Finite Group Databasebeta

← #14789915

Subgroups — #14789915

Order 2816.

1066 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623048C211yesmaximal, characteristic
2C2×#10622470C211yesmaximal, characteristic, complemented
3C2×#10622490C211yesmaximal, characteristic, complemented
4#13071144C211yesmaximal, characteristic
5#13069947C211yesmaximal, characteristic, complemented
6#13069942C211yesmaximal, characteristic, complemented
7#13069756C211yesmaximal, characteristic, complemented
8#13069756C211yesmaximal, characteristic, complemented
9#13069572C211yesmaximal, characteristic, complemented
10#13069570C211yesmaximal, characteristic, complemented
11#13068928C211yesmaximal, characteristic
12#13068926C211yesmaximal, characteristic
13#13068813C211yesmaximal, characteristic
14#13068594C211yesmaximal, characteristic
15C11×#1854C211yesmaximal, characteristic
16C2×C11×#117C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C2×#66977C2211yescharacteristic
19C22×C4×Dic11C2211yescharacteristic
20#10623048—24no—
21#10623048—24no—
22C2×#66943C2211yescharacteristic
23C2×#66943C2211yescharacteristic
24C2×#66941C2211yescharacteristic
25C2×#66941C2211yescharacteristic
26C2×#66940C2211yescharacteristic
27C2×#66931—21no—
28C2×#66931—21no—
29C2×C4×Dic22—21no—
30C2×C4×Dic22—21no—
31C2×C11×#107C2211yescharacteristic
32C2×C11×#106C2211yescharacteristic
33C2×C11×C22⋊C8C2211yescharacteristic
34C11×#380C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39C2×Dic11⋊C8C2211yescharacteristic
40C4⋊C4×Dic11C2211yescharacteristic
41#10622587C2211yescharacteristic
42#10622586C2211yescharacteristic
43C2×#66874C2211yescharacteristic
44C2×#66874C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47#10622559—21no—
48C22⋊C4×Dic11—21no—
49#10622490—24no—
50#10622470—24no—
51#10622265—21no—
52#10622262—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11D411yescharacteristic
65C23×Dic11D411yescharacteristic
66C22×Dic22—21no—
67C22×Dic22—21no—
68C22×Dic22C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C11×#117—22no—
72C11×#117—22no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C42×C11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82#66979—22no—
83#66979—22no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89#66977—22no—
90#66977Q814yescomplemented
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—22no—
100C2×C4×Dic11—22no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11D411yescharacteristic
104C2×C4×Dic11D411yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109#66943—22no—
110#66943—22no—
111#66943D414yes—
112#66943D414yes—
113#66941—22no—
114#66941—22no—
115#66941—22no—
116#66941—22no—
117#66940—22no—
118#66940—22no—
119#66931—28no—
120#66931—28no—
121C4×Dic22—28no—
122C4×Dic22—28no—
123C11×#107—22no—
124C11×#106—22no—
125C11×C22⋊C8—22no—
126C11×#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C22⋊(C11⋊C8)—22no—
132#66880—22no—
133#66880—22no—
134Dic11⋊C8—22no—
135Dic11⋊C8—22no—
136#66874—22no—
137#66874—22no—
138#66872—22no—
139#66871—22no—
140#24306—111nomaximal, Sylow
141C24×C11C2×D411yescharacteristic
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×Q812yes—
152C22×C4×C11#4112yes—
153C22×C4×C11C2411yescharacteristic
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—41no—
163C22×Dic11—41no—
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C22×Dic11C2×D411yescharacteristic
168C2×Dic22—24no—
169C2×Dic22—24no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—42no—
176C2×Dic22—42no—
177C2×Dic22—42no—
178C2×Dic22—42no—
179C2×Dic22C2×Q812yes—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4C2×D412yes—
193C11×C4⋊C4C2×D412yes—
194C11×C22⋊C4—24no—
195C11×C22⋊C4—42no—
196C42×C11—24no—
197C22⋊Dic11—24no—
198C22⋊Dic11—24no—
199C4⋊Dic11—24no—
200C4⋊Dic11—24no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11C2×D412yes—
205C4⋊Dic11C2×D412yes—
206C4⋊Dic11C2×Q812yes—
207Dic11⋊C4—24no—
208Dic11⋊C4—24no—
209Dic11⋊C4—24no—
210Dic11⋊C4—24no—
211Dic11⋊C4—24no—
212Dic11⋊C4—42no—
213Dic11⋊C4—42no—
214C4×Dic11—24no—
215C4×Dic11—22no—
216C4×Dic11—22no—
217C4×Dic11—21no—
218C4×Dic11—21no—
219C4×Dic11—42no—
220C4×Dic11—42no—
221C4×Dic11C2×D412yes—
222C4×Dic11C2×D412yes—
223C2×C11⋊C8—21no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×#533—111no—
230C2×#479—111no—
231C2×#479—111no—
232C4×C22⋊Q8—111no—
233#2058—111no—
234#2057—111no—
235#2024—111no—
236#2024—111no—
237#1989—111no—
238#1989—111no—
239#1873—111no—
240#1873—111no—
241#1854—111no—
242#1854D1111yescharacteristic
243#1797—111no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11C22⋊Q812yes—
251C23×C11C22×D411yescharacteristic
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
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×C11—41no—
270C2×C4×C11C22⋊Q812yes—
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C22×Q811yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C112−1+411yescharacteristic
276C2×C4×C112−1+411yescharacteristic
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—22no—
289C2×Dic11—44no—
290C2×Dic11—44no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11#12012yes—
300C2×Dic11#12012yes—
301C2×Dic11#13512yes—
302C2×Dic11#13712yes—
303Dic22—22no—
304Dic22—22no—
305Dic22—48no—
306Dic22—48no—
307Dic22—41no—
308Dic22—41no—
309C8×C11—41no—
310C8×C11—41no—
311C11⋊C8—41no—
312C11⋊C8—41no—
313#533—224no—
314#533—224no—
315C2×C4⋊Q8—111no—
316C2×C4⋊Q8—111no—
317C2×#125—111no—
318C2×#125—111no—
319C2×C22⋊Q8—111no—
320C2×C22⋊Q8—221no—
321C2×C22⋊Q8—221no—
322C2×C4×Q8—111no—
323C2×C4×Q8—221no—
324C2×C4×Q8—221no—
325C2×#117—111no—
326C2×#117C2×D1111yescharacteristic
327C22×C42—111no—
328#479—224no—
329#479—224no—
330C2×#107—111no—
331C2×#107C2×D1111yescharacteristic
332C2×#106—111no—
333C2×#106C2×D1111yescharacteristic
334C2×C4⋊C8—111no—
335C2×C4⋊C8—111no—
336C2×#103—111no—
337C2×#103—111no—
338C2×#103—111no—
339C2×#103—111no—
340C2×C22⋊C8—111no—
341C2×C22⋊C8C2×D1111yescharacteristic
342#391—111no—
343#389—111no—
344#387—221no—
345#385—221no—
346#380C2×D1111yescharacteristic
347C4×C4⋊C4—111no—
348C4×C4⋊C4—221no—
349C4×C22⋊C4—221no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#340C2×D1111yescharacteristic
357#340C2×D1111yescharacteristic
358#336—111no—
359#336—111no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—22no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11C2×#12011yescharacteristic
368C22×C11C2×C22⋊Q811yescharacteristic
369C22×C11#53611yescharacteristic
370C22×C11C2×#13511yescharacteristic
371C22×C11C2×#13711yescharacteristic
372C22×C11#57511yescharacteristic
373C22×C11#57511yescharacteristic
374C4×C11—22no—
375C4×C11—42no—
376C4×C11—42no—
377C4×C11—81no—
378C4×C11—81no—
379C4×C11#54811yescharacteristic
380C4×C11#54811yescharacteristic
381C4×C11D4×Q811yescharacteristic
382C4×C11D4×Q811yescharacteristic
383Dic11—22no—
384Dic11—22no—
385Dic11—22no—
386Dic11—22no—
387Dic11—42no—
388Dic11—42no—
389Dic11—42no—
390Dic11—42no—
391C22×Q8—111no—
392C22×Q8—221no—
393C22×Q8—221no—
394C23×C4—111no—
395C23×C4—111no—
396C23×C4C22×D1111yescharacteristic
397C22×C8—111no—
398C22×C8—111no—
399C22×C8C22×D1111yescharacteristic
400C22×C8C22×D1111yescharacteristic
401C4⋊Q8—222no—
402C4⋊Q8—222no—
403C4⋊Q8—222no—
404C4⋊Q8—222no—
405#125—114no—
406#125—114no—
407#125—222no—
408#125—222no—
409C22⋊Q8—114no—
410C22⋊Q8—228no—
411C22⋊Q8—228no—
412C22⋊Q8—222no—
413C4×Q8—228no—
414C4×Q8—228no—
415C4×Q8—222no—
416C4×Q8—222no—
417#117—22no—
418#117—22no—
419#117—222no—
420#117—222no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C42—21no—
442C2×C42—111no—
443C2×C42—111no—
444C2×C42—111no—
445C2×C42—111no—
446C2×C42—222no—
447C2×C42—222no—
448C2×C42—221no—
449C2×C42—221no—
450C2×C42—221no—
451#107—22no—
452#107—222no—
453#106—22no—
454#106—222no—
455C4⋊C8—222no—
456C4⋊C8—222no—
457#103—222no—
458#103—222no—
459#103—222no—
460#103—222no—
461C22⋊C8—22no—
462C22⋊C8—222no—
463#95—21no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95—221no—
468C2×C11—42no—
469C2×C11#240911yescharacteristic
470C2×C11#300211yescharacteristic
471C2×C11#300711yescharacteristic
472C2×C11#307611yescharacteristic
473C2×C11#307811yescharacteristic
474C2×C11#323111yescharacteristic
475C2×C11#324011yescharacteristic
476C24D4×D1111yescharacteristic
477C2×Q8—112no—
478C2×Q8—224no—
479C2×Q8—224no—
480C2×Q8—221no—
481C2×Q8—221no—
482C2×Q8—221no—
483C2×Q8—221no—
484C2×Q8—221no—
485C2×Q8—442no—
486C2×Q8—442no—
487C2×Q8—442no—
488C2×Q8—442no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—111no—
498C22×C4—111no—
499C22×C4—111no—
500C22×C4—111no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—441no—
510C22×C4—441no—
511C22×C4#433912yes—
512C22×C4D4×D1111yescharacteristic
513C22×C4Q8×D1112yes—
514C22×C4C23×D1111yescharacteristic
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—112no—
534C4⋊C4—112no—
535C4⋊C4—112no—
536C4⋊C4—224no—
537C4⋊C4—224no—
538C4⋊C4—224no—
539C4⋊C4—224no—
540C4⋊C4—224no—
541C4⋊C4—224no—
542C4⋊C4—224no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—442no—
547C4⋊C4—442no—
548C4⋊C4D4×D1112yes—
549C4⋊C4D4×D1112yes—
550C22⋊C4—24no—
551C22⋊C4—42no—
552C22⋊C4—224no—
553C22⋊C4—224no—
554C42—24no—
555C42—112no—
556C42—112no—
557C42—222no—
558C42—222no—
559C42—224no—
560C42—221no—
561C42—221no—
562C42—442no—
563C42—442no—
564C11#2430611yescharacteristic, complemented, Sylow
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23#6694912yes—
572C23C2×D4×D1111yescharacteristic
573Q8—222no—
574Q8—222no—
575Q8—448no—
576Q8—448no—
577Q8—441no—
578Q8—441no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—112no—
598C2×C4—112no—
599C2×C4—112no—
600C2×C4—112no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—221no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—444no—
614C2×C4—444no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4#6694912yes—
624C2×C4C2×#433911yescharacteristic
625C2×C4C2×D4×D1111yescharacteristic
626C2×C4C2×D4×D1111yescharacteristic
627C2×C4C2×Q8×D1111yescharacteristic
628C2×C4#6704311yescharacteristic
629C2×C4#6704311yescharacteristic
630C8—41no—
631C8—41no—
632C8—441no—
633C8—441no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22C2×#6694911yescharacteristic
642C22D11×#12011yescharacteristic
643C22#1062317911yescharacteristic
644C22D11×#13511yescharacteristic
645C22#1062329911yescharacteristic
646C22#1062330411yescharacteristic
647C22D11×#13711yescharacteristic
648C4—22no—
649C4—42no—
650C4—42no—
651C4—81no—
652C4—81no—
653C4—222no—
654C4—222no—
655C4—222no—
656C4—222no—
657C4—442no—
658C4—442no—
659C4—442no—
660C4—442no—
661C4#1062308311yescharacteristic
662C4#1062308311yescharacteristic
663C4#1062316311yescharacteristic
664C4#1062316311yescharacteristic
665C2—42no—
666C2#1307198011yescharacteristic
667C2#1307783111yescharacteristic
668C2#1307787311yescharacteristic
669C2#1307840211yescharacteristic
670C2#1307842011yescharacteristic
671C2#1307977311yescharacteristic
672C2#1307985411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1854C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1854D11
hypocenterC11#24306
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
2. C2×#10622470C2semidirect
3. C2×#10622490C2semidirect
5. #13069947C2semidirect
6. #13069942C2semidirect
7. #13069756C2semidirect
8. #13069756C2semidirect
9. #13069572C2semidirect
10. #13069570C2semidirect
90. #66977Q8semidirect
564. C11#24306semidirect

Maximal subgroups

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

subgroupindex
C2×#106230482
C2×#106224702
C2×#106224902
#130711442
#130699472
#130699422
#130697562
#130695722
#130695702
#130689282
#130689262
#130688132
#130685942
C11×#18542
#2430611