Finite Group Databasebeta

← #14731505

Subgroups — #14731505

Order 2816.

912 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079928C211yesmaximal, characteristic
2#13079176C211yesmaximal, characteristic
3#13078088C211yesmaximal, characteristic
4#13067893C212yesmaximal, complemented
5#13067837C212yesmaximal, complemented
6#13067712C212yesmaximal, complemented
7#13067694C212yesmaximal, complemented
8#13067306C211yesmaximal, characteristic, complemented
9#13067071C211yesmaximal, characteristic, complemented
10C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
11C11×#3502C211yesmaximal, characteristic, complemented
12Q82×C11—21no—
13Q82×C11C2212yes—
14C11×#557—21no—
15C11×#557—22no—
16C11×#557—22no—
17C11×#557C2212yes—
18C11×#544—22no—
19C11×#544—21no—
20C11×#533—22no—
21C11×#533C2211yescharacteristic
22C11×#533C2211yescharacteristic
23C11×#519—21no—
24C2×C4×Q8×C11C2211yescharacteristic
25C2×#66995—21no—
26#10623008C2211yescharacteristic
27#10622701C2211yescharacteristic
28#10622698C2211yescharacteristic
29#10622697—21no—
30#10622696—21no—
31#10622694C2211yescharacteristic
32#10622692C2211yescharacteristic
33#10622661—22no—
34#10622661—22no—
35#10622644C2212yes—
36#10622641—22no—
37#10622640C2212yes—
38#10622640C2212yes—
39C4×#4325—22no—
40#10622633C2212yes—
41#10622579—21no—
42#10622537C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622185C2212yes—
46#10622184C2212yes—
47Q8⋊(C11⋊C8)C2212yes—
48Q8⋊(C11⋊C8)C2212yes—
49Q8⋊(C11⋊C8)C2212yes—
50Q8⋊(C11⋊C8)C2212yes—
51C22×Q8×C11D411yescharacteristic
52C2×#4339—21no—
53C11×C4⋊Q8—24no—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8—22no—
56C11×C4⋊Q8—24no—
57C11×C4⋊Q8—22no—
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8D411yescharacteristic
60C11×C4⋊Q8D411yescharacteristic
61C11×C4⋊Q8C2311yescharacteristic
62C11×C4⋊Q8C2311yescharacteristic
63C11×#125—24no—
64C11×#125—24no—
65C11×#125—22no—
66C11×#125—24no—
67C11×#125—22no—
68C11×#125—21no—
69C11×#125—21no—
70C11×C22⋊Q8—24no—
71C11×C22⋊Q8—21no—
72C11×C22⋊Q8—21no—
73C11×C22⋊Q8D412yes—
74C11×C22⋊Q8D412yes—
75C4×Q8×C11—22no—
76C4×Q8×C11—22no—
77C4×Q8×C11—24no—
78C4×Q8×C11—22no—
79C4×Q8×C11—22no—
80C4×Q8×C11—22no—
81C4×Q8×C11—22no—
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11—21no—
85C4×Q8×C11—21no—
86C4×Q8×C11D412yes—
87C4×Q8×C11D412yes—
88C4×Q8×C11C2312yes—
89C4×Q8×C11C2312yes—
90C11×#117—24no—
91C11×#117—21no—
92C11×#117—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4D411yescharacteristic
95C2×C42×C11—21no—
96C2×C42×C11C2311yescharacteristic
97C2×#4326—22no—
98#66995—44no—
99C2×#4325—22no—
100C2×#4325—22no—
101C2×#4325—22no—
102#66983—21no—
103#66983—21no—
104C2×#4318—21no—
105C22×C11⋊C8—21no—
106C22×C11⋊C8—21no—
107#66928—21no—
108#66927C2311yescharacteristic
109C4×D44—21no—
110C4×D44—21no—
111#66922C2311yescharacteristic
112#66899—22no—
113#66899—22no—
114#66874—22no—
115#66873—22no—
116#66873—22no—
117#66873—22no—
118#66872—22no—
119#66872—22no—
120C4⋊(C11⋊C8)—21no—
121C4⋊(C11⋊C8)—21no—
122C4⋊(C11⋊C8)C2312yes—
123C4⋊(C11⋊C8)C2312yes—
124C4×C11⋊C8—21no—
125C4×C11⋊C8C2311yescharacteristic
126C4×C11⋊C8C2311yescharacteristic
127#18676—111nomaximal, Sylow
128C2×Q8×C11—24no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—22no—
132C2×Q8×C11—21no—
133C2×Q8×C11SD1614yescomplemented
134C2×Q8×C11C2×D412yes—
135C2×Q8×C11C2×D412yes—
136C2×Q8×C11C2×D412yes—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C2×C22⋊D11—41no—
143#4339—42no—
144#4339—42no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×C4×D11—41no—
149C2×Dic22—21no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4C2×D412yes—
169C11×C4⋊C4C2×D412yes—
170C11×C4⋊C4C2×D412yes—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C42×C11—24no—
174C42×C11—24no—
175C42×C11—22no—
176C42×C11—22no—
177C42×C11—22no—
178C42×C11—22no—
179C42×C11C2×D411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11C2411yescharacteristic
183#4326—44no—
184#4325—44no—
185#4325—44no—
186#4325—82no—
187(C2×D11)⋊C4—41no—
188(C2×D11)⋊C4—41no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191#4318—42no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—42no—
197C2×C11⋊C8—81no—
198#3502D1111yescharacteristic, complemented
199#3246—111no—
200#3167—111no—
201#3037—111no—
202#1653—112no—
203#1645—112no—
204#1626—112no—
205#1623—112no—
206#1550—111no—
207#1493—111no—
208C2×Q8⋊C8—111no—
209C23×C11#12011yescharacteristic
210C22×D11—41no—
211Q8×C11—22no—
212Q8×C11—24no—
213Q8×C11—22no—
214Q8×C11—22no—
215Q8×C11—42no—
216Q8×C11—41no—
217Q8×C11—41no—
218Q8×C11—81no—
219Q8×C11—84no—
220Q8×C11C2×SD1614yes—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—41no—
231C2×C4×C11—81no—
232C2×C4×C11#12011yescharacteristic
233C2×C4×C11#12011yescharacteristic
234C2×C4×C11#12011yescharacteristic
235C2×C4×C11C2×SD1612yes—
236C2×C4×C11#13712yes—
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C22⋊D11—82no—
241C2×Dic11—41no—
242D44—42no—
243D44—41no—
244D44—41no—
245D44—41no—
246D44—41no—
247C4×D11—82no—
248Dic22—41no—
249Dic22—41no—
250C11⋊C8—22no—
251C11⋊C8—41no—
252C11⋊C8—42no—
253C11⋊C8—42no—
254C2×#137—221no—
255Q82—21no—
256Q82C2×D1112yes—
257#557—21no—
258#557—22no—
259#557—22no—
260#557C2×D1112yes—
261#544—22no—
262#544—21no—
263#533—22no—
264#533C2×D1111yescharacteristic
265#533C2×D1111yescharacteristic
266#532—111no—
267#519—21no—
268C2×C4×Q8C2×D1111yescharacteristic
269#498—111no—
270#492—111no—
271#487—111no—
272#486—111no—
273#476—221no—
274#475—112no—
275#465—222no—
276#465—222no—
277#464—222no—
278#462—112no—
279#461—221no—
280#460—112no—
281#460—112no—
282C4×SD16—222no—
283#423—111no—
284C2×C4⋊C8—111no—
285#417—221no—
286C2×C4×C8—111no—
287#333—112no—
288#332—112no—
289Q8⋊C8—112no—
290Q8⋊C8—112no—
291Q8⋊C8—112no—
292Q8⋊C8—112no—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11#44812yes—
296C22×C11C2×#12011yescharacteristic
297C2×D11—81no—
298C2×D11—81no—
299C2×D11—81no—
300C4×C11—24no—
301C4×C11—21no—
302C4×C11—21no—
303C4×C11—21no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11—42no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11#44812yes—
310C4×C11C22×SD1611yescharacteristic
311C4×C11C2×#13711yescharacteristic
312C4×C11#57711yescharacteristic
313C4×C11#57811yescharacteristic
314Dic11—81no—
315C2×#41—221no—
316C22×Q8C22⋊D1111yescharacteristic
317#137—444no—
318C2×Q16—222no—
319C2×SD16—222no—
320C2×SD16—222no—
321C2×SD16—222no—
322C2×M16—221no—
323C22×C8—221no—
324C22×C8—221no—
325C4⋊Q8—24no—
326C4⋊Q8—22no—
327C4⋊Q8—22no—
328C4⋊Q8—24no—
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8—111no—
332C4⋊Q8C22⋊D1111yescharacteristic
333C4⋊Q8C22⋊D1111yescharacteristic
334C4⋊Q8C22×D1111yescharacteristic
335C4⋊Q8C22×D1111yescharacteristic
336#127—111no—
337#125—24no—
338#125—24no—
339#125—22no—
340#125—24no—
341#125—22no—
342#125—21no—
343#125—21no—
344#124—221no—
345C22⋊Q8—24no—
346C22⋊Q8—21no—
347C22⋊Q8—21no—
348C22⋊Q8C22⋊D1112yes—
349C22⋊Q8C22⋊D1112yes—
350#121—221no—
351#121—221no—
352C4×Q8—22no—
353C4×Q8—22no—
354C4×Q8—24no—
355C4×Q8—22no—
356C4×Q8—22no—
357C4×Q8—22no—
358C4×Q8—22no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8C22⋊D1112yes—
364C4×Q8C22⋊D1112yes—
365C4×Q8C22×D1112yes—
366C4×Q8C22×D1112yes—
367C4×D4—221no—
368C4×D4—221no—
369#117—24no—
370#117—21no—
371#117—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4C22⋊D1111yescharacteristic
374C2×C42—21no—
375C2×C42C22×D1111yescharacteristic
376#106—222no—
377#106—222no—
378C4⋊C8—112no—
379C4⋊C8—112no—
380C4⋊C8—221no—
381C4⋊C8—221no—
382#103—222no—
383#103—222no—
384#103—222no—
385#102—222no—
386#102—222no—
387#102—222no—
388C4×C8—111no—
389C4×C8—111no—
390C4×C8—221no—
391C2×C11—22no—
392C2×C11C2×#44811yescharacteristic
393C2×C11#301311yescharacteristic
394C2×C11#301811yescharacteristic
395D11—161no—
396#41—442no—
397#41—442no—
398C2×Q8—24no—
399C2×Q8—22no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—221no—
404C2×Q8#432514yescomplemented
405C2×Q8C2×C22⋊D1112yes—
406C2×Q8C2×C22⋊D1112yes—
407C2×Q8C2×C22⋊D1112yes—
408C2×D4—221no—
409C2×D4—221no—
410C2×D4—221no—
411C2×D4—441no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—441no—
415C22×C4C2×C22⋊D1111yescharacteristic
416C22×C4C2×C22⋊D1111yescharacteristic
417C22×C4C2×C22⋊D1111yescharacteristic
418Q16—444no—
419SD16—444no—
420SD16—444no—
421SD16—882no—
422M16—442no—
423C2×C8—221no—
424C2×C8—221no—
425C2×C8—222no—
426C2×C8—222no—
427C2×C8—442no—
428C2×C8—881no—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—24no—
433C4⋊C4—24no—
434C4⋊C4—22no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—221no—
448C4⋊C4—221no—
449C4⋊C4C2×C22⋊D1112yes—
450C4⋊C4C2×C22⋊D1112yes—
451C4⋊C4C2×C22⋊D1112yes—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—441no—
455C22⋊C4—441no—
456C42—24no—
457C42—24no—
458C42—22no—
459C42—22no—
460C42—22no—
461C42—22no—
462C42C2×C22⋊D1111yescharacteristic
463C42C2×C22⋊D1111yescharacteristic
464C42C2×C22⋊D1111yescharacteristic
465C42C23×D1111yescharacteristic
466C11#1867611yescharacteristic, complemented, Sylow
467C23—441no—
468C23#6700611yescharacteristic
469Q8—22no—
470Q8—24no—
471Q8—22no—
472Q8—22no—
473Q8—42no—
474Q8—41no—
475Q8—41no—
476Q8—81no—
477Q8—84no—
478Q8—441no—
479Q8—441no—
480Q8C2×#432514yes—
481D4—442no—
482D4—441no—
483D4—441no—
484D4—441no—
485D4—441no—
486D4—882no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—41no—
497C2×C4—81no—
498C2×C4—441no—
499C2×C4—882no—
500C2×C4C2×#432512yes—
501C2×C4#6699512yes—
502C2×C4#6700611yescharacteristic
503C2×C4#6700611yescharacteristic
504C2×C4#6700611yescharacteristic
505C2×C4C22×C22⋊D1111yescharacteristic
506C2×C4C22×C22⋊D1111yescharacteristic
507C2×C4C22×C22⋊D1111yescharacteristic
508C8—222no—
509C8—441no—
510C8—442no—
511C8—442no—
512C22—21no—
513C22—21no—
514C22—881no—
515C22—881no—
516C22—881no—
517C22#1062284012yes—
518C22C2×#6700611yescharacteristic
519C4—24no—
520C4—21no—
521C4—21no—
522C4—21no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4—42no—
528C4—881no—
529C4#1062284012yes—
530C4C22×#432511yescharacteristic
531C4C2×#6699511yescharacteristic
532C4#1062336811yescharacteristic
533C4#1062336911yescharacteristic
534C2—22no—
535C2—1761no—
536C2C2×#1062284011yescharacteristic
537C2#1307793111yescharacteristic
538C2#1307796511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3502C2
socleC22×C11C2×#120
prime radical#10623008C22
hypercenter#3502D11
hypocenterC11#18676
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3502

Complements

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

NH ≅ G/Ntype
4. #13067893C2semidirect
5. #13067837C2semidirect
6. #13067712C2semidirect
7. #13067694C2semidirect
8. #13067306C2semidirect
9. #13067071C2semidirect
10. C2×Q8⋊(C11⋊C8)C2semidirect
11. C11×#3502C2semidirect
133. C2×Q8×C11SD16semidirect
198. #3502D11semidirect
404. C2×Q8#4325semidirect
466. C11#18676semidirect

Maximal subgroups

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

subgroupindex
#130799282
#130791762
#130780882
#130678932
#130678372
#130677122
#130676942
#130673062
#130670712
C2×Q8⋊(C11⋊C8)2
C11×#35022
#1867611