Finite Group Databasebeta

← #15618751

Subgroups — #15618751

Order 2816.

1702 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#533C211yesmaximal, characteristic
2#13077720C214yesmaximal, complemented
3#13077718C211yesmaximal, characteristic, complemented
4#13077717C212yesmaximal, complemented
5#13077712C214yesmaximal, complemented
6#13077707C214yesmaximal, complemented
7#13077568C214yesmaximal, complemented
8Q8×#4313C214yesmaximal, complemented
9#13077250C214yesmaximal
10#13077244C212yesmaximal
11C11×#2986C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13#10623259C412yes—
14D11×C4⋊Q8C412yes—
15#10623219C412yes—
16D11×#125C412yes—
17D11×C22⋊Q8C414yes—
18#10623153C414yes—
19#10623109C2214yes—
20C4×Q8×D11C2214yes—
21D11×#117C2212yes—
22#10623048C2212yes—
23C2×C42×D11C2211yescharacteristic
24#10623001C2211yescharacteristic
25C11×#446C2214yescomplemented
26C8×Q8×C11C2214yescomplemented
27C11×#433C2214yes—
28C11×#431C2212yes—
29#10622637C2214yescomplemented
30Q8×C11⋊C8C2214yescomplemented
31#10622613C2214yes—
32#10622538C2212yes—
33#10622453C2218yes—
34#10622450C2218yes—
35#10622450C2212yes—
36#10622450C2212yes—
37#10622448C2212yes—
38#10622448C2212yes—
39#10622444C2214yescomplemented
40#10622444C2218yescomplemented
41#10622443C2214yescomplemented
42#10622441C2218yescomplemented
43#10622339C2214yes—
44#10622333C2218yes—
45#10622332C2214yes—
46#10622322C2214yes—
47#10622320C2214yes—
48#10622314C2218yescomplemented
49#10622303C2214yes—
50C4×#4313C2214yes—
51C4×#4313C2214yes—
52#10622298C2214yes—
53#10622292C2218yescomplemented
54#10622292C2214yescomplemented
55C8×Dic22C2214yescomplemented
56C2×Q8×D11C2×C414yes—
57C22×C4×D11C2×C412yes—
58C22×C4×D11C2311yescharacteristic
59C11×C4⋊Q8C2×C412yes—
60C11×#125C2×C412yes—
61C11×C22⋊Q8C2×C414yes—
62C4×Q8×C11C2314yes—
63C11×#117C2312yes—
64C2×C42×C11C2311yescharacteristic
65#66999C2×C414yes—
66Q8×Dic11C2×C414yes—
67#66997C2×C414yes—
68#66979C2312yes—
69#66977C2×C414yes—
70C2×C4×Dic11C2×C412yes—
71C2×C4×Dic11C2311yescharacteristic
72C2×#4313C2314yes—
73C2×#4313C2314yes—
74#66950C2×C414yes—
75#66949C2×C418yes—
76#66945C2×C414yes—
77C4⋊C4×D11C2×C414yes—
78C4⋊C4×D11C2×C414yes—
79C4⋊C4×D11C2×C418yes—
80#66943C2×C414yes—
81#66942C2×C418yes—
82#66941C2×C414yes—
83#66941C2×C414yes—
84#66940C2×C414yes—
85#66940C2×C418yes—
86C22⋊C4×D11C2×C414yes—
87#66931C2×C418yes—
88#66930C2×C414yes—
89#66925C2314yes—
90C42×D11C2×C411yescharacteristic
91C42×D11C2×C411yescharacteristic
92C42×D11C2×C411yescharacteristic
93C42×D11C2×C411yescharacteristic
94C42×D11C2312yes—
95C42×D11C2312yes—
96C42×D11C2314yes—
97#66923C2×C412yes—
98#66922C2×C412yes—
99C4×Dic22C2314yes—
100C4×Dic22C2318yes—
101C11×C4⋊C8C2312yes—
102C11×C4⋊C8C2312yes—
103C11×C4⋊C8C2318yes—
104C11×C22⋊C8C2314yes—
105C11×#97C2314yes—
106C4×C8×C11C2314yes—
107C4×C8×C11C2314yes—
108C22⋊(C11⋊C8)C2314yes—
109(C2×D11)⋊C8C2314yes—
110(C2×D11)⋊C8C2314yes—
111#66879C2314yes—
112#66879C2318yes—
113#66879C2314yes—
114Dic11⋊C8C2318yes—
115Dic11⋊C8C2314yes—
116Dic11⋊C8C2318yes—
117Dic11⋊C8C2314yes—
118C8×Dic11C2318yes—
119C4⋊(C11⋊C8)C2312yes—
120C4⋊(C11⋊C8)C2312yes—
121C4⋊(C11⋊C8)C2318yes—
122#66867C2314yes—
123C4×C11⋊C8C2314yes—
124C4×C11⋊C8C2314yes—
125#60249—111nomaximal, Sylow
126C23×D11C22×C411yescharacteristic
127C2×Q8×C11C22×C414yes—
128C22×C4×C11C22×C412yes—
129C22×C4×C11C2411yescharacteristic
130C22×Dic11C22×C411yescharacteristic
131C22×Dic11C22×C412yes—
132Q8×D11—48no—
133C2×C4×D11—24no—
134C2×C4×D11—44no—
135C2×C4×D11C22×C411yescharacteristic
136C2×C4×D11C22×C411yescharacteristic
137C2×C4×D11C22×C412yes—
138C2×C4×D11C22×C412yes—
139C2×C4×D11C22×C412yes—
140C2×C4×D11C22×C412yes—
141C2×C4×D11C22×C418yes—
142C2×C4×D11C2411yescharacteristic
143C2×C4×D11C2411yescharacteristic
144C2×Dic22C22×C414yes—
145C2×Dic22C22×C418yes—
146C2×C8×C11C2414yes—
147C2×C8×C11C2414yes—
148C11×C4⋊C4C22×C414yes—
149C11×C4⋊C4C22×C418yes—
150C11×C4⋊C4C22×C414yes—
151C11×C22⋊C4C22×C414yes—
152C42×C11C22×C411yescharacteristic
153C42×C11C22×C411yescharacteristic
154C42×C11C2412yes—
155C42×C11C2414yes—
156C22⋊Dic11C22×C414yes—
157(C2×D11)⋊C4C22×C418yes—
158C4⋊Dic11C22×C414yes—
159C4⋊Dic11C22×C418yes—
160C4⋊Dic11C22×C414yes—
161Dic11⋊C4C22×C418yes—
162Dic11⋊C4C22×C418yes—
163Dic11⋊C4C22×C418yes—
164Dic11⋊C4C22×C418yes—
165C4×Dic11C22×C411yescharacteristic
166C4×Dic11C22×C411yescharacteristic
167C4×Dic11C22×C412yes—
168C4×Dic11C22×C412yes—
169C4×Dic11C22×C412yes—
170C4×Dic11C22×C412yes—
171C4×Dic11C22×C418yes—
172C4×Dic11C2414yes—
173C4×Dic11C2412yes—
174C2×C11⋊C8C2414yes—
175C2×C11⋊C8C2414yes—
176#4313—28no—
177#4313—28no—
178C2×#533—111no—
179#2987—114no—
180#2986—112no—
181#2986—111no—
182#2986D1111yescharacteristic, complemented
183#2985—114no—
184#2985—114no—
185Q8×M16—114no—
186Q8×M16—114no—
187#2921—114no—
188#2920—112no—
189C23×C11C23×C411yescharacteristic
190C22×D11—22no—
191C22×D11—42no—
192C22×D11C23×C411yescharacteristic
193C22×D11C23×C411yescharacteristic
194Q8×C11—28no—
195C2×C4×C11—24no—
196C2×C4×C11—22no—
197C2×C4×C11C23×C412yes—
198C2×C4×C11C23×C411yescharacteristic
199C2×C4×C11C23×C418yes—
200C2×C4×C11C23×C412yes—
201C2×C4×C11C2511yescharacteristic
202C2×Dic11—22no—
203C2×Dic11—42no—
204C2×Dic11C23×C411yescharacteristic
205C2×Dic11C23×C412yes—
206C2×Dic11C23×C412yes—
207C2×Dic11C23×C418yes—
208C2×Dic11C23×C411yescharacteristic
209C4×D11—22no—
210C4×D11—24no—
211C4×D11—24no—
212C4×D11—22no—
213C4×D11—22no—
214C4×D11—42no—
215C4×D11—42no—
216C4×D11—48no—
217C4×D112−1+414yes—
218Dic22—28no—
219Dic22—48no—
220C8×C11—24no—
221C8×C11—24no—
222C11⋊C8—24no—
223C11⋊C8—24no—
224#533—112no—
225#533—112no—
226#533—114no—
227#533—114no—
228#533—112no—
229#533—111no—
230#533C2×D1111yescharacteristic
231C2×C4⋊Q8—112no—
232C2×#125—112no—
233C2×C22⋊Q8—114no—
234C2×C4×Q8—114no—
235C2×#117—112no—
236C22×C42—111no—
237#446—114no—
238#446—114no—
239#446—118no—
240#446—118no—
241#446—118no—
242#446—114no—
243#446—118no—
244#446C2×D1114yescomplemented
245C8×Q8—114no—
246C8×Q8—114no—
247C8×Q8—114no—
248C8×Q8C2×D1114yescomplemented
249#433—114no—
250#433—118no—
251#433—118no—
252#433—114no—
253#433—114no—
254#433C2×D1114yes—
255#432—112no—
256#432—112no—
257#432—114no—
258#431—112no—
259#431—114no—
260#431C2×D1112yes—
261#423—112no—
262#423—112no—
263#423—118no—
264#407—114no—
265C4×M16—114no—
266C4×M16—114no—
267C4×M16—114no—
268C22×C11—21no—
269C22×C11—22no—
270C22×C11C24×C411yescharacteristic
271C2×D11—22no—
272C2×D11—21no—
273C2×D11—22no—
274C2×D11—44no—
275C2×D11#51912yes—
276C4×C11—21no—
277C4×C11—22no—
278C4×C11—28no—
279C4×C11#56814yes—
280C4×C11C2×2−1+412yes—
281Dic11—21no—
282Dic11—28no—
283Dic11—22no—
284Dic11—22no—
285Dic11#51912yes—
286C22×Q8—114no—
287C23×C4—111no—
288C23×C4—112no—
289C2×M16—114no—
290C2×M16—114no—
291C4⋊Q8—114no—
292C4⋊Q8—114no—
293C4⋊Q8—114no—
294C4⋊Q8—112no—
295C4⋊Q8C4×D1112yes—
296#125—118no—
297#125—114no—
298#125—112no—
299#125C4×D1112yes—
300C22⋊Q8—114no—
301C22⋊Q8—114no—
302C22⋊Q8—118no—
303C22⋊Q8—114no—
304C22⋊Q8—118no—
305C22⋊Q8C4×D1114yes—
306C4×Q8—114no—
307C4×Q8—114no—
308C4×Q8—118no—
309C4×Q8—114no—
310C4×Q8—118no—
311C4×Q8C22×D1114yes—
312#117—112no—
313#117—114no—
314#117—114no—
315#117—114no—
316#117C22×D1112yes—
317C2×C4⋊C4—114no—
318C2×C4⋊C4—118no—
319C2×C4⋊C4—114no—
320C2×C22⋊C4—114no—
321C2×C42—112no—
322C2×C42—111no—
323C2×C42—111no—
324C2×C42—111no—
325C2×C42—111no—
326C2×C42—111no—
327C2×C42—114no—
328C2×C42—112no—
329C2×C42—112no—
330C2×C42C22×D1111yescharacteristic
331C4⋊C8—114no—
332C4⋊C8—114no—
333C4⋊C8—118no—
334C4⋊C8—118no—
335C4⋊C8—112no—
336C4⋊C8—112no—
337C4⋊C8—118no—
338C4⋊C8C22×D1112yes—
339C4⋊C8C22×D1112yes—
340C4⋊C8C22×D1118yes—
341C22⋊C8—114no—
342C22⋊C8—114no—
343C22⋊C8—114no—
344C22⋊C8C22×D1114yes—
345#97—114no—
346#97—114no—
347#97—118no—
348#97—114no—
349#97C22×D1114yes—
350C4×C8—118no—
351C4×C8—114no—
352C4×C8—114no—
353C4×C8C22×D1114yes—
354C4×C8C22×D1114yes—
355C2×C11—41no—
356C2×C11C2×#51911yescharacteristic
357C2×C11C2×#56812yes—
358D11—22no—
359D11—41no—
360C24—111no—
361C2×Q8—114no—
362C2×Q8—118no—
363C2×Q8—448no—
364C2×Q8C2×C4×D1114yes—
365C22×C4—111no—
366C22×C4—111no—
367C22×C4—112no—
368C22×C4—111no—
369C22×C4—112no—
370C22×C4—111no—
371C22×C4—112no—
372C22×C4—111no—
373C22×C4—112no—
374C22×C4—112no—
375C22×C4—118no—
376C22×C4—224no—
377C22×C4—444no—
378C22×C4C2×C4×D1112yes—
379C22×C4C23×D1111yescharacteristic
380M16—228no—
381M16—228no—
382C2×C8—114no—
383C2×C8—114no—
384C2×C8C23×D1114yes—
385C2×C8C23×D1114yes—
386C4⋊C4—118no—
387C4⋊C4—114no—
388C4⋊C4—118no—
389C4⋊C4—118no—
390C4⋊C4—118no—
391C4⋊C4—118no—
392C4⋊C4—114no—
393C4⋊C4C2×C4×D1114yes—
394C4⋊C4C2×C4×D1118yes—
395C4⋊C4C2×C4×D1114yes—
396C22⋊C4—114no—
397C22⋊C4—118no—
398C22⋊C4C2×C4×D1114yes—
399C42—112no—
400C42—112no—
401C42—111no—
402C42—112no—
403C42—112no—
404C42—111no—
405C42—118no—
406C42—114no—
407C42—112no—
408C42C2×C4×D1111yescharacteristic
409C42C2×C4×D1111yescharacteristic
410C42C23×D1112yes—
411C42C23×D1114yes—
412C11#6024911yescharacteristic, complemented, Sylow
413C23—111no—
414C23—111no—
415C23—222no—
416C23—442no—
417C23C22×C4×D1111yescharacteristic
418Q8—28no—
419Q8—228no—
420Q8—448no—
421C2×C4—24no—
422C2×C4—22no—
423C2×C4—111no—
424C2×C4—114no—
425C2×C4—112no—
426C2×C4—111no—
427C2×C4—112no—
428C2×C4—118no—
429C2×C4—222no—
430C2×C4—222no—
431C2×C4—222no—
432C2×C4—224no—
433C2×C4—224no—
434C2×C4—222no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—448no—
438C2×C4—442no—
439C2×C4C22×C4×D1111yescharacteristic
440C2×C4C22×C4×D1112yes—
441C2×C4C22×C4×D1118yes—
442C2×C4C22×C4×D1112yes—
443C2×C4C24×D1111yescharacteristic
444C8—24no—
445C8—24no—
446C8—224no—
447C8—224no—
448C22—22no—
449C22—21no—
450C22—112no—
451C22—222no—
452C22—222no—
453C22—221no—
454C22—444no—
455C22C23×C4×D1111yescharacteristic
456C4—22no—
457C4—28no—
458C4—21no—
459C4—112no—
460C4—222no—
461C4—222no—
462C4—228no—
463C4—221no—
464C4#1062328114yes—
465C4D11×2−1+412yes—
466C2—41no—
467C2—222no—
468C2—441no—
469C2D11×#51911yescharacteristic
470C2C2×#1062328112yes—
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2986C2
prime radicalC23×D11C22×C4
cosocleC2×C4×C11C25
hypercenter#2986D11
hypocenterC11#60249
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2986

Complements

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

NH ≅ G/Ntype
2. #13077720C2semidirect
3. #13077718C2semidirect
4. #13077717C2semidirect
5. #13077712C2semidirect
6. #13077707C2semidirect
7. #13077568C2semidirect
8. Q8×#4313C2semidirect
11. C11×#2986C2semidirect
25. C11×#446C22semidirect
26. C8×Q8×C11C22semidirect
29. #10622637C22semidirect
30. Q8×C11⋊C8C22semidirect
39. #10622444C22semidirect
40. #10622444C22semidirect
41. #10622443C22semidirect
42. #10622441C22semidirect
48. #10622314C22semidirect
53. #10622292C22semidirect
54. #10622292C22semidirect
55. C8×Dic22C22semidirect
182. #2986D11semidirect
244. #446C2×D11semidirect
248. C8×Q8C2×D11semidirect
412. C11#60249semidirect

Maximal subgroups

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

subgroupindex
D11×#5332
#130777202
#130777182
#130777172
#130777122
#130777072
#130775682
Q8×#43132
#130772502
#130772442
C11×#29862
#6024911