Finite Group Databasebeta

← #14769425

Subgroups — #14769425

Order 2816.

1530 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622625C211yesmaximal, characteristic, complemented
2C2×#10622845C212yesmaximal, complemented
3D4×C4⋊Dic11C211yesmaximal, characteristic, complemented
4#13069540C211yesmaximal, characteristic, complemented
5#13069419C211yesmaximal, characteristic, complemented
6#13069050C212yesmaximal, complemented
7#13068924C212yesmaximal, complemented
8#13068616C211yesmaximal, characteristic, complemented
9#13068556C212yesmaximal, complemented
10C4×#66896C211yesmaximal, characteristic, complemented
11C2×C11×#547C211yesmaximal, characteristic
12C22×C11×#41C2212yes—
13C11×#547—24no—
14C11×#547C418yescomplemented
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#123—22no—
17C2×C11×C22⋊Q8C2212yes—
18C2×C11×#121—21no—
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C22×C11×C4⋊C4—21no—
22C2×D4×Dic11—21no—
23C22×C4⋊Dic11C2212yes—
24C22×#4318C2212yes—
25#10622845—28no—
26C2×#66899C2212yes—
27C2×#66899C2212yes—
28C2×#66899C2212yes—
29C2×#66899C2212yes—
30C2×#66896C2211yescharacteristic
31C2×#66896C2212yes—
32C2×#66896C2211yescharacteristic
33#10622825C2212yes—
34C2×C22⋊(C11⋊C8)C2212yes—
35#10622625—24no—
36#10622598—21no—
37#10622563—22no—
38#10622548C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2211yescharacteristic
44#10622167C2211yescharacteristic
45C2×C11×#41—24no—
46C2×C11×#41—24no—
47C2×C11×#41—24no—
48C2×C11×#41—42no—
49C2×C11×#41—42no—
50C2×C11×#41C2×C418yescomplemented
51C22×Q8×C11C2312yes—
52C22×D4×C11—22no—
53C22×D4×C11D411yescharacteristic
54C22×D4×C11C2311yescharacteristic
55C23×C4×C11—21no—
56C23×C4×C11—22no—
57C23×C4×C11C2312yes—
58C23×Dic11—22no—
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8C2×C414yescomplemented
61C11×#123—216no—
62C11×C22⋊Q8—24no—
63C11×C22⋊Q8C2×C418yescomplemented
64C11×#121—28no—
65C4×D4×C11—22no—
66C4×D4×C11C2×C414yes—
67C4×D4×C11C2×C414yescomplemented
68C4×D4×C11D414yes—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—28no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4D412yes—
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—22no—
80D4×Dic11—44no—
81C2×C4⋊Dic11—24no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—42no—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2312yes—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4×Dic11—21no—
90C2×#4318—24no—
91C2×#4318—24no—
92C2×#4318—42no—
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2312yes—
95C22×C11⋊C8C2311yescharacteristic
96#66899—24no—
97#66899—24no—
98#66899—42no—
99#66899—42no—
100#66896—24no—
101#66896—22no—
102#66896D414yescomplemented
103C11⋊#95—21no—
104C11⋊#95—22no—
105C22⋊(C11⋊C8)—24no—
106C4⋊(C11⋊C8)—22no—
107C4×C11⋊C8—22no—
108#22431—111nomaximal, Sylow
109C24×C11—21no—
110C24×C11C2×D412yes—
111C11×#41—216no—
112C11×#41—48no—
113C11×#41—48no—
114C11×#41—48no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11C22×C414yes—
121C2×D4×C11—28no—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—44no—
128C2×D4×C11—44no—
129C2×D4×C11C22⋊C414yes—
130C2×D4×C11C22×C412yes—
131C2×D4×C11C2×D412yes—
132C2×D4×C11#4112yes—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—24no—
140C22×C4×C11—28no—
141C22×C4×C11—44no—
142C22×C4×C11—44no—
143C22×C4×C11—42no—
144C22×C4×C11—42no—
145C22×C4×C11C22×C414yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D414yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—22no—
154C22×Dic11—44no—
155C22×Dic11—44no—
156C22×Dic11—82no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—28no—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4C22⋊C414yes—
162C11×C4⋊C4C22×C412yes—
163C11×C22⋊C4—28no—
164C11×C22⋊C4—24no—
165C11×C22⋊C4C22⋊C418yes—
166C42×C11C22×C412yes—
167C42×C11C2×D412yes—
168C22⋊Dic11—44no—
169C4⋊Dic11—22no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—22no—
174C4⋊Dic11—44no—
175C4⋊Dic11—42no—
176C4⋊Dic11—81no—
177C4⋊Dic11C2×D412yes—
178C4×Dic11—42no—
179#4318—48no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8C2×D412yes—
189C2×#547D1111yescharacteristic
190C2×#436—111no—
191C2×#417—112no—
192D4×C4⋊C4—111no—
193#1981—111no—
194#1956—111no—
195#1894—112no—
196#1872—112no—
197#1802—111no—
198#1788—112no—
199C4×#102—111no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11C2×C22⋊C414yes—
214C23×C11C22×D411yescharacteristic
215Q8×C11—24no—
216Q8×C11—24no—
217Q8×C11—42no—
218Q8×C11—42no—
219D4×C11—22no—
220D4×C11—22no—
221D4×C11—22no—
222D4×C11—28no—
223D4×C11—416no—
224D4×C11C4×D414yescomplemented
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—416no—
236C2×C4×C11—42no—
237C2×C4×C11—42no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—48no—
241C2×C4×C11C2×C22⋊C412yes—
242C2×C4×C11C2×C22⋊C414yes—
243C2×C4×C11C2×C22⋊C412yes—
244C2×C4×C11AGL(1,ℤ/8)12yes—
245C2×C4×C11#13712yes—
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11H(5,𝔽2)11yescharacteristic
251C2×C4×C11H(5,𝔽2)11yescharacteristic
252C2×Dic11—22no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—42no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—41no—
261C2×Dic11—88no—
262C11⋊C8—22no—
263C11⋊C8—42no—
264C11⋊C8—41no—
265C22×#41C2×D1112yes—
266C22×M16—112no—
267#547—24no—
268#547Dic1118yescomplemented
269C2×C4⋊Q8C2×D1111yescharacteristic
270C2×#123—22no—
271C2×C22⋊Q8C2×D1112yes—
272C2×#121—21no—
273C2×C4×D4—221no—
274C2×C4×D4C2×D1111yescharacteristic
275C2×C4×D4C2×D1111yescharacteristic
276C22×C4⋊C4—21no—
277C22×C4⋊C4—112no—
278#436—224no—
279C2×C4⋊C8—111no—
280#417—228no—
281C2×#103—112no—
282C2×#103—112no—
283C2×#103—112no—
284C2×#103—112no—
285C2×#102—111no—
286C2×#102—112no—
287C2×#102—111no—
288C2×C22⋊C8—112no—
289C2×C4×C8—111no—
290#389—221no—
291#385—222no—
292#384—111no—
293#380—112no—
294C4×C4⋊C4—111no—
295#340—112no—
296#340—111no—
297#340—111no—
298C22×C11—24no—
299C22×C11—24no—
300C22×C11—24no—
301C22×C11—24no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11C22×C22⋊C411yescharacteristic
313C22×C11D4211yescharacteristic
314C22×C11#54611yescharacteristic
315C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
316C22×C11C2×#13711yescharacteristic
317C22×C11#57711yescharacteristic
318C22×C11#57811yescharacteristic
319C4×C11—24no—
320C4×C11—22no—
321C4×C11—44no—
322C4×C11—42no—
323C4×C11#41714yescomplemented
324C4×C11C2×C4×D411yescharacteristic
325C4×C11#51811yescharacteristic
326C4×C11D4211yescharacteristic
327C4×C11#54611yescharacteristic
328Dic11—42no—
329Dic11—81no—
330Dic11—82no—
331C2×#41—24no—
332C2×#41—24no—
333C2×#41—24no—
334C2×#41—42no—
335C2×#41—42no—
336C2×#41C2×Dic1118yescomplemented
337C22×Q8C22×D1112yes—
338C22×D4—22no—
339C22×D4C22⋊D1111yescharacteristic
340C22×D4C22×D1111yescharacteristic
341C23×C4—21no—
342C23×C4—22no—
343C23×C4—222no—
344C23×C4C22×D1112yes—
345C2×M16—224no—
346C2×M16—224no—
347C2×M16—442no—
348C22×C8—111no—
349C22×C8—112no—
350C22×C8—111no—
351C4⋊Q8—22no—
352C4⋊Q8C2×Dic1114yescomplemented
353#123—216no—
354C22⋊Q8—24no—
355C22⋊Q8C2×Dic1118yescomplemented
356#121—28no—
357C4×D4—22no—
358C4×D4—444no—
359C4×D4C2×Dic1114yes—
360C4×D4C2×Dic1114yescomplemented
361C4×D4C22⋊D1114yes—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—28no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—112no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—224no—
370C2×C4⋊C4—222no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—442no—
374C2×C4⋊C4C22⋊D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C22⋊C4—22no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—222no—
379C2×C22⋊C4C22⋊D1112yes—
380C2×C42—221no—
381C2×C42C22×D1111yescharacteristic
382C4⋊C8—222no—
383#103—224no—
384#103—224no—
385#103—442no—
386#103—442no—
387#102—114no—
388#102—224no—
389#102—222no—
390C22⋊C8—224no—
391C4×C8—222no—
392#95—221no—
393#95—222no—
394C2×C11—44no—
395C2×C11—44no—
396C2×C11D4×C22⋊C411yescharacteristic
397C2×C11C2×#41711yescharacteristic
398C2×C11#289811yescharacteristic
399C2×C11#327211yescharacteristic
400C2×C11#327611yescharacteristic
401C2×C11#333011yescharacteristic
402C2×C11#333111yescharacteristic
403C24—21no—
404C24C2×C22⋊D1112yes—
405#41—216no—
406#41—48no—
407#41—48no—
408#41—48no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8C22×Dic1114yes—
415C2×D4—28no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—44no—
422C2×D4—44no—
423C2×D4C22⋊Dic1114yes—
424C2×D4D4×D1112yes—
425C2×D4#434112yes—
426C2×D4C22×Dic1112yes—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—28no—
435C22×C4—44no—
436C22×C4—44no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—222no—
442C22×C4—444no—
443C22×C4—444no—
444C22×C4—882no—
445C22×C4C22×Dic1114yes—
446C22×C4C2×C22⋊D1111yescharacteristic
447C22×C4C2×C22⋊D1112yes—
448C22×C4C2×C22⋊D1114yes—
449C22×C4C2×C22⋊D1111yescharacteristic
450C22×C4C23×D1111yescharacteristic
451M16—448no—
452C2×C8—112no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—222no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—222no—
459C2×C8—221no—
460C2×C8—222no—
461C4⋊C4—24no—
462C4⋊C4—28no—
463C4⋊C4—24no—
464C4⋊C4—21no—
465C4⋊C4—112no—
466C4⋊C4—221no—
467C4⋊C4—222no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—222no—
471C4⋊C4—444no—
472C4⋊C4—442no—
473C4⋊C4—881no—
474C4⋊C4C22⋊Dic1114yes—
475C4⋊C4C22×Dic1112yes—
476C22⋊C4—28no—
477C22⋊C4—24no—
478C22⋊C4—444no—
479C22⋊C4C22⋊Dic1118yes—
480C42—442no—
481C42C22×Dic1112yes—
482C42C2×C22⋊D1112yes—
483C11#2243111yescharacteristic, complemented, Sylow
484C23—22no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23C2×C22⋊Dic1114yes—
498C23C22×C22⋊D1111yescharacteristic
499Q8—24no—
500Q8—24no—
501Q8—42no—
502Q8—42no—
503D4—22no—
504D4—22no—
505D4—22no—
506D4—28no—
507D4—416no—
508D4D4×Dic1114yescomplemented
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—416no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—48no—
525C2×C4—222no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—442no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—442no—
532C2×C4—442no—
533C2×C4—441no—
534C2×C4—888no—
535C2×C4#6700212yes—
536C2×C4#6700412yes—
537C2×C4C2×C22⋊Dic1112yes—
538C2×C4C2×C22⋊Dic1114yes—
539C2×C4C2×C22⋊Dic1112yes—
540C2×C4C2×D4×D1111yescharacteristic
541C2×C4C2×#434111yescharacteristic
542C2×C4#6703711yescharacteristic
543C2×C4#6703711yescharacteristic
544C2×C4C23×Dic1111yescharacteristic
545C2×C4C22×C22⋊D1111yescharacteristic
546C8—222no—
547C8—442no—
548C8—441no—
549C22—24no—
550C22—24no—
551C22—24no—
552C22—24no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22D4×C22⋊D1111yescharacteristic
564C22#1062333711yescharacteristic
565C22C2×#6700211yescharacteristic
566C22C2×#6700411yescharacteristic
567C22#1062336811yescharacteristic
568C22#1062336911yescharacteristic
569C22C22×C22⋊Dic1111yescharacteristic
570C4—24no—
571C4—22no—
572C4—44no—
573C4—42no—
574C4—442no—
575C4—881no—
576C4—882no—
577C4#1062284514yescomplemented
578C4C2×D4×Dic1111yescharacteristic
579C4#1062332911yescharacteristic
580C4D4×C22⋊D1111yescharacteristic
581C4#1062333711yescharacteristic
582C2—44no—
583C2—44no—
584C2D4×C22⋊Dic1111yescharacteristic
585C2C2×#1062284511yescharacteristic
586C2#1307714911yescharacteristic
587C2#1308021611yescharacteristic
588C2#1308025811yescharacteristic
589C2#1308092111yescharacteristic
590C2#1308093211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#547C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#547D11
hypocenterC11#22431
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#10622625C2semidirect
2. C2×#10622845C2semidirect
3. D4×C4⋊Dic11C2semidirect
4. #13069540C2semidirect
5. #13069419C2semidirect
6. #13069050C2semidirect
7. #13068924C2semidirect
8. #13068616C2semidirect
9. #13068556C2semidirect
10. C4×#66896C2semidirect
14. C11×#547C4semidirect
50. C2×C11×#41C2×C4semidirect
60. C11×C4⋊Q8C2×C4semidirect
63. C11×C22⋊Q8C2×C4semidirect
67. C4×D4×C11C2×C4semidirect
102. #66896D4semidirect
224. D4×C11C4×D4semidirect
268. #547Dic11semidirect
323. C4×C11#417semidirect
336. C2×#41C2×Dic11semidirect
352. C4⋊Q8C2×Dic11semidirect
355. C22⋊Q8C2×Dic11semidirect
360. C4×D4C2×Dic11semidirect
483. C11#22431semidirect
508. D4D4×Dic11semidirect
577. C4#10622845semidirect

Maximal subgroups

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

subgroupindex
C2×#106226252
C2×#106228452
D4×C4⋊Dic112
#130695402
#130694192
#130690502
#130689242
#130686162
#130685562
C4×#668962
C2×C11×#5472
#2243111