Finite Group Databasebeta

← #14804238

Subgroups — #14804238

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622705C211yesmaximal, characteristic, complemented
2C2×#10622411C212yesmaximal
3C2×#10622454C211yesmaximal, characteristic
4#13073612C211yesmaximal, characteristic
5#13071674C211yesmaximal, characteristic, complemented
6#13069937C212yesmaximal, complemented
7#13069711C212yesmaximal
8#13069332C211yesmaximal, characteristic, complemented
9#13068954C212yesmaximal, complemented
10C4×#66873C211yesmaximal, characteristic
11C11×#1981C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#67000C2212yes—
14C22×#4326C2212yes—
15C22×#4326C2212yes—
16C22×#4314C2212yes—
17C2×#66940C2212yes—
18C2×C4×D44C2211yescharacteristic
19C2×#66922C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×#103C2212yes—
22C2×C11×#103C2212yes—
23C4×C11×C4⋊C4C2211yescharacteristic
24#10622843C2212yes—
25C2×#66880C2212yes—
26C2×Dic11⋊C8C2212yes—
27#10622705—24no—
28#10622606—22no—
29#10622600—21no—
30#10622600—21no—
31#10622587C2212yes—
32C2×#66873C2211yescharacteristic
33C2×#66873C2211yescharacteristic
34C4×C4⋊Dic11—21no—
35C4×C4⋊Dic11C2211yescharacteristic
36#10622541—21no—
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622454—24no—
39#10622411—28no—
40#10622266—22no—
41#10622188C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×Q8×C11C2312yes—
45C22×D44C2311yescharacteristic
46C22×C4×D11—21no—
47C22×Dic22C2312yes—
48C22×C8×C11C2312yes—
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C42×C11—21no—
56C2×C42×C11C2311yescharacteristic
57#67000—24no—
58#67000—42no—
59C2×#4326—24no—
60C2×#4326—24no—
61C2×#4326—24no—
62C2×#4326—24no—
63C2×#4326—42no—
64C2×#4326—42no—
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11D411yescharacteristic
71C2×C4⋊Dic11D411yescharacteristic
72C2×C4⋊Dic11C2311yescharacteristic
73C2×Dic11⋊C4—22no—
74C2×C4×Dic11—22no—
75C2×C4×Dic11C2312yes—
76C22×C11⋊C8C2311yescharacteristic
77C22×C11⋊C8C2311yescharacteristic
78C2×#4314—24no—
79C2×#4314—24no—
80C2×#4314—42no—
81#66940—24no—
82#66940—42no—
83C4×D44—22no—
84C4×D44—22no—
85#66922—22no—
86#66922D414yes—
87C11×C4⋊C8—22no—
88C11×#103—24no—
89C11×#103—42no—
90C11×#95—21no—
91C11⋊#95—22no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94C11⋊#95—22no—
95C11⋊#95D412yes—
96#66880—24no—
97Dic11⋊C8—24no—
98#66873—22no—
99#66873D414yes—
100C4×C11⋊C8—22no—
101#25365—111nomaximal, Sylow
102C23×D11—21no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2411yescharacteristic
115C22×Dic11—22no—
116C22×Dic11—21no—
117C22×Dic11C2×D412yes—
118C22×Dic11C2×D412yes—
119C2×D44—21no—
120C2×D44—21no—
121C2×D44—21no—
122C2×D44—21no—
123C2×D44—21no—
124C2×D44C2×D412yes—
125C2×C4×D11—42no—
126C2×C4×D11—42no—
127C2×C4×D11—42no—
128C2×Dic22—22no—
129C2×Dic22—22no—
130C2×Dic22—22no—
131C2×Dic22—22no—
132C2×Dic22—22no—
133C2×Dic22C2×D414yes—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—42no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4C2×D412yes—
143C42×C11—42no—
144C42×C11C2×D412yes—
145C42×C11#4112yes—
146#4326—48no—
147#4326—48no—
148(C2×D11)⋊C4—44no—
149(C2×D11)⋊C4—44no—
150(C2×D11)⋊C4—42no—
151C4⋊Dic11—24no—
152C4⋊Dic11—24no—
153C4⋊Dic11—22no—
154C4⋊Dic11—22no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157Dic11⋊C4—44no—
158C4×Dic11—22no—
159C4×Dic11—22no—
160C4×Dic11—44no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8C2×D412yes—
166C2×C11⋊C8#4112yes—
167#4314—48no—
168C2×#494—111no—
169C2×#464—112no—
170C2×#461—111no—
171#2547—111no—
172#2365—111no—
173#2056—112no—
174#2015—112no—
175#1981D1111yescharacteristic, complemented
176#1939—111no—
177#1878—112no—
178C4×#102—111no—
179C23×C11C22×D411yescharacteristic
180C22×D11—22no—
181C22×D11—41no—
182C22×D11—41no—
183C22×D11—41no—
184C22×D11—41no—
185C22×D11—41no—
186C22×D11—41no—
187Q8×C11—42no—
188Q8×C11—42no—
189Q8×C11—42no—
190Q8×C11—42no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—22no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—41no—
199C2×C4×C11—42no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11#12112yes—
203C2×C4×C11#12112yes—
204C2×C4×C11#13512yes—
205C2×C4×C11#13712yes—
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C2×#4111yescharacteristic
209C2×C4×C11C2×#4111yescharacteristic
210C2×C4×C11H(5,𝔽2)11yescharacteristic
211C2×C4×C11H(5,𝔽2)11yescharacteristic
212C2×Dic11—24no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224D44—22no—
225D44—22no—
226D44—41no—
227D44—41no—
228C4×D11—84no—
229Dic22—24no—
230Dic22—24no—
231Dic22—42no—
232Dic22—42no—
233C8×C11—42no—
234C11⋊C8—22no—
235C11⋊C8—22no—
236C22×Q16—112no—
237C22×Q16—112no—
238C22×SD16—112no—
239C2×C4⋊Q8—111no—
240C2×C4⋊Q8C2×D1111yescharacteristic
241C2×#124—112no—
242C2×C4×Q8—112no—
243C2×C4×D4—111no—
244#494—224no—
245#464—228no—
246#461—224no—
247C2×C4⋊C8—112no—
248C2×C4⋊C8C2×D1111yescharacteristic
249C2×#103—112no—
250C2×#103C2×D1112yes—
251C2×#103C2×D1112yes—
252C2×#102—111no—
253C2×#102—111no—
254C2×C4×C8—111no—
255#397—222no—
256#391—112no—
257#391—112no—
258#389—221no—
259#387—222no—
260#380—221no—
261#380—221no—
262C4×C4⋊C4—111no—
263C4×C4⋊C4—221no—
264C4×C4⋊C4C2×D1111yescharacteristic
265#340—111no—
266#340—111no—
267#336—112no—
268C22×C11C2×#12111yescharacteristic
269C22×C11D4211yescharacteristic
270C22×C11#55011yescharacteristic
271C22×C11C2×#13511yescharacteristic
272C22×C11C2×#13711yescharacteristic
273C22×C11#57811yescharacteristic
274C22×C11#57811yescharacteristic
275C2×D11—42no—
276C2×D11—42no—
277C2×D11—42no—
278C2×D11—81no—
279C2×D11—81no—
280C2×D11—81no—
281C2×D11—81no—
282C4×C11—22no—
283C4×C11—42no—
284C4×C11—81no—
285C4×C11—82no—
286C4×C11#46414yescomplemented
287C4×C11#53211yescharacteristic
288C4×C11#54011yescharacteristic
289C4×C11D4211yescharacteristic
290C4×C11#54611yescharacteristic
291Dic11—44no—
292Dic11—42no—
293Dic11—42no—
294Dic11—81no—
295C22×Q8—112no—
296C22×Q8C22×D1112yes—
297C22×D4—111no—
298C23×C4—221no—
299C2×Q16—224no—
300C2×Q16—224no—
301C2×Q16—224no—
302C2×Q16—224no—
303C2×Q16—442no—
304C2×Q16—442no—
305C2×SD16—224no—
306C2×SD16—224no—
307C2×SD16—442no—
308C22×C8—111no—
309C22×C8—111no—
310C22×C8C22×D1112yes—
311C4⋊Q8—22no—
312C4⋊Q8—22no—
313C4⋊Q8—114no—
314C4⋊Q8—222no—
315#124—224no—
316#124—442no—
317C4×Q8—224no—
318C4×Q8—442no—
319C4×D4—222no—
320C4×D4—222no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—111no—
325C2×C4⋊C4—111no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4C22×D1111yescharacteristic
330C2×C4⋊C4C22×D1111yescharacteristic
331C2×C22⋊C4—222no—
332C2×C22⋊C4—222no—
333C2×C22⋊C4—221no—
334C2×C42—21no—
335C2×C42—112no—
336C2×C42—222no—
337C2×C42C22×D1111yescharacteristic
338C4⋊C8—22no—
339C4⋊C8—224no—
340#103—24no—
341#103—42no—
342#103—224no—
343#102—114no—
344#102—222no—
345C4×C8—222no—
346#95—21no—
347#95—112no—
348#95—222no—
349#95—222no—
350#95—222no—
351#95—222no—
352C2×C11#242811yescharacteristic
353C2×C11C2×#46411yescharacteristic
354C2×C11#304411yescharacteristic
355C2×C11#327611yescharacteristic
356C2×C11#328311yescharacteristic
357C2×C11#339311yescharacteristic
358C2×C11#339811yescharacteristic
359D11—82no—
360C24—221no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—114no—
368C2×Q8—222no—
369C2×Q8—222no—
370C2×Q8—222no—
371C2×Q8—222no—
372C2×Q8—222no—
373C2×D4—112no—
374C2×D4—221no—
375C2×D4—221no—
376C2×D4—221no—
377C2×D4—221no—
378C2×D4—221no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—112no—
383C22×C4—112no—
384C22×C4—222no—
385C22×C4—221no—
386C22×C4—442no—
387C22×C4—442no—
388C22×C4—442no—
389C22×C4D4×D1111yescharacteristic
390C22×C4D4×D1111yescharacteristic
391C22×C4C23×D1111yescharacteristic
392Q16—448no—
393Q16—448no—
394SD16—448no—
395C2×C8—22no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8—112no—
399C2×C8—112no—
400C2×C8—221no—
401C2×C8—221no—
402C2×C8—221no—
403C2×C8—221no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—42no—
408C4⋊C4—42no—
409C4⋊C4—224no—
410C4⋊C4—224no—
411C4⋊C4—222no—
412C4⋊C4—222no—
413C4⋊C4—221no—
414C4⋊C4—221no—
415C4⋊C4—444no—
416C4⋊C4D4×D1112yes—
417C22⋊C4—444no—
418C22⋊C4—444no—
419C22⋊C4—442no—
420C42—42no—
421C42—222no—
422C42—222no—
423C42—444no—
424C42#433912yes—
425C42D4×D1112yes—
426C11#2536511yescharacteristic, complemented, Sylow
427C23—222no—
428C23—441no—
429C23—441no—
430C23—441no—
431C23—441no—
432C23—441no—
433C23—441no—
434C23C2×D4×D1111yescharacteristic
435Q8—42no—
436Q8—42no—
437Q8—42no—
438Q8—42no—
439Q8—224no—
440Q8—224no—
441Q8—442no—
442Q8—442no—
443D4—222no—
444D4—222no—
445D4—441no—
446D4—441no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—22no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—224no—
459C2×C4—222no—
460C2×C4—222no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—222no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—884no—
471C2×C4#6693712yes—
472C2×C4#6693712yes—
473C2×C4#6696912yes—
474C2×C4#6697112yes—
475C2×C4C2×#433911yescharacteristic
476C2×C4C2×D4×D1111yescharacteristic
477C2×C4C2×D4×D1111yescharacteristic
478C2×C4#6703711yescharacteristic
479C2×C4#41×D1111yescharacteristic
480C2×C4#6704211yescharacteristic
481C8—42no—
482C8—222no—
483C8—222no—
484C22—442no—
485C22—442no—
486C22—442no—
487C22—881no—
488C22—881no—
489C22—881no—
490C22—881no—
491C22C2×#6693711yescharacteristic
492C22#1062313011yescharacteristic
493C22#1062314011yescharacteristic
494C22C2×#6696911yescharacteristic
495C22C2×#6697111yescharacteristic
496C22#1062331011yescharacteristic
497C22#1062331011yescharacteristic
498C4—22no—
499C4—42no—
500C4—81no—
501C4—82no—
502C4—442no—
503C4—444no—
504C4—442no—
505C4—881no—
506C4#1062241114yescomplemented
507C4#1062307911yescharacteristic
508C4#1062309311yescharacteristic
509C4#1062320711yescharacteristic
510C4#1062324811yescharacteristic
511C2—882no—
512C2#1307220511yescharacteristic
513C2C2×#1062241111yescharacteristic
514C2#1307814511yescharacteristic
515C2#1308025711yescharacteristic
516C2#1308033311yescharacteristic
517C2#1308160311yescharacteristic
518C2#1308164611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1981C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1981D11
hypocenterC11#25365
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
1. C2×#10622705C2semidirect
5. #13071674C2semidirect
6. #13069937C2semidirect
8. #13069332C2semidirect
9. #13068954C2semidirect
11. C11×#1981C2semidirect
175. #1981D11semidirect
286. C4×C11#464semidirect
426. C11#25365semidirect
506. C4#10622411semidirect

Maximal subgroups

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

subgroupindex
C2×#106227052
C2×#106224112
C2×#106224542
#130736122
#130716742
#130699372
#130697112
#130693322
#130689542
C4×#668732
C11×#19812
#2536511