Finite Group Databasebeta

← #14916594

Subgroups — #14916594

Order 2816.

2238 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×D11×C4⋊Q8C211yesmaximal, characteristic
2#13071794C214yesmaximal, complemented
3#13071703C212yesmaximal, complemented
4#13071702C212yesmaximal, complemented
5#13071484C212yesmaximal
6#13071482C214yesmaximal
7#13071481C212yesmaximal
8#13071365C211yesmaximal, characteristic, complemented
9#13071364C211yesmaximal, characteristic, complemented
10#13071362C211yesmaximal, characteristic, complemented
11#13071359C214yesmaximal, complemented
12#13071199C214yesmaximal
13#13071009C211yesmaximal, characteristic
14#13071008C211yesmaximal, characteristic
15C11×#2331C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2212yes—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×#66997C2212yes—
19D11×C4⋊Q8C4116yescomplemented
20C2×#66945C2214yes—
21C2×C4⋊C4×D11C2212yes—
22C2×C4⋊C4×D11C2212yes—
23C2×#66941C2212yes—
24C2×#66941C2212yes—
25C2×#66925C2214yes—
26C2×C42×D11C2211yescharacteristic
27C2×#66922C2211yescharacteristic
28C11×#391C2214yes—
29C11×#389C2212yes—
30C11×#387C2214yes—
31C11×#382C2211yescharacteristic
32C4×C11×C4⋊C4C2212yes—
33C11×#376C2211yescharacteristic
34#10622843C2214yes—
35#10622600C2212yes—
36#10622598C2212yes—
37#10622594C2214yes—
38#10622591C2214yes—
39C4⋊C4×Dic11C2212yes—
40C4⋊C4×Dic11C2212yes—
41C4⋊C4×Dic11C2212yes—
42#10622587C2214yes—
43#10622586C2212yes—
44#10622585C2214yes—
45C4×(C2×D11)⋊C4C2211yescharacteristic
46C4×(C2×D11)⋊C4C2211yescharacteristic
47#10622549C2211yescharacteristic
48C4×C4⋊Dic11C2212yes—
49#10622546C2214yes—
50#10622545C2211yescharacteristic
51C4×Dic11⋊C4C2211yescharacteristic
52C4×Dic11⋊C4C2211yescharacteristic
53C4×Dic11⋊C4C2214yes—
54#10622542C2214yes—
55#10622541C2212yes—
56#10622280C2212yes—
57#10622279C2212yes—
58#10622277C2212yes—
59#10622277C2212yes—
60#10622277C2214yes—
61#10622277C2214yes—
62#10622268C2214yes—
63#10622267C2214yes—
64#10622266C2214yes—
65#10622265C2214yes—
66#10622264C2212yes—
67#10622264C2212yes—
68#10622263C2212yes—
69#10622262C2214yes—
70#10622261C2212yes—
71#10622260C2214yes—
72#10622259C2214yes—
73#10622259C2214yes—
74#10622259C2214yes—
75#10622259C2214yes—
76C22×Q8×C11C2312yes—
77C2×Q8×D11—48no—
78C2×Q8×D11C2×C4116yes—
79C22×C4×D11C2311yescharacteristic
80C22×C4×D11C2311yescharacteristic
81C22×C4×D11C2311yescharacteristic
82C22×C4×D11C2314yes—
83C22×Dic22C2312yes—
84C22×Dic22C2314yes—
85C11×C4⋊Q8C2×C418yes—
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C4⋊C4C2314yes—
88C2×C11×C4⋊C4C2312yes—
89C2×C11×C4⋊C4C2312yes—
90C2×C42×C11C2311yescharacteristic
91C2×C42×C11C2311yescharacteristic
92C2×C42×C11C2314yes—
93C2×C42×C11C2311yescharacteristic
94#66997C2×C4116yes—
95C2×(C2×D11)⋊C4C2312yes—
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2312yes—
98C2×C4⋊Dic11C2312yes—
99C2×C4⋊Dic11C2314yes—
100C2×C4⋊Dic11C2312yes—
101C2×C4⋊Dic11C2312yes—
102C2×Dic11⋊C4C2312yes—
103C2×Dic11⋊C4C2312yes—
104C2×Dic11⋊C4C2314yes—
105C2×Dic11⋊C4C2314yes—
106C2×Dic11⋊C4C2314yes—
107C2×Dic11⋊C4C2314yes—
108C2×C4×Dic11C2314yes—
109C2×C4×Dic11C2311yescharacteristic
110C2×C4×Dic11C2311yescharacteristic
111C2×C4×Dic11C2314yes—
112C2×C4×Dic11C2314yes—
113C2×C4×Dic11C2314yes—
114C2×C4×Dic11C2311yescharacteristic
115C2×C4×Dic11C2311yescharacteristic
116C2×C4×Dic11C2311yescharacteristic
117#66945—48no—
118C4⋊C4×D11C2×C4116yes—
119C4⋊C4×D11C2×C4116yes—
120#66941C2×C4116yes—
121#66941C2×C4116yes—
122#66925—48no—
123C42×D11C2×C418yes—
124#66922C2×C418yes—
125C11×#95C2312yes—
126C11×#95C2312yes—
127C11×#95C2314yes—
128C11×#95C2314yes—
129C11×#95C2312yes—
130C11×#95C2312yes—
131C11⋊#95C2312yes—
132C11⋊#95C2312yes—
133C11⋊#95C2312yes—
134C11⋊#95C2314yes—
135C11⋊#95C2312yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138C11⋊#95C2314yes—
139C11⋊#95C2314yes—
140C11⋊#95C2314yes—
141C11⋊#95C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2312yes—
144C11⋊#95C2312yes—
145C11⋊#95C2312yes—
146C11⋊#95C2312yes—
147#34365—111nomaximal, Sylow
148C23×D11C2411yescharacteristic
149C2×Q8×C11—44no—
150C2×Q8×C11C22×C418yes—
151C22×C4×C11C2412yes—
152C22×C4×C11C2414yes—
153C22×C4×C11C2412yes—
154C22×C4×C11C2411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C22×C4×C11C2414yes—
157C22×C4×C11C2411yescharacteristic
158C22×Dic11C2412yes—
159C22×Dic11C2414yes—
160C22×Dic11C2412yes—
161C22×Dic11C2411yescharacteristic
162C22×Dic11C2411yescharacteristic
163C22×Dic11C2414yes—
164C22×Dic11C2411yescharacteristic
165Q8×D11—432no—
166C2×C4×D11—24no—
167C2×C4×D11—28no—
168C2×C4×D11—28no—
169C2×C4×D11—24no—
170C2×C4×D11—22no—
171C2×C4×D11—22no—
172C2×C4×D11C22×C414yes—
173C2×C4×D11C22×C414yes—
174C2×C4×D11C22×C414yes—
175C2×C4×D11C22×C4116yes—
176C2×Dic22—44no—
177C2×Dic22—44no—
178C2×Dic22—44no—
179C2×Dic22C22×C418yes—
180C2×Dic22C22×C4116yes—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—44no—
183C11×C4⋊C4C22×C418yes—
184C11×C4⋊C4C22×C418yes—
185C42×C11—22no—
186C42×C11—22no—
187C42×C11—44no—
188C42×C11C22×C414yes—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—28no—
191(C2×D11)⋊C4—24no—
192C4⋊Dic11—24no—
193C4⋊Dic11—44no—
194C4⋊Dic11C22×C418yes—
195C4⋊Dic11C22×C418yes—
196Dic11⋊C4—24no—
197Dic11⋊C4—24no—
198Dic11⋊C4—44no—
199Dic11⋊C4—44no—
200Dic11⋊C4C22×C4116yes—
201Dic11⋊C4C22×C4116yes—
202C4×Dic11—28no—
203C4×Dic11—22no—
204C4×Dic11—22no—
205C4×Dic11—44no—
206C4×Dic11—44no—
207C4×Dic11—44no—
208C4×Dic11C22×C414yes—
209C4×Dic11C22×C414yes—
210C4×Dic11C22×C414yes—
211C22×C4⋊Q8—111no—
212#2381—114no—
213#2369—112no—
214#2369—112no—
215#2344—112no—
216#2344—114no—
217#2344—112no—
218#2331—114no—
219#2331—111no—
220#2331—111no—
221#2331—111no—
222#2331D1111yescharacteristic, complemented
223#2310—114no—
224#2283—111no—
225#2283—111no—
226C23×C11C2511yescharacteristic
227C22×D11—21no—
228C22×D11—21no—
229C22×D11—22no—
230C22×D11C23×C412yes—
231C22×D11H(5,𝔽2)14yes—
232Q8×C11—48no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—24no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—24no—
246C2×C4×C11C23×C412yes—
247C2×C4×C11C23×C412yes—
248C2×C4×C11C23×C418yes—
249C2×C4×C11C23×C412yes—
250C2×C4×C112−1+412yes—
251C2×C4×C112−1+412yes—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—22no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—22no—
258C2×Dic11—24no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—24no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—24no—
266C2×Dic11C23×C412yes—
267C2×Dic11C23×C412yes—
268C2×Dic11C23×C418yes—
269C2×Dic11C23×C412yes—
270C2×Dic112−1+414yes—
271C4×D11—232no—
272C4×D11—28no—
273C4×D11—28no—
274C4×D11—28no—
275Dic22—416no—
276Dic22—48no—
277C23×Q8—112no—
278C2×C4⋊Q8—112no—
279C2×C4⋊Q8—1116no—
280C2×C4⋊Q8—112no—
281C2×C4⋊Q8—112no—
282C2×C4⋊Q8—111no—
283C2×C4⋊Q8C2×D1111yescharacteristic
284C2×#117—114no—
285C2×#117—114no—
286C22×C4⋊C4—112no—
287C22×C4⋊C4—112no—
288C22×C42—111no—
289#391—114no—
290#391—114no—
291#391—114no—
292#391—114no—
293#391—114no—
294#391—114no—
295#391—114no—
296#391C2×D1114yes—
297#389—114no—
298#389—112no—
299#389—112no—
300#389—112no—
301#389—114no—
302#389C2×D1112yes—
303#387—114no—
304#387—114no—
305#387—114no—
306#387—114no—
307#387—114no—
308#387—114no—
309#387—114no—
310#387C2×D1114yes—
311#383—112no—
312#383—112no—
313#382—111no—
314#382—112no—
315#382C2×D1111yescharacteristic
316#381—112no—
317#381—112no—
318#381—114no—
319#381—114no—
320#380—112no—
321#380—112no—
322C4×C4⋊C4—112no—
323C4×C4⋊C4—112no—
324C4×C4⋊C4—112no—
325C4×C4⋊C4—114no—
326C4×C4⋊C4—112no—
327C4×C4⋊C4—111no—
328C4×C4⋊C4—111no—
329C4×C4⋊C4—114no—
330C4×C4⋊C4C2×D1112yes—
331C4×C22⋊C4—111no—
332C4×C22⋊C4—111no—
333C4×C22⋊C4—112no—
334#376—111no—
335#376—112no—
336#376C2×D1111yescharacteristic
337C22×C11C24×C411yescharacteristic
338C22×C11C2×H(5,𝔽2)12yes—
339C22×C11C2×2−1+411yescharacteristic
340C22×C11C2×2−1+411yescharacteristic
341C22×C11C2×2−1+412yes—
342C2×D11—22no—
343C2×D11—22no—
344C2×D11—24no—
345C2×D11—24no—
346C2×D11#51814yes—
347C4×C11—22no—
348C4×C11—28no—
349C4×C11—22no—
350C4×C11—42no—
351C4×C11—44no—
352C4×C11—42no—
353C4×C11#51914yes—
354Dic11—22no—
355Dic11—28no—
356Dic11—22no—
357Dic11—42no—
358Dic11—44no—
359Dic11—42no—
360Dic11#51914yes—
361C22×Q8—1116no—
362C22×Q8—114no—
363C22×Q8—112no—
364C22×Q8—448no—
365C22×Q8C22×D1112yes—
366C23×C4—114no—
367C23×C4—111no—
368C23×C4—111no—
369C23×C4—111no—
370C4⋊Q8—1116no—
371C4⋊Q8—1116no—
372C4⋊Q8—1116no—
373C4⋊Q8—118no—
374C4⋊Q8C4×D1118yes—
375#117—448no—
376#117—448no—
377C2×C4⋊C4—114no—
378C2×C4⋊C4—112no—
379C2×C4⋊C4—114no—
380C2×C4⋊C4—112no—
381C2×C4⋊C4—1116no—
382C2×C4⋊C4—1116no—
383C2×C4⋊C4—112no—
384C2×C4⋊C4—112no—
385C2×C4⋊C4—112no—
386C2×C4⋊C4—114no—
387C2×C4⋊C4—114no—
388C2×C4⋊C4—114no—
389C2×C4⋊C4C22×D1112yes—
390C2×C4⋊C4C22×D1114yes—
391C2×C4⋊C4C22×D1112yes—
392C2×C4⋊C4C22×D1112yes—
393C2×C22⋊C4—112no—
394C2×C22⋊C4—114no—
395C2×C22⋊C4—112no—
396C2×C42—111no—
397C2×C42—111no—
398C2×C42—111no—
399C2×C42—118no—
400C2×C42—114no—
401C2×C42—111no—
402C2×C42—111no—
403C2×C42—114no—
404C2×C42—114no—
405C2×C42—114no—
406C2×C42C22×D1111yescharacteristic
407C2×C42C22×D1111yescharacteristic
408C2×C42C22×D1114yes—
409C2×C42C22×D1111yescharacteristic
410#95—114no—
411#95—112no—
412#95—112no—
413#95—112no—
414#95—112no—
415#95—112no—
416#95—112no—
417#95—114no—
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×C11C2×#51811yescharacteristic
433C2×C11C2×#51911yescharacteristic
434C2×C11C2×#51911yescharacteristic
435C2×C11#354412yes—
436C2×C11#354412yes—
437D11—24no—
438C24—111no—
439C2×Q8—44no—
440C2×Q8—1116no—
441C2×Q8—118no—
442C2×Q8—444no—
443C2×Q8—444no—
444C2×Q8—444no—
445C2×Q8—4432no—
446C2×Q8C2×C4×D1118yes—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—114no—
451C22×C4—114no—
452C22×C4—114no—
453C22×C4—114no—
454C22×C4—1116no—
455C22×C4—112no—
456C22×C4—114no—
457C22×C4—112no—
458C22×C4—224no—
459C22×C4—228no—
460C22×C4—228no—
461C22×C4—224no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4C23×D1112yes—
465C22×C4C23×D1114yes—
466C22×C4C23×D1112yes—
467C22×C4C23×D1111yescharacteristic
468C22×C4C23×D1111yescharacteristic
469C22×C4C23×D1114yes—
470C22×C4C23×D1111yescharacteristic
471C4⋊C4—24no—
472C4⋊C4—44no—
473C4⋊C4—1116no—
474C4⋊C4—1116no—
475C4⋊C4—118no—
476C4⋊C4—118no—
477C4⋊C4—224no—
478C4⋊C4—224no—
479C4⋊C4—224no—
480C4⋊C4—444no—
481C4⋊C4—444no—
482C4⋊C4—444no—
483C4⋊C4C2×C4×D1118yes—
484C4⋊C4C2×C4×D1118yes—
485C22⋊C4—224no—
486C22⋊C4—228no—
487C22⋊C4—224no—
488C42—22no—
489C42—22no—
490C42—44no—
491C42—114no—
492C42—114no—
493C42—114no—
494C42—228no—
495C42—222no—
496C42—222no—
497C42—444no—
498C42—444no—
499C42—444no—
500C42C2×C4×D1114yes—
501C11#3436511yescharacteristic, complemented, Sylow
502C23—112no—
503C23—114no—
504C23—221no—
505C23—221no—
506C23—222no—
507C23C24×D1111yescharacteristic
508Q8—48no—
509Q8—448no—
510Q8—4416no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—22no—
521C2×C4—24no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—112no—
525C2×C4—114no—
526C2×C4—112no—
527C2×C4—112no—
528C2×C4—118no—
529C2×C4—228no—
530C2×C4—228no—
531C2×C4—2232no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—222no—
537C2×C4—228no—
538C2×C4—222no—
539C2×C4—224no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—224no—
543C2×C4—222no—
544C2×C4—224no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4C22×C4×D1112yes—
548C2×C4C22×C4×D1112yes—
549C2×C4C22×C4×D1118yes—
550C2×C4C22×C4×D1112yes—
551C2×C4#6704012yes—
552C2×C4#6704312yes—
553C22—114no—
554C22—224no—
555C22—224no—
556C22—222no—
557C22—222no—
558C22C23×C4×D1111yescharacteristic
559C22C2×#6704011yescharacteristic
560C22C2×#6704311yescharacteristic
561C22D11×H(5,𝔽2)12yes—
562C22D11×2−1+412yes—
563C4—22no—
564C4—28no—
565C4—22no—
566C4—42no—
567C4—44no—
568C4—42no—
569C4—114no—
570C4—222no—
571C4—228no—
572C4—222no—
573C4—442no—
574C4—442no—
575C4—444no—
576C4#1062310314yes—
577C2—224no—
578C2D11×#51811yescharacteristic
579C2D11×#51911yescharacteristic
580C2C2×#1062310311yescharacteristic
581C2#1308295312yes—
582C2#1308295912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2331C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2331D11
hypocenterC11#34365
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2331

Complements

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

NH ≅ G/Ntype
2. #13071794C2semidirect
3. #13071703C2semidirect
4. #13071702C2semidirect
8. #13071365C2semidirect
9. #13071364C2semidirect
10. #13071362C2semidirect
11. #13071359C2semidirect
15. C11×#2331C2semidirect
19. D11×C4⋊Q8C4semidirect
222. #2331D11semidirect
501. C11#34365semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
#130717942
#130717032
#130717022
#130714842
#130714822
#130714812
#130713652
#130713642
#130713622
#130713592
#130711992
#130710092
#130710082
C11×#23312
#3436511