Finite Group Databasebeta

← #15617135

Subgroups — #15617135

Order 2816.

1854 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076604C211yesmaximal, characteristic, complemented
2#13075648C211yesmaximal, characteristic, complemented
3#13075575C212yesmaximal, complemented
4#13074314C212yesmaximal, complemented
5#13074112C212yesmaximal, complemented
6#13073700C214yesmaximal, complemented
7#13072846C214yesmaximal, complemented
8#13072771C214yesmaximal, complemented
9#13072240C212yesmaximal
10#13071737C214yesmaximal, complemented
11#13071704C212yesmaximal, complemented
12#13071099C212yesmaximal, complemented
13C11×#2297C211yesmaximal, characteristic
14C22×C11×#41C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C2×#66997C2212yes—
18C2×#66989C2212yes—
19C2×#66979C2212yes—
20C2×#66979C2212yes—
21C2×#66977C2212yes—
22C2×#66932C2214yes—
23C2×#66923C2212yes—
24C11×#391C2211yescharacteristic
25C11×#391C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#390C2211yescharacteristic
28C11×#386C2214yes—
29C4×C11×C22⋊C4C2214yes—
30#10622843C2212yes—
31#10622835C2214yes—
32#10622835C2214yes—
33#10622834C2212yes—
34#10622823C2214yes—
35#10622823C2214yes—
36#10622823C2214yes—
37C4×C22⋊Dic11C2212yes—
38#10622599C2212yes—
39#10622596C2212yes—
40#10622585C2214yes—
41#10622566C2212yes—
42#10622564C2214yes—
43#10622564C2214yes—
44#10622564C2214yes—
45#10622562C2214yes—
46#10622562C2212yes—
47#10622561C2214yes—
48#10622558C2214yes—
49#10622558C2214yes—
50#10622558C2214yes—
51#10622546C2214yes—
52#10622545C2212yes—
53C4×Dic11⋊C4C2214yes—
54C4×Dic11⋊C4C2214yes—
55#10622541C2212yes—
56#10622541C2212yes—
57#10622541C2212yes—
58#10622541C2212yes—
59#10622274C2214yes—
60#10622269C2214yes—
61#10622268C2214yes—
62#10622266C2214yes—
63#10622262C2214yes—
64#10622262C2214yes—
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—
76C22×Dic22C2312yes—
77C11×#117—42no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4C2314yes—
81C2×C11×C22⋊C4C2314yes—
82C2×C11×C22⋊C4C2312yes—
83C2×C42×C11—42no—
84C2×C42×C11C2312yes—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2312yes—
87C2×C42×C11C2311yescharacteristic
88C2×C22⋊Dic11C2314yes—
89C2×C22⋊Dic11C2314yes—
90C2×C22⋊Dic11C2314yes—
91C2×C22⋊Dic11C2314yes—
92C2×C22⋊Dic11C2314yes—
93C2×C22⋊Dic11C2314yes—
94#66997—28no—
95#66989—44no—
96#66979—28no—
97#66979—44no—
98C2×C4⋊Dic11C2312yes—
99C2×C4⋊Dic11C2312yes—
100C2×C4⋊Dic11C2312yes—
101C2×C4⋊Dic11C2312yes—
102C2×C4⋊Dic11C2312yes—
103C2×C4⋊Dic11C2312yes—
104C2×C4⋊Dic11C2312yes—
105#66977—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×Dic11C2312yes—
116C2×C4×Dic11C2314yes—
117C2×C4×Dic11C2312yes—
118#66932—216no—
119#66923—44no—
120C11×#95C2314yes—
121C11×#95C2314yes—
122C11⋊#95C2314yes—
123C11⋊#95C2314yes—
124C11⋊#95C2314yes—
125C11⋊#95C2312yes—
126C11⋊#95C2314yes—
127C11⋊#95C2314yes—
128C11⋊#95C2312yes—
129C11⋊#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132#60047—111nomaximal, Sylow
133C24×C11C2412yes—
134C24×C11C2411yescharacteristic
135C11×#41—416no—
136C2×Q8×C11—41no—
137C2×Q8×C11—41no—
138C2×Q8×C11#4114yes—
139C2×D4×C11—24no—
140C2×D4×C11—24no—
141C2×D4×C11—22no—
142C2×D4×C11—42no—
143C2×D4×C11—41no—
144C2×D4×C11—41no—
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×C11C2411yescharacteristic
157C22×C4×C11C2412yes—
158C22×C4×C11C2412yes—
159C22×C4×C11C2411yescharacteristic
160C22×C4×C11C2412yes—
161C22×Dic11C2414yes—
162C22×Dic11C2414yes—
163C22×Dic11C2414yes—
164C22×Dic11C2414yes—
165C2×Dic22—24no—
166C2×Dic22—42no—
167C2×Dic22—42no—
168C11×C4⋊C4—41no—
169C11×C4⋊C4—41no—
170C11×C22⋊C4—28no—
171C11×C22⋊C4—28no—
172C11×C22⋊C4—42no—
173C42×C11—24no—
174C42×C11—41no—
175C42×C11—42no—
176C42×C11—41no—
177C22⋊Dic11—28no—
178C22⋊Dic11—28no—
179C22⋊Dic11—28no—
180C22⋊Dic11—28no—
181C22⋊Dic11—44no—
182C22⋊Dic11—44no—
183C4⋊Dic11—24no—
184C4⋊Dic11—42no—
185C4⋊Dic11—42no—
186C4⋊Dic11—42no—
187C4⋊Dic11—42no—
188C4⋊Dic11—42no—
189C4⋊Dic11#4118yescomplemented
190Dic11⋊C4—28no—
191Dic11⋊C4—28no—
192Dic11⋊C4—28no—
193Dic11⋊C4—28no—
194Dic11⋊C4—28no—
195Dic11⋊C4—28no—
196Dic11⋊C4—44no—
197C4×Dic11—28no—
198C4×Dic11—28no—
199C4×Dic11—24no—
200C4×Dic11—44no—
201C4×Dic11—42no—
202#2809—111no—
203#2734—111no—
204#2727—112no—
205#2611—112no—
206#2593—112no—
207#2556—114no—
208#2479—114no—
209#2474—114no—
210#2432—112no—
211#2373—114no—
212#2369—112no—
213#2297D1111yescharacteristic
214#2296—112no—
215C23×C11—22no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—22no—
219C23×C11—24no—
220C23×C11—22no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—24no—
224C23×C11H(5,𝔽2)12yes—
225C23×C11C2511yescharacteristic
226Q8×C11—44no—
227D4×C11—48no—
228D4×C11—44no—
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—22no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—48no—
246C2×C4×C11C2×#4114yes—
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×Dic11C2×#4118yes—
263Dic22—84no—
264C22×#41C2×D1111yescharacteristic
265C2×C4⋊Q8—112no—
266C2×#126—114no—
267C2×#125—112no—
268C2×#124—112no—
269C2×C22⋊Q8—112no—
270C2×#117—112no—
271C2×#117—112no—
272C2×#117C2×D1111yescharacteristic
273C22×C42C2×D1111yescharacteristic
274#400—112no—
275#399—112no—
276#399—114no—
277#398—112no—
278#398—114no—
279#397—112no—
280#396—114no—
281#395—114no—
282#394—114no—
283#394—114no—
284#391—112no—
285#391—114no—
286#391C2×D1111yescharacteristic
287#391C2×D1111yescharacteristic
288#390—112no—
289#390C2×D1111yescharacteristic
290#390C2×D1111yescharacteristic
291#389—114no—
292#389—112no—
293#389—112no—
294#389—112no—
295#389—112no—
296#389—114no—
297#388—114no—
298#388—114no—
299#388—114no—
300#388—114no—
301#388—114no—
302#388—114no—
303#387—114no—
304#387—114no—
305#387—114no—
306#386C2×D1114yes—
307#385—114no—
308#385—114no—
309#385—114no—
310C4×C4⋊C4—114no—
311C4×C4⋊C4—114no—
312C4×C4⋊C4—114no—
313C4×C4⋊C4—114no—
314C4×C22⋊C4—112no—
315C4×C22⋊C4C2×D1114yes—
316#376—112no—
317C22×C11—22no—
318C22×C11—24no—
319C22×C11—42no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11—44no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—44no—
326C22×C11—42no—
327C22×C11C22×#4111yescharacteristic
328C22×C11C22×#4112yes—
329C22×C11C2×H(5,𝔽2)11yescharacteristic
330C22×C11C2×H(5,𝔽2)11yescharacteristic
331C22×C11C2×2−1+412yes—
332C4×C11—22no—
333C4×C11—22no—
334C4×C11—24no—
335C4×C11—24no—
336C4×C11—24no—
337C4×C11—42no—
338C4×C11—42no—
339Dic11—28no—
340Dic11—44no—
341Dic11—44no—
342Dic11—44no—
343C2×#41—24no—
344C2×#41—42no—
345C2×#41—42no—
346C22×Q8—112no—
347C22×Q8C22×D1111yescharacteristic
348C22×D4C22×D1112yes—
349C22×D4C22×D1111yescharacteristic
350C23×C4C22×D1112yes—
351C23×C4C22×D1111yescharacteristic
352C23×C4C22×D1112yes—
353C4⋊Q8—228no—
354#126—2216no—
355#125—444no—
356#124—444no—
357C22⋊Q8—444no—
358#117—42no—
359#117—228no—
360#117—444no—
361C2×C4⋊C4—112no—
362C2×C4⋊C4—112no—
363C2×C4⋊C4—114no—
364C2×C4⋊C4—114no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—114no—
367C2×C4⋊C4—114no—
368C2×C4⋊C4—114no—
369C2×C4⋊C4—112no—
370C2×C4⋊C4—112no—
371C2×C4⋊C4—112no—
372C2×C4⋊C4—112no—
373C2×C4⋊C4—112no—
374C2×C4⋊C4—114no—
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C22⋊C4—114no—
378C2×C22⋊C4—114no—
379C2×C22⋊C4—114no—
380C2×C22⋊C4—114no—
381C2×C22⋊C4—114no—
382C2×C22⋊C4—114no—
383C2×C22⋊C4C22×D1114yes—
384C2×C22⋊C4C22×D1114yes—
385C2×C22⋊C4C22×D1112yes—
386C2×C42—42no—
387C2×C42—114no—
388C2×C42—114no—
389C2×C42—112no—
390C2×C42—114no—
391C2×C42—112no—
392C2×C42C22×D1112yes—
393C2×C42C22×D1112yes—
394C2×C42C22×D1111yescharacteristic
395C2×C42C22×D1111yescharacteristic
396#95—114no—
397#95—112no—
398#95—112no—
399#95—114no—
400#95—114no—
401#95—114no—
402#95—114no—
403#95—114no—
404#95—114no—
405#95—114no—
406#95C22×D1114yes—
407#95C22×D1114yes—
408C2×C11—42no—
409C2×C11—82no—
410C2×C11#348212yes—
411C2×C11#348311yescharacteristic
412C2×C11#349011yescharacteristic
413C2×C11#349212yes—
414C2×C11#355011yescharacteristic
415C24C23×D1112yes—
416C24C23×D1111yescharacteristic
417#41—416no—
418C2×Q8—41no—
419C2×Q8—41no—
420C2×Q8—224no—
421C2×Q8—442no—
422C2×Q8—442no—
423C2×Q8#433914yes—
424C2×D4—24no—
425C2×D4—24no—
426C2×D4—22no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4—42no—
430C22×C4—24no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—42no—
439C22×C4—114no—
440C22×C4—114no—
441C22×C4—114no—
442C22×C4—114no—
443C22×C4C23×D1112yes—
444C22×C4C23×D1112yes—
445C22×C4C23×D1111yescharacteristic
446C22×C4C23×D1112yes—
447C22×C4C23×D1111yescharacteristic
448C22×C4C23×D1112yes—
449C22×C4C23×D1112yes—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C4⋊C4—118no—
453C4⋊C4—228no—
454C4⋊C4—228no—
455C4⋊C4—228no—
456C4⋊C4—228no—
457C4⋊C4—224no—
458C4⋊C4—228no—
459C4⋊C4—228no—
460C4⋊C4—442no—
461C4⋊C4—442no—
462C4⋊C4—442no—
463C4⋊C4—444no—
464C4⋊C4—442no—
465C4⋊C4—442no—
466C22⋊C4—28no—
467C22⋊C4—28no—
468C22⋊C4—42no—
469C22⋊C4—228no—
470C22⋊C4—228no—
471C22⋊C4—228no—
472C22⋊C4—228no—
473C22⋊C4—444no—
474C22⋊C4—444no—
475C42—24no—
476C42—41no—
477C42—42no—
478C42—41no—
479C42—228no—
480C42—228no—
481C42—224no—
482C42—444no—
483C42—442no—
484C11#6004711yescharacteristic, complemented, Sylow
485C23—21no—
486C23—21no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—24no—
494C23#6703712yes—
495C23C24×D1111yescharacteristic
496Q8—44no—
497Q8—884no—
498D4—48no—
499D4—44no—
500C2×C4—216no—
501C2×C4—28no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—48no—
517C2×C4—118no—
518C2×C4—224no—
519C2×C4—224no—
520C2×C4—224no—
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×C4C2×#433914yes—
530C2×C4C2×#433912yes—
531C2×C4#6703712yes—
532C2×C4#41×D1114yes—
533C2×C4#6704314yes—
534C22—22no—
535C22—24no—
536C22—42no—
537C22—41no—
538C22—41no—
539C22—44no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—44no—
544C22C22×#433911yescharacteristic
545C22C2×#6703711yescharacteristic
546C22C2×#6703711yescharacteristic
547C22C2×#41×D1112yes—
548C22C2×#6704312yes—
549C4—22no—
550C4—22no—
551C4—24no—
552C4—24no—
553C4—24no—
554C4—42no—
555C4—42no—
556C4—228no—
557C4—444no—
558C4—444no—
559C4—444no—
560C2—42no—
561C2—82no—
562C2#1308223812yes—
563C2#1308224011yescharacteristic
564C2#1308230511yescharacteristic
565C2#1308231712yes—
566C2#1308303011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2297C2
prime radicalC22×C11×#41C22
hypercenter#2297D11
hypocenterC11#60047
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2297

Complements

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

NH ≅ G/Ntype
1. #13076604C2semidirect
2. #13075648C2semidirect
3. #13075575C2semidirect
4. #13074314C2semidirect
5. #13074112C2semidirect
6. #13073700C2semidirect
7. #13072846C2semidirect
8. #13072771C2semidirect
10. #13071737C2semidirect
11. #13071704C2semidirect
12. #13071099C2semidirect
189. C4⋊Dic11#41semidirect
484. C11#60047semidirect

Maximal subgroups

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

subgroupindex
#130766042
#130756482
#130755752
#130743142
#130741122
#130737002
#130728462
#130727712
#130722402
#130717372
#130717042
#130710992
C11×#22972
#6004711