Finite Group Databasebeta

← #14914220

Subgroups — #14914220

Order 2816.

2310 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623219C211yesmaximal, characteristic
2#13071624C214yesmaximal
3#13071618C214yesmaximal
4#13071570C214yesmaximal, complemented
5#13071530C214yesmaximal, complemented
6#13071358C211yesmaximal, characteristic, complemented
7#13071357C211yesmaximal, characteristic, complemented
8#13071355C211yesmaximal, characteristic, complemented
9#13071238C212yesmaximal
10#13071187C212yesmaximal, complemented
11C4×#66941C212yesmaximal, complemented
12D11×#384C211yesmaximal, characteristic
13#13070970C212yesmaximal
14#13070955C211yesmaximal, characteristic
15C11×#2330C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17#10623219C4116yescomplemented
18C2×#66949C2214yes—
19C2×#66945C2212yes—
20C2×C4⋊C4×D11C2212yes—
21C2×C4⋊C4×D11C2214yes—
22C2×#66941C2212yes—
23C2×#66940C2214yes—
24C2×#66940C2214yes—
25C2×#66925C2211yescharacteristic
26C2×#66925C2211yescharacteristic
27C2×C42×D11C2211yescharacteristic
28C2×#66923C2211yescharacteristic
29C2×C4×Dic22C2214yes—
30C11×#389C2214yes—
31C11×#389C2212yes—
32C11×#387C2214yes—
33C11×#384C2211yescharacteristic
34C4×C11×C4⋊C4C2212yes—
35C11×#376C2211yescharacteristic
36#10622602C2214yes—
37#10622598C2214yes—
38#10622598C2212yes—
39#10622594C2214yes—
40#10622591C2214yes—
41#10622589C2212yes—
42#10622589C2214yes—
43#10622589C2214yes—
44C4⋊C4×Dic11C2212yes—
45C4⋊C4×Dic11C2212yes—
46#10622586C2212yes—
47#10622585C2214yes—
48#10622585C2214yes—
49C4×(C2×D11)⋊C4C2214yes—
50#10622548C2211yescharacteristic
51C4×C4⋊Dic11C2212yes—
52#10622545C2211yescharacteristic
53C4×Dic11⋊C4C2214yes—
54C4×Dic11⋊C4C2214yes—
55C42×Dic11C2211yescharacteristic
56C42×Dic11C2211yescharacteristic
57#10622541C2212yes—
58#10622281C2214yes—
59#10622279C2212yes—
60#10622279C2214yes—
61#10622279C2212yes—
62#10622268C2214yes—
63#10622263C2214yes—
64#10622262C2214yes—
65#10622262C2212yes—
66#10622262C2212yes—
67#10622262C2214yes—
68#10622260C2214yes—
69#10622260C2214yes—
70#10622259C2214yes—
71#10622259C2214yes—
72C22×C4×D11C2312yes—
73C22×C4×D11C2314yes—
74C22×C4×D11C2311yescharacteristic
75C22×Dic22C2314yes—
76C11×#125C2×C418yescomplemented
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C4⋊C4C2312yes—
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2314yes—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×(C2×D11)⋊C4C2311yescharacteristic
87C2×(C2×D11)⋊C4C2311yescharacteristic
88C2×(C2×D11)⋊C4C2314yes—
89C2×(C2×D11)⋊C4C2312yes—
90C2×C4⋊Dic11C2312yes—
91C2×C4⋊Dic11C2314yes—
92C2×C4⋊Dic11C2314yes—
93C2×C4⋊Dic11C2312yes—
94C2×Dic11⋊C4C2314yes—
95C2×Dic11⋊C4C2311yescharacteristic
96C2×Dic11⋊C4C2311yescharacteristic
97C2×Dic11⋊C4C2314yes—
98C2×Dic11⋊C4C2314yes—
99C2×Dic11⋊C4C2314yes—
100C2×Dic11⋊C4C2314yes—
101C2×Dic11⋊C4C2314yes—
102C2×Dic11⋊C4C2314yes—
103C2×Dic11⋊C4C2312yes—
104C2×C4×Dic11C2312yes—
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2312yes—
107C2×C4×Dic11C2312yes—
108C2×C4×Dic11C2312yes—
109C2×C4×Dic11C2314yes—
110C2×C4×Dic11C2314yes—
111C2×C4×Dic11C2314yes—
112C2×C4×Dic11C2312yes—
113C2×C4×Dic11C2311yescharacteristic
114C2×C4×Dic11C2314yes—
115C2×C4×Dic11C2311yescharacteristic
116#66949C2×C4132yes—
117#66945C2×C4116yes—
118C4⋊C4×D11—28no—
119C4⋊C4×D11—48no—
120#66941C2×C4116yescomplemented
121#66940—48no—
122#66940C2×C4132yescomplemented
123#66925—24no—
124#66925Q818yescomplemented
125C42×D11C2×C418yes—
126#66923C2×C418yescomplemented
127C4×Dic22—48no—
128C11×#95C2314yes—
129C11×#95C2314yes—
130C11×#95C2312yes—
131C11×#95C2312yes—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138C11⋊#95C2312yes—
139C11⋊#95C2312yes—
140#34214—111nomaximal, Sylow
141C23×D11C2411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C22×C4×C11C2414yes—
144C22×C4×C11C2411yescharacteristic
145C22×C4×C11C2414yes—
146C22×C4×C11C2412yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2411yescharacteristic
149C22×Dic11C2411yescharacteristic
150C22×Dic11C2414yes—
151C22×Dic11C2411yescharacteristic
152C22×Dic11C2414yes—
153C22×Dic11C2412yes—
154C22×Dic11C2411yescharacteristic
155C22×Dic11C2412yes—
156C2×C4×D11—24no—
157C2×C4×D11—24no—
158C2×C4×D11—28no—
159C2×C4×D11—44no—
160C2×C4×D11—44no—
161C2×C4×D11C22×C418yes—
162C2×C4×D11C22×C414yes—
163C2×C4×D11C2×Q814yes—
164C2×C4×D11#4114yes—
165C2×Dic22—28no—
166C2×Dic22—28no—
167C2×Dic22C22×C4116yes—
168C11×C4⋊C4—24no—
169C11×C4⋊C4—44no—
170C11×C4⋊C4—44no—
171C11×C4⋊C4C22×C4116yes—
172C11×C4⋊C4C22×C418yes—
173C42×C11—22no—
174C42×C11—44no—
175C42×C11C22×C414yes—
176C42×C11C2×Q814yes—
177(C2×D11)⋊C4—22no—
178(C2×D11)⋊C4—22no—
179(C2×D11)⋊C4C22×C4116yes—
180(C2×D11)⋊C4C2×Q818yes—
181C4⋊Dic11—24no—
182C4⋊Dic11—44no—
183C4⋊Dic11—44no—
184C4⋊Dic11C22×C418yes—
185Dic11⋊C4—22no—
186Dic11⋊C4—22no—
187Dic11⋊C4—28no—
188Dic11⋊C4—28no—
189Dic11⋊C4—28no—
190Dic11⋊C4—44no—
191Dic11⋊C4—44no—
192Dic11⋊C4C22×C4116yes—
193Dic11⋊C4C22×C4116yes—
194Dic11⋊C4C2×Q818yes—
195C4×Dic11—24no—
196C4×Dic11—24no—
197C4×Dic11—24no—
198C4×Dic11—24no—
199C4×Dic11—22no—
200C4×Dic11—44no—
201C4×Dic11—44no—
202C4×Dic11—44no—
203C4×Dic11C22×C418yes—
204C4×Dic11C22×C414yes—
205C4×Dic11C22×C4116yes—
206C4×Dic11C2×Q814yes—
207C2×#533—111no—
208#2360—114no—
209#2360—114no—
210#2355—114no—
211Q8×C4⋊C4—114no—
212#2330—111no—
213#2330—111no—
214#2330—111no—
215#2330D1111yescharacteristic, complemented
216#2317—112no—
217C4×C4⋊Q8—112no—
218C4×C4⋊Q8—112no—
219C2×#384—111no—
220#2274—112no—
221C4×#117—111no—
222C23×C11C2511yescharacteristic
223C22×D11—22no—
224C22×D11—22no—
225C22×D11C23×C412yes—
226C22×D11C22×Q812yes—
227C22×D11C2×#4112yes—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—22no—
241C2×C4×C11C23×C414yes—
242C2×C4×C11C23×C418yes—
243C2×C4×C11C23×C412yes—
244C2×C4×C11C22×Q814yes—
245C2×C4×C11C22×Q812yes—
246C2×C4×C11C2×#4112yes—
247C2×Dic11—22no—
248C2×Dic11—24no—
249C2×Dic11—22no—
250C2×Dic11—24no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—24no—
254C2×Dic11—22no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—22no—
258C2×Dic11C23×C418yes—
259C2×Dic11C23×C412yes—
260C2×Dic11C23×C414yes—
261C2×Dic11C22×Q814yes—
262C2×Dic11C22×Q812yes—
263C2×Dic11C2×#4112yes—
264C2×Dic11H(5,𝔽2)14yes—
265C2×Dic112−1+414yes—
266C4×D11—216no—
267C4×D11—88no—
268C4×D11C4×Q8116yescomplemented
269Dic22—232no—
270#533—1116no—
271C2×C4⋊Q8—112no—
272C2×#125—111no—
273C2×#125C2×D1111yescharacteristic
274C2×C22⋊Q8—114no—
275C2×C4×Q8—114no—
276C2×C4×Q8—114no—
277C2×C4×Q8—114no—
278C2×#117—112no—
279C2×#117—111no—
280C2×#117—111no—
281C22×C4⋊C4—112no—
282C22×C4⋊C4—114no—
283C22×C42—111no—
284#391—114no—
285#391—114no—
286#389—112no—
287#389—112no—
288#389—114no—
289#389—114no—
290#389—114no—
291#389—112no—
292#389—114no—
293#389—114no—
294#389C2×D1112yes—
295#389C2×D1114yes—
296#387—114no—
297#387—114no—
298#387—114no—
299#387C2×D1114yes—
300#385—114no—
301#385—114no—
302#384—112no—
303#384—114no—
304#384—114no—
305#384—111no—
306#384C2×D1111yescharacteristic
307#382—114no—
308C4×C4⋊C4—112no—
309C4×C4⋊C4—112no—
310C4×C4⋊C4—112no—
311C4×C4⋊C4—114no—
312C4×C4⋊C4—114no—
313C4×C4⋊C4—114no—
314C4×C4⋊C4—112no—
315C4×C4⋊C4—114no—
316C4×C4⋊C4—112no—
317C4×C4⋊C4C2×D1112yes—
318C4×C22⋊C4—114no—
319C4×C22⋊C4—112no—
320C4×C22⋊C4—112no—
321C4×C22⋊C4—114no—
322#376—111no—
323#376C2×D1111yescharacteristic
324C43—111no—
325C43—111no—
326C22×C11C24×C411yescharacteristic
327C22×C11C23×Q811yescharacteristic
328C22×C11C22×#4111yescharacteristic
329C22×C11C2×H(5,𝔽2)12yes—
330C22×C11C2×2−1+412yes—
331C2×D11—24no—
332C2×D11—24no—
333C2×D11—22no—
334C2×D11—22no—
335C2×D11C2×C4×Q814yes—
336C4×C11—28no—
337C4×C11—24no—
338C4×C11—24no—
339C4×C11—41no—
340C4×C11—44no—
341C4×C11—41no—
342C4×C11C2×C4×Q814yes—
343Dic11—28no—
344Dic11—24no—
345Dic11—44no—
346Dic11—41no—
347Dic11—41no—
348Dic11C2×C4×Q814yes—
349Dic11#52018yes—
350C22×Q8—114no—
351C23×C4—111no—
352C23×C4—112no—
353C23×C4—114no—
354C4⋊Q8—1116no—
355#125—118no—
356#125C4×D1118yescomplemented
357C22⋊Q8—1132no—
358C4×Q8—1132no—
359C4×Q8—448no—
360C4×Q8—448no—
361#117—1116no—
362#117—118no—
363#117—224no—
364C2×C4⋊C4—112no—
365C2×C4⋊C4—112no—
366C2×C4⋊C4—114no—
367C2×C4⋊C4—114no—
368C2×C4⋊C4—114no—
369C2×C4⋊C4—114no—
370C2×C4⋊C4—114no—
371C2×C4⋊C4—112no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—114no—
375C2×C4⋊C4—114no—
376C2×C4⋊C4—114no—
377C2×C4⋊C4—114no—
378C2×C4⋊C4—228no—
379C2×C4⋊C4—448no—
380C2×C4⋊C4C22×D1112yes—
381C2×C4⋊C4C22×D1114yes—
382C2×C4⋊C4C22×D1114yes—
383C2×C4⋊C4C22×D1112yes—
384C2×C4⋊C4C22×D1114yes—
385C2×C22⋊C4—114no—
386C2×C22⋊C4—112no—
387C2×C22⋊C4—111no—
388C2×C22⋊C4—111no—
389C2×C42—114no—
390C2×C42—111no—
391C2×C42—112no—
392C2×C42—111no—
393C2×C42—118no—
394C2×C42—111no—
395C2×C42—112no—
396C2×C42—112no—
397C2×C42—112no—
398C2×C42—112no—
399C2×C42—114no—
400C2×C42—114no—
401C2×C42—114no—
402C2×C42C22×D1111yescharacteristic
403C2×C42C22×D1114yes—
404C2×C42C22×D1111yescharacteristic
405C2×C42C22×D1111yescharacteristic
406#95—112no—
407#95—112no—
408#95—114no—
409#95—114no—
410#95—114no—
411#95—114no—
412#95—114no—
413#95—114no—
414#95C22×D1112yes—
415#95C22×D1112yes—
416#95C22×D1114yes—
417#95C22×D1114yes—
418C2×C11C22×C4×Q811yescharacteristic
419C2×C11C2×#52012yes—
420C2×C11#350312yes—
421C2×C11#350811yescharacteristic
422C2×C11#350911yescharacteristic
423D11—24no—
424C24—111no—
425C2×Q8—1116no—
426C2×Q8—228no—
427C2×Q8—228no—
428C22×C4—111no—
429C22×C4—112no—
430C22×C4—114no—
431C22×C4—114no—
432C22×C4—114no—
433C22×C4—112no—
434C22×C4—114no—
435C22×C4—118no—
436C22×C4—111no—
437C22×C4—114no—
438C22×C4—111no—
439C22×C4—224no—
440C22×C4—224no—
441C22×C4—228no—
442C22×C4—444no—
443C22×C4—444no—
444C22×C4C23×D1111yescharacteristic
445C22×C4C23×D1114yes—
446C22×C4C23×D1111yescharacteristic
447C22×C4C23×D1114yes—
448C22×C4C23×D1112yes—
449C22×C4C23×D1112yes—
450C22×C4C23×D1111yescharacteristic
451C4⋊C4—24no—
452C4⋊C4—44no—
453C4⋊C4—44no—
454C4⋊C4—118no—
455C4⋊C4—1116no—
456C4⋊C4—1116no—
457C4⋊C4—118no—
458C4⋊C4—228no—
459C4⋊C4—228no—
460C4⋊C4—228no—
461C4⋊C4—222no—
462C4⋊C4—222no—
463C4⋊C4—224no—
464C4⋊C4—444no—
465C4⋊C4—444no—
466C4⋊C4—444no—
467C4⋊C4—444no—
468C4⋊C4C2×C4×D1118yes—
469C4⋊C4C2×C4×D11116yes—
470C22⋊C4—1116no—
471C22⋊C4—118no—
472C22⋊C4—222no—
473C22⋊C4—222no—
474C42—22no—
475C42—44no—
476C42—118no—
477C42—114no—
478C42—1116no—
479C42—114no—
480C42—224no—
481C42—224no—
482C42—224no—
483C42—224no—
484C42—222no—
485C42—444no—
486C42—444no—
487C42—444no—
488C42C2×C4×D1114yes—
489C42Q8×D1114yes—
490C11#3421411yescharacteristic, complemented, Sylow
491C23—112no—
492C23—112no—
493C23—112no—
494C23—222no—
495C23—222no—
496C23C24×D1111yescharacteristic
497Q8—2232no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—112no—
512C2×C4—114no—
513C2×C4—112no—
514C2×C4—112no—
515C2×C4—114no—
516C2×C4—114no—
517C2×C4—1116no—
518C2×C4—118no—
519C2×C4—114no—
520C2×C4—2216no—
521C2×C4—222no—
522C2×C4—224no—
523C2×C4—222no—
524C2×C4—224no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—224no—
528C2×C4—222no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—222no—
532C2×C4—888no—
533C2×C4C22×C4×D1114yes—
534C2×C4C22×C4×D1118yes—
535C2×C4C22×C4×D1112yes—
536C2×C4C2×Q8×D1114yes—
537C2×C4C2×Q8×D1112yes—
538C2×C4#41×D1112yes—
539C22—114no—
540C22—224no—
541C22—222no—
542C22—222no—
543C22—224no—
544C22C23×C4×D1111yescharacteristic
545C22C22×Q8×D1111yescharacteristic
546C22C2×#41×D1111yescharacteristic
547C22D11×H(5,𝔽2)12yes—
548C22D11×2−1+412yes—
549C4—24no—
550C4—24no—
551C4—28no—
552C4—44no—
553C4—41no—
554C4—41no—
555C4—114no—
556C4—118no—
557C4—224no—
558C4—228no—
559C4—444no—
560C4—441no—
561C4—441no—
562C4C4×Q8×D1114yes—
563C2—224no—
564C2C2×C4×Q8×D1111yescharacteristic
565C2D11×#52012yes—
566C2#1308243112yes—
567C2#1308248811yescharacteristic
568C2#1308249811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2330C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2330D11
hypocenterC11#34214
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2330

Complements

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

NH ≅ G/Ntype
4. #13071570C2semidirect
5. #13071530C2semidirect
6. #13071358C2semidirect
7. #13071357C2semidirect
8. #13071355C2semidirect
10. #13071187C2semidirect
11. C4×#66941C2semidirect
15. C11×#2330C2semidirect
17. #10623219C4semidirect
76. C11×#125C2×C4semidirect
120. #66941C2×C4semidirect
122. #66940C2×C4semidirect
124. #66925Q8semidirect
126. #66923C2×C4semidirect
215. #2330D11semidirect
268. C4×D11C4×Q8semidirect
356. #125C4×D11semidirect
490. C11#34214semidirect

Maximal subgroups

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

subgroupindex
C2×#106232192
#130716242
#130716182
#130715702
#130715302
#130713582
#130713572
#130713552
#130712382
#130711872
C4×#669412
D11×#3842
#130709702
#130709552
C11×#23302
#3421411