Finite Group Databasebeta

← #14917080

Subgroups — #14917080

Order 2816.

1898 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2#13071780C214yesmaximal
3#13071717C212yesmaximal, complemented
4#13071708C212yesmaximal, complemented
5#13071578C214yesmaximal, complemented
6#13071508C212yesmaximal
7#13071497C212yesmaximal
8#13071371C214yesmaximal
9#13071365C211yesmaximal, characteristic, complemented
10#13071364C211yesmaximal, characteristic, complemented
11#13071362C211yesmaximal, characteristic, complemented
12#13071261C214yesmaximal, complemented
13#13071009C211yesmaximal, characteristic
14#13071008C211yesmaximal, characteristic
15C11×#2331C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×#66999C2212yes—
18C2×Q8×Dic11C2212yes—
19#10623259C4116yescomplemented
20C2×#66950C2212yes—
21C2×#66945C2212yes—
22C2×#66943C2212yes—
23C2×#66940C2212yes—
24C2×C42×D11C2211yescharacteristic
25C2×#66922C2211yescharacteristic
26C11×#391C2214yes—
27C11×#389C2212yes—
28C11×#387C2214yes—
29C11×#382C2211yescharacteristic
30C4×C11×C4⋊C4C2212yes—
31C11×#376C2211yescharacteristic
32#10622843C2214yes—
33#10622603C2214yes—
34#10622600C2212yes—
35#10622598C2212yes—
36#10622594C2214yes—
37#10622591C2214yes—
38C4⋊C4×Dic11C2212yes—
39C4⋊C4×Dic11C2212yes—
40C4⋊C4×Dic11C2212yes—
41C4⋊C4×Dic11C2214yes—
42#10622586C2212yes—
43#10622586C2214yes—
44#10622553C2214yes—
45C4×(C2×D11)⋊C4C2211yescharacteristic
46C4×(C2×D11)⋊C4C2211yescharacteristic
47#10622549C2211yescharacteristic
48C4×C4⋊Dic11C2212yes—
49#10622545C2211yescharacteristic
50#10622545C2214yes—
51C4×Dic11⋊C4C2214yes—
52C4×Dic11⋊C4C2211yescharacteristic
53C4×Dic11⋊C4C2211yescharacteristic
54#10622541C2212yes—
55#10622541C2214yes—
56#10622283C2214yes—
57#10622282C2214yes—
58#10622280C2212yes—
59#10622279C2212yes—
60#10622277C2212yes—
61#10622277C2212yes—
62#10622268C2214yes—
63#10622267C2214yes—
64#10622267C2214yes—
65#10622266C2214yes—
66#10622266C2214yes—
67#10622264C2214yes—
68#10622264C2212yes—
69#10622264C2212yes—
70#10622263C2214yes—
71#10622263C2212yes—
72#10622262C2214yes—
73#10622261C2212yes—
74#10622259C2214yes—
75#10622259C2214yes—
76C22×Q8×C11C2312yes—
77C22×C4×D11C2311yescharacteristic
78C22×C4×D11C2311yescharacteristic
79C22×C4×D11C2311yescharacteristic
80C22×Dic22C2312yes—
81C11×C4⋊Q8C2×C418yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2312yes—
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2314yes—
89C2×C42×C11C2311yescharacteristic
90#66999C2×C4116yes—
91Q8×Dic11C2×C4116yes—
92C2×(C2×D11)⋊C4C2314yes—
93C2×(C2×D11)⋊C4C2312yes—
94C2×(C2×D11)⋊C4C2312yes—
95C2×(C2×D11)⋊C4C2314yes—
96C2×C4⋊Dic11C2312yes—
97C2×C4⋊Dic11C2314yes—
98C2×C4⋊Dic11C2312yes—
99C2×C4⋊Dic11C2312yes—
100C2×C4⋊Dic11C2314yes—
101C2×Dic11⋊C4C2314yes—
102C2×Dic11⋊C4C2314yes—
103C2×Dic11⋊C4C2312yes—
104C2×Dic11⋊C4C2312yes—
105C2×Dic11⋊C4C2314yes—
106C2×C4×Dic11C2311yescharacteristic
107C2×C4×Dic11C2311yescharacteristic
108C2×C4×Dic11C2314yes—
109C2×C4×Dic11C2314yes—
110C2×C4×Dic11C2314yes—
111C2×C4×Dic11C2314yes—
112C2×C4×Dic11C2311yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114C2×C4×Dic11C2311yescharacteristic
115C2×C4×Dic11C2314yes—
116#66950C2×C4116yes—
117#66945C2×C4116yes—
118#66943C2×C4116yes—
119#66940C2×C4116yes—
120C42×D11C2×C418yes—
121#66922C2×C418yes—
122C11×#95C2312yes—
123C11×#95C2312yes—
124C11×#95C2314yes—
125C11×#95C2312yes—
126C11×#95C2314yes—
127C11×#95C2312yes—
128C11⋊#95C2312yes—
129C11⋊#95C2312yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2312yes—
136C11⋊#95C2312yes—
137C11⋊#95C2312yes—
138C11⋊#95C2312yes—
139C11⋊#95C2314yes—
140C11⋊#95C2314yes—
141C11⋊#95C2312yes—
142C11⋊#95C2314yes—
143C11⋊#95C2312yes—
144#34403—111nomaximal, Sylow
145C23×D11C2411yescharacteristic
146C2×Q8×C11—44no—
147C2×Q8×C11C22×C418yes—
148C22×C4×C11C2412yes—
149C22×C4×C11C2414yes—
150C22×C4×C11C2412yes—
151C22×C4×C11C2411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×C4×C11C2414yes—
154C22×C4×C11C2411yescharacteristic
155C22×Dic11C2412yes—
156C22×Dic11C2412yes—
157C22×Dic11C2414yes—
158C22×Dic11C2411yescharacteristic
159C22×Dic11C2411yescharacteristic
160C22×Dic11C2414yes—
161C22×Dic11C2411yescharacteristic
162C2×C4×D11—22no—
163C2×C4×D11—22no—
164C2×C4×D11—42no—
165C2×C4×D11—42no—
166C2×C4×D11C22×C414yes—
167C2×C4×D11C22×C414yes—
168C2×C4×D11C22×C414yes—
169C2×Dic22—44no—
170C2×Dic22C22×C418yes—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—44no—
173C11×C4⋊C4C22×C418yes—
174C11×C4⋊C4C22×C418yes—
175C42×C11—22no—
176C42×C11—22no—
177C42×C11—44no—
178C42×C11C22×C414yes—
179(C2×D11)⋊C4—44no—
180(C2×D11)⋊C4—42no—
181(C2×D11)⋊C4—42no—
182(C2×D11)⋊C4C22×C4116yes—
183C4⋊Dic11—24no—
184C4⋊Dic11—44no—
185C4⋊Dic11C22×C418yes—
186C4⋊Dic11C22×C418yes—
187C4⋊Dic11C22×C4116yes—
188Dic11⋊C4—42no—
189Dic11⋊C4—44no—
190Dic11⋊C4—44no—
191Dic11⋊C4—42no—
192Dic11⋊C4C22×C4116yes—
193C4×Dic11—22no—
194C4×Dic11—22no—
195C4×Dic11—44no—
196C4×Dic11—44no—
197C4×Dic11—44no—
198C4×Dic11—44no—
199C4×Dic11C22×C414yes—
200C4×Dic11C22×C414yes—
201C4×Dic11C22×C414yes—
202C4×Dic11C22×C4116yes—
203C2×#533—111no—
204#2378—114no—
205#2370—112no—
206#2370—112no—
207#2356—114no—
208#2347—112no—
209#2346—112no—
210#2332—114no—
211#2331—111no—
212#2331—111no—
213#2331—111no—
214#2331D1111yescharacteristic, complemented
215#2320—114no—
216#2283—111no—
217#2283—111no—
218C23×C11C2511yescharacteristic
219C22×D11—21no—
220C22×D11—21no—
221C22×D11—22no—
222C22×D11—22no—
223C22×D11C23×C412yes—
224Q8×C11—48no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11C23×C418yes—
239C2×C4×C11C23×C412yes—
240C2×C4×C11C23×C412yes—
241C2×C4×C11C23×C412yes—
242C2×C4×C112−1+412yes—
243C2×C4×C112−1+412yes—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—24no—
247C2×Dic11—22no—
248C2×Dic11—24no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—22no—
254C2×Dic11—24no—
255C2×Dic11—22no—
256C2×Dic11—24no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11C23×C412yes—
260C2×Dic11C23×C412yes—
261C2×Dic11C23×C412yes—
262C2×Dic11C23×C418yes—
263C4×D11—28no—
264C4×D11—44no—
265C4×D11—44no—
266Dic22—48no—
267#533—1116no—
268C2×C4⋊Q8—111no—
269C2×C4⋊Q8C2×D1111yescharacteristic
270C2×#125—112no—
271C2×C22⋊Q8—112no—
272C2×C22⋊Q8—112no—
273C2×C4×Q8—112no—
274C2×C4×Q8—112no—
275C2×#117—112no—
276C22×C42—111no—
277#391—114no—
278#391—114no—
279#391—114no—
280#391C2×D1114yes—
281#389—114no—
282#389—112no—
283#389—112no—
284#389—114no—
285#389—112no—
286#389C2×D1112yes—
287#388—114no—
288#388—114no—
289#388—114no—
290#388—114no—
291#387—114no—
292#387—114no—
293#387—114no—
294#387—114no—
295#387—114no—
296#387—114no—
297#387—114no—
298#387C2×D1114yes—
299#383—112no—
300#383—114no—
301#383—112no—
302#382—111no—
303#382—112no—
304#382—114no—
305#382C2×D1111yescharacteristic
306#381—112no—
307#381—112no—
308#380—112no—
309#380—112no—
310C4×C4⋊C4—114no—
311C4×C4⋊C4—112no—
312C4×C4⋊C4—112no—
313C4×C4⋊C4—112no—
314C4×C4⋊C4—112no—
315C4×C4⋊C4—114no—
316C4×C4⋊C4—111no—
317C4×C4⋊C4—111no—
318C4×C4⋊C4—114no—
319C4×C4⋊C4C2×D1112yes—
320C4×C22⋊C4—111no—
321C4×C22⋊C4—111no—
322C4×C22⋊C4—112no—
323#376—114no—
324#376—111no—
325#376—112no—
326#376C2×D1111yescharacteristic
327C22×C11C24×C411yescharacteristic
328C22×C11C2×2−1+411yescharacteristic
329C22×C11C2×2−1+411yescharacteristic
330C22×C11#58512yes—
331C22×C11#58512yes—
332C2×D11—22no—
333C2×D11—22no—
334C2×D11—22no—
335C2×D11—42no—
336C2×D11—42no—
337C4×C11—28no—
338C4×C11—22no—
339C4×C11—22no—
340C4×C11—42no—
341C4×C11—42no—
342C4×C11—44no—
343C4×C11#51914yes—
344Dic11—22no—
345Dic11—28no—
346Dic11—22no—
347Dic11—22no—
348Dic11—42no—
349Dic11—44no—
350Dic11—42no—
351C22×Q8—112no—
352C22×Q8C22×D1112yes—
353C23×C4—111no—
354C23×C4—111no—
355C23×C4—111no—
356C4⋊Q8—118no—
357C4⋊Q8C4×D1118yes—
358#125—1116no—
359C22⋊Q8—1116no—
360C22⋊Q8—1116no—
361C4×Q8—1116no—
362C4×Q8—1116no—
363#117—1116no—
364C2×C4⋊C4—112no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—114no—
367C2×C4⋊C4—112no—
368C2×C4⋊C4—112no—
369C2×C4⋊C4—112no—
370C2×C4⋊C4—112no—
371C2×C4⋊C4—114no—
372C2×C4⋊C4—114no—
373C2×C4⋊C4—114no—
374C2×C4⋊C4C22×D1112yes—
375C2×C4⋊C4C22×D1114yes—
376C2×C4⋊C4C22×D1112yes—
377C2×C4⋊C4C22×D1112yes—
378C2×C22⋊C4—114no—
379C2×C22⋊C4—112no—
380C2×C22⋊C4—114no—
381C2×C22⋊C4—112no—
382C2×C42—114no—
383C2×C42—111no—
384C2×C42—111no—
385C2×C42—111no—
386C2×C42—118no—
387C2×C42—111no—
388C2×C42—111no—
389C2×C42—114no—
390C2×C42—114no—
391C2×C42—114no—
392C2×C42—114no—
393C2×C42C22×D1111yescharacteristic
394C2×C42C22×D1111yescharacteristic
395C2×C42C22×D1114yes—
396C2×C42C22×D1111yescharacteristic
397#95—112no—
398#95—114no—
399#95—112no—
400#95—112no—
401#95—112no—
402#95—114no—
403#95—114no—
404#95—112no—
405#95—112no—
406#95—112no—
407#95—112no—
408#95—114no—
409#95—114no—
410#95—114no—
411#95—114no—
412#95—114no—
413#95C22×D1112yes—
414#95C22×D1112yes—
415#95C22×D1112yes—
416#95C22×D1112yes—
417#95C22×D1114yes—
418#95C22×D1114yes—
419C2×C11C2×#51911yescharacteristic
420C2×C11#342811yescharacteristic
421C2×C11#342811yescharacteristic
422C2×C11#356512yes—
423C2×C11#356512yes—
424D11—42no—
425C24—111no—
426C2×Q8—44no—
427C2×Q8—118no—
428C2×Q8—444no—
429C2×Q8C2×C4×D1118yes—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—114no—
433C22×C4—111no—
434C22×C4—114no—
435C22×C4—114no—
436C22×C4—114no—
437C22×C4—112no—
438C22×C4—114no—
439C22×C4—112no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—442no—
443C22×C4—442no—
444C22×C4C23×D1112yes—
445C22×C4C23×D1114yes—
446C22×C4C23×D1112yes—
447C22×C4C23×D1111yescharacteristic
448C22×C4C23×D1111yescharacteristic
449C22×C4C23×D1114yes—
450C22×C4C23×D1111yescharacteristic
451C4⋊C4—24no—
452C4⋊C4—44no—
453C4⋊C4—118no—
454C4⋊C4—1116no—
455C4⋊C4—1116no—
456C4⋊C4—118no—
457C4⋊C4—224no—
458C4⋊C4—442no—
459C4⋊C4—444no—
460C4⋊C4—442no—
461C4⋊C4—444no—
462C4⋊C4—444no—
463C4⋊C4C2×C4×D1118yes—
464C4⋊C4C2×C4×D1118yes—
465C22⋊C4—1116no—
466C22⋊C4—442no—
467C22⋊C4—442no—
468C22⋊C4—444no—
469C42—22no—
470C42—22no—
471C42—44no—
472C42—114no—
473C42—114no—
474C42—114no—
475C42—1116no—
476C42—222no—
477C42—222no—
478C42—444no—
479C42—444no—
480C42—444no—
481C42—444no—
482C42C2×C4×D1114yes—
483C11#3440311yescharacteristic, complemented, Sylow
484C23—112no—
485C23—221no—
486C23—221no—
487C23—222no—
488C23—222no—
489C23C24×D1111yescharacteristic
490Q8—48no—
491Q8—448no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—112no—
506C2×C4—112no—
507C2×C4—112no—
508C2×C4—118no—
509C2×C4—221no—
510C2×C4—221no—
511C2×C4—222no—
512C2×C4—224no—
513C2×C4—222no—
514C2×C4—224no—
515C2×C4—228no—
516C2×C4—222no—
517C2×C4—224no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—224no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—224no—
524C2×C4—222no—
525C2×C4—444no—
526C2×C4—444no—
527C2×C4C22×C4×D1112yes—
528C2×C4C22×C4×D1112yes—
529C2×C4C22×C4×D1118yes—
530C2×C4C22×C4×D1112yes—
531C2×C4#6704012yes—
532C2×C4#6704312yes—
533C22—222no—
534C22—222no—
535C22—222no—
536C22—442no—
537C22—442no—
538C22C23×C4×D1111yescharacteristic
539C22C2×#6704011yescharacteristic
540C22C2×#6704311yescharacteristic
541C22#1062345512yes—
542C22#1062345712yes—
543C4—22no—
544C4—28no—
545C4—22no—
546C4—42no—
547C4—42no—
548C4—44no—
549C4—222no—
550C4—222no—
551C4—222no—
552C4—228no—
553C4—442no—
554C4—444no—
555C4—442no—
556C4#1062310314yes—
557C2—442no—
558C2C2×#1062310311yescharacteristic
559C2#1308181411yescharacteristic
560C2#1308181811yescharacteristic
561C2#1308325712yes—
562C2#1308326312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2331C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2331D11
hypocenterC11#34403
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2331

Complements

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

NH ≅ G/Ntype
3. #13071717C2semidirect
4. #13071708C2semidirect
5. #13071578C2semidirect
9. #13071365C2semidirect
10. #13071364C2semidirect
11. #13071362C2semidirect
12. #13071261C2semidirect
15. C11×#2331C2semidirect
19. #10623259C4semidirect
214. #2331D11semidirect
483. C11#34403semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
#130717802
#130717172
#130717082
#130715782
#130715082
#130714972
#130713712
#130713652
#130713642
#130713622
#130712612
#130710092
#130710082
C11×#23312
#3440311