Finite Group Databasebeta

← #14765612

Subgroups — #14765612

Order 2816.

780 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622609C211yesmaximal, characteristic
2#13071298C211yesmaximal, characteristic
3#13069356C211yesmaximal, characteristic, complemented
4#13069346C211yesmaximal, characteristic, complemented
5#13069305C211yesmaximal, characteristic, complemented
6#13069291C211yesmaximal, characteristic, complemented
7#13069191C211yesmaximal, characteristic, complemented
8#13069184C211yesmaximal, characteristic, complemented
9#13068923C211yesmaximal, characteristic
10#13068869C211yesmaximal, characteristic, complemented
11#13068869C211yesmaximal, characteristic, complemented
12#13068804C211yesmaximal, characteristic
13#13068711C211yesmaximal, characteristic
14#13068382C211yesmaximal, characteristic
15C11×#2317C211yesmaximal, characteristic
16C2×C11×#117C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C11×#389C2211yescharacteristic
22C11×#389C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#385—21no—
26C11×#385—21no—
27C11×#384—21no—
28C11×#382—21no—
29#10622825C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32#10622609C418yescomplemented
33#10622591—21no—
34#10622585—21no—
35C2×#66874C2211yescharacteristic
36C2×#66874C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622558—21no—
44#10622557—21no—
45C4×C4⋊Dic11C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622541C2211yescharacteristic
48C2×#66867C2211yescharacteristic
49C2×C4×C11⋊C8C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C22×Dic22C2311yescharacteristic
63C11×#117—22no—
64C11×#117—41no—
65C11×#117—41no—
66C11×#117C2×C414yes—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—41no—
73C2×C11×C4⋊C4—41no—
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C42×C11—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91#66977—22no—
92#66977C2×C414yes—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C4×Dic22—41no—
103C4×Dic22—41no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C22⋊(C11⋊C8)—22no—
114C22⋊(C11⋊C8)C2×C414yes—
115#66874—41no—
116#66874—41no—
117#66874C2×C414yescomplemented
118#66874C2×C414yescomplemented
119#66872C2×C414yescomplemented
120#66871—41no—
121#66871—41no—
122#66871C2×C414yescomplemented
123#66867—41no—
124C4×C11⋊C8—41no—
125#22094—111nomaximal, Sylow
126C24×C11C2×D411yescharacteristic
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—42no—
136C22×C4×C11—81no—
137C22×C4×C11—81no—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11#4112yes—
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22C22×C412yes—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—41no—
163C11×C4⋊C4—41no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4—81no—
166C11×C4⋊C4—81no—
167C11×C4⋊C4—81no—
168C11×C4⋊C4—81no—
169C11×C4⋊C4C22×C412yes—
170C11×C4⋊C4C22×C412yes—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—41no—
173C11×C22⋊C4—41no—
174C42×C11—24no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C22⋊Dic11—24no—
180C22⋊Dic11—81no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11C22×C412yes—
187Dic11⋊C4—24no—
188Dic11⋊C4—42no—
189Dic11⋊C4—81no—
190C4×Dic11—42no—
191C4×Dic11—81no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8C22×C412yes—
203C2×C11⋊C8C22×C412yes—
204C2×#485—111no—
205#2323—111no—
206#2317D1111yescharacteristic
207#1944—111no—
208#1942—111no—
209#1935—111no—
210#1933—111no—
211#1919—111no—
212#1918—111no—
213#1872—111no—
214#1863—111no—
215#1863—111no—
216#1852—111no—
217#1825—111no—
218#1750—111no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11C4×D412yes—
226C23×C11C22×D411yescharacteristic
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—84no—
258C2×C4×C11C4×D412yes—
259C2×C4×C11C23×C411yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C2×C4×C11H(5,𝔽2)11yescharacteristic
263C2×C4×C112−1+411yescharacteristic
264C2×C4×C112−1+411yescharacteristic
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277Dic22—22no—
278Dic22—22no—
279Dic22—41no—
280Dic22—41no—
281C11⋊C8—22no—
282C11⋊C8—22no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C2×C22⋊Q8—111no—
286C2×C4×Q8—111no—
287C2×#117C2×D1111yescharacteristic
288C2×#117C2×D1111yescharacteristic
289C22×C4⋊C4C2×D1111yescharacteristic
290#485—118no—
291C2×#107—111no—
292C2×#107—111no—
293C2×#107—111no—
294C2×#106—111no—
295C2×#103—111no—
296C2×#103—111no—
297C2×#103—111no—
298C2×#103—111no—
299C2×C22⋊C8—111no—
300C2×C22⋊C8—111no—
301C2×#97—111no—
302C2×C4×C8—111no—
303#391—111no—
304#389—111no—
305#389—221no—
306#389C2×D1111yescharacteristic
307#389C2×D1111yescharacteristic
308#389C2×D1111yescharacteristic
309#389C2×D1111yescharacteristic
310#388—221no—
311#388—221no—
312#387—221no—
313#385—21no—
314#385—21no—
315#384—21no—
316#382—21no—
317#380—111no—
318C4×C4⋊C4—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#336—111no—
328#336—111no—
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—22no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11C2×C4×D411yescharacteristic
337C22×C11#53411yescharacteristic
338C22×C11#53611yescharacteristic
339C22×C11#57611yescharacteristic
340C22×C11#57711yescharacteristic
341C22×C11#57811yescharacteristic
342C22×C11#57811yescharacteristic
343C4×C11—22no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—42no—
349C4×C11—42no—
350C4×C11—81no—
351C4×C11—81no—
352C4×C11#52011yescharacteristic
353C4×C11#52011yescharacteristic
354C4×C11#53911yescharacteristic
355C4×C11#53911yescharacteristic
356Dic11—42no—
357Dic11—42no—
358Dic11—81no—
359Dic11—81no—
360C22×Q8—111no—
361C23×C4—21no—
362C23×C4C22×D1111yescharacteristic
363C22×C8—111no—
364C22×C8—111no—
365C22×C8—111no—
366C22×C8—111no—
367C22⋊Q8—114no—
368C22⋊Q8—222no—
369C4×Q8—441no—
370C4×Q8—441no—
371#117—22no—
372#117—41no—
373#117—41no—
374#117C4×D1114yes—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—41no—
381C2×C4⋊C4—41no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4C22⋊D1111yescharacteristic
389C2×C4⋊C4C22⋊D1111yescharacteristic
390C2×C4⋊C4C22×D1111yescharacteristic
391C2×C4⋊C4C22×D1111yescharacteristic
392C2×C4⋊C4C22×D1111yescharacteristic
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4C22⋊D1111yescharacteristic
398C2×C22⋊C4C22⋊D1111yescharacteristic
399C2×C42—21no—
400C2×C42—221no—
401C2×C42—221no—
402C2×C42C22×D1111yescharacteristic
403C2×C42C22×D1111yescharacteristic
404#107—114no—
405#107—441no—
406#107—441no—
407#106—114no—
408#103—114no—
409#103—114no—
410#103—441no—
411#103—441no—
412C22⋊C8—114no—
413C22⋊C8—222no—
414#97—441no—
415C4×C8—441no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425C2×C11—42no—
426C2×C11#232211yescharacteristic
427C2×C11#294711yescharacteristic
428C2×C11#295111yescharacteristic
429C2×C11#319811yescharacteristic
430C2×C11#320211yescharacteristic
431C2×C11#324211yescharacteristic
432C2×C11#324311yescharacteristic
433C24C2×C22⋊D1111yescharacteristic
434C2×Q8—112no—
435C2×Q8—221no—
436C2×Q8—221no—
437C2×Q8—221no—
438C2×Q8—221no—
439C2×Q8—221no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—42no—
449C22×C4—81no—
450C22×C4—81no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4C2×C4×D1112yes—
456C22×C4#433912yes—
457C22×C4C2×C22⋊D1111yescharacteristic
458C22×C4C2×C22⋊D1111yescharacteristic
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461C22×C4C2×C22⋊D1111yescharacteristic
462C22×C4C23×D1111yescharacteristic
463C2×C8—112no—
464C2×C8—112no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4—42no—
484C4⋊C4—81no—
485C4⋊C4—81no—
486C4⋊C4—81no—
487C4⋊C4—81no—
488C4⋊C4—112no—
489C4⋊C4—224no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—442no—
496C4⋊C4—881no—
497C4⋊C4C2×C4×D1112yes—
498C4⋊C4C2×C4×D1112yes—
499C22⋊C4—24no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—224no—
503C22⋊C4—881no—
504C42—24no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—442no—
510C42—881no—
511C11#2209411yescharacteristic, complemented, Sylow
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23C4×C22⋊D1112yes—
519C23C22×C22⋊D1111yescharacteristic
520Q8—222no—
521Q8—222no—
522Q8—441no—
523Q8—441no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—84no—
555C2×C4—222no—
556C2×C4—222no—
557C2×C4—441no—
558C2×C4—441no—
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×C4C4×C22⋊D1112yes—
568C2×C4C22×C4×D1111yescharacteristic
569C2×C4C2×#433911yescharacteristic
570C2×C4#6703711yescharacteristic
571C2×C4#6703711yescharacteristic
572C2×C4#6704011yescharacteristic
573C2×C4#6704011yescharacteristic
574C8—222no—
575C8—222no—
576C8—441no—
577C8—441no—
578C22—22no—
579C22—22no—
580C22—22no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22C2×C4×C22⋊D1111yescharacteristic
586C22#1062333511yescharacteristic
587C22#1062334711yescharacteristic
588C22#1062336611yescharacteristic
589C22#1062336711yescharacteristic
590C22#1062336911yescharacteristic
591C22#1062336911yescharacteristic
592C4—22no—
593C4—41no—
594C4—41no—
595C4—42no—
596C4—41no—
597C4—41no—
598C4—42no—
599C4—81no—
600C4—81no—
601C4—442no—
602C4—442no—
603C4—881no—
604C4—881no—
605C4#1062303511yescharacteristic
606C4#1062303511yescharacteristic
607C4#1062304611yescharacteristic
608C4#1062304611yescharacteristic
609C2—42no—
610C2#1307128511yescharacteristic
611C2#1307745511yescharacteristic
612C2#1307748911yescharacteristic
613C2#1307946811yescharacteristic
614C2#1307950711yescharacteristic
615C2#1307988411yescharacteristic
616C2#1307989911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2317C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#2317D11
hypocenterC11#22094
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2317

Complements

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

NH ≅ G/Ntype
3. #13069356C2semidirect
4. #13069346C2semidirect
5. #13069305C2semidirect
6. #13069291C2semidirect
7. #13069191C2semidirect
8. #13069184C2semidirect
10. #13068869C2semidirect
11. #13068869C2semidirect
32. #10622609C4semidirect
117. #66874C2×C4semidirect
118. #66874C2×C4semidirect
119. #66872C2×C4semidirect
122. #66871C2×C4semidirect
511. C11#22094semidirect

Maximal subgroups

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

subgroupindex
C2×#106226092
#130712982
#130693562
#130693462
#130693052
#130692912
#130691912
#130691842
#130689232
#130688692
#130688042
#130687112
#130683822
C11×#23172
#2209411