Finite Group Databasebeta

← #14926811

Subgroups — #14926811

Order 2816.

2650 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C22⋊Q8C212yesmaximal
2#13076968C211yesmaximal, characteristic, complemented
3#13076964C212yesmaximal, complemented
4#13074733C214yesmaximal, complemented
5#13073994C218yesmaximal, complemented
6#13073093C212yesmaximal, complemented
7#13073091C212yesmaximal, complemented
8#13072259C212yesmaximal, complemented
9#13072257C212yesmaximal, complemented
10#13071229C214yesmaximal
11C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
12C11×#2857C211yesmaximal, characteristic, complemented
13C22×Q8×D11C2212yes—
14C23×C4×D11C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic, complemented
16C2×C11×C22⋊Q8C2212yes—
17C22×C42×C11C2211yescharacteristic
18C2×#66999C2212yes—
19C2×#66997C2212yescomplemented
20C22×(C2×D11)⋊C4C2212yes—
21C2×#66977C2212yes—
22C22×C4×Dic11C2211yescharacteristic
23D11×C22⋊Q8—216no—
24C2×#66950C2212yes—
25C2×#66949C2214yes—
26C2×C4⋊C4×D11C2214yes—
27C2×C4⋊C4×D11C2212yes—
28C2×C22⋊C4×D11C2214yes—
29C2×#66931C2214yes—
30C2×#66922C2211yescharacteristic, complemented
31C11×#391C2212yescomplemented
32C11×#389C2214yescomplemented
33C11×#384C2211yescharacteristic, complemented
34C11×#380C2214yes—
35#10622843C2212yescomplemented
36#10622825C2214yes—
37C2×C11⋊#95C2212yes—
38#10622602C2218yes—
39#10622602C2218yes—
40#10622597C2218yescomplemented
41#10622592C2218yescomplemented
42#10622589C2212yescomplemented
43#10622587C2212yescomplemented
44#10622585C2218yescomplemented
45#10622555C2218yes—
46C4×(C2×D11)⋊C4C2214yes—
47C4×(C2×D11)⋊C4C2212yes—
48C4×(C2×D11)⋊C4C2212yes—
49#10622548C2211yescharacteristic, complemented
50#10622542C2212yescomplemented
51#10622541C2214yescomplemented
52#10622281C2218yes—
53#10622281C2218yes—
54#10622270C2218yescomplemented
55#10622269C2218yescomplemented
56C24×D11C2311yescharacteristic
57C22×Q8×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2312yes—
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2312yes—
62C2×Q8×D11—28no—
63C2×Q8×D11—44no—
64C2×Q8×D11—44no—
65C22×C4×D11—42no—
66C22×C4×D11—42no—
67C22×C4×D11D418yes—
68C22×C4×D11C2312yes—
69C22×C4×D11C2314yes—
70C22×C4×D11C2314yes—
71C22×C4×D11C2312yes—
72C22×Dic22C2312yes—
73C22×Dic22C2314yes—
74C11×C4⋊Q8—42no—
75C11×C22⋊Q8—28no—
76C2×C11×C4⋊C4C2314yes—
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C22⋊C4C2314yes—
81C2×C42×C11—42no—
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2312yes—
85C2×C22⋊Dic11C2314yes—
86#66999—28no—
87#66997—44no—
88C2×(C2×D11)⋊C4Q8116yescomplemented
89C2×(C2×D11)⋊C4C2314yes—
90C2×(C2×D11)⋊C4C2314yes—
91C2×(C2×D11)⋊C4C2314yes—
92C2×(C2×D11)⋊C4C2314yes—
93C2×C4⋊Dic11C2314yes—
94C2×C4⋊Dic11C2312yes—
95C2×C4⋊Dic11C2314yes—
96C2×C4⋊Dic11C2314yes—
97#66977—28no—
98C2×Dic11⋊C4C2314yes—
99C2×Dic11⋊C4C2314yes—
100C2×Dic11⋊C4C2314yes—
101C2×Dic11⋊C4C2318yes—
102C2×Dic11⋊C4C2318yes—
103C2×C4×Dic11—42no—
104C2×C4×Dic11C2312yes—
105C2×C4×Dic11C2312yes—
106#66950—28no—
107#66949—216no—
108C4⋊C4×D11—28no—
109C4⋊C4×D11—216no—
110C22⋊C4×D11—216no—
111#66931—216no—
112#66922—42no—
113C11×#95C2318yes—
114C11⋊#95C2314yes—
115C11⋊#95C2318yes—
116C11⋊#95C2318yes—
117C11⋊#95C2318yes—
118C11⋊#95C2314yes—
119#35011—111nomaximal, Sylow
120C24×C11C2411yescharacteristic
121C23×D11—41no—
122C23×D11—41no—
123C23×D11—42no—
124C23×D11C2×D414yes—
125C23×D11C2×Q818yes—
126C23×D11C2412yes—
127C2×Q8×C11—24no—
128C2×Q8×C11—24no—
129C2×Q8×C11—24no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—42no—
133C22×C4×C11—42no—
134C22×C4×C11C2×D414yes—
135C22×C4×C11C2×Q818yescomplemented
136C22×C4×C11C2414yes—
137C22×C4×C11C2414yes—
138C22×C4×C11C2411yescharacteristic
139C22×C4×C11C2412yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—42no—
143C22×Dic11—41no—
144C22×Dic11—41no—
145C22×Dic11—42no—
146C22×Dic11C2×D414yes—
147C22×Dic11C2×Q818yescomplemented
148C22×Dic11C2414yes—
149C22×Dic11C2414yes—
150C22×Dic11C2412yes—
151C22×Dic11C2414yes—
152Q8×D11—432no—
153C2×C4×D11—28no—
154C2×C4×D11—28no—
155C2×C4×D11—24no—
156C2×C4×D11—24no—
157C2×C4×D11—42no—
158C2×C4×D11—42no—
159C2×C4×D11—48no—
160C2×C4×D11—44no—
161C2×C4×D11—44no—
162C2×C4×D11—416no—
163C2×C4×D11C2×D418yes—
164C2×C4×D11C2×D418yes—
165C2×Dic22—28no—
166C2×Dic22—24no—
167C2×Dic22—24no—
168C2×Dic22—24no—
169C2×Dic22—44no—
170C2×Dic22—44no—
171C11×C4⋊C4—28no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—44no—
174C11×C4⋊C4—44no—
175C11×C22⋊C4—28no—
176C42×C11—22no—
177C42×C11—22no—
178C42×C11—42no—
179C22⋊Dic11—28no—
180(C2×D11)⋊C4—28no—
181(C2×D11)⋊C4—28no—
182(C2×D11)⋊C4C2×Q8116yescomplemented
183(C2×D11)⋊C4C2×Q8116yescomplemented
184C4⋊Dic11—28no—
185C4⋊Dic11—24no—
186C4⋊Dic11—44no—
187C4⋊Dic11—44no—
188Dic11⋊C4—28no—
189Dic11⋊C4—28no—
190Dic11⋊C4—28no—
191Dic11⋊C4—48no—
192Dic11⋊C4—48no—
193C4×Dic11—24no—
194C4×Dic11—42no—
195C22×C22⋊Q8—112no—
196#2857—111no—
197#2857—112no—
198#2857D1111yescharacteristic, complemented
199#2659—114no—
200#2583—118no—
201#2502—112no—
202#2502—112no—
203#2434—112no—
204#2434—112no—
205#2315—114no—
206C2×C4×C22⋊C4—111no—
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—22no—
210C23×C11C22×D412yes—
211C23×C11C22×Q814yes—
212C23×C11C2511yescharacteristic
213C22×D11—22no—
214C22×D11—22no—
215C22×D11—24no—
216C22×D11—44no—
217C22×D11—44no—
218C22×D11—48no—
219C22×D11—48no—
220C22×D11C4⋊Q8116yescomplemented
221C22×D11C22×D414yes—
222C22×D11C22×Q818yes—
223Q8×C11—48no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—28no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—28no—
236C2×C4×C11—48no—
237C2×C4×C11C22×D412yes—
238C2×C4×C11C22×D412yes—
239C2×C4×C11C22×Q814yes—
240C2×C4×C11C22×Q814yes—
241C2×C4×C11H(5,𝔽2)12yes—
242C2×C4×C11H(5,𝔽2)12yes—
243C2×Dic11—24no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—28no—
252C2×Dic11—44no—
253C2×Dic11—48no—
254C2×Dic11C22×D414yes—
255C2×Dic11C22×Q818yes—
256C4×D11—216no—
257C4×D11—48no—
258C4×D11—416no—
259C4×D11—416no—
260Dic22—416no—
261Dic22—48no—
262C23×Q8—112no—
263C24×C4—111no—
264C2×C4⋊Q8—112no—
265C2×C4⋊Q8—111no—
266C2×C4⋊Q8C2×D1111yescharacteristic, complemented
267C2×C22⋊Q8—112no—
268C2×C22⋊Q8—112no—
269C2×C22⋊Q8—114no—
270C2×C22⋊Q8—112no—
271C2×C22⋊Q8—114no—
272C2×C22⋊Q8—2216no—
273C2×C22⋊Q8C2×D1112yes—
274C22×C4⋊C4—114no—
275C22×C4⋊C4—112no—
276C22×C22⋊C4—112no—
277C22×C22⋊C4—114no—
278C22×C42—111no—
279C22×C42C2×D1111yescharacteristic
280#398—118no—
281#398—118no—
282#395—118no—
283#395—118no—
284#391—112no—
285#391—112no—
286#391—112no—
287#391C2×D1112yescomplemented
288#389—118no—
289#389—114no—
290#389C2×D1114yescomplemented
291#385—118no—
292#385—118no—
293#385—118no—
294#385—118no—
295#384—112no—
296#384—111no—
297#384C2×D1111yescharacteristic, complemented
298#380—114no—
299#380—118no—
300#380C2×D1114yes—
301C4×C22⋊C4—114no—
302C4×C22⋊C4—112no—
303C4×C22⋊C4—112no—
304C2×#95—112no—
305C22×C11—22no—
306C22×C11—22no—
307C22×C11—24no—
308C22×C11—24no—
309C22×C11C2×C4⋊Q814yes—
310C22×C11C23×D411yescharacteristic
311C22×C11C23×Q812yes—
312C22×C11C2×H(5,𝔽2)11yescharacteristic
313C22×C11C2×H(5,𝔽2)11yescharacteristic
314C22×C11#58512yes—
315C2×D11—24no—
316C2×D11—24no—
317C2×D11—28no—
318C2×D11—28no—
319C2×D11—416no—
320C2×D11C2×C4⋊Q818yes—
321C4×C11—22no—
322C4×C11—24no—
323C4×C11—24no—
324C4×C11—44no—
325C4×C11—44no—
326C4×C11#53414yes—
327Dic11—24no—
328Dic11—28no—
329Dic11—44no—
330Dic11—44no—
331C25—111no—
332C22×Q8—112no—
333C22×Q8—114no—
334C22×Q8—228no—
335C22×Q8—444no—
336C22×Q8—444no—
337C22×Q8C22×D1112yes—
338C23×C4—112no—
339C23×C4—111no—
340C23×C4—112no—
341C23×C4—118no—
342C23×C4—112no—
343C23×C4—114no—
344C23×C4—114no—
345C23×C4—442no—
346C23×C4—442no—
347C23×C4C22×D1111yescharacteristic
348C23×C4C22×D1112yes—
349C4⋊Q8—42no—
350C4⋊Q8—442no—
351C4⋊Q8—444no—
352C22⋊Q8—28no—
353C22⋊Q8—2216no—
354C22⋊Q8—2216no—
355C22⋊Q8—228no—
356C22⋊Q8—228no—
357C22⋊Q8—228no—
358C2×C4⋊C4—112no—
359C2×C4⋊C4—114no—
360C2×C4⋊C4—114no—
361C2×C4⋊C4—114no—
362C2×C4⋊C4—114no—
363C2×C4⋊C4—118no—
364C2×C4⋊C4—114no—
365C2×C4⋊C4—118no—
366C2×C4⋊C4—114no—
367C2×C4⋊C4—228no—
368C2×C4⋊C4—2216no—
369C2×C4⋊C4C22×D1112yes—
370C2×C4⋊C4C22×D1114yes—
371C2×C4⋊C4C22×D1114yes—
372C2×C4⋊C4C22×D1114yes—
373C2×C22⋊C4—1116no—
374C2×C22⋊C4—114no—
375C2×C22⋊C4—114no—
376C2×C22⋊C4—114no—
377C2×C22⋊C4—114no—
378C2×C22⋊C4—114no—
379C2×C22⋊C4—2216no—
380C2×C22⋊C4C22×D1114yes—
381C2×C42—42no—
382C2×C42—112no—
383C2×C42—112no—
384C2×C42—442no—
385C2×C42C22×D1111yescharacteristic
386C2×C42C22×D1111yescharacteristic
387C2×C42C22×D1112yes—
388#95—114no—
389#95—114no—
390#95—118no—
391#95—118no—
392#95—118no—
393#95C22×D1118yes—
394C2×C11—24no—
395C2×C11C22×C4⋊Q811yescharacteristic
396C2×C11C2×#53411yescharacteristic
397C2×C11#344911yescharacteristic
398C2×C11#350112yes—
399C2×C11#350112yes—
400D11—28no—
401C24—112no—
402C24—114no—
403C24—118no—
404C24—441no—
405C24—441no—
406C24—442no—
407C24C23×D1111yescharacteristic
408C2×Q8—24no—
409C2×Q8—24no—
410C2×Q8—24no—
411C2×Q8—228no—
412C2×Q8—224no—
413C2×Q8—224no—
414C2×Q8—224no—
415C2×Q8—444no—
416C2×Q8—444no—
417C2×Q8—4432no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—114no—
423C22×C4—112no—
424C22×C4—114no—
425C22×C4—118no—
426C22×C4—118no—
427C22×C4—118no—
428C22×C4—114no—
429C22×C4—114no—
430C22×C4—228no—
431C22×C4—228no—
432C22×C4—224no—
433C22×C4—224no—
434C22×C4—4416no—
435C22×C4—442no—
436C22×C4—442no—
437C22×C4—444no—
438C22×C4—444no—
439C22×C4—448no—
440C22×C4—442no—
441C22×C4—441no—
442C22×C4—441no—
443C22×C4—442no—
444C22×C4D4×D1114yes—
445C22×C4Q8×D1118yescomplemented
446C22×C4C23×D1114yes—
447C22×C4C23×D1114yes—
448C22×C4C23×D1111yescharacteristic
449C22×C4C23×D1112yes—
450C22×C4C23×D1112yes—
451C22×C4C23×D1111yescharacteristic
452C4⋊C4—24no—
453C4⋊C4—28no—
454C4⋊C4—44no—
455C4⋊C4—44no—
456C4⋊C4—228no—
457C4⋊C4—228no—
458C4⋊C4—228no—
459C4⋊C4—228no—
460C4⋊C4—224no—
461C4⋊C4—448no—
462C4⋊C4—444no—
463C4⋊C4—448no—
464C4⋊C4—444no—
465C22⋊C4—28no—
466C22⋊C4—1116no—
467C22⋊C4—1116no—
468C22⋊C4—228no—
469C22⋊C4—228no—
470C22⋊C4—228no—
471C42—22no—
472C42—22no—
473C42—42no—
474C42—224no—
475C42—442no—
476C11#3501111yescharacteristic, complemented, Sylow
477C23—21no—
478C23—21no—
479C23—22no—
480C23—114no—
481C23—118no—
482C23—1116no—
483C23—222no—
484C23—222no—
485C23—224no—
486C23—444no—
487C23—448no—
488C23—448no—
489C23—444no—
490C23C2×D4×D1112yes—
491C23C2×Q8×D1114yes—
492C23C24×D1111yescharacteristic
493Q8—48no—
494Q8—4416no—
495Q8—448no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—28no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—28no—
508C2×C4—48no—
509C2×C4—114no—
510C2×C4—118no—
511C2×C4—222no—
512C2×C4—224no—
513C2×C4—222no—
514C2×C4—224no—
515C2×C4—2216no—
516C2×C4—224no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—224no—
520C2×C4—228no—
521C2×C4—448no—
522C2×C4—4416no—
523C2×C4—4416no—
524C2×C4—444no—
525C2×C4—448no—
526C2×C4C2×D4×D1112yes—
527C2×C4C2×D4×D1112yes—
528C2×C4#6703712yes—
529C2×C4C2×Q8×D1114yes—
530C2×C4C2×Q8×D1114yes—
531C2×C4#6704212yes—
532C22—24no—
533C22—24no—
534C22—22no—
535C22—22no—
536C22—118no—
537C22—228no—
538C22—228no—
539C22—224no—
540C22—224no—
541C22—4416no—
542C22D11×C4⋊Q814yes—
543C22C22×D4×D1111yescharacteristic
544C22C2×#6703711yescharacteristic
545C22C22×Q8×D1112yes—
546C22C2×#6704211yescharacteristic
547C22#1062345312yes—
548C4—24no—
549C4—24no—
550C4—22no—
551C4—44no—
552C4—44no—
553C4—228no—
554C4—224no—
555C4—444no—
556C4—444no—
557C4#1062313614yes—
558C2—24no—
559C2—228no—
560C2C2×D11×C4⋊Q811yescharacteristic
561C2C2×#1062313611yescharacteristic
562C2#1308194311yescharacteristic
563C2#1308241212yes—
564C2#1308241712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2857C2
prime radicalC24×D11C23
hypercenter#2857D11
hypocenterC11#35011
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2857

Complements

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

NH ≅ G/Ntype
2. #13076968C2semidirect
3. #13076964C2semidirect
4. #13074733C2semidirect
5. #13073994C2semidirect
6. #13073093C2semidirect
7. #13073091C2semidirect
8. #13072259C2semidirect
9. #13072257C2semidirect
12. C11×#2857C2semidirect
15. C2×C11×C4⋊Q8C22semidirect
19. C2×#66997C22semidirect
30. C2×#66922C22semidirect
31. C11×#391C22semidirect
32. C11×#389C22semidirect
33. C11×#384C22semidirect
35. #10622843C22semidirect
40. #10622597C22semidirect
41. #10622592C22semidirect
42. #10622589C22semidirect
43. #10622587C22semidirect
44. #10622585C22semidirect
49. #10622548C22semidirect
50. #10622542C22semidirect
51. #10622541C22semidirect
54. #10622270C22semidirect
55. #10622269C22semidirect
88. C2×(C2×D11)⋊C4Q8semidirect
135. C22×C4×C11C2×Q8semidirect
147. C22×Dic11C2×Q8semidirect
182. (C2×D11)⋊C4C2×Q8semidirect
183. (C2×D11)⋊C4C2×Q8semidirect
198. #2857D11semidirect
220. C22×D11C4⋊Q8semidirect
266. C2×C4⋊Q8C2×D11semidirect
287. #391C2×D11semidirect
290. #389C2×D11semidirect
297. #384C2×D11semidirect
445. C22×C4Q8×D11semidirect
476. C11#35011semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C22⋊Q82
#130769682
#130769642
#130747332
#130739942
#130730932
#130730912
#130722592
#130722572
#130712292
C2×C4×(C2×D11)⋊C42
C11×#28572
#3501111