Finite Group Databasebeta

← #14728025

Subgroups — #14728025

Order 2816.

950 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#13079615C212yesmaximal, complemented
2#13074303C211yesmaximal, characteristic
3#13067590C212yesmaximal, complemented
4#13067573C212yesmaximal, complemented
5#13067556C212yesmaximal, complemented
6#13067539C212yesmaximal
7#13067128C212yesmaximal, 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×#66928C2211yescharacteristic
22#10622826—21no—
23#10622702—22no—
24#10622699—22no—
25#10622663C2214yes—
26#10622659C2214yes—
27#10622641—24no—
28#10622604C2211yescharacteristic
29#10622603—21no—
30#10622592C2211yescharacteristic
31#10622573C2211yescharacteristic
32#10622570—21no—
33#10622560C2211yescharacteristic
34#10622553—21no—
35#10622545C2211yescharacteristic
36#10622539C2212yes—
37#10622176C2214yes—
38#10622176C2214yes—
39#10622166C2212yes—
40#10622163C2212yes—
41C23×C4×C11D411yescharacteristic
42C22×C22⋊D11—21no—
43C22×D44C2311yescharacteristic
44C22×Dic22C2311yescharacteristic
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×#4326—24no—
85C2×#4325—24no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93#66928—22no—
94#66928—22no—
95C11⋊#95—21no—
96C11⋊#95—21no—
97C11⋊#95—21no—
98C11⋊#95C2311yescharacteristic
99C11⋊#95C2311yescharacteristic
100C22⋊(C11⋊C8)C2314yes—
101#66874—24no—
102#66873—24no—
103C4⋊(C11⋊C8)—22no—
104#66867—22no—
105#18333—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—81no—
132C2×Dic22—22no—
133C2×Dic22—81no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—24no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4C2×D414yes—
148C11×C22⋊C4—24no—
149C11×C22⋊C4—24no—
150C11×C22⋊C4—22no—
151C11×C22⋊C4—22no—
152C42×C11—24no—
153C42×C11—24no—
154C42×C11—21no—
155C42×C11—21no—
156C42×C11C2×D412yes—
157C42×C11C2×D412yes—
158C22⋊Dic11—81no—
159#4326—84no—
160#4325—84no—
161(C2×D11)⋊C4—42no—
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4—41no—
164(C2×D11)⋊C4—42no—
165(C2×D11)⋊C4—42no—
166(C2×D11)⋊C4—81no—
167Dic11⋊C4—81no—
168C4×Dic11—42no—
169C2×C11⋊C8—24no—
170#3458D1111yescharacteristic, complemented
171#3215—112no—
172#2610—111no—
173#1605—112no—
174#1602—112no—
175#1599—112no—
176#1596—112no—
177#1506—112no—
178#1464—111no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11#13712yes—
184C23×C11C22×D411yescharacteristic
185C22×D11—41no—
186C22×D11—41no—
187C22×D11—41no—
188C22×D11—41no—
189C22×D11—41no—
190C22×D11—41no—
191C22×D11—41no—
192Q8×C11—44no—
193Q8×C11—82no—
194Q8×C11—82no—
195Q8×C11—82no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—24no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—24no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—82no—
211C2×C4×C11—82no—
212C2×C4×C11#12011yescharacteristic
213C2×C4×C11#12011yescharacteristic
214C2×C4×C11#12012yes—
215C2×C4×C11#13712yes—
216C2×C4×C11C22×D412yes—
217C22⋊D11—84no—
218C2×Dic11—22no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227D44—44no—
228Dic22—44no—
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×#124—111no—
240C2×#117—21no—
241C2×#117C2×D1111yescharacteristic
242#497—222no—
243#489—222no—
244#464—224no—
245#451—114no—
246#450—114no—
247#432—112no—
248#395—111no—
249#394—111no—
250#393—111no—
251#392—111no—
252#390—221no—
253#388—221no—
254#388—221no—
255#386—221no—
256#376—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—81no—
272C2×D11—81no—
273C2×D11—81no—
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—42no—
288Dic11—81no—
289Dic11—81no—
290C22×Q8—111no—
291C22×D4—111no—
292C22×D4—221no—
293C23×C4C22⋊D1111yescharacteristic
294C2×Q16—224no—
295C2×SD16—224no—
296C4⋊Q8—24no—
297C4⋊Q8—21no—
298C4⋊Q8—21no—
299C4⋊Q8—24no—
300C4⋊Q8C22⋊D1112yescomplemented
301C4⋊Q8C22⋊D1112yescomplemented
302#125—24no—
303#125—22no—
304#125—24no—
305#125—22no—
306#124—222no—
307#124—222no—
308C22⋊Q8—24no—
309C22⋊Q8—24no—
310C22⋊Q8—24no—
311C22⋊Q8—22no—
312C22⋊Q8—22no—
313C22⋊Q8—22no—
314C22⋊Q8—24no—
315C22⋊Q8C22×D1114yes—
316C4×Q8—22no—
317C4×Q8—22no—
318C4×Q8—22no—
319C4×Q8C22⋊D1114yescomplemented
320#117—22no—
321#117—22no—
322#117—22no—
323#117—22no—
324#117—22no—
325#117—22no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
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⋊C4—221no—
338C2×C22⋊C4C22⋊D1111yescharacteristic
339C2×C22⋊C4C22×D1111yescharacteristic
340C2×C42—22no—
341C2×C42—221no—
342C2×C42C22⋊D1111yescharacteristic
343C2×C42C22×D1111yescharacteristic
344C4⋊C8—222no—
345#103—224no—
346#102—224no—
347C22⋊C8—114no—
348#97—222no—
349#95—111no—
350#95—111no—
351#95—221no—
352#95—221no—
353#95—221no—
354C2×C11—21no—
355C2×C11—21no—
356C2×C11—42no—
357C2×C11#300411yescharacteristic
358C2×C11#301811yescharacteristic
359C2×C11#302711yescharacteristic
360D11—161no—
361C24—221no—
362C24C2×C22⋊D1111yescharacteristic
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—222no—
367C2×Q8—881no—
368C2×Q8C2×C22⋊D1114yes—
369C2×D4—222no—
370C2×D4—442no—
371C2×D4—442no—
372C2×D4—881no—
373C2×D4—881no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—221no—
381C22×C4—221no—
382C22×C4—221no—
383C22×C4C2×C22⋊D1111yescharacteristic
384C22×C4C2×C22⋊D1111yescharacteristic
385C22×C4C2×C22⋊D1111yescharacteristic
386C22×C4C2×C22⋊D1111yescharacteristic
387C22×C4C2×C22⋊D1111yescharacteristic
388C22×C4C23×D1111yescharacteristic
389Q16—884no—
390SD16—884no—
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—881no—
406C4⋊C4C2×C22⋊D1114yes—
407C22⋊C4—24no—
408C22⋊C4—24no—
409C22⋊C4—22no—
410C22⋊C4—22no—
411C22⋊C4—442no—
412C22⋊C4—442no—
413C22⋊C4—441no—
414C22⋊C4—441no—
415C22⋊C4—442no—
416C22⋊C4—881no—
417C22⋊C4—881no—
418C42—24no—
419C42—24no—
420C42—21no—
421C42—21no—
422C42—442no—
423C42C2×C22⋊D1112yes—
424C42C2×C22⋊D1112yes—
425C11#1833311yescharacteristic, complemented, Sylow
426C23—21no—
427C23—21no—
428C23—41no—
429C23—41no—
430C23—441no—
431C23—441no—
432C23—441no—
433C23—441no—
434C23—441no—
435C23—441no—
436C23—441no—
437C23#6699512yes—
438C23C22×C22⋊D1111yescharacteristic
439Q8—44no—
440Q8—82no—
441Q8—82no—
442Q8—82no—
443Q8—444no—
444D4—444no—
445D4—884no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—24no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—24no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—82no—
461C2×C4—82no—
462C2×C4—222no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—441no—
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—881no—
485C22—881no—
486C22—881no—
487C22—881no—
488C22—881no—
489C22—881no—
490C22—881no—
491C22C2×#6699511yescharacteristic
492C22C2×#6699511yescharacteristic
493C22C2×#6700611yescharacteristic
494C4—22no—
495C4—22no—
496C4—21no—
497C4—21no—
498C4—22no—
499C4—41no—
500C4—44no—
501C4—41no—
502C4—44no—
503C4—442no—
504C4—881no—
505C4—881no—
506C2—21no—
507C2—21no—
508C2—42no—
509C2—1761no—
510C2#1307785011yescharacteristic
511C2#1307796511yescharacteristic
512C2#1307801811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3458C2
socleC22×C11C2×#120
prime radical#10622573C22
hypercenter#3458D11
hypocenterC11#18333
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. #13079615C2semidirect
3. #13067590C2semidirect
4. #13067573C2semidirect
5. #13067556C2semidirect
7. #13067128C2semidirect
8. #13066950C2semidirect
9. C11×#3458C2semidirect
49. C11×C4⋊Q8D4semidirect
50. C11×C4⋊Q8D4semidirect
66. C4×Q8×C11D4semidirect
170. #3458D11semidirect
300. C4⋊Q8C22⋊D11semidirect
301. C4⋊Q8C22⋊D11semidirect
319. C4×Q8C22⋊D11semidirect
425. C11#18333semidirect

Maximal subgroups

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

subgroupindex
#130796152
#130743032
#130675902
#130675732
#130675562
#130675392
#130671282
#130669502
C11×#34582
#1833311