Finite Group Databasebeta

← #15618162

Subgroups — #15618162

Order 2816.

1810 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082019C211yesmaximal, characteristic
2#13077557C211yesmaximal, characteristic, complemented
3#13077555C212yesmaximal, complemented
4#13077553C211yesmaximal, characteristic, complemented
5#13077552C218yesmaximal, complemented
6#13077550C211yesmaximal, characteristic, complemented
7#13077548C212yesmaximal, complemented
8#13077545C218yesmaximal, complemented
9#13077178C211yesmaximal, characteristic
10#13077177C212yesmaximal
11C2×#10622302C211yesmaximal, characteristic
12D11×#405C212yesmaximal
13C11×#2960C211yesmaximal, characteristic, complemented
14C11×#533C2211yescharacteristic
15C2×M16×D11C2212yes—
16C22×#4313C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18#10623260C414yes—
19#10623220C414yes—
20#10623165C414yes—
21#10623154C414yes—
22#10623109C2218yes—
23D11×#117C2212yes—
24#10623048C2212yes—
25C2×#66925C2211yescharacteristic
26#10623001C2211yescharacteristic
27C11×#446C2214yescomplemented
28C8×Q8×C11C2214yescomplemented
29C11×#424C2212yes—
30C11×#423C2211yescharacteristic
31C11×#405C2212yes—
32C2×C4×C8×C11C2211yescharacteristic
33#10622735C2212yes—
34#10622732C2212yes—
35#10622731C2212yes—
36#10622715C2212yes—
37#10622714C2212yes—
38C2×#66879C2211yescharacteristic
39C2×C8×Dic11C2211yescharacteristic
40#10622637C2218yescomplemented
41#10622612C2212yes—
42#10622610C2212yes—
43#10622537C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45#10622452C2218yes—
46#10622452C2218yes—
47#10622450C2218yes—
48#10622444C2218yescomplemented
49#10622441C2218yescomplemented
50#10622441C2218yescomplemented
51#10622321C2214yes—
52D11×#97C2214yes—
53#10622314C2218yescomplemented
54#10622302C2214yes—
55#10622302C2214yes—
56#10622302C2214yes—
57C4×C8×D11C2214yes—
58#10622292C2214yescomplemented
59C8×Dic22C2218yescomplemented
60C8×Dic22C2214yescomplemented
61C22×C4×D11C2311yescharacteristic
62C2×C11×M16C2312yes—
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×C4⋊Q8C2×C412yes—
66C11×#125C2×C412yes—
67C11×C22⋊Q8C2×C414yes—
68C4×Q8×C11C2314yes—
69C11×#117C2312yes—
70C2×C42×C11C2311yescharacteristic
71#66999C2×C418yes—
72#66997C2×C418yes—
73C2×(C2×D11)⋊C4C2×C412yes—
74#66979C2312yes—
75#66977C2×C414yes—
76C2×Dic11⋊C4C2×C412yes—
77C2×C4×Dic11C2311yescharacteristic
78C2×#4318C2312yes—
79C22×C11⋊C8C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81M16×D11—28no—
82C2×#4313—24no—
83C2×#4313C2314yes—
84C2×#4313C2314yes—
85C2×C8×D11Q818yescomplemented
86C2×C8×D11C2314yes—
87C2×C8×D11C2312yes—
88C2×C8×D11C2312yes—
89#66950C2×C418yes—
90#66949C2×C418yes—
91#66949C2×C418yes—
92#66945C2×C414yes—
93C4⋊C4×D11C2×C414yes—
94#66943C2×C414yes—
95#66942C2×C418yes—
96#66942C2×C418yes—
97#66941C2×C414yes—
98#66941C2×C418yes—
99C22⋊C4×D11C2×C414yes—
100#66931C2×C418yes—
101#66930C2×C414yes—
102#66925C2×C412yes—
103#66925C2×C412yes—
104#66925C2314yes—
105#66925C2314yes—
106C42×D11C2314yes—
107#66923C2×C412yes—
108#66922C2×C412yes—
109C4×Dic22C2314yes—
110C4×Dic22C2318yes—
111C11×C4⋊C8C2314yes—
112C11×C4⋊C8C2318yes—
113C11×#97C2314yes—
114C4×C8×C11C2314yes—
115C4×C8×C11C2312yes—
116C4×C8×C11C2312yes—
117#66879C2314yes—
118#66879C2314yes—
119#66879C2314yes—
120Dic11⋊C8C2318yes—
121Dic11⋊C8C2318yes—
122Dic11⋊C8C2318yes—
123C8×Dic11C2314yes—
124C8×Dic11C2314yes—
125C8×Dic11C2312yes—
126C8×Dic11C2312yes—
127C4⋊(C11⋊C8)C2314yes—
128C4⋊(C11⋊C8)C2318yes—
129#66867C2314yes—
130#66867C2314yes—
131C4×C11⋊C8C2314yes—
132#60191—111nomaximal, Sylow
133C23×D11C22×C411yescharacteristic
134C2×Q8×C11C22×C414yes—
135C22×C4×C11C22×C412yes—
136C22×C4×C11C2411yescharacteristic
137C22×Dic11C22×C412yes—
138C22×Dic11C22×C411yescharacteristic
139C2×C4×D11C22×C418yes—
140C2×C4×D11C22×C412yes—
141C2×C4×D11C2×Q814yes—
142C2×C4×D11#4114yes—
143C2×C4×D11C2412yes—
144C2×Dic22C22×C414yes—
145C2×Dic22C22×C418yes—
146C11×M16—24no—
147C2×C8×C11—22no—
148C2×C8×C11C2×Q814yes—
149C2×C8×C11C2414yes—
150C2×C8×C11C2412yes—
151C2×C8×C11C2411yescharacteristic
152C2×C8×C11C2411yescharacteristic
153C11×C4⋊C4C22×C418yes—
154C11×C4⋊C4C22×C414yes—
155C11×C4⋊C4C22×C414yes—
156C11×C22⋊C4C22×C414yes—
157C42×C11C22×C411yescharacteristic
158C42×C11C22×C411yescharacteristic
159C42×C11C2414yes—
160C42×C11C2412yes—
161C22⋊Dic11C22×C414yes—
162(C2×D11)⋊C4C22×C414yes—
163(C2×D11)⋊C4C22×C414yes—
164(C2×D11)⋊C4C22×C418yes—
165C4⋊Dic11C22×C414yes—
166C4⋊Dic11C22×C418yes—
167C4⋊Dic11C22×C414yes—
168Dic11⋊C4C22×C418yes—
169Dic11⋊C4C22×C418yes—
170Dic11⋊C4C22×C418yes—
171Dic11⋊C4C22×C414yes—
172Dic11⋊C4C22×C414yes—
173Dic11⋊C4C22×C418yes—
174C4×Dic11C22×C418yes—
175C4×Dic11C22×C412yes—
176C4×Dic11C2414yes—
177C4×Dic11C2412yes—
178#4318—24no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8C2×Q814yes—
181C2×C11⋊C8C2414yes—
182C2×C11⋊C8C2412yes—
183C2×C11⋊C8C2412yes—
184#4313—28no—
185#4313—28no—
186C8×D11—28no—
187C8×D11C2×Q818yes—
188C8×D11C2×Q818yes—
189#3458—111no—
190#2961—118no—
191#2961—112no—
192#2961—111no—
193#2961—111no—
194#2960—118no—
195#2960—112no—
196#2960—111no—
197#2960D1111yescharacteristic, complemented
198#2905—112no—
199#2905—111no—
200C2×#405—112no—
201C2×#405—111no—
202C23×C11C23×C411yescharacteristic
203C22×D11—42no—
204C22×D11C4×Q814yes—
205C22×D11C23×C412yes—
206Q8×C11—44no—
207C2×C4×C11—42no—
208C2×C4×C11C23×C418yes—
209C2×C4×C11C23×C412yes—
210C2×C4×C11C23×C412yes—
211C2×C4×C11C23×C411yescharacteristic
212C2×C4×C11C22×Q812yes—
213C2×C4×C11C2×#4112yes—
214C2×C4×C11C2511yescharacteristic
215C2×Dic11—42no—
216C2×Dic11C4×Q814yes—
217C2×Dic11C23×C414yes—
218C2×Dic11C23×C418yes—
219C2×Dic11C23×C412yes—
220C4×D11—48no—
221C4×D11C4×Q818yes—
222C4×D11C22×Q814yes—
223C4×D11C2×#4114yes—
224Dic22—44no—
225Dic22—48no—
226C8×C11—24no—
227C8×C11—22no—
228C8×C11C22×Q812yes—
229C8×C11C22×Q812yes—
230C11⋊C8—24no—
231C11⋊C8—22no—
232C11⋊C8C22×Q814yes—
233C22×M16—112no—
234C22×M16—111no—
235C23×C8—111no—
236#544—114no—
237#544—114no—
238#544—114no—
239#543—114no—
240#533—118no—
241#533—112no—
242#533—111no—
243#533C2×D1111yescharacteristic
244C2×#117—112no—
245C2×#117—111no—
246#446—118no—
247#446—118no—
248#446—118no—
249#446—118no—
250#446—118no—
251#446—114no—
252#446C2×D1114yescomplemented
253C8×Q8—118no—
254C8×Q8—114no—
255C8×Q8C2×D1114yescomplemented
256#424—112no—
257#424—112no—
258#424—112no—
259#424—118no—
260#424—118no—
261#424C2×D1112yes—
262#423—112no—
263#423—111no—
264#423—118no—
265#423C2×D1111yescharacteristic
266#405—112no—
267#405—112no—
268#405—112no—
269#405—114no—
270#405—114no—
271#405—114no—
272#405—114no—
273#405C2×D1112yes—
274C2×#97—111no—
275C2×#97—111no—
276C2×#97—114no—
277C2×C4×C8—111no—
278C2×C4×C8—114no—
279C2×C4×C8C2×D1111yescharacteristic
280C22×C11—22no—
281C22×C11C2×C4×Q812yes—
282C22×C11C24×C411yescharacteristic
283C2×D11—24no—
284C2×D11—44no—
285C2×D11C2×C4×Q814yes—
286C4×C11—22no—
287C4×C11—22no—
288C4×C11—28no—
289C4×C11C2×C4×Q812yes—
290C4×C11C23×Q811yescharacteristic
291C4×C11C22×#4111yescharacteristic
292Dic11—28no—
293Dic11—24no—
294Dic11C2×C4×Q814yes—
295C23×C4—111no—
296C2×M16—112no—
297C2×M16—114no—
298C2×M16—114no—
299C2×M16—224no—
300C2×M16—228no—
301C2×M16C22×D1112yes—
302C22×C8—111no—
303C22×C8—118no—
304C22×C8—112no—
305C22×C8—112no—
306C22×C8—111no—
307C22×C8—114no—
308C22×C8C22×D1111yescharacteristic
309C22×C8C22×D1111yescharacteristic
310C4⋊Q8—118no—
311C4⋊Q8—118no—
312C4⋊Q8—114no—
313C4⋊Q8—112no—
314C4⋊Q8C4×D1112yes—
315#125—118no—
316#125—118no—
317#125—114no—
318#125—112no—
319#125C4×D1112yes—
320C22⋊Q8—118no—
321C22⋊Q8—114no—
322C22⋊Q8—118no—
323C22⋊Q8—118no—
324C22⋊Q8—118no—
325C22⋊Q8—118no—
326C22⋊Q8C4×D1114yes—
327C4×Q8—118no—
328C4×Q8—114no—
329C4×Q8C22×D1114yes—
330#117—112no—
331#117—114no—
332#117—114no—
333#117—112no—
334#117—112no—
335#117—114no—
336#117—114no—
337#117C22×D1112yes—
338C2×C4⋊C4—112no—
339C2×C4⋊C4—114no—
340C2×C22⋊C4—112no—
341C2×C22⋊C4—114no—
342C2×C42—111no—
343C2×C42—114no—
344C2×C42C22×D1111yescharacteristic
345C4⋊C8—118no—
346C4⋊C8—118no—
347C4⋊C8—118no—
348C4⋊C8—118no—
349C4⋊C8—114no—
350C4⋊C8C22×D1118yes—
351C4⋊C8C22×D1114yes—
352#97—114no—
353#97—114no—
354#97—114no—
355#97—114no—
356#97—114no—
357#97C22×D1114yes—
358C4×C8—114no—
359C4×C8—112no—
360C4×C8—114no—
361C4×C8—112no—
362C4×C8—114no—
363C4×C8C22×D1112yes—
364C4×C8C22×D1114yes—
365C4×C8C22×D1112yes—
366C2×C11—22no—
367C2×C11C22×C4×Q811yescharacteristic
368C2×C11#357312yes—
369D11—24no—
370C24—111no—
371C2×Q8—118no—
372C2×Q8—114no—
373C2×Q8C2×C4×D1114yes—
374C22×C4—111no—
375C22×C4—112no—
376C22×C4—114no—
377C22×C4—114no—
378C22×C4—112no—
379C22×C4—112no—
380C22×C4—118no—
381C22×C4C2×C4×D1112yes—
382C22×C4C23×D1111yescharacteristic
383M16—24no—
384M16—228no—
385M16—228no—
386M16—224no—
387C2×C8—22no—
388C2×C8—114no—
389C2×C8—112no—
390C2×C8—118no—
391C2×C8—118no—
392C2×C8—112no—
393C2×C8—114no—
394C2×C8—228no—
395C2×C8—222no—
396C2×C8Q8×D1114yes—
397C2×C8C23×D1114yes—
398C2×C8C23×D1112yes—
399C2×C8C23×D1111yescharacteristic
400C2×C8C23×D1111yescharacteristic
401C4⋊C4—118no—
402C4⋊C4—114no—
403C4⋊C4—114no—
404C4⋊C4—114no—
405C4⋊C4—118no—
406C4⋊C4—118no—
407C4⋊C4—118no—
408C4⋊C4—118no—
409C4⋊C4—114no—
410C4⋊C4C2×C4×D1114yes—
411C4⋊C4C2×C4×D1114yes—
412C4⋊C4C2×C4×D1118yes—
413C22⋊C4—114no—
414C22⋊C4—118no—
415C22⋊C4—114no—
416C22⋊C4—114no—
417C22⋊C4C2×C4×D1114yes—
418C42—118no—
419C42—112no—
420C42—112no—
421C42—114no—
422C42C2×C4×D1111yescharacteristic
423C42C2×C4×D1111yescharacteristic
424C42C23×D1114yes—
425C42C23×D1112yes—
426C11#6019111yescharacteristic, complemented, Sylow
427C23—112no—
428C23—114no—
429C23—442no—
430C23C22×C4×D1111yescharacteristic
431Q8—44no—
432Q8—444no—
433Q8—448no—
434C2×C4—42no—
435C2×C4—114no—
436C2×C4—112no—
437C2×C4—118no—
438C2×C4—114no—
439C2×C4—114no—
440C2×C4—118no—
441C2×C4—114no—
442C2×C4—448no—
443C2×C4—442no—
444C2×C4C22×C4×D1118yes—
445C2×C4C22×C4×D1112yes—
446C2×C4C22×C4×D1112yes—
447C2×C4C22×C4×D1111yescharacteristic
448C2×C4C2×Q8×D1112yes—
449C2×C4#41×D1112yes—
450C2×C4C24×D1111yescharacteristic
451C8—22no—
452C8—24no—
453C8—114no—
454C8—224no—
455C8—222no—
456C8C2×Q8×D1112yes—
457C8C2×Q8×D1112yes—
458C22—22no—
459C22—114no—
460C22—224no—
461C22—444no—
462C22C4×Q8×D1112yes—
463C22C23×C4×D1111yescharacteristic
464C4—22no—
465C4—22no—
466C4—28no—
467C4—114no—
468C4—228no—
469C4—224no—
470C4C4×Q8×D1112yes—
471C4C22×Q8×D1111yescharacteristic
472C4C2×#41×D1111yescharacteristic
473C2—22no—
474C2—224no—
475C2C2×C4×Q8×D1111yescharacteristic
476C2#1308332712yes—
subgroupG/H
centerC2×C8C23×D11
commutator, socleC22×C11C24×C4
FrattiniC2×C4C24×D11
FittingC11×#2960C2
prime radicalC23×D11C22×C4
cosocleC2×C4×C11C25
hypercenter#2960D11
hypocenterC11#60191
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C8 ◁ #2960

Complements

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

NH ≅ G/Ntype
2. #13077557C2semidirect
3. #13077555C2semidirect
4. #13077553C2semidirect
5. #13077552C2semidirect
6. #13077550C2semidirect
7. #13077548C2semidirect
8. #13077545C2semidirect
13. C11×#2960C2semidirect
27. C11×#446C22semidirect
28. C8×Q8×C11C22semidirect
40. #10622637C22semidirect
48. #10622444C22semidirect
49. #10622441C22semidirect
50. #10622441C22semidirect
53. #10622314C22semidirect
58. #10622292C22semidirect
59. C8×Dic22C22semidirect
60. C8×Dic22C22semidirect
85. C2×C8×D11Q8semidirect
197. #2960D11semidirect
252. #446C2×D11semidirect
255. C8×Q8C2×D11semidirect
426. C11#60191semidirect

Maximal subgroups

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

subgroupindex
#130820192
#130775572
#130775552
#130775532
#130775522
#130775502
#130775482
#130775452
#130771782
#130771772
C2×#106223022
D11×#4052
C11×#29602
#6019111