Finite Group Databasebeta

← #15618782

Subgroups — #15618782

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#13077559C214yesmaximal, complemented
6#13077556C212yesmaximal, complemented
7#13077550C212yesmaximal, complemented
8#13077270C214yesmaximal
9#13077254C211yesmaximal, characteristic
10C2×C11×#433C211yesmaximal, 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×#433C2212yes—
23C11×#433C2212yes—
24C2×C11×C4⋊C8C2212yes—
25C2×C11×C22⋊C8C2212yes—
26C2×C11×#97C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28#10622820C2212yes—
29#10622715C2214yes—
30#10622715C2214yes—
31#10622714C2214yes—
32#10622714C2214yes—
33#10622613C2214yes—
34#10622613C2214yes—
35#10622537C2212yes—
36C4×#4318C2212yes—
37#10622444C2218yescomplemented
38#10622443C2218yescomplemented
39#10622441C2218yescomplemented
40#10622441C2218yescomplemented
41#10622333C2218yes—
42#10622333C2218yes—
43#10622332C2218yes—
44#10622331C2218yes—
45#10622314C2218yescomplemented
46#10622314C2218yescomplemented
47#10622292C2214yescomplemented
48#10622292C2214yescomplemented
49C8×Dic22C2214yescomplemented
50C8×Dic22C2214yescomplemented
51C23×C4×C11C2311yescharacteristic
52C22×C8×C11C2312yes—
53C22×C8×C11C2312yes—
54C11×#117C2×C414yes—
55C11×#117C2312yes—
56C11×#117C2312yes—
57C2×C11×C4⋊C4C2×C412yes—
58C2×C11×C22⋊C4C2×C412yes—
59C2×C42×C11C2311yescharacteristic
60C2×C42×C11C2311yescharacteristic
61C2×C22⋊Dic11C2×C414yes—
62#66979C2×C414yes—
63#66979C2×C412yes—
64#66979C2×C412yes—
65#66979C2314yes—
66#66979C2314yes—
67C2×C4⋊Dic11C2×C414yes—
68#66977C2×C414yes—
69#66977C2×C414yes—
70#66977C2×C418yes—
71C2×C4×Dic11C2314yes—
72C2×#4318C2314yes—
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×Dic22C2314yes—
88C4×Dic22C2314yes—
89C4×Dic22C2318yes—
90C11×C4⋊C8C2314yes—
91C11×C4⋊C8C2314yes—
92C11×C22⋊C8C2314yes—
93C11×C22⋊C8C2314yes—
94C11×#97C2312yes—
95C11×#97C2312yes—
96C4×C8×C11C2311yescharacteristic
97C4×C8×C11C2312yes—
98C4×C8×C11C2311yescharacteristic
99C22⋊(C11⋊C8)C2318yes—
100#66879C2318yes—
101#66879C2318yes—
102Dic11⋊C8C2318yes—
103Dic11⋊C8C2318yes—
104Dic11⋊C8C2318yes—
105Dic11⋊C8C2318yes—
106C8×Dic11C2318yes—
107C8×Dic11C2318yes—
108C4⋊(C11⋊C8)C2314yes—
109C4⋊(C11⋊C8)C2314yes—
110#66867C2314yes—
111C4×C11⋊C8C2314yes—
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×C414yes—
123C2×Dic22C22×C414yes—
124C2×Dic22C22×C418yes—
125C2×C8×C11—24no—
126C2×C8×C11—24no—
127C2×C8×C11C2412yes—
128C2×C8×C11C2414yes—
129C2×C8×C11C2412yes—
130C11×C4⋊C4C22×C414yes—
131C11×C4⋊C4C22×C414yes—
132C11×C22⋊C4C22×C414yes—
133C11×C22⋊C4C22×C414yes—
134C42×C11C22×C412yes—
135C42×C11C22×C412yes—
136C42×C11C2412yes—
137C42×C11C2411yescharacteristic
138C42×C11C2411yescharacteristic
139C22⋊Dic11C22×C414yes—
140C22⋊Dic11C22×C414yes—
141C22⋊Dic11C22×C418yes—
142C4⋊Dic11C22×C414yes—
143C4⋊Dic11C22×C414yes—
144C4⋊Dic11C22×C418yes—
145C4⋊Dic11C22×C414yes—
146C4⋊Dic11C22×C414yes—
147C4⋊Dic11C22×C418yes—
148Dic11⋊C4C22×C418yes—
149Dic11⋊C4C22×C418yes—
150Dic11⋊C4C22×C418yes—
151Dic11⋊C4C22×C418yes—
152C4×Dic11C22×C414yes—
153C4×Dic11C22×C414yes—
154C4×Dic11C2418yes—
155#4318—28no—
156C2×C11⋊C8C2418yes—
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#2921—111no—
166C2×#433D1111yescharacteristic
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×C414yes—
178C2×C4×C11C23×C412yes—
179C2×C4×C11C23×C412yes—
180C2×C4×C11C23×C411yescharacteristic
181C2×C4×C112−1+414yes—
182C2×C4×C11C2511yescharacteristic
183C2×Dic11—48no—
184C2×Dic11C23×C418yes—
185C2×Dic11C23×C418yes—
186Dic22—44no—
187Dic22—44no—
188Dic22—48no—
189C8×C11—22no—
190C8×C11—24no—
191C8×C11—22no—
192C11⋊C8—28no—
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—118no—
204#446—118no—
205#446—118no—
206#446—118no—
207#446—118no—
208#446—114no—
209#446—114no—
210C8×Q8—118no—
211C8×Q8—114no—
212C8×Q8—114no—
213#433—114no—
214#433—114no—
215#433—118no—
216#433—118no—
217#433C2×D1114yes—
218#433C2×D1112yes—
219#433C2×D1112yes—
220#432—118no—
221#431—118no—
222#424—114no—
223#424—114no—
224#423—112no—
225C2×C4⋊C8C2×D1112yes—
226#407—112no—
227C2×C22⋊C8C2×D1112yes—
228#405—114no—
229#405—114no—
230C4×M16—112no—
231C2×#97C2×D1111yescharacteristic
232C2×C4×C8C2×D1111yescharacteristic
233C22×C11—22no—
234C22×C11—22no—
235C22×C11—24no—
236C22×C11—82no—
237C22×C11#51912yes—
238C22×C11C24×C411yescharacteristic
239C4×C11—22no—
240C4×C11—24no—
241C4×C11—22no—
242C4×C11—22no—
243C4×C11#51912yes—
244C4×C11C2×2−1+412yes—
245Dic11—28no—
246Dic11—28no—
247C23×C4C22×D1111yescharacteristic
248C2×M16—114no—
249C22×C8C22×D1112yes—
250C22×C8C22×D1112yes—
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—118no—
269C4×Q8—114no—
270C4×Q8—114no—
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—118no—
295C22⋊C8C22×D1114yes—
296C22⋊C8C22×D1114yes—
297#97—118no—
298#97—118no—
299#97—114no—
300#97C22×D1112yes—
301#97C22×D1112yes—
302C4×C8—118no—
303C4×C8—118no—
304C4×C8—114no—
305C4×C8C22×D1111yescharacteristic
306C4×C8C22×D1112yes—
307C4×C8C22×D1111yescharacteristic
308C2×C11—22no—
309C2×C11—42no—
310C2×C11C2×#51911yescharacteristic
311C2×C11#357312yes—
312C24C2×C4×D1111yescharacteristic
313C2×Q8—118no—
314C2×Q8—114no—
315C2×Q8—114no—
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—228no—
325C2×C8—24no—
326C2×C8—24no—
327C2×C8—118no—
328C2×C8C23×D1112yes—
329C2×C8C23×D1114yes—
330C2×C8C23×D1112yes—
331C4⋊C4—118no—
332C4⋊C4—114no—
333C4⋊C4—114no—
334C4⋊C4—118no—
335C4⋊C4—118no—
336C4⋊C4—118no—
337C4⋊C4—118no—
338C4⋊C4—118no—
339C4⋊C4—114no—
340C4⋊C4—114no—
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×D1112yes—
354C42C23×D1111yescharacteristic
355C42C23×D1111yescharacteristic
356C11#6025211yescharacteristic, complemented, Sylow
357C23—22no—
358C23—42no—
359C23C22×C4×D1112yes—
360C23C22×C4×D1111yescharacteristic
361Q8—448no—
362Q8—444no—
363Q8—444no—
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×D1114yes—
374C2×C4C22×C4×D1112yes—
375C2×C4C22×C4×D1112yes—
376C2×C4C22×C4×D1111yescharacteristic
377C2×C4#6704314yes—
378C2×C4C24×D1111yescharacteristic
379C8—22no—
380C8—24no—
381C8—22no—
382C8—228no—
383C22—22no—
384C22—24no—
385C22—22no—
386C22—82no—
387C22#1062304712yes—
388C22C23×C4×D1111yescharacteristic
389C4—24no—
390C4—22no—
391C4—22no—
392C4—22no—
393C4—228no—
394C4—228no—
395C4#1062304712yes—
396C4C2×#6704312yes—
397C2—22no—
398C2—42no—
399C2C2×#1062304711yescharacteristic
400C2#1308332712yes—
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC2×C11×#433C2
prime radicalC24×C11C22×C4
cosocleC2×C4×C11C25
hypercenterC2×#433D11
hypocenterC11#60252
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #13077720C2semidirect
3. #13077715C2semidirect
4. #13077708C2semidirect
5. #13077559C2semidirect
6. #13077556C2semidirect
7. #13077550C2semidirect
37. #10622444C22semidirect
38. #10622443C22semidirect
39. #10622441C22semidirect
40. #10622441C22semidirect
45. #10622314C22semidirect
46. #10622314C22semidirect
47. #10622292C22semidirect
48. #10622292C22semidirect
49. C8×Dic22C22semidirect
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
#130775592
#130775562
#130775502
#130772702
#130772542
C2×C11×#4332
#6025211