Finite Group Databasebeta

← #14765606

Subgroups — #14765606

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×#10622658C211yesmaximal, characteristic
2#13071236C211yesmaximal, characteristic
3#13069356C211yesmaximal, characteristic, complemented
4#13069346C211yesmaximal, characteristic, complemented
5#13069309C211yesmaximal, characteristic, complemented
6#13069295C211yesmaximal, characteristic, complemented
7#13069194C211yesmaximal, characteristic, complemented
8#13069187C211yesmaximal, characteristic, complemented
9#13068924C211yesmaximal, characteristic
10#13068870C211yesmaximal, characteristic, complemented
11#13068870C211yesmaximal, characteristic, complemented
12#13068803C211yesmaximal, characteristic
13#13068708C211yesmaximal, characteristic
14#13068382C211yesmaximal, characteristic
15C11×#2323C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C11×#391C2211yescharacteristic
22C11×#389—21no—
23C11×#389C2211yescharacteristic
24C11×#388—21no—
25C11×#388—21no—
26C11×#387—21no—
27C11×#380C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35#10622658C418yescomplemented
36#10622590—21no—
37#10622589—21no—
38C2×#66872C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42#10622559—21no—
43#10622559—21no—
44#10622541C2211yescharacteristic
45#10622541C2211yescharacteristic
46#10622541C2211yescharacteristic
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
60C22×Q8×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C11×C22⋊Q8—22no—
64C11×C22⋊Q8C2×C414yes—
65C4×Q8×C11—41no—
66C4×Q8×C11—41no—
67C11×#117—41no—
68C11×#117—41no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C22⋊Dic11—21no—
86#66979—22no—
87#66979C2×C414yes—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—41no—
90C2×C4⋊Dic11—41no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95—21no—
109#66899—41no—
110#66899—41no—
111#66899C2×C414yescomplemented
112#66899C2×C414yescomplemented
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C22⋊(C11⋊C8)—22no—
118C22⋊(C11⋊C8)C2×C414yes—
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
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×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4112yes—
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—42no—
154C22×Dic11—81no—
155C22×Dic11—81no—
156C11×C4⋊C4—24no—
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⋊C4C22×C412yes—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—41no—
169C11×C22⋊C4—41no—
170C11×C22⋊C4—81no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—42no—
176C42×C11—81no—
177C22⋊Dic11—24no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—42no—
185C4⋊Dic11C22×C412yes—
186C4⋊Dic11C22×C412yes—
187Dic11⋊C4—81no—
188Dic11⋊C4—81no—
189Dic11⋊C4—81no—
190Dic11⋊C4—81no—
191C4×Dic11—24no—
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#2323D1111yescharacteristic
206#2317—111no—
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
227Q8×C11—22no—
228Q8×C11—22no—
229Q8×C11—41no—
230Q8×C11—41no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
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—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
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—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11C4×D412yes—
262C2×C4×C11C23×C411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×C4×C112−1+411yescharacteristic
267C2×C4×C112−1+411yescharacteristic
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—41no—
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—84no—
281C11⋊C8—22no—
282C11⋊C8—22no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C2×C22⋊Q8C2×D1111yescharacteristic
286C2×C4×Q8C2×D1111yescharacteristic
287C2×#117—111no—
288C2×#117C2×D1111yescharacteristic
289C22×C4⋊C4—111no—
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#391C2×D1111yescharacteristic
304#389—21no—
305#389—111no—
306#389—111no—
307#389—111no—
308#389—111no—
309#389C2×D1111yescharacteristic
310#388—21no—
311#388—21no—
312#387—21no—
313#385—221no—
314#385—221no—
315#384—221no—
316#382—221no—
317#380C2×D1111yescharacteristic
318C4×C4⋊C4C2×D1111yescharacteristic
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—42no—
345C4×C11—41no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—41no—
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×Q8C22×D1111yescharacteristic
361C23×C4—221no—
362C23×C4C22×D1111yescharacteristic
363C22×C8—111no—
364C22×C8—111no—
365C22×C8—111no—
366C22×C8—111no—
367C22⋊Q8—22no—
368C22⋊Q8C4×D1114yes—
369C4×Q8—41no—
370C4×Q8—41no—
371#117—41no—
372#117—41no—
373#117—114no—
374#117—222no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—441no—
388C2×C4⋊C4—441no—
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—21no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4C22⋊D1111yescharacteristic
398C2×C22⋊C4C22⋊D1111yescharacteristic
399C2×C42—21no—
400C2×C42—21no—
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—21no—
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—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8C2×C4×D1112yes—
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—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—442no—
453C22×C4—881no—
454C22×C4—881no—
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—24no—
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—112no—
486C4⋊C4—112no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—442no—
494C4⋊C4—881no—
495C4⋊C4—881no—
496C4⋊C4—881no—
497C4⋊C4—881no—
498C4⋊C4C2×C4×D1112yes—
499C22⋊C4—24no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—81no—
503C22⋊C4—224no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—42no—
509C42—81no—
510C42—224no—
511C11#2209411yescharacteristic, complemented, Sylow
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23C4×C22⋊D1112yes—
519C23C22×C22⋊D1111yescharacteristic
520Q8—22no—
521Q8—22no—
522Q8—41no—
523Q8—41no—
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—222no—
555C2×C4—222no—
556C2×C4—441no—
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—884no—
567C2×C4C4×C22⋊D1112yes—
568C2×C4C22×C4×D1111yescharacteristic
569C2×C4C2×#433911yescharacteristic
570C2×C4#6703711yescharacteristic
571C2×C4#6703711yescharacteristic
572C2×C4#6704311yescharacteristic
573C2×C4#6704311yescharacteristic
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#1062335611yescharacteristic
588C22#1062336611yescharacteristic
589C22#1062336811yescharacteristic
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#1062307711yescharacteristic
606C4#1062307711yescharacteristic
607C4#1062309511yescharacteristic
608C4#1062309511yescharacteristic
609C2—42no—
610C2#1307128111yescharacteristic
611C2#1307745911yescharacteristic
612C2#1307748911yescharacteristic
613C2#1307946211yescharacteristic
614C2#1307950711yescharacteristic
615C2#1307987811yescharacteristic
616C2#1307989311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2323C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#2323D11
hypocenterC11#22094
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
3. #13069356C2semidirect
4. #13069346C2semidirect
5. #13069309C2semidirect
6. #13069295C2semidirect
7. #13069194C2semidirect
8. #13069187C2semidirect
10. #13068870C2semidirect
11. #13068870C2semidirect
35. #10622658C4semidirect
111. #66899C2×C4semidirect
112. #66899C2×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×#106226582
#130712362
#130693562
#130693462
#130693092
#130692952
#130691942
#130691872
#130689242
#130688702
#130688032
#130687082
#130683822
C11×#23232
#2209411