Finite Group Databasebeta

← #14759136

Subgroups — #14759136

Order 2816.

1162 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
1C2×#10623176C211yesmaximal, characteristic
2#13071218C211yesmaximal, characteristic, complemented
3#13070971C211yesmaximal, characteristic, complemented
4#13069602C211yesmaximal, characteristic, complemented
5#13069452C211yesmaximal, characteristic
6#13069451C211yesmaximal, characteristic
7#13069073C214yesmaximal, complemented
8#13068403C214yesmaximal, complemented
9C11×#1996C211yesmaximal, characteristic, complemented
10C2×C11×C22⋊Q8C2211yescharacteristic
11C2×#66999C412yescomplemented
12C2×#66983C2211yescharacteristic
13C22×Dic11⋊C4C2211yescharacteristic
14#10623176—22no—
15#10623176—22no—
16#10623176—22no—
17#10623176—22no—
18C2×#66951C412yescomplemented
19C2×#66947C412yescomplemented
20C2×#66943C412yescomplemented
21C2×#66939C2212yes—
22C2×(C22⋊D11)⋊C4C2212yes—
23C2×#66930C2212yes—
24C11×#380C2211yescharacteristic
25C4×C11×C22⋊C4C2211yescharacteristic
26#10622825C2211yescharacteristic
27C4×C22⋊Dic11C2211yescharacteristic
28#10622591—22no—
29C2×#66870C2214yes—
30C2×#66870C2214yes—
31#10622556C2212yes—
32C22⋊C4×Dic11C2212yes—
33C22⋊C4×Dic11C2212yes—
34C4×Dic11⋊C4—22no—
35#10622268—22no—
36#10622262—22no—
37C11×#342C2214yes—
38#10622164C2214yes—
39C22×Q8×C11C2×C411yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C22×C22⋊D11C2312yes—
42C23×Dic11C2311yescharacteristic
43C23×Dic11C2311yescharacteristic
44C22×D44C2×C411yescharacteristic
45C22×C4×D11C2×C412yes—
46C11×C22⋊Q8—21no—
47C11×C22⋊Q8—21no—
48C11×C22⋊Q8—21no—
49C11×C22⋊Q8—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4C2×C412yes—
52C2×C11×C4⋊C4C2×C411yescharacteristic
53C2×C11×C22⋊C4C2312yes—
54C2×C11×C22⋊C4C2312yes—
55C2×C11×C22⋊C4C2312yes—
56C2×C42×C11—21no—
57C2×C22⋊Dic11C2312yes—
58C2×C22⋊Dic11C2312yes—
59#66999—24no—
60#66999—24no—
61#66983—21no—
62#66983—21no—
63#66983—21no—
64#66983—21no—
65C2×(C2×D11)⋊C4C2×C412yes—
66C2×(C2×D11)⋊C4C2×C412yes—
67C2×(C2×D11)⋊C4C2×C412yes—
68C2×(C2×D11)⋊C4C2×C412yes—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11C2×C412yes—
71C2×C4⋊Dic11C2×C412yes—
72C2×C4⋊Dic11C2×C411yescharacteristic
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4C2×C412yes—
75C2×Dic11⋊C4C2×C412yes—
76C2×Dic11⋊C4C2×C412yes—
77C2×Dic11⋊C4D412yes—
78C2×Dic11⋊C4D412yes—
79C2×Dic11⋊C4D412yes—
80C2×Dic11⋊C4D412yes—
81C2×C4×Dic11—22no—
82C2×C4×Dic11—21no—
83C2×C4×Dic11—22no—
84C2×C4×Dic11—22no—
85C2×C4×Dic11C2×C412yes—
86#66951—24no—
87#66951—24no—
88#66947—24no—
89#66947—24no—
90#66943—24no—
91#66943—24no—
92#66939—24no—
93#66939—24no—
94(C22⋊D11)⋊C4—24no—
95(C22⋊D11)⋊C4—24no—
96#66930—24no—
97#66930—24no—
98C11×#95—21no—
99C11×#95—21no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—22no—
103C11⋊#95—22no—
104C11⋊#95—24no—
105#66870—28no—
106#66870—28no—
107#21423—111nomaximal, Sylow
108C24×C11C2411yescharacteristic
109C23×D11C22×C412yes—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11—81no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—81no—
116C22×C4×C11C22×C412yes—
117C22×C4×C11C22×C412yes—
118C22×C4×C11C22×C411yescharacteristic
119C22×C4×C11C22×C411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C2×C22⋊D11—22no—
125C2×C22⋊D11—22no—
126C2×C22⋊D11—24no—
127C2×C22⋊D11—24no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—81no—
133C22×Dic11C22×C412yes—
134C22×Dic11C22×C412yes—
135C22×Dic11C22×C412yes—
136C22×Dic11C2×D412yes—
137C22×Dic11C2×D412yes—
138C22×Dic11C2×D412yes—
139C22×Dic11C2×D412yes—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—81no—
143C2×C4×D11—24no—
144C2×C4×D11—82no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—81no—
150C11×C22⋊C4—22no—
151C11×C22⋊C4—22no—
152C11×C22⋊C4—22no—
153C11×C22⋊C4—24no—
154C11×C22⋊C4#4114yes—
155C42×C11—81no—
156C22⋊Dic11—22no—
157C22⋊Dic11—24no—
158C22⋊Dic11#4114yes—
159(C2×D11)⋊C4—24no—
160(C2×D11)⋊C4—24no—
161(C2×D11)⋊C4—24no—
162(C2×D11)⋊C4—22no—
163(C2×D11)⋊C4—22no—
164C4⋊Dic11—24no—
165C4⋊Dic11—24no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—81no—
169Dic11⋊C4—28no—
170Dic11⋊C4—24no—
171Dic11⋊C4C22⋊C414yes—
172Dic11⋊C4C22⋊C414yes—
173Dic11⋊C4C22⋊C414yes—
174Dic11⋊C4C22⋊C414yes—
175C4×Dic11—28no—
176C4×Dic11—24no—
177C4×Dic11—81no—
178C4×Dic11—82no—
179C4×Dic11—82no—
180C2×#539—111no—
181#2313—111no—
182#2274—111no—
183#1996—111no—
184#1996D1111yescharacteristic, complemented
185#1964—111no—
186#1964—111no—
187#1899—114no—
188C4×#99—114no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11C23×C411yescharacteristic
192C23×C11C22×D411yescharacteristic
193C23×C11C22×D411yescharacteristic
194C23×C11C2×#4112yes—
195C23×C11C2×#4112yes—
196C22×D11—22no—
197C22×D11—24no—
198C22×D11—42no—
199C22×D11—42no—
200Q8×C11—81no—
201Q8×C11—81no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—24no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11C2×C22⋊C411yescharacteristic
219C2×C4×C11C2×C22⋊C411yescharacteristic
220C2×C4×C11C2×C22⋊C411yescharacteristic
221C2×C4×C11C2×C22⋊C411yescharacteristic
222C22⋊D11—44no—
223C22⋊D11—42no—
224C22⋊D11—42no—
225C2×Dic11—24no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11C2×C22⋊C414yes—
242C2×Dic11C2×C22⋊C414yes—
243D44—81no—
244D44—81no—
245C4×D11—84no—
246#539—222no—
247#539—222no—
248#539—222no—
249#539—222no—
250C2×#126—112no—
251C2×#125—112no—
252C2×#123—112no—
253C2×#123—112no—
254C2×C22⋊Q8—112no—
255C2×C22⋊Q8C2×D1111yescharacteristic
256C2×#121—111no—
257C2×C4×D4—112no—
258C2×#117—112no—
259C22×C4⋊C4—111no—
260C2×#99—114no—
261C2×#99—114no—
262#387—222no—
263#387—222no—
264#381—112no—
265#380—111no—
266#380C2×D1111yescharacteristic
267C4×C4⋊C4—222no—
268C4×C4⋊C4—222no—
269C4×C22⋊C4—111no—
270C4×C22⋊C4—112no—
271C4×C22⋊C4—112no—
272C4×C22⋊C4C2×D1111yescharacteristic
273#342—114no—
274#342C2×D1114yes—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11—21no—
279C22×C11—21no—
280C22×C11—21no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11C22×C22⋊C411yescharacteristic
284C22×C11C4×#4112yes—
285C22×C11#52512yes—
286C22×C11#53211yescharacteristic
287C22×C11#53211yescharacteristic
288C2×D11—42no—
289C2×D11—42no—
290C2×D11—42no—
291C2×D11—84no—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—21no—
295C4×C11—21no—
296C4×C11—44no—
297C4×C11—42no—
298C4×C11—42no—
299C4×C11—82no—
300Dic11—24no—
301Dic11—24no—
302Dic11—44no—
303Dic11—42no—
304Dic11—82no—
305C22×Q8C4×D1111yescharacteristic
306C22×D4—112no—
307C22×D4—111no—
308C23×C4—111no—
309C23×C4—111no—
310C23×C4—112no—
311C23×C4C22×D1111yescharacteristic
312#126—224no—
313#126—224no—
314#125—224no—
315#125—224no—
316#123—224no—
317#123—224no—
318#123—224no—
319#123—224no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323C22⋊Q8—21no—
324C22⋊Q8—224no—
325C22⋊Q8—224no—
326#121—221no—
327#121—221no—
328#121—221no—
329#121—221no—
330C4×D4—224no—
331C4×D4—224no—
332#117—224no—
333#117—224no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—112no—
336C2×C4⋊C4—112no—
337C2×C4⋊C4—112no—
338C2×C4⋊C4—112no—
339C2×C4⋊C4—112no—
340C2×C4⋊C4—112no—
341C2×C4⋊C4—112no—
342C2×C4⋊C4—111no—
343C2×C4⋊C4—112no—
344C2×C4⋊C4—112no—
345C2×C4⋊C4—222no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4C4×D1112yes—
348C2×C4⋊C4C4×D1111yescharacteristic
349C2×C22⋊C4—112no—
350C2×C22⋊C4—112no—
351C2×C22⋊C4—112no—
352C2×C22⋊C4—112no—
353C2×C22⋊C4—112no—
354C2×C22⋊C4—112no—
355C2×C22⋊C4C22×D1112yes—
356C2×C22⋊C4C22×D1112yes—
357C2×C22⋊C4C22×D1112yes—
358C2×C42—21no—
359C2×C42—112no—
360C2×C42—222no—
361C2×C42—222no—
362C2×C42—222no—
363C2×C42—221no—
364#99—228no—
365#99—228no—
366#95—21no—
367#95—21no—
368#95—222no—
369#95—222no—
370#95—224no—
371#95—221no—
372#95—221no—
373C2×C11—22no—
374C2×C11—21no—
375C2×C11—21no—
376C2×C11—22no—
377C2×C11#229711yescharacteristic
378C2×C11#288311yescharacteristic
379C2×C11#288411yescharacteristic
380D11—82no—
381C24—112no—
382C24C23×D1111yescharacteristic
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—81no—
386C2×D4—222no—
387C2×D4—222no—
388C2×D4—224no—
389C2×D4—224no—
390C2×D4—221no—
391C2×D4—221no—
392C2×D4—881no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—81no—
396C22×C4—112no—
397C22×C4—112no—
398C22×C4—112no—
399C22×C4—112no—
400C22×C4—112no—
401C22×C4—112no—
402C22×C4—112no—
403C22×C4—224no—
404C22×C4—222no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—882no—
409C22×C4—881no—
410C22×C4C2×C4×D1112yes—
411C22×C4C2×C4×D1112yes—
412C22×C4C2×C4×D1111yescharacteristic
413C22×C4C2×C4×D1111yescharacteristic
414C22×C4D4×D1111yescharacteristic
415C22×C4D4×D1111yescharacteristic
416C22×C4D4×D1111yescharacteristic
417C22×C4D4×D1111yescharacteristic
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—81no—
423C4⋊C4—114no—
424C4⋊C4—114no—
425C4⋊C4—114no—
426C4⋊C4—114no—
427C4⋊C4—224no—
428C4⋊C4—224no—
429C4⋊C4—224no—
430C4⋊C4—228no—
431C4⋊C4—221no—
432C4⋊C4—221no—
433C4⋊C4—881no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—24no—
438C22⋊C4—114no—
439C22⋊C4—224no—
440C22⋊C4—224no—
441C22⋊C4—224no—
442C22⋊C4—222no—
443C22⋊C4—222no—
444C22⋊C4—222no—
445C22⋊C4—224no—
446C22⋊C4#434314yes—
447C42—81no—
448C42—224no—
449C42—228no—
450C42—881no—
451C42—882no—
452C42—882no—
453C11#2142311yescharacteristic, complemented, Sylow
454C23—41no—
455C23—41no—
456C23—222no—
457C23—224no—
458C23—442no—
459C23—442no—
460C23C22×C4×D1111yescharacteristic
461C23C2×D4×D1111yescharacteristic
462C23C2×D4×D1111yescharacteristic
463C23C2×#434312yes—
464C23#41×D1112yes—
465Q8—81no—
466Q8—81no—
467D4—442no—
468D4—444no—
469D4—442no—
470D4—881no—
471D4—881no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—114no—
489C2×C4—114no—
490C2×C4—222no—
491C2×C4—224no—
492C2×C4—222no—
493C2×C4—222no—
494C2×C4—222no—
495C2×C4—222no—
496C2×C4—224no—
497C2×C4—224no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—884no—
507C2×C4C22⋊C4×D1111yescharacteristic
508C2×C4C22⋊C4×D1111yescharacteristic
509C2×C4C22⋊C4×D1111yescharacteristic
510C2×C4C22⋊C4×D1111yescharacteristic
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—42no—
518C22—42no—
519C22—442no—
520C22—442no—
521C22—442no—
522C22—884no—
523C22C2×C22⋊C4×D1111yescharacteristic
524C22C4×#434312yes—
525C22#1062315812yes—
526C22#1062319911yescharacteristic
527C22#1062325611yescharacteristic
528C4—21no—
529C4—21no—
530C4—21no—
531C4—21no—
532C4—44no—
533C4—42no—
534C4—42no—
535C4—82no—
536C4—224no—
537C4—224no—
538C4—444no—
539C4—442no—
540C4—882no—
541C2—22no—
542C2—21no—
543C2—21no—
544C2—22no—
545C2—882no—
546C2#1307110511yescharacteristic
547C2#1307707411yescharacteristic
548C2#1307707811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC11×#1996C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#66983C22
cosocleC24×C11C24
hypercenter#1996D11
hypocenterC11#21423
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1996

Complements

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

NH ≅ G/Ntype
2. #13071218C2semidirect
3. #13070971C2semidirect
4. #13069602C2semidirect
7. #13069073C2semidirect
8. #13068403C2semidirect
9. C11×#1996C2semidirect
11. C2×#66999C4semidirect
18. C2×#66951C4semidirect
19. C2×#66947C4semidirect
20. C2×#66943C4semidirect
184. #1996D11semidirect
453. C11#21423semidirect

Maximal subgroups

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

subgroupindex
C2×#106231762
#130712182
#130709712
#130696022
#130694522
#130694512
#130690732
#130684032
C11×#19962
#2142311