Finite Group Databasebeta

← #15617122

Subgroups — #15617122

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#13076571C212yesmaximal, complemented
2#13075546C211yesmaximal, characteristic, complemented
3#13074988C211yesmaximal, characteristic, complemented
4#13074193C212yesmaximal, complemented
5#13074027C212yesmaximal, complemented
6#13073875C214yesmaximal, complemented
7#13072814C214yesmaximal, complemented
8#13072709C214yesmaximal, complemented
9#13071947C212yesmaximal
10#13071751C212yesmaximal, complemented
11#13071622C214yesmaximal, complemented
12#13071099C212yesmaximal, complemented
13C11×#2297C211yesmaximal, characteristic
14C22×C11×#41C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C2×#66988C2212yes—
18C2×#66988C2212yes—
19C2×#66979C2212yes—
20C2×#66979C2212yes—
21C22×Dic11⋊C4C2212yes—
22C2×#66931C2214yes—
23C2×C4×Dic22C2212yes—
24C11×#391C2211yescharacteristic
25C11×#391C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#390C2211yescharacteristic
28C11×#386C2214yes—
29C4×C11×C22⋊C4C2214yes—
30#10622842C2214yes—
31#10622835C2214yes—
32#10622833C2212yes—
33#10622833C2212yes—
34#10622824C2212yes—
35#10622823C2214yes—
36#10622823C2214yes—
37#10622823C2214yes—
38#10622596C2212yes—
39#10622592C2212yes—
40#10622591C2214yes—
41#10622566C2212yes—
42#10622566C2214yes—
43#10622563C2214yes—
44#10622561C2214yes—
45#10622560C2212yes—
46#10622558C2214yes—
47#10622558C2214yes—
48#10622557C2214yes—
49C22⋊C4×Dic11C2214yes—
50C22⋊C4×Dic11C2214yes—
51#10622550C2212yes—
52#10622546C2214yes—
53C4×Dic11⋊C4C2214yes—
54C4×Dic11⋊C4C2214yes—
55#10622541C2212yes—
56#10622541C2212yes—
57#10622541C2212yes—
58#10622541C2212yes—
59#10622273C2214yes—
60#10622272C2214yes—
61#10622267C2214yes—
62#10622265C2214yes—
63#10622265C2214yes—
64#10622260C2214yes—
65#10622260C2214yes—
66#10622259C2214yes—
67C2×C11×#41—24no—
68C2×C11×#41—42no—
69C2×C11×#41—42no—
70C22×Q8×C11C2311yescharacteristic
71C22×D4×C11C2312yes—
72C22×D4×C11C2311yescharacteristic
73C23×C4×C11C2312yes—
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2312yes—
76C23×Dic11C2312yes—
77C23×Dic11C2312yes—
78C22×Dic22C2312yes—
79C11×#117—42no—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C22⋊C4C2314yes—
83C2×C11×C22⋊C4C2314yes—
84C2×C11×C22⋊C4C2312yes—
85C2×C42×C11—42no—
86C2×C42×C11C2312yes—
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2312yes—
89C2×C42×C11C2311yescharacteristic
90C2×C22⋊Dic11C2314yes—
91C2×C22⋊Dic11C2314yes—
92C2×C22⋊Dic11C2314yes—
93C2×C22⋊Dic11C2314yes—
94C2×C22⋊Dic11C2312yes—
95C2×C22⋊Dic11C2312yes—
96#66988—28no—
97#66988—44no—
98#66979—28no—
99#66979—44no—
100C2×C4⋊Dic11C2312yes—
101C2×C4⋊Dic11C2312yes—
102C2×C4⋊Dic11C2312yes—
103C2×C4⋊Dic11C2312yes—
104C2×C4⋊Dic11C2312yes—
105C2×Dic11⋊C4—44no—
106C2×Dic11⋊C4C2314yes—
107C2×Dic11⋊C4C2314yes—
108C2×Dic11⋊C4C2314yes—
109C2×Dic11⋊C4C2314yes—
110C2×Dic11⋊C4C2314yes—
111C2×Dic11⋊C4C2314yes—
112C2×Dic11⋊C4C2314yes—
113C2×C4×Dic11C2314yes—
114C2×C4×Dic11C2314yes—
115C2×C4×Dic11C2314yes—
116#66931—216no—
117C4×Dic22—44no—
118C11×#95C2314yes—
119C11×#95C2314yes—
120C11⋊#95C2314yes—
121C11⋊#95C2314yes—
122C11⋊#95C2314yes—
123C11⋊#95C2314yes—
124C11⋊#95C2314yes—
125C11⋊#95C2312yes—
126C11⋊#95C2312yes—
127C11⋊#95C2314yes—
128C11⋊#95C2314yes—
129C11⋊#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132#60046—111nomaximal, Sylow
133C24×C11C2412yes—
134C24×C11C2411yescharacteristic
135C11×#41—416no—
136C2×Q8×C11—22no—
137C2×Q8×C11—41no—
138C2×Q8×C11—41no—
139C2×D4×C11—24no—
140C2×D4×C11—24no—
141C2×D4×C11—41no—
142C2×D4×C11—41no—
143C2×D4×C11—42no—
144C2×D4×C11#4114yes—
145C22×C4×C11—24no—
146C22×C4×C11—22no—
147C22×C4×C11—24no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—24no—
151C22×C4×C11—24no—
152C22×C4×C11—24no—
153C22×C4×C11—42no—
154C22×C4×C11C2412yes—
155C22×C4×C11C2412yes—
156C22×C4×C11C2412yes—
157C22×C4×C11C2411yescharacteristic
158C22×C4×C11C2412yes—
159C22×C4×C11C2411yescharacteristic
160C22×C4×C11C2412yes—
161C22×Dic11—28no—
162C22×Dic11—24no—
163C22×Dic11—42no—
164C22×Dic11—42no—
165C22×Dic11—42no—
166C22×Dic11C2414yes—
167C22×Dic11C2414yes—
168C22×Dic11C2414yes—
169C22×Dic11C2414yes—
170C2×Dic22—28no—
171C2×Dic22—42no—
172C11×C4⋊C4—41no—
173C11×C4⋊C4—41no—
174C11×C22⋊C4—28no—
175C11×C22⋊C4—28no—
176C11×C22⋊C4—42no—
177C42×C11—24no—
178C42×C11—41no—
179C42×C11—42no—
180C42×C11—41no—
181C22⋊Dic11—28no—
182C22⋊Dic11—28no—
183C22⋊Dic11—24no—
184C22⋊Dic11—28no—
185C22⋊Dic11—28no—
186C22⋊Dic11—42no—
187C4⋊Dic11—24no—
188C4⋊Dic11—42no—
189C4⋊Dic11—42no—
190C4⋊Dic11—42no—
191C4⋊Dic11#4118yescomplemented
192Dic11⋊C4—28no—
193Dic11⋊C4—28no—
194Dic11⋊C4—28no—
195Dic11⋊C4—28no—
196Dic11⋊C4—28no—
197Dic11⋊C4—44no—
198Dic11⋊C4—44no—
199C4×Dic11—28no—
200C4×Dic11—44no—
201C4×Dic11—44no—
202#2805—112no—
203#2724—111no—
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#2297D1111yescharacteristic
214#2296—112no—
215C23×C11—22no—
216C23×C11—24no—
217C23×C11—21no—
218C23×C11—22no—
219C23×C11—21no—
220C23×C11—22no—
221C23×C11—24no—
222C23×C11—22no—
223C23×C11C2×#4114yes—
224C23×C11H(5,𝔽2)12yes—
225C23×C11C2511yescharacteristic
226Q8×C11—44no—
227D4×C11—44no—
228D4×C11—48no—
229C2×C4×C11—216no—
230C2×C4×C11—28no—
231C2×C4×C11—22no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—24no—
246C2×C4×C11—48no—
247C2×C4×C11C2×#4112yes—
248C2×C4×C11C2×#4114yes—
249C2×C4×C11H(5,𝔽2)12yes—
250C2×C4×C112−1+414yes—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—24no—
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×Dic11—84no—
264C2×Dic11C2×#4118yes—
265Dic22—48no—
266C22×#41C2×D1111yescharacteristic
267C2×#123—112no—
268C2×#123—112no—
269C2×C22⋊Q8—114no—
270C2×C4×Q8—112no—
271C2×#117—112no—
272C2×#117—112no—
273C2×#117C2×D1111yescharacteristic
274C22×C4⋊C4—112no—
275C22×C42C2×D1111yescharacteristic
276#400—114no—
277#400—114no—
278#398—112no—
279#397—114no—
280#397—112no—
281#396—114no—
282#395—114no—
283#395—112no—
284#394—114no—
285#393—112no—
286#391—114no—
287#391C2×D1111yescharacteristic
288#391C2×D1111yescharacteristic
289#390C2×D1111yescharacteristic
290#390C2×D1111yescharacteristic
291#389—112no—
292#389—112no—
293#389—112no—
294#389—112no—
295#389—114no—
296#389—114no—
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#386C2×D1114yes—
308#385—114no—
309#385—114no—
310#385—114no—
311#385—114no—
312#383—112no—
313#381—112no—
314C4×C4⋊C4—114no—
315C4×C4⋊C4—114no—
316C4×C22⋊C4—114no—
317C4×C22⋊C4—114no—
318C4×C22⋊C4C2×D1114yes—
319C22×C11—28no—
320C22×C11—22no—
321C22×C11—24no—
322C22×C11—24no—
323C22×C11—41no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11—44no—
327C22×C11—41no—
328C22×C11—42no—
329C22×C11C22×#4111yescharacteristic
330C22×C11C22×#4112yes—
331C22×C11C2×H(5,𝔽2)11yescharacteristic
332C22×C11C2×H(5,𝔽2)11yescharacteristic
333C22×C11C2×2−1+412yes—
334C4×C11—22no—
335C4×C11—22no—
336C4×C11—24no—
337C4×C11—24no—
338C4×C11—42no—
339C4×C11—42no—
340C4×C11—42no—
341Dic11—28no—
342Dic11—44no—
343Dic11—44no—
344Dic11—44no—
345C2×#41—24no—
346C2×#41—42no—
347C2×#41—42no—
348C22×Q8—112no—
349C22×Q8C22×D1111yescharacteristic
350C22×D4C22×D1112yes—
351C22×D4C22×D1111yescharacteristic
352C23×C4—112no—
353C23×C4—112no—
354C23×C4C22×D1112yes—
355C23×C4C22×D1111yescharacteristic
356C23×C4C22×D1112yes—
357#123—228no—
358#123—444no—
359C22⋊Q8—2216no—
360C4×Q8—444no—
361#117—42no—
362#117—228no—
363#117—444no—
364C2×C4⋊C4—112no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—112no—
367C2×C4⋊C4—114no—
368C2×C4⋊C4—114no—
369C2×C4⋊C4—114no—
370C2×C4⋊C4—114no—
371C2×C4⋊C4—114no—
372C2×C4⋊C4—112no—
373C2×C4⋊C4—112no—
374C2×C4⋊C4—112no—
375C2×C4⋊C4—114no—
376C2×C4⋊C4—444no—
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C4⋊C4C22×D1111yescharacteristic
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—42no—
389C2×C42—114no—
390C2×C42—114no—
391C2×C42—114no—
392C2×C42C22×D1112yes—
393C2×C42C22×D1112yes—
394C2×C42C22×D1111yescharacteristic
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—112no—
404#95—112no—
405#95—114no—
406#95—114no—
407#95—114no—
408#95C22×D1114yes—
409#95C22×D1114yes—
410C2×C11—44no—
411C2×C11—42no—
412C2×C11#348111yescharacteristic
413C2×C11#348212yes—
414C2×C11#349011yescharacteristic
415C2×C11#349212yes—
416C2×C11#355011yescharacteristic
417C24C23×D1112yes—
418C24C23×D1111yescharacteristic
419#41—416no—
420C2×Q8—22no—
421C2×Q8—41no—
422C2×Q8—41no—
423C2×Q8—228no—
424C2×Q8—442no—
425C2×D4—24no—
426C2×D4—24no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—42no—
430C2×D4#433914yes—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—42no—
440C22×C4—114no—
441C22×C4—114no—
442C22×C4—114no—
443C22×C4—114no—
444C22×C4—228no—
445C22×C4—224no—
446C22×C4—442no—
447C22×C4—442no—
448C22×C4—442no—
449C22×C4C23×D1112yes—
450C22×C4C23×D1112yes—
451C22×C4C23×D1112yes—
452C22×C4C23×D1111yescharacteristic
453C22×C4C23×D1111yescharacteristic
454C22×C4C23×D1112yes—
455C22×C4C23×D1112yes—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—118no—
459C4⋊C4—228no—
460C4⋊C4—228no—
461C4⋊C4—228no—
462C4⋊C4—224no—
463C4⋊C4—228no—
464C4⋊C4—228no—
465C4⋊C4—444no—
466C4⋊C4—442no—
467C4⋊C4—442no—
468C4⋊C4—442no—
469C4⋊C4—444no—
470C22⋊C4—28no—
471C22⋊C4—28no—
472C22⋊C4—42no—
473C22⋊C4—228no—
474C22⋊C4—228no—
475C22⋊C4—224no—
476C22⋊C4—228no—
477C22⋊C4—228no—
478C22⋊C4—442no—
479C42—24no—
480C42—41no—
481C42—42no—
482C42—41no—
483C42—228no—
484C42—444no—
485C42—444no—
486C11#6004611yescharacteristic, complemented, Sylow
487C23—21no—
488C23—21no—
489C23—22no—
490C23—22no—
491C23—24no—
492C23—22no—
493C23—24no—
494C23—22no—
495C23C2×#433914yes—
496C23#6703712yes—
497C23C24×D1111yescharacteristic
498Q8—44no—
499Q8—448no—
500D4—44no—
501D4—48no—
502C2×C4—216no—
503C2×C4—28no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—48no—
520C2×C4—118no—
521C2×C4—224no—
522C2×C4—224no—
523C2×C4—224no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—224no—
527C2×C4—224no—
528C2×C4—224no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—224no—
532C2×C4—448no—
533C2×C4—884no—
534C2×C4C2×#433912yes—
535C2×C4#6703712yes—
536C2×C4#41×D1114yes—
537C2×C4#6704314yes—
538C22—28no—
539C22—22no—
540C22—24no—
541C22—24no—
542C22—42no—
543C22—41no—
544C22—42no—
545C22—41no—
546C22—42no—
547C22—44no—
548C22C22×#433911yescharacteristic
549C22C2×#6703711yescharacteristic
550C22C2×#6703711yescharacteristic
551C22C2×#41×D1112yes—
552C22C2×#6704312yes—
553C4—22no—
554C4—22no—
555C4—24no—
556C4—24no—
557C4—42no—
558C4—42no—
559C4—42no—
560C4—228no—
561C4—444no—
562C4—444no—
563C4—444no—
564C2—44no—
565C2—42no—
566C2#1308222411yescharacteristic
567C2#1308223112yes—
568C2#1308230511yescharacteristic
569C2#1308231712yes—
570C2#1308303011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2297C2
prime radicalC22×C11×#41C22
hypercenter#2297D11
hypocenterC11#60046
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2297

Complements

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

NH ≅ G/Ntype
1. #13076571C2semidirect
2. #13075546C2semidirect
3. #13074988C2semidirect
4. #13074193C2semidirect
5. #13074027C2semidirect
6. #13073875C2semidirect
7. #13072814C2semidirect
8. #13072709C2semidirect
10. #13071751C2semidirect
11. #13071622C2semidirect
12. #13071099C2semidirect
191. C4⋊Dic11#41semidirect
486. C11#60046semidirect

Maximal subgroups

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

subgroupindex
#130765712
#130755462
#130749882
#130741932
#130740272
#130738752
#130728142
#130727092
#130719472
#130717512
#130716222
#130710992
C11×#22972
#6004611