Finite Group Databasebeta

← #14770452

Subgroups — #14770452

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623100C211yesmaximal, characteristic
2C2×#10622441C211yesmaximal, characteristic
3#13071575C211yesmaximal, characteristic
4#13069587C211yesmaximal, characteristic
5#13069584C211yesmaximal, characteristic
6#13069579C211yesmaximal, characteristic
7#13069572C211yesmaximal, characteristic
8#13069571C211yesmaximal, characteristic
9#13069562C211yesmaximal, characteristic
10#13068629C211yesmaximal, characteristic
11#13068629C211yesmaximal, characteristic
12#13068448C211yesmaximal, characteristic
13#13068446C211yesmaximal, characteristic
14#103×Dic11C211yesmaximal, characteristic
15C11×#1803C211yesmaximal, characteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19#10623100—24no—
20#10623100C418yescomplemented
21C2×#66943—21no—
22C2×#66943C2211yescharacteristic
23C2×#66941—21no—
24C2×#66941C2211yescharacteristic
25C2×#66923—21no—
26C2×#66923C2211yescharacteristic
27C2×C4×Dic22—21no—
28C2×C4×Dic22C2211yescharacteristic
29C2×C11×C4⋊C8C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C11×#384C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C2×C8×Dic11C2211yescharacteristic
39#10622591—21no—
40#10622591—21no—
41#10622590C2211yescharacteristic
42#10622590C2211yescharacteristic
43C4⋊C4×Dic11—21no—
44C4⋊C4×Dic11C2211yescharacteristic
45C4⋊C4×Dic11C2211yescharacteristic
46#10622587—21no—
47C4×C4⋊Dic11C2211yescharacteristic
48C2×#66867C2211yescharacteristic
49#10622441—24no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×Q8×C11C2311yescharacteristic
63C22×Dic22—21no—
64C22×Dic22D411yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C4×Q8×C11—22no—
68C4×Q8×C11C2×C414yes—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77Q8×Dic11—22no—
78Q8×Dic11—22no—
79Q8×Dic11C2×C414yes—
80Q8×Dic11C2×C414yes—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11D411yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4D411yescharacteristic
94C2×Dic11⋊C4D411yescharacteristic
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104#66943—28no—
105#66943—22no—
106#66943C2×C414yes—
107#66941—28no—
108#66941—22no—
109#66941C2×C414yes—
110#66923—22no—
111#66923—28no—
112#66923C2×C414yes—
113C4×Dic22—28no—
114C4×Dic22C2×C414yes—
115C4×Dic22D414yes—
116C11×C4⋊C8—22no—
117C11×#103—22no—
118C11×#103—22no—
119#66899—22no—
120#66899Q814yescomplemented
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128#66879—22no—
129Dic11⋊C8—22no—
130Dic11⋊C8—22no—
131C8×Dic11—22no—
132#66867—22no—
133#22527—111nomaximal, Sylow
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11C22×C412yes—
138C2×Q8×C11C2×Q812yes—
139C2×Q8×C11#4112yes—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C2×Dic22—24no—
156C2×Dic22—41no—
157C2×Dic22—41no—
158C2×Dic22—42no—
159C2×Dic22—42no—
160C2×Dic22C22⋊C414yes—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C11×C4⋊C4—24no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—42no—
174C11×C4⋊C4—81no—
175C11×C4⋊C4C22×C412yes—
176C42×C11—24no—
177C42×C11C22×C412yes—
178C42×C11C2×D412yes—
179C4⋊Dic11—24no—
180C4⋊Dic11—24no—
181C4⋊Dic11—24no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11C22⋊C414yes—
188C4⋊Dic11C22×C412yes—
189C4⋊Dic11C22×C412yes—
190C4⋊Dic11C2×Q812yes—
191Dic11⋊C4—24no—
192Dic11⋊C4—24no—
193Dic11⋊C4—24no—
194Dic11⋊C4—24no—
195Dic11⋊C4C22⋊C414yes—
196Dic11⋊C4C22⋊C414yes—
197C4×Dic11—24no—
198C4×Dic11—24no—
199C4×Dic11—42no—
200C4×Dic11—81no—
201C4×Dic11—81no—
202C4×Dic11C22×C412yes—
203C4×Dic11C22×C412yes—
204C4×Dic11C2×D412yes—
205C4×Dic11C2×D412yes—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8C2×Q812yes—
212C2×#557—111no—
213C2×#446—111no—
214#2355—111no—
215#1993—111no—
216#1992—111no—
217#1991—111no—
218#1989—111no—
219#1989—111no—
220#1987—111no—
221#1805—111no—
222#1805—111no—
223#1803D1111yescharacteristic
224#1763—111no—
225#1763—111no—
226C4×#103—111no—
227C23×C11C22×D411yescharacteristic
228Q8×C11—22no—
229Q8×C11—22no—
230Q8×C11—22no—
231Q8×C11C4×Q814yes—
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—22no—
240C2×C4×C11—41no—
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×C11C2×C22⋊C412yes—
249C2×C4×C11C2×C22⋊C412yes—
250C2×C4×C11C23×C411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11C22×Q811yescharacteristic
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C112−1+411yescharacteristic
255C2×C4×C112−1+411yescharacteristic
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—22no—
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×Dic11C2×C22⋊C412yes—
277C2×Dic11C2×C22⋊C412yes—
278C2×Dic11C2×C22⋊C412yes—
279C2×Dic11C2×C22⋊C412yes—
280Dic22—44no—
281Dic22—48no—
282C8×C11—41no—
283C8×C11—41no—
284C11⋊C8—22no—
285C11⋊C8—41no—
286#557—118no—
287#557—224no—
288C2×C4⋊Q8—111no—
289C2×C4⋊Q8—221no—
290C2×#125—111no—
291C2×#125—111no—
292C2×#125—221no—
293C2×#125—221no—
294C2×C4×Q8—111no—
295C2×C4×Q8—111no—
296C2×C4×Q8—111no—
297C2×C4×Q8—221no—
298C2×C4×Q8C2×D1111yescharacteristic
299#446—224no—
300C2×C4⋊C8—111no—
301C2×C4⋊C8—111no—
302C2×C4⋊C8C2×D1111yescharacteristic
303C2×#103—111no—
304C2×#103—111no—
305C2×#103C2×D1111yescharacteristic
306C2×#103C2×D1111yescharacteristic
307C2×#97—111no—
308C2×#97—111no—
309C2×C4×C8—111no—
310#391—221no—
311#387—221no—
312#387—221no—
313#384C2×D1111yescharacteristic
314#382—111no—
315#382—111no—
316C4×C4⋊C4—111no—
317C4×C4⋊C4—111no—
318C4×C4⋊C4—111no—
319C4×C4⋊C4—221no—
320#340—111no—
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#340—111no—
330#340C2×D1111yescharacteristic
331#340C2×D1111yescharacteristic
332C22×C11C22×C22⋊C411yescharacteristic
333C22×C11#54811yescharacteristic
334C22×C11D4×Q811yescharacteristic
335C22×C11#57511yescharacteristic
336C22×C11#57511yescharacteristic
337C22×C11#57711yescharacteristic
338C22×C11#57811yescharacteristic
339C4×C11—24no—
340C4×C11—22no—
341C4×C11—22no—
342C4×C11—42no—
343C4×C11—81no—
344C4×C11—81no—
345C4×C11C2×C4×Q811yescharacteristic
346C4×C11#51911yescharacteristic
347C4×C11#54811yescharacteristic
348C4×C11D4×Q811yescharacteristic
349Dic11—22no—
350Dic11—22no—
351Dic11—22no—
352Dic11—22no—
353Dic11—42no—
354Dic11—42no—
355Dic11—42no—
356Dic11—81no—
357C22×Q8—111no—
358C22×Q8—221no—
359C22×Q8C22×D1111yescharacteristic
360C22×C8—111no—
361C22×C8—111no—
362C22×C8C22×D1111yescharacteristic
363C22×C8C22×D1111yescharacteristic
364C4⋊Q8—114no—
365C4⋊Q8—222no—
366C4⋊Q8—228no—
367#125—114no—
368#125—114no—
369#125—228no—
370#125—222no—
371#125—228no—
372#125—222no—
373C4×Q8—22no—
374C4×Q8—114no—
375C4×Q8—114no—
376C4×Q8—114no—
377C4×Q8—114no—
378C4×Q8—228no—
379C4×Q8—222no—
380C4×Q8—222no—
381C4×Q8C4×D1114yes—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C42—21no—
403C2×C42—111no—
404C2×C42—111no—
405C2×C42—221no—
406C2×C42—221no—
407C2×C42—221no—
408C2×C42—221no—
409C2×C42—221no—
410C2×C42C22×D1111yescharacteristic
411C4⋊C8—22no—
412C4⋊C8—222no—
413C4⋊C8—222no—
414#103—22no—
415#103—22no—
416#103—114no—
417#103—222no—
418#97—222no—
419#97—222no—
420C4×C8—222no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428C2×C11Q8×C22⋊C411yescharacteristic
429C2×C11#289611yescharacteristic
430C2×C11#289811yescharacteristic
431C2×C11#337111yescharacteristic
432C2×C11#337711yescharacteristic
433C2×C11#338811yescharacteristic
434C2×C11#339011yescharacteristic
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—114no—
439C2×Q8—224no—
440C2×Q8—441no—
441C2×Q8—441no—
442C2×Q8—442no—
443C2×Q8—442no—
444C2×Q8C2×C4×D1112yes—
445C2×Q8#434112yes—
446C2×Q8Q8×D1112yes—
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—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4D4×D1111yescharacteristic
460C22×C4D4×D1111yescharacteristic
461C22×C4C23×D1111yescharacteristic
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—112no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C4⋊C4—24no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—42no—
481C4⋊C4—81no—
482C4⋊C4—114no—
483C4⋊C4—114no—
484C4⋊C4—114no—
485C4⋊C4—112no—
486C4⋊C4—112no—
487C4⋊C4—112no—
488C4⋊C4—224no—
489C4⋊C4—224no—
490C4⋊C4—224no—
491C4⋊C4—224no—
492C4⋊C4—224no—
493C4⋊C4—224no—
494C4⋊C4—224no—
495C4⋊C4—221no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4C2×C4×D1112yes—
501C42—24no—
502C42—112no—
503C42—112no—
504C42—112no—
505C42—112no—
506C42—224no—
507C42—224no—
508C42—442no—
509C42—881no—
510C42—881no—
511C42C2×C4×D1112yes—
512C42D4×D1112yes—
513C11#2252711yescharacteristic, complemented, Sylow
514C23C2×D4×D1111yescharacteristic
515Q8—22no—
516Q8—22no—
517Q8—22no—
518Q8—444no—
519Q8—448no—
520Q8#6694014yes—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—112no—
538C2×C4—112no—
539C2×C4—112no—
540C2×C4—112no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—222no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4C22⋊C4×D1112yes—
562C2×C4C22⋊C4×D1112yes—
563C2×C4C22×C4×D1111yescharacteristic
564C2×C4C2×D4×D1111yescharacteristic
565C2×C4C2×#434111yescharacteristic
566C2×C4C2×Q8×D1111yescharacteristic
567C2×C4#6704311yescharacteristic
568C2×C4#6704311yescharacteristic
569C8—41no—
570C8—41no—
571C8—222no—
572C8—441no—
573C22C2×C22⋊C4×D1111yescharacteristic
574C22#1062312911yescharacteristic
575C22#1062316311yescharacteristic
576C22#1062329311yescharacteristic
577C22#1062329711yescharacteristic
578C22#1062330411yescharacteristic
579C22#1062330811yescharacteristic
580C4—24no—
581C4—22no—
582C4—22no—
583C4—42no—
584C4—81no—
585C4—81no—
586C4—222no—
587C4—222no—
588C4—222no—
589C4—222no—
590C4—442no—
591C4—442no—
592C4—442no—
593C4—881no—
594C4C2×#6694011yescharacteristic
595C4#1062304711yescharacteristic
596C4#1062312911yescharacteristic
597C4#1062316311yescharacteristic
598C2#1307144811yescharacteristic
599C2#1307713211yescharacteristic
600C2#1307714411yescharacteristic
601C2#1308137711yescharacteristic
602C2#1308145111yescharacteristic
603C2#1308156811yescharacteristic
604C2#1308157811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1803C2
socle, prime radicalC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenter#1803D11
hypocenterC11#22527
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
20. #10623100C4semidirect
120. #66899Q8semidirect
513. C11#22527semidirect

Maximal subgroups

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

subgroupindex
C2×#106231002
C2×#106224412
#130715752
#130695872
#130695842
#130695792
#130695722
#130695712
#130695622
#130686292
#130684482
#130684462
#103×Dic112
C11×#18032
#2252711