Finite Group Databasebeta

← #14726318

Subgroups — #14726318

Order 2816.

960 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078711C212yesmaximal, complemented
2#13074182C211yesmaximal, characteristic
3#13067658C212yesmaximal, complemented
4#13067641C212yesmaximal, complemented
5#13067556C212yesmaximal, complemented
6#13067539C212yesmaximal
7#13067167C212yesmaximal, complemented
8#13066950C211yesmaximal, characteristic, complemented
9C11×#3458C211yesmaximal, characteristic, complemented
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×C4×D44C2211yescharacteristic
22#10622826—21no—
23#10622700—22no—
24#10622696—22no—
25#10622659C2214yes—
26#10622657C2214yes—
27#10622639—24no—
28#10622604C2211yescharacteristic
29#10622602—21no—
30#10622599C2211yescharacteristic
31#10622573C2211yescharacteristic
32#10622569—21no—
33#10622562C2211yescharacteristic
34#10622553—21no—
35#10622550C2211yescharacteristic
36#10622539C2212yes—
37#10622176C2214yes—
38#10622176C2214yes—
39#10622166C2212yes—
40#10622163C2212yes—
41C23×C4×C11D411yescharacteristic
42C22×C22⋊D11—21no—
43C22×D44C2311yescharacteristic
44C22×C4×D11—21no—
45C11×C4⋊Q8—24no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—24no—
49C11×C4⋊Q8D412yescomplemented
50C11×C4⋊Q8D412yescomplemented
51C11×#125—24no—
52C11×#125—22no—
53C11×#125—24no—
54C11×#125—22no—
55C11×C22⋊Q8—24no—
56C11×C22⋊Q8—24no—
57C11×C22⋊Q8—24no—
58C11×C22⋊Q8—22no—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—24no—
62C11×C22⋊Q8C2314yes—
63C4×Q8×C11—22no—
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×Q8×C11D414yescomplemented
67C11×#117—22no—
68C11×#117—22no—
69C11×#117—22no—
70C11×#117—22no—
71C11×#117—22no—
72C11×#117—22no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4D411yescharacteristic
79C2×C11×C22⋊C4C2311yescharacteristic
80C2×C42×C11—22no—
81C2×C42×C11D411yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C22⋊Dic11—21no—
84C2×#4325—24no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C4×D44—22no—
92C4×D44—22no—
93#66899—24no—
94C11⋊#95—21no—
95C11⋊#95—21no—
96C11⋊#95—21no—
97C11⋊#95—21no—
98C11⋊#95C2311yescharacteristic
99C11⋊#95C2311yescharacteristic
100C22⋊(C11⋊C8)C2314yes—
101#66873—24no—
102#66871—24no—
103C4⋊(C11⋊C8)—22no—
104#66867—22no—
105#18154—111nomaximal, Sylow
106C24×C11C2×D411yescharacteristic
107C23×D11—21no—
108C2×Q8×C11—22no—
109C2×Q8×C11—22no—
110C2×Q8×C11—22no—
111C2×Q8×C11C2×D414yes—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C2×C22⋊D11—42no—
125C2×C22⋊D11—42no—
126C2×C22⋊D11—81no—
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C2×D44—22no—
131C2×D44—42no—
132C2×C4×D11—42no—
133C2×C4×D11—81no—
134C2×C4×D11—81no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4C2×D414yes—
149C11×C22⋊C4—24no—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—22no—
152C11×C22⋊C4—22no—
153C42×C11—24no—
154C42×C11—24no—
155C42×C11—21no—
156C42×C11—21no—
157C42×C11C2×D412yes—
158C42×C11C2×D412yes—
159C22⋊Dic11—81no—
160#4325—48no—
161(C2×D11)⋊C4—42no—
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4—41no—
164(C2×D11)⋊C4—42no—
165(C2×D11)⋊C4—81no—
166C4⋊Dic11—22no—
167Dic11⋊C4—81no—
168C2×C11⋊C8—24no—
169#3458D1111yescharacteristic, complemented
170#3110—112no—
171#2598—111no—
172#1617—112no—
173#1614—112no—
174#1599—112no—
175#1596—112no—
176#1515—112no—
177#1464—111no—
178C23×C11—21no—
179C23×C11—21no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11#13712yes—
183C23×C11C22×D411yescharacteristic
184C22×D11—22no—
185C22×D11—41no—
186C22×D11—41no—
187C22×D11—41no—
188C22×D11—41no—
189C22×D11—41no—
190C22×D11—41no—
191Q8×C11—44no—
192Q8×C11—82no—
193Q8×C11—82no—
194Q8×C11—82no—
195C2×C4×C11—24no—
196C2×C4×C11—24no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—24no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—24no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—82no—
210C2×C4×C11—82no—
211C2×C4×C11#12011yescharacteristic
212C2×C4×C11#12011yescharacteristic
213C2×C4×C11#12012yes—
214C2×C4×C11#13712yes—
215C2×C4×C11C22×D412yes—
216C22⋊D11—84no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226D44—24no—
227D44—42no—
228C4×D11—84no—
229C11⋊C8—44no—
230#544—22no—
231#544—22no—
232#544—21no—
233#544C2×D1112yes—
234#543—21no—
235#543C2×D1112yes—
236#533—24no—
237#533—21no—
238#533C2×D1112yes—
239C2×C4×D4—111no—
240C2×#117—21no—
241C2×#117C2×D1111yescharacteristic
242#484—114no—
243#474—222no—
244#461—222no—
245#450—114no—
246#440—224no—
247#432—112no—
248#400—111no—
249#399—111no—
250#394—111no—
251#392—111no—
252#388—221no—
253#386—221no—
254#386—221no—
255#385—221no—
256#383—111no—
257#328—114no—
258#328—114no—
259#324—112no—
260#323—112no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—22no—
264C22×C11—42no—
265C22×C11—41no—
266C22×C11—41no—
267C22×C11—81no—
268C22×C11C2×#12011yescharacteristic
269C22×C11C2×#13711yescharacteristic
270C22×C11C2×#13711yescharacteristic
271C2×D11—42no—
272C2×D11—42no—
273C2×D11—42no—
274C2×D11—81no—
275C2×D11—81no—
276C2×D11—81no—
277C2×D11—81no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—22no—
281C4×C11—22no—
282C4×C11—22no—
283C4×C11—41no—
284C4×C11—44no—
285C4×C11—41no—
286C4×C11—44no—
287Dic11—81no—
288Dic11—81no—
289Dic11—81no—
290C22×D4—111no—
291C22×D4—221no—
292C23×C4—221no—
293C23×C4C22⋊D1111yescharacteristic
294C2×SD16—224no—
295C4⋊Q8—24no—
296C4⋊Q8—21no—
297C4⋊Q8—21no—
298C4⋊Q8—24no—
299C4⋊Q8C22⋊D1112yescomplemented
300C4⋊Q8C22⋊D1112yescomplemented
301#125—24no—
302#125—22no—
303#125—24no—
304#125—22no—
305C22⋊Q8—24no—
306C22⋊Q8—24no—
307C22⋊Q8—24no—
308C22⋊Q8—22no—
309C22⋊Q8—22no—
310C22⋊Q8—22no—
311C22⋊Q8—24no—
312C22⋊Q8C22×D1114yes—
313C4×Q8—22no—
314C4×Q8—22no—
315C4×Q8—22no—
316C4×Q8C22⋊D1114yescomplemented
317C4×D4—222no—
318C4×D4—222no—
319#117—22no—
320#117—22no—
321#117—22no—
322#117—22no—
323#117—22no—
324#117—22no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—111no—
328C2×C4⋊C4—221no—
329C2×C4⋊C4C22⋊D1111yescharacteristic
330C2×C4⋊C4C22×D1111yescharacteristic
331C2×C22⋊C4—22no—
332C2×C22⋊C4—221no—
333C2×C22⋊C4—221no—
334C2×C22⋊C4—221no—
335C2×C22⋊C4—221no—
336C2×C22⋊C4—221no—
337C2×C22⋊C4C22⋊D1111yescharacteristic
338C2×C22⋊C4C22×D1111yescharacteristic
339C2×C42—22no—
340C2×C42C22⋊D1111yescharacteristic
341C2×C42C22×D1111yescharacteristic
342#107—224no—
343C4⋊C8—222no—
344#103—224no—
345#102—224no—
346C22⋊C8—114no—
347#97—222no—
348#95—111no—
349#95—111no—
350#95—221no—
351#95—221no—
352#95—221no—
353#95—221no—
354C2×C11—21no—
355C2×C11—21no—
356C2×C11—42no—
357C2×C11#300411yescharacteristic
358C2×C11#302111yescharacteristic
359C2×C11#302511yescharacteristic
360D11—82no—
361C24—221no—
362C24C2×C22⋊D1111yescharacteristic
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8C2×C22⋊D1114yes—
367C2×D4—222no—
368C2×D4—442no—
369C2×D4—442no—
370C2×D4—442no—
371C2×D4—881no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—221no—
379C22×C4—221no—
380C22×C4—221no—
381C22×C4—442no—
382C22×C4—881no—
383C22×C4—881no—
384C22×C4C2×C22⋊D1111yescharacteristic
385C22×C4C2×C22⋊D1111yescharacteristic
386C22×C4C2×C22⋊D1111yescharacteristic
387C22×C4C2×C22⋊D1111yescharacteristic
388C22×C4C2×C22⋊D1111yescharacteristic
389C22×C4C23×D1111yescharacteristic
390SD16—448no—
391C2×C8—224no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—24no—
396C4⋊C4—24no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—24no—
403C4⋊C4—22no—
404C4⋊C4—24no—
405C4⋊C4—222no—
406C4⋊C4—881no—
407C4⋊C4C2×C22⋊D1114yes—
408C22⋊C4—24no—
409C22⋊C4—24no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—442no—
413C22⋊C4—442no—
414C22⋊C4—441no—
415C22⋊C4—441no—
416C22⋊C4—881no—
417C22⋊C4—881no—
418C42—24no—
419C42—24no—
420C42—21no—
421C42—21no—
422C42C2×C22⋊D1112yes—
423C42C2×C22⋊D1112yes—
424C11#1815411yescharacteristic, complemented, Sylow
425C23—21no—
426C23—21no—
427C23—41no—
428C23—41no—
429C23—222no—
430C23—441no—
431C23—441no—
432C23—441no—
433C23—441no—
434C23—441no—
435C23—441no—
436C23#6699512yes—
437C23C22×C22⋊D1111yescharacteristic
438Q8—44no—
439Q8—82no—
440Q8—82no—
441Q8—82no—
442D4—224no—
443D4—442no—
444D4—884no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—24no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—24no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—82no—
460C2×C4—82no—
461C2×C4—441no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—884no—
471C2×C4#6699512yes—
472C2×C4#6700611yescharacteristic
473C2×C4#6700611yescharacteristic
474C2×C4#6700612yes—
475C2×C4C22×C22⋊D1112yes—
476C8—444no—
477C22—21no—
478C22—21no—
479C22—22no—
480C22—42no—
481C22—41no—
482C22—41no—
483C22—81no—
484C22—442no—
485C22—442no—
486C22—442no—
487C22—881no—
488C22—881no—
489C22—881no—
490C22—881no—
491C22C2×#6699511yescharacteristic
492C22C2×#6699511yescharacteristic
493C22C2×#6700611yescharacteristic
494C4—22no—
495C4—21no—
496C4—21no—
497C4—22no—
498C4—22no—
499C4—41no—
500C4—44no—
501C4—41no—
502C4—44no—
503C4—881no—
504C4—881no—
505C4—881no—
506C2—21no—
507C2—21no—
508C2—42no—
509C2—882no—
510C2#1307785011yescharacteristic
511C2#1307798811yescharacteristic
512C2#1307800811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3458C2
socleC22×C11C2×#120
prime radical#10622573C22
hypercenter#3458D11
hypocenterC11#18154
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. #13078711C2semidirect
3. #13067658C2semidirect
4. #13067641C2semidirect
5. #13067556C2semidirect
7. #13067167C2semidirect
8. #13066950C2semidirect
9. C11×#3458C2semidirect
49. C11×C4⋊Q8D4semidirect
50. C11×C4⋊Q8D4semidirect
66. C4×Q8×C11D4semidirect
169. #3458D11semidirect
299. C4⋊Q8C22⋊D11semidirect
300. C4⋊Q8C22⋊D11semidirect
316. C4×Q8C22⋊D11semidirect
424. C11#18154semidirect

Maximal subgroups

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

subgroupindex
#130787112
#130741822
#130676582
#130676412
#130675562
#130675392
#130671672
#130669502
C11×#34582
#1815411