Finite Group Databasebeta

← #14760425

Subgroups — #14760425

Order 2816.

1002 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622665C211yesmaximal, characteristic
2C2×#10622403C211yesmaximal, characteristic, complemented
3C2×M16×Dic11C211yesmaximal, characteristic
4C22⋊Q8×Dic11C211yesmaximal, characteristic
5#13071144C211yesmaximal, characteristic
6#13069484C211yesmaximal, characteristic, complemented
7#13069358C211yesmaximal, characteristic, complemented
8#13069307C211yesmaximal, characteristic, complemented
9#13069303C211yesmaximal, characteristic, complemented
10#13069049C211yesmaximal, characteristic
11#13068647C211yesmaximal, characteristic
12#13068504C211yesmaximal, characteristic, complemented
13#103×Dic11C211yesmaximal, characteristic, complemented
14#13068435C211yesmaximal, characteristic, complemented
15C11×#1894C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C2×#66977C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C2×#66940C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C11×#380C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29#10622825C2211yescharacteristic
30M16×Dic11—24no—
31C2×#66880C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66879C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37#10622665C418yescomplemented
38#10622598C2211yescharacteristic
39#10622594—21no—
40C4⋊C4×Dic11—21no—
41C4⋊C4×Dic11C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43#10622587C2211yescharacteristic
44#10622586C2211yescharacteristic
45C2×#66874C2211yescharacteristic
46C2×#66872C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622563—21no—
50#10622559—21no—
51C22⋊C4×Dic11—21no—
52C22⋊C4×Dic11—21no—
53#10622403—24no—
54#10622265—21no—
55#10622262—21no—
56C11×#340C2211yescharacteristic
57C11×#340C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11D411yescharacteristic
65C23×Dic11D411yescharacteristic
66C22×Dic22C2311yescharacteristic
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C2×C11×M16—22no—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C11×C22⋊Q8—22no—
73C11×C22⋊Q8C2×C414yes—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82Q8×Dic11—22no—
83Q8×Dic11—22no—
84C2×#4326—22no—
85C2×#4326—22no—
86C2×#4326C2×C414yescomplemented
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92#66977—22no—
93#66977C2×C414yes—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×C4×Dic11—22no—
98C2×C4×Dic11—22no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11D411yescharacteristic
104C2×C4×Dic11D411yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C2×#4318—22no—
108C2×#4318—22no—
109C2×#4318C2×C414yes—
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112#66940—22no—
113#66940—22no—
114C11×#103—22no—
115C11×#103—22no—
116C11×#95—21no—
117#66899C2×C414yescomplemented
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127#66880—22no—
128#66880—22no—
129#66879—22no—
130#66879—22no—
131C8×Dic11—22no—
132C8×Dic11D414yes—
133#66874C2×C414yescomplemented
134#66872—22no—
135#66872C2×C414yescomplemented
136#66871—22no—
137C4×#470—111nomaximal, Sylow
138C24×C11C2×D411yescharacteristic
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11C22×C412yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C22×C412yes—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11#4112yes—
156C22×C4×C11C2411yescharacteristic
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—41no—
166C22×Dic11—41no—
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D411yescharacteristic
170C22×Dic11C2×D411yescharacteristic
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22C22×C412yes—
177C11×M16—28no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11C2×D412yes—
183C2×C8×C11#4112yes—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4C22×C412yes—
191C11×C22⋊C4—24no—
192C11×C22⋊C4—42no—
193C22⋊Dic11—24no—
194C22⋊Dic11—42no—
195#4326—28no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—42no—
202C4⋊Dic11—42no—
203C4⋊Dic11C22×C412yes—
204Dic11⋊C4—24no—
205Dic11⋊C4—42no—
206Dic11⋊C4—42no—
207C4×Dic11—22no—
208C4×Dic11—22no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—42no—
212C4×Dic11—42no—
213C4×Dic11—42no—
214C4×Dic11—42no—
215C4×Dic11C2×D412yes—
216C4×Dic11#4112yes—
217#4318—28no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8C22×C412yes—
221C2×C11⋊C8C22×C412yes—
222C2×C11⋊C8C2×D412yes—
223C2×C11⋊C8#4112yes—
224C2×#470—111no—
225C2×C4×Q16—111no—
226C2×C4×M16—111no—
227C4×C22⋊Q8—111no—
228C4×C22⋊Q8—111no—
229#1971—111no—
230#1944—111no—
231#1935—111no—
232#1935—111no—
233#1894—111no—
234#1894D1111yescharacteristic
235#1809—111no—
236C4×#106—111no—
237C4×#103—111no—
238C4×#103—111no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11C4×D412yes—
246C23×C11C22×D411yescharacteristic
247Q8×C11—22no—
248Q8×C11—22no—
249Q8×C11—41no—
250Q8×C11—41no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11C4×D412yes—
270C2×C4×C11C23×C411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—44no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—44no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11#12112yes—
299C2×Dic11#12112yes—
300C2×Dic11#13712yes—
301C2×Dic11#13712yes—
302Dic22—22no—
303Dic22—22no—
304Dic22—41no—
305Dic22—41no—
306C8×C11—22no—
307C8×C11—22no—
308C11⋊C8—22no—
309C11⋊C8C4×D414yes—
310C22×Q16—111no—
311C22×M16—111no—
312C22×M16C2×D1111yescharacteristic
313C2×C22⋊Q8—111no—
314C2×C22⋊Q8C2×D1111yescharacteristic
315C2×C4×Q8—111no—
316C2×C4×Q8—111no—
317C22×C42—111no—
318#470—118no—
319C4×Q16—224no—
320C2×#107—111no—
321C2×#106—111no—
322C2×#106—111no—
323C2×#103—111no—
324C2×#103—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#103C2×D1111yescharacteristic
328C2×#103C2×D1111yescharacteristic
329C4×M16—224no—
330C2×#97—111no—
331C2×#97—111no—
332C2×C4×C8—111no—
333C2×C4×C8—111no—
334#391—111no—
335#391—111no—
336#389—111no—
337#389—111no—
338#387—221no—
339#387—221no—
340#385—221no—
341#385—221no—
342#380—111no—
343#380C2×D1111yescharacteristic
344C4×C4⋊C4—111no—
345C4×C4⋊C4—111no—
346C4×C4⋊C4—221no—
347C4×C4⋊C4—221no—
348C4×C22⋊C4—221no—
349C4×C22⋊C4—221no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340C2×D1111yescharacteristic
355#340C2×D1111yescharacteristic
356C22×C11—22no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11C2×C4×D411yescharacteristic
364C22×C11C2×#12111yescharacteristic
365C22×C11#53211yescharacteristic
366C22×C11C2×#13711yescharacteristic
367C22×C11C2×#13711yescharacteristic
368C22×C11#57511yescharacteristic
369C22×C11#57511yescharacteristic
370C4×C11—22no—
371C4×C11—42no—
372C4×C11—42no—
373C4×C11—81no—
374C4×C11—81no—
375C4×C11C2×C4×D411yescharacteristic
376C4×C11C4×#4111yescharacteristic
377C4×C11#52511yescharacteristic
378C4×C11#52911yescharacteristic
379Dic11—22no—
380Dic11—42no—
381Dic11—41no—
382Dic11—41no—
383Dic11—42no—
384Dic11—81no—
385Dic11—81no—
386Dic11#47014yescomplemented
387C22×Q8—111no—
388C22×Q8C22×D1111yescharacteristic
389C23×C4—111no—
390C23×C4—111no—
391C23×C4C22×D1111yescharacteristic
392C2×Q16—114no—
393C2×Q16—222no—
394C2×Q16—222no—
395C2×M16—22no—
396C2×M16—22no—
397C2×M16—22no—
398C2×M16—114no—
399C2×M16—222no—
400C2×M16—222no—
401C22×C8—111no—
402C22×C8—111no—
403C22×C8C22×D1111yescharacteristic
404C22×C8C22×D1111yescharacteristic
405C22⋊Q8—22no—
406C22⋊Q8—114no—
407C22⋊Q8—222no—
408C22⋊Q8C4×D1114yes—
409C4×Q8—222no—
410C4×Q8—222no—
411C4×Q8—222no—
412C4×Q8—222no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C4⋊C4C22×D1111yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C42—111no—
430C2×C42—111no—
431C2×C42—111no—
432C2×C42—111no—
433C2×C42—222no—
434C2×C42—222no—
435C2×C42—221no—
436C2×C42—221no—
437C2×C42—221no—
438C2×C42—221no—
439#107—222no—
440#106—114no—
441#106—222no—
442#103—22no—
443#103—22no—
444#103—114no—
445#103—114no—
446#103—222no—
447#103—222no—
448#97—222no—
449#97—222no—
450C4×C8—114no—
451C4×C8—222no—
452#95—21no—
453#95—221no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462C2×C11—42no—
463C2×C11C4×#12111yescharacteristic
464C2×C11C4×#13711yescharacteristic
465C2×C11C4×#13711yescharacteristic
466C2×C11C2×#47011yescharacteristic
467C2×C11#305411yescharacteristic
468C2×C11#317211yescharacteristic
469C2×C11#317211yescharacteristic
470C24D4×D1111yescharacteristic
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—112no—
477C2×Q8—221no—
478C2×Q8—221no—
479C2×Q8—221no—
480C2×Q8—221no—
481C2×Q8—221no—
482C2×Q8C2×C4×D1112yes—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—111no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—441no—
504C22×C4—441no—
505C22×C4C2×C4×D1112yes—
506C22×C4D4×D1111yescharacteristic
507C22×C4#434112yes—
508C22×C4C23×D1111yescharacteristic
509Q16—228no—
510M16—28no—
511M16—228no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—112no—
517C2×C8—112no—
518C2×C8—112no—
519C2×C8—112no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8D4×D1112yes—
523C2×C8#434112yes—
524C4⋊C4—24no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—112no—
531C4⋊C4—224no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—442no—
538C4⋊C4—442no—
539C4⋊C4—442no—
540C4⋊C4—442no—
541C4⋊C4C2×C4×D1112yes—
542C22⋊C4—24no—
543C22⋊C4—42no—
544C22⋊C4—224no—
545C22⋊C4—442no—
546C42—112no—
547C42—112no—
548C42—222no—
549C42—222no—
550C42—221no—
551C42—221no—
552C42—442no—
553C42—442no—
554C42—442no—
555C42—442no—
556C11C4×#47011yescharacteristic, complemented, Sylow
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23(C22⋊D11)⋊C412yes—
564C23C2×D4×D1111yescharacteristic
565Q8—22no—
566Q8—22no—
567Q8—41no—
568Q8—41no—
569Q8—222no—
570Q8—222no—
571Q8—441no—
572Q8—441no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—112no—
592C2×C4—112no—
593C2×C4—112no—
594C2×C4—112no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—444no—
606C2×C4—444no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4(C22⋊D11)⋊C412yes—
618C2×C4C22×C4×D1111yescharacteristic
619C2×C4C2×D4×D1111yescharacteristic
620C2×C4C2×#434111yescharacteristic
621C2×C4C2×#434111yescharacteristic
622C2×C4#41×D1111yescharacteristic
623C2×C4#41×D1111yescharacteristic
624C8—22no—
625C8—22no—
626C8—114no—
627C8—222no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22C2×(C22⋊D11)⋊C411yescharacteristic
636C22#1062312711yescharacteristic
637C22D11×#12111yescharacteristic
638C22#1062330411yescharacteristic
639C22D11×#13711yescharacteristic
640C22D11×#13711yescharacteristic
641C22#1062330811yescharacteristic
642C4—22no—
643C4—42no—
644C4—42no—
645C4—81no—
646C4—81no—
647C4—114no—
648C4—222no—
649C4—442no—
650C4—442no—
651C4—441no—
652C4—441no—
653C4—881no—
654C4—881no—
655C4C4×#434111yescharacteristic
656C4C4×D4×D1111yescharacteristic
657C4#1062311711yescharacteristic
658C4#1062318011yescharacteristic
659C2—42no—
660C2#1307112611yescharacteristic
661C2#1307743111yescharacteristic
662C2#1307744011yescharacteristic
663C2D11×#47011yescharacteristic
664C2#1307822011yescharacteristic
665C2#1307921511yescharacteristic
666C2#1307921711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1894C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1894D11
hypocenterC11C4×#470
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
2. C2×#10622403C2semidirect
6. #13069484C2semidirect
7. #13069358C2semidirect
8. #13069307C2semidirect
9. #13069303C2semidirect
12. #13068504C2semidirect
13. #103×Dic11C2semidirect
14. #13068435C2semidirect
37. #10622665C4semidirect
86. C2×#4326C2×C4semidirect
117. #66899C2×C4semidirect
133. #66874C2×C4semidirect
135. #66872C2×C4semidirect
386. Dic11#470semidirect
556. C11C4×#470semidirect

Maximal subgroups

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

subgroupindex
C2×#106226652
C2×#106224032
C2×M16×Dic112
C22⋊Q8×Dic112
#130711442
#130694842
#130693582
#130693072
#130693032
#130690492
#130686472
#130685042
#103×Dic112
#130684352
C11×#18942
C4×#47011