Finite Group Databasebeta

← #14726488

Subgroups — #14726488

Order 2816.

998 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078536C212yesmaximal, complemented
2C2×#10622599C211yesmaximal, characteristic, complemented
3#13067658C212yesmaximal, complemented
4#13067653C212yesmaximal, complemented
5#13067647C214yesmaximal, complemented
6#13067120C212yesmaximal, complemented
7#13066946C211yesmaximal, characteristic, complemented
8C11×#3492C211yesmaximal, characteristic
9C11×#554—22no—
10C11×#553—22no—
11C11×#552—22no—
12C11×#547—22no—
13C11×#544C2211yescharacteristic
14C11×#539—21no—
15C11×#539C2212yes—
16C11×#537C2211yescharacteristic
17C11×#525—21no—
18C11×#525—21no—
19C11×#525C2212yes—
20C11×#520—21no—
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23#10622845—22no—
24C2×C11⋊#95—21no—
25C2×C11⋊#95—21no—
26C2×C11⋊#95C2211yescharacteristic
27#10622820C2212yes—
28#10622657C2214yes—
29#10622656—22no—
30#10622647C2214yes—
31#10622646—22no—
32#10622608—22no—
33#10622599—21no—
34#10622599—21no—
35#10622599C2212yes—
36#10622599C2212yes—
37#10622176C2214yes—
38#10622175C2214yes—
39#10622166C2212yes—
40#10622166C2212yes—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41D412yes—
44C23×C4×C11D411yescharacteristic
45C23×C4×C11D411yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×Dic11—21no—
48C23×Dic11—21no—
49C11×C4⋊Q8—22no—
50C11×#126—22no—
51C11×#126—22no—
52C11×#125—22no—
53C11×#125—22no—
54C11×#125—22no—
55C11×#123—22no—
56C11×#123—22no—
57C11×#123—22no—
58C11×#123—22no—
59C11×#123—22no—
60C11×C22⋊Q8—21no—
61C11×C22⋊Q8—21no—
62C11×C22⋊Q8—21no—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8D412yes—
68C11×C22⋊Q8C2312yes—
69C11×#121—21no—
70C11×#121—21no—
71C11×#121—21no—
72C11×#121—22no—
73C11×#121—21no—
74C11×#121D412yes—
75C11×#121C2312yes—
76C11×#120—22no—
77C4×Q8×C11—22no—
78C4×D4×C11—22no—
79C4×D4×C11—22no—
80C4×D4×C11—22no—
81C4×D4×C11—22no—
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C11×#117—22no—
86C11×#117—21no—
87C11×#117—21no—
88C11×#117D412yes—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4—22no—
91C2×C11×C4⋊C4—22no—
92C2×C11×C4⋊C4D411yescharacteristic
93C2×C11×C4⋊C4D411yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C4⋊Dic11—22no—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11C2312yes—
100C2×#4318—22no—
101#66899—24no—
102#66896—24no—
103C11⋊#95—22no—
104C11⋊#95—22no—
105C11⋊#95—22no—
106C11⋊#95—22no—
107C11⋊#95—21no—
108C11⋊#95C2312yes—
109C22⋊(C11⋊C8)—22no—
110C22⋊(C11⋊C8)C2314yes—
111#66872—24no—
112#66871—24no—
113#18172—111nomaximal, Sylow
114C24×C11C2×D411yescharacteristic
115C11×#41—42no—
116C11×#41—44no—
117C11×#41—42no—
118C11×#41—82no—
119C2×Q8×C11—21no—
120C2×Q8×C11—21no—
121C2×Q8×C11C2×D412yes—
122C2×D4×C11—21no—
123C2×D4×C11—22no—
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—21no—
127C2×D4×C11C2×D412yes—
128C22×C4×C11—22no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—41no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—42no—
150C22×Dic11—42no—
151C22×Dic11—44no—
152C22×Dic11—42no—
153C22×Dic11—41no—
154C22×Dic11—41no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4C2×D412yes—
170C11×C4⋊C4C2×D412yes—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—22no—
180C42×C11—22no—
181C42×C11—22no—
182C42×C11—22no—
183C4⋊Dic11—24no—
184C4⋊Dic11—42no—
185#4318—44no—
186C2×C11⋊C8—24no—
187#3492D1111yescharacteristic
188#3092—112no—
189C2×#400—111no—
190#1617—112no—
191#1616—112no—
192#1615—114no—
193#1504—112no—
194#1463—111no—
195C23×C11—21no—
196C23×C11—21no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11#12011yescharacteristic
201C23×C11#12011yescharacteristic
202C23×C11C22×D411yescharacteristic
203Q8×C11—42no—
204Q8×C11—42no—
205Q8×C11—81no—
206D4×C11—42no—
207D4×C11—42no—
208D4×C11—42no—
209D4×C11—42no—
210D4×C11—44no—
211D4×C11—44no—
212D4×C11—81no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—24no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—21no—
219C2×C4×C11—22no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—44no—
230C2×C4×C11—42no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—82no—
234C2×C4×C11—81no—
235C2×C4×C11—82no—
236C2×C4×C11#12012yes—
237C2×C4×C11#13712yes—
238C2×C4×C11C22×D412yes—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—44no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—84no—
245C2×Dic11—82no—
246C2×Dic11—82no—
247C11⋊C8—44no—
248#554—22no—
249#553—22no—
250#552—22no—
251#547—22no—
252#544C2×D1111yescharacteristic
253#539—21no—
254#539C2×D1112yes—
255#537C2×D1111yescharacteristic
256#525—21no—
257#525—21no—
258#525C2×D1112yes—
259#520—21no—
260C22×C4⋊C4—111no—
261C22×C4⋊C4C2×D1111yescharacteristic
262#484—114no—
263#483—222no—
264#481—114no—
265#480—222no—
266#428—222no—
267#417—222no—
268#407—112no—
269#400—112no—
270#400—112no—
271#400—221no—
272#400—221no—
273C2×#95—111no—
274C2×#95—221no—
275C2×#95—221no—
276#328—114no—
277#327—114no—
278#324—112no—
279#324—112no—
280C22×C11—24no—
281C22×C11—24no—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—21no—
285C22×C11—21no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11#45412yes—
292C22×C11#45812yes—
293C22×C11C2×#12011yescharacteristic
294C22×C11C2×#13711yescharacteristic
295C22×C11#57511yescharacteristic
296C4×C11—22no—
297C4×C11—22no—
298C4×C11—22no—
299C4×C11—41no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11—41no—
303C4×C11—41no—
304C4×C11—42no—
305Dic11—82no—
306Dic11—82no—
307C2×#41—21no—
308C2×#41—21no—
309C2×#41C22⋊D1112yes—
310C23×C4—221no—
311C23×C4—221no—
312C23×C4C22⋊D1111yescharacteristic
313C23×C4C22⋊D1111yescharacteristic
314C23×C4C22×D1111yescharacteristic
315C2×M16—222no—
316C4⋊Q8—22no—
317#126—22no—
318#126—22no—
319#125—22no—
320#125—22no—
321#125—22no—
322#123—22no—
323#123—22no—
324#123—22no—
325#123—22no—
326#123—22no—
327C22⋊Q8—21no—
328C22⋊Q8—21no—
329C22⋊Q8—21no—
330C22⋊Q8—22no—
331C22⋊Q8—22no—
332C22⋊Q8—21no—
333C22⋊Q8—22no—
334C22⋊Q8C22⋊D1112yes—
335C22⋊Q8C22×D1112yes—
336#121—21no—
337#121—21no—
338#121—21no—
339#121—22no—
340#121—21no—
341#121C22⋊D1112yes—
342#121C22×D1112yes—
343#120—22no—
344C4×Q8—22no—
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—22no—
352#117—22no—
353#117—21no—
354#117—21no—
355#117C22⋊D1112yes—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—112no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4—222no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4C22⋊D1111yescharacteristic
364C2×C4⋊C4C22⋊D1111yescharacteristic
365C2×C4⋊C4C22×D1111yescharacteristic
366C2×C4⋊C4C22×D1111yescharacteristic
367#107—224no—
368#106—224no—
369#103—224no—
370#102—224no—
371C22⋊C8—114no—
372C22⋊C8—222no—
373#95—112no—
374#95—221no—
375#95—222no—
376#95—222no—
377#95—222no—
378#95—222no—
379C2×C11—21no—
380C2×C11—21no—
381C2×C11—22no—
382C2×C11—22no—
383C2×C11—82no—
384C2×C11#300711yescharacteristic
385C2×C11C2×#45411yescharacteristic
386C2×C11C2×#45811yescharacteristic
387C24C2×C22⋊D1111yescharacteristic
388#41—42no—
389#41—44no—
390#41—42no—
391#41—82no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8C2×C22⋊D1112yes—
395C2×D4—21no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—21no—
400C2×D4C2×C22⋊D1112yes—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—42no—
410C22×C4—41no—
411C22×C4—42no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4—442no—
415C22×C4—442no—
416C22×C4—444no—
417C22×C4—442no—
418C22×C4—441no—
419C22×C4—441no—
420C22×C4C2×C22⋊D1111yescharacteristic
421C22×C4C2×C22⋊D1111yescharacteristic
422C22×C4C2×C22⋊D1112yes—
423C22×C4C2×C22⋊D1111yescharacteristic
424C22×C4C2×C22⋊D1111yescharacteristic
425C22×C4C2×C22⋊D1111yescharacteristic
426C22×C4C2×C22⋊D1112yes—
427C22×C4C23×D1111yescharacteristic
428M16—444no—
429C2×C8—224no—
430C4⋊C4—21no—
431C4⋊C4—22no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—224no—
445C4⋊C4—442no—
446C4⋊C4C2×C22⋊D1112yes—
447C4⋊C4C2×C22⋊D1112yes—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C42—22no—
458C42—22no—
459C42—22no—
460C11#1817211yescharacteristic, complemented, Sylow
461C23—21no—
462C23—21no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23#6700611yescharacteristic
467C23#6700611yescharacteristic
468C23C22×C22⋊D1111yescharacteristic
469Q8—42no—
470Q8—42no—
471Q8—81no—
472D4—42no—
473D4—42no—
474D4—42no—
475D4—42no—
476D4—44no—
477D4—44no—
478D4—81no—
479C2×C4—21no—
480C2×C4—24no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—21no—
487C2×C4—22no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—44no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—82no—
500C2×C4—81no—
501C2×C4—82no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—444no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4—884no—
508C2×C4—882no—
509C2×C4—882no—
510C2×C4#6700412yes—
511C2×C4#6700612yes—
512C2×C4C22×C22⋊D1112yes—
513C8—444no—
514C22—24no—
515C22—24no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22#1062285612yes—
526C22#1062285812yes—
527C22#1062335311yescharacteristic
528C22C2×#6700411yescharacteristic
529C22C2×#6700611yescharacteristic
530C4—22no—
531C4—22no—
532C4—22no—
533C4—41no—
534C4—42no—
535C4—42no—
536C4—41no—
537C4—41no—
538C4—42no—
539C4—882no—
540C4—882no—
541C2—21no—
542C2—21no—
543C2—22no—
544C2—22no—
545C2—82no—
546C2#1307787611yescharacteristic
547C2C2×#1062285811yescharacteristic
548C2C2×#1062285611yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3492C2
socleC22×C11C2×#120
hypercenter#3492D11
hypocenterC11#18172
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3492

Complements

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

NH ≅ G/Ntype
1. #13078536C2semidirect
2. C2×#10622599C2semidirect
3. #13067658C2semidirect
4. #13067653C2semidirect
5. #13067647C2semidirect
6. #13067120C2semidirect
7. #13066946C2semidirect
460. C11#18172semidirect

Maximal subgroups

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

subgroupindex
#130785362
C2×#106225992
#130676582
#130676532
#130676472
#130671202
#130669462
C11×#34922
#1817211