Finite Group Databasebeta

← #15618317

Subgroups — #15618317

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#13081913C211yesmaximal, characteristic
2#13077629C218yesmaximal, complemented
3#13077609C218yesmaximal, complemented
4#13077557C211yesmaximal, characteristic, complemented
5#13077335C211yesmaximal, characteristic, complemented
6#13077333C211yesmaximal, characteristic, complemented
7#13077312C212yesmaximal, complemented
8#13077309C212yesmaximal, complemented
9#13077266C212yesmaximal, complemented
10#13077248C211yesmaximal, characteristic, complemented
11#13077043C212yesmaximal, complemented
12C2×D11×#97C211yesmaximal, characteristic, complemented
13C11×#2961C211yesmaximal, characteristic, complemented
14C11×#533C2211yescharacteristic
15C2×#66960C2212yes—
16C2×#66954C2212yes—
17C22×C8×D11C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19#10623259C412yes—
20#10623256C412yes—
21#10623222C414yes—
22#10623158C414yes—
23#10623155C414yes—
24#10623111C2214yes—
25C4×#4343C2214yes—
26#10623055C2212yes—
27#10623053C2212yes—
28#10623008C2211yescharacteristic
29C2×C42×D11C2211yescharacteristic
30C11×#446C2218yescomplemented
31C11×#424C2212yes—
32C11×#423C2211yescharacteristic
33C11×#405C2212yes—
34C2×C11×#97C2211yescharacteristic
35#10622742C2212yes—
36#10622739C2212yes—
37M16×Dic11C2212yes—
38#10622723C2212yes—
39C2×#66879C2211yescharacteristic
40C2×#66879C2211yescharacteristic
41#10622637C2218yescomplemented
42#10622612C2212yes—
43#10622610C2212yes—
44#10622537C2211yescharacteristic
45C2×#66867C2211yescharacteristic
46#10622453C2218yescomplemented
47#10622449C2218yes—
48#10622449C2218yescomplemented
49#10622448C2214yes—
50#10622448C2218yescomplemented
51#10622447C2218yes—
52#10622446C2214yes—
53#10622321C2214yescomplemented
54#10622319C2218yes—
55#10622319C2218yescomplemented
56D11×#97C2214yes—
57D11×#97C2214yes—
58D11×#97C2214yescomplemented
59#10622302C2214yescomplemented
60C4×#4313C2214yescomplemented
61C8×D44C2218yes—
62C2×#4343C2×C414yes—
63C2×#4339C2312yes—
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#67000C2×C414yes—
76#66999C2×C414yes—
77Q8×Dic11C2×C414yes—
78#66983C2×C414yes—
79C2×C4×Dic11C2×C412yes—
80C2×C4×Dic11C2311yescharacteristic
81C2×#4318C2312yes—
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2311yescharacteristic
84#66960—28no—
85#66954—28no—
86C2×#4313C2314yes—
87C2×#4313C2314yes—
88C2×C8×D11—24no—
89C2×C8×D11—24no—
90C2×C8×D11C2314yes—
91C2×C8×D11C2314yes—
92C2×C8×D11C2314yes—
93C2×C8×D11C2314yes—
94#66951C2×C418yes—
95#66950C2×C414yes—
96#66948C2×C414yes—
97#66948C2×C414yes—
98#66947C2×C418yes—
99#66946C2×C414yes—
100#66946C2×C414yes—
101#66946C2×C418yes—
102#66945C2×C414yes—
103#66945C2×C418yes—
104#66943C2×C414yes—
105#66940C2×C414yes—
106#66939C2×C414yes—
107#66935C2×C414yes—
108(C22⋊D11)⋊C4C2×C418yes—
109#66928C2×C412yes—
110#66927C2×C411yescharacteristic
111C4×D44C2314yes—
112C4×D44C2318yes—
113#66925C2314yes—
114C42×D11C2×C412yes—
115C42×D11C2×C412yes—
116C42×D11C2312yes—
117C42×D11C2312yes—
118C42×D11C2314yes—
119#66922C2×C411yescharacteristic
120C11×C4⋊C8C2314yes—
121C11×C4⋊C8C2318yes—
122C11×#97C2314yes—
123C11×#97C2314yes—
124C4×C8×C11C2314yes—
125(C2×D11)⋊C8C2318yes—
126(C2×D11)⋊C8C2318yes—
127(C2×D11)⋊C8C2318yes—
128#66879C2314yes—
129#66879C2312yes—
130#66879C2312yes—
131#66879C2312yes—
132#66879C2312yes—
133C8×Dic11C2314yes—
134C4⋊(C11⋊C8)C2314yes—
135C4⋊(C11⋊C8)C2318yes—
136#66867C2314yes—
137#66867C2314yes—
138C4×C11⋊C8C2314yes—
139#60207—111nomaximal, Sylow
140C23×D11C22×C411yescharacteristic
141C2×Q8×C11C22×C414yes—
142C22×C4×C11C22×C412yes—
143C22×C4×C11C2411yescharacteristic
144C2×C22⋊D11C22×C414yes—
145C22×Dic11C22×C411yescharacteristic
146C22×Dic11C22×C412yes—
147#4343—48no—
148#4339—24no—
149#4339—24no—
150C2×D44C22×C418yes—
151C2×D44C22×C412yes—
152C2×D44C22×C414yes—
153C2×C4×D11—22no—
154C2×C4×D11—22no—
155C2×C4×D11—44no—
156C2×C4×D11C22×C412yes—
157C2×C4×D11C22×C412yes—
158C2×C4×D11C22×C412yes—
159C2×C4×D11C22×C412yes—
160C2×C4×D11C22×C412yes—
161C2×C4×D11C22×C418yes—
162C2×C4×D11C2412yes—
163C2×C4×D11C2414yes—
164C2×Dic22C22×C412yes—
165C11×M16—24no—
166C2×C8×C11—22no—
167C2×C8×C11#4114yescomplemented
168C2×C8×C11C2414yes—
169C2×C8×C11C2412yes—
170C2×C8×C11C2412yes—
171C11×C4⋊C4C22×C414yes—
172C11×C4⋊C4C22×C414yes—
173C11×C4⋊C4C22×C418yes—
174C11×C22⋊C4C22×C414yes—
175C42×C11C22×C411yescharacteristic
176C42×C11C22×C411yescharacteristic
177C42×C11C2414yes—
178C42×C11C2412yes—
179(C2×D11)⋊C4C22×C418yes—
180(C2×D11)⋊C4C22×C418yes—
181(C2×D11)⋊C4C22×C418yes—
182(C2×D11)⋊C4C22×C418yes—
183C4⋊Dic11C22×C414yes—
184C4⋊Dic11C22×C418yes—
185Dic11⋊C4C22×C418yes—
186C4×Dic11C22×C412yes—
187C4×Dic11C22×C412yes—
188C4×Dic11C22×C412yes—
189C4×Dic11C22×C412yes—
190C4×Dic11C22×C412yes—
191C4×Dic11C22×C418yes—
192C4×Dic11C2411yescharacteristic
193C4×Dic11C2411yescharacteristic
194#4318—24no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8#4114yescomplemented
197C2×C11⋊C8C2414yes—
198C2×C11⋊C8C2412yes—
199C2×C11⋊C8C2412yes—
200#4313—28no—
201#4313—28no—
202C8×D11—28no—
203C8×D11—28no—
204C8×D11—28no—
205C8×D11—28no—
206#3444—111no—
207#2970—118no—
208#2968—118no—
209#2961—111no—
210#2961D1111yescharacteristic, complemented
211#2932—111no—
212#2932—111no—
213#2929—112no—
214#2929—112no—
215#2923—112no—
216#2920—111no—
217#2875—112no—
218C22×#97—111no—
219C23×C11C23×C411yescharacteristic
220C22×D11—22no—
221C22×D11—24no—
222C22×D11C23×C414yes—
223C22×D11C23×C412yes—
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×C11C2×#4112yes—
231C2×C4×C11C2×#4112yes—
232C2×C4×C11C2511yescharacteristic
233C22⋊D11—28no—
234C2×Dic11—22no—
235C2×Dic11—42no—
236C2×Dic11C23×C412yes—
237C2×Dic11C23×C412yes—
238C2×Dic11C23×C412yes—
239C2×Dic11C23×C414yes—
240D44—216no—
241D44—24no—
242D44—44no—
243C4×D11—24no—
244C4×D11—24no—
245C4×D11—24no—
246C4×D11—22no—
247C4×D11—22no—
248C4×D11—24no—
249C4×D11—24no—
250C4×D11—42no—
251C4×D11—42no—
252C4×D11—48no—
253Dic22—24no—
254C8×C11—22no—
255C8×C11—24no—
256C8×C11C2×#4114yes—
257C11⋊C8—22no—
258C11⋊C8—24no—
259C11⋊C8C2×#4114yes—
260C2×#131—112no—
261C2×#131—112no—
262C23×C8—111no—
263C23×C8—111no—
264#533—112no—
265#533C2×D1111yescharacteristic
266#532—112no—
267#532—111no—
268#529—114no—
269#529—114no—
270#529—114no—
271#525—114no—
272#525—112no—
273C4×#41—114no—
274C4×#41—112no—
275C22×C42—111no—
276#446—118no—
277#446C2×D1118yescomplemented
278#435—118no—
279#435—118no—
280#435—118no—
281#435—118no—
282C8×D4—118no—
283C8×D4—118no—
284#433—118no—
285#432—114no—
286#432—118no—
287#431—114no—
288#424—112no—
289#424C2×D1112yes—
290#423—111no—
291#423C2×D1111yescharacteristic
292#408—112no—
293#408—112no—
294#407—112no—
295#405—112no—
296#405—114no—
297#405—114no—
298#405C2×D1112yes—
299C4×M16—112no—
300C4×M16—114no—
301C2×#97—111no—
302C2×#97—111no—
303C2×#97—111no—
304C2×#97—114no—
305C2×#97—114no—
306C2×#97—114no—
307C2×#97C2×D1111yescharacteristic
308C22×C11—22no—
309C22×C11C4×#4112yes—
310C22×C11C24×C411yescharacteristic
311C2×D11—28no—
312C2×D11—22no—
313C2×D11—22no—
314C2×D11—24no—
315C2×D11—28no—
316C2×D11#56814yes—
317C4×C11—22no—
318C4×C11—22no—
319C4×C11—28no—
320C4×C11C4×#4112yes—
321C4×C11C22×#4111yescharacteristic
322C4×C11C22×#4111yescharacteristic
323Dic11—24no—
324Dic11—22no—
325Dic11—22no—
326Dic11—22no—
327C2×#41—114no—
328C2×#41—112no—
329C23×C4—111no—
330C23×C4—112no—
331#131—228no—
332#131—228no—
333C2×M16—112no—
334C2×M16—114no—
335C2×M16—114no—
336C2×M16C22×D1112yes—
337C22×C8—111no—
338C22×C8—111no—
339C22×C8—114no—
340C22×C8—114no—
341C22×C8—114no—
342C22×C8—114no—
343C22×C8—224no—
344C22×C8—224no—
345C22×C8C22×D1111yescharacteristic
346C22×C8C22×D1111yescharacteristic
347C4⋊Q8—111no—
348C4⋊Q8C4×D1112yes—
349#127—111no—
350#126—118no—
351#125—114no—
352#125C4×D1112yes—
353#124—114no—
354#124—112no—
355#123—118no—
356#123—114no—
357C22⋊Q8—114no—
358C22⋊Q8—114no—
359C22⋊Q8C4×D1114yes—
360#121—114no—
361#121—114no—
362#121—114no—
363#120—114no—
364C4×Q8—114no—
365C4×Q8—114no—
366C4×Q8C22×D1114yes—
367C4×D4—118no—
368C4×D4—114no—
369C4×D4—114no—
370C4×D4—118no—
371C4×D4—118no—
372C4×D4—114no—
373#117—114no—
374#117—118no—
375#117—114no—
376#117C22×D1112yes—
377C2×C42—112no—
378C2×C42—111no—
379C2×C42—112no—
380C2×C42—112no—
381C2×C42—114no—
382C2×C42—112no—
383C2×C42—112no—
384C2×C42C22×D1111yescharacteristic
385C4⋊C8—114no—
386C4⋊C8—118no—
387C4⋊C8C22×D1114yes—
388C4⋊C8C22×D1118yes—
389C22⋊C8—118no—
390C22⋊C8—118no—
391C22⋊C8—118no—
392#97—112no—
393#97—112no—
394#97—112no—
395#97—112no—
396#97—114no—
397#97—114no—
398#97—114no—
399#97C22×D1114yes—
400#97C22×D1114yes—
401C4×C8—114no—
402C4×C8—114no—
403C4×C8C22×D1114yes—
404C2×C11—22no—
405C2×C11C2×C4×#4111yescharacteristic
406C2×C11C2×#56812yes—
407D11—24no—
408D11—44no—
409C24—111no—
410#41—224no—
411#41—224no—
412#41—448no—
413C2×Q8—112no—
414C2×Q8C2×C4×D1114yes—
415C2×D4—114no—
416C2×D4—118no—
417C2×D4—112no—
418C2×D4—114no—
419C22×C4—111no—
420C22×C4—112no—
421C22×C4—112no—
422C22×C4—112no—
423C22×C4—112no—
424C22×C4—112no—
425C22×C4—114no—
426C22×C4—112no—
427C22×C4—112no—
428C22×C4—118no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—444no—
432C22×C4C2×C4×D1112yes—
433C22×C4C23×D1111yescharacteristic
434M16—24no—
435M16—228no—
436M16—224no—
437M16—228no—
438C2×C8—22no—
439C2×C8—114no—
440C2×C8—112no—
441C2×C8—114no—
442C2×C8—112no—
443C2×C8—228no—
444C2×C8—228no—
445C2×C8—222no—
446C2×C8—228no—
447C2×C8—228no—
448C2×C8#434314yescomplemented
449C2×C8C23×D1114yes—
450C2×C8C23×D1112yes—
451C2×C8C23×D1112yes—
452C4⋊C4—114no—
453C4⋊C4—118no—
454C4⋊C4—118no—
455C4⋊C4C2×C4×D1114yes—
456C4⋊C4C2×C4×D1118yes—
457C4⋊C4C2×C4×D1114yes—
458C22⋊C4—118no—
459C22⋊C4—118no—
460C22⋊C4—118no—
461C22⋊C4—118no—
462C22⋊C4C2×C4×D1114yes—
463C42—112no—
464C42—112no—
465C42—112no—
466C42—112no—
467C42—112no—
468C42—118no—
469C42—111no—
470C42—111no—
471C42C2×C4×D1111yescharacteristic
472C42C2×C4×D1111yescharacteristic
473C42C23×D1114yes—
474C42C23×D1112yes—
475C11#6020711yescharacteristic, complemented, Sylow
476C23—112no—
477C23—114no—
478C23—224no—
479C23—222no—
480C23C22×C4×D1111yescharacteristic
481Q8—44no—
482Q8—224no—
483D4—2216no—
484D4—228no—
485D4—224no—
486D4—444no—
487C2×C4—42no—
488C2×C4—112no—
489C2×C4—112no—
490C2×C4—112no—
491C2×C4—114no—
492C2×C4—224no—
493C2×C4—224no—
494C2×C4—222no—
495C2×C4—224no—
496C2×C4—222no—
497C2×C4—224no—
498C2×C4—222no—
499C2×C4—224no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4—448no—
503C2×C4—442no—
504C2×C4C22×C4×D1112yes—
505C2×C4C22×C4×D1112yes—
506C2×C4C22×C4×D1118yes—
507C2×C4C22×C4×D1111yescharacteristic
508C2×C4C2×#434312yes—
509C2×C4#41×D1112yes—
510C2×C4C24×D1111yescharacteristic
511C8—22no—
512C8—24no—
513C8—114no—
514C8—222no—
515C8—224no—
516C8C2×#434314yes—
517C22—22no—
518C22—114no—
519C22—228no—
520C22—222no—
521C22—222no—
522C22—228no—
523C22—224no—
524C22C4×#434312yes—
525C22C23×C4×D1111yescharacteristic
526C4—22no—
527C4—22no—
528C4—28no—
529C4—222no—
530C4—222no—
531C4—222no—
532C4—224no—
533C4C4×#434312yes—
534C4C22×#434311yescharacteristic
535C4C2×#41×D1111yescharacteristic
536C2—22no—
537C2—224no—
538C2—444no—
539C2C2×C4×#434311yescharacteristic
540C2D11×#56812yes—
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2961C2
prime radical#13081913C2
cosocleC2×C4×C11C25
hypercenter#2961D11
hypocenterC11#60207
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2961

Complements

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

NH ≅ G/Ntype
2. #13077629C2semidirect
3. #13077609C2semidirect
4. #13077557C2semidirect
5. #13077335C2semidirect
6. #13077333C2semidirect
7. #13077312C2semidirect
8. #13077309C2semidirect
9. #13077266C2semidirect
10. #13077248C2semidirect
11. #13077043C2semidirect
12. C2×D11×#97C2semidirect
13. C11×#2961C2semidirect
30. C11×#446C22semidirect
41. #10622637C22semidirect
46. #10622453C22semidirect
48. #10622449C22semidirect
50. #10622448C22semidirect
53. #10622321C22semidirect
55. #10622319C22semidirect
58. D11×#97C22semidirect
59. #10622302C22semidirect
60. C4×#4313C22semidirect
167. C2×C8×C11#41semidirect
196. C2×C11⋊C8#41semidirect
210. #2961D11semidirect
277. #446C2×D11semidirect
448. C2×C8#4343semidirect
475. C11#60207semidirect

Maximal subgroups

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

subgroupindex
#130819132
#130776292
#130776092
#130775572
#130773352
#130773332
#130773122
#130773092
#130772662
#130772482
#130770432
C2×D11×#972
C11×#29612
#6020711