Finite Group Databasebeta

← #14789834

Subgroups — #14789834

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×#10622459C211yesmaximal, characteristic, complemented
3C2×#10622700C211yesmaximal, characteristic, complemented
4C4×#66948C211yesmaximal, characteristic
5#13069943C212yesmaximal, complemented
6#13069751C212yesmaximal, complemented
7#13069568C211yesmaximal, characteristic, complemented
8#13068932C212yesmaximal
9#13068805C212yesmaximal, complemented
10#13068593C211yesmaximal, characteristic, complemented
11C11×#1988C211yesmaximal, characteristic, complemented
12C22×Q8×D11—21no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#66997—21no—
15D11×C4⋊Q8—24no—
16D11×C4⋊Q8—24no—
17C2×#66948C2211yescharacteristic
18C2×C4⋊C4×D11—21no—
19C2×C4⋊C4×D11C2212yes—
20C2×#66941—21no—
21C2×#66941C2212yes—
22C2×C4×D44—21no—
23C2×C4×D44C2211yescharacteristic
24C2×C42×D11C2211yescharacteristic
25C2×#66922C2211yescharacteristic
26C2×C11×C4⋊C8C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C2×#66885C2212yes—
29C2×(C2×D11)⋊C8C2212yes—
30C2×#66882C2212yes—
31#10622700—24no—
32#10622601C2211yescharacteristic
33#10622600C2211yescharacteristic
34#10622598C2211yescharacteristic
35C2×#66873C2212yes—
36C2×#66871C2212yes—
37C4×(C2×D11)⋊C4—21no—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39#10622459—24no—
40#10622283—21no—
41#10622278—21no—
42C11×#340C2212yes—
43C11×#340C2212yes—
44#10622188C2212yes—
45#10622167C2212yes—
46#10622167C2212yes—
47C22×Q8×C11—21no—
48C2×Q8×D11—28no—
49C2×Q8×D11—44no—
50C2×Q8×D11—44no—
51C22×D44—21no—
52C22×D44C2311yescharacteristic
53C22×C4×D11—22no—
54C22×C4×D11—21no—
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
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C42×C11—21no—
68C2×C42×C11C2311yescharacteristic
69#66997—28no—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2312yes—
79C2×Dic11⋊C4—22no—
80C2×Dic11⋊C4—22no—
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C22×C11⋊C8C2312yes—
85#66948—22no—
86#66948Q814yescomplemented
87C4⋊C4×D11—28no—
88C4⋊C4×D11—24no—
89C4⋊C4×D11—24no—
90#66941—28no—
91#66941—24no—
92#66941—24no—
93C4×D44—22no—
94C4×D44—22no—
95C4×D44—44no—
96C42×D11—22no—
97C42×D11—22no—
98#66922—22no—
99#66922D414yescomplemented
100C11×C4⋊C8—22no—
101C11×#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104#66885—24no—
105(C2×D11)⋊C8—24no—
106#66882—24no—
107#66873—24no—
108#66871—24no—
109C4⋊(C11⋊C8)—22no—
110#24298—111nomaximal, Sylow
111C23×D11—21no—
112C23×D11C2×D411yescharacteristic
113C2×Q8×C11—24no—
114C2×Q8×C11—42no—
115C2×Q8×C11—42no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2411yescharacteristic
122C22×Dic11—22no—
123C22×Dic11—21no—
124C22×Dic11C2×D411yescharacteristic
125C22×Dic11C2×D411yescharacteristic
126C22×Dic11C2×D411yescharacteristic
127Q8×D11—432no—
128C2×D44—24no—
129C2×D44—21no—
130C2×D44—21no—
131C2×D44—21no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44—42no—
135C2×D44—42no—
136C2×D44C2×Q812yescomplemented
137C2×C4×D11—22no—
138C2×C4×D11—28no—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—22no—
142C2×C4×D11—22no—
143C2×C4×D11—21no—
144C2×C4×D11—21no—
145C2×C4×D11—21no—
146C2×C4×D11—21no—
147C2×C4×D11—44no—
148C2×C4×D11—44no—
149C2×C4×D11—42no—
150C2×C4×D11—42no—
151C2×C4×D11—42no—
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⋊C4—21no—
169C11×C4⋊C4C2×D414yes—
170C11×C4⋊C4C2×Q812yescomplemented
171C42×C11—42no—
172C42×C11C2×D412yes—
173C42×C11C2×D412yes—
174(C2×D11)⋊C4—24no—
175(C2×D11)⋊C4—42no—
176(C2×D11)⋊C4—42no—
177(C2×D11)⋊C4—42no—
178(C2×D11)⋊C4—42no—
179C4⋊Dic11—24no—
180C4⋊Dic11—22no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—42no—
184C4⋊Dic11C2×D414yes—
185Dic11⋊C4—28no—
186Dic11⋊C4—28no—
187C4×Dic11—22no—
188C4×Dic11—22no—
189C4×Dic11—21no—
190C4×Dic11—21no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C22×C4⋊Q8—111no—
195C2×#474—111no—
196C2×#474—111no—
197C4×#121—111no—
198#2057—112no—
199#2023—112no—
200#1988—111no—
201#1988D1111yescharacteristic, complemented
202#1874—112no—
203#1852—112no—
204#1797—111no—
205C23×C11C22×D411yescharacteristic
206C22×D11—21no—
207C22×D11—21no—
208C22×D11—21no—
209C22×D11—21no—
210C22×D11—22no—
211C22×D11—41no—
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11C22⋊Q812yes—
218C22×D11C2×D812yes—
219C22×D11#13712yes—
220Q8×C11—48no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—41no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11#12012yes—
233C2×C4×C11#12012yes—
234C2×C4×C11C2×D812yes—
235C2×C4×C11AGL(1,ℤ/8)12yes—
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×Q811yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C112−1+411yescharacteristic
241C2×C4×C112−1+411yescharacteristic
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—24no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11C22⋊Q812yes—
255C2×Dic11C2×D812yes—
256C2×Dic11#13712yes—
257D44—22no—
258D44—22no—
259D44—48no—
260D44—41no—
261D44—41no—
262C4×D11—28no—
263C4×D11—22no—
264C4×D11—22no—
265C4×D11—22no—
266C4×D11—22no—
267C4×D11—28no—
268C4×D11—416no—
269C4×D11—84no—
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—111no—
284C2×C4×D4—221no—
285C22×C4⋊C4—112no—
286C22×C4⋊C4—221no—
287C22×C42—111no—
288#474—224no—
289#474—224no—
290C2×#107—112no—
291C2×#107—112no—
292C2×C4⋊C8—111no—
293C2×C4⋊C8C2×D1111yescharacteristic
294C2×#102—112no—
295C2×#102—112no—
296C2×C22⋊C8—112no—
297#390—111no—
298#389—111no—
299#388—221no—
300#386—221no—
301#380—111no—
302C4×C4⋊C4C2×D1111yescharacteristic
303C4×C22⋊C4—221no—
304#340—112no—
305#340—112no—
306#340C2×D1112yes—
307#340C2×D1112yes—
308#336—112no—
309C22×C11C2×#12011yescharacteristic
310C22×C11C2×C22⋊Q811yescharacteristic
311C22×C11#53611yescharacteristic
312C22×C11C22×D811yescharacteristic
313C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
314C22×C11C2×#13711yescharacteristic
315C22×C11C2×#13711yescharacteristic
316C2×D11—22no—
317C2×D11—22no—
318C2×D11—22no—
319C2×D11—22no—
320C2×D11—22no—
321C2×D11—22no—
322C2×D11—42no—
323C2×D11—42no—
324C2×D11—42no—
325C2×D11—81no—
326C2×D11—81no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11#47414yescomplemented
330C4×C11—22no—
331C4×C11—44no—
332C4×C11—42no—
333C4×C11—81no—
334C4×C11#44714yes—
335C4×C11#54811yescharacteristic
336C4×C11#54811yescharacteristic
337C4×C11D4×Q811yescharacteristic
338C4×C11D4×Q811yescharacteristic
339Dic11—22no—
340Dic11—22no—
341Dic11—22no—
342Dic11—44no—
343Dic11—81no—
344C22×Q8—21no—
345C22×Q8—222no—
346C22×Q8—228no—
347C22×Q8—221no—
348C22×Q8—444no—
349C22×Q8—444no—
350C22×D4—111no—
351C22×D4—221no—
352C23×C4—111no—
353C23×C4—111no—
354C23×C4—111no—
355C23×C4—222no—
356C23×C4—221no—
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⋊Q8D4414yescomplemented
367#121—114no—
368#121—222no—
369C4×D4—222no—
370C4×D4—222no—
371C4×D4—444no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—112no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—224no—
376C2×C4⋊C4—228no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—222no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—224no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4C22×D1111yescharacteristic
383C2×C4⋊C4C22×D1112yes—
384C2×C4⋊C4C22×D1111yescharacteristic
385C2×C22⋊C4—221no—
386C2×C22⋊C4—221no—
387C2×C22⋊C4—221no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C42—21no—
391C2×C42—111no—
392C2×C42—111no—
393C2×C42—111no—
394C2×C42—222no—
395C2×C42—222no—
396C2×C42C22×D1111yescharacteristic
397#107—224no—
398#107—224no—
399C4⋊C8—22no—
400C4⋊C8—222no—
401#102—224no—
402#102—224no—
403C22⋊C8—224no—
404#95—21no—
405#95—221no—
406#95—221no—
407C2×C11#240911yescharacteristic
408C2×C11C2×#44711yescharacteristic
409C2×C11#300411yescharacteristic
410C2×C11C2×#47411yescharacteristic
411C2×C11#307911yescharacteristic
412C2×C11#322611yescharacteristic
413C2×C11#323911yescharacteristic
414D11—24no—
415D11—82no—
416C24—111no—
417C24—221no—
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—112no—
429C2×D4—224no—
430C2×D4—221no—
431C2×D4—221no—
432C2×D4—221no—
433C2×D4—221no—
434C2×D4—221no—
435C2×D4—442no—
436C2×D4—442no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—114no—
444C22×C4—112no—
445C22×C4—112no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—228no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—222no—
457C22×C4—221no—
458C22×C4—444no—
459C22×C4—444no—
460C22×C4—442no—
461C22×C4—442no—
462C22×C4—442no—
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—21no—
477C4⋊C4—114no—
478C4⋊C4—228no—
479C4⋊C4—228no—
480C4⋊C4—224no—
481C4⋊C4—222no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—442no—
485C4⋊C4C2×D4414yes—
486C4⋊C4Q8×D1112yescomplemented
487C22⋊C4—224no—
488C22⋊C4—442no—
489C22⋊C4—442no—
490C22⋊C4—442no—
491C22⋊C4—442no—
492C42—42no—
493C42—222no—
494C42—222no—
495C42—221no—
496C42—221no—
497C42C2×D4412yes—
498C42D4×D1112yes—
499C11#2429811yescharacteristic, complemented, Sylow
500C23—112no—
501C23—112no—
502C23—112no—
503C23—221no—
504C23—221no—
505C23—221no—
506C23—221no—
507C23—222no—
508C23—441no—
509C23—441no—
510C23—441no—
511C23—441no—
512C23—441no—
513C23—441no—
514C23C2×D4×D1111yescharacteristic
515Q8—48no—
516Q8—4416no—
517Q8—448no—
518D4—222no—
519D4—222no—
520D4—448no—
521D4—441no—
522D4—441no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—112no—
535C2×C4—112no—
536C2×C4—112no—
537C2×C4—228no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4—228no—
548C2×C4—222no—
549C2×C4—224no—
550C2×C4—4416no—
551C2×C4—442no—
552C2×C4—442no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—884no—
557C2×C4#6693512yes—
558C2×C4#6693512yes—
559C2×C4D8×D1112yes—
560C2×C4#6696712yes—
561C2×C4C22×D4411yescharacteristic
562C2×C4C2×D4×D1111yescharacteristic
563C2×C4C2×Q8×D1111yescharacteristic
564C2×C4#6704011yescharacteristic
565C2×C4#41×D1111yescharacteristic
566C2×C4#6704311yescharacteristic
567C8—42no—
568C8—442no—
569C22—114no—
570C22—222no—
571C22—222no—
572C22—222no—
573C22—222no—
574C22—222no—
575C22—222no—
576C22—442no—
577C22—442no—
578C22—442no—
579C22—881no—
580C22—881no—
581C22—881no—
582C22—881no—
583C22C2×#6693511yescharacteristic
584C22D11×C22⋊Q811yescharacteristic
585C22#1062315911yescharacteristic
586C22C2×D8×D1111yescharacteristic
587C22C2×#6696711yescharacteristic
588C22D11×#13711yescharacteristic
589C22D11×#13711yescharacteristic
590C4—22no—
591C4—44no—
592C4—42no—
593C4—81no—
594C4—222no—
595C4—222no—
596C4—222no—
597C4—444no—
598C4—881no—
599C4#1062238614yes—
600C4Q8×D4411yescharacteristic
601C4#1062310711yescharacteristic
602C4#1062320811yescharacteristic
603C4#1062325811yescharacteristic
604C2—224no—
605C2—882no—
606C2#1307197911yescharacteristic
607C2C2×#1062238611yescharacteristic
608C2#1307785211yescharacteristic
609C2D11×#47411yescharacteristic
610C2#1307842611yescharacteristic
611C2#1307973611yescharacteristic
612C2#1307985011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1988C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenter#1988D11
hypocenterC11#24298
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
1. C2×D11×C4⋊Q8C2semidirect
2. C2×#10622459C2semidirect
3. C2×#10622700C2semidirect
5. #13069943C2semidirect
6. #13069751C2semidirect
7. #13069568C2semidirect
9. #13068805C2semidirect
10. #13068593C2semidirect
11. C11×#1988C2semidirect
62. C11×C4⋊Q8D4semidirect
86. #66948Q8semidirect
99. #66922D4semidirect
136. C2×D44C2×Q8semidirect
170. C11×C4⋊C4C2×Q8semidirect
201. #1988D11semidirect
329. C2×D11#474semidirect
366. C4⋊Q8D44semidirect
486. C4⋊C4Q8×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×#106224592
C2×#106227002
C4×#669482
#130699432
#130697512
#130695682
#130689322
#130688052
#130685932
C11×#19882
#2429811