Finite Group Databasebeta

← #14760119

Subgroups — #14760119

Order 2816.

1056 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622432C211yesmaximal, characteristic
2C2×#10622482C211yesmaximal, characteristic
3C2×#10622401C211yesmaximal, characteristic, complemented
4#13071330C211yesmaximal, characteristic, complemented
5#13070976C211yesmaximal, characteristic, complemented
6#13069545C211yesmaximal, characteristic, complemented
7#13069376C211yesmaximal, characteristic, complemented
8#13069243C211yesmaximal, characteristic, complemented
9#13068963C211yesmaximal, characteristic
10#13068953C211yesmaximal, characteristic, complemented
11#13068615C211yesmaximal, characteristic, complemented
12#13068472C211yesmaximal, characteristic, complemented
13#13068448C211yesmaximal, characteristic, complemented
14#13068430C211yesmaximal, characteristic, complemented
15C11×#1927C211yesmaximal, characteristic, complemented
16C2×#67000C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C22×#4325C2211yescharacteristic
19C22×D88C2211yescharacteristic
20C2×#66946C2211yescharacteristic
21C2×#66946C2211yescharacteristic
22C2×#66946C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C11×#391C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66879C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622589C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43#10622552C2211yescharacteristic
44C4×(C2×D11)⋊C4—21no—
45C4×(C2×D11)⋊C4—21no—
46#10622545C2211yescharacteristic
47#10622482—24no—
48#10622432C418yescomplemented
49#10622401—24no—
50#10622282—21no—
51#10622282—21no—
52#10622281—21no—
53#10622281—21no—
54#10622279—21no—
55D11×#95—21no—
56C11×#340C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×C4×D11—21no—
67C22×C4×D11—21no—
68C22×C4×D11—21no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76#67000—22no—
77#67000C2×C414yescomplemented
78Q8×Dic11—22no—
79Q8×Dic11—22no—
80C2×#4325—22no—
81C2×#4325—22no—
82C2×#4325C2×C414yescomplemented
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11C2311yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C2×D88—22no—
104C2×D88—22no—
105C2×D88C2×C414yes—
106#66946—22no—
107#66946—22no—
108#66946—22no—
109#66946—22no—
110#66946C2×C414yescomplemented
111#66946D414yes—
112C4×D44—22no—
113C4×D44—22no—
114C11×#106—22no—
115C11×#103—22no—
116C11×#103C2×C414yescomplemented
117C11×#95—21no—
118C11×#95—21no—
119C11×#95—21no—
120#66899—22no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95D411yescharacteristic
124C11⋊#95D411yescharacteristic
125C11⋊#95D411yescharacteristic
126C11⋊#95D411yescharacteristic
127#66885—22no—
128#66885—22no—
129#66879—22no—
130Dic11⋊C8—22no—
131Dic11⋊C8C2×C414yescomplemented
132C8×Dic11—22no—
133#66873—22no—
134#66873—22no—
135#66873C2×C414yescomplemented
136#66872—22no—
137#21510—111nomaximal, Sylow
138C23×D11—21no—
139C23×D11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11C22×C412yes—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44C22×C412yes—
168C2×D44C22×C412yes—
169C2×D44C2×D412yes—
170C2×D44#4112yes—
171C2×C4×D11—24no—
172C2×C4×D11—24no—
173C2×C4×D11—24no—
174C2×C4×D11—42no—
175C2×C4×D11—81no—
176C2×C4×D11—81no—
177C2×C4×D11—81no—
178C2×C4×D11—81no—
179C2×C4×D11—81no—
180C2×C4×D11—81no—
181C2×C4×D11—81no—
182C2×C4×D11—81no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11C22×C412yes—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4C22×C412yes—
194C11×C4⋊C4C2×D412yes—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11—81no—
198#4325—28no—
199(C2×D11)⋊C4—24no—
200(C2×D11)⋊C4—24no—
201(C2×D11)⋊C4—24no—
202(C2×D11)⋊C4—24no—
203(C2×D11)⋊C4—24no—
204(C2×D11)⋊C4—42no—
205(C2×D11)⋊C4—81no—
206(C2×D11)⋊C4—81no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—42no—
211C4⋊Dic11#4112yes—
212Dic11⋊C4—81no—
213Dic11⋊C4—81no—
214C4×Dic11—42no—
215C4×Dic11—81no—
216C4×Dic11—81no—
217C4×Dic11C22×C412yes—
218C4×Dic11C2×D412yes—
219C4×Dic11#4112yes—
220C4×Dic11#4112yes—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8C22×C412yes—
227D88—28no—
228C2×#463—111no—
229C2×#442—111no—
230C2×C4×SD16—111no—
231#2326—111no—
232#2275—111no—
233#1983—111no—
234#1948—111no—
235#1927D1111yescharacteristic, complemented
236#1926—111no—
237#1879—111no—
238#1877—111no—
239#1802—111no—
240#1768—111no—
241#1763—111no—
242C4×#102—111no—
243C23×C11C22×D411yescharacteristic
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—22no—
247C22×D11—22no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11—41no—
258Q8×C11—22no—
259Q8×C11—22no—
260Q8×C11—41no—
261Q8×C11—41no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11C23×C411yescharacteristic
281C2×C4×C11C22×D411yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—22no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11C4×D412yes—
301C2×Dic11C4×D412yes—
302C2×Dic11#12112yes—
303C2×Dic11#12112yes—
304D44—22no—
305D44—22no—
306D44—22no—
307D44—22no—
308D44—22no—
309D44—41no—
310D44—41no—
311D44C4×D414yes—
312C4×D11—84no—
313C4×D11—84no—
314C4×D11—84no—
315C4×D11—84no—
316C8×C11—22no—
317C8×C11—41no—
318C11⋊C8—22no—
319C11⋊C8—41no—
320C22×SD16—111no—
321C22×D8—111no—
322C2×#124—111no—
323C2×C4×Q8—111no—
324C2×C4×D4—111no—
325C2×C4×D4—111no—
326C2×C4×D4—111no—
327C2×C4×D4—111no—
328#463—118no—
329#442—224no—
330C4×SD16—224no—
331C2×#106—111no—
332C2×#106C2×D1111yescharacteristic
333C2×C4⋊C8—111no—
334C2×C4⋊C8—111no—
335C2×#103—111no—
336C2×#103C2×D1111yescharacteristic
337C2×#103C2×D1111yescharacteristic
338C2×#102—111no—
339C2×#102—111no—
340C2×#102—111no—
341C2×#102—111no—
342C2×#102—111no—
343C2×#97—111no—
344C2×C4×C8—111no—
345#391C2×D1111yescharacteristic
346#390—111no—
347#388—221no—
348#388—221no—
349#385—221no—
350#385—221no—
351#384—111no—
352C4×C4⋊C4—111no—
353C4×C4⋊C4—111no—
354C4×C4⋊C4C2×D1111yescharacteristic
355C4×C22⋊C4—221no—
356C4×C22⋊C4—221no—
357C4×C22⋊C4—221no—
358#376—111no—
359C2×#95—221no—
360#340—111no—
361#340—111no—
362#340—111no—
363#340C2×D1111yescharacteristic
364#336—111no—
365#336C2×D1111yescharacteristic
366C22×C11C2×C4×D411yescharacteristic
367C22×C11C2×#12111yescharacteristic
368C22×C11#52511yescharacteristic
369C22×C11#57611yescharacteristic
370C22×C11#57711yescharacteristic
371C22×C11#57711yescharacteristic
372C22×C11#57711yescharacteristic
373C2×D11—24no—
374C2×D11—42no—
375C2×D11—42no—
376C2×D11—42no—
377C2×D11—42no—
378C2×D11—42no—
379C2×D11—42no—
380C2×D11—42no—
381C2×D11—42no—
382C2×D11—42no—
383C2×D11—81no—
384C2×D11—81no—
385C2×D11—81no—
386C2×D11—81no—
387C4×C11—41no—
388C4×C11—41no—
389C4×C11—42no—
390C4×C11—42no—
391C4×C11—42no—
392C4×C11—81no—
393C4×C11C2×C4×D411yescharacteristic
394C4×C11C4×#4111yescharacteristic
395C4×C11#52911yescharacteristic
396C4×C11#53211yescharacteristic
397Dic11—22no—
398Dic11—22no—
399Dic11—22no—
400Dic11—22no—
401Dic11—42no—
402Dic11—81no—
403C22×Q8C22×D1111yescharacteristic
404C22×D4—111no—
405C22×D4—111no—
406C23×C4—221no—
407C23×C4—221no—
408C23×C4—221no—
409C23×C4—221no—
410C2×SD16—114no—
411C2×SD16—222no—
412C2×SD16—222no—
413C2×D8—114no—
414C2×D8—222no—
415C2×D8—222no—
416C22×C8—111no—
417C22×C8—111no—
418C22×C8C22×D1111yescharacteristic
419C22×C8C22×D1111yescharacteristic
420#124—114no—
421#124—222no—
422C4×Q8—222no—
423C4×Q8—222no—
424C4×D4—114no—
425C4×D4—114no—
426C4×D4—222no—
427C4×D4—222no—
428C4×D4—222no—
429C4×D4—222no—
430C4×D4—222no—
431C4×D4—222no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4C22×D1111yescharacteristic
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C22⋊C4—221no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C42—21no—
449C2×C42—111no—
450C2×C42—111no—
451C2×C42—221no—
452C2×C42—221no—
453C2×C42—221no—
454C2×C42C22×D1111yescharacteristic
455#106—22no—
456#106—222no—
457C4⋊C8—114no—
458C4⋊C8—222no—
459#103—22no—
460#103—222no—
461#103C4×D1114yescomplemented
462#102—114no—
463#102—222no—
464#102—222no—
465#102—222no—
466#102—222no—
467#97—222no—
468C4×C8—222no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—111no—
473#95—111no—
474#95—111no—
475#95—111no—
476#95—221no—
477#95—221no—
478C2×C11C4×#12111yescharacteristic
479C2×C11#294611yescharacteristic
480C2×C11#295211yescharacteristic
481C2×C11#304211yescharacteristic
482C2×C11#304511yescharacteristic
483C2×C11#311811yescharacteristic
484C2×C11#312511yescharacteristic
485D11—44no—
486D11—82no—
487C24—221no—
488C24—221no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8C2×C4×D1112yes—
495C2×D4—112no—
496C2×D4—112no—
497C2×D4—112no—
498C2×D4—112no—
499C2×D4—221no—
500C2×D4—221no—
501C2×D4—221no—
502C2×D4—221no—
503C2×D4—221no—
504C2×D4—221no—
505C2×D4—221no—
506C2×D4—221no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—111no—
512C22×C4—111no—
513C22×C4—111no—
514C22×C4—111no—
515C22×C4—224no—
516C22×C4—224no—
517C22×C4—224no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—442no—
521C22×C4—881no—
522C22×C4—881no—
523C22×C4—881no—
524C22×C4—881no—
525C22×C4—881no—
526C22×C4—881no—
527C22×C4—881no—
528C22×C4—881no—
529C22×C4D4×D1111yescharacteristic
530C22×C4D4×D1111yescharacteristic
531C22×C4C23×D1111yescharacteristic
532SD16—228no—
533D8—228no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—112no—
540C2×C8—221no—
541C2×C8—221no—
542C2×C8—221no—
543C2×C8—221no—
544C2×C8—221no—
545C2×C8C2×C4×D1112yes—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—112no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—442no—
555C4⋊C4—881no—
556C4⋊C4—881no—
557C4⋊C4C2×C4×D1112yes—
558C4⋊C4D4×D1112yes—
559C22⋊C4—224no—
560C22⋊C4—224no—
561C22⋊C4—224no—
562C22⋊C4—224no—
563C22⋊C4—224no—
564C22⋊C4—442no—
565C22⋊C4—881no—
566C22⋊C4—881no—
567C42—21no—
568C42—21no—
569C42—81no—
570C42—112no—
571C42—112no—
572C42—112no—
573C42—112no—
574C42—442no—
575C42—881no—
576C42—881no—
577C11#2151011yescharacteristic, complemented, Sylow
578C23—222no—
579C23—222no—
580C23—222no—
581C23—222no—
582C23—441no—
583C23—441no—
584C23—441no—
585C23—441no—
586C23—441no—
587C23—441no—
588C23—441no—
589C23—441no—
590C23—441no—
591C23—441no—
592C23C2×D4×D1111yescharacteristic
593Q8—22no—
594Q8—22no—
595Q8—41no—
596Q8—41no—
597D4—114no—
598D4—222no—
599D4—222no—
600D4—222no—
601D4—222no—
602D4—222no—
603D4—441no—
604D4—441no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—112no—
624C2×C4—112no—
625C2×C4—112no—
626C2×C4—112no—
627C2×C4—221no—
628C2×C4—221no—
629C2×C4—221no—
630C2×C4—221no—
631C2×C4—221no—
632C2×C4—221no—
633C2×C4—221no—
634C2×C4—221no—
635C2×C4—222no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4—441no—
641C2×C4—884no—
642C2×C4—884no—
643C2×C4—884no—
644C2×C4—884no—
645C2×C4C22×C4×D1111yescharacteristic
646C2×C4C2×D4×D1111yescharacteristic
647C2×C4#41×D1111yescharacteristic
648C2×C4#41×D1111yescharacteristic
649C2×C4#41×D1111yescharacteristic
650C2×C4#41×D1111yescharacteristic
651C8—22no—
652C8—41no—
653C8—222no—
654C8—441no—
655C22—224no—
656C22—442no—
657C22—442no—
658C22—442no—
659C22—442no—
660C22—442no—
661C22—442no—
662C22—442no—
663C22—442no—
664C22—442no—
665C22—881no—
666C22—881no—
667C22—881no—
668C22—881no—
669C22C4×D4×D1111yescharacteristic
670C22D11×#12111yescharacteristic
671C22#1062318711yescharacteristic
672C22#1062329311yescharacteristic
673C22#1062330011yescharacteristic
674C22#1062330911yescharacteristic
675C22#1062330911yescharacteristic
676C4—41no—
677C4—42no—
678C4—41no—
679C4—42no—
680C4—42no—
681C4—81no—
682C4—222no—
683C4—222no—
684C4—222no—
685C4—222no—
686C4—442no—
687C4—881no—
688C4#1062305311yescharacteristic
689C4C4×D4×D1111yescharacteristic
690C4#1062319911yescharacteristic
691C4#1062323711yescharacteristic
692C2—444no—
693C2—882no—
694C2#1307112811yescharacteristic
695C2#1307744311yescharacteristic
696C2#1307749611yescharacteristic
697C2#1307812311yescharacteristic
698C2#1307815811yescharacteristic
699C2#1307880311yescharacteristic
700C2#1307888811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1927C2
socleC23×C11C22×D4
prime radicalC22×D88C22
cosocleC22×C4×C11C24
hypercenter#1927D11
hypocenterC11#21510
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1927

Complements

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

NH ≅ G/Ntype
3. C2×#10622401C2semidirect
4. #13071330C2semidirect
5. #13070976C2semidirect
6. #13069545C2semidirect
7. #13069376C2semidirect
8. #13069243C2semidirect
10. #13068953C2semidirect
11. #13068615C2semidirect
12. #13068472C2semidirect
13. #13068448C2semidirect
14. #13068430C2semidirect
15. C11×#1927C2semidirect
48. #10622432C4semidirect
77. #67000C2×C4semidirect
82. C2×#4325C2×C4semidirect
110. #66946C2×C4semidirect
116. C11×#103C2×C4semidirect
131. Dic11⋊C8C2×C4semidirect
135. #66873C2×C4semidirect
235. #1927D11semidirect
461. #103C4×D11semidirect
577. C11#21510semidirect

Maximal subgroups

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

subgroupindex
C2×#106224322
C2×#106224822
C2×#106224012
#130713302
#130709762
#130695452
#130693762
#130692432
#130689632
#130689532
#130686152
#130684722
#130684482
#130684302
C11×#19272
#2151011