
68#10622262C2212yes—
69#10622262C2214yes—
70#10622262C2212yes—
71#10622260C2214yes—
72C22×Q8×C11C2312yes—
73C22×C4×D11C2311yescharacteristic
74C22×C4×D11C2311yescharacteristic
75C22×C4×D11C2311yescharacteristic
76C11×C4⋊Q8C2×C418yescomplemented
77C4×Q8×C11—28no—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2314yes—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85#66999C2×C4116yes—
86Q8×Dic11—28no—
87Q8×Dic11C2×C4116yescomplemented
88C2×(C2×D11)⋊C4C2312yes—
89C2×(C2×D11)⋊C4C2314yes—
90C2×(C2×D11)⋊C4C2312yes—
91C2×(C2×D11)⋊C4C2314yes—
92C2×C4⋊Dic11C2314yes—
93C2×C4⋊Dic11C2312yes—
94C2×C4⋊Dic11C2314yes—
95C2×C4⋊Dic11C2312yes—
96C2×C4⋊Dic11C2314yes—
97C2×Dic11⋊C4C2312yes—
98C2×Dic11⋊C4C2314yes—
99C2×Dic11⋊C4C2314yes—
100C2×Dic11⋊C4C2314yes—
101C2×Dic11⋊C4C2312yes—
102C2×Dic11⋊C4C2314yes—
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2312yes—
107C2×C4×Dic11C2314yes—
108C2×C4×Dic11C2312yes—
109C2×C4×Dic11C2314yes—
110C2×C4×Dic11C2314yes—
111C2×C4×Dic11C2312yes—
112C2×C4×Dic11C2312yes—
113C2×C4×Dic11C2314yes—
114C2×C4×Dic11C2311yescharacteristic
115C2×C4×Dic11C2314yes—
116C2×C4×Dic11C2311yescharacteristic
117#66951C2×C4132yes—
118#66942C2×C4132yescomplemented
119#66925—24no—
120#66925C2×C418yes—
121C42×D11—24no—
122#66923C2×C418yescomplemented
123C11×#95C2312yes—
124C11×#95C2314yes—
125C11×#95C2314yes—
126C11×#95C2312yes—
127C11×#95C2314yes—
128C11⋊#95C2314yes—
129C11⋊#95C2312yes—
130C11⋊#95C2312yes—
131C11⋊#95C2314yes—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138C4×#541—111nomaximal, Sylow
139C23×D11C2411yescharacteristic
140C2×Q8×C11—24no—
141C2×Q8×C11—24no—
142C2×Q8×C11C22×C418yes—
143C22×C4×C11C2411yescharacteristic
144C22×C4×C11C2414yes—
145C22×C4×C11C2411yescharacteristic
146C22×C4×C11C2414yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2412yes—
149C22×C4×C11C2411yescharacteristic
150C22×Dic11C2412yes—
151C22×Dic11C2414yes—
152C22×Dic11C2412yes—
153C22×Dic11C2414yes—
154C22×Dic11C2411yescharacteristic
155C22×Dic11C2411yescharacteristic
156C22×Dic11C2411yescharacteristic
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11—24no—
160C2×C4×D11—22no—
161C2×C4×D11—22no—
162C2×C4×D11—42no—
163C2×C4×D11C22×C414yes—
164C11×C4⋊C4—28no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4C22×C4116yes—
167C42×C11—22no—
168C42×C11—28no—
169C42×C11C22×C414yes—
170C42×C11#4114yes—
171(C2×D11)⋊C4—24no—
172(C2×D11)⋊C4—44no—
173(C2×D11)⋊C4C22×C418yes—
174(C2×D11)⋊C4C22×C4116yes—
175C4⋊Dic11—28no—
176C4⋊Dic11—24no—
177C4⋊Dic11—44no—
178C4⋊Dic11C22×C418yes—
179C4⋊Dic11C22×C4116yes—
180Dic11⋊C4—24no—
181Dic11⋊C4—44no—
182Dic11⋊C4—44no—
183Dic11⋊C4C22×C4116yes—
184Dic11⋊C4C22×C418yes—
185Dic11⋊C4C22×C4116yes—
186C4×Dic11—22no—
187C4×Dic11—22no—
188C4×Dic11—28no—
189C4×Dic11—24no—
190C4×Dic11—24no—
191C4×Dic11—28no—
192C4×Dic11—22no—
193C4×Dic11—42no—
194C4×Dic11—44no—
195C4×Dic11—42no—
196C4×Dic11—44no—
197C4×Dic11C22×C414yes—
198C4×Dic11C22×C4116yes—
199C4×Dic11#4114yes—
200C2×#541—111no—
201#2336—114no—
202#2334—114no—
203#2330—111no—
204#2327D1111yescharacteristic, complemented
205#2323—112no—
206#2320—112no—
207#2314—111no—
208C4×C4⋊Q8—111no—
209C4×#125—114no—
210C4×#125—111no—
211C4×#126—114no—
212C4×C22⋊Q8—112no—
213C42×Q8—112no—
214C4×#117—111no—
215C23×C11C2511yescharacteristic
216C22×D11—21no—
217C22×D11—21no—
218C22×D11—22no—
219C22×D11—22no—
220C22×D11C23×C412yes—
221Q8×C11—216no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11C23×C418yes—
236C2×C4×C11C23×C414yes—
237C2×C4×C11C23×C412yes—
238C2×C4×C11C2×#4114yes—
239C2×C4×C11C2×#4112yes—
240C2×C4×C11C2×#4112yes—
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—22no—
244C2×Dic11—24no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—24no—
248C2×Dic11—22no—
249C2×Dic11—24no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11C23×C414yes—
255C2×Dic11C23×C418yes—
256C2×Dic11C23×C412yes—
257C2×Dic11C2×#4112yes—
258C2×Dic11C2×#4112yes—
259C2×Dic112−1+414yes—
260C4×D11—28no—
261C4×D11—44no—
262C4×D11—44no—
263#541—1116no—
264C2×C4⋊Q8C2×D1111yescharacteristic
265C2×#126—114no—
266C2×#125—114no—
267C2×#125—111no—
268C2×C22⋊Q8—112no—
269C2×C4×Q8—112no—
270C2×C4×Q8—112no—
271C2×C4×Q8C2×D1112yes—
272C2×#117—111no—
273C2×#117—111no—
274C22×C42—111no—
275#391—112no—
276#391C2×D1112yes—
277#389—112no—
278#389—114no—
279#389—114no—
280#389—112no—
281#389—114no—
282#388—114no—
283#388—114no—
284#388—114no—
285#387—114no—
286#387—114no—
287#387—114no—
288#387—114no—
289#387—114no—
290#387—114no—
291#387—114no—
292#387C2×D1114yes—
293#387C2×D1114yes—
294#385—114no—
295#384—111no—
296#383—114no—
297#382—114no—
298#382C2×D1111yescharacteristic
299#380—112no—
300C4×C4⋊C4—114no—
301C4×C4⋊C4—114no—
302C4×C4⋊C4—112no—
303C4×C4⋊C4—112no—
304C4×C4⋊C4—114no—
305C4×C4⋊C4—112no—
306C4×C4⋊C4—114no—
307C4×C4⋊C4—114no—
308C4×C4⋊C4—112no—
309C4×C4⋊C4—114no—
310C4×C4⋊C4—112no—
311C4×C22⋊C4—112no—
312C4×C22⋊C4—114no—
313C4×C22⋊C4—112no—
314#376—111no—
315#376C2×D1111yescharacteristic
316C43—114no—
317C43—111no—
318C43—111no—
319C22×C11C24×C411yescharacteristic
320C22×C11C22×#4111yescharacteristic
321C22×C11C22×#4111yescharacteristic
322C22×C11C2×2−1+412yes—
323C22×C11#58512yes—
324C2×D11—22no—
325C2×D11—24no—
326C2×D11—41no—
327C2×D11—41no—
328C2×D11—42no—
329C4×C11—28no—
330C4×C11—24no—
331C4×C11—24no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—44no—
335C4×C11C4×#4114yes—
336Dic11—22no—
337Dic11—24no—
338Dic11—28no—
339Dic11—22no—
340Dic11—44no—
341Dic11—42no—
342Dic11#54114yescomplemented
343C22×Q8C22×D1112yes—
344C23×C4—111no—
345C23×C4—111no—
346C23×C4—111no—
347C4⋊Q8C4×D1118yescomplemented
348#126—1132no—
349#125—1132no—
350#125—118no—
351C22⋊Q8—1116no—
352C4×Q8—28no—
353C4×Q8—1116no—
354C4×Q8—228no—
355#117—118no—
356#117—224no—
357C2×C4⋊C4—112no—
358C2×C4⋊C4—112no—
359C2×C4⋊C4—114no—
360C2×C4⋊C4—114no—
361C2×C4⋊C4—114no—
362C2×C4⋊C4—112no—
363C2×C4⋊C4—112no—
364C2×C4⋊C4—114no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—114no—
367C2×C4⋊C4—114no—
368C2×C4⋊C4C22×D1112yes—
369C2×C4⋊C4C22×D1114yes—
370C2×C4⋊C4C22×D1114yes—
371C2×C22⋊C4—112no—
372C2×C22⋊C4—114no—
373C2×C22⋊C4—112no—
374C2×C22⋊C4—114no—
375C2×C42—111no—
376C2×C42—111no—
377C2×C42—114no—
378C2×C42—111no—
379C2×C42—114no—
380C2×C42—112no—
381C2×C42—114no—
382C2×C42—112no—
383C2×C42—111no—
384C2×C42—111no—
385C2×C42—112no—
386C2×C42—112no—
387C2×C42—114no—
388C2×C42—114no—
389C2×C42—224no—
390C2×C42C22×D1114yes—
391C2×C42C22×D1111yescharacteristic
392C2×C42C22×D1111yescharacteristic
393C2×C42C22×D1111yescharacteristic
394#95—112no—
395#95—112no—
396#95—114no—
397#95—114no—
398#95—114no—
399#95—114no—
400#95—114no—
401#95—114no—
402#95—114no—
403#95—114no—
404#95C22×D1112yes—
405#95C22×D1112yes—
406#95C22×D1114yes—
407#95C22×D1114yes—
408#95C22×D1114yes—
409C2×C11C2×C4×#4111yescharacteristic
410C2×C11C4×2−1+412yes—
411C2×C11C2×#54111yescharacteristic
412C2×C11#345511yescharacteristic
413C2×C11#346112yes—
414D11—42no—
415C24—111no—
416C2×Q8—24no—
417C2×Q8—24no—
418C2×Q8C2×C4×D1118yes—
419C22×C4—111no—
420C22×C4—112no—
421C22×C4—111no—
422C22×C4—114no—
423C22×C4—111no—
424C22×C4—114no—
425C22×C4—112no—
426C22×C4—114no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—224no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—442no—
433C22×C4C23×D1111yescharacteristic
434C22×C4C23×D1114yes—
435C22×C4C23×D1111yescharacteristic
436C22×C4C23×D1114yes—
437C22×C4C23×D1112yes—
438C22×C4C23×D1112yes—
439C22×C4C23×D1111yescharacteristic
440C4⋊C4—28no—
441C4⋊C4—24no—
442C4⋊C4—118no—
443C4⋊C4—118no—
444C4⋊C4—1116no—
445C4⋊C4—1116no—
446C4⋊C4—1116no—
447C4⋊C4—228no—
448C4⋊C4—224no—
449C4⋊C4—224no—
450C4⋊C4—444no—
451C4⋊C4—444no—
452C4⋊C4—444no—
453C4⋊C4C2×C4×D11116yes—
454C22⋊C4—118no—
455C22⋊C4—1116no—
456C22⋊C4—224no—
457C22⋊C4—444no—
458C42—28no—
459C42—22no—
460C42—114no—
461C42—1116no—
462C42—114no—
463C42—222no—
464C42—222no—
465C42—228no—
466C42—224no—
467C42—224no—
468C42—228no—
469C42—222no—
470C42—442no—
471C42—444no—
472C42—442no—
473C42—444no—
474C42C2×C4×D1114yes—
475C42#434114yes—
476C11C4×#54111yescharacteristic, complemented, Sylow
477C23—112no—
478C23—221no—
479C23—221no—
480C23—222no—
481C23—222no—
482C23C24×D1111yescharacteristic
483Q8—216no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—22no—
497C2×C4—112no—
498C2×C4—114no—
499C2×C4—114no—
500C2×C4—118no—
501C2×C4—112no—
502C2×C4—112no—
503C2×C4—221no—
504C2×C4—221no—
505C2×C4—222no—
506C2×C4—224no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—224no—
510C2×C4—228no—
511C2×C4—222no—
512C2×C4—224no—
513C2×C4—222no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—222no—
517C2×C4—444no—
518C2×C4—444no—
519C2×C4C22×C4×D1118yes—
520C2×C4C22×C4×D1114yes—
521C2×C4C22×C4×D1112yes—
522C2×C4C2×#434114yes—
523C2×C4C2×#434112yes—
524C2×C4#41×D1112yes—
525C22—222no—
526C22—224no—
527C22—441no—
528C22—441no—
529C22—442no—
530C22C23×C4×D1111yescharacteristic
531C22C22×#434111yescharacteristic
532C22C2×#41×D1111yescharacteristic
533C22D11×2−1+412yes—
534C22#1062345712yes—
535C4—24no—
536C4—28no—
537C4—24no—
538C4—41no—
539C4—41no—
540C4—44no—
541C4—114no—
542C4—222no—
543C4—222no—
544C4—224no—
545C4—228no—
546C4—444no—
547C4—442no—
548C4C4×#434114yes—
549C2—442no—
550C2C2×C4×#434111yescharacteristic
551C2#1308182512yes—
552C2D11×#54111yescharacteristic
553C2#1308200711yescharacteristic
554C2#1308204012yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2327C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2327D11
hypocenterC11C4×#541
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2327

Complements

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

NH ≅ G/Ntype
2. #13071421C2semidirect
4. #13071357C2semidirect
6. #13071261C2semidirect
8. C4⋊Q8×Dic11C2semidirect
9. #13071173C2semidirect
10. #13071171C2semidirect
13. C4×Q8×Dic11C2semidirect
15. C11×#2327C2semidirect
21. #10623262C4semidirect
76. C11×C4⋊Q8C2×C4semidirect
87. Q8×Dic11C2×C4semidirect
118. #66942C2×C4semidirect
122. #66923C2×C4semidirect
204. #2327D11semidirect
342. Dic11#541semidirect
347. C4⋊Q8C4×D11semidirect
476. C11C4×#541semidirect

Maximal subgroups

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

subgroupindex
C2×#106232622
#130714212
#130713962
#130713572
#130712922
#130712612
#130712262
C4⋊Q8×Dic112
#130711732
#130711712
#130711662
#130711542
C4×Q8×Dic112
#130709552
C11×#23272
C4×#54111