Finite Group Databasebeta

← #14912439

Subgroups — #14912439

Order 2816.

2358 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623053C211yesmaximal, characteristic
2#13071265C214yesmaximal, complemented
3#13071257C214yesmaximal, complemented
4#13071248C214yesmaximal, complemented
5#13071246C214yesmaximal, complemented
6#13071114C211yesmaximal, characteristic, complemented
7#13071113C211yesmaximal, characteristic, complemented
8#13071111C211yesmaximal, characteristic, complemented
9#13071102C212yesmaximal
10#13071096C212yesmaximal, complemented
11#13071012C212yesmaximal, complemented
12#13071010C212yesmaximal, complemented
13C4×#66925C211yesmaximal, characteristic, complemented
14D11×#376C211yesmaximal, characteristic, complemented
15C11×#2298C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19#10623053C4116yescomplemented
20C2×#66946C2212yes—
21C2×#66940C2212yes—
22C2×(C22⋊D11)⋊C4C2212yes—
23C2×(C22⋊D11)⋊C4C2212yes—
24C2×#66925C2212yes—
25C2×#66925C2211yescharacteristic
26C2×#66925C2211yescharacteristic
27C2×C42×D11C2212yes—
28C2×C42×D11C2211yescharacteristic
29C2×C42×D11C2211yescharacteristic
30C11×#388C2214yes—
31C11×#387C2214yes—
32C4×C11×C4⋊C4C2212yes—
33C4×C11×C22⋊C4C2212yes—
34C11×#376C2211yescharacteristic
35C43×C11C2211yescharacteristic
36C4×C22⋊Dic11C2212yes—
37#10622602C2214yes—
38#10622600C2214yes—
39#10622594C2214yes—
40#10622590C2214yes—
41#10622585C2214yes—
42#10622570C2214yes—
43#10622569C2214yes—
44#10622564C2214yes—
45#10622556C2214yes—
46#10622555C2214yes—
47#10622553C2214yes—
48C4×(C2×D11)⋊C4C2212yes—
49C4×(C2×D11)⋊C4C2212yes—
50C4×(C2×D11)⋊C4C2214yes—
51C4×C4⋊Dic11C2212yes—
52#10622546C2214yes—
53#10622545C2211yescharacteristic
54#10622545C2212yes—
55#10622545C2212yes—
56C4×Dic11⋊C4C2212yes—
57C4×Dic11⋊C4C2212yes—
58C4×Dic11⋊C4C2214yes—
59C42×Dic11C2211yescharacteristic
60#10622282C2214yes—
61#10622281C2214yes—
62#10622278C2214yes—
63#10622277C2214yes—
64D11×#95C2214yes—
65#10622265C2214yes—
66#10622264C2214yes—
67#10622264C2214yes—
68#10622263C2214yes—
69#10622261C2214yes—
70#10622260C2214yes—
71#10622259C2214yes—
72C23×C4×C11C2311yescharacteristic
73C22×C22⋊D11C2311yescharacteristic
74C22×C22⋊D11C2311yescharacteristic
75C23×Dic11C2312yes—
76C2×#4339—28no—
77C2×#4339C2×C418yes—
78C22×D44C2311yescharacteristic
79C22×C4×D11C2311yescharacteristic
80C22×C4×D11C2314yes—
81C22×C4×D11C2312yes—
82C22×C4×D11C2312yes—
83C22×C4×D11C2311yescharacteristic
84C22×Dic22C2311yescharacteristic
85C11×#117C2×C418yescomplemented
86C2×C11×C4⋊C4C2314yes—
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C22⋊C4C2314yes—
89C2×C11×C22⋊C4C2312yes—
90C2×C42×C11C2312yes—
91C2×C42×C11C2312yes—
92C2×C42×C11C2314yes—
93C2×C42×C11C2311yescharacteristic
94C2×C42×C11C2311yescharacteristic
95C2×C22⋊Dic11C2314yes—
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2312yes—
100C2×(C2×D11)⋊C4C2312yes—
101C2×C4⋊Dic11C2314yes—
102C2×Dic11⋊C4C2314yes—
103C2×Dic11⋊C4C2314yes—
104C2×Dic11⋊C4C2314yes—
105C2×Dic11⋊C4C2312yes—
106C2×Dic11⋊C4C2312yes—
107C2×C4×Dic11C2×C418yescomplemented
108C2×C4×Dic11C2314yes—
109C2×C4×Dic11C2312yes—
110C2×C4×Dic11C2312yes—
111C2×C4×Dic11C2314yes—
112C2×C4×Dic11C2311yescharacteristic
113C2×C4×Dic11C2312yes—
114C2×C4×Dic11C2312yes—
115C2×C4×Dic11C2311yescharacteristic
116C2×C4×Dic11C2312yes—
117#66946C2×C4116yes—
118#66940C2×C4116yescomplemented
119(C22⋊D11)⋊C4C2×C4116yes—
120(C22⋊D11)⋊C4C2×C4116yescomplemented
121#66925—28no—
122#66925C2×C418yes—
123#66925C2×C418yescomplemented
124C42×D11—28no—
125C42×D11C2×C418yes—
126C42×D11C2×C418yescomplemented
127C11×#95C2314yes—
128C11×#95C2314yes—
129C11×#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138C11⋊#95C2314yes—
139C11⋊#95C2314yes—
140C11⋊#95C2314yes—
141#34056—111nomaximal, Sylow
142C24×C11C2411yescharacteristic
143C23×D11C2411yescharacteristic
144C23×D11C2411yescharacteristic
145C22×C4×C11—24no—
146C22×C4×C11C22×C414yes—
147C22×C4×C11C2414yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2411yescharacteristic
150C22×C4×C11C2412yes—
151C22×C4×C11C2412yes—
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—24no—
154C2×C22⋊D11—24no—
155C2×C22⋊D11C22×C414yes—
156C2×C22⋊D11C22×C414yes—
157C22×Dic11—44no—
158C22×Dic11C22×C418yes—
159C22×Dic11C2414yes—
160C22×Dic11C2414yes—
161C22×Dic11C2412yes—
162C22×Dic11C2411yescharacteristic
163C22×Dic11C2412yes—
164C22×Dic11C2411yescharacteristic
165#4339—232no—
166C2×D44—24no—
167C2×D44C22×C414yes—
168C2×C4×D11—28no—
169C2×C4×D11—24no—
170C2×C4×D11—44no—
171C2×C4×D11—44no—
172C2×C4×D11—44no—
173C2×C4×D11—44no—
174C2×C4×D11C22×C414yes—
175C2×C4×D11C22×C418yes—
176C2×C4×D11C22×C418yes—
177C2×C4×D11C22×C414yes—
178C2×C4×D11#4118yes—
179C2×Dic22—24no—
180C2×Dic22C22×C414yes—
181C11×C4⋊C4—44no—
182C11×C4⋊C4C22×C418yes—
183C11×C22⋊C4—44no—
184C11×C22⋊C4C22×C418yes—
185C42×C11—24no—
186C42×C11—24no—
187C42×C11—44no—
188C42×C11C22×C414yes—
189C42×C11C22×C414yes—
190C22⋊Dic11—44no—
191(C2×D11)⋊C4—28no—
192(C2×D11)⋊C4—44no—
193(C2×D11)⋊C4—44no—
194(C2×D11)⋊C4C22×C418yes—
195(C2×D11)⋊C4C22×C418yes—
196C4⋊Dic11—44no—
197Dic11⋊C4—28no—
198Dic11⋊C4—44no—
199Dic11⋊C4—44no—
200Dic11⋊C4C22×C418yes—
201Dic11⋊C4C22×C418yes—
202C4×Dic11—28no—
203C4×Dic11—24no—
204C4×Dic11—24no—
205C4×Dic11—44no—
206C4×Dic11C22×C414yes—
207C4×Dic11C22×C418yes—
208C4×Dic11C22×C418yes—
209C4×Dic11C22×C414yes—
210C4×Dic11C22×C418yes—
211C2×C4×#41—111no—
212#2320—114no—
213#2319—114no—
214#2318—114no—
215#2318—114no—
216#2298—111no—
217#2298—111no—
218#2298—111no—
219#2298D1111yescharacteristic, complemented
220#2297—112no—
221#2296—112no—
222#2283—112no—
223#2283—112no—
224C4×#117—111no—
225C2×#376—111no—
226C23×C11—22no—
227C23×C11—24no—
228C23×C11C23×C412yes—
229C23×C11C2511yescharacteristic
230C22×D11—24no—
231C22×D11—22no—
232C22×D11—24no—
233C22×D11C23×C412yes—
234C22×D11C23×C412yes—
235C22×D11C2×#4114yes—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—28no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11C23×C412yes—
247C2×C4×C11C23×C414yes—
248C2×C4×C11C23×C414yes—
249C2×C4×C11C23×C412yes—
250C2×C4×C11C2×#4114yes—
251C22⋊D11—28no—
252C22⋊D11—28no—
253C2×Dic11—22no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—48no—
263C2×Dic11C23×C414yes—
264C2×Dic11C23×C414yes—
265C2×Dic11C23×C412yes—
266C2×Dic11C23×C412yes—
267C2×Dic11C2×#4114yes—
268D44—28no—
269C4×D11—28no—
270C4×D11—48no—
271C4×D11—48no—
272C4×D11—416no—
273C4×D11#117116yes—
274Dic22—28no—
275C22×#41—111no—
276C4×#41—1116no—
277C2×C4×Q8—112no—
278C2×C4×D4—112no—
279C2×C4×D4—112no—
280C2×C4×D4—112no—
281C2×#117—111no—
282C2×#117—111no—
283C2×#117—112no—
284C2×#117C2×D1111yescharacteristic
285C22×C42—111no—
286C22×C42—111no—
287C22×C42—111no—
288C22×C42—112no—
289#391—114no—
290#390—114no—
291#389—114no—
292#389—114no—
293#388—114no—
294#388—114no—
295#388—114no—
296#388C2×D1114yes—
297#387—114no—
298#387—114no—
299#387—114no—
300#387C2×D1114yes—
301#386—114no—
302#386—114no—
303#385—114no—
304#385—114no—
305#383—114no—
306#383—114no—
307#382—114no—
308#382—114no—
309#381—114no—
310#381—114no—
311#380—114no—
312#380—114no—
313C4×C4⋊C4—114no—
314C4×C4⋊C4—112no—
315C4×C4⋊C4—112no—
316C4×C4⋊C4—112no—
317C4×C4⋊C4C2×D1112yes—
318C4×C22⋊C4—112no—
319C4×C22⋊C4—114no—
320C4×C22⋊C4—112no—
321C4×C22⋊C4—112no—
322C4×C22⋊C4C2×D1112yes—
323#376—112no—
324#376—111no—
325#376—112no—
326#376—114no—
327#376C2×D1111yescharacteristic
328C2×#95—114no—
329C43—111no—
330C43C2×D1111yescharacteristic
331C22×C11—22no—
332C22×C11—24no—
333C22×C11—44no—
334C22×C11C24×C411yescharacteristic
335C22×C11C22×#4112yes—
336C22×C11#58514yes—
337C2×D11—24no—
338C2×D11—28no—
339C2×D11—22no—
340C2×D11—24no—
341C2×D11—44no—
342C2×D11C2×#11714yes—
343C4×C11—22no—
344C4×C11—24no—
345C4×C11—24no—
346C4×C11—44no—
347C4×C11—44no—
348C4×C11C2×#11714yes—
349Dic11—22no—
350Dic11—24no—
351Dic11—24no—
352Dic11—44no—
353Dic11—44no—
354Dic11C2×#11714yes—
355C2×#41—118no—
356C2×#41—228no—
357C22×Q8—111no—
358C22×D4—111no—
359C22×D4—111no—
360C22×D4—111no—
361C23×C4—111no—
362C23×C4—112no—
363C23×C4—111no—
364C23×C4—112no—
365C23×C4—112no—
366C23×C4—114no—
367C23×C4C22×D1111yescharacteristic
368C4×Q8—1116no—
369C4×D4—1116no—
370C4×D4—1116no—
371C4×D4—1116no—
372#117—118no—
373#117—118no—
374#117—228no—
375#117C4×D1118yescomplemented
376C2×C4⋊C4—112no—
377C2×C4⋊C4—112no—
378C2×C4⋊C4—114no—
379C2×C4⋊C4—114no—
380C2×C4⋊C4—114no—
381C2×C4⋊C4—114no—
382C2×C4⋊C4C22×D1114yes—
383C2×C4⋊C4C22×D1112yes—
384C2×C22⋊C4—112no—
385C2×C22⋊C4—112no—
386C2×C22⋊C4—114no—
387C2×C22⋊C4—114no—
388C2×C22⋊C4—114no—
389C2×C22⋊C4—114no—
390C2×C22⋊C4C22×D1114yes—
391C2×C22⋊C4C22×D1112yes—
392C2×C42—118no—
393C2×C42—112no—
394C2×C42—112no—
395C2×C42—112no—
396C2×C42—111no—
397C2×C42—111no—
398C2×C42—118no—
399C2×C42—118no—
400C2×C42—114no—
401C2×C42—112no—
402C2×C42—112no—
403C2×C42—114no—
404C2×C42—228no—
405C2×C42C22×D1112yes—
406C2×C42C22×D1112yes—
407C2×C42C22×D1114yes—
408C2×C42C22×D1111yescharacteristic
409C2×C42C22×D1111yescharacteristic
410#95—114no—
411#95—114no—
412#95—114no—
413#95—114no—
414#95—114no—
415#95—114no—
416#95—114no—
417#95—114no—
418#95—114no—
419#95—114no—
420#95—114no—
421#95C22×D1114yes—
422#95C22×D1114yes—
423#95C22×D1114yes—
424C2×C11—42no—
425C2×C11C22×#11711yescharacteristic
426C2×C11#342812yes—
427C2×C11#345514yes—
428D11—24no—
429D11—42no—
430C24—111no—
431C24—111no—
432C24C23×D1111yescharacteristic
433#41—2232no—
434C2×Q8—114no—
435C2×Q8—224no—
436C2×D4—114no—
437C2×D4—114no—
438C2×D4—114no—
439C2×D4—224no—
440C2×D4—224no—
441C2×D4—224no—
442C22×C4—24no—
443C22×C4—111no—
444C22×C4—114no—
445C22×C4—118no—
446C22×C4—112no—
447C22×C4—111no—
448C22×C4—112no—
449C22×C4—118no—
450C22×C4—114no—
451C22×C4—118no—
452C22×C4—118no—
453C22×C4—114no—
454C22×C4—114no—
455C22×C4—228no—
456C22×C4—224no—
457C22×C4—444no—
458C22×C4—444no—
459C22×C4—444no—
460C22×C4—444no—
461C22×C4—444no—
462C22×C4C2×C4×D1114yes—
463C22×C4C23×D1114yes—
464C22×C4C23×D1114yes—
465C22×C4C23×D1111yescharacteristic
466C22×C4C23×D1112yes—
467C22×C4C23×D1112yes—
468C22×C4C23×D1111yescharacteristic
469C4⋊C4—44no—
470C4⋊C4—118no—
471C4⋊C4—118no—
472C4⋊C4—228no—
473C4⋊C4—444no—
474C4⋊C4—444no—
475C4⋊C4—444no—
476C4⋊C4C2×C4×D1118yes—
477C22⋊C4—44no—
478C22⋊C4—118no—
479C22⋊C4—118no—
480C22⋊C4—228no—
481C22⋊C4—444no—
482C22⋊C4—444no—
483C22⋊C4—444no—
484C22⋊C4C2×C4×D1118yes—
485C42—24no—
486C42—24no—
487C42—44no—
488C42—114no—
489C42—114no—
490C42—118no—
491C42—118no—
492C42—118no—
493C42—228no—
494C42—224no—
495C42—224no—
496C42—444no—
497C42C2×C4×D1114yes—
498C42C2×C4×D1114yes—
499C11#3405611yescharacteristic, complemented, Sylow
500C23—22no—
501C23—24no—
502C23—112no—
503C23—114no—
504C23—112no—
505C23—224no—
506C23—222no—
507C23—224no—
508C23C22×C4×D1112yes—
509C23C24×D1111yescharacteristic
510Q8—228no—
511D4—228no—
512D4—228no—
513D4—228no—
514C2×C4—22no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—28no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—112no—
525C2×C4—114no—
526C2×C4—1116no—
527C2×C4—114no—
528C2×C4—114no—
529C2×C4—112no—
530C2×C4—222no—
531C2×C4—224no—
532C2×C4—224no—
533C2×C4—228no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—224no—
538C2×C4—224no—
539C2×C4—224no—
540C2×C4—448no—
541C2×C4—448no—
542C2×C4—4416no—
543C2×C4—448no—
544C2×C4C22×C4×D1112yes—
545C2×C4C22×C4×D1114yes—
546C2×C4C22×C4×D1114yes—
547C2×C4C22×C4×D1112yes—
548C2×C4#41×D1114yes—
549C22—22no—
550C22—24no—
551C22—44no—
552C22—114no—
553C22—228no—
554C22—224no—
555C22—222no—
556C22—224no—
557C22—444no—
558C22C23×C4×D1111yescharacteristic
559C22C2×#41×D1112yes—
560C22#1062345314yes—
561C4—22no—
562C4—24no—
563C4—24no—
564C4—44no—
565C4—44no—
566C4—114no—
567C4—222no—
568C4—224no—
569C4—224no—
570C4—444no—
571C4—444no—
572C4D11×#11714yes—
573C2—42no—
574C2—224no—
575C2—442no—
576C2C2×D11×#11711yescharacteristic
577C2#1308181512yes—
578C2#1308199914yes—
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC11×#2298C2
socle, cosocleC23×C11C25
prime radicalC22×#4339C22
hypercenter#2298D11
hypocenterC11#34056
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2298

Complements

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

NH ≅ G/Ntype
2. #13071265C2semidirect
3. #13071257C2semidirect
4. #13071248C2semidirect
5. #13071246C2semidirect
6. #13071114C2semidirect
7. #13071113C2semidirect
8. #13071111C2semidirect
10. #13071096C2semidirect
11. #13071012C2semidirect
12. #13071010C2semidirect
13. C4×#66925C2semidirect
14. D11×#376C2semidirect
15. C11×#2298C2semidirect
19. #10623053C4semidirect
85. C11×#117C2×C4semidirect
107. C2×C4×Dic11C2×C4semidirect
118. #66940C2×C4semidirect
120. (C22⋊D11)⋊C4C2×C4semidirect
123. #66925C2×C4semidirect
126. C42×D11C2×C4semidirect
219. #2298D11semidirect
375. #117C4×D11semidirect
499. C11#34056semidirect

Maximal subgroups

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

subgroupindex
C2×#106230532
#130712652
#130712572
#130712482
#130712462
#130711142
#130711132
#130711112
#130711022
#130710962
#130710122
#130710102
C4×#669252
D11×#3762
C11×#22982
#3405611