Finite Group Databasebeta

← #15618786

Subgroups — #15618786

Order 2816.

1626 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082021C211yesmaximal, characteristic
2#13077720C214yesmaximal, complemented
3#13077715C214yesmaximal, complemented
4#13077708C218yesmaximal, complemented
5#13077563C214yesmaximal, complemented
6#13077553C212yesmaximal, complemented
7#13077546C212yesmaximal, complemented
8#13077276C214yesmaximal
9C2×#10622613C211yesmaximal, characteristic
10C11×#2921C211yesmaximal, characteristic
11C2×C11×#117C2211yescharacteristic
12C2×#66979C2212yes—
13#10623050C414yes—
14#10623050C414yes—
15#10623048C2214yes—
16#10623048C2214yes—
17#10623031C414yes—
18#10623014C414yes—
19#10623001C2212yes—
20#10623001C2212yes—
21C11×#433C2214yes—
22C11×#433C2214yes—
23C11×#423C2212yes—
24C11×#407C2212yes—
25C4×C11×M16C2212yes—
26C2×C22⋊(C11⋊C8)C2212yes—
27#10622735C2214yes—
28#10622735C2214yes—
29#10622732C2214yes—
30#10622732C2214yes—
31#10622613C2214yes—
32#10622613C2212yes—
33#10622613C2212yes—
34C2×C4⋊(C11⋊C8)C2212yes—
35C2×#66867C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622444C2214yescomplemented
38#10622444C2214yescomplemented
39#10622443C2214yescomplemented
40#10622443C2214yescomplemented
41#10622441C2218yescomplemented
42#10622441C2218yescomplemented
43#10622333C2218yes—
44#10622333C2218yes—
45#10622332C2218yes—
46#10622331C2218yes—
47#10622314C2218yescomplemented
48#10622314C2218yescomplemented
49#10622292C2218yescomplemented
50C8×Dic22C2218yescomplemented
51C23×C4×C11C2311yescharacteristic
52C2×C11×M16C2314yes—
53C11×#117C2×C414yes—
54C11×#117C2312yes—
55C11×#117C2312yes—
56C2×C11×C4⋊C4C2×C412yes—
57C2×C11×C22⋊C4C2×C412yes—
58C2×C42×C11C2311yescharacteristic
59C2×C42×C11C2311yescharacteristic
60C2×C22⋊Dic11C2×C414yes—
61#66979C2×C414yes—
62#66979C2×C412yes—
63#66979C2×C412yes—
64#66979C2314yes—
65#66979C2314yes—
66C2×C4⋊Dic11C2×C414yes—
67#66977C2×C414yes—
68#66977C2×C414yes—
69#66977C2×C418yes—
70C2×C4×Dic11C2314yes—
71C22×C11⋊C8C2312yes—
72C22×C11⋊C8C2312yes—
73#66943C2×C418yes—
74#66943C2×C418yes—
75#66941C2×C418yes—
76#66941C2×C418yes—
77#66931C2×C418yes—
78#66931C2×C418yes—
79#66931C2×C418yes—
80#66931C2×C418yes—
81#66923C2×C414yes—
82#66923C2×C412yes—
83#66923C2×C412yes—
84#66922C2×C412yes—
85#66922C2×C412yes—
86#66922C2×C414yes—
87C4×Dic22C2318yes—
88C4×Dic22C2314yes—
89C4×Dic22C2314yes—
90C11×C4⋊C8C2314yes—
91C11×C4⋊C8C2314yes—
92C11×C22⋊C8C2318yes—
93C11×#97C2314yes—
94C4×C8×C11C2314yes—
95C22⋊(C11⋊C8)C2314yes—
96C22⋊(C11⋊C8)C2314yes—
97#66879C2318yes—
98#66879C2318yes—
99Dic11⋊C8C2318yes—
100Dic11⋊C8C2318yes—
101Dic11⋊C8C2318yes—
102Dic11⋊C8C2318yes—
103C8×Dic11C2318yes—
104C8×Dic11C2318yes—
105C4⋊(C11⋊C8)C2314yes—
106C4⋊(C11⋊C8)C2314yes—
107#66867C2312yes—
108#66867C2312yes—
109C4×C11⋊C8C2311yescharacteristic
110C4×C11⋊C8C2312yes—
111C4×C11⋊C8C2311yescharacteristic
112#60252—111nomaximal, Sylow
113C24×C11C22×C411yescharacteristic
114C22×C4×C11—24no—
115C22×C4×C11C22×C412yes—
116C22×C4×C11C22×C411yescharacteristic
117C22×C4×C11C22×C412yes—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C2412yes—
120C22×C4×C11C2411yescharacteristic
121C22×Dic11C22×C418yes—
122C2×Dic22C22×C418yes—
123C2×Dic22C22×C414yes—
124C2×Dic22C22×C414yes—
125C11×M16—28no—
126C2×C8×C11C2418yes—
127C11×C4⋊C4C22×C414yes—
128C11×C4⋊C4C22×C414yes—
129C11×C22⋊C4C22×C414yes—
130C11×C22⋊C4C22×C414yes—
131C42×C11C22×C412yes—
132C42×C11C22×C412yes—
133C42×C11C2411yescharacteristic
134C42×C11C2411yescharacteristic
135C42×C11C2412yes—
136C22⋊Dic11C22×C414yes—
137C22⋊Dic11C22×C414yes—
138C22⋊Dic11C22×C418yes—
139C4⋊Dic11C22×C418yes—
140C4⋊Dic11C22×C414yes—
141C4⋊Dic11C22×C414yes—
142C4⋊Dic11C22×C414yes—
143C4⋊Dic11C22×C414yes—
144C4⋊Dic11C22×C418yes—
145Dic11⋊C4C22×C418yes—
146Dic11⋊C4C22×C418yes—
147Dic11⋊C4C22×C418yes—
148Dic11⋊C4C22×C418yes—
149C4×Dic11C22×C414yes—
150C4×Dic11C22×C414yes—
151C4×Dic11C2418yes—
152C2×C11⋊C8—24no—
153C2×C11⋊C8—24no—
154C2×C11⋊C8C2412yes—
155C2×C11⋊C8C2412yes—
156C2×C11⋊C8C2414yes—
157#3458—111no—
158#2987—114no—
159#2986—114no—
160#2985—118no—
161#2962—114no—
162#2961—112no—
163#2960—112no—
164#2924—114no—
165#2921D1111yescharacteristic
166C2×#433—111no—
167C23×C11—22no—
168C23×C11—42no—
169C23×C11C23×C412yes—
170C23×C11C23×C411yescharacteristic
171C2×C4×C11—22no—
172C2×C4×C11—24no—
173C2×C4×C11—24no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11C23×C412yes—
177C2×C4×C11C23×C412yes—
178C2×C4×C11C23×C412yes—
179C2×C4×C11C23×C414yes—
180C2×C4×C11C23×C411yescharacteristic
181C2×C4×C112−1+414yes—
182C2×C4×C11C2511yescharacteristic
183C2×Dic11—48no—
184C2×Dic11C23×C418yes—
185C2×Dic11C23×C418yes—
186Dic22—48no—
187Dic22—44no—
188Dic22—44no—
189C8×C11—28no—
190C11⋊C8—22no—
191C11⋊C8—22no—
192C11⋊C8—24no—
193#544—114no—
194#544—114no—
195#544—114no—
196#543—114no—
197#533—114no—
198#533—114no—
199#533—112no—
200#533—112no—
201C2×#117—112no—
202C2×#117C2×D1111yescharacteristic
203#446—114no—
204#446—114no—
205#446—118no—
206#446—118no—
207#446—118no—
208#446—118no—
209#446—118no—
210C8×Q8—114no—
211C8×Q8—114no—
212C8×Q8—118no—
213#433—114no—
214#433—112no—
215#433—112no—
216#433—118no—
217#433—118no—
218#433C2×D1114yes—
219#433C2×D1114yes—
220#432—118no—
221#431—118no—
222#424—114no—
223#424—114no—
224#423C2×D1112yes—
225C2×C4⋊C8—112no—
226#407C2×D1112yes—
227C2×C22⋊C8—112no—
228#405—114no—
229#405—114no—
230C4×M16C2×D1112yes—
231C2×#97—111no—
232C2×C4×C8—111no—
233C22×C11—22no—
234C22×C11—22no—
235C22×C11—24no—
236C22×C11—82no—
237C22×C11#51912yes—
238C22×C11C24×C411yescharacteristic
239C4×C11—22no—
240C4×C11—22no—
241C4×C11—22no—
242C4×C11—24no—
243C4×C11#51912yes—
244C4×C11C2×2−1+412yes—
245Dic11—28no—
246Dic11—28no—
247C23×C4C22×D1111yescharacteristic
248C2×M16C22×D1114yes—
249C22×C8—112no—
250C22×C8—112no—
251C4⋊Q8—118no—
252C4⋊Q8—118no—
253C4⋊Q8—112no—
254C4⋊Q8—112no—
255C4⋊Q8—114no—
256#125—118no—
257#125—118no—
258#125—114no—
259#125—112no—
260#125—112no—
261C22⋊Q8—114no—
262C22⋊Q8—114no—
263C22⋊Q8—118no—
264C22⋊Q8—118no—
265C22⋊Q8—118no—
266C22⋊Q8—118no—
267C22⋊Q8—118no—
268C4×Q8—114no—
269C4×Q8—114no—
270C4×Q8—118no—
271#117—112no—
272#117—112no—
273#117—114no—
274#117—114no—
275#117—114no—
276#117C4×D1114yes—
277#117C22×D1112yes—
278#117C22×D1112yes—
279C2×C4⋊C4—114no—
280C2×C4⋊C4C4×D1112yes—
281C2×C22⋊C4—114no—
282C2×C22⋊C4C4×D1112yes—
283C2×C42—114no—
284C2×C42C22×D1111yescharacteristic
285C2×C42C22×D1111yescharacteristic
286C4⋊C8—118no—
287C4⋊C8—118no—
288C4⋊C8—118no—
289C4⋊C8—118no—
290C4⋊C8—114no—
291C4⋊C8—114no—
292C4⋊C8C22×D1114yes—
293C4⋊C8C22×D1114yes—
294C22⋊C8—114no—
295C22⋊C8—114no—
296C22⋊C8C22×D1118yes—
297#97—118no—
298#97—118no—
299#97—112no—
300#97—112no—
301#97C22×D1114yes—
302C4×C8—118no—
303C4×C8—118no—
304C4×C8—111no—
305C4×C8—112no—
306C4×C8—111no—
307C4×C8C22×D1114yes—
308C2×C11—22no—
309C2×C11—42no—
310C2×C11C2×#51911yescharacteristic
311C2×C11#357312yes—
312C24C2×C4×D1111yescharacteristic
313C2×Q8—114no—
314C2×Q8—114no—
315C2×Q8—118no—
316C22×C4—24no—
317C22×C4—118no—
318C22×C4C2×C4×D1112yes—
319C22×C4C2×C4×D1111yescharacteristic
320C22×C4C2×C4×D1112yes—
321C22×C4C2×C4×D1112yes—
322C22×C4C23×D1112yes—
323C22×C4C23×D1111yescharacteristic
324M16—28no—
325C2×C8—112no—
326C2×C8—114no—
327C2×C8—112no—
328C2×C8—224no—
329C2×C8—224no—
330C2×C8C23×D1118yes—
331C4⋊C4—118no—
332C4⋊C4—114no—
333C4⋊C4—114no—
334C4⋊C4—118no—
335C4⋊C4—118no—
336C4⋊C4—118no—
337C4⋊C4—118no—
338C4⋊C4—114no—
339C4⋊C4—114no—
340C4⋊C4—118no—
341C4⋊C4C2×C4×D1114yes—
342C4⋊C4C2×C4×D1114yes—
343C22⋊C4—114no—
344C22⋊C4—114no—
345C22⋊C4—118no—
346C22⋊C4C2×C4×D1114yes—
347C22⋊C4C2×C4×D1114yes—
348C42—114no—
349C42—114no—
350C42—118no—
351C42C2×C4×D1112yes—
352C42C2×C4×D1112yes—
353C42C23×D1111yescharacteristic
354C42C23×D1111yescharacteristic
355C42C23×D1112yes—
356C11#6025211yescharacteristic, complemented, Sylow
357C23—22no—
358C23—42no—
359C23C22×C4×D1112yes—
360C23C22×C4×D1111yescharacteristic
361Q8—444no—
362Q8—444no—
363Q8—448no—
364C2×C4—22no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—118no—
370C2×C4—118no—
371C2×C4—448no—
372C2×C4C22×C4×D1112yes—
373C2×C4C22×C4×D1112yes—
374C2×C4C22×C4×D1112yes—
375C2×C4C22×C4×D1114yes—
376C2×C4C22×C4×D1111yescharacteristic
377C2×C4#6704314yes—
378C2×C4C24×D1111yescharacteristic
379C8—28no—
380C8—222no—
381C8—224no—
382C8—222no—
383C22—22no—
384C22—24no—
385C22—22no—
386C22—82no—
387C22#1062304712yes—
388C22C23×C4×D1111yescharacteristic
389C4—22no—
390C4—22no—
391C4—24no—
392C4—22no—
393C4—228no—
394C4—228no—
395C4#1062304712yes—
396C4C2×#6704312yes—
397C2—22no—
398C2—42no—
399C2C2×#1062304711yescharacteristic
400C2#1308332912yes—
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2921C2
prime radicalC24×C11C22×C4
cosocleC2×C4×C11C25
hypercenter#2921D11
hypocenterC11#60252
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2921

Complements

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

NH ≅ G/Ntype
2. #13077720C2semidirect
3. #13077715C2semidirect
4. #13077708C2semidirect
5. #13077563C2semidirect
6. #13077553C2semidirect
7. #13077546C2semidirect
37. #10622444C22semidirect
38. #10622444C22semidirect
39. #10622443C22semidirect
40. #10622443C22semidirect
41. #10622441C22semidirect
42. #10622441C22semidirect
47. #10622314C22semidirect
48. #10622314C22semidirect
49. #10622292C22semidirect
50. C8×Dic22C22semidirect
356. C11#60252semidirect

Maximal subgroups

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

subgroupindex
#130820212
#130777202
#130777152
#130777082
#130775632
#130775532
#130775462
#130772762
C2×#106226132
C11×#29212
#6025211