Finite Group Databasebeta

← #14753898

Subgroups — #14753898

Order 2816.

1336 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×Dic11C211yesmaximal, characteristic
2#13077245C211yesmaximal, characteristic, complemented
3#13071010C211yesmaximal, characteristic, complemented
4#13068716C211yesmaximal, characteristic, complemented
5#13068713C211yesmaximal, characteristic, complemented
6#13068634C214yesmaximal, complemented
7#13068560C211yesmaximal, characteristic
8#13068428C214yesmaximal, complemented
9C11×#1789C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11#41×Dic11—21no—
12#41×Dic11—21no—
13#41×Dic11—21no—
14#41×Dic11—21no—
15#41×Dic11C412yescomplemented
16#41×Dic11C412yescomplemented
17#41×Dic11C2212yes—
18#41×Dic11C2212yes—
19C2×Q8×Dic11C411yescharacteristic, complemented
20C2×Q8×Dic11C411yescharacteristic, complemented
21C2×D4×Dic11—21no—
22C2×D4×Dic11—21no—
23C2×D4×Dic11C411yescharacteristic, complemented
24C2×D4×Dic11C411yescharacteristic, complemented
25C2×#66979—21no—
26C2×#66979C2211yescharacteristic
27C22×C4×Dic11—21no—
28C22×C4×Dic11C2211yescharacteristic
29C2×C11×#104C2214yes—
30C11×#407C2211yescharacteristic
31C4×C11×C22⋊C4C2211yescharacteristic
32C2×#66901C2214yes—
33C4×C22⋊Dic11C2211yescharacteristic
34#10622820C2211yescharacteristic
35#10622731C2212yescomplemented
36M16×Dic11C2212yescomplemented
37#10622556—21no—
38#10622555—21no—
39#10622545C2212yescomplemented
40C4×Dic11⋊C4C2212yescomplemented
41#10622332—21no—
42#10622332—21no—
43#10622331—21no—
44#10622331—21no—
45#10622264—21no—
46#10622263—21no—
47#10622193C2214yescomplemented
48#10622161C2214yescomplemented
49C2×C11×#41—28no—
50C2×C11×#41—21no—
51C2×C11×#41—21no—
52C2×C11×#41C2×C412yes—
53C2×C11×#41C2312yes—
54C22×Q8×C11C2×C411yescharacteristic
55C22×D4×C11—21no—
56C22×D4×C11C2×C411yescharacteristic
57C23×C4×C11—21no—
58C23×C4×C11C2311yescharacteristic
59C23×Dic11—21no—
60C23×Dic11—21no—
61C23×Dic11D411yescharacteristic
62C23×Dic11D411yescharacteristic
63C2×C11×M16C2312yes—
64C2×C11×C22⋊C4—21no—
65C2×C42×C11C2312yes—
66C2×C22⋊Dic11—21no—
67C2×C22⋊Dic11—21no—
68C2×C22⋊Dic11—21no—
69C2×C22⋊Dic11—21no—
70Q8×Dic11—21no—
71Q8×Dic11—21no—
72Q8×Dic11—21no—
73Q8×Dic11—21no—
74Q8×Dic11C2×C412yes—
75Q8×Dic11C2×C412yes—
76Q8×Dic11C2×C412yes—
77Q8×Dic11C2×C412yes—
78D4×Dic11—22no—
79D4×Dic11—22no—
80D4×Dic11—22no—
81D4×Dic11—22no—
82D4×Dic11—22no—
83D4×Dic11—22no—
84D4×Dic11—22no—
85D4×Dic11—22no—
86D4×Dic11—21no—
87D4×Dic11—21no—
88D4×Dic11—21no—
89D4×Dic11—21no—
90D4×Dic11C2×C412yes—
91D4×Dic11C2×C412yes—
92D4×Dic11C2×C412yes—
93D4×Dic11C2×C412yes—
94#66979—21no—
95#66979—21no—
96#66979—22no—
97#66979—22no—
98#66979—22no—
99#66979—22no—
100#66979C2×C412yes—
101#66979C2312yes—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11C2×C411yescharacteristic
105C2×C4⋊Dic11C2×C411yescharacteristic
106C2×Dic11⋊C4—22no—
107C2×C4×Dic11—21no—
108C2×C4×Dic11—21no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11—22no—
111C2×C4×Dic11—22no—
112C2×C4×Dic11—22no—
113C2×C4×Dic11—22no—
114C2×C4×Dic11C2×C411yescharacteristic
115C2×C4×Dic11C2×C411yescharacteristic
116C2×C4×Dic11C2×C411yescharacteristic
117C2×C4×Dic11C2×C411yescharacteristic
118C2×C4×Dic11D411yescharacteristic
119C2×C4×Dic11D411yescharacteristic
120C2×C4×Dic11D411yescharacteristic
121C2×C4×Dic11D411yescharacteristic
122C2×C4×Dic11D411yescharacteristic
123C2×C4×Dic11D411yescharacteristic
124C2×C4×Dic11C2312yes—
125C2×C4×Dic11C2311yescharacteristic
126C2×C4×Dic11C2311yescharacteristic
127C2×#4318C2312yes—
128C11×#104—28no—
129C11×C22⋊C8—21no—
130C11×C22⋊C8—21no—
131C11×#95—21no—
132#66901—28no—
133C11⋊#95—21no—
134C11⋊#95—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C22⋊(C11⋊C8)—21no—
138C22⋊(C11⋊C8)—21no—
139#66879—22no—
140Dic11⋊C8—22no—
141Dic11⋊C8—22no—
142C8×Dic11—22no—
143#20748—111nomaximal, Sylow
144C24×C11—21no—
145C24×C11C2×D411yescharacteristic
146C11×#41—28no—
147C11×#41—28no—
148C11×#41—24no—
149C11×#41—24no—
150C11×#41—24no—
151C11×#41#4118yes—
152C2×Q8×C11—24no—
153C2×Q8×C11—21no—
154C2×Q8×C11C22×C412yes—
155C2×D4×C11—28no—
156C2×D4×C11—22no—
157C2×D4×C11—22no—
158C2×D4×C11—24no—
159C2×D4×C11—21no—
160C2×D4×C11C22×C412yes—
161C22×C4×C11—28no—
162C22×C4×C11—21no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—24no—
166C22×C4×C11—22no—
167C22×C4×C11C22×C411yescharacteristic
168C22×C4×C11C22×C411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2×D411yescharacteristic
172C22×C4×C11C2411yescharacteristic
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—22no—
180C22×Dic11—42no—
181C22×Dic11—42no—
182C22×Dic11—44no—
183C22×Dic11—44no—
184C22×Dic11C22⋊C411yescharacteristic
185C22×Dic11C22⋊C411yescharacteristic
186C22×Dic11C22⋊C411yescharacteristic
187C22×Dic11C22⋊C411yescharacteristic
188C22×Dic11C22⋊C411yescharacteristic
189C22×Dic11C22⋊C411yescharacteristic
190C22×Dic11C22⋊C411yescharacteristic
191C22×Dic11C22⋊C411yescharacteristic
192C22×Dic11C2×D411yescharacteristic
193C22×Dic11C2×D411yescharacteristic
194C22×Dic11C2×D411yescharacteristic
195C22×Dic11C2×D411yescharacteristic
196C11×M16—24no—
197C2×C8×C11—22no—
198C11×C22⋊C4—42no—
199C42×C11—24no—
200C22⋊Dic11—22no—
201C22⋊Dic11—22no—
202C22⋊Dic11—22no—
203C22⋊Dic11—22no—
204C22⋊Dic11—22no—
205C22⋊Dic11—22no—
206C22⋊Dic11—42no—
207C4⋊Dic11—22no—
208C4⋊Dic11—22no—
209C4⋊Dic11—22no—
210C4⋊Dic11—22no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11C22×C412yes—
214C4⋊Dic11C22×C412yes—
215Dic11⋊C4—44no—
216C4×Dic11—22no—
217C4×Dic11—22no—
218C4×Dic11—22no—
219C4×Dic11—22no—
220C4×Dic11—22no—
221C4×Dic11—22no—
222C4×Dic11—24no—
223C4×Dic11C22⋊C411yescharacteristic
224C4×Dic11C22⋊C411yescharacteristic
225C4×Dic11C22⋊C411yescharacteristic
226C4×Dic11C22⋊C411yescharacteristic
227C4×Dic11C22⋊C411yescharacteristic
228C4×Dic11C22⋊C411yescharacteristic
229C4×Dic11C22⋊C411yescharacteristic
230C4×Dic11C22⋊C411yescharacteristic
231C4×Dic11C22×C411yescharacteristic
232C4×Dic11C22×C411yescharacteristic
233C4×Dic11C22×C411yescharacteristic
234C4×Dic11C22×C411yescharacteristic
235C4×Dic11C2×D411yescharacteristic
236C4×Dic11C2×D411yescharacteristic
237C4×Dic11C2×D411yescharacteristic
238C4×Dic11C2×D411yescharacteristic
239#4318—24no—
240C2×C11⋊C8—22no—
241C2×C4×#41—111no—
242#2920—111no—
243#2283—111no—
244#1826—111no—
245#1826—111no—
246#1806—114no—
247#1789—111no—
248#1789D1111yescharacteristic
249#1759—114no—
250C23×C11—24no—
251C23×C11—22no—
252C23×C11—22no—
253C23×C11—22no—
254C23×C11—41no—
255C23×C11—42no—
256C23×C11—42no—
257C23×C11C2×C22⋊C411yescharacteristic
258C23×C11C2×C22⋊C411yescharacteristic
259C23×C11C22×D411yescharacteristic
260Q8×C11—24no—
261Q8×C11—22no—
262Q8×C11#11714yes—
263D4×C11—28no—
264D4×C11—24no—
265D4×C11—28no—
266D4×C11—22no—
267D4×C11#11714yes—
268C2×C4×C11—24no—
269C2×C4×C11—28no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—28no—
276C2×C4×C11—22no—
277C2×C4×C11—42no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11C2×C22⋊C411yescharacteristic
281C2×C4×C11C2×C22⋊C411yescharacteristic
282C2×C4×C11C23×C411yescharacteristic
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C2×#4114yes—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—22no—
291C2×Dic11—22no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—44no—
300C2×Dic11—44no—
301C2×Dic11—44no—
302C2×Dic11—42no—
303C2×Dic11—42no—
304C2×Dic11—44no—
305C2×Dic11—42no—
306C2×Dic11—42no—
307C2×Dic11—42no—
308C2×Dic11C2×C22⋊C411yescharacteristic
309C2×Dic11C2×C22⋊C411yescharacteristic
310C2×Dic11C2×C22⋊C411yescharacteristic
311C2×Dic11C2×C22⋊C411yescharacteristic
312C2×Dic11C2×C22⋊C411yescharacteristic
313C2×Dic11C2×C22⋊C411yescharacteristic
314C2×Dic11C2×C22⋊C411yescharacteristic
315C2×Dic11C2×C22⋊C411yescharacteristic
316C8×C11—42no—
317C11⋊C8—42no—
318C22×#41C2×D1111yescharacteristic
319C4×#41—112no—
320C4×#41—112no—
321C4×#41—112no—
322C4×#41—112no—
323C4×#41—221no—
324C4×#41—221no—
325C4×#41—221no—
326C4×#41—221no—
327C2×C4×Q8—111no—
328C2×C4×Q8—111no—
329C2×C4×D4—111no—
330C2×C4×D4—111no—
331C2×C4×D4—221no—
332C2×C4×D4—221no—
333C2×#117—111no—
334C2×#117—221no—
335C22×C42—111no—
336C22×C42—221no—
337#432—221no—
338#432—221no—
339#431—221no—
340#431—221no—
341#423—112no—
342C2×#104—114no—
343C2×#104C2×D1114yes—
344#407—111no—
345#407C2×D1111yescharacteristic
346C4×M16—112no—
347#383—221no—
348#382—221no—
349#381—221no—
350#380—221no—
351C4×C4⋊C4—112no—
352C4×C22⋊C4—111no—
353C4×C22⋊C4C2×D1111yescharacteristic
354#376—112no—
355#339—114no—
356#339—114no—
357C22×C11—21no—
358C22×C11—21no—
359C22×C11—21no—
360C22×C11—21no—
361C22×C11—21no—
362C22×C11—21no—
363C22×C11—21no—
364C22×C11—24no—
365C22×C11—44no—
366C22×C11—48no—
367C22×C11—42no—
368C22×C11—42no—
369C22×C11#42112yes—
370C22×C11C22×C22⋊C411yescharacteristic
371C22×C11#52512yes—
372C4×C11—21no—
373C4×C11—24no—
374C4×C11—21no—
375C4×C11—82no—
376C4×C11C2×#11712yes—
377C4×C11#52512yes—
378Dic11—21no—
379Dic11—21no—
380Dic11—21no—
381Dic11—21no—
382Dic11—21no—
383Dic11—21no—
384Dic11—21no—
385Dic11—42no—
386Dic11—42no—
387Dic11—82no—
388Dic11#42112yes—
389C2×#41—28no—
390C2×#41—21no—
391C2×#41—21no—
392C2×#41C4×D1112yes—
393C2×#41C22×D1112yes—
394C22×Q8C4×D1111yescharacteristic
395C22×D4—21no—
396C22×D4C4×D1111yescharacteristic
397C23×C4—21no—
398C23×C4—111no—
399C23×C4—111no—
400C23×C4—221no—
401C23×C4—221no—
402C23×C4C22×D1111yescharacteristic
403C2×M16—112no—
404C2×M16C22×D1112yes—
405C4×Q8—112no—
406C4×Q8—112no—
407C4×Q8—112no—
408C4×Q8—112no—
409C4×Q8—221no—
410C4×Q8—221no—
411C4×Q8—221no—
412C4×Q8—221no—
413C4×D4—112no—
414C4×D4—112no—
415C4×D4—112no—
416C4×D4—112no—
417C4×D4—221no—
418C4×D4—221no—
419C4×D4—221no—
420C4×D4—221no—
421C4×D4—222no—
422C4×D4—222no—
423C4×D4—222no—
424C4×D4—222no—
425C4×D4—222no—
426C4×D4—222no—
427C4×D4—222no—
428C4×D4—222no—
429#117—112no—
430#117—112no—
431#117—222no—
432#117—222no—
433#117—222no—
434#117—222no—
435#117—221no—
436#117—221no—
437C2×C4⋊C4—111no—
438C2×C4⋊C4—111no—
439C2×C4⋊C4—221no—
440C2×C4⋊C4—221no—
441C2×C4⋊C4—222no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C42—111no—
448C2×C42—111no—
449C2×C42—111no—
450C2×C42—111no—
451C2×C42—111no—
452C2×C42—111no—
453C2×C42—111no—
454C2×C42—111no—
455C2×C42—111no—
456C2×C42—111no—
457C2×C42—111no—
458C2×C42—111no—
459C2×C42—112no—
460C2×C42—222no—
461C2×C42—222no—
462C2×C42—222no—
463C2×C42—222no—
464C2×C42—221no—
465C2×C42—221no—
466C2×C42—221no—
467C2×C42C22×D1112yes—
468C4⋊C8—222no—
469C4⋊C8—222no—
470#104—28no—
471#104—228no—
472C22⋊C8—21no—
473C22⋊C8—21no—
474C22⋊C8—221no—
475C22⋊C8—221no—
476#97—222no—
477C4×C8—222no—
478#95—21no—
479#95—222no—
480#95—222no—
481#95—222no—
482#95—221no—
483C2×C11—22no—
484C2×C11—22no—
485C2×C11—41no—
486C2×C11—44no—
487C2×C11#228011yescharacteristic
488C2×C11C2×#42111yescharacteristic
489C2×C11C2×#42111yescharacteristic
490C24—21no—
491C24D4×D1111yescharacteristic
492#41—28no—
493#41—28no—
494#41—24no—
495#41—24no—
496#41—24no—
497#41#434118yes—
498C2×Q8—24no—
499C2×Q8—21no—
500C2×Q8C2×C4×D1112yes—
501C2×D4—28no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—24no—
505C2×D4—21no—
506C2×D4C2×C4×D1112yes—
507C22×C4—28no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—111no—
514C22×C4—111no—
515C22×C4—111no—
516C22×C4—111no—
517C22×C4—111no—
518C22×C4—111no—
519C22×C4—111no—
520C22×C4—111no—
521C22×C4—111no—
522C22×C4—111no—
523C22×C4—111no—
524C22×C4—111no—
525C22×C4—222no—
526C22×C4—222no—
527C22×C4—222no—
528C22×C4—222no—
529C22×C4—221no—
530C22×C4—221no—
531C22×C4—222no—
532C22×C4—442no—
533C22×C4—442no—
534C22×C4—444no—
535C22×C4—444no—
536C22×C4C2×C4×D1111yescharacteristic
537C22×C4C2×C4×D1111yescharacteristic
538C22×C4D4×D1111yescharacteristic
539C22×C4D4×D1111yescharacteristic
540C22×C4D4×D1111yescharacteristic
541C22×C4C23×D1111yescharacteristic
542M16—24no—
543M16—224no—
544C2×C8—22no—
545C2×C8—222no—
546C4⋊C4—112no—
547C4⋊C4—112no—
548C4⋊C4—222no—
549C4⋊C4—222no—
550C4⋊C4—222no—
551C4⋊C4—222no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—444no—
555C22⋊C4—42no—
556C22⋊C4—222no—
557C22⋊C4—222no—
558C22⋊C4—222no—
559C22⋊C4—222no—
560C22⋊C4—222no—
561C22⋊C4—222no—
562C22⋊C4—442no—
563C42—24no—
564C42—111no—
565C42—111no—
566C42—111no—
567C42—111no—
568C42—111no—
569C42—111no—
570C42—111no—
571C42—111no—
572C42—111no—
573C42—111no—
574C42—111no—
575C42—111no—
576C42—111no—
577C42—111no—
578C42—111no—
579C42—111no—
580C42—222no—
581C42—222no—
582C42—222no—
583C42—222no—
584C42—222no—
585C42—222no—
586C42—224no—
587C11#2074811yescharacteristic, complemented, Sylow
588C23—24no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—41no—
593C23—42no—
594C23—42no—
595C23C22⋊C4×D1111yescharacteristic
596C23C22⋊C4×D1111yescharacteristic
597C23C2×D4×D1111yescharacteristic
598Q8—24no—
599Q8—22no—
600Q8#6693014yes—
601D4—28no—
602D4—24no—
603D4—28no—
604D4—22no—
605D4#6693014yes—
606C2×C4—24no—
607C2×C4—28no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—28no—
614C2×C4—22no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—111no—
619C2×C4—111no—
620C2×C4—111no—
621C2×C4—111no—
622C2×C4—111no—
623C2×C4—111no—
624C2×C4—111no—
625C2×C4—111no—
626C2×C4—222no—
627C2×C4—222no—
628C2×C4—222no—
629C2×C4—222no—
630C2×C4—222no—
631C2×C4—222no—
632C2×C4—222no—
633C2×C4—444no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4—441no—
641C2×C4—444no—
642C2×C4—444no—
643C2×C4—444no—
644C2×C4—442no—
645C2×C4—442no—
646C2×C4—442no—
647C2×C4—442no—
648C2×C4—442no—
649C2×C4C22⋊C4×D1111yescharacteristic
650C2×C4C22⋊C4×D1111yescharacteristic
651C2×C4C22×C4×D1111yescharacteristic
652C2×C4C2×D4×D1111yescharacteristic
653C2×C4C2×#434114yes—
654C8—42no—
655C8—442no—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—24no—
662C22—21no—
663C22—21no—
664C22—44no—
665C22—48no—
666C22—42no—
667C22—42no—
668C22#1062243412yes—
669C22C2×C22⋊C4×D1111yescharacteristic
670C22#1062311712yes—
671C4—21no—
672C4—24no—
673C4—21no—
674C4—82no—
675C4—112no—
676C4—221no—
677C4—221no—
678C4—221no—
679C4—221no—
680C4—221no—
681C4—221no—
682C4—221no—
683C4—442no—
684C4—442no—
685C4—882no—
686C4C2×#6693012yes—
687C4#1062311712yes—
688C2—22no—
689C2—22no—
690C2—41no—
691C2—44no—
692C2#1307099411yescharacteristic
693C2D11×#42111yescharacteristic
694C2C2×#1062243411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1789C2
socleC22×C11C22×C22⋊C4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenter#1789D11
hypocenterC11#20748
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. #13077245C2semidirect
3. #13071010C2semidirect
4. #13068716C2semidirect
5. #13068713C2semidirect
6. #13068634C2semidirect
8. #13068428C2semidirect
15. #41×Dic11C4semidirect
16. #41×Dic11C4semidirect
19. C2×Q8×Dic11C4semidirect
20. C2×Q8×Dic11C4semidirect
23. C2×D4×Dic11C4semidirect
24. C2×D4×Dic11C4semidirect
35. #10622731C22semidirect
36. M16×Dic11C22semidirect
39. #10622545C22semidirect
40. C4×Dic11⋊C4C22semidirect
47. #10622193C22semidirect
48. #10622161C22semidirect
587. C11#20748semidirect

Maximal subgroups

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

subgroupindex
C2×#41×Dic112
#130772452
#130710102
#130687162
#130687132
#130686342
#130685602
#130684282
C11×#17892
#2074811