Finite Group Databasebeta

← #14765459

Subgroups — #14765459

Order 2816.

812 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×Dic11C211yesmaximal, characteristic
2#13071100C211yesmaximal, characteristic
3#13069360C211yesmaximal, characteristic, complemented
4#13069355C211yesmaximal, characteristic, complemented
5#13069308C211yesmaximal, characteristic, complemented
6#13069308C211yesmaximal, characteristic, complemented
7#13069210C211yesmaximal, characteristic, complemented
8#13069196C211yesmaximal, characteristic, complemented
9#13068929C211yesmaximal, characteristic
10#13068886C211yesmaximal, characteristic, complemented
11#13068872C211yesmaximal, characteristic, complemented
12#13068817C211yesmaximal, characteristic
13#13068711C211yesmaximal, characteristic
14#13068380C211yesmaximal, characteristic
15C2×C11×#485C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C11×#485C418yescomplemented
22C2×C11×#107C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30#10622825C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66879C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622598C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622598C2211yescharacteristic
41#10622594—21no—
42C4⋊C4×Dic11—21no—
43C4⋊C4×Dic11C2211yescharacteristic
44#10622563—21no—
45#10622563—21no—
46#10622563—21no—
47C22⋊C4×Dic11—21no—
48C4×C4⋊Dic11—21no—
49C4×C4⋊Dic11—21no—
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11D411yescharacteristic
63C23×Dic11D411yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8C2×C414yes—
68C11×#117—22no—
69C11×#117C2×C414yes—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79Q8×Dic11—41no—
80Q8×Dic11—41no—
81#66979—41no—
82#66979—41no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—41no—
97C2×C4×Dic11—41no—
98C2×C4×Dic11D411yescharacteristic
99C2×C4×Dic11D411yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C11×#107C2×C414yescomplemented
105C11×#106C2×C414yescomplemented
106C11×#103C2×C414yescomplemented
107C11×#103C2×C414yescomplemented
108C11×C22⋊C8C2×C414yes—
109#66899—41no—
110#66899—41no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C22⋊(C11⋊C8)—22no—
121#66882—41no—
122#66881—41no—
123#66879—41no—
124#66879—41no—
125#22083—111nomaximal, Sylow
126C24×C11C2×D411yescharacteristic
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11C22×C412yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11C22×C412yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11#4112yes—
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—22no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—41no—
151C22×Dic11—41no—
152C22×Dic11—41no—
153C22×Dic11—41no—
154C22×Dic11—41no—
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11C22×C412yes—
164C2×C8×C11C22×C412yes—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4C22×C412yes—
170C11×C4⋊C4C22×C412yes—
171C11×C4⋊C4C22×C412yes—
172C11×C22⋊C4—24no—
173C11×C22⋊C4—24no—
174C42×C11—24no—
175C22⋊Dic11—42no—
176C22⋊Dic11—42no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—42no—
186C4⋊Dic11—42no—
187C4⋊Dic11—42no—
188C4⋊Dic11—42no—
189C4⋊Dic11—42no—
190C4⋊Dic11—42no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—41no—
196C4×Dic11—41no—
197C4×Dic11—42no—
198C4×Dic11—42no—
199C4×Dic11—42no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×#485D1111yescharacteristic
207C4×C22⋊Q8—111no—
208#2296—111no—
209#1944—111no—
210#1943—111no—
211#1935—111no—
212#1935—111no—
213#1921—111no—
214#1919—111no—
215#1873—111no—
216#1865—111no—
217#1863—111no—
218#1854—111no—
219#1825—111no—
220#1749—111no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11C4×D412yes—
228C23×C11C22×D411yescharacteristic
229Q8×C11—22no—
230Q8×C11—22no—
231Q8×C11—41no—
232Q8×C11—41no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11C4×D412yes—
252C2×C4×C11C23×C411yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11H(5,𝔽2)11yescharacteristic
255C2×C4×C11H(5,𝔽2)11yescharacteristic
256C2×C4×C112−1+411yescharacteristic
257C2×C4×C112−1+411yescharacteristic
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—44no—
270C2×Dic11—44no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11#13712yes—
284C8×C11—22no—
285C8×C11—22no—
286C11⋊C8—41no—
287C11⋊C8—41no—
288C2×C22⋊Q8C2×D1111yescharacteristic
289C2×C4×Q8—111no—
290C2×#117—111no—
291C2×#117C2×D1111yescharacteristic
292C22×C42—111no—
293#485Dic1118yescomplemented
294C2×#107—111no—
295C2×#107C2×D1111yescharacteristic
296C2×#106—111no—
297C2×#106C2×D1111yescharacteristic
298C2×#103—111no—
299C2×#103—111no—
300C2×#103C2×D1111yescharacteristic
301C2×#103C2×D1111yescharacteristic
302C2×C22⋊C8—111no—
303C2×C22⋊C8C2×D1111yescharacteristic
304C2×#97—111no—
305C2×#97—111no—
306#391—111no—
307#389—111no—
308#389—111no—
309#389—111no—
310#389—111no—
311#389—111no—
312#387—221no—
313#385—221no—
314#385—221no—
315#385—221no—
316#380—111no—
317C4×C4⋊C4—111no—
318C4×C4⋊C4—221no—
319C4×C4⋊C4—221no—
320C4×C4⋊C4—221no—
321C4×C22⋊C4—221no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#336—111no—
331#336—111no—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11C2×C4×D411yescharacteristic
340C22×C11#53411yescharacteristic
341C22×C11#53611yescharacteristic
342C22×C11C2×#13711yescharacteristic
343C22×C11#57511yescharacteristic
344C22×C11#57511yescharacteristic
345C22×C11#57511yescharacteristic
346C4×C11—22no—
347C4×C11—42no—
348C4×C11—42no—
349C4×C11—42no—
350C4×C11—42no—
351C4×C11#52011yescharacteristic
352C4×C11#52011yescharacteristic
353C4×C11#53911yescharacteristic
354C4×C11#53911yescharacteristic
355Dic11—22no—
356Dic11—41no—
357Dic11—41no—
358Dic11—41no—
359Dic11—81no—
360Dic11—81no—
361Dic11—81no—
362Dic11—81no—
363C22×Q8C22×D1111yescharacteristic
364C23×C4—111no—
365C23×C4—111no—
366C23×C4C22×D1111yescharacteristic
367C22×C8—111no—
368C22×C8—111no—
369C22×C8C22×D1111yescharacteristic
370C22×C8C22×D1111yescharacteristic
371C22⋊Q8—22no—
372C22⋊Q8C2×Dic1114yes—
373C4×Q8—441no—
374C4×Q8—441no—
375#117—22no—
376#117—441no—
377#117—441no—
378#117C2×Dic1114yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C4⋊C4C22×D1111yescharacteristic
392C2×C4⋊C4C22×D1111yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C42—21no—
398C2×C42—111no—
399C2×C42—111no—
400C2×C42—111no—
401C2×C42—111no—
402C2×C42—221no—
403C2×C42—221no—
404C2×C42—221no—
405C2×C42—441no—
406C2×C42—441no—
407#107—441no—
408#107C2×Dic1114yescomplemented
409#106—441no—
410#106C2×Dic1114yescomplemented
411#103—441no—
412#103—441no—
413#103C2×Dic1114yescomplemented
414#103C2×Dic1114yescomplemented
415C22⋊C8—222no—
416C22⋊C8C2×Dic1114yes—
417#97—441no—
418#97—441no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428C2×C11—42no—
429C2×C11#232211yescharacteristic
430C2×C11#294311yescharacteristic
431C2×C11C4×#13711yescharacteristic
432C2×C11#319611yescharacteristic
433C2×C11#319711yescharacteristic
434C2×C11#323711yescharacteristic
435C2×C11#324011yescharacteristic
436C24D4×D1111yescharacteristic
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C22×Dic1112yes—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—222no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—441no—
461C22×C4—441no—
462C22×C4—441no—
463C22×C4—441no—
464C22×C4—441no—
465C22×C4D4×D1111yescharacteristic
466C22×C4#434112yes—
467C22×C4C22×Dic1112yes—
468C22×C4C23×D1111yescharacteristic
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8C22×Dic1112yes—
480C2×C8C22×Dic1112yes—
481C4⋊C4—24no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—442no—
494C4⋊C4—442no—
495C4⋊C4—442no—
496C4⋊C4—442no—
497C4⋊C4—442no—
498C4⋊C4—442no—
499C4⋊C4C22×Dic1112yes—
500C4⋊C4C22×Dic1112yes—
501C4⋊C4C22×Dic1112yes—
502C22⋊C4—24no—
503C22⋊C4—24no—
504C22⋊C4—442no—
505C22⋊C4—442no—
506C42—24no—
507C42—221no—
508C42—221no—
509C42—221no—
510C42—221no—
511C42—441no—
512C42—441no—
513C42—442no—
514C42—442no—
515C42—442no—
516C11#2208311yescharacteristic, complemented, Sylow
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23D4×Dic1112yes—
524C23C2×D4×D1111yescharacteristic
525Q8—22no—
526Q8—22no—
527Q8—41no—
528Q8—41no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—112no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—444no—
560C2×C4—444no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4D4×Dic1112yes—
574C2×C4C2×#434111yescharacteristic
575C2×C4#6704211yescharacteristic
576C2×C4#6704211yescharacteristic
577C2×C4#6704311yescharacteristic
578C2×C4#6704311yescharacteristic
579C2×C4C23×Dic1111yescharacteristic
580C8—22no—
581C8—22no—
582C8—441no—
583C8—441no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22#1062317911yescharacteristic
592C22#1062318411yescharacteristic
593C22#1062329911yescharacteristic
594C22#1062329911yescharacteristic
595C22D11×#13711yescharacteristic
596C22#1062330811yescharacteristic
597C22C2×D4×Dic1111yescharacteristic
598C4—22no—
599C4—42no—
600C4—42no—
601C4—42no—
602C4—42no—
603C4—222no—
604C4—441no—
605C4—441no—
606C4—441no—
607C4—881no—
608C4—881no—
609C4—881no—
610C4—881no—
611C4#1062319611yescharacteristic
612C4#1062319611yescharacteristic
613C4#1062335811yescharacteristic
614C4#1062335811yescharacteristic
615C2—42no—
616C2#1307128811yescharacteristic
617C2#1307741711yescharacteristic
618C2#137×Dic1111yescharacteristic
619C2#1307945011yescharacteristic
620C2#1307946011yescharacteristic
621C2#1307982711yescharacteristic
622C2#1307986011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#485C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#485D11
hypocenterC11#22083
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
3. #13069360C2semidirect
4. #13069355C2semidirect
5. #13069308C2semidirect
6. #13069308C2semidirect
7. #13069210C2semidirect
8. #13069196C2semidirect
10. #13068886C2semidirect
11. #13068872C2semidirect
21. C11×#485C4semidirect
104. C11×#107C2×C4semidirect
105. C11×#106C2×C4semidirect
106. C11×#103C2×C4semidirect
107. C11×#103C2×C4semidirect
293. #485Dic11semidirect
408. #107C2×Dic11semidirect
410. #106C2×Dic11semidirect
413. #103C2×Dic11semidirect
414. #103C2×Dic11semidirect
516. C11#22083semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×Dic112
#130711002
#130693602
#130693552
#130693082
#130692102
#130691962
#130689292
#130688862
#130688722
#130688172
#130687112
#130683802
C2×C11×#4852
#2208311