Finite Group Databasebeta

← #14775143

Subgroups — #14775143

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
1C2×#10622422C211yesmaximal, characteristic
2#13071617C211yesmaximal, characteristic
3#13071492C211yesmaximal, characteristic
4#13069351C211yesmaximal, characteristic, complemented
5#13069308C211yesmaximal, characteristic, complemented
6#13069253C211yesmaximal, characteristic, complemented
7#13069190C211yesmaximal, characteristic, complemented
8#13069188C211yesmaximal, characteristic, complemented
9#13069036C211yesmaximal, characteristic
10#13068807C211yesmaximal, characteristic
11#13068516C211yesmaximal, characteristic, complemented
12#13068446C211yesmaximal, characteristic, complemented
13#13068391C211yesmaximal, characteristic
14D11×#340C211yesmaximal, characteristic
15C11×#1865C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19C2×C4⋊C4×D11C2211yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×#103C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C11×#389C2211yescharacteristic
25#10622843C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31#10622602—21no—
32#10622600—21no—
33#10622600C2211yescharacteristic
34#10622598C2211yescharacteristic
35#10622591—21no—
36C4⋊C4×Dic11C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38#10622585—21no—
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C4×(C2×D11)⋊C4—21no—
42C4×(C2×D11)⋊C4C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44#10622546—21no—
45#10622541C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47#10622422C418yescomplemented
48#10622279—21no—
49#10622268—21no—
50C11×#340C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C4×Q8×C11—22no—
67C4×Q8×C11—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11—21no—
74C2×C42×C11C2311yescharacteristic
75#66999—22no—
76#66999C2×C414yes—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4D411yescharacteristic
80C2×(C2×D11)⋊C4D411yescharacteristic
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C2×C8×D11—22no—
97C2×C8×D11—22no—
98C2×C8×D11—41no—
99C4⋊C4×D11—22no—
100C4⋊C4×D11—22no—
101C4⋊C4×D11—41no—
102C4⋊C4×D11C2×C414yes—
103C11×#106—22no—
104C11×#103—41no—
105C11×#103C2×C414yescomplemented
106C11×#95—21no—
107#66899—22no—
108#66899C2×C414yescomplemented
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95D411yescharacteristic
118C11⋊#95D411yescharacteristic
119(C2×D11)⋊C8C2×C414yes—
120#66882C2×C414yescomplemented
121#66879—22no—
122#66872—41no—
123#66871C2×C414yescomplemented
124#66867—41no—
125#22932—111nomaximal, Sylow
126C23×D11C2×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×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11C2×D411yescharacteristic
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C2×C4×D11—24no—
148C2×C4×D11—21no—
149C2×C4×D11—21no—
150C2×C4×D11—21no—
151C2×C4×D11—21no—
152C2×C4×D11—42no—
153C2×C4×D11—42no—
154C2×C4×D11—81no—
155C2×C4×D11—81no—
156C2×C4×D11—81no—
157C2×C4×D11C22×C412yes—
158C2×C4×D11#4112yes—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11C22×C412yes—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—81no—
171C11×C4⋊C4C22×C412yes—
172C11×C4⋊C4#4112yes—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—42no—
176(C2×D11)⋊C4—24no—
177(C2×D11)⋊C4—22no—
178(C2×D11)⋊C4—22no—
179(C2×D11)⋊C4—42no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—81no—
187C4⋊Dic11C22×C412yes—
188C4⋊Dic11C22×C412yes—
189Dic11⋊C4—24no—
190Dic11⋊C4—24no—
191Dic11⋊C4—42no—
192Dic11⋊C4—81no—
193C4×Dic11—21no—
194C4×Dic11—21no—
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⋊C8C22×C412yes—
203C2×C11⋊C8#4112yes—
204C8×D11—44no—
205C2×#484—111no—
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#1865D1111yescharacteristic, complemented
215#1853—111no—
216#1776—111no—
217#1763—111no—
218#1752—111no—
219C2×#340—111no—
220C23×C11C22×D411yescharacteristic
221C22×D11—21no—
222C22×D11—21no—
223C22×D11—21no—
224C22×D11—21no—
225C22×D11C4×D412yes—
226C22×D11#13712yes—
227C22×D11#13712yes—
228Q8×C11—22no—
229Q8×C11—22no—
230Q8×C11—41no—
231Q8×C11—41no—
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—41no—
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×C11C23×C411yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11H(5,𝔽2)11yescharacteristic
255C2×C4×C112−1+411yescharacteristic
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—41no—
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×Dic11C4×D412yes—
277C4×D11—22no—
278C4×D11—22no—
279C4×D11—22no—
280C4×D11—22no—
281C4×D11—84no—
282C4×D11—84no—
283C8×C11—22no—
284C8×C11—41no—
285C11⋊C8—22no—
286C11⋊C8—22no—
287C23×C8—111no—
288C2×C22⋊Q8—111no—
289C2×C4×Q8C2×D1111yescharacteristic
290C22×C4⋊C4—111no—
291C22×C4⋊C4—111no—
292#484—118no—
293C2×#107—111no—
294C2×#107—111no—
295C2×#106—111no—
296C2×#106C2×D1111yescharacteristic
297C2×#103—111no—
298C2×#103—111no—
299C2×#103C2×D1111yescharacteristic
300C2×#103C2×D1111yescharacteristic
301C2×C22⋊C8—111no—
302C2×#97—111no—
303C2×#97—111no—
304#391—111no—
305#389—111no—
306#389—111no—
307#389—221no—
308#389C2×D1111yescharacteristic
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#340C2×D1111yescharacteristic
329#336—111no—
330#336C2×D1111yescharacteristic
331C22×C11C2×C4×D411yescharacteristic
332C22×C11#54611yescharacteristic
333C22×C11#54711yescharacteristic
334C22×C11C2×#13711yescharacteristic
335C22×C11C2×#13711yescharacteristic
336C22×C11#57611yescharacteristic
337C22×C11#57711yescharacteristic
338C2×D11—22no—
339C2×D11—22no—
340C2×D11—22no—
341C2×D11—22no—
342C2×D11—22no—
343C2×D11—22no—
344C2×D11#44114yes—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11—41no—
348C4×C11—42no—
349C4×C11—41no—
350C4×C11—81no—
351C4×C11C4×#4111yescharacteristic
352C4×C11#52011yescharacteristic
353C4×C11#55111yescharacteristic
354C4×C11#55211yescharacteristic
355Dic11—22no—
356Dic11—41no—
357Dic11—41no—
358Dic11—42no—
359Dic11—42no—
360Dic11—81no—
361Dic11—81no—
362C22×Q8C22×D1111yescharacteristic
363C23×C4—111no—
364C23×C4—221no—
365C23×C4—221no—
366C22×C8—111no—
367C22×C8—111no—
368C22×C8—222no—
369C22×C8—222no—
370C22×C8—441no—
371C22×C8C22×D1111yescharacteristic
372C22×C8C22×D1111yescharacteristic
373C22⋊Q8—114no—
374C22⋊Q8—222no—
375C4×Q8—22no—
376C4×Q8—41no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—114no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—222no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—222no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—441no—
392C2×C4⋊C4C22×D1111yescharacteristic
393C2×C4⋊C4C22×D1111yescharacteristic
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C22⋊C4—111no—
396C2×C22⋊C4—111no—
397C2×C22⋊C4—221no—
398C2×C22⋊C4—221no—
399C2×C42—21no—
400C2×C42—111no—
401C2×C42—221no—
402C2×C42—221no—
403C2×C42—221no—
404C2×C42C22×D1111yescharacteristic
405#107—114no—
406#107—114no—
407#106—22no—
408#106—441no—
409#103—41no—
410#103—114no—
411#103—222no—
412#103C4×D1114yescomplemented
413C22⋊C8—114no—
414#97—222no—
415#97—441no—
416#95—21no—
417#95—111no—
418#95—111no—
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#235911yescharacteristic
428C2×C11C2×#44111yescharacteristic
429C2×C11#294611yescharacteristic
430C2×C11#331411yescharacteristic
431C2×C11#332011yescharacteristic
432C2×C11#334411yescharacteristic
433C2×C11#334611yescharacteristic
434D11—24no—
435C24—111no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8C2×C4×D1112yes—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—111no—
447C22×C4—112no—
448C22×C4—112no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—224no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—442no—
461C22×C4—442no—
462C22×C4—881no—
463C22×C4—881no—
464C22×C4—881no—
465C22×C4D4×D1111yescharacteristic
466C22×C4D4×D1111yescharacteristic
467C22×C4C23×D1111yescharacteristic
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—112no—
474C2×C8—112no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—444no—
480C2×C8C2×C4×D1112yes—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—42no—
486C4⋊C4—81no—
487C4⋊C4—112no—
488C4⋊C4—112no—
489C4⋊C4—224no—
490C4⋊C4—224no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—442no—
498C4⋊C4—881no—
499C4⋊C4—881no—
500C4⋊C4C2×C4×D1112yes—
501C4⋊C4#434112yes—
502C22⋊C4—222no—
503C22⋊C4—222no—
504C22⋊C4—224no—
505C22⋊C4—442no—
506C42—21no—
507C42—21no—
508C42—42no—
509C42—221no—
510C42—221no—
511C42—881no—
512C42—881no—
513C42—881no—
514C11#2293211yescharacteristic, complemented, Sylow
515C23—112no—
516C23—112no—
517C23—112no—
518C23—221no—
519C23—221no—
520C23—221no—
521C23—221no—
522C23C2×D4×D1111yescharacteristic
523Q8—22no—
524Q8—22no—
525Q8—41no—
526Q8—41no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—41no—
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—112no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—222no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—222no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—222no—
557C2×C4—222no—
558C2×C4—221no—
559C2×C4—221no—
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×C4—884no—
572C2×C4C22×C4×D1111yescharacteristic
573C2×C4C2×#434111yescharacteristic
574C2×C4#6703711yescharacteristic
575C2×C4#6704011yescharacteristic
576C2×C4#41×D1111yescharacteristic
577C2×C4#41×D1111yescharacteristic
578C8—22no—
579C8—41no—
580C8—222no—
581C8—222no—
582C22—114no—
583C22—222no—
584C22—222no—
585C22—222no—
586C22—222no—
587C22—222no—
588C22—222no—
589C22C4×D4×D1111yescharacteristic
590C22#1062312211yescharacteristic
591C22#1062316211yescharacteristic
592C22#1062329311yescharacteristic
593C22#1062330011yescharacteristic
594C22D11×#13711yescharacteristic
595C22D11×#13711yescharacteristic
596C4—41no—
597C4—42no—
598C4—42no—
599C4—41no—
600C4—42no—
601C4—81no—
602C4—222no—
603C4—441no—
604C4—442no—
605C4—442no—
606C4—441no—
607C4—881no—
608C4—881no—
609C4#1062303511yescharacteristic
610C4C4×#434111yescharacteristic
611C4#1062317011yescharacteristic
612C4#1062319011yescharacteristic
613C2—224no—
614C2#1307161111yescharacteristic
615C2D11×#44111yescharacteristic
616C2#1307744311yescharacteristic
617C2#1308069011yescharacteristic
618C2#1308078011yescharacteristic
619C2#1308106811yescharacteristic
620C2#1308110811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1865C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1865D11
hypocenterC11#22932
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
4. #13069351C2semidirect
5. #13069308C2semidirect
6. #13069253C2semidirect
7. #13069190C2semidirect
8. #13069188C2semidirect
11. #13068516C2semidirect
12. #13068446C2semidirect
15. C11×#1865C2semidirect
47. #10622422C4semidirect
105. C11×#103C2×C4semidirect
108. #66899C2×C4semidirect
120. #66882C2×C4semidirect
123. #66871C2×C4semidirect
214. #1865D11semidirect
412. #103C4×D11semidirect
514. C11#22932semidirect

Maximal subgroups

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

subgroupindex
C2×#106224222
#130716172
#130714922
#130693512
#130693082
#130692532
#130691902
#130691882
#130690362
#130688072
#130685162
#130684462
#130683912
D11×#3402
C11×#18652
#2293211