Finite Group Databasebeta

← #14769436

Subgroups — #14769436

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×#10622625C211yesmaximal, characteristic, complemented
2C2×#10622845C212yesmaximal, complemented
3D4×C4⋊Dic11C211yesmaximal, characteristic, complemented
4#13069544C211yesmaximal, characteristic, complemented
5#13069423C211yesmaximal, characteristic, complemented
6#13069055C212yesmaximal, complemented
7#13068934C212yesmaximal, complemented
8#13068621C211yesmaximal, characteristic, complemented
9#13068556C212yesmaximal, complemented
10C4×#66899C211yesmaximal, characteristic, complemented
11C2×C11×#550C211yesmaximal, characteristic
12C22×C11×#41C2212yes—
13C11×#550—24no—
14C11×#550C418yescomplemented
15C2×C11×#127—21no—
16C2×C11×#127C2211yescharacteristic
17C2×C11×#121—22no—
18C2×C11×#121C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×D4×Dic11—21no—
23C22×C4⋊Dic11C2212yes—
24C22×#4318C2212yes—
25#10622845—28no—
26C2×#66899C2211yescharacteristic
27C2×#66899C2212yes—
28C2×#66899C2211yescharacteristic
29C2×#66896C2212yes—
30C2×#66896C2212yes—
31C2×#66896C2212yes—
32C2×#66896C2212yes—
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×C11C2311yescharacteristic
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C22×D4×C11D411yescharacteristic
57C22×D4×C11C2312yes—
58C23×C4×C11—22no—
59C23×C4×C11C2312yes—
60C23×Dic11—22no—
61C11×#127—28no—
62C11×#127—22no—
63C11×#127C2×C414yescomplemented
64C11×#121—24no—
65C11×#121—216no—
66C11×#121C2×C418yescomplemented
67C4×Q8×C11—22no—
68C4×Q8×C11C2×C414yescomplemented
69C4×D4×C11—28no—
70C4×D4×C11C2×C414yes—
71C4×D4×C11D414yes—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—22no—
76C2×C11×C22⋊C4D412yes—
77C2×C42×C11—21no—
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—22no—
98#66899D414yescomplemented
99#66896—24no—
100#66896—24no—
101#66896—42no—
102#66896—42no—
103C11⋊#95—21no—
104C11⋊#95—22no—
105C22⋊(C11⋊C8)—24no—
106C4⋊(C11⋊C8)—22no—
107C4×C11⋊C8—22no—
108#22432—111nomaximal, Sylow
109C24×C11—22no—
110C24×C11C2×D412yes—
111C11×#41—216no—
112C11×#41—48no—
113C11×#41—48no—
114C11×#41—48no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11C22×C412yes—
119C2×Q8×C11C2×D412yes—
120C2×Q8×C11#4112yes—
121C2×D4×C11—28no—
122C2×D4×C11—28no—
123C2×D4×C11—24no—
124C2×D4×C11—24no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—44no—
133C2×D4×C11—44no—
134C2×D4×C11—42no—
135C2×D4×C11—42no—
136C2×D4×C11—81no—
137C2×D4×C11—81no—
138C2×D4×C11—82no—
139C2×D4×C11—82no—
140C2×D4×C11C22⋊C414yes—
141C2×D4×C11C22×C414yes—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—28no—
149C22×C4×C11—44no—
150C22×C4×C11—44no—
151C22×C4×C11C22×C414yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D414yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—22no—
160C22×Dic11—44no—
161C22×Dic11—44no—
162C22×Dic11—82no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4C22⋊C414yes—
166C11×C4⋊C4C22×C412yes—
167C11×C22⋊C4—28no—
168C11×C22⋊C4C22⋊C418yes—
169C42×C11—24no—
170C42×C11C22×C412yes—
171C42×C11C2×D412yes—
172C22⋊Dic11—44no—
173C4⋊Dic11—22no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—22no—
178C4⋊Dic11—44no—
179C4⋊Dic11—42no—
180C4⋊Dic11—81no—
181C4⋊Dic11C2×D412yes—
182C4×Dic11—42no—
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×#550D1111yescharacteristic
194C2×#436—111no—
195C2×#417—112no—
196D4×C4⋊C4—111no—
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×C11—24no—
211C23×C11—42no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11C2×C22⋊C414yes—
218C23×C11C22×D411yescharacteristic
219Q8×C11—22no—
220Q8×C11—22no—
221Q8×C11—22no—
222Q8×C11C4×D414yescomplemented
223D4×C11—24no—
224D4×C11—24no—
225D4×C11—28no—
226D4×C11—416no—
227D4×C11—42no—
228D4×C11—42no—
229D4×C11—48no—
230D4×C11—84no—
231D4×C11—88no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—416no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11C2×C22⋊C412yes—
248C2×C4×C11C2×C22⋊C414yes—
249C2×C4×C11C2×C22⋊C412yes—
250C2×C4×C11AGL(1,ℤ/8)12yes—
251C2×C4×C11#13712yes—
252C2×C4×C11C23×C411yescharacteristic
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×D411yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11H(5,𝔽2)11yescharacteristic
257C2×C4×C11H(5,𝔽2)11yescharacteristic
258C2×Dic11—22no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—42no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—41no—
267C2×Dic11—88no—
268C11⋊C8—22no—
269C11⋊C8—42no—
270C11⋊C8—41no—
271C22×#41C2×D1112yes—
272C22×M16—112no—
273#550—24no—
274#550Dic1118yescomplemented
275C2×#127—21no—
276C2×#127C2×D1111yescharacteristic
277C2×#121—22no—
278C2×#121C2×D1112yes—
279C2×C4×Q8C2×D1111yescharacteristic
280C2×C4×D4—21no—
281C2×C4×D4—221no—
282C2×C4×D4C2×D1111yescharacteristic
283C22×C4⋊C4—112no—
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—221no—
297#385—222no—
298#384—111no—
299#380—112no—
300C4×C4⋊C4—111no—
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×C11—44no—
312C22×C11—44no—
313C22×C11—44no—
314C22×C11—82no—
315C22×C11—82no—
316C22×C11—82no—
317C22×C11—82no—
318C22×C11C22×C22⋊C411yescharacteristic
319C22×C11D4211yescharacteristic
320C22×C11#54611yescharacteristic
321C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
322C22×C11C2×#13711yescharacteristic
323C22×C11#57611yescharacteristic
324C22×C11#57711yescharacteristic
325C4×C11—24no—
326C4×C11—24no—
327C4×C11—22no—
328C4×C11—42no—
329C4×C11#41714yescomplemented
330C4×C11C2×C4×D411yescharacteristic
331C4×C11#51811yescharacteristic
332C4×C11D4211yescharacteristic
333C4×C11#54611yescharacteristic
334Dic11—42no—
335Dic11—81no—
336Dic11—82no—
337C2×#41—24no—
338C2×#41—24no—
339C2×#41—24no—
340C2×#41—42no—
341C2×#41—42no—
342C2×#41C2×Dic1118yescomplemented
343C22×Q8C22×D1111yescharacteristic
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—21no—
347C22×D4—21no—
348C22×D4C22⋊D1111yescharacteristic
349C22×D4C22×D1112yes—
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—28no—
360#127—22no—
361#127C2×Dic1114yescomplemented
362#121—24no—
363#121—216no—
364#121C2×Dic1118yescomplemented
365C4×Q8—22no—
366C4×Q8C2×Dic1114yescomplemented
367C4×D4—28no—
368C4×D4—444no—
369C4×D4C2×Dic1114yes—
370C4×D4C22⋊D1114yes—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—112no—
374C2×C4⋊C4—111no—
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—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—224no—
391#103—222no—
392#102—224no—
393#102—224no—
394#102—442no—
395#102—442no—
396C22⋊C8—224no—
397C4×C8—222no—
398#95—221no—
399#95—222no—
400C2×C11—44no—
401C2×C11—84no—
402C2×C11D4×C22⋊C411yescharacteristic
403C2×C11C2×#41711yescharacteristic
404C2×C11#289711yescharacteristic
405C2×C11#327411yescharacteristic
406C2×C11#327811yescharacteristic
407C2×C11#333211yescharacteristic
408C2×C11#333311yescharacteristic
409C24—22no—
410C24C2×C22⋊D1112yes—
411#41—216no—
412#41—48no—
413#41—48no—
414#41—48no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8D4×D1112yes—
419C2×Q8#434112yes—
420C2×Q8C22×Dic1112yes—
421C2×D4—28no—
422C2×D4—28no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—24no—
426C2×D4—24no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—42no—
435C2×D4—42no—
436C2×D4—81no—
437C2×D4—81no—
438C2×D4—82no—
439C2×D4—82no—
440C2×D4C22⋊Dic1114yes—
441C2×D4C22×Dic1114yes—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—28no—
449C22×C4—44no—
450C22×C4—44no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—222no—
454C22×C4—444no—
455C22×C4—444no—
456C22×C4—882no—
457C22×C4C22×Dic1114yes—
458C22×C4C2×C22⋊D1111yescharacteristic
459C22×C4C2×C22⋊D1112yes—
460C22×C4C2×C22⋊D1114yes—
461C22×C4C2×C22⋊D1111yescharacteristic
462C22×C4C23×D1111yescharacteristic
463M16—448no—
464C2×C8—112no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—222no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—222no—
471C2×C8—221no—
472C2×C8—222no—
473C4⋊C4—24no—
474C4⋊C4—21no—
475C4⋊C4—112no—
476C4⋊C4—221no—
477C4⋊C4—222no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—222no—
481C4⋊C4—444no—
482C4⋊C4—442no—
483C4⋊C4—881no—
484C4⋊C4C22⋊Dic1114yes—
485C4⋊C4C22×Dic1112yes—
486C22⋊C4—28no—
487C22⋊C4—444no—
488C22⋊C4C22⋊Dic1118yes—
489C42—24no—
490C42—442no—
491C42C22×Dic1112yes—
492C42C2×C22⋊D1112yes—
493C11#2243211yescharacteristic, complemented, Sylow
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—22no—
499C23—22no—
500C23—24no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23C2×C22⋊Dic1114yes—
508C23C22×C22⋊D1111yescharacteristic
509Q8—22no—
510Q8—22no—
511Q8—22no—
512Q8D4×Dic1114yescomplemented
513D4—24no—
514D4—24no—
515D4—28no—
516D4—416no—
517D4—42no—
518D4—42no—
519D4—48no—
520D4—84no—
521D4—88no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—22no—
534C2×C4—416no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—222no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—442no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4—441no—
546C2×C4—888no—
547C2×C4#6700212yes—
548C2×C4#6700412yes—
549C2×C4C2×C22⋊Dic1112yes—
550C2×C4C2×C22⋊Dic1114yes—
551C2×C4C2×C22⋊Dic1112yes—
552C2×C4C2×D4×D1111yescharacteristic
553C2×C4C2×#434111yescharacteristic
554C2×C4#6703711yescharacteristic
555C2×C4#6703711yescharacteristic
556C2×C4C23×Dic1111yescharacteristic
557C2×C4C22×C22⋊D1111yescharacteristic
558C8—222no—
559C8—442no—
560C8—441no—
561C22—24no—
562C22—24no—
563C22—24no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—44no—
569C22—44no—
570C22—44no—
571C22—82no—
572C22—82no—
573C22—82no—
574C22—82no—
575C22D4×C22⋊D1111yescharacteristic
576C22#1062333711yescharacteristic
577C22C2×#6700211yescharacteristic
578C22C2×#6700411yescharacteristic
579C22#1062336611yescharacteristic
580C22#1062336711yescharacteristic
581C22C22×C22⋊Dic1111yescharacteristic
582C4—24no—
583C4—24no—
584C4—22no—
585C4—42no—
586C4—442no—
587C4—881no—
588C4—882no—
589C4#1062284514yescomplemented
590C4C2×D4×Dic1111yescharacteristic
591C4#1062332911yescharacteristic
592C4D4×C22⋊D1111yescharacteristic
593C4#1062333711yescharacteristic
594C2—44no—
595C2—84no—
596C2D4×C22⋊Dic1111yescharacteristic
597C2C2×#1062284511yescharacteristic
598C2#1307714211yescharacteristic
599C2#1308023611yescharacteristic
600C2#1308028211yescharacteristic
601C2#1308094311yescharacteristic
602C2#1308095411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#550C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#550D11
hypocenterC11#22432
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

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. #13069544C2semidirect
5. #13069423C2semidirect
6. #13069055C2semidirect
7. #13068934C2semidirect
8. #13068621C2semidirect
9. #13068556C2semidirect
10. C4×#66899C2semidirect
14. C11×#550C4semidirect
50. C2×C11×#41C2×C4semidirect
63. C11×#127C2×C4semidirect
66. C11×#121C2×C4semidirect
68. C4×Q8×C11C2×C4semidirect
98. #66899D4semidirect
222. Q8×C11C4×D4semidirect
274. #550Dic11semidirect
329. C4×C11#417semidirect
342. C2×#41C2×Dic11semidirect
361. #127C2×Dic11semidirect
364. #121C2×Dic11semidirect
366. C4×Q8C2×Dic11semidirect
493. C11#22432semidirect
512. Q8D4×Dic11semidirect
589. 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
#130695442
#130694232
#130690552
#130689342
#130686212
#130685562
C4×#668992
C2×C11×#5502
#2243211