Finite Group Databasebeta

← #14728086

Subgroups — #14728086

Order 2816.

876 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079818C212yesmaximal, complemented
2#13074314C211yesmaximal, characteristic
3#13067658C212yesmaximal, complemented
4#13067641C212yesmaximal
5#13067624C212yesmaximal, complemented
6#13067607C212yesmaximal
7#13067128C212yesmaximal, complemented
8#13066950C211yesmaximal, characteristic
9C11×#3458C211yesmaximal, characteristic
10C11×#544—22no—
11C11×#544—22no—
12C11×#544—21no—
13C11×#544C2212yes—
14C11×#543—21no—
15C11×#543C2212yes—
16C11×#533—24no—
17C11×#533—21no—
18C11×#533C2212yes—
19C2×C11×#117—21no—
20C2×C11×#117C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22#10622823—21no—
23#10622695—22no—
24#10622693—22no—
25#10622657C2214yes—
26#10622656C2214yes—
27#10622635—24no—
28#10622599C2211yescharacteristic
29#10622596C2211yescharacteristic
30#10622585—21no—
31#10622566C2211yescharacteristic
32#10622562C2211yescharacteristic
33#10622558—21no—
34#10622546—21no—
35#10622545C2211yescharacteristic
36#10622539C2212yes—
37#10622176C2214yes—
38#10622176C2214yes—
39#10622166C2212yes—
40#10622163C2212yes—
41C23×C4×C11D411yescharacteristic
42C11×C4⋊Q8—24no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8—24no—
46C11×C4⋊Q8D412yes—
47C11×C4⋊Q8D412yes—
48C11×#125—24no—
49C11×#125—22no—
50C11×#125—24no—
51C11×#125—22no—
52C11×C22⋊Q8—24no—
53C11×C22⋊Q8—24no—
54C11×C22⋊Q8—24no—
55C11×C22⋊Q8—22no—
56C11×C22⋊Q8—22no—
57C11×C22⋊Q8—22no—
58C11×C22⋊Q8—24no—
59C11×C22⋊Q8C2314yes—
60C4×Q8×C11—22no—
61C4×Q8×C11—22no—
62C4×Q8×C11—22no—
63C4×Q8×C11D414yes—
64C11×#117—22no—
65C11×#117—22no—
66C11×#117—22no—
67C11×#117—22no—
68C11×#117—22no—
69C11×#117—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4D411yescharacteristic
76C2×C11×C22⋊C4C2311yescharacteristic
77C2×C42×C11—22no—
78C2×C42×C11D411yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×C4×Dic11—21no—
89#66923—22no—
90#66923—22no—
91#66899—24no—
92#66899—24no—
93C11⋊#95—21no—
94C11⋊#95—21no—
95C11⋊#95—21no—
96C11⋊#95—21no—
97C11⋊#95—21no—
98C11⋊#95C2311yescharacteristic
99C11⋊#95C2311yescharacteristic
100C22⋊(C11⋊C8)C2314yes—
101#66872—24no—
102#66871—24no—
103C4⋊(C11⋊C8)—22no—
104#66867—22no—
105#18340—111nomaximal, Sylow
106C24×C11C2×D411yescharacteristic
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11C2×D414yes—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C22×Dic11—21no—
124C22×Dic11—21no—
125C22×Dic11—21no—
126C22×Dic11—21no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—24no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4C2×D414yes—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—24no—
143C11×C22⋊C4—22no—
144C11×C22⋊C4—22no—
145C42×C11—24no—
146C42×C11—24no—
147C42×C11—21no—
148C42×C11—21no—
149C42×C11C2×D412yes—
150C42×C11C2×D412yes—
151C22⋊Dic11—42no—
152C22⋊Dic11—42no—
153C4⋊Dic11—22no—
154C4⋊Dic11—22no—
155Dic11⋊C4—42no—
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—42no—
159Dic11⋊C4—42no—
160C4×Dic11—42no—
161C2×C11⋊C8—24no—
162#3458D1111yescharacteristic
163#3236—112no—
164#2611—111no—
165#1617—112no—
166#1614—112no—
167#1611—112no—
168#1608—112no—
169#1506—112no—
170#1464—111no—
171C23×C11—21no—
172C23×C11—21no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11#13712yes—
176C23×C11C22×D411yescharacteristic
177Q8×C11—44no—
178Q8×C11—82no—
179Q8×C11—82no—
180Q8×C11—82no—
181C2×C4×C11—24no—
182C2×C4×C11—24no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—24no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—24no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—82no—
196C2×C4×C11—82no—
197C2×C4×C11#12011yescharacteristic
198C2×C4×C11#12011yescharacteristic
199C2×C4×C11#12012yes—
200C2×C4×C11#13712yes—
201C2×C4×C11C22×D412yes—
202C2×Dic11—22no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C11⋊C8—44no—
215#544—22no—
216#544—22no—
217#544—21no—
218#544C2×D1112yes—
219#543—21no—
220#543C2×D1112yes—
221#533—24no—
222#533—21no—
223#533C2×D1112yes—
224C2×#125—111no—
225C2×#117—21no—
226C2×#117C2×D1111yescharacteristic
227#501—222no—
228#491—222no—
229#484—114no—
230#483—114no—
231#479—224no—
232#432—112no—
233#400—111no—
234#399—111no—
235#398—111no—
236#397—111no—
237#389—221no—
238#388—221no—
239#387—221no—
240#385—221no—
241#376—111no—
242#328—114no—
243#328—114no—
244#324—112no—
245#323—112no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—22no—
249C22×C11—42no—
250C22×C11—41no—
251C22×C11—41no—
252C22×C11—81no—
253C22×C11C2×#12011yescharacteristic
254C22×C11C2×#13711yescharacteristic
255C22×C11C2×#13711yescharacteristic
256C4×C11—21no—
257C4×C11—21no—
258C4×C11—22no—
259C4×C11—22no—
260C4×C11—22no—
261C4×C11—41no—
262C4×C11—44no—
263C4×C11—41no—
264C4×C11—44no—
265Dic11—42no—
266Dic11—81no—
267Dic11—81no—
268Dic11—81no—
269C23×C4C22⋊D1111yescharacteristic
270C4⋊Q8—24no—
271C4⋊Q8—21no—
272C4⋊Q8—21no—
273C4⋊Q8—24no—
274C4⋊Q8C22⋊D1112yes—
275C4⋊Q8C22⋊D1112yes—
276#125—24no—
277#125—22no—
278#125—24no—
279#125—22no—
280#125—222no—
281#125—222no—
282C22⋊Q8—24no—
283C22⋊Q8—24no—
284C22⋊Q8—24no—
285C22⋊Q8—22no—
286C22⋊Q8—22no—
287C22⋊Q8—22no—
288C22⋊Q8—24no—
289C22⋊Q8C22×D1114yes—
290C4×Q8—22no—
291C4×Q8—22no—
292C4×Q8—22no—
293C4×Q8C22⋊D1114yes—
294#117—22no—
295#117—22no—
296#117—22no—
297#117—22no—
298#117—22no—
299#117—22no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4C22⋊D1111yescharacteristic
309C2×C4⋊C4C22×D1111yescharacteristic
310C2×C22⋊C4—22no—
311C2×C22⋊C4—221no—
312C2×C22⋊C4—221no—
313C2×C22⋊C4C22⋊D1111yescharacteristic
314C2×C22⋊C4C22×D1111yescharacteristic
315C2×C42—22no—
316C2×C42—221no—
317C2×C42C22⋊D1111yescharacteristic
318C2×C42C22×D1111yescharacteristic
319#107—224no—
320#106—224no—
321C4⋊C8—222no—
322#103—224no—
323#103—224no—
324C22⋊C8—114no—
325#97—222no—
326#95—111no—
327#95—111no—
328#95—221no—
329#95—221no—
330#95—221no—
331#95—221no—
332#95—221no—
333C2×C11—21no—
334C2×C11—21no—
335C2×C11—42no—
336C2×C11#300411yescharacteristic
337C2×C11#301811yescharacteristic
338C2×C11#302811yescharacteristic
339C24C2×C22⋊D1111yescharacteristic
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—22no—
343C2×Q8C2×C22⋊D1114yes—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—221no—
351C22×C4—221no—
352C22×C4—221no—
353C22×C4—221no—
354C22×C4C2×C22⋊D1111yescharacteristic
355C22×C4C2×C22⋊D1111yescharacteristic
356C22×C4C2×C22⋊D1111yescharacteristic
357C22×C4C2×C22⋊D1111yescharacteristic
358C22×C4C2×C22⋊D1111yescharacteristic
359C22×C4C23×D1111yescharacteristic
360C2×C8—224no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—24no—
365C4⋊C4—24no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—24no—
372C4⋊C4—22no—
373C4⋊C4—24no—
374C4⋊C4—222no—
375C4⋊C4—222no—
376C4⋊C4—442no—
377C4⋊C4—442no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C4⋊C4—442no—
381C4⋊C4C2×C22⋊D1114yes—
382C22⋊C4—24no—
383C22⋊C4—24no—
384C22⋊C4—22no—
385C22⋊C4—22no—
386C22⋊C4—442no—
387C22⋊C4—442no—
388C42—24no—
389C42—24no—
390C42—21no—
391C42—21no—
392C42—442no—
393C42C2×C22⋊D1112yes—
394C42C2×C22⋊D1112yes—
395C11#1834011yescharacteristic, complemented, Sylow
396C23—21no—
397C23—21no—
398C23—41no—
399C23—41no—
400C23#6699512yes—
401C23C22×C22⋊D1111yescharacteristic
402Q8—44no—
403Q8—82no—
404Q8—82no—
405Q8—82no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—24no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—24no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—82no—
421C2×C4—82no—
422C2×C4—222no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4#6699512yes—
435C2×C4#6700611yescharacteristic
436C2×C4#6700611yescharacteristic
437C2×C4#6700612yes—
438C2×C4C22×C22⋊D1112yes—
439C8—444no—
440C22—21no—
441C22—21no—
442C22—22no—
443C22—42no—
444C22—41no—
445C22—41no—
446C22—81no—
447C22C2×#6699511yescharacteristic
448C22C2×#6699511yescharacteristic
449C22C2×#6700611yescharacteristic
450C4—22no—
451C4—22no—
452C4—21no—
453C4—21no—
454C4—22no—
455C4—41no—
456C4—44no—
457C4—41no—
458C4—44no—
459C4—442no—
460C4—881no—
461C4—881no—
462C4—881no—
463C2—21no—
464C2—21no—
465C2—42no—
466C2#1307785011yescharacteristic
467C2#1307796511yescharacteristic
468C2#1307802211yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3458C2
socleC22×C11C2×#120
prime radicalC24×C11C2×D4
hypercenter#3458D11
hypocenterC11#18340
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3458

Complements

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

NH ≅ G/Ntype
1. #13079818C2semidirect
3. #13067658C2semidirect
5. #13067624C2semidirect
7. #13067128C2semidirect
395. C11#18340semidirect

Maximal subgroups

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

subgroupindex
#130798182
#130743142
#130676582
#130676412
#130676242
#130676072
#130671282
#130669502
C11×#34582
#1834011