Finite Group Databasebeta

← #15618172

Subgroups — #15618172

Order 2816.

1882 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#533C211yesmaximal, characteristic
2#13077568C218yesmaximal, complemented
3#13077561C218yesmaximal, complemented
4#13077557C211yesmaximal, characteristic, complemented
5#13077556C211yesmaximal, characteristic, complemented
6#13077553C211yesmaximal, characteristic, complemented
7#13077549C212yesmaximal, complemented
8#13077548C212yesmaximal, complemented
9#13077177C212yesmaximal
10D11×#423C211yesmaximal, characteristic
11#13077032C212yesmaximal
12C2×#10622320C211yesmaximal, characteristic
13C11×#2961C211yesmaximal, characteristic, complemented
14C11×#533C2211yescharacteristic
15C2×M16×D11C2212yes—
16C22×#4313C2211yescharacteristic
17C22×#4313C2211yescharacteristic
18#10623259C412yes—
19D11×C4⋊Q8C412yes—
20#10623219C412yes—
21D11×#125C412yes—
22D11×C22⋊Q8C414yes—
23#10623153C414yes—
24#10623109C2214yes—
25C4×Q8×D11C2214yes—
26D11×#117C2212yes—
27#10623048C2212yes—
28C2×C42×D11C2211yescharacteristic
29#10623001C2211yescharacteristic
30C11×#446C2218yescomplemented
31C11×#424C2212yes—
32C11×#423C2211yescharacteristic
33C11×#405C2212yes—
34C2×C11×#97C2211yescharacteristic
35#10622735C2212yes—
36#10622732C2212yes—
37#10622731C2212yes—
38#10622715C2212yes—
39#10622714C2212yes—
40C2×C8×Dic11C2211yescharacteristic
41C2×C8×Dic11C2211yescharacteristic
42#10622637C2218yescomplemented
43#10622612C2212yes—
44#10622610C2212yes—
45#10622537C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47#10622452C2218yes—
48#10622450C2214yes—
49#10622450C2218yes—
50D11×C4⋊C8C2214yes—
51#10622443C2218yescomplemented
52#10622441C2218yescomplemented
53#10622441C2218yescomplemented
54#10622321C2214yes—
55#10622320C2214yes—
56#10622320C2214yes—
57#10622320C2214yes—
58#10622314C2218yescomplemented
59#10622314C2218yescomplemented
60#10622302C2214yes—
61C4×#4313C2214yes—
62C8×Dic22C2218yescomplemented
63C2×Q8×D11C2×C414yes—
64C22×C4×D11C2×C412yes—
65C22×C4×D11C2311yescharacteristic
66C2×C11×M16C2312yes—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×C4⋊Q8C2×C412yes—
70C11×#125C2×C412yes—
71C11×C22⋊Q8C2×C414yes—
72C4×Q8×C11C2314yes—
73C11×#117C2312yes—
74C2×C42×C11C2311yescharacteristic
75#66999C2×C414yes—
76Q8×Dic11C2×C414yes—
77#66997C2×C414yes—
78#66979C2312yes—
79#66977C2×C414yes—
80C2×C4×Dic11C2×C412yes—
81C2×C4×Dic11C2311yescharacteristic
82C2×#4318C2312yes—
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2311yescharacteristic
85M16×D11—28no—
86C2×#4313—24no—
87C2×#4313Q818yescomplemented
88C2×#4313C2312yes—
89C2×#4313C2312yes—
90C2×#4313C2314yes—
91C2×#4313C2312yes—
92C2×#4313C2312yes—
93C2×C8×D11C2314yes—
94#66950C2×C414yes—
95#66949C2×C418yes—
96#66945C2×C414yes—
97C4⋊C4×D11C2×C414yes—
98C4⋊C4×D11C2×C414yes—
99C4⋊C4×D11C2×C418yes—
100#66943C2×C414yes—
101#66942C2×C418yes—
102#66941C2×C414yes—
103#66941C2×C414yes—
104#66940C2×C414yes—
105#66940C2×C418yes—
106C22⋊C4×D11C2×C414yes—
107#66931C2×C418yes—
108#66930C2×C414yes—
109#66925C2314yes—
110C42×D11C2×C411yescharacteristic
111C42×D11C2×C411yescharacteristic
112C42×D11C2×C411yescharacteristic
113C42×D11C2×C411yescharacteristic
114C42×D11C2312yes—
115C42×D11C2312yes—
116C42×D11C2314yes—
117#66923C2×C412yes—
118#66922C2×C412yes—
119C4×Dic22C2314yes—
120C4×Dic22C2318yes—
121C11×C4⋊C8C2314yes—
122C11×C4⋊C8C2318yes—
123C11×#97C2314yes—
124C11×#97C2314yes—
125C4×C8×C11C2314yes—
126#66879C2314yes—
127#66879C2314yes—
128Dic11⋊C8C2318yes—
129Dic11⋊C8C2318yes—
130Dic11⋊C8C2318yes—
131C8×Dic11C2314yes—
132C8×Dic11C2314yes—
133C8×Dic11C2314yes—
134C8×Dic11C2314yes—
135C4⋊(C11⋊C8)C2314yes—
136C4⋊(C11⋊C8)C2318yes—
137#66867C2314yes—
138#66867C2314yes—
139C4×C11⋊C8C2314yes—
140#60192—111nomaximal, Sylow
141C23×D11C22×C411yescharacteristic
142C2×Q8×C11C22×C414yes—
143C22×C4×C11C22×C412yes—
144C22×C4×C11C2411yescharacteristic
145C22×Dic11C22×C412yes—
146C22×Dic11C22×C411yescharacteristic
147Q8×D11—48no—
148C2×C4×D11—44no—
149C2×C4×D11C22×C412yes—
150C2×C4×D11C22×C412yes—
151C2×C4×D11C22×C412yes—
152C2×C4×D11C22×C412yes—
153C2×C4×D11C22×C418yes—
154C2×C4×D11C22×C411yescharacteristic
155C2×C4×D11C22×C411yescharacteristic
156C2×C4×D11C2×Q814yes—
157C2×C4×D11#4114yes—
158C2×C4×D11C2411yescharacteristic
159C2×C4×D11C2411yescharacteristic
160C2×Dic22C22×C418yes—
161C2×Dic22C22×C414yes—
162C11×M16—24no—
163C2×C8×C11—22no—
164C2×C8×C11C2×Q814yescomplemented
165C2×C8×C11C2412yes—
166C2×C8×C11C2414yes—
167C2×C8×C11C2412yes—
168C11×C4⋊C4C22×C414yes—
169C11×C4⋊C4C22×C418yes—
170C11×C4⋊C4C22×C414yes—
171C11×C22⋊C4C22×C414yes—
172C42×C11C22×C411yescharacteristic
173C42×C11C22×C411yescharacteristic
174C42×C11C2414yes—
175C42×C11C2412yes—
176C22⋊Dic11C22×C414yes—
177(C2×D11)⋊C4C22×C418yes—
178C4⋊Dic11C22×C414yes—
179C4⋊Dic11C22×C418yes—
180C4⋊Dic11C22×C414yes—
181Dic11⋊C4C22×C418yes—
182Dic11⋊C4C22×C418yes—
183Dic11⋊C4C22×C418yes—
184Dic11⋊C4C22×C418yes—
185C4×Dic11C22×C411yescharacteristic
186C4×Dic11C22×C411yescharacteristic
187C4×Dic11C22×C412yes—
188C4×Dic11C22×C412yes—
189C4×Dic11C22×C412yes—
190C4×Dic11C22×C412yes—
191C4×Dic11C22×C418yes—
192C4×Dic11C2412yes—
193C4×Dic11C2414yes—
194#4318—24no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8C2×Q814yescomplemented
197C2×C11⋊C8C2414yes—
198C2×C11⋊C8C2412yes—
199C2×C11⋊C8C2412yes—
200#4313—24no—
201#4313—24no—
202#4313—28no—
203#4313C2×Q818yes—
204#4313C2×Q818yescomplemented
205C8×D11—28no—
206C2×#533—111no—
207Q8×M16—118no—
208#2962—118no—
209#2961—111no—
210#2961—111no—
211#2961—111no—
212#2961D1111yescharacteristic, complemented
213#2960—112no—
214#2960—112no—
215#2905—112no—
216C2×#423—111no—
217#2873—112no—
218C2×C4×M16—111no—
219C23×C11C23×C411yescharacteristic
220C22×D11—42no—
221C22×D11C4×Q814yes—
222C22×D11C23×C411yescharacteristic
223C22×D11C23×C411yescharacteristic
224Q8×C11—44no—
225C2×C4×C11—42no—
226C2×C4×C11C23×C412yes—
227C2×C4×C11C23×C412yes—
228C2×C4×C11C23×C418yes—
229C2×C4×C11C23×C411yescharacteristic
230C2×C4×C11C22×Q812yes—
231C2×C4×C11C2×#4112yes—
232C2×C4×C11C2511yescharacteristic
233C2×Dic11—24no—
234C2×Dic11C4×Q814yes—
235C2×Dic11C23×C412yes—
236C2×Dic11C23×C418yes—
237C2×Dic11C23×C411yescharacteristic
238C2×Dic11C23×C411yescharacteristic
239C2×Dic11C23×C412yes—
240C4×D11—24no—
241C4×D11—24no—
242C4×D11—42no—
243C4×D11—42no—
244C4×D11—48no—
245C4×D11C4×Q814yes—
246C4×D11C4×Q814yes—
247C4×D11C22×Q812yes—
248C4×D11C22×Q812yes—
249C4×D11C2×#4112yes—
250C4×D11C2×#4112yes—
251Dic22—216no—
252Dic22—44no—
253C8×C11—24no—
254C8×C11—22no—
255C8×C11C22×Q814yes—
256C11⋊C8—24no—
257C11⋊C8—22no—
258C11⋊C8C22×Q814yes—
259C22×M16—112no—
260C22×M16—111no—
261C22×M16—111no—
262#533—112no—
263#533—112no—
264#533—114no—
265#533—114no—
266#533—112no—
267#533—111no—
268#533C2×D1111yescharacteristic
269C2×C4⋊Q8—112no—
270C2×#125—112no—
271C2×C22⋊Q8—114no—
272C2×C4×Q8—114no—
273C2×#117—112no—
274C22×C42—111no—
275#446—118no—
276#446—118no—
277#446—118no—
278#446—118no—
279#446—118no—
280#446C2×D1118yescomplemented
281C8×Q8—118no—
282C8×Q8—118no—
283#424—112no—
284#424—112no—
285#424—112no—
286#424—118no—
287#424C2×D1112yes—
288#423—112no—
289#423—111no—
290#423—114no—
291#423—118no—
292#423C2×D1111yescharacteristic
293C2×C4⋊C8—114no—
294#405—112no—
295#405—112no—
296#405—112no—
297#405—114no—
298#405—114no—
299#405C2×D1112yes—
300C4×M16—114no—
301C4×M16—114no—
302C4×M16—114no—
303C4×M16—114no—
304C2×#97—111no—
305C2×#97C2×D1111yescharacteristic
306C2×C4×C8—111no—
307C2×C4×C8—111no—
308C22×C11—22no—
309C22×C11C2×C4×Q812yes—
310C22×C11C24×C411yescharacteristic
311C2×D11—22no—
312C2×D11—22no—
313C2×D11—44no—
314C2×D11C2×C4×Q812yes—
315C2×D11C2×C4×Q812yes—
316C4×C11—22no—
317C4×C11—22no—
318C4×C11—28no—
319C4×C11C2×C4×Q812yes—
320C4×C11C23×Q811yescharacteristic
321C4×C11C22×#4111yescharacteristic
322Dic11—28no—
323Dic11—22no—
324Dic11C2×C4×Q812yes—
325Dic11C2×C4×Q812yes—
326Dic11#56814yes—
327C22×Q8—114no—
328C23×C4—111no—
329C23×C4—112no—
330C2×M16—112no—
331C2×M16—118no—
332C2×M16—112no—
333C2×M16—112no—
334C2×M16—112no—
335C2×M16—114no—
336C2×M16—112no—
337C2×M16—224no—
338C2×M16—228no—
339C2×M16C22×D1112yes—
340C22×C8—111no—
341C22×C8—111no—
342C22×C8—114no—
343C22×C8C22×D1111yescharacteristic
344C22×C8C22×D1111yescharacteristic
345C4⋊Q8—114no—
346C4⋊Q8—114no—
347C4⋊Q8—114no—
348C4⋊Q8—112no—
349C4⋊Q8C4×D1112yes—
350#125—118no—
351#125—114no—
352#125—112no—
353#125C4×D1112yes—
354C22⋊Q8—114no—
355C22⋊Q8—114no—
356C22⋊Q8—118no—
357C22⋊Q8—114no—
358C22⋊Q8—118no—
359C22⋊Q8C4×D1114yes—
360C4×Q8—114no—
361C4×Q8—114no—
362C4×Q8—118no—
363C4×Q8—118no—
364C4×Q8—114no—
365C4×Q8C22×D1114yes—
366#117—112no—
367#117—114no—
368#117—114no—
369#117—114no—
370#117C22×D1112yes—
371C2×C4⋊C4—114no—
372C2×C4⋊C4—118no—
373C2×C4⋊C4—114no—
374C2×C22⋊C4—114no—
375C2×C42—112no—
376C2×C42—111no—
377C2×C42—111no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—111no—
381C2×C42—114no—
382C2×C42—112no—
383C2×C42—112no—
384C2×C42C22×D1111yescharacteristic
385C4⋊C8—118no—
386C4⋊C8—118no—
387C4⋊C8—118no—
388C4⋊C8—114no—
389C4⋊C8—118no—
390C4⋊C8C22×D1114yes—
391C4⋊C8C22×D1118yes—
392#97—114no—
393#97—114no—
394#97—114no—
395#97—114no—
396#97C22×D1114yes—
397#97C22×D1114yes—
398C4×C8—114no—
399C4×C8—114no—
400C4×C8—114no—
401C4×C8—114no—
402C4×C8—114no—
403C4×C8C22×D1114yes—
404C2×C11—22no—
405C2×C11C22×C4×Q811yescharacteristic
406C2×C11C2×#56812yes—
407D11—22no—
408D11—22no—
409C24—111no—
410C2×Q8—118no—
411C2×Q8—114no—
412C2×Q8—448no—
413C2×Q8C2×C4×D1114yes—
414C22×C4—111no—
415C22×C4—111no—
416C22×C4—111no—
417C22×C4—114no—
418C22×C4—114no—
419C22×C4—111no—
420C22×C4—111no—
421C22×C4—112no—
422C22×C4—112no—
423C22×C4—112no—
424C22×C4—112no—
425C22×C4—112no—
426C22×C4—118no—
427C22×C4—444no—
428C22×C4C2×C4×D1112yes—
429C22×C4C23×D1111yescharacteristic
430M16—24no—
431M16—118no—
432M16—118no—
433M16—224no—
434M16—224no—
435M16—228no—
436M16—224no—
437C2×C8—22no—
438C2×C8—114no—
439C2×C8—112no—
440C2×C8—112no—
441C2×C8—114no—
442C2×C8—228no—
443C2×C8—222no—
444C2×C8Q8×D1114yescomplemented
445C2×C8C23×D1112yes—
446C2×C8C23×D1114yes—
447C2×C8C23×D1112yes—
448C4⋊C4—118no—
449C4⋊C4—114no—
450C4⋊C4—118no—
451C4⋊C4—118no—
452C4⋊C4—118no—
453C4⋊C4—118no—
454C4⋊C4—114no—
455C4⋊C4C2×C4×D1114yes—
456C4⋊C4C2×C4×D1118yes—
457C4⋊C4C2×C4×D1114yes—
458C22⋊C4—114no—
459C22⋊C4—118no—
460C22⋊C4C2×C4×D1114yes—
461C42—112no—
462C42—112no—
463C42—112no—
464C42—111no—
465C42—112no—
466C42—111no—
467C42—118no—
468C42—112no—
469C42—114no—
470C42C2×C4×D1111yescharacteristic
471C42C2×C4×D1111yescharacteristic
472C42C23×D1114yes—
473C42C23×D1112yes—
474C11#6019211yescharacteristic, complemented, Sylow
475C23—111no—
476C23—111no—
477C23—114no—
478C23—442no—
479C23C22×C4×D1111yescharacteristic
480Q8—44no—
481Q8—2216no—
482Q8—444no—
483C2×C4—42no—
484C2×C4—114no—
485C2×C4—111no—
486C2×C4—111no—
487C2×C4—112no—
488C2×C4—114no—
489C2×C4—114no—
490C2×C4—112no—
491C2×C4—112no—
492C2×C4—112no—
493C2×C4—112no—
494C2×C4—112no—
495C2×C4—118no—
496C2×C4—224no—
497C2×C4—224no—
498C2×C4—224no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—448no—
502C2×C4C22×C4×D1112yes—
503C2×C4C22×C4×D1112yes—
504C2×C4C22×C4×D1118yes—
505C2×C4C22×C4×D1111yescharacteristic
506C2×C4C2×Q8×D1112yes—
507C2×C4#41×D1112yes—
508C2×C4C24×D1111yescharacteristic
509C8—22no—
510C8—24no—
511C8—114no—
512C8—224no—
513C8—222no—
514C8C2×Q8×D1114yes—
515C22—22no—
516C22—112no—
517C22—112no—
518C22—222no—
519C22—222no—
520C22—444no—
521C22C4×Q8×D1112yes—
522C22C23×C4×D1111yescharacteristic
523C4—22no—
524C4—22no—
525C4—28no—
526C4—114no—
527C4—112no—
528C4—112no—
529C4—222no—
530C4—228no—
531C4C4×Q8×D1112yes—
532C4C22×Q8×D1111yescharacteristic
533C4C2×#41×D1111yescharacteristic
534C2—22no—
535C2—222no—
536C2—222no—
537C2C2×C4×Q8×D1111yescharacteristic
538C2D11×#56812yes—
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2961C2
prime radicalC23×D11C22×C4
cosocleC2×C4×C11C25
hypercenter#2961D11
hypocenterC11#60192
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2961

Complements

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

NH ≅ G/Ntype
2. #13077568C2semidirect
3. #13077561C2semidirect
4. #13077557C2semidirect
5. #13077556C2semidirect
6. #13077553C2semidirect
7. #13077549C2semidirect
8. #13077548C2semidirect
13. C11×#2961C2semidirect
30. C11×#446C22semidirect
42. #10622637C22semidirect
51. #10622443C22semidirect
52. #10622441C22semidirect
53. #10622441C22semidirect
58. #10622314C22semidirect
59. #10622314C22semidirect
62. C8×Dic22C22semidirect
87. C2×#4313Q8semidirect
164. C2×C8×C11C2×Q8semidirect
196. C2×C11⋊C8C2×Q8semidirect
204. #4313C2×Q8semidirect
212. #2961D11semidirect
280. #446C2×D11semidirect
444. C2×C8Q8×D11semidirect
474. C11#60192semidirect

Maximal subgroups

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

subgroupindex
D11×#5332
#130775682
#130775612
#130775572
#130775562
#130775532
#130775492
#130775482
#130771772
D11×#4232
#130770322
C2×#106223202
C11×#29612
#6019211