Finite Group Databasebeta

← #15623447

Subgroups — #15623447

Order 2816.

1834 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082432C212yesmaximal
2#13079158C212yesmaximal, complemented
3#13079157C214yesmaximal, complemented
4#13079144C214yesmaximal, complemented
5#13079141C218yesmaximal, complemented
6#13079130C211yesmaximal, characteristic, complemented
7#13079125C212yesmaximal, complemented
8D11×#498C212yesmaximal, complemented
9#13077207C214yesmaximal
10C4×#66954C211yesmaximal, characteristic
11C2×C11×#498C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2212yes—
13Q8×C22⋊D11—24no—
14C2×#66954C2212yes—
15#10623261—22no—
16#10623260C2218yes—
17#10623259C2214yes—
18#10623258—22no—
19D11×C4⋊Q8C2214yes—
20#10623253—22no—
21#10623252—22no—
22#10623042—24no—
23#10623035C2214yes—
24#10623031C2214yes—
25C4×#4339C2211yescharacteristic
26#10623001C2212yes—
27C11×#498C2212yes—
28C11×#498C2214yes—
29C11×#498C2212yes—
30C2×C11×#106C2214yes—
31C2×C4×C8×C11C2211yescharacteristic
32#10622719C2214yes—
33#10622714C2212yes—
34#10622693C2218yes—
35#10622692C2214yes—
36#10622691C2214yes—
37#10622577C2218yes—
38C4×#4318C2211yescharacteristic
39#10622474C22116yes—
40#10622473C2218yes—
41D11×#106C2218yes—
42#10622471C2218yes—
43#10622469C22116yes—
44#10622468C2218yes—
45#10622302C2214yes—
46C4×#4313C2212yes—
47C4×C8×D11C2212yes—
48#10622296C2214yes—
49#10622295C2212yes—
50#10622293C2211yescharacteristic
51#10622293C2211yescharacteristic
52C22×Q8×C11—22no—
53C2×Q8×D11—24no—
54C2×#4339C2311yescharacteristic
55C22×C8×C11C2312yes—
56C11×C4⋊Q8—22no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8C2314yes—
59C11×C4⋊Q8C2314yes—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4C2314yes—
62C2×C42×C11C2311yescharacteristic
63#66999—24no—
64#66999—28no—
65Q8×Dic11—24no—
66#66997—28no—
67#66997—24no—
68C4×C22⋊D11—28no—
69C4×C22⋊D11D414yes—
70#66979C2314yes—
71#66979C2311yescharacteristic
72#66977—22no—
73#66977—22no—
74#66977—28no—
75C2×#4318C2312yes—
76#66954Q8116yescomplemented
77C2×#4313C2314yes—
78C2×C8×D11C2314yes—
79#66950—24no—
80#66949—28no—
81#66946—24no—
82#66945C2318yes—
83C4⋊C4×D11—24no—
84C4⋊C4×D11C2318yes—
85#66943—24no—
86#66943C2318yes—
87#66942—28no—
88#66941—24no—
89#66941—24no—
90#66941C2318yes—
91#66940—24no—
92#66940—24no—
93C4×D44D412yes—
94#66925C2312yes—
95C42×D11C2312yes—
96#66923C2314yes—
97#66922C2312yes—
98#66922C2312yes—
99C4×Dic22—22no—
100C4×Dic22—22no—
101C4×Dic22D412yes—
102C11×#106C2318yes—
103C11×#106C2318yes—
104C4×C8×C11C2311yescharacteristic
105C4×C8×C11C2311yescharacteristic
106C4×C8×C11C2312yes—
107#66882C2318yes—
108#66881C2314yes—
109#66881C2314yes—
110#66879C2314yes—
111C8×Dic11C2314yes—
112#66872C23116yes—
113#66871C23116yes—
114#66867C2312yes—
115C4×C11⋊C8C2312yes—
116#60665—111nomaximal, Sylow
117C2×Q8×C11—24no—
118C2×Q8×C11—24no—
119C2×Q8×C11—84no—
120C22×C4×C11—24no—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2411yescharacteristic
123C2×C22⋊D11C2×D412yes—
124Q8×D11—88no—
125#4339C2×Q818yes—
126C2×D44C2×D411yescharacteristic
127C2×C4×D11—28no—
128C2×C4×D11C2×D414yes—
129C2×C4×D11C2412yes—
130C2×Dic22—28no—
131C2×Dic22—22no—
132C2×Dic22—22no—
133C2×Dic22C2×D411yescharacteristic
134C2×C8×C11C2×Q818yescomplemented
135C2×C8×C11C2412yes—
136C2×C8×C11C2412yes—
137C11×C4⋊C4—24no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4C2418yes—
141C42×C11C2×D412yes—
142C42×C11C2411yescharacteristic
143C42×C11C2411yescharacteristic
144C22⋊Dic11—24no—
145C22⋊Dic11C2×D412yes—
146(C2×D11)⋊C4—28no—
147(C2×D11)⋊C4C2×D414yes—
148C4⋊Dic11—28no—
149C4⋊Dic11—22no—
150C4⋊Dic11—22no—
151C4⋊Dic11C2×D412yes—
152C4⋊Dic11C2414yes—
153C4⋊Dic11C2414yes—
154Dic11⋊C4—28no—
155Dic11⋊C4—28no—
156Dic11⋊C4—28no—
157Dic11⋊C4—24no—
158Dic11⋊C4—24no—
159Dic11⋊C4C2×D414yes—
160C4×Dic11—28no—
161C4×Dic11—24no—
162C4×Dic11C2×D414yes—
163C4×Dic11C2412yes—
164#4318C2×Q818yescomplemented
165C2×C11⋊C8C2414yes—
166#4313C2×Q8116yescomplemented
167C8×D11C2×Q8116yescomplemented
168#3503—112no—
169#3165—114no—
170#3165—112no—
171#3163—118no—
172#3163—114no—
173#3160—112no—
174#3160—111no—
175C2×#498—112no—
176C2×#498D1111yescharacteristic, complemented
177#2912—114no—
178C4×#131—111no—
179C23×C11C22×D411yescharacteristic
180C22×D11C22×D412yes—
181Q8×C11—48no—
182Q8×C11—84no—
183C2×C4×C11—24no—
184C2×C4×C11—28no—
185C2×C4×C11—84no—
186C2×C4×C11C22×D412yes—
187C2×C4×C11C22×D411yescharacteristic
188C2×C4×C11C22×D412yes—
189C2×C4×C11C22×Q814yes—
190C2×C4×C11C2511yescharacteristic
191C22⋊D11C4⋊Q818yes—
192C2×Dic11—24no—
193C2×Dic11—24no—
194C2×Dic11C22×D414yes—
195C2×Dic11C22×D412yes—
196D44C4⋊Q814yes—
197C4×D11—28no—
198C4×D11—88no—
199C4×D11C22×Q818yes—
200Dic22—44no—
201Dic22—44no—
202Dic22—88no—
203Dic22C4⋊Q814yes—
204C8×C11C22×Q814yes—
205C8×C11C22×Q814yes—
206C11⋊C8C22×Q818yes—
207C2×#131—112no—
208Q82—222no—
209#557—222no—
210#554—224no—
211#554—222no—
212D4×Q8—222no—
213D4×Q8—224no—
214#544—118no—
215#544—114no—
216#533—114no—
217#533—112no—
218C2×C4⋊Q8—114no—
219C2×C4⋊Q8C2×D1112yes—
220#520—114no—
221C4×#41—111no—
222#501—118no—
223#501—1116no—
224#500—114no—
225#500—112no—
226#499—118no—
227#499—114no—
228#498—114no—
229#498—118no—
230#498—111no—
231#498—111no—
232#498C2×D1112yes—
233#498C2×D1114yes—
234#498C2×D1112yes—
235#428—118no—
236#428—1116no—
237#427—114no—
238#427—118no—
239C2×#106—118no—
240C2×#106C2×D1114yes—
241#405—112no—
242#405—114no—
243C4×M16—111no—
244C4×M16—112no—
245C2×C4×C8—112no—
246C2×C4×C8C2×D1111yescharacteristic
247C22×C11—22no—
248C22×C11C2×C4⋊Q812yes—
249C22×C11C23×D411yescharacteristic
250C2×D11—24no—
251C2×D11C2×C4⋊Q814yes—
252C4×C11—22no—
253C4×C11—48no—
254C4×C11C2×C4⋊Q812yes—
255C4×C11#57714yes—
256C4×C11C23×Q812yes—
257Dic11—24no—
258Dic11—44no—
259Dic11—44no—
260Dic11C2×C4⋊Q814yes—
261C2×#41—111no—
262C22×Q8—22no—
263C22×Q8—224no—
264#131—1116no—
265C2×M16—112no—
266C2×M16—114no—
267C22×C8—114no—
268C22×C8C22×D1112yes—
269C4⋊Q8—22no—
270C4⋊Q8—22no—
271C4⋊Q8—118no—
272C4⋊Q8—112no—
273C4⋊Q8—112no—
274C4⋊Q8—224no—
275C4⋊Q8—224no—
276C4⋊Q8—224no—
277C4⋊Q8—228no—
278C4⋊Q8C22×D1114yes—
279C4⋊Q8C22×D1114yes—
280#125—118no—
281#125—114no—
282#125—228no—
283#125—224no—
284C22⋊Q8—228no—
285C22⋊Q8—228no—
286C22⋊Q8—228no—
287C22⋊Q8—224no—
288C22⋊Q8—224no—
289C22⋊Q8—222no—
290C22⋊Q8—222no—
291C4×Q8—112no—
292C4×Q8—224no—
293C4×Q8—224no—
294C4×Q8—224no—
295C4×Q8—222no—
296C4×Q8—222no—
297C4×D4—114no—
298C4×D4—112no—
299C4×D4—224no—
300C4×D4—228no—
301#117—111no—
302#117—112no—
303#117—114no—
304#117—118no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—118no—
307C2×C4⋊C4—224no—
308C2×C4⋊C4C22×D1114yes—
309C2×C42—112no—
310C2×C42C22×D1111yescharacteristic
311#107—118no—
312#107—1116no—
313#106—114no—
314#106—114no—
315#106—1116no—
316#106C22×D1118yes—
317#106C22×D1118yes—
318#97—114no—
319#97—112no—
320C4×C8—114no—
321C4×C8—112no—
322C4×C8C22×D1111yescharacteristic
323C4×C8C22×D1111yescharacteristic
324C4×C8C22×D1112yes—
325C2×C11—22no—
326C2×C11C22×C4⋊Q811yescharacteristic
327C2×C11C2×#57712yes—
328D11—24no—
329#41—118no—
330C2×Q8—24no—
331C2×Q8—24no—
332C2×Q8—84no—
333C2×Q8—111no—
334C2×Q8—228no—
335C2×Q8—222no—
336C2×Q8—222no—
337C2×Q8—888no—
338C2×D4—112no—
339C2×D4—111no—
340C22×C4—24no—
341C22×C4—112no—
342C22×C4—114no—
343C22×C4—228no—
344C22×C4D4×D1112yes—
345C22×C4C23×D1111yescharacteristic
346M16—118no—
347M16—1116no—
348C2×C8—114no—
349C2×C8—1116no—
350C2×C8Q8×D1118yescomplemented
351C2×C8C23×D1112yes—
352C2×C8C23×D1112yes—
353C4⋊C4—24no—
354C4⋊C4—24no—
355C4⋊C4—24no—
356C4⋊C4—114no—
357C4⋊C4—112no—
358C4⋊C4—114no—
359C4⋊C4—114no—
360C4⋊C4—228no—
361C4⋊C4—228no—
362C4⋊C4—228no—
363C4⋊C4—228no—
364C4⋊C4—222no—
365C4⋊C4—222no—
366C4⋊C4—224no—
367C4⋊C4—224no—
368C4⋊C4C23×D1118yes—
369C22⋊C4—112no—
370C22⋊C4—114no—
371C22⋊C4—228no—
372C22⋊C4—224no—
373C42—114no—
374C42—112no—
375C42—228no—
376C42—224no—
377C42D4×D1112yes—
378C42C23×D1111yescharacteristic
379C42C23×D1111yescharacteristic
380C11#6066511yescharacteristic, complemented, Sylow
381C23—112no—
382C23C2×D4×D1111yescharacteristic
383Q8—48no—
384Q8—84no—
385Q8—114no—
386Q8—444no—
387Q8—444no—
388Q8—888no—
389D4—118no—
390D4—114no—
391C2×C4—24no—
392C2×C4—28no—
393C2×C4—84no—
394C2×C4—112no—
395C2×C4—118no—
396C2×C4—114no—
397C2×C4—228no—
398C2×C4—224no—
399C2×C4—224no—
400C2×C4—888no—
401C2×C4C2×D4×D1112yes—
402C2×C4C2×D4×D1111yescharacteristic
403C2×C4C2×D4×D1112yes—
404C2×C4C2×Q8×D1114yes—
405C2×C4C24×D1111yescharacteristic
406C8—118no—
407C8C2×Q8×D1114yes—
408C8C2×Q8×D1114yes—
409C22—22no—
410C22—114no—
411C22—224no—
412C22D11×C4⋊Q812yes—
413C22C22×D4×D1111yescharacteristic
414C4—22no—
415C4—48no—
416C4—114no—
417C4—224no—
418C4—444no—
419C4—444no—
420C4D11×C4⋊Q812yes—
421C4#1062329314yes—
422C4C22×Q8×D1112yes—
423C2—22no—
424C2—224no—
425C2C2×D11×C4⋊Q811yescharacteristic
426C2C2×#1062329312yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#498C2
socleC22×C11C23×D4
prime radicalC2×#4339C23
hypercenterC2×#498D11
hypocenterC11#60665
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
2. #13079158C2semidirect
3. #13079157C2semidirect
4. #13079144C2semidirect
5. #13079141C2semidirect
6. #13079130C2semidirect
7. #13079125C2semidirect
8. D11×#498C2semidirect
11. C2×C11×#498C2semidirect
76. #66954Q8semidirect
134. C2×C8×C11C2×Q8semidirect
164. #4318C2×Q8semidirect
166. #4313C2×Q8semidirect
167. C8×D11C2×Q8semidirect
176. C2×#498D11semidirect
350. C2×C8Q8×D11semidirect
380. C11#60665semidirect

Maximal subgroups

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

subgroupindex
#130824322
#130791582
#130791572
#130791442
#130791412
#130791302
#130791252
D11×#4982
#130772072
C4×#669542
C2×C11×#4982
#6066511