Finite Group Databasebeta

← #14769439

Subgroups — #14769439

Order 2816.

1582 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623249C211yesmaximal, characteristic
2C2×#10622451C211yesmaximal, characteristic, complemented
3C2×#10622384C212yesmaximal, complemented
4C4⋊C4×D44C211yesmaximal, characteristic, complemented
5#13069423C211yesmaximal, characteristic, complemented
6#13069051C212yesmaximal, complemented
7#13068930C212yesmaximal, complemented
8#13068622C211yesmaximal, characteristic, complemented
9#13068553C212yesmaximal, complemented
10C4×#66874C211yesmaximal, characteristic, complemented
11C11×#1982C211yesmaximal, characteristic, complemented
12C22×#4341C2212yes—
13C2×C11×#127C2211yescharacteristic
14C2×#66993—21no—
15C2×#66992—22no—
16C2×#66991C2212yes—
17C2×D4×Dic11—21no—
18C22×#4313C2212yes—
19#10623249—24no—
20#10623249C418yescomplemented
21C2×C4⋊C4×D11C2212yes—
22C2×C4×D44—21no—
23C2×C4×D44C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#102C2212yes—
27C2×C11×#102C2212yes—
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×#66896C2212yes—
30C2×#66896C2212yes—
31C2×(C2×D11)⋊C8C2212yes—
32C2×#66880C2212yes—
33#10622600C2212yes—
34C2×#66874C2211yescharacteristic
35C2×#66874C2211yescharacteristic
36#10622548C2211yescharacteristic
37#10622541—21no—
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622451—24no—
40#10622384—28no—
41#10622281—22no—
42#10622189C2212yes—
43#10622167C2211yescharacteristic
44#10622167C2211yescharacteristic
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11C2312yes—
48C22×C22⋊D11—22no—
49C22×C22⋊D11—22no—
50C23×Dic11—22no—
51C2×#4341—24no—
52C2×#4341—24no—
53C2×#4341—24no—
54C2×#4341—42no—
55C2×#4341—42no—
56C2×#4341C2×C418yescomplemented
57C22×D44D411yescharacteristic
58C22×C4×D11—22no—
59C22×C4×D11C2312yes—
60C22×Dic22C2311yescharacteristic
61C22×C8×C11C2312yes—
62C11×#127—22no—
63C11×#127C2×C414yescomplemented
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C42×C11—21no—
67C2×C42×C11C2311yescharacteristic
68C2×C22⋊Dic11—22no—
69#66993—28no—
70#66992—216no—
71#66991—24no—
72#66991C2×C418yescomplemented
73D4×Dic11—28no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4D412yes—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11D411yescharacteristic
79C2×C4⋊Dic11C2312yes—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—22no—
83C2×C4×Dic11—21no—
84C22×C11⋊C8C2311yescharacteristic
85C22×C11⋊C8C2311yescharacteristic
86C2×#4313—24no—
87C2×#4313—24no—
88C2×#4313—42no—
89C4⋊C4×D11—24no—
90C4⋊C4×D11—42no—
91C4×D44—44no—
92C4×D44C2×C414yes—
93C4×D44D414yes—
94C4×Dic22—22no—
95C4×Dic22C2×C414yescomplemented
96C11×C4⋊C8—22no—
97C11×#102—24no—
98C11×#102—42no—
99C11×#95—21no—
100#66896—24no—
101#66896—42no—
102C11⋊#95—22no—
103(C2×D11)⋊C8—24no—
104#66880—24no—
105#66874—22no—
106#66874D414yescomplemented
107C4×C11⋊C8—22no—
108#22432—111nomaximal, Sylow
109C24×C11—22no—
110C23×D11C2×D412yes—
111C2×D4×C11—24no—
112C2×D4×C11—24no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11—81no—
121C2×D4×C11—81no—
122C2×D4×C11C22×C414yes—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C2×C22⋊D11—28no—
129C2×C22⋊D11—28no—
130C2×C22⋊D11—44no—
131C2×C22⋊D11—44no—
132C2×C22⋊D11—82no—
133C2×C22⋊D11—82no—
134C22×Dic11—28no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—22no—
138C22×Dic11—44no—
139C22×Dic11—44no—
140C22×Dic11C2×D412yes—
141#4341—216no—
142#4341—48no—
143#4341—48no—
144#4341—48no—
145C2×D44—22no—
146C2×D44—22no—
147C2×D44C22⋊C414yes—
148C2×C4×D11—22no—
149C2×C4×D11—22no—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—44no—
153C2×C4×D11—44no—
154C2×C4×D11—82no—
155C2×C4×D11C22×C414yes—
156C2×C4×D11C2×D414yes—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22C22×C412yes—
161C2×Dic22C2×D412yes—
162C2×Dic22#4112yes—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4C2×D412yes—
170C42×C11—42no—
171C42×C11C22×C412yes—
172C42×C11C2×D412yes—
173C22⋊Dic11—28no—
174(C2×D11)⋊C4—44no—
175(C2×D11)⋊C4C22⋊C418yes—
176C4⋊Dic11—21no—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179C4⋊Dic11—42no—
180C4⋊Dic11—81no—
181C4⋊Dic11C22⋊C414yes—
182C4⋊Dic11C22×C412yes—
183Dic11⋊C4—24no—
184Dic11⋊C4—44no—
185C4×Dic11—24no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8C2×D412yes—
192#4313—48no—
193C2×#550—111no—
194C2×#436—111no—
195C2×#417—112no—
196D4×C4⋊C4—111no—
197#1982D1111yescharacteristic, complemented
198#1957—111no—
199#1895—112no—
200#1874—112no—
201#1803—111no—
202#1788—112no—
203C4×#103—111no—
204C23×C11—24no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11C22×D411yescharacteristic
212C22×D11—22no—
213C22×D11—22no—
214C22×D11—22no—
215C22×D11—22no—
216C22×D11—22no—
217C22×D11—22no—
218C22×D11C2×C22⋊C414yes—
219D4×C11—24no—
220D4×C11—24no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—48no—
224D4×C11—84no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—22no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11C2×C22⋊C412yes—
234C2×C4×C11C2×C22⋊C412yes—
235C2×C4×C11AGL(1,ℤ/8)12yes—
236C2×C4×C11#13712yes—
237C2×C4×C11C23×C411yescharacteristic
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11H(5,𝔽2)11yescharacteristic
242C2×C4×C11H(5,𝔽2)11yescharacteristic
243C22⋊D11—416no—
244C22⋊D11—88no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—416no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11C2×C22⋊C414yes—
258D44—28no—
259C4×D11—24no—
260C4×D11—24no—
261C4×D11—24no—
262C4×D11—24no—
263C4×D11—88no—
264Dic22—22no—
265Dic22—22no—
266Dic22—22no—
267Dic22C4×D414yescomplemented
268C8×C11—42no—
269C11⋊C8—22no—
270C11⋊C8—41no—
271C22×#41—112no—
272C22×M16—112no—
273#550—118no—
274#550—224no—
275C2×#127—221no—
276C2×#127C2×D1111yescharacteristic
277C2×#121—112no—
278C2×#121—222no—
279C2×C4×Q8—111no—
280C2×C4×D4—111no—
281C2×C4×D4—221no—
282C2×C4×D4—221no—
283C22×C4⋊C4—112no—
284#436—224no—
285C2×C4⋊C8C2×D1111yescharacteristic
286#417—228no—
287C2×#103—111no—
288C2×#103—112no—
289C2×#103—111no—
290C2×#102—112no—
291C2×#102—112no—
292C2×#102C2×D1112yes—
293C2×#102C2×D1112yes—
294C2×C22⋊C8—112no—
295C2×C4×C8—111no—
296#389—221no—
297#385—222no—
298#384—111no—
299#380—112no—
300C4×C4⋊C4C2×D1111yescharacteristic
301#340—112no—
302#340—111no—
303#340—111no—
304C22×C11—44no—
305C22×C11—44no—
306C22×C11—44no—
307C22×C11—82no—
308C22×C11—82no—
309C22×C11—82no—
310C22×C11—82no—
311C22×C11C22×C22⋊C411yescharacteristic
312C22×C11D4211yescharacteristic
313C22×C11#54611yescharacteristic
314C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
315C22×C11C2×#13711yescharacteristic
316C22×C11#57611yescharacteristic
317C22×C11#57711yescharacteristic
318C2×D11—24no—
319C2×D11—24no—
320C2×D11—24no—
321C2×D11—42no—
322C2×D11—42no—
323C2×D11—42no—
324C2×D11—42no—
325C4×C11—22no—
326C4×C11—42no—
327C4×C11—81no—
328C4×C11#41714yescomplemented
329C4×C11C2×C4×D411yescharacteristic
330C4×C11#51811yescharacteristic
331C4×C11D4211yescharacteristic
332C4×C11#54611yescharacteristic
333Dic11—24no—
334Dic11—24no—
335Dic11—42no—
336Dic11—82no—
337C2×#41—118no—
338C2×#41—224no—
339C2×#41—224no—
340C2×#41—224no—
341C2×#41—442no—
342C2×#41—442no—
343C22×Q8—111no—
344C22×D4—21no—
345C22×D4—21no—
346C22×D4—111no—
347C22×D4—222no—
348C22×D4—222no—
349C22×D4C22×D1112yes—
350C23×C4—112no—
351C23×C4—222no—
352C23×C4—222no—
353C2×M16—224no—
354C2×M16—224no—
355C2×M16—442no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8C22×D1112yes—
359#127—22no—
360#127—228no—
361#127C4×D1114yescomplemented
362#121—118no—
363#121—2216no—
364#121—224no—
365C4×Q8—114no—
366C4×Q8—222no—
367C4×D4—114no—
368C4×D4—114no—
369C4×D4—228no—
370C4×D4—444no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—112no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—224no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—442no—
380C2×C4⋊C4C22×D1111yescharacteristic
381C2×C4⋊C4C22×D1111yescharacteristic
382C2×C22⋊C4—112no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4—222no—
385C2×C42—21no—
386C2×C42—221no—
387C2×C42C22×D1111yescharacteristic
388C4⋊C8—22no—
389#103—114no—
390#103—222no—
391#103—224no—
392#102—24no—
393#102—42no—
394#102—224no—
395#102—442no—
396C22⋊C8—224no—
397C4×C8—222no—
398#95—21no—
399#95—222no—
400C2×C11—84no—
401C2×C11D4×C22⋊C411yescharacteristic
402C2×C11C2×#41711yescharacteristic
403C2×C11#289711yescharacteristic
404C2×C11#327411yescharacteristic
405C2×C11#327811yescharacteristic
406C2×C11#333211yescharacteristic
407C2×C11#333311yescharacteristic
408D11—44no—
409C24—22no—
410C24—112no—
411#41—2216no—
412#41—448no—
413#41—448no—
414#41—448no—
415C2×Q8—112no—
416C2×Q8—112no—
417C2×Q8—112no—
418C2×Q8—221no—
419C2×Q8—221no—
420C2×Q8—221no—
421C2×D4—24no—
422C2×D4—24no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—42no—
429C2×D4—42no—
430C2×D4—81no—
431C2×D4—81no—
432C2×D4—114no—
433C2×D4—228no—
434C2×D4—228no—
435C2×D4—222no—
436C2×D4—222no—
437C2×D4—444no—
438C2×D4—444no—
439C2×D4—882no—
440C2×D4—882no—
441C2×D4C2×C4×D1114yes—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—112no—
445C22×C4—114no—
446C22×C4—114no—
447C22×C4—228no—
448C22×C4—221no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—221no—
454C22×C4—222no—
455C22×C4—444no—
456C22×C4—444no—
457C22×C4—444no—
458C22×C4—444no—
459C22×C4—882no—
460C22×C4D4×D1111yescharacteristic
461C22×C4D4×D1111yescharacteristic
462C22×C4C23×D1111yescharacteristic
463M16—448no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—112no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—114no—
477C4⋊C4—112no—
478C4⋊C4—224no—
479C4⋊C4—221no—
480C4⋊C4—222no—
481C4⋊C4—222no—
482C4⋊C4—444no—
483C4⋊C4—442no—
484C4⋊C4—881no—
485C4⋊C4D4×D1112yes—
486C22⋊C4—118no—
487C22⋊C4—228no—
488C22⋊C4—444no—
489C42—42no—
490C42—224no—
491C42C2×C4×D1112yes—
492C42D4×D1112yes—
493C11#2243211yescharacteristic, complemented, Sylow
494C23—24no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—114no—
502C23—222no—
503C23—222no—
504C23—222no—
505C23—222no—
506C23—222no—
507C23—222no—
508C23C2×D4×D1111yescharacteristic
509Q8—114no—
510Q8—222no—
511Q8—222no—
512Q8—222no—
513D4—24no—
514D4—24no—
515D4—42no—
516D4—48no—
517D4—42no—
518D4—84no—
519D4—228no—
520D4—4416no—
521D4—888no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—114no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—222no—
535C2×C4—222no—
536C2×C4—224no—
537C2×C4—224no—
538C2×C4—224no—
539C2×C4—224no—
540C2×C4—222no—
541C2×C4—4416no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—442no—
545C2×C4—442no—
546C2×C4—442no—
547C2×C4—888no—
548C2×C4C22⋊C4×D1112yes—
549C2×C4C22⋊C4×D1112yes—
550C2×C4#6696412yes—
551C2×C4#6696812yes—
552C2×C4C22×C4×D1111yescharacteristic
553C2×C4C2×D4×D1111yescharacteristic
554C2×C4C2×D4×D1111yescharacteristic
555C2×C4#6703711yescharacteristic
556C2×C4#41×D1111yescharacteristic
557C2×C4#6704211yescharacteristic
558C8—42no—
559C8—222no—
560C8—441no—
561C22—44no—
562C22—44no—
563C22—44no—
564C22—82no—
565C22—82no—
566C22—82no—
567C22—82no—
568C22—224no—
569C22—224no—
570C22—224no—
571C22—442no—
572C22—442no—
573C22—442no—
574C22—442no—
575C22C2×C22⋊C4×D1111yescharacteristic
576C22#1062314011yescharacteristic
577C22#1062314311yescharacteristic
578C22C2×#6696411yescharacteristic
579C22C2×#6696811yescharacteristic
580C22#1062330511yescharacteristic
581C22#1062330611yescharacteristic
582C4—22no—
583C4—42no—
584C4—81no—
585C4—224no—
586C4—224no—
587C4—442no—
588C4—882no—
589C4#1062238414yescomplemented
590C4C4×D4×D1111yescharacteristic
591C4#1062307611yescharacteristic
592C4#1062320711yescharacteristic
593C4#1062324811yescharacteristic
594C2—84no—
595C2—444no—
596C2#1307143711yescharacteristic
597C2C2×#1062238411yescharacteristic
598C2#1307714111yescharacteristic
599C2#1308023911yescharacteristic
600C2#1308028511yescharacteristic
601C2#1308094611yescharacteristic
602C2#1308095711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1982C2
socleC23×C11C22×D4
prime radicalC2×#10623249C2
cosocleC22×C4×C11C24
hypercenter#1982D11
hypocenterC11#22432
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1982

Complements

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

NH ≅ G/Ntype
2. C2×#10622451C2semidirect
3. C2×#10622384C2semidirect
4. C4⋊C4×D44C2semidirect
5. #13069423C2semidirect
6. #13069051C2semidirect
7. #13068930C2semidirect
8. #13068622C2semidirect
9. #13068553C2semidirect
10. C4×#66874C2semidirect
11. C11×#1982C2semidirect
20. #10623249C4semidirect
56. C2×#4341C2×C4semidirect
63. C11×#127C2×C4semidirect
72. #66991C2×C4semidirect
95. C4×Dic22C2×C4semidirect
106. #66874D4semidirect
197. #1982D11semidirect
267. Dic22C4×D4semidirect
328. C4×C11#417semidirect
361. #127C4×D11semidirect
493. C11#22432semidirect
589. C4#10622384semidirect

Maximal subgroups

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

subgroupindex
C2×#106232492
C2×#106224512
C2×#106223842
C4⋊C4×D442
#130694232
#130690512
#130689302
#130686222
#130685532
C4×#668742
C11×#19822
#2243211