Finite Group Databasebeta

← #14721541

Subgroups — #14721541

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077645C211yesmaximal, characteristic
2#13071556C211yesmaximal, characteristic
3#13067188C212yesmaximal, complemented
4#13067167C212yesmaximal, complemented
5#13067149C212yesmaximal, complemented
6#13067136C212yesmaximal, complemented
7#13067128C212yesmaximal, complemented
8C2×#10622176C212yesmaximal, complemented
9C11×#3501C211yesmaximal, characteristic
10C11×#554—24no—
11C11×#554C414yescomplemented
12D4×Q8×C11C414yescomplemented
13C11×#544—21no—
14C11×#543—21no—
15C11×#543—21no—
16C11×#533C2212yes—
17C2×C11×C22⋊Q8C2212yes—
18C2×C11×C22⋊Q8C2212yes—
19C11×#518—21no—
20C2×C4×D4×C11C2211yescharacteristic
21#10622833—21no—
22#10622825C2211yescharacteristic
23#10622824C2211yescharacteristic
24C4×C22⋊Dic11C2211yescharacteristic
25C2×C11⋊#95C2211yescharacteristic
26#10622820C2212yes—
27C2×C22⋊(C11⋊C8)C2212yes—
28#10622624—24no—
29#10622594—21no—
30#10622564—21no—
31C22⋊C4×Dic11—21no—
32#10622550C2211yescharacteristic
33#10622545C2211yescharacteristic
34#10622539C2212yes—
35#10622176C2214yes—
36#10622176C2214yes—
37#10622176C2214yes—
38#10622176C2214yes—
39C22×Q8×C11C2×C412yes—
40C22×Q8×C11C2×C412yescomplemented
41C22×D4×C11D411yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×Dic11—21no—
45C11×C4⋊Q8—24no—
46C11×C4⋊Q8C2×C412yescomplemented
47C11×C4⋊Q8C2×C412yescomplemented
48C11×#125—24no—
49C11×#125—22no—
50C11×C22⋊Q8—22no—
51C11×C22⋊Q8—22no—
52C11×C22⋊Q8—22no—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8—22no—
55C11×C22⋊Q8—24no—
56C11×C22⋊Q8—24no—
57C11×C22⋊Q8—24no—
58C11×C22⋊Q8—24no—
59C11×C22⋊Q8C2×C414yes—
60C11×C22⋊Q8C2×C414yescomplemented
61C11×C22⋊Q8C2314yes—
62C4×Q8×C11—22no—
63C4×Q8×C11C2×C414yescomplemented
64C4×D4×C11—24no—
65C4×D4×C11—24no—
66C4×D4×C11C2×C414yes—
67C4×D4×C11D414yes—
68C11×#117—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4C2×C412yes—
72C2×C11×C4⋊C4C2×C412yescomplemented
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4D411yescharacteristic
77C2×C11×C22⋊C4D411yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4×Dic11—21no—
84C2×C4×Dic11—21no—
85C2×#4318—22no—
86C22×C11⋊C8—22no—
87C11⋊#95—21no—
88C11⋊#95—21no—
89C11⋊#95—21no—
90C11⋊#95—21no—
91C11⋊#95—21no—
92C11⋊#95C2311yescharacteristic
93C11⋊#95C2311yescharacteristic
94C11⋊#95C2311yescharacteristic
95C11⋊#95C2311yescharacteristic
96C22⋊(C11⋊C8)—22no—
97C22⋊(C11⋊C8)—22no—
98C22⋊(C11⋊C8)C2314yes—
99C4⋊(C11⋊C8)—22no—
100#66867—22no—
101#17621—111nomaximal, Sylow
102C24×C11C2×D411yescharacteristic
103C24×C11C2×D411yescharacteristic
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—82no—
108C2×Q8×C11—82no—
109C2×Q8×C11C22×C414yes—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11C22⋊C414yes—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—81no—
118C22×C4×C11—81no—
119C22×C4×C11C22×C412yes—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2411yescharacteristic
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—42no—
133C22×Dic11—42no—
134C22×Dic11—81no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4C22⋊C414yes—
145C11×C4⋊C4C22×C414yes—
146C11×C22⋊C4—24no—
147C11×C22⋊C4—24no—
148C11×C22⋊C4—24no—
149C11×C22⋊C4C22⋊C414yes—
150C11×C22⋊C4C22⋊C414yes—
151C42×C11—24no—
152C42×C11C22×C412yes—
153C42×C11C2×D412yes—
154C22⋊Dic11—42no—
155C22⋊Dic11—42no—
156C22⋊Dic11—81no—
157C4⋊Dic11—81no—
158C4×Dic11—42no—
159C4×Dic11—81no—
160#4318—82no—
161C2×C11⋊C8—24no—
162C2×C11⋊C8—82no—
163#3501D1111yescharacteristic
164#2973—111no—
165#2353—111no—
166#1520—112no—
167#1515—112no—
168#1511—112no—
169#1508—112no—
170#1506—112no—
171C2×#328—112no—
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11—41no—
178C23×C11C2×C22⋊C412yes—
179C23×C11C2×C22⋊C412yes—
180C23×C11#13712yes—
181C23×C11#13712yes—
182C23×C11C22×D411yescharacteristic
183Q8×C11—44no—
184Q8×C11—82no—
185Q8×C11—82no—
186Q8×C11—82no—
187D4×C11—28no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—24no—
191C2×C4×C11—24no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—82no—
201C2×C4×C11—82no—
202C2×C4×C11—82no—
203C2×C4×C11—82no—
204C2×C4×C11C2×C22⋊C412yes—
205C2×C4×C11C2×C22⋊C412yes—
206C2×C4×C11C2×C22⋊C412yes—
207C2×C4×C11C2×C22⋊C412yes—
208C2×C4×C11C23×C411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×Dic11—22no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—84no—
223C11⋊C8—44no—
224#554—24no—
225#554Dic1114yescomplemented
226D4×Q8Dic1114yescomplemented
227#544—21no—
228#543—21no—
229#543—21no—
230#533C2×D1112yes—
231C2×C22⋊Q8C2×D1112yes—
232C2×C22⋊Q8C2×D1112yes—
233#518—21no—
234C2×C4×D4C2×D1111yescharacteristic
235#435—224no—
236#432—112no—
237#407—112no—
238C2×C22⋊C8—112no—
239#388—221no—
240#387—221no—
241#386—221no—
242#383—111no—
243#381—111no—
244#380—111no—
245C4×C22⋊C4—111no—
246C4×C22⋊C4—221no—
247#376—111no—
248C2×#95—111no—
249#328—114no—
250#328—114no—
251#328—114no—
252#328—114no—
253C22×C11—21no—
254C22×C11—22no—
255C22×C11—21no—
256C22×C11—22no—
257C22×C11—22no—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—81no—
263C22×C11—81no—
264C22×C11#41914yes—
265C22×C11C22×C22⋊C411yescharacteristic
266C22×C11C2×#13711yescharacteristic
267C22×C11C2×#13711yescharacteristic
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—22no—
271C4×C11—22no—
272C4×C11—22no—
273C4×C11—22no—
274C4×C11—44no—
275C4×C11—44no—
276Dic11—42no—
277Dic11—81no—
278Dic11—81no—
279Dic11—81no—
280C22×Q8C2×Dic1112yes—
281C22×Q8C2×Dic1112yescomplemented
282C22×D4C22⋊D1111yescharacteristic
283C23×C4—221no—
284C23×C4C22×D1111yescharacteristic
285C23×C4C22×D1111yescharacteristic
286C2×M16—222no—
287C22×C8—222no—
288C4⋊Q8—24no—
289C4⋊Q8C2×Dic1112yescomplemented
290C4⋊Q8C2×Dic1112yescomplemented
291#125—24no—
292#125—22no—
293C22⋊Q8—22no—
294C22⋊Q8—22no—
295C22⋊Q8—22no—
296C22⋊Q8—22no—
297C22⋊Q8—22no—
298C22⋊Q8—24no—
299C22⋊Q8—24no—
300C22⋊Q8—24no—
301C22⋊Q8—24no—
302C22⋊Q8C2×Dic1114yes—
303C22⋊Q8C2×Dic1114yescomplemented
304C22⋊Q8C22×D1114yes—
305C4×Q8—22no—
306C4×Q8C2×Dic1114yescomplemented
307C4×D4—24no—
308C4×D4—24no—
309C4×D4C2×Dic1114yes—
310C4×D4C22⋊D1114yes—
311#117—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4C2×Dic1112yes—
316C2×C4⋊C4C2×Dic1112yescomplemented
317C2×C4⋊C4C22⋊D1111yescharacteristic
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—221no—
321C2×C22⋊C4—221no—
322C2×C22⋊C4—221no—
323C2×C22⋊C4C22⋊D1111yescharacteristic
324C2×C22⋊C4C22⋊D1111yescharacteristic
325C2×C42—221no—
326C2×C42—221no—
327C2×C42C22×D1111yescharacteristic
328C4⋊C8—222no—
329C22⋊C8—114no—
330C22⋊C8—222no—
331C22⋊C8—222no—
332#97—222no—
333#95—111no—
334#95—111no—
335#95—111no—
336#95—111no—
337#95—221no—
338#95—221no—
339#95—221no—
340#95—221no—
341#95—221no—
342C2×C11—21no—
343C2×C11—21no—
344C2×C11—24no—
345C2×C11—42no—
346C2×C11#288311yescharacteristic
347C2×C11C2×#41911yescharacteristic
348C2×C11#290111yescharacteristic
349C24C2×C22⋊D1111yescharacteristic
350C24C2×C22⋊D1111yescharacteristic
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—82no—
355C2×Q8—82no—
356C2×Q8C22×Dic1114yes—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4C22⋊Dic1114yes—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—81no—
365C22×C4—81no—
366C22×C4—221no—
367C22×C4—221no—
368C22×C4—221no—
369C22×C4—221no—
370C22×C4—442no—
371C22×C4—442no—
372C22×C4—881no—
373C22×C4C22×Dic1112yes—
374C22×C4C22×Dic1112yes—
375C22×C4C2×C22⋊D1111yescharacteristic
376C22×C4C2×C22⋊D1111yescharacteristic
377C22×C4C2×C22⋊D1111yescharacteristic
378C22×C4C2×C22⋊D1111yescharacteristic
379C22×C4C2×C22⋊D1112yes—
380C22×C4C2×C22⋊D1112yes—
381C22×C4C23×D1111yescharacteristic
382M16—882no—
383C2×C8—224no—
384C2×C8—882no—
385C4⋊C4—24no—
386C4⋊C4—24no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—24no—
393C4⋊C4—24no—
394C4⋊C4—881no—
395C4⋊C4C22⋊Dic1114yes—
396C4⋊C4C22×Dic1114yes—
397C22⋊C4—24no—
398C22⋊C4—24no—
399C22⋊C4—24no—
400C22⋊C4—442no—
401C22⋊C4—442no—
402C22⋊C4—881no—
403C22⋊C4C22⋊Dic1114yes—
404C22⋊C4C22⋊Dic1114yes—
405C42—24no—
406C42—442no—
407C42—881no—
408C42C22×Dic1112yes—
409C42C2×C22⋊D1112yes—
410C11#1762111yescharacteristic, complemented, Sylow
411C23—21no—
412C23—21no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23#6699512yes—
418C23#6699512yes—
419C23C2×C22⋊Dic1112yes—
420C23C2×C22⋊Dic1112yes—
421C23C22×C22⋊D1111yescharacteristic
422Q8—44no—
423Q8—82no—
424Q8—82no—
425Q8—82no—
426D4—28no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—82no—
440C2×C4—82no—
441C2×C4—82no—
442C2×C4—82no—
443C2×C4—222no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4—884no—
456C2×C4C2×C22⋊Dic1112yes—
457C2×C4C2×C22⋊Dic1112yes—
458C2×C4C2×C22⋊Dic1112yes—
459C2×C4C2×C22⋊Dic1112yes—
460C2×C4C23×Dic1111yescharacteristic
461C2×C4C22×C22⋊D1111yescharacteristic
462C8—444no—
463C22—21no—
464C22—22no—
465C22—21no—
466C22—22no—
467C22—22no—
468C22—22no—
469C22—22no—
470C22—42no—
471C22—42no—
472C22—81no—
473C22—81no—
474C22#1062283814yes—
475C22C2×#6699511yescharacteristic
476C22C2×#6699511yescharacteristic
477C22C22×C22⋊Dic1111yescharacteristic
478C4—21no—
479C4—21no—
480C4—22no—
481C4—22no—
482C4—22no—
483C4—22no—
484C4—44no—
485C4—44no—
486C4—442no—
487C4—881no—
488C4—881no—
489C4—881no—
490C2—21no—
491C2—21no—
492C2—24no—
493C2—42no—
494C2#1307707711yescharacteristic
495C2C2×#1062283811yescharacteristic
496C2#1307716311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#3501C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D4×C11D4
cosocleC22×C4×C11C24
hypercenter#3501D11
hypocenterC11#17621
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3501

Complements

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

NH ≅ G/Ntype
3. #13067188C2semidirect
4. #13067167C2semidirect
5. #13067149C2semidirect
6. #13067136C2semidirect
7. #13067128C2semidirect
8. C2×#10622176C2semidirect
11. C11×#554C4semidirect
12. D4×Q8×C11C4semidirect
40. C22×Q8×C11C2×C4semidirect
46. C11×C4⋊Q8C2×C4semidirect
47. C11×C4⋊Q8C2×C4semidirect
60. C11×C22⋊Q8C2×C4semidirect
63. C4×Q8×C11C2×C4semidirect
72. C2×C11×C4⋊C4C2×C4semidirect
225. #554Dic11semidirect
226. D4×Q8Dic11semidirect
281. C22×Q8C2×Dic11semidirect
289. C4⋊Q8C2×Dic11semidirect
290. C4⋊Q8C2×Dic11semidirect
303. C22⋊Q8C2×Dic11semidirect
306. C4×Q8C2×Dic11semidirect
316. C2×C4⋊C4C2×Dic11semidirect
410. C11#17621semidirect

Maximal subgroups

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

subgroupindex
#130776452
#130715562
#130671882
#130671672
#130671492
#130671362
#130671282
C2×#106221762
C11×#35012
#1762111