Finite Group Databasebeta

← #14804239

Subgroups — #14804239

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×#10622779C212yesmaximal
3#13073608C211yesmaximal, characteristic
4#13071676C211yesmaximal, characteristic, complemented
5#13069937C212yesmaximal, complemented
6#13069708C212yesmaximal
7#13069538C211yesmaximal, characteristic, complemented
8#13069332C211yesmaximal, characteristic, complemented
9#13068955C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic
11C2×C11×#461C211yesmaximal, characteristic
12C22×C11×SD16C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×Q8×Dic11C2212yes—
16C22×#4326C2212yes—
17C22×#4326C2212yes—
18C2×#66989C2212yes—
19C2×#66922C2211yescharacteristic
20C11×#461—24no—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#103C2212yes—
23#10622843C2212yes—
24C2×#66896C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26#10622825—21no—
27#10622825—21no—
28#10622779—28no—
29C2×#66880C2212yes—
30C2×#66880C2212yes—
31C2×Dic11⋊C8C2212yes—
32#10622705—24no—
33#10622598—21no—
34#10622594—22no—
35C4⋊C4×Dic11—21no—
36#10622587C2212yes—
37#10622566—22no—
38C4×C4⋊Dic11C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622188C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2211yescharacteristic
44C22×Q8×C11C2312yes—
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11—21no—
47C22×Dic22C2312yes—
48C2×C11×SD16—24no—
49C2×C11×SD16—24no—
50C2×C11×SD16—42no—
51C22×C8×C11C2312yes—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8D414yes—
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—21no—
60C2×C42×C11C2311yescharacteristic
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—22no—
63Q8×Dic11—24no—
64Q8×Dic11—42no—
65C2×#4326—24no—
66C2×#4326—24no—
67C2×#4326—24no—
68C2×#4326—24no—
69C2×#4326—42no—
70C2×#4326—42no—
71#66989—24no—
72#66989—42no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11D411yescharacteristic
77C2×C4⋊Dic11D411yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4×Dic11—21no—
81C2×C4×Dic11—22no—
82C2×C4×Dic11C2312yes—
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2311yescharacteristic
85#66922—22no—
86#66922—22no—
87C11×C4⋊C8—22no—
88C11×#103—24no—
89#66896—22no—
90#66896D414yes—
91C11⋊#95—21no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94C11⋊#95—22no—
95C11⋊#95—22no—
96C11⋊#95D412yes—
97#66880—24no—
98#66880—42no—
99Dic11⋊C8—24no—
100C4×C11⋊C8—22no—
101#25365—111nomaximal, Sylow
102C24×C11—21no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—22no—
108C2×Q8×C11C2×D414yes—
109C2×D4×C11—21no—
110C2×D4×C11—21no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11C2×D412yes—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C22×Dic11—21no—
124C22×Dic11—21no—
125C22×Dic11—22no—
126C22×Dic11C2×D412yes—
127C22×Dic11C2×D412yes—
128C2×Dic22—22no—
129C2×Dic22—22no—
130C2×Dic22—22no—
131C2×Dic22—22no—
132C2×Dic22—22no—
133C2×Dic22—22no—
134C11×SD16—48no—
135C2×C8×C11—22no—
136C2×C8×C11—22no—
137C2×C8×C11—22no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C22⋊C4—42no—
143C42×C11C2×D412yes—
144C42×C11#4112yes—
145C22⋊Dic11—44no—
146C22⋊Dic11—44no—
147#4326—48no—
148#4326—48no—
149C4⋊Dic11—22no—
150C4⋊Dic11—22no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11—44no—
155C4⋊Dic11—42no—
156C4⋊Dic11—42no—
157C4⋊Dic11C2×D412yes—
158C4×Dic11—22no—
159C4×Dic11—22no—
160C4×Dic11—44no—
161C4×Dic11—42no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—21no—
166C2×C11⋊C8C2×D412yes—
167C2×C11⋊C8#4112yes—
168C2×#494—111no—
169C2×#464—112no—
170C2×#461D1111yescharacteristic
171#2547—111no—
172#2365—111no—
173#2056—112no—
174#2015—112no—
175#1981—111no—
176#1939—111no—
177#1878—112no—
178C4×#102—111no—
179C23×C11—22no—
180C23×C11—41no—
181C23×C11—41no—
182C23×C11—41no—
183C23×C11—41no—
184C23×C11—41no—
185C23×C11—41no—
186C23×C11C22×D411yescharacteristic
187Q8×C11—24no—
188Q8×C11—24no—
189Q8×C11—42no—
190Q8×C11—42no—
191D4×C11—22no—
192D4×C11—22no—
193D4×C11—41no—
194D4×C11—41no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—24no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—84no—
204C2×C4×C11#12112yes—
205C2×C4×C11#12112yes—
206C2×C4×C11#13512yes—
207C2×C4×C11#13712yes—
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C2×C4×C11C2×#4111yescharacteristic
212C2×C4×C11H(5,𝔽2)11yescharacteristic
213C2×C4×C11H(5,𝔽2)11yescharacteristic
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—41no—
226C2×Dic11—42no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229Dic22—42no—
230Dic22—42no—
231Dic22—42no—
232Dic22—42no—
233C8×C11—42no—
234C11⋊C8—22no—
235C11⋊C8—22no—
236C22×Q16—112no—
237C22×Q16—112no—
238C22×SD16C2×D1112yes—
239C2×C4⋊Q8—111no—
240C2×C4⋊Q8C2×D1111yescharacteristic
241C2×#124—112no—
242C2×C4×Q8—112no—
243C2×C4×D4C2×D1111yescharacteristic
244#494—224no—
245#464—228no—
246#461—24no—
247C2×C4⋊C8—112no—
248C2×C4⋊C8C2×D1111yescharacteristic
249C2×#103—112no—
250C2×#103—112no—
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—111no—
264C4×C4⋊C4—221no—
265#340—111no—
266#340—111no—
267#336—112no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11—81no—
275C22×C11C2×#12111yescharacteristic
276C22×C11D4211yescharacteristic
277C22×C11#55011yescharacteristic
278C22×C11C2×#13511yescharacteristic
279C22×C11C2×#13711yescharacteristic
280C22×C11#57811yescharacteristic
281C22×C11#57811yescharacteristic
282C4×C11—22no—
283C4×C11—44no—
284C4×C11—81no—
285C4×C11#46414yescomplemented
286C4×C11#53211yescharacteristic
287C4×C11#54011yescharacteristic
288C4×C11D4211yescharacteristic
289C4×C11#54611yescharacteristic
290Dic11—42no—
291Dic11—42no—
292Dic11—42no—
293Dic11—81no—
294Dic11—82no—
295C22×Q8—112no—
296C22×Q8C22×D1112yes—
297C22×D4C22×D1111yescharacteristic
298C23×C4—21no—
299C2×Q16—224no—
300C2×Q16—224no—
301C2×Q16—224no—
302C2×Q16—224no—
303C2×Q16—442no—
304C2×Q16—442no—
305C2×SD16—24no—
306C2×SD16—24no—
307C2×SD16—42no—
308C22×C8—111no—
309C22×C8—111no—
310C22×C8C22×D1112yes—
311C4⋊Q8—22no—
312C4⋊Q8—222no—
313C4⋊Q8—222no—
314C4⋊Q8C22⋊D1114yes—
315#124—224no—
316#124—442no—
317C4×Q8—224no—
318C4×Q8—442no—
319C4×D4—22no—
320C4×D4—22no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—111no—
325C2×C4⋊C4—111no—
326C2×C4⋊C4—111no—
327C2×C4⋊C4—222no—
328C2×C4⋊C4—221no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4C22×D1111yescharacteristic
331C2×C22⋊C4—21no—
332C2×C22⋊C4—222no—
333C2×C22⋊C4—222no—
334C2×C42—112no—
335C2×C42—222no—
336C2×C42—221no—
337C2×C42C22×D1111yescharacteristic
338C4⋊C8—22no—
339C4⋊C8—224no—
340#103—24no—
341#103—224no—
342#103—442no—
343#102—114no—
344#102—222no—
345C4×C8—222no—
346#95—112no—
347#95—222no—
348#95—222no—
349#95—222no—
350#95—222no—
351#95—221no—
352C2×C11—82no—
353C2×C11#242811yescharacteristic
354C2×C11C2×#46411yescharacteristic
355C2×C11#304411yescharacteristic
356C2×C11#327611yescharacteristic
357C2×C11#328311yescharacteristic
358C2×C11#339311yescharacteristic
359C2×C11#339811yescharacteristic
360C24—21no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—222no—
367C2×Q8—222no—
368C2×Q8—222no—
369C2×Q8—222no—
370C2×Q8—222no—
371C2×Q8—222no—
372C2×Q8C2×C22⋊D1114yes—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4D4×D1112yes—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—112no—
385C22×C4—112no—
386C22×C4—221no—
387C22×C4—221no—
388C22×C4—222no—
389C22×C4D4×D1111yescharacteristic
390C22×C4D4×D1111yescharacteristic
391C22×C4C23×D1111yescharacteristic
392Q16—448no—
393Q16—448no—
394SD16—48no—
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—24no—
405C4⋊C4—24no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—112no—
409C4⋊C4—222no—
410C4⋊C4—222no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C4⋊C4—221no—
414C4⋊C4—444no—
415C4⋊C4—442no—
416C4⋊C4—442no—
417C22⋊C4—42no—
418C22⋊C4—444no—
419C22⋊C4—444no—
420C42—222no—
421C42—222no—
422C42—444no—
423C42—442no—
424C42#434112yes—
425C42C2×C22⋊D1112yes—
426C11#2536511yescharacteristic, complemented, Sylow
427C23—22no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23C2×D4×D1111yescharacteristic
435Q8—24no—
436Q8—24no—
437Q8—42no—
438Q8—42no—
439Q8—442no—
440Q8—442no—
441Q8—442no—
442Q8—442no—
443D4—22no—
444D4—22no—
445D4—41no—
446D4—41no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—24no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—84no—
456C2×C4—222no—
457C2×C4—222no—
458C2×C4—222no—
459C2×C4—222no—
460C2×C4—222no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—442no—
468C2×C4—441no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4#6696812yes—
472C2×C4#6696912yes—
473C2×C4#6699212yes—
474C2×C4#6699212yes—
475C2×C4C2×D4×D1111yescharacteristic
476C2×C4C2×#434111yescharacteristic
477C2×C4#6703711yescharacteristic
478C2×C4#41×D1111yescharacteristic
479C2×C4#6704211yescharacteristic
480C2×C4C22×C22⋊D1111yescharacteristic
481C8—42no—
482C8—222no—
483C8—222no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22—81no—
491C22#1062313011yescharacteristic
492C22#1062314011yescharacteristic
493C22C2×#6696811yescharacteristic
494C22C2×#6696911yescharacteristic
495C22#1062331011yescharacteristic
496C22#1062331011yescharacteristic
497C22C2×#6699211yescharacteristic
498C4—22no—
499C4—44no—
500C4—81no—
501C4—442no—
502C4—442no—
503C4—442no—
504C4—881no—
505C4—882no—
506C4#1062277914yescomplemented
507C4#1062312711yescharacteristic
508C4#1062315011yescharacteristic
509C4D4×C22⋊D1111yescharacteristic
510C4#1062336011yescharacteristic
511C2—82no—
512C2#1307220611yescharacteristic
513C2C2×#1062277911yescharacteristic
514C2#1307814811yescharacteristic
515C2#1308026511yescharacteristic
516C2#1308033311yescharacteristic
517C2#1308160311yescharacteristic
518C2#1308165111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#461C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#461D11
hypocenterC11#25365
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#10622705C2semidirect
4. #13071676C2semidirect
5. #13069937C2semidirect
7. #13069538C2semidirect
8. #13069332C2semidirect
9. #13068955C2semidirect
285. C4×C11#464semidirect
426. C11#25365semidirect
506. C4#10622779semidirect

Maximal subgroups

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

subgroupindex
C2×#106227052
C2×#106227792
#130736082
#130716762
#130699372
#130697082
#130695382
#130693322
#130689552
C4×#668962
C2×C11×#4612
#2536511