Finite Group Databasebeta

← #14660240

Subgroups — #14660240

Order 2816.

1526 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66870C212yesmaximal
2C2×#10622826C211yesmaximal, characteristic
3C2×#10622165C212yesmaximal, complemented
4#13066839C211yesmaximal, characteristic, complemented
5C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
6C24×C4×C11C2211yescharacteristic
7C23×C22⋊D11C2211yescharacteristic
8C22×C11×C22⋊C4C2212yes—
9C22×C42×C11—21no—
10C22×C22⋊Dic11C2211yescharacteristic
11C22×C22⋊Dic11C2212yes—
12C22×(C2×D11)⋊C4C412yescomplemented
13C4×C11×C22⋊C4—24no—
14C2×C11×#95—21no—
15#10622826—22no—
16#10622826—21no—
17#10622826—21no—
18C2×C11⋊#95—22no—
19C2×C11⋊#95C412yescomplemented
20C2×#66870—24no—
21C2×#66870—24no—
22C2×#66870C418yescomplemented
23#10622165—24no—
24C25×C11C2311yescharacteristic
25C24×D11C2×C411yescharacteristic
26C23×C4×C11—22no—
27C23×C4×C11—22no—
28C23×C4×C11—22no—
29C23×C4×C11—44no—
30C23×C4×C11C2×C412yes—
31C23×C4×C11D412yes—
32C23×C4×C11D411yescharacteristic
33C23×C4×C11D411yescharacteristic
34C22×C22⋊D11—22no—
35C22×C22⋊D11—22no—
36C22×C22⋊D11—21no—
37C22×C22⋊D11—21no—
38C22×C22⋊D11—22no—
39C22×C22⋊D11—22no—
40C22×C22⋊D11—22no—
41C22×C22⋊D11C2×C414yes—
42C23×Dic11—22no—
43C23×Dic11C2×C411yescharacteristic
44C23×Dic11C2×C412yes—
45C2×C11×C22⋊C4—22no—
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4—22no—
48C2×C11×C22⋊C4C2×C414yes—
49C2×C11×C22⋊C4D414yes—
50C2×C11×C22⋊C4D414yes—
51C2×C42×C11—24no—
52C2×C42×C11—44no—
53C2×C22⋊Dic11—22no—
54C2×C22⋊Dic11—22no—
55C2×C22⋊Dic11—22no—
56C2×C22⋊Dic11—22no—
57C2×C22⋊Dic11—21no—
58C2×C22⋊Dic11—21no—
59C2×C22⋊Dic11—22no—
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11C2×C414yes—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—44no—
66C11×#95—24no—
67C11⋊#95—22no—
68C11⋊#95—22no—
69C11⋊#95—44no—
70#66870—216no—
71#10960—111nomaximal, Sylow
72C24×C11—42no—
73C24×C11—42no—
74C24×C11C22×C411yescharacteristic
75C24×C11C22×C412yes—
76C24×C11C2×D411yescharacteristic
77C24×C11C2×D411yescharacteristic
78C24×C11C2×D412yes—
79C24×C11C2×D412yes—
80C24×C11#4112yes—
81C24×C11#4112yes—
82C24×C11#4112yes—
83C23×D11—21no—
84C23×D11—21no—
85C23×D11—22no—
86C23×D11—22no—
87C23×D11—42no—
88C23×D11—42no—
89C23×D11C4212yescomplemented
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—24no—
93C22×C4×C11—24no—
94C22×C4×C11—24no—
95C22×C4×C11—21no—
96C22×C4×C11—24no—
97C22×C4×C11—24no—
98C22×C4×C11—24no—
99C22×C4×C11—21no—
100C22×C4×C11—24no—
101C22×C4×C11—24no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11—48no—
106C22×C4×C11—48no—
107C22×C4×C11—44no—
108C22×C4×C11—44no—
109C22×C4×C11C22⋊C412yes—
110C22×C4×C11C22⋊C412yes—
111C2×C22⋊D11—24no—
112C2×C22⋊D11—24no—
113C2×C22⋊D11—24no—
114C2×C22⋊D11—24no—
115C2×C22⋊D11—24no—
116C2×C22⋊D11—24no—
117C2×C22⋊D11—41no—
118C2×C22⋊D11—42no—
119C2×C22⋊D11—42no—
120C2×C22⋊D11—42no—
121C2×C22⋊D11—41no—
122C2×C22⋊D11—42no—
123C2×C22⋊D11—42no—
124C2×C22⋊D11—41no—
125C2×C22⋊D11—42no—
126C2×C22⋊D11—41no—
127C22×Dic11—21no—
128C22×Dic11—22no—
129C22×Dic11—21no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—24no—
133C22×Dic11—24no—
134C22×Dic11—44no—
135C22×Dic11—44no—
136C22×Dic11—42no—
137C22×Dic11—42no—
138C22×Dic11—42no—
139C22×Dic11—42no—
140C22×Dic11C4212yescomplemented
141C11×C22⋊C4—24no—
142C11×C22⋊C4—24no—
143C11×C22⋊C4—24no—
144C11×C22⋊C4C22⋊C418yescomplemented
145C42×C11—48no—
146C22⋊Dic11—24no—
147C22⋊Dic11—24no—
148C22⋊Dic11—42no—
149C22⋊Dic11—42no—
150C22⋊Dic11—41no—
151C22⋊Dic11—42no—
152C22⋊Dic11—41no—
153(C2×D11)⋊C4—44no—
154(C2×D11)⋊C4—44no—
155C22×#99—112no—
156C2×#386—111no—
157C2×C4×C22⋊C4D1111yescharacteristic, complemented
158C2×#342—112no—
159C22⋊#95—111no—
160C23×C11—22no—
161C23×C11—22no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11—22no—
165C23×C11—22no—
166C23×C11—42no—
167C23×C11—42no—
168C23×C11—44no—
169C23×C11—44no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11—44no—
173C23×C11—44no—
174C23×C11C2×C4211yescharacteristic
175C23×C11C2×C22⋊C412yes—
176C23×C11C2×C22⋊C411yescharacteristic
177C23×C11#11711yescharacteristic
178C23×C11#11712yes—
179C23×C11C4×D412yes—
180C23×C11C4×D412yes—
181C23×C11C4×D412yes—
182C23×C11C4×D412yes—
183C23×C11C4×D412yes—
184C23×C11C4×D412yes—
185C23×C11#12011yescharacteristic
186C23×C11#12112yes—
187C23×C11#12112yes—
188C23×C11#12112yes—
189C23×C11#12311yescharacteristic
190C23×C11#12312yes—
191C23×C11#12411yescharacteristic
192C23×C11#12412yes—
193C23×C11#12612yes—
194C23×C11#12711yescharacteristic
195C22×D11—22no—
196C22×D11—24no—
197C22×D11—44no—
198C22×D11—41no—
199C22×D11—42no—
200C22×D11—41no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—44no—
204C22×D11—82no—
205C22×D11—82no—
206C22×D11—84no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—28no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—48no—
216C2×C4×C11—48no—
217C2×C4×C11—44no—
218C2×C4×C11—44no—
219C2×C4×C11—48no—
220C2×C4×C11—48no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11#9914yescomplemented
224C22⋊D11—44no—
225C22⋊D11—44no—
226C22⋊D11—44no—
227C22⋊D11—44no—
228C2×Dic11—24no—
229C2×Dic11—22no—
230C2×Dic11—41no—
231C2×Dic11—42no—
232C2×Dic11—41no—
233C2×Dic11—48no—
234C2×Dic11—44no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—82no—
239C2×Dic11—82no—
240C2×Dic11—84no—
241C2×Dic11—84no—
242C23×D4—111no—
243C24×C4C2×D1111yescharacteristic
244C22×C22⋊C4—112no—
245C22×C22⋊C4—111no—
246C22×C22⋊C4—112no—
247C22×C22⋊C4C2×D1112yes—
248C22×C42—21no—
249C2×#99—118no—
250C2×#99—224no—
251C2×#99—224no—
252#386—222no—
253#386—221no—
254#386—221no—
255C4×C22⋊C4—24no—
256C2×#95—21no—
257C2×#95—112no—
258C2×#95—222no—
259#342—224no—
260C22×C11—21no—
261C22×C11—21no—
262C22×C11—22no—
263C22×C11—22no—
264C22×C11—21no—
265C22×C11—22no—
266C22×C11—22no—
267C22×C11—21no—
268C22×C11—24no—
269C22×C11—24no—
270C22×C11—22no—
271C22×C11—22no—
272C22×C11—24no—
273C22×C11—22no—
274C22×C11—22no—
275C22×C11—24no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11C4×C22⋊C412yes—
285C22×C11C4×C22⋊C411yescharacteristic
286C22×C11#38612yes—
287C22×C11#38611yescharacteristic
288C22×C11#38812yes—
289C22×C11#38812yes—
290C22×C11#38812yes—
291C22×C11#39012yes—
292C22×C11#39011yescharacteristic
293C22×C11C2×#9912yes—
294C22×C11#41012yes—
295C2×D11—42no—
296C2×D11—44no—
297C2×D11—84no—
298C2×D11—81no—
299C2×D11—81no—
300C2×D11—82no—
301C2×D11—84no—
302C4×C11—24no—
303C4×C11—48no—
304C4×C11—42no—
305Dic11—42no—
306Dic11—84no—
307Dic11—82no—
308C25—111no—
309C25C22×D1111yescharacteristic
310C22×D4—114no—
311C22×D4—221no—
312C22×D4—222no—
313C22×D4—222no—
314C22×D4—222no—
315C22×D4—222no—
316C22×D4—221no—
317C22×D4—222no—
318C23×C4—22no—
319C23×C4—22no—
320C23×C4—22no—
321C23×C4—44no—
322C23×C4—111no—
323C23×C4—112no—
324C23×C4—222no—
325C23×C4C4×D1112yes—
326C23×C4D4412yes—
327C23×C4C22⋊D1111yescharacteristic
328C23×C4C22⋊D1111yescharacteristic
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—114no—
333C2×C22⋊C4—222no—
334C2×C22⋊C4—222no—
335C2×C22⋊C4—222no—
336C2×C22⋊C4—222no—
337C2×C22⋊C4—222no—
338C2×C22⋊C4—221no—
339C2×C22⋊C4—222no—
340C2×C22⋊C4—222no—
341C2×C22⋊C4—221no—
342C2×C22⋊C4—222no—
343C2×C22⋊C4—222no—
344C2×C22⋊C4—444no—
345C2×C22⋊C4C4×D1114yes—
346C2×C22⋊C4D4414yes—
347C2×C22⋊C4C22⋊D1114yes—
348C2×C42—24no—
349C2×C42—44no—
350#99—2216no—
351#95—24no—
352#95—222no—
353#95—222no—
354#95—444no—
355C2×C11—22no—
356C2×C11—22no—
357C2×C11—22no—
358C2×C11—22no—
359C2×C11—22no—
360C2×C11—22no—
361C2×C11#143711yescharacteristic
362C2×C11C4×#9912yes—
363C2×C11#189811yescharacteristic
364C2×C11#189911yescharacteristic
365C2×C11#196412yes—
366D11—82no—
367C24—42no—
368C24—42no—
369C24—112no—
370C24—221no—
371C24—221no—
372C24—222no—
373C24—222no—
374C24—442no—
375C24—442no—
376C24C2×C4×D1111yescharacteristic
377C24C2×C4×D1112yes—
378C24C2×D4411yescharacteristic
379C24C2×D4412yes—
380C24#433912yes—
381C24#433912yes—
382C24#433912yes—
383C24C2×C22⋊D1111yescharacteristic
384C24C2×C22⋊D1112yes—
385C2×D4—224no—
386C2×D4—224no—
387C2×D4—224no—
388C2×D4—224no—
389C2×D4—224no—
390C2×D4—224no—
391C2×D4—441no—
392C2×D4—441no—
393C2×D4—442no—
394C2×D4—442no—
395C2×D4—442no—
396C2×D4—441no—
397C2×D4—442no—
398C2×D4—442no—
399C2×D4—442no—
400C2×D4—441no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—21no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—21no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—24no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—48no—
417C22×C4—48no—
418C22×C4—44no—
419C22×C4—44no—
420C22×C4—112no—
421C22×C4—221no—
422C22×C4—222no—
423C22×C4—221no—
424C22×C4—222no—
425C22×C4—224no—
426C22×C4—222no—
427C22×C4—224no—
428C22×C4—444no—
429C22×C4—444no—
430C22×C4—442no—
431C22×C4—442no—
432C22×C4—442no—
433C22×C4—442no—
434C22×C4(C2×D11)⋊C412yes—
435C22×C4(C2×D11)⋊C412yes—
436C22⋊C4—24no—
437C22⋊C4—24no—
438C22⋊C4—24no—
439C22⋊C4—224no—
440C22⋊C4—224no—
441C22⋊C4—444no—
442C22⋊C4—441no—
443C22⋊C4—442no—
444C22⋊C4—441no—
445C22⋊C4—442no—
446C22⋊C4—442no—
447C22⋊C4—444no—
448C22⋊C4(C2×D11)⋊C418yescomplemented
449C42—48no—
450C11#1096011yescharacteristic, complemented, Sylow
451C23—22no—
452C23—22no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—22no—
457C23—42no—
458C23—42no—
459C23—44no—
460C23—44no—
461C23—42no—
462C23—44no—
463C23—44no—
464C23—42no—
465C23—222no—
466C23—224no—
467C23—444no—
468C23—444no—
469C23—441no—
470C23—442no—
471C23—442no—
472C23—441no—
473C23—442no—
474C23—882no—
475C23—882no—
476C23—884no—
477C23C42×D1111yescharacteristic
478C23#6692511yescharacteristic
479C23#6692512yes—
480C23C4×D4412yes—
481C23C4×D4412yes—
482C23C4×D4412yes—
483C23#6692711yescharacteristic
484C23#6692811yescharacteristic
485C23#6692812yes—
486C23#6692912yes—
487C23C2×(C2×D11)⋊C412yes—
488C23C2×(C2×D11)⋊C411yescharacteristic
489C23C4×C22⋊D1112yes—
490C23C4×C22⋊D1112yes—
491C23C4×C22⋊D1112yes—
492C23#6698211yescharacteristic
493C23#6698212yes—
494C23#6698312yes—
495C23#6698312yes—
496C23#6698312yes—
497C23#6700611yescharacteristic
498D4—444no—
499D4—444no—
500D4—444no—
501D4—444no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—28no—
509C2×C4—22no—
510C2×C4—48no—
511C2×C4—48no—
512C2×C4—44no—
513C2×C4—44no—
514C2×C4—48no—
515C2×C4—48no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—224no—
519C2×C4—222no—
520C2×C4—441no—
521C2×C4—442no—
522C2×C4—441no—
523C2×C4—448no—
524C2×C4—444no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—442no—
528C2×C4—882no—
529C2×C4—882no—
530C2×C4—884no—
531C2×C4—884no—
532C2×C4#6687014yescomplemented
533C22—21no—
534C22—21no—
535C22—22no—
536C22—22no—
537C22—21no—
538C22—22no—
539C22—22no—
540C22—21no—
541C22—24no—
542C22—24no—
543C22—22no—
544C22—22no—
545C22—24no—
546C22—22no—
547C22—24no—
548C22—22no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—442no—
558C22—444no—
559C22—884no—
560C22—884no—
561C22—881no—
562C22—881no—
563C22—882no—
564C22C4×(C2×D11)⋊C412yes—
565C22C4×(C2×D11)⋊C411yescharacteristic
566C22#1062255212yes—
567C22#1062255211yescharacteristic
568C22#1062255312yes—
569C22#1062255312yes—
570C22#1062255312yes—
571C22C2×#6687012yes—
572C22#1062261912yes—
573C22#1062282612yes—
574C22#1062282611yescharacteristic
575C4—24no—
576C4—48no—
577C4—42no—
578C4—442no—
579C4—884no—
580C4—882no—
581C2—22no—
582C2—22no—
583C2—22no—
584C2—22no—
585C2—22no—
586C2—22no—
587C2—882no—
588C2#1306685411yescharacteristic
589C2C4×#6687012yes—
590C2#1306906911yescharacteristic
591C2#1306907411yescharacteristic
592C2#1306945212yes—
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC23×C11C2×C42
FrattiniC25C22×D11
FittingC2×C4×C11×C22⋊C4C2
socleC23×C11C2×C22⋊C4
prime radicalC23×C22⋊D11C22
cosocleC25×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#10960
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#10622165C2semidirect
4. #13066839C2semidirect
5. C2×C4×C11×C22⋊C4C2semidirect
12. C22×(C2×D11)⋊C4C4semidirect
19. C2×C11⋊#95C4semidirect
22. C2×#66870C4semidirect
89. C23×D11C42semidirect
140. C22×Dic11C42semidirect
144. C11×C22⋊C4C22⋊C4semidirect
157. C2×C4×C22⋊C4D11semidirect
223. C2×C4×C11#99semidirect
448. C22⋊C4(C2×D11)⋊C4semidirect
450. C11#10960semidirect
532. C2×C4#66870semidirect

Maximal subgroups

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

subgroupindex
C22×#668702
C2×#106228262
C2×#106221652
#130668392
C2×C4×C11×C22⋊C42
#1096011