Finite Group Databasebeta

← #14775144

Subgroups — #14775144

Order 2816.

846 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071625C211yesmaximal, characteristic
2#13071493C211yesmaximal, characteristic
3#13069355C211yesmaximal, characteristic, complemented
4#13069308C211yesmaximal, characteristic, complemented
5#13069252C211yesmaximal, characteristic, complemented
6#13069189C211yesmaximal, characteristic, complemented
7#13069189C211yesmaximal, characteristic, complemented
8#13069040C211yesmaximal, characteristic
9#13068886C211yesmaximal, characteristic, complemented
10#13068811C211yesmaximal, characteristic
11#13068515C211yesmaximal, characteristic, complemented
12#13068448C211yesmaximal, characteristic, complemented
13#13068395C211yesmaximal, characteristic
14C2×#10622167C211yesmaximal, characteristic
15C2×C11×#484C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C23×C11⋊C8C2211yescharacteristic
21C11×#484C418yescomplemented
22C2×C11×#107C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30#10622825—21no—
31#10622825C2211yescharacteristic
32C4×C22⋊Dic11—21no—
33C4×C22⋊Dic11C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37C2×#66879C2211yescharacteristic
38#10622598—21no—
39#10622598C2211yescharacteristic
40#10622598C2211yescharacteristic
41#10622598C2211yescharacteristic
42#10622594—21no—
43#10622594—21no—
44#10622594—21no—
45C4⋊C4×Dic11C2211yescharacteristic
46C4⋊C4×Dic11C2211yescharacteristic
47C4⋊C4×Dic11C2211yescharacteristic
48#10622563—21no—
49C22⋊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×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C23×Dic11—21no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×C22⋊Q8—22no—
67C11×C22⋊Q8C2×C414yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4C2×C414yes—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11D411yescharacteristic
78C2×C22⋊Dic11D411yescharacteristic
79Q8×Dic11—22no—
80Q8×Dic11—41no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—41no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11C2311yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C22×C11⋊C8—22no—
99C22×C11⋊C8—22no—
100C22×C11⋊C8—41no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C11×#107C2×C414yescomplemented
104C11×#107C2×C414yescomplemented
105C11×#103C2×C414yescomplemented
106C11×#103C2×C414yescomplemented
107C11×C22⋊C8C2×C414yes—
108#66899—22no—
109#66899—41no—
110C11⋊#95—21no—
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⋊#95D411yescharacteristic
120C11⋊#95D411yescharacteristic
121#66881—22no—
122#66881—41no—
123#66879—22no—
124#66879—41no—
125#22932—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×C11—24no—
142C22×C4×C11—81no—
143C22×C4×C11—81no—
144C22×C4×C11C22×C412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11#4112yes—
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—42no—
153C22×Dic11—42no—
154C22×Dic11—81no—
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—24no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4C22×C412yes—
171C11×C4⋊C4C22×C412yes—
172C11×C4⋊C4C22×C412yes—
173C11×C22⋊C4—24no—
174C22⋊Dic11—22no—
175C22⋊Dic11—22no—
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—42no—
185C4⋊Dic11—42no—
186C4⋊Dic11—81no—
187C4⋊Dic11—81no—
188C4⋊Dic11—81no—
189C4⋊Dic11#4112yes—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—42no—
195C4×Dic11—81no—
196C4×Dic11—81no—
197C4×Dic11—81no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—44no—
204C2×C11⋊C8#4112yes—
205C2×#484D1111yescharacteristic
206#2360—111no—
207#2345—111no—
208#1943—111no—
209#1935—111no—
210#1927—111no—
211#1918—111no—
212#1918—111no—
213#1892—111no—
214#1865—111no—
215#1853—111no—
216#1776—111no—
217#1763—111no—
218#1752—111no—
219C2×#340—111no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11C4×D412yes—
225C23×C11#13712yes—
226C23×C11#13712yes—
227C23×C11C22×D411yescharacteristic
228Q8×C11—22no—
229Q8×C11—22no—
230Q8×C11—41no—
231Q8×C11—41no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
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—41no—
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—84no—
251C2×C4×C11C4×D412yes—
252C2×C4×C11C23×C411yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11H(5,𝔽2)11yescharacteristic
257C2×C4×C112−1+411yescharacteristic
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—22no—
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—21no—
270C2×Dic11—21no—
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—84no—
283C8×C11—22no—
284C8×C11—22no—
285C11⋊C8—22no—
286C11⋊C8—41no—
287C23×C8—111no—
288C2×C22⋊Q8C2×D1111yescharacteristic
289C2×C4×Q8—111no—
290C22×C4⋊C4—111no—
291C22×C4⋊C4C2×D1111yescharacteristic
292#484Dic1118yescomplemented
293C2×#107C2×D1111yescharacteristic
294C2×#107C2×D1111yescharacteristic
295C2×#106—111no—
296C2×#106—111no—
297C2×#103—111no—
298C2×#103—111no—
299C2×#103C2×D1111yescharacteristic
300C2×#103C2×D1111yescharacteristic
301C2×C22⋊C8C2×D1111yescharacteristic
302C2×#97—111no—
303C2×#97—111no—
304#391—111no—
305#389—111no—
306#389—111no—
307#389—111no—
308#389—221no—
309#387—221no—
310#387—221no—
311#387—221no—
312#385—221no—
313#380—111no—
314#380—221no—
315C4×C4⋊C4—111no—
316C4×C4⋊C4—111no—
317C4×C4⋊C4—111no—
318C4×C22⋊C4—111no—
319C4×C22⋊C4—221no—
320C4×C22⋊C4—221no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#336—111no—
330#336—111no—
331C22×C11—22no—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—22no—
335C22×C11—22no—
336C22×C11—22no—
337C22×C11#44114yes—
338C22×C11C2×C4×D411yescharacteristic
339C22×C11#54611yescharacteristic
340C22×C11#54711yescharacteristic
341C22×C11C2×#13711yescharacteristic
342C22×C11C2×#13711yescharacteristic
343C22×C11#57611yescharacteristic
344C22×C11#57711yescharacteristic
345C4×C11—22no—
346C4×C11—42no—
347C4×C11—42no—
348C4×C11—42no—
349C4×C11—42no—
350C4×C11C4×#4111yescharacteristic
351C4×C11#52011yescharacteristic
352C4×C11#55111yescharacteristic
353C4×C11#55211yescharacteristic
354Dic11—41no—
355Dic11—41no—
356Dic11—41no—
357Dic11—42no—
358Dic11—41no—
359Dic11—81no—
360Dic11—81no—
361Dic11—81no—
362C22×Q8C22×D1111yescharacteristic
363C23×C4—21no—
364C23×C4—221no—
365C23×C4C22×D1111yescharacteristic
366C22×C8—111no—
367C22×C8—111no—
368C22×C8—222no—
369C22×C8—222no—
370C22×C8—441no—
371C22×C8C22×D1111yescharacteristic
372C22×C8C22×D1111yescharacteristic
373C22⋊Q8—22no—
374C22⋊Q8C2×Dic1114yes—
375C4×Q8—222no—
376C4×Q8—441no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—222no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—441no—
391C2×C4⋊C4C2×Dic1114yes—
392C2×C4⋊C4C22×D1111yescharacteristic
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—111no—
397C2×C22⋊C4—111no—
398C2×C22⋊C4—221no—
399C2×C42—111no—
400C2×C42—111no—
401C2×C42—221no—
402C2×C42—221no—
403C2×C42—221no—
404C2×C42—221no—
405#107C2×Dic1114yescomplemented
406#107C2×Dic1114yescomplemented
407#106—222no—
408#106—441no—
409#103—222no—
410#103—441no—
411#103C2×Dic1114yescomplemented
412#103C2×Dic1114yescomplemented
413C22⋊C8C2×Dic1114yes—
414#97—222no—
415#97—441no—
416#95—111no—
417#95—111no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427C2×C11—24no—
428C2×C11#235911yescharacteristic
429C2×C11C2×#44111yescharacteristic
430C2×C11#294611yescharacteristic
431C2×C11#331411yescharacteristic
432C2×C11#332011yescharacteristic
433C2×C11#334411yescharacteristic
434C2×C11#334611yescharacteristic
435C24D4×D1111yescharacteristic
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8C22×Dic1112yes—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—24no—
451C22×C4—81no—
452C22×C4—81no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—442no—
462C22×C4—442no—
463C22×C4—881no—
464C22×C4D4×D1111yescharacteristic
465C22×C4#434112yes—
466C22×C4C22×Dic1112yes—
467C22×C4C23×D1111yescharacteristic
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—112no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—444no—
479C2×C8C22×Dic1112yes—
480C2×C8C22×Dic1112yes—
481C4⋊C4—24no—
482C4⋊C4—24no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—112no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—442no—
495C4⋊C4—442no—
496C4⋊C4—881no—
497C4⋊C4—881no—
498C4⋊C4—881no—
499C4⋊C4C22×Dic1112yes—
500C4⋊C4C22×Dic1112yes—
501C4⋊C4C22×Dic1112yes—
502C22⋊C4—24no—
503C22⋊C4—222no—
504C22⋊C4—222no—
505C22⋊C4—442no—
506C42—221no—
507C42—221no—
508C42—221no—
509C42—221no—
510C42—442no—
511C42—881no—
512C42—881no—
513C42—881no—
514C11#2293211yescharacteristic, complemented, Sylow
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23#6697112yes—
520C23#6697112yes—
521C23D4×Dic1112yes—
522C23C2×D4×D1111yescharacteristic
523Q8—22no—
524Q8—22no—
525Q8—41no—
526Q8—41no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—84no—
546C2×C4—221no—
547C2×C4—221no—
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—222no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—441no—
560C2×C4—441no—
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—884no—
571C2×C4D4×Dic1112yes—
572C2×C4C2×#434111yescharacteristic
573C2×C4#41×D1111yescharacteristic
574C2×C4#41×D1111yescharacteristic
575C2×C4#6704211yescharacteristic
576C2×C4#6704311yescharacteristic
577C2×C4C23×Dic1111yescharacteristic
578C8—22no—
579C8—22no—
580C8—222no—
581C8—441no—
582C22—22no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—22no—
588C22#1062279714yes—
589C22#1062318511yescharacteristic
590C22#1062318611yescharacteristic
591C22C2×#6697111yescharacteristic
592C22C2×#6697111yescharacteristic
593C22#1062330511yescharacteristic
594C22#1062330611yescharacteristic
595C22C2×D4×Dic1111yescharacteristic
596C4—22no—
597C4—42no—
598C4—42no—
599C4—42no—
600C4—42no—
601C4—441no—
602C4—441no—
603C4—442no—
604C4—441no—
605C4—441no—
606C4—881no—
607C4—881no—
608C4—881no—
609C4#1062318111yescharacteristic
610C4#1062318911yescharacteristic
611C4#41×Dic1111yescharacteristic
612C4#1062335811yescharacteristic
613C2—24no—
614C2#1307161211yescharacteristic
615C2C2×#1062279711yescharacteristic
616C2#1307744911yescharacteristic
617C2#1308069511yescharacteristic
618C2#1308078511yescharacteristic
619C2#1308106911yescharacteristic
620C2#1308110511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#484C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#484D11
hypocenterC11#22932
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. #13069355C2semidirect
4. #13069308C2semidirect
5. #13069252C2semidirect
6. #13069189C2semidirect
7. #13069189C2semidirect
9. #13068886C2semidirect
11. #13068515C2semidirect
12. #13068448C2semidirect
21. C11×#484C4semidirect
103. C11×#107C2×C4semidirect
104. C11×#107C2×C4semidirect
105. C11×#103C2×C4semidirect
106. C11×#103C2×C4semidirect
292. #484Dic11semidirect
405. #107C2×Dic11semidirect
406. #107C2×Dic11semidirect
411. #103C2×Dic11semidirect
412. #103C2×Dic11semidirect
514. C11#22932semidirect

Maximal subgroups

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

subgroupindex
#130716252
#130714932
#130693552
#130693082
#130692522
#130691892
#130690402
#130688862
#130688112
#130685152
#130684482
#130683952
C2×#106221672
C2×C11×#4842
#2293211