Finite Group Databasebeta

← #14769430

Subgroups — #14769430

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×#10623084C211yesmaximal, characteristic
2C2×#10622625C211yesmaximal, characteristic, complemented
3C2×#10622579C212yesmaximal, complemented
4#13069543C211yesmaximal, characteristic, complemented
5#13069421C211yesmaximal, characteristic, complemented
6#13069052C212yesmaximal, complemented
7#13068933C212yesmaximal, complemented
8#13068618C211yesmaximal, characteristic, complemented
9#13068554C212yesmaximal, complemented
10C4×#66874C211yesmaximal, characteristic, complemented
11D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
12C22×#4339C2212yes—
13C2×C4×D4×C11—21no—
14C2×C4×D4×C11C2211yescharacteristic
15C22×C11×C4⋊C4C2212yes—
16C2×#66993—21no—
17C2×#66983C2212yes—
18C22×#4318C2212yes—
19#10623084—24no—
20#10623084C418yescomplemented
21C2×#66946—21no—
22C2×#66937—22no—
23C2×#66927C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C11×#389—21no—
26C11×#385—22no—
27C11×#384C2211yescharacteristic
28C11×#380C2212yes—
29C4×C11×C4⋊C4C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2212yes—
31#10622625—24no—
32C2×#66874C2211yescharacteristic
33C2×#66874C2212yes—
34C2×#66874C2211yescharacteristic
35#10622579—28no—
36C2×#66873C2212yes—
37C2×#66873C2212yes—
38C2×#66873C2212yes—
39C2×#66873C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2211yescharacteristic
44#10622167C2211yescharacteristic
45C22×D4×C11D411yescharacteristic
46C23×C4×C11—22no—
47C23×C4×C11C2312yes—
48C22×C22⋊D11—22no—
49C22×C22⋊D11—22no—
50C2×#4339—24no—
51C2×#4339—24no—
52C2×#4339—24no—
53C2×#4339—42no—
54C2×#4339—42no—
55C2×#4339C2×C418yescomplemented
56C22×D44—21no—
57C22×D44—21no—
58C22×D44C2312yes—
59C22×C4×D11—22no—
60C22×Dic22C2311yescharacteristic
61C4×D4×C11—44no—
62C4×D4×C11C2×C414yes—
63C4×D4×C11D414yes—
64C2×C11×C4⋊C4—24no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—42no—
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—22no—
74C2×C11×C22⋊C4D412yes—
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77#66993—28no—
78#66983—24no—
79#66983C2×C418yescomplemented
80C2×(C2×D11)⋊C4—22no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×C4×Dic11—21no—
84C2×#4318—24no—
85C2×#4318—24no—
86C2×#4318—42no—
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2312yes—
89C22×C11⋊C8C2311yescharacteristic
90#66946—28no—
91#66937—216no—
92#66927—22no—
93#66927C2×C414yescomplemented
94C4×Dic22—22no—
95C4×Dic22C2×C414yescomplemented
96C11×#95—21no—
97C11×#95—22no—
98C22⋊(C11⋊C8)—24no—
99#66874—24no—
100#66874—22no—
101#66874D414yescomplemented
102#66873—24no—
103#66873—24no—
104#66873—42no—
105#66873—42no—
106C4⋊(C11⋊C8)—22no—
107C4×C11⋊C8—22no—
108#22432—111nomaximal, Sylow
109C24×C11C2×D412yes—
110C23×D11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11C22⋊C414yes—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—44no—
122C22×C4×C11—44no—
123C22×C4×C11—82no—
124C22×C4×C11C22×C414yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D414yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C2×C22⋊D11—28no—
131C2×C22⋊D11—28no—
132C2×C22⋊D11—44no—
133C2×C22⋊D11—44no—
134C2×C22⋊D11—82no—
135C2×C22⋊D11—82no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138#4339—216no—
139#4339—48no—
140#4339—48no—
141#4339—48no—
142C2×D44—24no—
143C2×D44—24no—
144C2×D44—22no—
145C2×D44—22no—
146C2×D44—22no—
147C2×D44—22no—
148C2×D44—22no—
149C2×D44—42no—
150C2×D44—42no—
151C2×D44—81no—
152C2×D44—81no—
153C2×D44C22×C414yes—
154C2×C4×D11—28no—
155C2×C4×D11—44no—
156C2×C4×D11—44no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22C22×C412yes—
161C2×Dic22C2×D412yes—
162C2×Dic22#4112yes—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—44no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—81no—
171C11×C4⋊C4C22⋊C414yes—
172C11×C4⋊C4C2×D412yes—
173C11×C22⋊C4—44no—
174C11×C22⋊C4C22⋊C418yes—
175C42×C11—42no—
176C42×C11C22×C412yes—
177C42×C11C2×D412yes—
178(C2×D11)⋊C4—28no—
179C4⋊Dic11—21no—
180C4⋊Dic11C22×C412yes—
181Dic11⋊C4—24no—
182C4×Dic11—24no—
183#4318—48no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8C2×D412yes—
193C2×#550—111no—
194C2×#436—111no—
195C2×#417—112no—
196D4×C4⋊C4D1111yescharacteristic, complemented
197#1982—111no—
198#1957—111no—
199#1895—112no—
200#1874—112no—
201#1803—111no—
202#1788—112no—
203C4×#103—111no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11C2×C22⋊C414yes—
211C23×C11C22×D411yescharacteristic
212C22×D11—24no—
213C22×D11—42no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—42no—
219D4×C11—28no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—42no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11—41no—
237C2×C4×C11—88no—
238C2×C4×C11C2×C22⋊C412yes—
239C2×C4×C11C2×C22⋊C414yes—
240C2×C4×C11C2×C22⋊C412yes—
241C2×C4×C11AGL(1,ℤ/8)12yes—
242C2×C4×C11#13712yes—
243C2×C4×C11C23×C411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11H(5,𝔽2)11yescharacteristic
248C2×C4×C11H(5,𝔽2)11yescharacteristic
249C22⋊D11—416no—
250C22⋊D11—88no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257D44—24no—
258D44—24no—
259D44—42no—
260D44—42no—
261D44—48no—
262D44—84no—
263C4×D11—416no—
264Dic22—22no—
265Dic22—22no—
266Dic22—22no—
267Dic22C4×D414yescomplemented
268C11⋊C8—22no—
269C11⋊C8—42no—
270C11⋊C8—41no—
271C22×#41—112no—
272C22×M16—112no—
273#550—118no—
274#550—224no—
275C2×#127—111no—
276C2×#127—221no—
277C2×#121—112no—
278C2×#121—222no—
279C2×C4×Q8—111no—
280C2×C4×D4—21no—
281C2×C4×D4—221no—
282C2×C4×D4C2×D1111yescharacteristic
283C22×C4⋊C4C2×D1112yes—
284#436—224no—
285C2×C4⋊C8—111no—
286#417—228no—
287C2×#103—111no—
288C2×#103—112no—
289C2×#103—111no—
290C2×#102—112no—
291C2×#102—112no—
292C2×#102—112no—
293C2×#102—112no—
294C2×C22⋊C8—112no—
295C2×C4×C8—111no—
296#389—21no—
297#385—22no—
298#384C2×D1111yescharacteristic
299#380C2×D1112yes—
300C4×C4⋊C4C2×D1111yescharacteristic
301#340—112no—
302#340—111no—
303#340—111no—
304C22×C11—24no—
305C22×C11—24no—
306C22×C11—24no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—42no—
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—44no—
319C2×D11—44no—
320C2×D11—44no—
321C2×D11—82no—
322C2×D11—82no—
323C2×D11—82no—
324C2×D11—82no—
325C4×C11—24no—
326C4×C11—22no—
327C4×C11—42no—
328C4×C11—81no—
329C4×C11—82no—
330C4×C11#41714yescomplemented
331C4×C11C2×C4×D411yescharacteristic
332C4×C11#51811yescharacteristic
333C4×C11D4211yescharacteristic
334C4×C11#54611yescharacteristic
335Dic11—24no—
336Dic11—42no—
337C2×#41—118no—
338C2×#41—224no—
339C2×#41—224no—
340C2×#41—224no—
341C2×#41—442no—
342C2×#41—442no—
343C22×Q8—111no—
344C22×D4—112no—
345C22×D4—222no—
346C22×D4—222no—
347C22×D4—221no—
348C22×D4—221no—
349C22×D4C22⋊D1111yescharacteristic
350C23×C4—22no—
351C23×C4—222no—
352C23×C4C22×D1112yes—
353C2×M16—224no—
354C2×M16—224no—
355C2×M16—442no—
356C22×C8—111no—
357C22×C8—112no—
358C22×C8—111no—
359#127—114no—
360#127—228no—
361#127—222no—
362#121—118no—
363#121—224no—
364#121—2216no—
365C4×Q8—114no—
366C4×Q8—222no—
367C4×D4—44no—
368C4×D4—228no—
369C4×D4C4×D1114yes—
370C4×D4D4414yes—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—42no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4C22⋊D1111yescharacteristic
379C2×C4⋊C4C22×D1112yes—
380C2×C4⋊C4C22×D1111yescharacteristic
381C2×C4⋊C4C22×D1111yescharacteristic
382C2×C22⋊C4—22no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4C22⋊D1112yes—
385C2×C42—21no—
386C2×C42—221no—
387C2×C42C22×D1111yescharacteristic
388C4⋊C8—222no—
389#103—114no—
390#103—222no—
391#103—224no—
392#102—224no—
393#102—224no—
394#102—442no—
395#102—442no—
396C22⋊C8—224no—
397C4×C8—222no—
398#95—21no—
399#95—22no—
400C2×C11—44no—
401C2×C11D4×C22⋊C411yescharacteristic
402C2×C11C2×#41711yescharacteristic
403C2×C11#289711yescharacteristic
404C2×C11#327411yescharacteristic
405C2×C11#327811yescharacteristic
406C2×C11#333211yescharacteristic
407C2×C11#333311yescharacteristic
408D11—84no—
409C24—222no—
410C24C2×C22⋊D1112yes—
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—22no—
422C2×D4—22no—
423C2×D4—114no—
424C2×D4—228no—
425C2×D4—228no—
426C2×D4—224no—
427C2×D4—224no—
428C2×D4—222no—
429C2×D4—222no—
430C2×D4—222no—
431C2×D4—222no—
432C2×D4—222no—
433C2×D4—444no—
434C2×D4—444no—
435C2×D4—442no—
436C2×D4—442no—
437C2×D4—881no—
438C2×D4—881no—
439C2×D4—882no—
440C2×D4—882no—
441C2×D4(C2×D11)⋊C414yes—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—44no—
450C22×C4—44no—
451C22×C4—82no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—228no—
455C22×C4—444no—
456C22×C4—444no—
457C22×C4C2×C4×D1114yes—
458C22×C4C2×D4414yes—
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1112yes—
461C22×C4C2×C22⋊D1111yescharacteristic
462C22×C4C23×D1111yescharacteristic
463M16—448no—
464C2×C8—112no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—222no—
469C2×C8—222no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—222no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—44no—
479C4⋊C4—42no—
480C4⋊C4—81no—
481C4⋊C4—112no—
482C4⋊C4—224no—
483C4⋊C4—221no—
484C4⋊C4(C2×D11)⋊C414yes—
485C4⋊C4D4×D1112yes—
486C22⋊C4—44no—
487C22⋊C4—228no—
488C22⋊C4(C2×D11)⋊C418yes—
489C42—42no—
490C42—224no—
491C42C2×C4×D1112yes—
492C42C2×D4412yes—
493C11#2243211yescharacteristic, complemented, Sylow
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23—22no—
500C23—224no—
501C23—442no—
502C23—442no—
503C23—442no—
504C23—442no—
505C23—442no—
506C23—442no—
507C23C2×(C2×D11)⋊C414yes—
508C23C22×C22⋊D1111yescharacteristic
509Q8—114no—
510Q8—222no—
511Q8—222no—
512Q8—222no—
513D4—28no—
514D4—224no—
515D4—224no—
516D4—4416no—
517D4—442no—
518D4—442no—
519D4—448no—
520D4—884no—
521D4—888no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—41no—
539C2×C4—88no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—222no—
543C2×C4—222no—
544C2×C4—4416no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4C2×(C2×D11)⋊C412yes—
548C2×C4C2×(C2×D11)⋊C414yes—
549C2×C4C2×(C2×D11)⋊C412yes—
550C2×C4#6698512yes—
551C2×C4#6699512yes—
552C2×C4C22×C4×D1111yescharacteristic
553C2×C4C22×D4411yescharacteristic
554C2×C4C2×D4×D1111yescharacteristic
555C2×C4#6703711yescharacteristic
556C2×C4#41×D1111yescharacteristic
557C2×C4#6704211yescharacteristic
558C8—222no—
559C8—442no—
560C8—441no—
561C22—24no—
562C22—24no—
563C22—24no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—444no—
569C22—444no—
570C22—444no—
571C22—882no—
572C22—882no—
573C22—882no—
574C22—882no—
575C22C22×(C2×D11)⋊C411yescharacteristic
576C22C2×#6698511yescharacteristic
577C22D4×C22⋊D1111yescharacteristic
578C22C2×#6699511yescharacteristic
579C22#1062336011yescharacteristic
580C22#1062336611yescharacteristic
581C22#1062336811yescharacteristic
582C4—24no—
583C4—22no—
584C4—42no—
585C4—81no—
586C4—82no—
587C4—224no—
588C4—442no—
589C4#1062257914yescomplemented
590C4C4×D4×D1111yescharacteristic
591C4#1062307611yescharacteristic
592C4D4×D4411yescharacteristic
593C4#1062308511yescharacteristic
594C2—44no—
595C2—884no—
596C2D4×(C2×D11)⋊C411yescharacteristic
597C2C2×#1062257911yescharacteristic
598C2#1307713911yescharacteristic
599C2#1308023211yescharacteristic
600C2#1308027811yescharacteristic
601C2#1308093711yescharacteristic
602C2#1308094811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingD4×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC2×#10623084C2
cosocleC22×C4×C11C24
hypercenterD4×C4⋊C4D11
hypocenterC11#22432
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622625C2semidirect
3. C2×#10622579C2semidirect
4. #13069543C2semidirect
5. #13069421C2semidirect
6. #13069052C2semidirect
7. #13068933C2semidirect
8. #13068618C2semidirect
9. #13068554C2semidirect
10. C4×#66874C2semidirect
11. D4×C11×C4⋊C4C2semidirect
20. #10623084C4semidirect
55. C2×#4339C2×C4semidirect
79. #66983C2×C4semidirect
93. #66927C2×C4semidirect
95. C4×Dic22C2×C4semidirect
101. #66874D4semidirect
196. D4×C4⋊C4D11semidirect
267. Dic22C4×D4semidirect
330. C4×C11#417semidirect
493. C11#22432semidirect
589. C4#10622579semidirect

Maximal subgroups

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

subgroupindex
C2×#106230842
C2×#106226252
C2×#106225792
#130695432
#130694212
#130690522
#130689332
#130686182
#130685542
C4×#668742
D4×C11×C4⋊C42
#2243211