Finite Group Databasebeta

← #15622306

Subgroups — #15622306

Order 2816.

2010 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081817C211yesmaximal, characteristic
2#13078911C214yesmaximal, complemented
3#13078863C214yesmaximal, complemented
4#13078824C218yesmaximal, complemented
5#13078560C212yesmaximal, complemented
6#13078434C212yesmaximal, complemented
7#13078099C212yesmaximal, complemented
8#13077874C212yesmaximal
9C4×#66995C214yesmaximal, complemented
10#13077254C211yesmaximal, characteristic, complemented
11C2×C11×#541C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C11×#541—22no—
14C11×#541—22no—
15C11×#541C2214yes—
16C11×#541C2214yescomplemented
17C2×C11×C4⋊Q8C2211yescharacteristic, complemented
18C2×C11×#126—22no—
19C2×C11×#125—22no—
20C2×C11×#125C2211yescharacteristic, complemented
21C2×C11×C22⋊Q8C2212yes—
22C2×C4×Q8×C11C2212yescomplemented
23C2×C11×#117C2211yescharacteristic
24C2×#66995C2214yes—
25C2×#66979C2211yescharacteristic
26#10623054C2214yes—
27#10623053—22no—
28#10623052C2212yes—
29D11×#117—22no—
30#10623047C2212yes—
31#10623035—22no—
32#10623017—22no—
33C4×#4339C2212yes—
34C4×#4339C2212yes—
35#10622838C2214yescomplemented
36#10622820C2212yes—
37#10622703C2218yescomplemented
38#10622696C2218yescomplemented
39#10622679C2218yescomplemented
40#10622676C2218yescomplemented
41#10622663C2214yes—
42#10622660C2218yes—
43#10622659C2214yes—
44#10622658C2218yes—
45#10622657C2214yescomplemented
46#10622656C2214yescomplemented
47#10622643C2218yescomplemented
48C4×#4326C2218yescomplemented
49#10622639C2218yescomplemented
50C4×#4325C2218yescomplemented
51#10622613C2214yes—
52#10622613C2214yescomplemented
53#10622579C2214yes—
54#10622577C2214yescomplemented
55#10622537C2212yescomplemented
56C4×#4318C2212yescomplemented
57C22×Q8×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11—21no—
60C2×#4339—21no—
61C2×#4339—21no—
62C2×#4339—28no—
63C2×#4339C2312yes—
64C2×#4339C2312yes—
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C22×Dic22C2311yescharacteristic
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8C2314yes—
70C11×#126—28no—
71C11×#126—28no—
72C11×#125—28no—
73C11×#125—28no—
74C11×#125—22no—
75C11×#125C2314yes—
76C11×C22⋊Q8—22no—
77C11×C22⋊Q8—22no—
78C11×C22⋊Q8C2314yes—
79C11×C22⋊Q8C2314yes—
80C4×Q8×C11—24no—
81C4×Q8×C11C2318yes—
82C11×#117D412yes—
83C11×#117D412yes—
84C11×#117C2312yes—
85C11×#117C2312yes—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—22no—
90C2×C11×C4⋊C4D412yes—
91C2×C11×C4⋊C4C2312yes—
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4D412yes—
94C2×C42×C11—22no—
95C2×C42×C11C2311yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C22⋊Dic11—21no—
98C2×#4326C2318yes—
99#66995—216no—
100C2×#4325C2318yes—
101C4×C22⋊D11—24no—
102C4×C22⋊D11—24no—
103#66979—21no—
104#66979—21no—
105#66979C2312yes—
106#66979C2312yes—
107C2×C4⋊Dic11C2312yes—
108C2×C4×Dic11—21no—
109C2×#4318C2314yes—
110#66946—24no—
111#66945—24no—
112C4⋊C4×D11—24no—
113#66940—24no—
114(C22⋊D11)⋊C4—24no—
115(C22⋊D11)⋊C4—24no—
116C22⋊C4×D11—24no—
117#66930—24no—
118C4×D44C2314yes—
119C4×D44C2314yes—
120#66925—22no—
121#66925—22no—
122C42×D11—22no—
123C42×D11—22no—
124C4×Dic22C2314yes—
125C4×Dic22C2314yes—
126#66899C2318yes—
127#66899C2318yes—
128C22⋊(C11⋊C8)C2314yes—
129C22⋊(C11⋊C8)C2314yes—
130#66874C2318yes—
131#66873C2318yes—
132#66872C2318yes—
133#66871C2318yes—
134C4⋊(C11⋊C8)C2318yes—
135#66867C2314yes—
136C4×C11⋊C8C2314yes—
137#60569—111nomaximal, Sylow
138C24×C11C2×D411yescharacteristic
139C23×D11—21no—
140C2×Q8×C11—22no—
141C2×Q8×C11—28no—
142C2×Q8×C11C2414yes—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C2×C22⋊D11—28no—
155C2×C22⋊D11—22no—
156C2×C22⋊D11—22no—
157C22×Dic11—21no—
158C22×Dic11—22no—
159#4339—28no—
160#4339—28no—
161#4339—24no—
162#4339—24no—
163#4339—24no—
164#4339#4118yes—
165C2×D44—24no—
166C2×D44—21no—
167C2×D44C2412yes—
168C2×C4×D11—28no—
169C2×C4×D11—22no—
170C2×C4×D11—22no—
171C2×C4×D11—24no—
172C2×C4×D11—24no—
173C2×Dic22—24no—
174C2×Dic22—21no—
175C2×Dic22C2412yes—
176C11×C4⋊C4—28no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—24no—
179C11×C4⋊C4—28no—
180C11×C4⋊C4—28no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4C2×D414yes—
183C11×C4⋊C4C2×D414yes—
184C11×C4⋊C4C2414yes—
185C11×C22⋊C4—24no—
186C11×C22⋊C4—24no—
187C11×C22⋊C4C2×D414yes—
188C11×C22⋊C4C2×D414yes—
189C42×C11—28no—
190C42×C11C2×D412yes—
191C42×C11C2×D412yes—
192C42×C11C2412yes—
193C42×C11C2412yes—
194C22⋊Dic11—22no—
195C22⋊Dic11—22no—
196#4326—216no—
197#4325—216no—
198(C2×D11)⋊C4—24no—
199(C2×D11)⋊C4—24no—
200C4⋊Dic11—22no—
201C4⋊Dic11C2414yes—
202Dic11⋊C4—24no—
203Dic11⋊C4—24no—
204C4×Dic11—24no—
205C4×Dic11—24no—
206C4×Dic11—22no—
207C4×Dic11—22no—
208#4318—28no—
209C2×C11⋊C8C2418yes—
210C2×#541D1111yescharacteristic, complemented
211#3428—111no—
212#3127—114no—
213#3123—114no—
214#3120—118no—
215#3095—112no—
216#3080—112no—
217#3039—112no—
218#3007—112no—
219C4×#137—114no—
220#2921—111no—
221C23×C11—22no—
222C23×C11—42no—
223C23×C11C22×D411yescharacteristic
224C23×C11C22×D411yescharacteristic
225C23×C11C22×D411yescharacteristic
226C22×D11—22no—
227C22×D11—24no—
228C22×D11—82no—
229Q8×C11—28no—
230Q8×C11—44no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—44no—
241C2×C4×C11—44no—
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D414yes—
244C2×C4×C11C22×D414yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4114yes—
248C2×C4×C11C2511yescharacteristic
249C22⋊D11—28no—
250C22⋊D11—28no—
251C2×Dic11—24no—
252C2×Dic11—22no—
253C2×Dic11—24no—
254C2×Dic11—82no—
255D44—24no—
256D44—22no—
257D44C2×#4114yes—
258C4×D11—28no—
259C4×D11—28no—
260C4×D11—84no—
261C4×D11—84no—
262Dic22—24no—
263Dic22—22no—
264Dic22C2×#4114yes—
265C11⋊C8—28no—
266C22×#41—111no—
267C2×#137—114no—
268#541—22no—
269#541—22no—
270#541C2×D1114yes—
271#541C2×D1114yescomplemented
272C2×C4⋊Q8C2×D1111yescharacteristic, complemented
273C2×#126—22no—
274C2×#125—22no—
275C2×#125C2×D1111yescharacteristic, complemented
276C2×C22⋊Q8C2×D1112yes—
277#520—114no—
278#520—222no—
279#519—112no—
280#518—112no—
281#518—222no—
282C4×#41—112no—
283C4×#41—112no—
284C4×#41—222no—
285C2×C4×Q8C2×D1112yescomplemented
286C2×#117—111no—
287C2×#117—222no—
288C2×#117C2×D1111yescharacteristic
289#485—118no—
290#484—114no—
291#483—114no—
292#479—118no—
293#478—118no—
294#462—118no—
295#461—118no—
296#452—118no—
297#451—114no—
298#450—114no—
299#441—118no—
300#440—118no—
301C4×Q16—118no—
302C4×SD16—118no—
303#433—114no—
304#433—114no—
305#428—114no—
306#423—112no—
307#419—114no—
308#417—114no—
309#407—112no—
310C4×M16—112no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—22no—
314C22×C11—21no—
315C22×C11—21no—
316C22×C11—82no—
317C22×C11#52512yes—
318C22×C11C23×D411yescharacteristic
319C2×D11—24no—
320C2×D11—44no—
321C2×D11—84no—
322C4×C11—24no—
323C4×C11—24no—
324C4×C11—21no—
325C4×C11—21no—
326C4×C11—44no—
327C4×C11—44no—
328C4×C11#52512yes—
329C4×C11C22×#4112yes—
330Dic11—24no—
331Dic11—44no—
332C2×#41—112no—
333C2×#41—112no—
334C2×#41—228no—
335C2×#41—221no—
336C2×#41—221no—
337C22×Q8—111no—
338C22×Q8C22×D1112yes—
339C22×D4—111no—
340C22×D4—221no—
341C23×C4—221no—
342C23×C4C22×D1111yescharacteristic
343#137—2216no—
344C2×Q16—118no—
345C2×SD16—118no—
346C2×M16—114no—
347C4⋊Q8—22no—
348C4⋊Q8C22×D1114yes—
349#126—28no—
350#126—28no—
351#125—28no—
352#125—28no—
353#125—22no—
354#125C22×D1114yes—
355C22⋊Q8—22no—
356C22⋊Q8—22no—
357C22⋊Q8C22×D1114yes—
358C22⋊Q8C22×D1114yes—
359C4×Q8—24no—
360C4×Q8—114no—
361C4×Q8—114no—
362C4×Q8—224no—
363C4×Q8C22×D1118yes—
364C4×D4—114no—
365C4×D4—114no—
366C4×D4—224no—
367C4×D4—224no—
368C4×D4—224no—
369C4×D4—224no—
370C4×D4—224no—
371#117—112no—
372#117—112no—
373#117—221no—
374#117—221no—
375#117—224no—
376#117—224no—
377#117—222no—
378#117—222no—
379#117C22⋊D1112yes—
380#117C22⋊D1112yes—
381#117C22×D1112yes—
382#117C22×D1112yes—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—112no—
388C2×C4⋊C4—224no—
389C2×C4⋊C4C22⋊D1112yes—
390C2×C4⋊C4C22×D1112yes—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—224no—
394C2×C22⋊C4C22⋊D1112yes—
395C2×C42—22no—
396C2×C42—221no—
397C2×C42—222no—
398C2×C42—222no—
399C2×C42C22×D1111yescharacteristic
400C2×C42C22×D1111yescharacteristic
401#107—118no—
402#106—118no—
403C4⋊C8—118no—
404#103—118no—
405#103—118no—
406#103—118no—
407#102—118no—
408C22⋊C8—114no—
409C22⋊C8—114no—
410#97—114no—
411C4×C8—114no—
412C2×C11—22no—
413C2×C11—41no—
414C2×C11—41no—
415C2×C11C2×#52511yescharacteristic
416C2×C11#358612yes—
417D11—44no—
418C24—221no—
419C24C2×C22⋊D1111yescharacteristic
420#41—118no—
421#41—224no—
422#41—224no—
423#41—228no—
424#41—228no—
425#41—224no—
426C2×Q8—22no—
427C2×Q8—28no—
428C2×Q8—112no—
429C2×Q8—224no—
430C2×Q8—221no—
431C2×Q8C23×D1114yes—
432C2×D4—112no—
433C2×D4—224no—
434C2×D4—228no—
435C2×D4—222no—
436C2×D4—222no—
437C2×D4—221no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—228no—
442C22×C4—221no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—224no—
447C22×C4—224no—
448C22×C4C2×C22⋊D1111yescharacteristic
449C22×C4C2×C22⋊D1111yescharacteristic
450C22×C4C2×C22⋊D1111yescharacteristic
451C22×C4C2×C22⋊D1112yes—
452C22×C4C2×C22⋊D1112yes—
453C22×C4C23×D1111yescharacteristic
454C22×C4C23×D1111yescharacteristic
455C22×C4C23×D1111yescharacteristic
456Q16—2216no—
457SD16—2216no—
458M16—228no—
459C2×C8—118no—
460C4⋊C4—28no—
461C4⋊C4—24no—
462C4⋊C4—24no—
463C4⋊C4—28no—
464C4⋊C4—28no—
465C4⋊C4—22no—
466C4⋊C4—114no—
467C4⋊C4—222no—
468C4⋊C4—224no—
469C4⋊C4—224no—
470C4⋊C4C2×C22⋊D1114yes—
471C4⋊C4C2×C22⋊D1114yes—
472C4⋊C4C23×D1114yes—
473C22⋊C4—24no—
474C22⋊C4—24no—
475C22⋊C4—222no—
476C22⋊C4—222no—
477C22⋊C4—224no—
478C22⋊C4—224no—
479C22⋊C4C2×C22⋊D1114yes—
480C22⋊C4C2×C22⋊D1114yes—
481C42—28no—
482C42—222no—
483C42—222no—
484C42—224no—
485C42—224no—
486C42C2×C22⋊D1112yes—
487C42C2×C22⋊D1112yes—
488C42C23×D1112yes—
489C42C23×D1112yes—
490C11#6056911yescharacteristic, complemented, Sylow
491C23—22no—
492C23—42no—
493C23—224no—
494C23—222no—
495C23—882no—
496C23C22×C22⋊D1111yescharacteristic
497C23C22×C22⋊D1111yescharacteristic
498C23C22×C22⋊D1111yescharacteristic
499Q8—28no—
500Q8—44no—
501Q8—114no—
502Q8—224no—
503Q8—222no—
504D4—114no—
505D4—224no—
506D4—228no—
507D4—228no—
508D4—222no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—44no—
519C2×C4—44no—
520C2×C4—228no—
521C2×C4—224no—
522C2×C4—222no—
523C2×C4—228no—
524C2×C4—224no—
525C2×C4—884no—
526C2×C4—884no—
527C2×C4—882no—
528C2×C4#41×D1114yes—
529C2×C4C22×C22⋊D1114yes—
530C2×C4C22×C22⋊D1111yescharacteristic
531C2×C4C22×C22⋊D1114yes—
532C2×C4C22×C22⋊D1111yescharacteristic
533C2×C4C22×C22⋊D1111yescharacteristic
534C2×C4C24×D1111yescharacteristic
535C8—228no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—21no—
540C22—21no—
541C22—82no—
542C22—224no—
543C22—444no—
544C22—884no—
545C22#1062335912yes—
546C22C23×C22⋊D1111yescharacteristic
547C4—24no—
548C4—24no—
549C4—21no—
550C4—21no—
551C4—44no—
552C4—44no—
553C4—224no—
554C4—444no—
555C4#1062335912yes—
556C4C2×#41×D1112yes—
557C2—22no—
558C2—41no—
559C2—41no—
560C2—444no—
561C2C2×#1062335911yescharacteristic
562C2#1308340312yes—
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#541C2
socleC22×C11C23×D4
prime radicalC22×#4339C22
hypercenterC2×#541D11
hypocenterC11#60569
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
2. #13078911C2semidirect
3. #13078863C2semidirect
4. #13078824C2semidirect
5. #13078560C2semidirect
6. #13078434C2semidirect
7. #13078099C2semidirect
9. C4×#66995C2semidirect
10. #13077254C2semidirect
11. C2×C11×#541C2semidirect
16. C11×#541C22semidirect
17. C2×C11×C4⋊Q8C22semidirect
20. C2×C11×#125C22semidirect
22. C2×C4×Q8×C11C22semidirect
35. #10622838C22semidirect
37. #10622703C22semidirect
38. #10622696C22semidirect
39. #10622679C22semidirect
40. #10622676C22semidirect
45. #10622657C22semidirect
46. #10622656C22semidirect
47. #10622643C22semidirect
48. C4×#4326C22semidirect
49. #10622639C22semidirect
50. C4×#4325C22semidirect
52. #10622613C22semidirect
54. #10622577C22semidirect
55. #10622537C22semidirect
56. C4×#4318C22semidirect
210. C2×#541D11semidirect
271. #541C2×D11semidirect
272. C2×C4⋊Q8C2×D11semidirect
275. C2×#125C2×D11semidirect
285. C2×C4×Q8C2×D11semidirect
490. C11#60569semidirect

Maximal subgroups

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

subgroupindex
#130818172
#130789112
#130788632
#130788242
#130785602
#130784342
#130780992
#130778742
C4×#669952
#130772542
C2×C11×#5412
#6056911