Finite Group Databasebeta

← #14959860

Subgroups — #14959860

Order 2816.

2130 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076997C213yesmaximal, complemented
2#13076996C211yesmaximal, characteristic, complemented
3#13076982C213yesmaximal, complemented
4#13076981C211yesmaximal, characteristic, complemented
5#13076934C213yesmaximal, complemented
6#13076932C211yesmaximal, characteristic, complemented
7#13076930C213yesmaximal, complemented
8#13076928C211yesmaximal, characteristic, complemented
9C4×#66951C213yesmaximal, complemented
10C4×#66929C211yesmaximal, characteristic, complemented
11C4×#66932C213yesmaximal, complemented
12#13071102C213yesmaximal
13#13071096C213yesmaximal, complemented
14C43×D11C211yesmaximal, characteristic, complemented
15C4×C11×#126C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C2×C11×#126C2211yescharacteristic
18C2×#66951C2213yes—
19C2×#66932C2213yes—
20C2×#66929C2211yescharacteristic
21C2×#66925C2213yes—
22C2×C42×D11C2211yescharacteristic
23C2×C42×D11C2213yes—
24C2×C42×D11C2213yes—
25C11×#388C2213yes—
26C11×#387C2213yes—
27C11×#383C2211yescharacteristic
28C4×C11×C4⋊C4C2213yes—
29C4×C11×C22⋊C4C2213yes—
30C43×C11C2211yescharacteristic
31C4×C22⋊Dic11C2213yes—
32#10622603C2213yes—
33#10622602C2213yes—
34#10622602C2213yes—
35#10622594C2213yes—
36#10622591C2213yes—
37#10622585C2213yes—
38#10622585C2213yes—
39#10622570C2213yes—
40#10622570C2213yes—
41#10622569C2213yes—
42#10622569C2213yes—
43#10622564C2213yes—
44#10622558C2213yes—
45#10622557C2213yes—
46#10622553C2213yes—
47C4×(C2×D11)⋊C4C2213yes—
48C4×(C2×D11)⋊C4C2213yes—
49#10622550C2211yescharacteristic
50C4×C4⋊Dic11C2213yes—
51#10622546C2213yes—
52C4×Dic11⋊C4C2213yes—
53C4×Dic11⋊C4C2213yes—
54C42×Dic11C2211yescharacteristic
55C42×Dic11C2213yes—
56C42×Dic11C2213yes—
57#10622283C2213yes—
58#10622282C2213yes—
59#10622281C2213yes—
60#10622281C2213yes—
61#10622278C2213yes—
62#10622278C2213yes—
63#10622268C2213yes—
64#10622267C2213yes—
65#10622266C2213yes—
66#10622265C2213yes—
67#10622264C2213yes—
68#10622264C2213yes—
69#10622260C2213yes—
70#10622260C2213yes—
71#10622259C2213yes—
72#10622259C2213yes—
73C23×C4×C11C2311yescharacteristic
74C22×C22⋊D11C2311yescharacteristic
75C22×C22⋊D11C2311yescharacteristic
76C2×#4339—212no—
77C22×D44C2311yescharacteristic
78C22×C4×D11C2313yes—
79C22×C4×D11C2313yes—
80C22×C4×D11C2311yescharacteristic
81C22×C4×D11C2311yescharacteristic
82C22×Dic22C2311yescharacteristic
83C11×#126—24no—
84C2×C11×C4⋊C4C2313yes—
85C2×C11×C4⋊C4C2313yes—
86C2×C11×C22⋊C4C2313yes—
87C2×C11×C22⋊C4C2313yes—
88C2×C42×C11C2313yes—
89C2×C42×C11C2313yes—
90C2×C42×C11C2313yes—
91C2×C42×C11C2311yescharacteristic
92C2×C22⋊Dic11C2313yes—
93C2×C22⋊Dic11C2313yes—
94C2×(C2×D11)⋊C4C2313yes—
95C2×(C2×D11)⋊C4C2313yes—
96C2×(C2×D11)⋊C4C2313yes—
97C2×(C2×D11)⋊C4C2313yes—
98C2×(C2×D11)⋊C4C2313yes—
99C2×(C2×D11)⋊C4C2313yes—
100C2×C4⋊Dic11C2313yes—
101C2×C4⋊Dic11C2313yes—
102C2×Dic11⋊C4C2313yes—
103C2×Dic11⋊C4C2313yes—
104C2×Dic11⋊C4C2313yes—
105C2×Dic11⋊C4C2313yes—
106C2×Dic11⋊C4C2313yes—
107C2×Dic11⋊C4C2313yes—
108C2×C4×Dic11C2313yes—
109C2×C4×Dic11C2313yes—
110C2×C4×Dic11C2313yes—
111C2×C4×Dic11C2313yes—
112C2×C4×Dic11C2313yes—
113C2×C4×Dic11C2313yes—
114C2×C4×Dic11C2313yes—
115C2×C4×Dic11C2313yes—
116#66951—212no—
117#66932—212no—
118#66929—24no—
119#66925—212no—
120C42×D11—212no—
121C42×D11—24no—
122C42×D11—212no—
123C11×#95C2313yes—
124C11×#95C2313yes—
125C11×#95C2313yes—
126C11×#95C2313yes—
127C11⋊#95C2313yes—
128C11⋊#95C2313yes—
129C11⋊#95C2313yes—
130C11⋊#95C2313yes—
131C11⋊#95C2313yes—
132C11⋊#95C2313yes—
133C11⋊#95C2313yes—
134C11⋊#95C2313yes—
135C11⋊#95C2313yes—
136C11⋊#95C2313yes—
137C11⋊#95C2313yes—
138C11⋊#95C2313yes—
139#36641—111nomaximal, Sylow
140C24×C11C2411yescharacteristic
141C23×D11C2411yescharacteristic
142C23×D11C2411yescharacteristic
143C22×C4×C11—26no—
144C22×C4×C11C2411yescharacteristic
145C22×C4×C11C2413yes—
146C22×C4×C11C2413yes—
147C22×C4×C11C2413yes—
148C22×C4×C11C2413yes—
149C22×C4×C11C2411yescharacteristic
150C2×C22⋊D11—26no—
151C2×C22⋊D11—26no—
152C22×Dic11C2411yescharacteristic
153C22×Dic11C2413yes—
154C22×Dic11C2413yes—
155C22×Dic11C2413yes—
156C22×Dic11C2413yes—
157C22×Dic11C2411yescharacteristic
158#4339—416no—
159C2×D44—26no—
160C2×C4×D11—26no—
161C2×C4×D11—26no—
162C2×C4×D11—26no—
163C2×C4×D11—26no—
164C2×C4×D11—26no—
165C2×C4×D11—26no—
166C2×C4×D11—26no—
167C2×C4×D11#41112yes—
168C2×Dic22—26no—
169C11×C4⋊C4—26no—
170C11×C4⋊C4—26no—
171C11×C22⋊C4—26no—
172C11×C22⋊C4—26no—
173C42×C11—26no—
174C42×C11—26no—
175C42×C11—26no—
176C42×C11#4114yescomplemented
177C22⋊Dic11—26no—
178C22⋊Dic11—26no—
179(C2×D11)⋊C4—26no—
180(C2×D11)⋊C4—26no—
181(C2×D11)⋊C4—26no—
182(C2×D11)⋊C4—26no—
183(C2×D11)⋊C4—26no—
184(C2×D11)⋊C4—26no—
185C4⋊Dic11—26no—
186C4⋊Dic11—26no—
187Dic11⋊C4—26no—
188Dic11⋊C4—26no—
189Dic11⋊C4—26no—
190Dic11⋊C4—26no—
191Dic11⋊C4—26no—
192Dic11⋊C4—26no—
193C4×Dic11—26no—
194C4×Dic11—26no—
195C4×Dic11—26no—
196C4×Dic11—26no—
197C4×Dic11—26no—
198C4×Dic11—26no—
199C4×Dic11—26no—
200C4×Dic11#41112yescomplemented
201#2863—113no—
202#2863—111no—
203#2860—113no—
204#2860—111no—
205#2852—113no—
206#2852—113no—
207#2852—111no—
208#2852—111no—
209C4×#126—113no—
210C4×#126—113no—
211C4×#126—111no—
212C4×#126D1111yescharacteristic, complemented
213#2297—113no—
214#2296—113no—
215C2×C43—111no—
216C23×C11—23no—
217C23×C11—21no—
218C23×C11—23no—
219C23×C11C2511yescharacteristic
220C22×D11—21no—
221C22×D11—23no—
222C22×D11—21no—
223C22×D11—23no—
224C22×D11—23no—
225C22×D11C2×#4116yes—
226C2×C4×C11—23no—
227C2×C4×C11—23no—
228C2×C4×C11—23no—
229C2×C4×C11—23no—
230C2×C4×C11—23no—
231C2×C4×C11—23no—
232C2×C4×C11—23no—
233C2×C4×C11—23no—
234C2×C4×C11—23no—
235C2×C4×C11—23no—
236C2×C4×C11—23no—
237C2×C4×C11—44no—
238C2×C4×C11C2×#4116yes—
239C2×C4×C11C2×#4116yes—
240C2×C4×C11C2×#4116yes—
241C22⋊D11—44no—
242C22⋊D11—44no—
243C2×Dic11—23no—
244C2×Dic11—23no—
245C2×Dic11—23no—
246C2×Dic11—23no—
247C2×Dic11—23no—
248C2×Dic11—23no—
249C2×Dic11—23no—
250C2×Dic11—23no—
251C2×Dic11—23no—
252C2×Dic11—23no—
253C2×Dic11—23no—
254C2×Dic11C2×#4116yes—
255C2×Dic11C2×#4116yes—
256C2×Dic11C2×#4116yes—
257D44—44no—
258C4×D11—224no—
259C4×D11—224no—
260C4×D11—44no—
261C4×D11#126116yescomplemented
262Dic22—44no—
263C22×#41—111no—
264C2×#126—113no—
265C2×#126—113no—
266C2×#126—111no—
267C2×#126C2×D1111yescharacteristic
268C2×#117—113no—
269C22×C42—113no—
270C22×C42—111no—
271C22×C42—113no—
272#391—113no—
273#391—113no—
274#390—113no—
275#390—113no—
276#389—113no—
277#389—113no—
278#389—113no—
279#389—113no—
280#388—113no—
281#388—113no—
282#388—113no—
283#388—113no—
284#388—113no—
285#388—113no—
286#388—113no—
287#388C2×D1113yes—
288#387—113no—
289#387—113no—
290#387—113no—
291#387—113no—
292#387—113no—
293#387—113no—
294#387—113no—
295#387C2×D1113yes—
296#386—113no—
297#386—113no—
298#386—113no—
299#386—113no—
300#385—113no—
301#385—113no—
302#385—113no—
303#385—113no—
304#383—111no—
305#383—113no—
306#383—113no—
307#383C2×D1111yescharacteristic
308C4×C4⋊C4—113no—
309C4×C4⋊C4—113no—
310C4×C4⋊C4—113no—
311C4×C4⋊C4C2×D1113yes—
312C4×C22⋊C4—113no—
313C4×C22⋊C4—113no—
314C4×C22⋊C4—113no—
315C4×C22⋊C4C2×D1113yes—
316C43—113no—
317C43—113no—
318C43—111no—
319C43C2×D1111yescharacteristic
320C22×C11—41no—
321C22×C11—43no—
322C22×C11—43no—
323C22×C11C22×#4111yescharacteristic
324C22×C11C22×#4113yes—
325C22×C11C22×#4113yes—
326C2×D11—26no—
327C2×D11—26no—
328C2×D11—41no—
329C2×D11—43no—
330C2×D11—43no—
331C2×D11C2×#12614yes—
332C4×C11—26no—
333C4×C11—26no—
334C4×C11—41no—
335C4×C11—43no—
336C4×C11—43no—
337C4×C11C2×#12614yes—
338Dic11—26no—
339Dic11—26no—
340Dic11—41no—
341Dic11—43no—
342Dic11—43no—
343Dic11C2×#12614yes—
344C2×#41—2212no—
345C22×Q8—111no—
346C22×D4—111no—
347C22×D4—111no—
348C22×D4—111no—
349C23×C4—111no—
350C23×C4—113no—
351C23×C4—113no—
352C23×C4—111no—
353C23×C4C22×D1111yescharacteristic
354#126—24no—
355#126—2212no—
356#126—2212no—
357#126—224no—
358#117—2212no—
359C2×C4⋊C4—113no—
360C2×C4⋊C4—113no—
361C2×C4⋊C4—113no—
362C2×C4⋊C4—113no—
363C2×C4⋊C4—113no—
364C2×C4⋊C4—113no—
365C2×C4⋊C4—113no—
366C2×C4⋊C4—113no—
367C2×C4⋊C4C22×D1113yes—
368C2×C4⋊C4C22×D1113yes—
369C2×C22⋊C4—113no—
370C2×C22⋊C4—113no—
371C2×C22⋊C4—113no—
372C2×C22⋊C4—113no—
373C2×C22⋊C4—113no—
374C2×C22⋊C4—113no—
375C2×C22⋊C4—113no—
376C2×C22⋊C4—113no—
377C2×C22⋊C4C22×D1113yes—
378C2×C22⋊C4C22×D1113yes—
379C2×C42—113no—
380C2×C42—113no—
381C2×C42—113no—
382C2×C42—113no—
383C2×C42—113no—
384C2×C42—113no—
385C2×C42—113no—
386C2×C42—113no—
387C2×C42—2212no—
388C2×C42—2212no—
389C2×C42—224no—
390C2×C42C22×D1113yes—
391C2×C42C22×D1113yes—
392C2×C42C22×D1113yes—
393C2×C42C22×D1111yescharacteristic
394#95—113no—
395#95—113no—
396#95—113no—
397#95—113no—
398#95—113no—
399#95—113no—
400#95—113no—
401#95—113no—
402#95—113no—
403#95—113no—
404#95—113no—
405#95—113no—
406#95C22×D1113yes—
407#95C22×D1113yes—
408#95C22×D1113yes—
409#95C22×D1113yes—
410C2×C11—81no—
411C2×C11C22×#12611yescharacteristic
412C2×C11#344413yes—
413C2×C11#344413yes—
414D11—24no—
415D11—81no—
416C24—111no—
417C24—111no—
418C24C23×D1111yescharacteristic
419#41—4416no—
420C2×Q8—226no—
421C2×D4—226no—
422C2×D4—226no—
423C2×D4—226no—
424C22×C4—26no—
425C22×C4—111no—
426C22×C4—1112no—
427C22×C4—113no—
428C22×C4—113no—
429C22×C4—111no—
430C22×C4—113no—
431C22×C4—113no—
432C22×C4—226no—
433C22×C4—226no—
434C22×C4—226no—
435C22×C4—226no—
436C22×C4—226no—
437C22×C4—226no—
438C22×C4—226no—
439C22×C4C23×D1111yescharacteristic
440C22×C4C23×D1113yes—
441C22×C4C23×D1113yes—
442C22×C4C23×D1113yes—
443C22×C4C23×D1113yes—
444C22×C4C23×D1111yescharacteristic
445C4⋊C4—26no—
446C4⋊C4—26no—
447C4⋊C4—226no—
448C4⋊C4—226no—
449C4⋊C4—226no—
450C4⋊C4—226no—
451C4⋊C4—226no—
452C4⋊C4—226no—
453C4⋊C4—226no—
454C4⋊C4—226no—
455C22⋊C4—26no—
456C22⋊C4—26no—
457C22⋊C4—226no—
458C22⋊C4—226no—
459C22⋊C4—226no—
460C22⋊C4—226no—
461C22⋊C4—226no—
462C22⋊C4—226no—
463C22⋊C4—226no—
464C22⋊C4—226no—
465C42—26no—
466C42—26no—
467C42—26no—
468C42—1112no—
469C42—226no—
470C42—226no—
471C42—226no—
472C42—226no—
473C42—226no—
474C42—226no—
475C42—226no—
476C42#433914yescomplemented
477C11#3664111yescharacteristic, complemented, Sylow
478C23—21no—
479C23—23no—
480C23—23no—
481C23—116no—
482C23—221no—
483C23—223no—
484C23—221no—
485C23—223no—
486C23—223no—
487C23C24×D1111yescharacteristic
488Q8—444no—
489D4—444no—
490D4—444no—
491D4—444no—
492C2×C4—23no—
493C2×C4—23no—
494C2×C4—23no—
495C2×C4—23no—
496C2×C4—23no—
497C2×C4—23no—
498C2×C4—23no—
499C2×C4—23no—
500C2×C4—23no—
501C2×C4—23no—
502C2×C4—23no—
503C2×C4—44no—
504C2×C4—116no—
505C2×C4—1116no—
506C2×C4—116no—
507C2×C4—116no—
508C2×C4—2224no—
509C2×C4—2224no—
510C2×C4—223no—
511C2×C4—223no—
512C2×C4—223no—
513C2×C4—223no—
514C2×C4—223no—
515C2×C4—223no—
516C2×C4—223no—
517C2×C4—223no—
518C2×C4—223no—
519C2×C4—223no—
520C2×C4—223no—
521C2×C4—444no—
522C2×C4C2×#433916yes—
523C2×C4#41×D1116yes—
524C2×C4#41×D1116yes—
525C22—41no—
526C22—43no—
527C22—43no—
528C22—114no—
529C22—226no—
530C22—226no—
531C22—441no—
532C22—443no—
533C22—443no—
534C22C22×#433911yescharacteristic
535C22C2×#41×D1113yes—
536C22C2×#41×D1113yes—
537C4—26no—
538C4—26no—
539C4—41no—
540C4—43no—
541C4—43no—
542C4—114no—
543C4—226no—
544C4—226no—
545C4—441no—
546C4—443no—
547C4—443no—
548C4D11×#12614yes—
549C2—81no—
550C2—224no—
551C2—881no—
552C2C2×D11×#12611yescharacteristic
553C2#1308190913yes—
554C2#1308191013yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC4×C11×#126C2
prime radicalC22×#4339C22
hypercenterC4×#126D11
hypocenterC11#36641
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#126

Complements

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

NH ≅ G/Ntype
1. #13076997C2semidirect
2. #13076996C2semidirect
3. #13076982C2semidirect
4. #13076981C2semidirect
5. #13076934C2semidirect
6. #13076932C2semidirect
7. #13076930C2semidirect
8. #13076928C2semidirect
9. C4×#66951C2semidirect
10. C4×#66929C2semidirect
11. C4×#66932C2semidirect
13. #13071096C2semidirect
14. C43×D11C2semidirect
15. C4×C11×#126C2semidirect
176. C42×C11#41semidirect
200. C4×Dic11#41semidirect
212. C4×#126D11semidirect
261. C4×D11#126semidirect
476. C42#4339semidirect
477. C11#36641semidirect

Maximal subgroups

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

subgroupindex
#130769972
#130769962
#130769822
#130769812
#130769342
#130769322
#130769302
#130769282
C4×#669512
C4×#669292
C4×#669322
#130711022
#130710962
C43×D112
C4×C11×#1262
#3664111