Finite Group Databasebeta

← #15617123

Subgroups — #15617123

Order 2816.

1898 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076566C212yesmaximal, complemented
2#13074988C211yesmaximal, characteristic, complemented
3#13074196C212yesmaximal, complemented
4#13074021C212yesmaximal, complemented
5#13073876C214yesmaximal, complemented
6#13072810C214yesmaximal, complemented
7#13072716C214yesmaximal, complemented
8#13071948C212yesmaximal
9#13071752C212yesmaximal, complemented
10#13071616C214yesmaximal, complemented
11#13071103C211yesmaximal, characteristic
12#13071097C212yesmaximal, complemented
13C11×#2724C211yesmaximal, characteristic, complemented
14C22×#4341C2211yescharacteristic
15C2×C11×#123C2212yes—
16C2×#66982C2212yes—
17C22×Dic11⋊C4C2212yes—
18C2×#66945C2212yes—
19C2×#66945C2211yescharacteristic
20C2×#66945C2212yes—
21C2×#66940C2212yes—
22C2×#66931C2214yes—
23C2×C42×D11C2211yescharacteristic
24C11×#398C2212yes—
25C11×#397C2214yes—
26C11×#390C2211yescharacteristic
27C11×#389C2212yes—
28C11×#385C2214yes—
29#10622834C2211yescharacteristic
30#10622833C2212yes—
31C4×C22⋊Dic11C2214yes—
32#10622606C2212yes—
33#10622602C2214yes—
34#10622598C2212yes—
35#10622595C2214yes—
36#10622594C2214yes—
37#10622592C2212yes—
38#10622592C2214yes—
39C4⋊C4×Dic11C2214yes—
40#10622587C2211yescharacteristic
41#10622586C2212yes—
42#10622585C2214yes—
43#10622585C2214yes—
44#10622572C2214yes—
45#10622571C2212yes—
46#10622569C2214yes—
47#10622564C2214yes—
48#10622564C2214yes—
49#10622561C2214yes—
50#10622559C2214yes—
51#10622556C2212yes—
52C22⋊C4×Dic11C2214yes—
53C22⋊C4×Dic11C2214yes—
54#10622542C2211yescharacteristic
55#10622541C2212yes—
56#10622286C2212yes—
57#10622282C2214yes—
58#10622281C2214yes—
59#10622273C2214yes—
60#10622267C2214yes—
61#10622266C2214yes—
62#10622266C2214yes—
63#10622265C2214yes—
64#10622264C2212yes—
65#10622262C2214yes—
66#10622259C2214yes—
67C22×D4×C11C2311yescharacteristic
68C23×C4×C11C2312yes—
69C22×C22⋊D11C2312yes—
70C23×Dic11C2312yes—
71C23×Dic11C2312yes—
72C2×#4341—24no—
73C2×#4341—42no—
74C2×#4341—42no—
75C22×C4×D11C2312yes—
76C22×C4×D11C2311yescharacteristic
77C22×Dic22C2312yes—
78C22×Dic22C2311yescharacteristic
79C11×#123—28no—
80C2×C11×C4⋊C4C2312yes—
81C2×C11×C4⋊C4C2314yes—
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4C2314yes—
86C2×C11×C22⋊C4C2314yes—
87C2×C11×C22⋊C4C2312yes—
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11C2314yes—
90C2×C22⋊Dic11C2314yes—
91C2×C22⋊Dic11C2312yes—
92#66982—44no—
93C2×(C2×D11)⋊C4C2314yes—
94C2×(C2×D11)⋊C4C2314yes—
95C2×(C2×D11)⋊C4C2312yes—
96C2×C4⋊Dic11C2314yes—
97C2×C4⋊Dic11C2312yes—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2312yes—
100C2×Dic11⋊C4—44no—
101C2×Dic11⋊C4C2314yes—
102C2×Dic11⋊C4C2314yes—
103C2×Dic11⋊C4C2314yes—
104C2×Dic11⋊C4C2314yes—
105C2×Dic11⋊C4C2314yes—
106C2×C4×Dic11C2314yes—
107C2×C4×Dic11C2312yes—
108C2×C4×Dic11C2312yes—
109C2×C4×Dic11C2311yescharacteristic
110C2×C4×Dic11C2314yes—
111C2×C4×Dic11C2314yes—
112#66945—28no—
113#66945—42no—
114#66945—44no—
115#66940—44no—
116#66931—216no—
117C42×D11—42no—
118C11×#95C2314yes—
119C11×#95C2314yes—
120C11×#95C2312yes—
121C11⋊#95C2314yes—
122C11⋊#95C2314yes—
123C11⋊#95C2314yes—
124C11⋊#95C2314yes—
125C11⋊#95C2312yes—
126C11⋊#95C2314yes—
127C11⋊#95C2314yes—
128C11⋊#95C2314yes—
129C11⋊#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132#60046—111nomaximal, Sylow
133C24×C11C2412yes—
134C23×D11C2411yescharacteristic
135C2×D4×C11—41no—
136C2×D4×C11—41no—
137C2×D4×C11#4114yes—
138C22×C4×C11—24no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11C2414yes—
142C22×C4×C11C2412yes—
143C22×C4×C11C2414yes—
144C22×C4×C11C2411yescharacteristic
145C22×C4×C11C2412yes—
146C2×C22⋊D11—24no—
147C2×C22⋊D11—24no—
148C2×C22⋊D11—42no—
149C22×Dic11—28no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—42no—
153C22×Dic11—42no—
154C22×Dic11C2412yes—
155C22×Dic11C2412yes—
156C22×Dic11C2414yes—
157C22×Dic11C2414yes—
158C22×Dic11C2411yescharacteristic
159C22×Dic11C2412yes—
160#4341—416no—
161C2×C4×D11—22no—
162C2×C4×D11—24no—
163C2×C4×D11—24no—
164C2×C4×D11—22no—
165C2×C4×D11—24no—
166C2×C4×D11—22no—
167C2×Dic22—28no—
168C2×Dic22—22no—
169C2×Dic22—42no—
170C2×Dic22—41no—
171C2×Dic22—41no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—28no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4—41no—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—28no—
179C11×C22⋊C4—28no—
180C42×C11—41no—
181C22⋊Dic11—28no—
182C22⋊Dic11—28no—
183C22⋊Dic11—42no—
184(C2×D11)⋊C4—28no—
185(C2×D11)⋊C4—28no—
186(C2×D11)⋊C4—42no—
187C4⋊Dic11—28no—
188C4⋊Dic11—42no—
189C4⋊Dic11—41no—
190C4⋊Dic11#4118yescomplemented
191Dic11⋊C4—28no—
192Dic11⋊C4—28no—
193Dic11⋊C4—28no—
194Dic11⋊C4—44no—
195Dic11⋊C4—44no—
196C4×Dic11—28no—
197C4×Dic11—24no—
198C4×Dic11—42no—
199C4×Dic11—41no—
200C4×Dic11—44no—
201C4×Dic11—44no—
202#2805—112no—
203#2724D1111yescharacteristic, complemented
204#2683—111no—
205#2599—112no—
206#2586—112no—
207#2573—114no—
208#2477—114no—
209#2470—114no—
210#2406—112no—
211#2374—112no—
212#2360—114no—
213#2297—111no—
214#2296—112no—
215C23×C11—24no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—24no—
219C23×C11C2×#4114yes—
220C23×C11C2511yescharacteristic
221C22×D11—22no—
222C22×D11—21no—
223C22×D11—21no—
224C22×D11—22no—
225C22×D11H(5,𝔽2)12yes—
226D4×C11—44no—
227C2×C4×C11—22no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—84no—
240C2×C4×C11C2×#4112yes—
241C2×C4×C11C2×#4114yes—
242C22⋊D11—48no—
243C2×Dic11—22no—
244C2×Dic11—24no—
245C2×Dic11—21no—
246C2×Dic11—22no—
247C2×Dic11—21no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—48no—
258C2×Dic11—48no—
259C2×Dic11C2×#4118yes—
260C2×Dic11H(5,𝔽2)12yes—
261C2×Dic112−1+414yes—
262C4×D11—216no—
263C4×D11—28no—
264Dic22—48no—
265Dic22—44no—
266C22×#41—111no—
267C2×#123—112no—
268C2×#123C2×D1112yes—
269C2×C22⋊Q8—114no—
270C2×C4×Q8—112no—
271C2×#117—112no—
272C2×#117—111no—
273C2×#117—112no—
274C22×C4⋊C4—112no—
275C22×C42—111no—
276#400—114no—
277#400—114no—
278#398C2×D1112yes—
279#397—112no—
280#397C2×D1114yes—
281#396—114no—
282#395—112no—
283#395—114no—
284#394—114no—
285#393—112no—
286#391—111no—
287#391—111no—
288#391—114no—
289#390—111no—
290#390C2×D1111yescharacteristic
291#389—112no—
292#389—114no—
293#389—112no—
294#389—114no—
295#389—112no—
296#389C2×D1112yes—
297#388—114no—
298#388—114no—
299#388—114no—
300#387—114no—
301#387—114no—
302#387—114no—
303#387—114no—
304#387—114no—
305#386—112no—
306#386—112no—
307#386—114no—
308#385—114no—
309#385—114no—
310#385—114no—
311#385C2×D1114yes—
312#383—112no—
313#381—112no—
314C4×C4⋊C4—114no—
315C4×C4⋊C4—114no—
316C4×C22⋊C4—114no—
317C4×C22⋊C4—114no—
318C4×C22⋊C4—114no—
319C22×C11—28no—
320C22×C11—24no—
321C22×C11—42no—
322C22×C11—44no—
323C22×C11—42no—
324C22×C11C22×#4111yescharacteristic
325C22×C11C22×#4112yes—
326C22×C11C2×H(5,𝔽2)11yescharacteristic
327C22×C11C2×H(5,𝔽2)11yescharacteristic
328C22×C11C2×2−1+412yes—
329C2×D11—22no—
330C2×D11—24no—
331C2×D11—41no—
332C2×D11—42no—
333C2×D11—41no—
334C4×C11—22no—
335C4×C11—24no—
336C4×C11—42no—
337C4×C11—44no—
338C4×C11—44no—
339Dic11—28no—
340Dic11—22no—
341Dic11—24no—
342Dic11—42no—
343Dic11—44no—
344Dic11—42no—
345C2×#41—224no—
346C2×#41—442no—
347C2×#41—442no—
348C22×Q8—112no—
349C22×Q8—111no—
350C22×D4—112no—
351C22×D4C22×D1111yescharacteristic
352C23×C4—112no—
353C23×C4—112no—
354C23×C4—112no—
355C23×C4—111no—
356C23×C4C22×D1112yes—
357#123—28no—
358#123—444no—
359C22⋊Q8—2216no—
360C4×Q8—444no—
361#117—228no—
362#117—442no—
363#117—444no—
364C2×C4⋊C4—112no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—114no—
367C2×C4⋊C4—114no—
368C2×C4⋊C4—114no—
369C2×C4⋊C4—114no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—112no—
372C2×C4⋊C4—114no—
373C2×C4⋊C4—444no—
374C2×C4⋊C4C22×D1112yes—
375C2×C4⋊C4C22×D1114yes—
376C2×C4⋊C4C22×D1112yes—
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C4⋊C4C22×D1112yes—
379C2×C22⋊C4—114no—
380C2×C22⋊C4—114no—
381C2×C22⋊C4—114no—
382C2×C22⋊C4—114no—
383C2×C22⋊C4—112no—
384C2×C22⋊C4—112no—
385C2×C22⋊C4C22×D1114yes—
386C2×C22⋊C4C22×D1114yes—
387C2×C22⋊C4C22×D1112yes—
388C2×C42—112no—
389C2×C42—114no—
390C2×C42—114no—
391C2×C42—114no—
392C2×C42—112no—
393C2×C42—111no—
394C2×C42—442no—
395C2×C42C22×D1111yescharacteristic
396#95—114no—
397#95—114no—
398#95—114no—
399#95—114no—
400#95—114no—
401#95—114no—
402#95—114no—
403#95—114no—
404#95—112no—
405#95—114no—
406#95—114no—
407#95C22×D1114yes—
408#95C22×D1112yes—
409#95C22×D1114yes—
410C2×C11—44no—
411C2×C11#348111yescharacteristic
412C2×C11#348212yes—
413C2×C11#349011yescharacteristic
414C2×C11#349212yes—
415C2×C11#355011yescharacteristic
416D11—42no—
417C24—111no—
418C24C23×D1112yes—
419#41—4416no—
420C2×Q8—228no—
421C2×Q8—222no—
422C2×Q8—442no—
423C2×Q8—441no—
424C2×Q8—441no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—224no—
428C2×D4—224no—
429C2×D4—442no—
430C2×D4#434114yes—
431C22×C4—24no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—112no—
435C22×C4—111no—
436C22×C4—114no—
437C22×C4—112no—
438C22×C4—112no—
439C22×C4—114no—
440C22×C4—222no—
441C22×C4—224no—
442C22×C4—224no—
443C22×C4—222no—
444C22×C4—224no—
445C22×C4—228no—
446C22×C4—222no—
447C22×C4—224no—
448C22×C4—224no—
449C22×C4—442no—
450C22×C4—442no—
451C22×C4C23×D1114yes—
452C22×C4C23×D1112yes—
453C22×C4C23×D1114yes—
454C22×C4C23×D1111yescharacteristic
455C22×C4C23×D1112yes—
456C4⋊C4—28no—
457C4⋊C4—24no—
458C4⋊C4—42no—
459C4⋊C4—41no—
460C4⋊C4—42no—
461C4⋊C4—118no—
462C4⋊C4—228no—
463C4⋊C4—228no—
464C4⋊C4—228no—
465C4⋊C4—228no—
466C4⋊C4—444no—
467C4⋊C4—442no—
468C4⋊C4—441no—
469C4⋊C4—444no—
470C22⋊C4—24no—
471C22⋊C4—28no—
472C22⋊C4—28no—
473C22⋊C4—228no—
474C22⋊C4—228no—
475C22⋊C4—228no—
476C22⋊C4—228no—
477C22⋊C4—442no—
478C22⋊C4—442no—
479C42—41no—
480C42—228no—
481C42—224no—
482C42—442no—
483C42—441no—
484C42—444no—
485C42—444no—
486C11#6004611yescharacteristic, complemented, Sylow
487C23—24no—
488C23—22no—
489C23—22no—
490C23—24no—
491C23—112no—
492C23—221no—
493C23—222no—
494C23—221no—
495C23—222no—
496C23C2×#434114yes—
497C23C24×D1111yescharacteristic
498Q8—444no—
499Q8—448no—
500D4—44no—
501D4—448no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—84no—
515C2×C4—118no—
516C2×C4—112no—
517C2×C4—114no—
518C2×C4—228no—
519C2×C4—2216no—
520C2×C4—221no—
521C2×C4—222no—
522C2×C4—224no—
523C2×C4—222no—
524C2×C4—221no—
525C2×C4—224no—
526C2×C4—222no—
527C2×C4—224no—
528C2×C4—222no—
529C2×C4—224no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—224no—
533C2×C4—224no—
534C2×C4—448no—
535C2×C4—448no—
536C2×C4C2×#434112yes—
537C2×C4#41×D1114yes—
538C22—28no—
539C22—24no—
540C22—42no—
541C22—42no—
542C22—44no—
543C22—222no—
544C22—224no—
545C22—441no—
546C22—442no—
547C22—441no—
548C22C22×#434111yescharacteristic
549C22C2×#41×D1112yes—
550C22D11×H(5,𝔽2)11yescharacteristic
551C22D11×H(5,𝔽2)11yescharacteristic
552C22D11×2−1+412yes—
553C4—22no—
554C4—24no—
555C4—42no—
556C4—44no—
557C4—44no—
558C4—228no—
559C4—222no—
560C4—224no—
561C4—442no—
562C4—442no—
563C4—444no—
564C2—44no—
565C2—442no—
566C2#1308222511yescharacteristic
567C2#1308222812yes—
568C2#1308230411yescharacteristic
569C2#1308232112yes—
570C2#1308302611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2724C2
prime radicalC22×#4341C22
hypercenter#2724D11
hypocenterC11#60046
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2724

Complements

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

NH ≅ G/Ntype
1. #13076566C2semidirect
2. #13074988C2semidirect
3. #13074196C2semidirect
4. #13074021C2semidirect
5. #13073876C2semidirect
6. #13072810C2semidirect
7. #13072716C2semidirect
9. #13071752C2semidirect
10. #13071616C2semidirect
12. #13071097C2semidirect
13. C11×#2724C2semidirect
190. C4⋊Dic11#41semidirect
203. #2724D11semidirect
486. C11#60046semidirect

Maximal subgroups

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

subgroupindex
#130765662
#130749882
#130741962
#130740212
#130738762
#130728102
#130727162
#130719482
#130717522
#130716162
#130711032
#130710972
C11×#27242
#6004611