Finite Group Databasebeta

← #14755403

Subgroups — #14755403

Order 2816.

2126 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623335C211yesmaximal, characteristic
2C2×#10623329C211yesmaximal, characteristic, complemented
3#13071191C212yesmaximal, complemented
4#13069027C214yesmaximal, complemented
5#13069022C214yesmaximal, complemented
6C2×#10622165C212yesmaximal, complemented
7C22×C11×#99C211yesmaximal, characteristic, complemented
8C23×D4×C11C2211yescharacteristic
9C23×C22⋊D11C2211yescharacteristic
10C22×C11×C22⋊C4C2212yes—
11C2×#67006—21no—
12C22×C22⋊Dic11—21no—
13C22×C22⋊Dic11C2212yes—
14C22×C22⋊Dic11C2211yescharacteristic
15#10623335—24no—
16#10623335C418yescomplemented
17C2×#66992—22no—
18C2×#66990C2212yes—
19#10623329—22no—
20#10623329—24no—
21#10623329C2214yes—
22C2×#66988C2212yes—
23C2×D4×Dic11—24no—
24C2×#66982—21no—
25C2×#66979—21no—
26C2×C11×#99—24no—
27C2×C11×#99C2214yes—
28#10622826—24no—
29#10622571—24no—
30#10622568C2214yescomplemented
31#10622556C2214yescomplemented
32#10622165C2218yescomplemented
33C25×C11D411yescharacteristic
34C25×C11C2311yescharacteristic
35C24×D11C2311yescharacteristic
36C22×D4×C11—22no—
37C22×D4×C11—22no—
38C22×D4×C11—24no—
39C22×D4×C11C2×C414yes—
40C22×D4×C11D412yes—
41C22×D4×C11D414yes—
42C22×D4×C11C2312yes—
43C23×C4×C11—22no—
44C23×C4×C11D411yescharacteristic
45C22×C22⋊D11—21no—
46C22×C22⋊D11—21no—
47C22×C22⋊D11—22no—
48C22×C22⋊D11—22no—
49C22×C22⋊D11—22no—
50C22×C22⋊D11—24no—
51C22×C22⋊D11—22no—
52C22×C22⋊D11C2×C414yescomplemented
53C23×Dic11—22no—
54C23×Dic11—21no—
55C23×Dic11D414yescomplemented
56C23×Dic11C2311yescharacteristic
57C2×C11×C22⋊C4—24no—
58C2×C11×C22⋊C4—24no—
59C2×C11×C22⋊C4—22no—
60C2×C11×C22⋊C4C2314yes—
61#67006—28no—
62C2×C22⋊Dic11—22no—
63C2×C22⋊Dic11—24no—
64C2×C22⋊Dic11—22no—
65C2×C22⋊Dic11—21no—
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11—22no—
68C2×C22⋊Dic11—22no—
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—24no—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11C2×C414yescomplemented
73C2×C22⋊Dic11D414yescomplemented
74C2×C22⋊Dic11C2314yes—
75C2×C22⋊Dic11C2312yes—
76#66992—216no—
77#66990—24no—
78#66990C2×C418yescomplemented
79#66988—24no—
80#66988C2×C418yescomplemented
81D4×Dic11—216no—
82D4×Dic11—216no—
83#66982—28no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—28no—
86#66979—24no—
87#66979—24no—
88C2×C4⋊Dic11—22no—
89C2×Dic11⋊C4—22no—
90C2×C4×Dic11—22no—
91C11×#99—28no—
92C11⋊#95—28no—
93#20960—111nomaximal, Sylow
94C24×C11—21no—
95C24×C11—21no—
96C24×C11—22no—
97C24×C11—82no—
98C24×C11—82no—
99C24×C11C22⋊C414yescomplemented
100C24×C11C22×C412yes—
101C24×C11C2×D412yes—
102C24×C11C2×D411yescharacteristic
103C24×C11C2×D411yescharacteristic
104C24×C11C2×D412yes—
105C24×C11C2×D412yes—
106C24×C11C2×D412yes—
107C24×C11#4114yes—
108C24×C11C2411yescharacteristic
109C23×D11—22no—
110C23×D11—21no—
111C23×D11—21no—
112C23×D11—22no—
113C23×D11—82no—
114C23×D11C22×C412yescomplemented
115C2×D4×C11—28no—
116C2×D4×C11—28no—
117C2×D4×C11—24no—
118C2×D4×C11—28no—
119C2×D4×C11—28no—
120C2×D4×C11—24no—
121C2×D4×C11—24no—
122C2×D4×C11—24no—
123C2×D4×C11C22⋊C418yescomplemented
124C2×D4×C11C22×C414yes—
125C2×D4×C11C2×D414yes—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—24no—
130C22×C4×C11—44no—
131C22×C4×C11—84no—
132C22×C4×C11C22⋊C414yescomplemented
133C22×C4×C11C2×D412yes—
134C2×C22⋊D11—24no—
135C2×C22⋊D11—24no—
136C2×C22⋊D11—28no—
137C2×C22⋊D11—28no—
138C2×C22⋊D11—28no—
139C2×C22⋊D11—41no—
140C2×C22⋊D11—42no—
141C2×C22⋊D11—41no—
142C2×C22⋊D11—44no—
143C2×C22⋊D11—44no—
144C2×C22⋊D11—42no—
145C2×C22⋊D11—42no—
146C2×C22⋊D11—84no—
147C22×Dic11—28no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—22no—
152C22×Dic11—21no—
153C22×Dic11—22no—
154C22×Dic11—21no—
155C22×Dic11—22no—
156C22×Dic11—84no—
157C22×Dic11—82no—
158C22×Dic11—84no—
159C22×Dic11C22×C412yescomplemented
160C22×Dic11C2×D418yes—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—44no—
164C22⋊Dic11—28no—
165C22⋊Dic11—24no—
166C22⋊Dic11—28no—
167C22⋊Dic11—24no—
168C22⋊Dic11—24no—
169C22⋊Dic11—24no—
170C22⋊Dic11—24no—
171C22⋊Dic11—22no—
172C22⋊Dic11C22×C414yescomplemented
173(C2×D11)⋊C4—28no—
174(C2×D11)⋊C4—88no—
175C4⋊Dic11—28no—
176Dic11⋊C4—28no—
177C4×Dic11—28no—
178C2×#534—111no—
179C2×#518—111no—
180C22×#99D1111yescharacteristic, complemented
181#2308—112no—
182#1890—114no—
183#1889—114no—
184C2×#342—112no—
185C23×C11—22no—
186C23×C11—24no—
187C23×C11—22no—
188C23×C11—24no—
189C23×C11—42no—
190C23×C11—44no—
191C23×C11—44no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—44no—
195C23×C11—44no—
196C23×C11—82no—
197C23×C11—82no—
198C23×C11—82no—
199C23×C11—84no—
200C23×C11—84no—
201C23×C11—84no—
202C23×C11C2×C22⋊C414yes—
203C23×C11C2×C22⋊C412yes—
204C23×C11C2×C22⋊C412yes—
205C23×C11C4×D414yes—
206C23×C11C4×D414yes—
207C23×C11#12011yescharacteristic
208C23×C11#12012yes—
209C23×C11#12011yescharacteristic
210C23×C11#12114yes—
211C23×C11#12114yes—
212C23×C11#12312yes—
213C23×C11#12312yes—
214C23×C11C23×C411yescharacteristic
215C23×C11C22×D411yescharacteristic
216C23×C11C22×D412yes—
217C23×C11C22×D411yescharacteristic
218C23×C11C2×#4112yes—
219C22×D11—22no—
220C22×D11—24no—
221C22×D11—48no—
222C22×D11—44no—
223C22×D11—41no—
224C22×D11—42no—
225C22×D11—41no—
226C22×D11—82no—
227C22×D11—84no—
228C22×D11—82no—
229D4×C11—28no—
230D4×C11—28no—
231D4×C11—216no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—48no—
237C2×C4×C11—44no—
238C2×C4×C11—88no—
239C2×C4×C11C2×C22⋊C414yes—
240C22⋊D11—44no—
241C22⋊D11—44no—
242C22⋊D11—48no—
243C22⋊D11—88no—
244C2×Dic11—22no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—28no—
248C2×Dic11—48no—
249C2×Dic11—44no—
250C2×Dic11—41no—
251C2×Dic11—42no—
252C2×Dic11—41no—
253C2×Dic11—48no—
254C2×Dic11—84no—
255C2×Dic11—84no—
256C2×Dic11—88no—
257C23×D4—111no—
258C23×D4C2×D1111yescharacteristic
259#534—118no—
260#534—224no—
261C2×#123—112no—
262C2×#123—221no—
263C2×#121—222no—
264C2×#120—112no—
265C2×#120—221no—
266#518—114no—
267#518—224no—
268#518—222no—
269C2×C4×D4—224no—
270C2×#117—221no—
271C22×C22⋊C4—111no—
272C22×C22⋊C4—112no—
273C22×C22⋊C4—221no—
274C22×C22⋊C4C2×D1112yes—
275C2×#99—24no—
276C2×#99C2×D1114yes—
277#386—224no—
278#386—224no—
279#381—114no—
280#379—114no—
281#342—118no—
282C22×C11—24no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—24no—
287C22×C11—24no—
288C22×C11—44no—
289C22×C11—41no—
290C22×C11—41no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—44no—
296C22×C11—44no—
297C22×C11—44no—
298C22×C11—42no—
299C22×C11—44no—
300C22×C11—48no—
301C22×C11—44no—
302C22×C11—82no—
303C22×C11—84no—
304C22×C11#38612yes—
305C22×C11#38612yes—
306C22×C11#38614yes—
307C22×C11C22×C22⋊C411yescharacteristic
308C22×C11C2×C4×D412yes—
309C22×C11C2×#12011yescharacteristic
310C22×C11C2×#12112yes—
311C22×C11C2×#12311yescharacteristic
312C2×D11—48no—
313C2×D11—44no—
314C2×D11—42no—
315C2×D11—84no—
316C2×D11—82no—
317C2×D11—82no—
318C4×C11—24no—
319C4×C11—84no—
320Dic11—44no—
321Dic11—48no—
322Dic11—42no—
323C25—111no—
324C25D4411yescharacteristic
325C25C22×D1111yescharacteristic
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—24no—
329C22×D4—114no—
330C22×D4—221no—
331C22×D4—221no—
332C22×D4—222no—
333C22×D4—222no—
334C22×D4—224no—
335C22×D4—222no—
336C22×D4—222no—
337C22×D4C4×D1114yes—
338C22×D4D4412yes—
339C22×D4C22⋊D1114yes—
340C22×D4C22×D1112yes—
341C23×C4—22no—
342C23×C4—111no—
343C23×C4—114no—
344C23×C4—222no—
345C23×C4—221no—
346C23×C4D4411yescharacteristic
347#123—118no—
348#123—224no—
349#123—228no—
350#121—2216no—
351#120—118no—
352#120—228no—
353#120—224no—
354C4×D4—2216no—
355C4×D4—2216no—
356#117—224no—
357#117—224no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—222no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—114no—
364C2×C22⋊C4—112no—
365C2×C22⋊C4—114no—
366C2×C22⋊C4—114no—
367C2×C22⋊C4—222no—
368C2×C22⋊C4—224no—
369C2×C22⋊C4—222no—
370C2×C22⋊C4—222no—
371C2×C22⋊C4—221no—
372C2×C22⋊C4—224no—
373C2×C22⋊C4—222no—
374C2×C22⋊C4—222no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4—222no—
377C2×C22⋊C4—222no—
378C2×C22⋊C4—228no—
379C2×C22⋊C4C22×D1114yes—
380C2×C42—222no—
381#99—28no—
382#95—228no—
383C2×C11—21no—
384C2×C11—22no—
385C2×C11—22no—
386C2×C11—21no—
387C2×C11—22no—
388C2×C11—22no—
389C2×C11—24no—
390C2×C11—44no—
391C2×C11C2×#38611yescharacteristic
392C2×C11#302612yes—
393D11—82no—
394C24—21no—
395C24—21no—
396C24—22no—
397C24—82no—
398C24—82no—
399C24—112no—
400C24—221no—
401C24—222no—
402C24—222no—
403C24—221no—
404C24—882no—
405C24(C2×D11)⋊C414yescomplemented
406C24C2×C4×D1112yes—
407C24C2×D4412yes—
408C24C2×D4411yescharacteristic
409C24C2×D4411yescharacteristic
410C24D4×D1112yes—
411C24D4×D1112yes—
412C24#434114yes—
413C24C2×C22⋊D1112yes—
414C24C23×D1111yescharacteristic
415C2×D4—28no—
416C2×D4—28no—
417C2×D4—24no—
418C2×D4—24no—
419C2×D4—28no—
420C2×D4—28no—
421C2×D4—24no—
422C2×D4—24no—
423C2×D4—228no—
424C2×D4—228no—
425C2×D4—224no—
426C2×D4—224no—
427C2×D4—228no—
428C2×D4—441no—
429C2×D4—442no—
430C2×D4—441no—
431C2×D4—442no—
432C2×D4—442no—
433C2×D4—444no—
434C2×D4—444no—
435C2×D4—884no—
436C2×D4(C2×D11)⋊C418yescomplemented
437C2×D4C2×C4×D1114yes—
438C2×D4C2×C22⋊D1114yes—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—24no—
443C22×C4—44no—
444C22×C4—84no—
445C22×C4—112no—
446C22×C4—118no—
447C22×C4—224no—
448C22×C4—222no—
449C22×C4—221no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—221no—
453C22×C4—228no—
454C22×C4—224no—
455C22×C4—224no—
456C22×C4—884no—
457C22×C4—884no—
458C22×C4—882no—
459C22×C4(C2×D11)⋊C414yescomplemented
460C22×C4C2×D4412yes—
461C4⋊C4—228no—
462C4⋊C4—228no—
463C22⋊C4—24no—
464C22⋊C4—24no—
465C22⋊C4—44no—
466C22⋊C4—114no—
467C22⋊C4—228no—
468C22⋊C4—224no—
469C22⋊C4—224no—
470C22⋊C4—224no—
471C22⋊C4—228no—
472C22⋊C4—224no—
473C22⋊C4—224no—
474C22⋊C4—222no—
475C22⋊C4—228no—
476C22⋊C4—888no—
477C42—228no—
478C11#2096011yescharacteristic, complemented, Sylow
479C23—22no—
480C23—24no—
481C23—22no—
482C23—24no—
483C23—44no—
484C23—42no—
485C23—44no—
486C23—42no—
487C23—42no—
488C23—44no—
489C23—44no—
490C23—82no—
491C23—82no—
492C23—84no—
493C23—82no—
494C23—84no—
495C23—84no—
496C23—224no—
497C23—222no—
498C23—448no—
499C23—444no—
500C23—441no—
501C23—441no—
502C23—442no—
503C23—882no—
504C23—884no—
505C23—882no—
506C23(C22⋊D11)⋊C414yes—
507C23(C22⋊D11)⋊C414yes—
508C23#6693511yescharacteristic
509C23#6693512yes—
510C23#6693511yescharacteristic
511C23#6693912yes—
512C23#6693912yes—
513C23C2×(C2×D11)⋊C414yes—
514C23C2×(C2×D11)⋊C412yes—
515C23C2×(C2×D11)⋊C412yes—
516C23#6699214yes—
517C23#6699214yes—
518C23C22×C4×D1111yescharacteristic
519C23C22×D4411yescharacteristic
520C23C2×D4×D1112yes—
521C23C2×#434112yes—
522C23C22×C22⋊D1111yescharacteristic
523D4—28no—
524D4—28no—
525D4—216no—
526D4—444no—
527D4—444no—
528D4—448no—
529D4—888no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—48no—
535C2×C4—44no—
536C2×C4—88no—
537C2×C4—224no—
538C2×C4—228no—
539C2×C4—224no—
540C2×C4—222no—
541C2×C4—448no—
542C2×C4—444no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—442no—
546C2×C4—448no—
547C2×C4—884no—
548C2×C4—884no—
549C2×C4—888no—
550C2×C4C2×(C2×D11)⋊C414yes—
551C22—24no—
552C22—22no—
553C22—22no—
554C22—24no—
555C22—22no—
556C22—24no—
557C22—44no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—41no—
562C22—42no—
563C22—41no—
564C22—44no—
565C22—44no—
566C22—42no—
567C22—44no—
568C22—44no—
569C22—48no—
570C22—44no—
571C22—82no—
572C22—84no—
573C22—444no—
574C22—448no—
575C22—442no—
576C22—884no—
577C22—882no—
578C22—882no—
579C22#1062257112yes—
580C22#1062257112yes—
581C22#1062257114yes—
582C22C2×(C22⋊D11)⋊C412yes—
583C22C2×#6693511yescharacteristic
584C22C2×#6693911yescharacteristic
585C22C22×(C2×D11)⋊C411yescharacteristic
586C22C2×#6699212yes—
587C4—24no—
588C4—84no—
589C4—444no—
590C4—442no—
591C4—448no—
592C2—22no—
593C2—21no—
594C2—22no—
595C2—21no—
596C2—22no—
597C2—22no—
598C2—24no—
599C2—44no—
600C2—882no—
601C2C2×#1062257111yescharacteristic
602C2#1307801512yes—
subgroupG/H
centerC22C2×#66935
commutatorC23×C11C23×C4
FrattiniC24C23×D11
FittingC22×C11×#99C2
socleC22×C11C2×#120
prime radicalC2×#10623335C2
cosocleC24×C11C24
hypercenterC22×#99D11
hypocenterC11#20960
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
2. C2×#10623329C2semidirect
3. #13071191C2semidirect
4. #13069027C2semidirect
5. #13069022C2semidirect
6. C2×#10622165C2semidirect
7. C22×C11×#99C2semidirect
16. #10623335C4semidirect
30. #10622568C22semidirect
31. #10622556C22semidirect
32. #10622165C22semidirect
52. C22×C22⋊D11C2×C4semidirect
55. C23×Dic11D4semidirect
72. C2×C22⋊Dic11C2×C4semidirect
73. C2×C22⋊Dic11D4semidirect
78. #66990C2×C4semidirect
80. #66988C2×C4semidirect
99. C24×C11C22⋊C4semidirect
114. C23×D11C22×C4semidirect
123. C2×D4×C11C22⋊C4semidirect
132. C22×C4×C11C22⋊C4semidirect
159. C22×Dic11C22×C4semidirect
172. C22⋊Dic11C22×C4semidirect
180. C22×#99D11semidirect
405. C24(C2×D11)⋊C4semidirect
436. C2×D4(C2×D11)⋊C4semidirect
459. C22×C4(C2×D11)⋊C4semidirect
478. C11#20960semidirect

Maximal subgroups

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

subgroupindex
C2×#106233352
C2×#106233292
#130711912
#130690272
#130690222
C2×#106221652
C22×C11×#992
#2096011