Finite Group Databasebeta

← #14789832

Subgroups — #14789832

Order 2816.

1378 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#10622620C211yesmaximal, characteristic, complemented
3C4×#66991C211yesmaximal, characteristic
4#13069942C212yesmaximal, complemented
5#13069750C212yesmaximal, complemented
6#13069569C211yesmaximal, characteristic, complemented
7#13069567C211yesmaximal, characteristic, complemented
8#13068930C212yesmaximal
9#13068802C212yesmaximal, complemented
10#13068593C211yesmaximal, characteristic, complemented
11C2×C11×#474C211yesmaximal, characteristic, complemented
12C22×Q8×D11—21no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66997—21no—
16C2×#66991C2211yescharacteristic
17C2×C4×C22⋊D11—21no—
18D11×C4⋊Q8—24no—
19D11×C4⋊Q8—24no—
20C2×C4⋊C4×D11—21no—
21C2×C4⋊C4×D11C2212yes—
22C2×#66941—21no—
23C2×#66941C2212yes—
24C2×C42×D11C2211yescharacteristic
25C2×#66922C2211yescharacteristic
26C11×#474—24no—
27C2×C11×#107C2212yes—
28C2×C11×C4⋊C8C2211yescharacteristic
29C2×C11×#102C2212yes—
30#10622834C2211yescharacteristic
31C2×#66896C2212yes—
32C4×C22⋊Dic11—21no—
33C2×(C2×D11)⋊C8C2212yes—
34#10622620—24no—
35#10622600C2211yescharacteristic
36#10622586C2211yescharacteristic
37C2×#66871C2212yes—
38#10622569—21no—
39#10622557—21no—
40C4×C4⋊Dic11C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42#10622189C2212yes—
43#10622189C2212yes—
44#10622188C2212yes—
45#10622167C2212yes—
46#10622167C2212yes—
47C22×Q8×C11—21no—
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C22×C22⋊D11—21no—
51C2×Q8×D11—28no—
52C2×Q8×D11—44no—
53C2×Q8×D11—44no—
54C22×C4×D11—22no—
55C22×C4×D11D411yescharacteristic
56C22×C4×D11D411yescharacteristic
57C22×C4×D11C2311yescharacteristic
58C22×Dic22—21no—
59C22×Dic22—22no—
60C22×C8×C11C2312yes—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8D414yescomplemented
63C4×D4×C11—22no—
64C4×D4×C11—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C22⋊C4—21no—
69C2×C42×C11C2311yescharacteristic
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11—21no—
72C2×C22⋊Dic11—21no—
73#66997—28no—
74#66991—22no—
75#66991Q814yescomplemented
76C4×C22⋊D11—44no—
77C2×(C2×D11)⋊C4—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2312yes—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—22no—
83C2×Dic11⋊C4—22no—
84C2×Dic11⋊C4—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11D411yescharacteristic
87C2×C4×Dic11D411yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C22×C11⋊C8C2312yes—
90C4⋊C4×D11—28no—
91C4⋊C4×D11—24no—
92C4⋊C4×D11—24no—
93#66941—28no—
94#66941—24no—
95#66941—24no—
96C42×D11—22no—
97C42×D11—22no—
98#66922—22no—
99#66922D414yescomplemented
100C11×#107—24no—
101C11×C4⋊C8—22no—
102C11×#102—24no—
103#66896—24no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107(C2×D11)⋊C8—24no—
108#66871—24no—
109C4⋊(C11⋊C8)—22no—
110#24298—111nomaximal, Sylow
111C24×C11—21no—
112C23×D11C2×D411yescharacteristic
113C2×Q8×C11—24no—
114C2×Q8×C11—42no—
115C2×Q8×C11—42no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11C2×Q812yescomplemented
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—42no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C2×C22⋊D11—24no—
131C2×C22⋊D11—42no—
132C2×C22⋊D11—42no—
133C22×Dic11—21no—
134C22×Dic11—22no—
135C22×Dic11—21no—
136C22×Dic11C2×D411yescharacteristic
137C22×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139Q8×D11—432no—
140C2×C4×D11—22no—
141C2×C4×D11—28no—
142C2×C4×D11—22no—
143C2×C4×D11—22no—
144C2×C4×D11—22no—
145C2×C4×D11—22no—
146C2×C4×D11—21no—
147C2×C4×D11—21no—
148C2×C4×D11—21no—
149C2×C4×D11—21no—
150C2×C4×D11—44no—
151C2×C4×D11—44no—
152C2×C4×D11D814yes—
153C2×C4×D11C2×Q812yes—
154C2×C4×D11#4112yes—
155C2×Dic22—28no—
156C2×Dic22—24no—
157C2×Dic22—44no—
158C2×Dic22—44no—
159C2×Dic22—42no—
160C2×Dic22—42no—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4C2×D414yes—
169C11×C22⋊C4—42no—
170C42×C11C2×D412yes—
171C42×C11C2×D412yes—
172C22⋊Dic11—24no—
173C22⋊Dic11—42no—
174C22⋊Dic11—42no—
175(C2×D11)⋊C4—42no—
176C4⋊Dic11—24no—
177C4⋊Dic11—22no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11C2×D414yes—
182C4⋊Dic11C2×Q812yescomplemented
183Dic11⋊C4—28no—
184Dic11⋊C4—28no—
185Dic11⋊C4—42no—
186C4×Dic11—22no—
187C4×Dic11—22no—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C4×Dic11—42no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C22×C4⋊Q8—111no—
195C2×#474—111no—
196C2×#474D1111yescharacteristic, complemented
197C4×#121—111no—
198#2057—112no—
199#2023—112no—
200#1988—111no—
201#1988—111no—
202#1874—112no—
203#1852—112no—
204#1797—111no—
205C23×C11—22no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11C22×D411yescharacteristic
213C22×D11—21no—
214C22×D11—21no—
215C22×D11—21no—
216C22×D11—21no—
217C22×D11C22⋊Q812yes—
218C22×D11C2×D812yes—
219C22×D11#13712yes—
220Q8×C11—48no—
221D4×C11—22no—
222D4×C11—22no—
223D4×C11—41no—
224D4×C11—41no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—24no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—84no—
234C2×C4×C11#12012yes—
235C2×C4×C11#12012yes—
236C2×C4×C11C2×D812yes—
237C2×C4×C11AGL(1,ℤ/8)12yes—
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×Q811yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C112−1+411yescharacteristic
243C2×C4×C112−1+411yescharacteristic
244C22⋊D11—48no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—24no—
252C2×Dic11—22no—
253C2×Dic11—41no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11C22⋊Q812yes—
261C2×Dic11C2×D812yes—
262C2×Dic11#13712yes—
263C4×D11—28no—
264C4×D11—22no—
265C4×D11—22no—
266C4×D11—22no—
267C4×D11—22no—
268C4×D11—28no—
269C4×D11—416no—
270Dic22—416no—
271Dic22—48no—
272C8×C11—42no—
273C11⋊C8—42no—
274C23×Q8—221no—
275C2×C4⋊Q8—112no—
276C2×C4⋊Q8—111no—
277C2×C4⋊Q8—221no—
278C2×C4⋊Q8—221no—
279C2×C4⋊Q8—224no—
280C2×C4⋊Q8—224no—
281C2×C4⋊Q8C2×D1111yescharacteristic
282C2×#121—111no—
283C2×C4×D4—221no—
284C2×C4×D4C2×D1111yescharacteristic
285C22×C4⋊C4—112no—
286C22×C4⋊C4—221no—
287C22×C42—111no—
288#474—24no—
289#474—224no—
290C2×#107—112no—
291C2×#107C2×D1112yes—
292C2×C4⋊C8—111no—
293C2×C4⋊C8C2×D1111yescharacteristic
294C2×#102—112no—
295C2×#102C2×D1112yes—
296C2×C22⋊C8—112no—
297#390—111no—
298#389—111no—
299#388—221no—
300#386—221no—
301#380—111no—
302C4×C4⋊C4—111no—
303C4×C22⋊C4—221no—
304#340—112no—
305#340—112no—
306#340—112no—
307#340—112no—
308#336—112no—
309C22×C11—42no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—81no—
313C22×C11—81no—
314C22×C11—81no—
315C22×C11—81no—
316C22×C11C2×#12011yescharacteristic
317C22×C11C2×C22⋊Q811yescharacteristic
318C22×C11#53611yescharacteristic
319C22×C11C22×D811yescharacteristic
320C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
321C22×C11C2×#13711yescharacteristic
322C22×C11C2×#13711yescharacteristic
323C2×D11—22no—
324C2×D11—22no—
325C2×D11—22no—
326C2×D11—22no—
327C2×D11—22no—
328C2×D11—22no—
329C2×D11#47414yescomplemented
330C4×C11—22no—
331C4×C11—44no—
332C4×C11—81no—
333C4×C11#44714yes—
334C4×C11#54811yescharacteristic
335C4×C11#54811yescharacteristic
336C4×C11D4×Q811yescharacteristic
337C4×C11D4×Q811yescharacteristic
338Dic11—22no—
339Dic11—22no—
340Dic11—22no—
341Dic11—44no—
342Dic11—42no—
343Dic11—81no—
344C22×Q8—21no—
345C22×Q8—222no—
346C22×Q8—228no—
347C22×Q8—221no—
348C22×Q8—444no—
349C22×Q8—444no—
350C22×D4—221no—
351C22×D4C22×D1111yescharacteristic
352C23×C4—21no—
353C23×C4—111no—
354C23×C4—111no—
355C23×C4—111no—
356C23×C4—222no—
357C22×C8—112no—
358C22×C8C22×D1112yes—
359C4⋊Q8—22no—
360C4⋊Q8—114no—
361C4⋊Q8—224no—
362C4⋊Q8—228no—
363C4⋊Q8—228no—
364C4⋊Q8—224no—
365C4⋊Q8—222no—
366C4⋊Q8C22⋊D1114yescomplemented
367#121—114no—
368#121—222no—
369C4×D4—22no—
370C4×D4—22no—
371C4×D4—444no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—112no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—224no—
377C2×C4⋊C4—228no—
378C2×C4⋊C4—222no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—224no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C4⋊C4C22×D1112yes—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—221no—
387C2×C22⋊C4—221no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C42—111no—
391C2×C42—111no—
392C2×C42—111no—
393C2×C42—222no—
394C2×C42—222no—
395C2×C42—221no—
396C2×C42C22×D1111yescharacteristic
397#107—24no—
398#107—224no—
399C4⋊C8—22no—
400C4⋊C8—222no—
401#102—24no—
402#102—224no—
403C22⋊C8—224no—
404#95—221no—
405#95—221no—
406#95—221no—
407C2×C11—82no—
408C2×C11#240911yescharacteristic
409C2×C11C2×#44711yescharacteristic
410C2×C11#300411yescharacteristic
411C2×C11C2×#47411yescharacteristic
412C2×C11#307911yescharacteristic
413C2×C11#322611yescharacteristic
414C2×C11#323911yescharacteristic
415D11—24no—
416C24—21no—
417C24—111no—
418C2×Q8—24no—
419C2×Q8—42no—
420C2×Q8—42no—
421C2×Q8—228no—
422C2×Q8—224no—
423C2×Q8—444no—
424C2×Q8—444no—
425C2×Q8—4432no—
426C2×Q8—442no—
427C2×Q8—442no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—224no—
434C2×D4—442no—
435C2×D4—442no—
436C2×D4Q8×D1112yescomplemented
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—42no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—111no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—114no—
446C22×C4—112no—
447C22×C4—112no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—228no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—222no—
460C22×C4—221no—
461C22×C4—444no—
462C22×C4—444no—
463C22×C4D4×D1111yescharacteristic
464C22×C4D4×D1111yescharacteristic
465C22×C4C23×D1111yescharacteristic
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—222no—
470C2×C8—222no—
471C2×C8—222no—
472C4⋊C4—24no—
473C4⋊C4—22no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—114no—
477C4⋊C4—112no—
478C4⋊C4—228no—
479C4⋊C4—228no—
480C4⋊C4—224no—
481C4⋊C4—221no—
482C4⋊C4—222no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—442no—
486C4⋊C4C2×C22⋊D1114yes—
487C22⋊C4—42no—
488C22⋊C4—224no—
489C22⋊C4—442no—
490C22⋊C4—442no—
491C22⋊C4—442no—
492C42—222no—
493C42—222no—
494C42—221no—
495C42—221no—
496C42—442no—
497C42D4×D1112yes—
498C42C2×C22⋊D1112yes—
499C11#2429811yescharacteristic, complemented, Sylow
500C23—22no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—112no—
508C23—112no—
509C23—112no—
510C23—221no—
511C23—221no—
512C23—221no—
513C23—221no—
514C23C2×D4×D1111yescharacteristic
515Q8—48no—
516Q8—4416no—
517Q8—448no—
518D4—22no—
519D4—22no—
520D4—41no—
521D4—41no—
522D4—448no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—24no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—84no—
532C2×C4—112no—
533C2×C4—112no—
534C2×C4—112no—
535C2×C4—228no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—228no—
543C2×C4—222no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4—224no—
548C2×C4—222no—
549C2×C4—4416no—
550C2×C4—441no—
551C2×C4—442no—
552C2×C4—442no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4D8×D1112yes—
558C2×C4#6696412yes—
559C2×C4#6699012yes—
560C2×C4#6699012yes—
561C2×C4C2×D4×D1111yescharacteristic
562C2×C4C2×Q8×D1111yescharacteristic
563C2×C4#6704011yescharacteristic
564C2×C4#41×D1111yescharacteristic
565C2×C4#6704311yescharacteristic
566C2×C4C22×C22⋊D1111yescharacteristic
567C8—42no—
568C8—442no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—114no—
577C22—222no—
578C22—222no—
579C22—222no—
580C22—222no—
581C22—222no—
582C22—222no—
583C22D11×C22⋊Q811yescharacteristic
584C22#1062315911yescharacteristic
585C22C2×D8×D1111yescharacteristic
586C22C2×#6696411yescharacteristic
587C22D11×#13711yescharacteristic
588C22D11×#13711yescharacteristic
589C22C2×#6699011yescharacteristic
590C4—22no—
591C4—44no—
592C4—81no—
593C4—222no—
594C4—222no—
595C4—222no—
596C4—444no—
597C4—442no—
598C4—881no—
599C4#1062276914yes—
600C4#1062316311yescharacteristic
601C4#1062316411yescharacteristic
602C4Q8×C22⋊D1111yescharacteristic
603C4#1062336211yescharacteristic
604C2—82no—
605C2—224no—
606C2#1307197711yescharacteristic
607C2C2×#1062276911yescharacteristic
608C2#1307784811yescharacteristic
609C2D11×#47411yescharacteristic
610C2#1307842411yescharacteristic
611C2#1307973611yescharacteristic
612C2#1307984511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#474C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenterC2×#474D11
hypocenterC11#24298
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×D11×C4⋊Q8C2semidirect
2. C2×#10622620C2semidirect
4. #13069942C2semidirect
5. #13069750C2semidirect
6. #13069569C2semidirect
7. #13069567C2semidirect
9. #13068802C2semidirect
10. #13068593C2semidirect
11. C2×C11×#474C2semidirect
62. C11×C4⋊Q8D4semidirect
75. #66991Q8semidirect
99. #66922D4semidirect
121. C2×D4×C11C2×Q8semidirect
182. C4⋊Dic11C2×Q8semidirect
196. C2×#474D11semidirect
329. C2×D11#474semidirect
366. C4⋊Q8C22⋊D11semidirect
436. C2×D4Q8×D11semidirect
499. C11#24298semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
C2×#106226202
C4×#669912
#130699422
#130697502
#130695692
#130695672
#130689302
#130688022
#130685932
C2×C11×#4742
#2429811