Finite Group Databasebeta

← #15618315

Subgroups — #15618315

Order 2816.

1962 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081911C211yesmaximal, characteristic
2#13077626C218yesmaximal, complemented
3#13077607C218yesmaximal, complemented
4#13077556C211yesmaximal, characteristic, complemented
5#13077553C211yesmaximal, characteristic, complemented
6#13077334C211yesmaximal, characteristic, complemented
7#13077313C212yesmaximal, complemented
8#13077308C212yesmaximal, complemented
9#13077263C212yesmaximal, complemented
10#13077248C211yesmaximal, characteristic, complemented
11#13077042C212yesmaximal, complemented
12C2×D11×#97C211yesmaximal, characteristic, complemented
13C11×#2932C211yesmaximal, characteristic, complemented
14C2×C11×#131C2212yes—
15C11×#532C2211yescharacteristic
16#10623359C2212yes—
17#41×Dic11C2212yes—
18C2×#67001C2212yes—
19C22×C8×D11C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21#10623259C412yes—
22#10623247C412yes—
23#10623211C414yes—
24#10623137C414yes—
25#10623131C414yes—
26#10623088C2214yes—
27C4×#4341C2214yes—
28C2×C42×D11C2211yescharacteristic
29#10623001C2211yescharacteristic
30C11×#435C2218yescomplemented
31C11×#423C2211yescharacteristic
32C11×#408C2212yes—
33C2×C11×#97C2211yescharacteristic
34#10622847C2212yes—
35#10622740C2218yes—
36#10622739C2212yes—
37#10622735C2212yes—
38#10622735C2214yescomplemented
39#10622732C2212yes—
40M16×Dic11C2212yes—
41M16×Dic11C2214yescomplemented
42C8×C22⋊D11C2218yes—
43#10622715C2212yes—
44#10622714C2212yes—
45#10622714C2214yescomplemented
46C2×#66879C2211yescharacteristic
47C2×#66879C2211yescharacteristic
48C2×#66879C2214yescomplemented
49#10622624C2218yescomplemented
50#10622537C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52#10622448C2214yes—
53#10622446C2214yes—
54#10622441C2218yescomplemented
55#10622341C2218yes—
56(C22⋊D11)⋊C8C2218yes—
57#10622333C2218yescomplemented
58#10622332C2218yescomplemented
59D11×#97C2214yes—
60D11×#97C2214yes—
61#10622314C2218yescomplemented
62C2×C11×#41C2312yes—
63C2×#4341C2×C414yes—
64C22×C4×D11C2×C412yes—
65C22×C4×D11C2311yescharacteristic
66C11×#131—28no—
67C2×C11×M16C2312yes—
68C2×C11×M16C2314yes—
69C22×C8×C11C2314yes—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C11×C4⋊Q8C2×C411yescharacteristic
73C11×#127C2×C411yescharacteristic
74C11×#124C2×C412yes—
75C11×#121C2×C414yes—
76C4×D4×C11C2314yes—
77C2×C42×C11C2311yescharacteristic
78#67001—28no—
79#66999C2×C414yes—
80Q8×Dic11C2×C414yes—
81#66991C2×C414yes—
82#66991C2×C414yes—
83#66990C2×C414yes—
84#66989C2×C414yes—
85#66988C2×C414yes—
86D4×Dic11C2×C414yes—
87D4×Dic11C2×C414yes—
88D4×Dic11C2×C418yes—
89C4×C22⋊D11C2318yes—
90#66979C2312yes—
91#66979C2314yes—
92#66977C2×C414yes—
93C2×C4×Dic11C2×C412yes—
94C2×C4×Dic11C2311yescharacteristic
95C2×C4×Dic11C2314yes—
96C2×#4318C2312yes—
97C2×#4318C2314yes—
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2314yes—
100C22×C11⋊C8C2311yescharacteristic
101C2×C8×D11—24no—
102C2×C8×D11—24no—
103C2×C8×D11C2314yes—
104C2×C8×D11C2314yes—
105#66950C2×C414yes—
106#66945C2×C414yes—
107#66943C2×C414yes—
108#66940C2×C414yes—
109#66936C2×C418yes—
110(C22⋊D11)⋊C4C2×C418yes—
111#66932C2×C418yes—
112#66930C2×C418yes—
113C42×D11C2×C412yes—
114C42×D11C2×C412yes—
115C42×D11C2312yes—
116C42×D11C2312yes—
117#66923C2×C412yes—
118#66922C2×C412yes—
119C4×Dic22C2314yes—
120C11×C4⋊C8C2314yes—
121C11×C22⋊C8C2318yes—
122C11×#97C2314yes—
123C22⋊(C11⋊C8)C2318yes—
124(C2×D11)⋊C8C2318yes—
125#66879C2314yes—
126#66879C2312yes—
127#66879C2314yes—
128#66879C2312yes—
129#66879C2314yes—
130#66879C2312yes—
131#66879C2312yes—
132Dic11⋊C8C2318yes—
133Dic11⋊C8C2318yes—
134C8×Dic11C2314yes—
135C8×Dic11C2314yes—
136C8×Dic11C2314yes—
137C4⋊(C11⋊C8)C2314yes—
138#66867C2314yes—
139#60207—111nomaximal, Sylow
140C23×D11C22×C411yescharacteristic
141C11×#41—24no—
142C11×#41—24no—
143C2×Q8×C11C22×C412yes—
144C2×D4×C11C22×C414yes—
145C2×D4×C11C22×C412yes—
146C2×D4×C11C22×C414yes—
147C22×C4×C11C22×C412yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2411yescharacteristic
150C2×C22⋊D11C22×C418yes—
151C22×Dic11C22×C411yescharacteristic
152C22×Dic11C22×C418yes—
153C22×Dic11C22×C412yes—
154#4341—48no—
155C2×C4×D11—22no—
156C2×C4×D11—22no—
157C2×C4×D11—44no—
158C2×C4×D11C22×C412yes—
159C2×C4×D11C22×C412yes—
160C2×C4×D11C22×C412yes—
161C2×C4×D11C22×C412yes—
162C2×C4×D11C22×C412yes—
163C2×C4×D11C2412yes—
164C2×Dic22C22×C414yes—
165C11×M16—28no—
166C11×M16—24no—
167C2×C8×C11—28no—
168C2×C8×C11—22no—
169C2×C8×C11#4114yescomplemented
170C2×C8×C11C2414yes—
171C2×C8×C11C2412yes—
172C2×C8×C11C2412yes—
173C11×C4⋊C4C22×C414yes—
174C11×C22⋊C4C22×C418yes—
175C42×C11C22×C411yescharacteristic
176C42×C11C22×C411yescharacteristic
177C42×C11C2412yes—
178C22⋊Dic11C22×C418yes—
179C22⋊Dic11C22×C418yes—
180C22⋊Dic11C22×C414yes—
181(C2×D11)⋊C4C22×C418yes—
182C4⋊Dic11C22×C414yes—
183C4⋊Dic11C22×C414yes—
184C4⋊Dic11C22×C418yes—
185Dic11⋊C4C22×C418yes—
186Dic11⋊C4C22×C418yes—
187C4×Dic11C22×C412yes—
188C4×Dic11C22×C412yes—
189C4×Dic11C22×C412yes—
190C4×Dic11C22×C412yes—
191C4×Dic11C22×C412yes—
192C4×Dic11C22×C418yes—
193C4×Dic11C2411yescharacteristic
194C4×Dic11C2414yes—
195C4×Dic11C2411yescharacteristic
196#4318—28no—
197#4318—24no—
198C2×C11⋊C8—28no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8#4114yescomplemented
201C2×C11⋊C8C2412yes—
202C2×C11⋊C8C2414yes—
203C2×C11⋊C8C2412yes—
204C8×D11—28no—
205C8×D11—28no—
206#3444—111no—
207#2970—118no—
208#2968—118no—
209#2961—111no—
210#2961—111no—
211#2932—111no—
212#2932D1111yescharacteristic, complemented
213#2929—112no—
214#2929—112no—
215#2923—112no—
216#2920—111no—
217#2875—112no—
218C22×#97—111no—
219C23×C11C23×C414yes—
220C23×C11C23×C411yescharacteristic
221C22×D11—22no—
222C22×D11—24no—
223C22×D11C23×C412yes—
224Q8×C11—24no—
225D4×C11—28no—
226D4×C11—24no—
227D4×C11—44no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—42no—
231C2×C4×C11C23×C412yes—
232C2×C4×C11C23×C414yes—
233C2×C4×C11C23×C412yes—
234C2×C4×C11C23×C411yescharacteristic
235C2×C4×C11C2×#4112yes—
236C2×C4×C11C2×#4112yes—
237C2×C4×C11C2511yescharacteristic
238C22⋊D11—216no—
239C2×Dic11—22no—
240C2×Dic11—42no—
241C2×Dic11—48no—
242C2×Dic11C23×C412yes—
243C2×Dic11C23×C412yes—
244C2×Dic11C23×C412yes—
245C2×Dic11C23×C418yes—
246C4×D11—24no—
247C4×D11—24no—
248C4×D11—24no—
249C4×D11—22no—
250C4×D11—22no—
251C4×D11—42no—
252C4×D11—42no—
253Dic22—44no—
254C8×C11—22no—
255C8×C11—24no—
256C8×C11C2×#4114yes—
257C11⋊C8—22no—
258C11⋊C8—24no—
259C11⋊C8C2×#4114yes—
260C2×#131—112no—
261C2×#131C2×D1112yes—
262C23×C8—111no—
263C23×C8—111no—
264#533—112no—
265#533—111no—
266#532—112no—
267#532C2×D1111yescharacteristic
268#529—114no—
269#529—114no—
270#529—114no—
271#525—112no—
272#525—114no—
273C4×#41—112no—
274C4×#41—114no—
275C22×C42—111no—
276#446—118no—
277#446—118no—
278#435—118no—
279#435—118no—
280#435—118no—
281#435C2×D1118yescomplemented
282C8×D4—118no—
283C8×D4—118no—
284#433—118no—
285#432—114no—
286#432—118no—
287#431—114no—
288#424—112no—
289#424—112no—
290#423—111no—
291#423C2×D1111yescharacteristic
292#408—112no—
293#408C2×D1112yes—
294#407—112no—
295#405—112no—
296#405—114no—
297#405—112no—
298#405—114no—
299C4×M16—112no—
300C4×M16—114no—
301C2×#97—111no—
302C2×#97—111no—
303C2×#97—114no—
304C2×#97—111no—
305C2×#97—114no—
306C2×#97—114no—
307C2×#97C2×D1111yescharacteristic
308C22×C11—22no—
309C22×C11—24no—
310C22×C11—28no—
311C22×C11C4×#4112yes—
312C22×C11C24×C411yescharacteristic
313C2×D11—28no—
314C2×D11—22no—
315C2×D11—22no—
316C2×D11#56814yes—
317C4×C11—24no—
318C4×C11—22no—
319C4×C11—22no—
320C4×C11C4×#4112yes—
321C4×C11C22×#4111yescharacteristic
322C4×C11C22×#4111yescharacteristic
323Dic11—22no—
324Dic11—28no—
325Dic11—22no—
326Dic11—22no—
327C2×#41—114no—
328C2×#41C22×D1112yes—
329C23×C4—111no—
330C23×C4—112no—
331#131—28no—
332#131—228no—
333C2×M16—112no—
334C2×M16—114no—
335C2×M16C22×D1112yes—
336C2×M16C22×D1114yes—
337C22×C8—111no—
338C22×C8—111no—
339C22×C8—114no—
340C22×C8—114no—
341C22×C8—114no—
342C22×C8—224no—
343C22×C8—224no—
344C22×C8C22×D1111yescharacteristic
345C22×C8C22×D1114yes—
346C22×C8C22×D1111yescharacteristic
347C4⋊Q8—112no—
348C4⋊Q8C4×D1111yescharacteristic
349#127C4×D1111yescharacteristic
350#126—118no—
351#125—114no—
352#125—112no—
353#124—114no—
354#124C4×D1112yes—
355#123—114no—
356#123—118no—
357C22⋊Q8—114no—
358C22⋊Q8—114no—
359C22⋊Q8—114no—
360#121—114no—
361#121—114no—
362#121C4×D1114yes—
363#120—114no—
364C4×Q8—114no—
365C4×Q8—114no—
366C4×Q8—114no—
367C4×D4—118no—
368C4×D4—114no—
369C4×D4—114no—
370C4×D4—118no—
371C4×D4—118no—
372C4×D4C22×D1114yes—
373#117—112no—
374#117—114no—
375#117—114no—
376#117—118no—
377C2×C42—112no—
378C2×C42—114no—
379C2×C42—111no—
380C2×C42—112no—
381C2×C42—112no—
382C2×C42—112no—
383C2×C42—112no—
384C2×C42C22×D1111yescharacteristic
385C4⋊C8—118no—
386C4⋊C8—118no—
387C4⋊C8—114no—
388C4⋊C8C22×D1114yes—
389C22⋊C8—118no—
390C22⋊C8—118no—
391C22⋊C8C22×D1118yes—
392#97—112no—
393#97—112no—
394#97—112no—
395#97—112no—
396#97—114no—
397#97—114no—
398#97—114no—
399#97—114no—
400#97C22×D1114yes—
401C4×C8—114no—
402C4×C8—114no—
403C4×C8—114no—
404C2×C11—22no—
405C2×C11—44no—
406C2×C11C2×C4×#4111yescharacteristic
407C2×C11C2×#56812yes—
408D11—24no—
409C24—111no—
410#41—24no—
411#41—24no—
412#41—448no—
413C2×Q8—114no—
414C2×Q8C2×C4×D1112yes—
415C2×D4—118no—
416C2×D4C2×C4×D1114yes—
417C2×D4C2×C4×D1112yes—
418C2×D4C2×C4×D1114yes—
419C22×C4—111no—
420C22×C4—112no—
421C22×C4—118no—
422C22×C4—112no—
423C22×C4—112no—
424C22×C4—112no—
425C22×C4—112no—
426C22×C4—112no—
427C22×C4—112no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—444no—
431C22×C4C2×C4×D1112yes—
432C22×C4C23×D1114yes—
433C22×C4C23×D1111yescharacteristic
434M16—24no—
435M16—28no—
436M16—228no—
437M16—224no—
438C2×C8—22no—
439C2×C8—28no—
440C2×C8—114no—
441C2×C8—112no—
442C2×C8—114no—
443C2×C8—112no—
444C2×C8—228no—
445C2×C8—228no—
446C2×C8—222no—
447C2×C8—228no—
448C2×C8#434114yescomplemented
449C2×C8C23×D1114yes—
450C2×C8C23×D1112yes—
451C2×C8C23×D1112yes—
452C4⋊C4—114no—
453C4⋊C4—114no—
454C4⋊C4—118no—
455C4⋊C4—118no—
456C4⋊C4—118no—
457C4⋊C4C2×C4×D1114yes—
458C22⋊C4—114no—
459C22⋊C4—118no—
460C22⋊C4—118no—
461C22⋊C4—118no—
462C22⋊C4C2×C4×D1118yes—
463C42—112no—
464C42—112no—
465C42—112no—
466C42—112no—
467C42—112no—
468C42—118no—
469C42—111no—
470C42—114no—
471C42—111no—
472C42C2×C4×D1111yescharacteristic
473C42C2×C4×D1111yescharacteristic
474C42C23×D1112yes—
475C11#6020711yescharacteristic, complemented, Sylow
476C23—112no—
477C23—224no—
478C23—222no—
479C23C22×C4×D1114yes—
480C23C22×C4×D1111yescharacteristic
481Q8—24no—
482Q8—444no—
483D4—28no—
484D4—24no—
485D4—44no—
486D4—2216no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—42no—
490C2×C4—112no—
491C2×C4—112no—
492C2×C4—112no—
493C2×C4—118no—
494C2×C4—224no—
495C2×C4—224no—
496C2×C4—222no—
497C2×C4—224no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—448no—
504C2×C4C22×C4×D1112yes—
505C2×C4C22×C4×D1112yes—
506C2×C4C22×C4×D1114yes—
507C2×C4C22×C4×D1111yescharacteristic
508C2×C4C2×#434112yes—
509C2×C4#41×D1112yes—
510C2×C4C24×D1111yescharacteristic
511C8—24no—
512C8—22no—
513C8—114no—
514C8—222no—
515C8—224no—
516C8C2×#434114yes—
517C22—22no—
518C22—28no—
519C22—24no—
520C22—114no—
521C22—228no—
522C22—222no—
523C22—222no—
524C22C4×#434112yes—
525C22C23×C4×D1111yescharacteristic
526C4—22no—
527C4—22no—
528C4—24no—
529C4—222no—
530C4—222no—
531C4—228no—
532C4—222no—
533C4C4×#434112yes—
534C4C22×#434111yescharacteristic
535C4C2×#41×D1111yescharacteristic
536C2—22no—
537C2—44no—
538C2—224no—
539C2C2×C4×#434111yescharacteristic
540C2D11×#56812yes—
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2932C2
prime radical#13081911C2
cosocleC2×C4×C11C25
hypercenter#2932D11
hypocenterC11#60207
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2932

Complements

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

NH ≅ G/Ntype
2. #13077626C2semidirect
3. #13077607C2semidirect
4. #13077556C2semidirect
5. #13077553C2semidirect
6. #13077334C2semidirect
7. #13077313C2semidirect
8. #13077308C2semidirect
9. #13077263C2semidirect
10. #13077248C2semidirect
11. #13077042C2semidirect
12. C2×D11×#97C2semidirect
13. C11×#2932C2semidirect
30. C11×#435C22semidirect
38. #10622735C22semidirect
41. M16×Dic11C22semidirect
45. #10622714C22semidirect
48. C2×#66879C22semidirect
49. #10622624C22semidirect
54. #10622441C22semidirect
57. #10622333C22semidirect
58. #10622332C22semidirect
61. #10622314C22semidirect
169. C2×C8×C11#41semidirect
200. C2×C11⋊C8#41semidirect
212. #2932D11semidirect
281. #435C2×D11semidirect
448. C2×C8#4341semidirect
475. C11#60207semidirect

Maximal subgroups

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

subgroupindex
#130819112
#130776262
#130776072
#130775562
#130775532
#130773342
#130773132
#130773082
#130772632
#130772482
#130770422
C2×D11×#972
C11×#29322
#6020711