Finite Group Databasebeta

← #14914230

Subgroups — #14914230

Order 2816.

2110 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2#13071698C214yesmaximal
3#13071695C214yesmaximal
4#13071572C214yesmaximal, complemented
5#13071570C214yesmaximal, complemented
6#13071365C211yesmaximal, characteristic, complemented
7#13071364C211yesmaximal, characteristic, complemented
8#13071362C211yesmaximal, characteristic, complemented
9#13071238C212yesmaximal
10#13071175C212yesmaximal, complemented
11C4×#66943C212yesmaximal, complemented
12D11×#382C211yesmaximal, characteristic
13#13070970C212yesmaximal
14#13070955C211yesmaximal, characteristic
15C11×#2331C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×#66999C2212yes—
18C2×Q8×Dic11C2212yes—
19#10623259C4116yescomplemented
20C2×#66950C2212yes—
21C2×#66945C2212yes—
22C2×C4⋊C4×D11C2212yes—
23C2×#66943C2212yes—
24C2×#66940C2212yes—
25C2×#66925C2211yescharacteristic
26C2×#66925C2211yescharacteristic
27C2×C42×D11C2211yescharacteristic
28C2×#66922C2211yescharacteristic
29C11×#391C2214yes—
30C11×#389C2212yes—
31C11×#387C2214yes—
32C11×#382C2211yescharacteristic
33C4×C11×C4⋊C4C2212yes—
34C11×#376C2211yescharacteristic
35#10622843C2214yes—
36#10622602C2214yes—
37#10622598C2212yes—
38#10622594C2214yes—
39#10622591C2214yes—
40#10622590C2212yes—
41#10622589C2214yes—
42C4⋊C4×Dic11C2212yes—
43C4⋊C4×Dic11C2212yes—
44C4⋊C4×Dic11C2214yes—
45#10622586C2212yes—
46C4×(C2×D11)⋊C4C2214yes—
47#10622549C2211yescharacteristic
48C4×C4⋊Dic11C2212yes—
49C4×C4⋊Dic11C2214yes—
50#10622545C2211yescharacteristic
51C4×Dic11⋊C4C2214yes—
52C4×Dic11⋊C4C2214yes—
53C42×Dic11C2211yescharacteristic
54C42×Dic11C2211yescharacteristic
55#10622541C2212yes—
56#10622281C2214yes—
57#10622279C2212yes—
58#10622279C2214yes—
59#10622279C2212yes—
60D11×#95C2212yes—
61D11×#95C2212yes—
62#10622268C2214yes—
63#10622267C2214yes—
64#10622267C2214yes—
65#10622266C2214yes—
66#10622266C2214yes—
67#10622263C2214yes—
68#10622263C2212yes—
69#10622263C2212yes—
70#10622262C2214yes—
71#10622262C2212yes—
72#10622262C2212yes—
73#10622262C2214yes—
74#10622259C2214yes—
75#10622259C2214yes—
76C22×Q8×C11C2312yes—
77C22×C4×D11C2314yes—
78C22×C4×D11C2311yescharacteristic
79C22×C4×D11C2311yescharacteristic
80C22×C4×D11C2311yescharacteristic
81C22×Dic22C2312yes—
82C11×C4⋊Q8C2×C418yescomplemented
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2314yes—
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2312yes—
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2314yes—
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91#66999C2×C4116yes—
92Q8×Dic11C2×C4116yescomplemented
93C2×(C2×D11)⋊C4C2312yes—
94C2×(C2×D11)⋊C4C2314yes—
95C2×(C2×D11)⋊C4C2312yes—
96C2×C4⋊Dic11C2312yes—
97C2×C4⋊Dic11C2314yes—
98C2×C4⋊Dic11C2312yes—
99C2×C4⋊Dic11C2312yes—
100C2×C4⋊Dic11C2314yes—
101C2×Dic11⋊C4C2312yes—
102C2×Dic11⋊C4C2314yes—
103C2×Dic11⋊C4C2314yes—
104C2×Dic11⋊C4C2314yes—
105C2×Dic11⋊C4C2314yes—
106C2×Dic11⋊C4C2312yes—
107C2×C4×Dic11C2311yescharacteristic
108C2×C4×Dic11C2314yes—
109C2×C4×Dic11C2314yes—
110C2×C4×Dic11C2312yes—
111C2×C4×Dic11C2312yes—
112C2×C4×Dic11C2312yes—
113C2×C4×Dic11C2312yes—
114C2×C4×Dic11C2314yes—
115C2×C4×Dic11C2311yescharacteristic
116C2×C4×Dic11C2311yescharacteristic
117C2×C4×Dic11C2311yescharacteristic
118C2×C4×Dic11C2314yes—
119C2×C4×Dic11C2311yescharacteristic
120#66950C2×C4116yes—
121#66945C2×C4116yes—
122C4⋊C4×D11—28no—
123#66943C2×C4116yescomplemented
124#66940C2×C4116yescomplemented
125#66925—24no—
126#66925Q818yescomplemented
127C42×D11C2×C418yes—
128#66922C2×C418yescomplemented
129C11×#95C2312yes—
130C11×#95C2312yes—
131C11×#95C2314yes—
132C11×#95C2312yes—
133C11×#95C2314yes—
134C11×#95C2312yes—
135C11⋊#95C2312yes—
136C11⋊#95C2312yes—
137C11⋊#95C2314yes—
138C11⋊#95C2314yes—
139C11⋊#95C2314yes—
140C11⋊#95C2314yes—
141C11⋊#95C2314yes—
142C11⋊#95C2312yes—
143C11⋊#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2312yes—
146C11⋊#95C2314yes—
147#34215—111nomaximal, Sylow
148C23×D11C2411yescharacteristic
149C2×Q8×C11—44no—
150C2×Q8×C11C22×C418yes—
151C22×C4×C11C2414yes—
152C22×C4×C11C2412yes—
153C22×C4×C11C2411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C22×C4×C11C2414yes—
156C22×C4×C11C2412yes—
157C22×C4×C11C2411yescharacteristic
158C22×Dic11C2414yes—
159C22×Dic11C2412yes—
160C22×Dic11C2411yescharacteristic
161C22×Dic11C2411yescharacteristic
162C22×Dic11C2414yes—
163C22×Dic11C2412yes—
164C22×Dic11C2411yescharacteristic
165C2×C4×D11—28no—
166C2×C4×D11—42no—
167C2×C4×D11—42no—
168C2×C4×D11—44no—
169C2×C4×D11—44no—
170C2×C4×D11C22×C414yes—
171C2×C4×D11C22×C414yes—
172C2×C4×D11C22×C414yes—
173C2×C4×D11C2×Q814yes—
174C2×C4×D11#4114yes—
175C2×Dic22—44no—
176C2×Dic22C22×C418yes—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—44no—
179C11×C4⋊C4C22×C418yes—
180C11×C4⋊C4C22×C418yes—
181C42×C11—22no—
182C42×C11—44no—
183C42×C11C22×C414yes—
184C42×C11C2×Q814yes—
185(C2×D11)⋊C4—24no—
186(C2×D11)⋊C4C22×C4116yes—
187(C2×D11)⋊C4C2×Q818yes—
188C4⋊Dic11—24no—
189C4⋊Dic11—44no—
190C4⋊Dic11C22×C418yes—
191C4⋊Dic11C22×C418yes—
192C4⋊Dic11C22×C4116yes—
193Dic11⋊C4—24no—
194Dic11⋊C4—28no—
195Dic11⋊C4—44no—
196Dic11⋊C4—44no—
197Dic11⋊C4C22×C4116yes—
198Dic11⋊C4C2×Q818yes—
199C4×Dic11—22no—
200C4×Dic11—44no—
201C4×Dic11—42no—
202C4×Dic11—42no—
203C4×Dic11—44no—
204C4×Dic11—42no—
205C4×Dic11—44no—
206C4×Dic11—42no—
207C4×Dic11C22×C414yes—
208C4×Dic11C22×C414yes—
209C4×Dic11C22×C414yes—
210C4×Dic11C22×C4116yes—
211C4×Dic11C2×Q814yes—
212C2×#533—111no—
213#2368—114no—
214#2368—114no—
215#2355—114no—
216#2355—114no—
217#2331—111no—
218#2331—111no—
219#2331—111no—
220#2331D1111yescharacteristic, complemented
221#2317—112no—
222C4×#125—112no—
223C4×#125—112no—
224C2×#382—111no—
225#2274—112no—
226C4×#117—111no—
227C23×C11C2511yescharacteristic
228C22×D11—22no—
229C22×D11—22no—
230C22×D11C23×C412yes—
231C22×D11C22×Q812yes—
232C22×D11C2×#4112yes—
233Q8×C11—48no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—22no—
243C2×C4×C11—24no—
244C2×C4×C11—22no—
245C2×C4×C11—24no—
246C2×C4×C11C23×C418yes—
247C2×C4×C11C23×C412yes—
248C2×C4×C11C23×C412yes—
249C2×C4×C11C23×C412yes—
250C2×C4×C11C22×Q814yes—
251C2×C4×C11C22×Q812yes—
252C2×C4×C11C2×#4112yes—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—24no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—24no—
259C2×Dic11—22no—
260C2×Dic11—24no—
261C2×Dic11—22no—
262C2×Dic11—24no—
263C2×Dic11—22no—
264C2×Dic11—24no—
265C2×Dic11C23×C412yes—
266C2×Dic11C23×C412yes—
267C2×Dic11C23×C418yes—
268C2×Dic11C23×C412yes—
269C2×Dic11C22×Q814yes—
270C2×Dic11C22×Q812yes—
271C2×Dic11C2×#4112yes—
272C4×D11—44no—
273C4×D11—44no—
274C4×D11—88no—
275C4×D11C4×Q8116yes—
276Dic22—48no—
277#533—1116no—
278C2×C4⋊Q8—111no—
279C2×C4⋊Q8C2×D1111yescharacteristic
280C2×#125—112no—
281C2×C22⋊Q8—112no—
282C2×C22⋊Q8—112no—
283C2×C4×Q8—112no—
284C2×C4×Q8—112no—
285C2×#117—112no—
286C2×#117—111no—
287C2×#117—111no—
288C22×C4⋊C4—112no—
289C22×C42—111no—
290#391—114no—
291#391—114no—
292#391—114no—
293#391C2×D1114yes—
294#389—112no—
295#389—112no—
296#389—112no—
297#389C2×D1112yes—
298#387—114no—
299#387—114no—
300#387—114no—
301#387—114no—
302#387—114no—
303#387—114no—
304#387—114no—
305#387C2×D1114yes—
306#385—114no—
307#385—114no—
308#384—114no—
309#382—112no—
310#382—111no—
311#382—114no—
312#382—112no—
313#382—112no—
314#382C2×D1111yescharacteristic
315C4×C4⋊C4—112no—
316C4×C4⋊C4—112no—
317C4×C4⋊C4—114no—
318C4×C4⋊C4—112no—
319C4×C4⋊C4—114no—
320C4×C4⋊C4—114no—
321C4×C4⋊C4—114no—
322C4×C4⋊C4—114no—
323C4×C4⋊C4—112no—
324C4×C4⋊C4—112no—
325C4×C4⋊C4—114no—
326C4×C4⋊C4C2×D1112yes—
327C4×C22⋊C4—114no—
328C4×C22⋊C4—112no—
329C4×C22⋊C4—112no—
330C4×C22⋊C4—114no—
331#376—111no—
332#376C2×D1111yescharacteristic
333C2×#95—112no—
334C2×#95—112no—
335C43—111no—
336C43—111no—
337C22×C11C24×C411yescharacteristic
338C22×C11C23×Q811yescharacteristic
339C22×C11C22×#4111yescharacteristic
340C22×C11#58512yes—
341C22×C11#58512yes—
342C2×D11—22no—
343C2×D11—22no—
344C2×D11—24no—
345C2×D11—24no—
346C2×D11C2×C4×Q814yes—
347C4×C11—28no—
348C4×C11—22no—
349C4×C11—22no—
350C4×C11—24no—
351C4×C11—42no—
352C4×C11—44no—
353C4×C11C2×C4×Q814yes—
354Dic11—28no—
355Dic11—22no—
356Dic11—22no—
357Dic11—24no—
358Dic11—44no—
359Dic11—42no—
360Dic11C2×C4×Q814yes—
361C22×Q8—112no—
362C22×Q8C22×D1112yes—
363C23×C4—111no—
364C23×C4—111no—
365C23×C4—111no—
366C23×C4—114no—
367C4⋊Q8—118no—
368C4⋊Q8C4×D1118yescomplemented
369#125—1116no—
370C22⋊Q8—1116no—
371C22⋊Q8—1116no—
372C4×Q8—1116no—
373C4×Q8—1116no—
374#117—1116no—
375#117—118no—
376#117—224no—
377C2×C4⋊C4—112no—
378C2×C4⋊C4—112no—
379C2×C4⋊C4—114no—
380C2×C4⋊C4—114no—
381C2×C4⋊C4—112no—
382C2×C4⋊C4—114no—
383C2×C4⋊C4—112no—
384C2×C4⋊C4—112no—
385C2×C4⋊C4—114no—
386C2×C4⋊C4—114no—
387C2×C4⋊C4—114no—
388C2×C4⋊C4—228no—
389C2×C4⋊C4C22×D1112yes—
390C2×C4⋊C4C22×D1114yes—
391C2×C4⋊C4C22×D1112yes—
392C2×C4⋊C4C22×D1112yes—
393C2×C22⋊C4—114no—
394C2×C22⋊C4—112no—
395C2×C22⋊C4—112no—
396C2×C42—114no—
397C2×C42—111no—
398C2×C42—111no—
399C2×C42—111no—
400C2×C42—111no—
401C2×C42—118no—
402C2×C42—111no—
403C2×C42—112no—
404C2×C42—112no—
405C2×C42—112no—
406C2×C42—112no—
407C2×C42—114no—
408C2×C42—114no—
409C2×C42—114no—
410C2×C42C22×D1111yescharacteristic
411C2×C42C22×D1114yes—
412C2×C42C22×D1111yescharacteristic
413C2×C42C22×D1111yescharacteristic
414#95—114no—
415#95—114no—
416#95—112no—
417#95—112no—
418#95—112no—
419#95—112no—
420#95—114no—
421#95—114no—
422#95—114no—
423#95—114no—
424#95—114no—
425#95—114no—
426#95C22×D1112yes—
427#95C22×D1112yes—
428#95C22×D1112yes—
429#95C22×D1112yes—
430#95C22×D1114yes—
431#95C22×D1114yes—
432C2×C11C22×C4×Q811yescharacteristic
433C2×C11#342811yescharacteristic
434C2×C11#342811yescharacteristic
435C2×C11#350412yes—
436C2×C11#351012yes—
437D11—24no—
438C24—111no—
439C2×Q8—44no—
440C2×Q8—118no—
441C2×Q8—444no—
442C2×Q8C2×C4×D1118yes—
443C22×C4—111no—
444C22×C4—114no—
445C22×C4—114no—
446C22×C4—114no—
447C22×C4—112no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—114no—
451C22×C4—114no—
452C22×C4—114no—
453C22×C4—114no—
454C22×C4—112no—
455C22×C4—228no—
456C22×C4—442no—
457C22×C4—442no—
458C22×C4—444no—
459C22×C4—444no—
460C22×C4C23×D1114yes—
461C22×C4C23×D1112yes—
462C22×C4C23×D1111yescharacteristic
463C22×C4C23×D1111yescharacteristic
464C22×C4C23×D1114yes—
465C22×C4C23×D1112yes—
466C22×C4C23×D1111yescharacteristic
467C4⋊C4—24no—
468C4⋊C4—44no—
469C4⋊C4—118no—
470C4⋊C4—1116no—
471C4⋊C4—1116no—
472C4⋊C4—118no—
473C4⋊C4—118no—
474C4⋊C4—228no—
475C4⋊C4—224no—
476C4⋊C4—224no—
477C4⋊C4—444no—
478C4⋊C4—444no—
479C4⋊C4—444no—
480C4⋊C4C2×C4×D1118yes—
481C4⋊C4C2×C4×D1118yes—
482C22⋊C4—1116no—
483C22⋊C4—118no—
484C22⋊C4—224no—
485C42—22no—
486C42—44no—
487C42—114no—
488C42—114no—
489C42—114no—
490C42—1116no—
491C42—114no—
492C42—222no—
493C42—442no—
494C42—444no—
495C42—442no—
496C42—444no—
497C42—442no—
498C42—442no—
499C42—444no—
500C42C2×C4×D1114yes—
501C42Q8×D1114yes—
502C11#3421511yescharacteristic, complemented, Sylow
503C23—112no—
504C23—112no—
505C23—112no—
506C23—222no—
507C23—222no—
508C23C24×D1111yescharacteristic
509Q8—48no—
510Q8—448no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—112no—
524C2×C4—112no—
525C2×C4—112no—
526C2×C4—1116no—
527C2×C4—112no—
528C2×C4—112no—
529C2×C4—118no—
530C2×C4—114no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—222no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—222no—
538C2×C4—224no—
539C2×C4—222no—
540C2×C4—224no—
541C2×C4—222no—
542C2×C4—224no—
543C2×C4—444no—
544C2×C4—444no—
545C2×C4—888no—
546C2×C4C22×C4×D1112yes—
547C2×C4C22×C4×D1112yes—
548C2×C4C22×C4×D1118yes—
549C2×C4C22×C4×D1112yes—
550C2×C4C2×Q8×D1114yes—
551C2×C4C2×Q8×D1112yes—
552C2×C4#41×D1112yes—
553C22—114no—
554C22—224no—
555C22—224no—
556C22—222no—
557C22—222no—
558C22C23×C4×D1111yescharacteristic
559C22C22×Q8×D1111yescharacteristic
560C22C2×#41×D1111yescharacteristic
561C22#1062345512yes—
562C22#1062345712yes—
563C4—24no—
564C4—22no—
565C4—28no—
566C4—22no—
567C4—44no—
568C4—42no—
569C4—114no—
570C4—224no—
571C4—222no—
572C4—222no—
573C4—228no—
574C4—444no—
575C4—442no—
576C4C4×Q8×D1114yes—
577C2—224no—
578C2C2×C4×Q8×D1111yescharacteristic
579C2#1308181411yescharacteristic
580C2#1308181811yescharacteristic
581C2#1308243912yes—
582C2#1308250812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2331C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2331D11
hypocenterC11#34215
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2331

Complements

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

NH ≅ G/Ntype
4. #13071572C2semidirect
5. #13071570C2semidirect
6. #13071365C2semidirect
7. #13071364C2semidirect
8. #13071362C2semidirect
10. #13071175C2semidirect
11. C4×#66943C2semidirect
15. C11×#2331C2semidirect
19. #10623259C4semidirect
82. C11×C4⋊Q8C2×C4semidirect
92. Q8×Dic11C2×C4semidirect
123. #66943C2×C4semidirect
124. #66940C2×C4semidirect
126. #66925Q8semidirect
128. #66922C2×C4semidirect
220. #2331D11semidirect
368. C4⋊Q8C4×D11semidirect
502. C11#34215semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
#130716982
#130716952
#130715722
#130715702
#130713652
#130713642
#130713622
#130712382
#130711752
C4×#669432
D11×#3822
#130709702
#130709552
C11×#23312
#3421511