Finite Group Databasebeta

← #14789829

Subgroups — #14789829

Order 2816.

1378 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#10622372C212yesmaximal, complemented
3#13071132C211yesmaximal, characteristic
4#13069945C211yesmaximal, characteristic, complemented
5#13069941C211yesmaximal, characteristic, complemented
6#13069752C211yesmaximal, characteristic, complemented
7#13069566C212yesmaximal, complemented
8#13068930C212yesmaximal
9#13068805C212yesmaximal, complemented
10#13068595C211yesmaximal, characteristic, complemented
11C11×#2023C211yesmaximal, characteristic, complemented
12C22×Q8×D11—21no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#66997—21no—
15C2×#66991C2211yescharacteristic
16C2×D4×Dic11C2211yescharacteristic
17D11×C4⋊Q8—28no—
18C2×C4⋊C4×D11—21no—
19C2×C4⋊C4×D11C2212yes—
20C2×#66941—21no—
21C2×#66941C2212yes—
22C2×(C22⋊D11)⋊C4—21no—
23C2×C42×D11C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C2×C11×#102C2212yes—
26C11×#390C2211yescharacteristic
27C2×#66896C2212yes—
28C2×(C2×D11)⋊C8C2212yes—
29C2×#66882C2212yes—
30C2×Dic11⋊C8C2212yes—
31#10622600C2211yescharacteristic
32C4⋊C4×Dic11C2211yescharacteristic
33C2×#66871C2212yes—
34#10622569—21no—
35#10622558—21no—
36C22⋊C4×Dic11—21no—
37#10622541C2211yescharacteristic
38#10622372—28no—
39C11×#340C2212yes—
40C11×#336C2211yescharacteristic
41#10622189C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44#10622162C2211yescharacteristic
45C22×Q8×C11—21no—
46C22×D4×C11C2311yescharacteristic
47C22×C22⋊D11—21no—
48C23×Dic11—21no—
49C2×Q8×D11—28no—
50C2×Q8×D11—44no—
51C2×Q8×D11—44no—
52C22×C4×D11—22no—
53C22×C4×D11D411yescharacteristic
54C22×C4×D11D411yescharacteristic
55C22×C4×D11C2311yescharacteristic
56C22×Dic22—21no—
57C22×Dic22—22no—
58C22×C8×C11C2312yes—
59C11×C4⋊Q8—24no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4—21no—
64C2×C11×C22⋊C4—21no—
65C2×C42×C11C2311yescharacteristic
66C2×C22⋊Dic11—21no—
67C2×C22⋊Dic11—21no—
68#66997—28no—
69#66991—22no—
70#66991Q814yescomplemented
71D4×Dic11—24no—
72C2×(C2×D11)⋊C4—21no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2312yes—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4—21no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C22×C11⋊C8C2312yes—
85C4⋊C4×D11—28no—
86C4⋊C4×D11—24no—
87C4⋊C4×D11—24no—
88#66941—28no—
89#66941—24no—
90#66941D418yescomplemented
91(C22⋊D11)⋊C4—44no—
92C42×D11—24no—
93#66922—24no—
94C11×#102—24no—
95#66896—24no—
96C11⋊#95—21no—
97C11⋊#95—21no—
98C11⋊#95—21no—
99(C2×D11)⋊C8—24no—
100#66882—24no—
101Dic11⋊C8—24no—
102#66871—24no—
103#24298—111nomaximal, Sylow
104C24×C11—21no—
105C23×D11C2×D411yescharacteristic
106C2×Q8×C11—24no—
107C2×Q8×C11—42no—
108C2×Q8×C11—42no—
109C2×D4×C11—22no—
110C2×D4×C11—21no—
111C2×D4×C11—22no—
112C2×D4×C11C2×Q812yescomplemented
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2411yescharacteristic
118C2×C22⋊D11—24no—
119C2×C22⋊D11—42no—
120C2×C22⋊D11—42no—
121C22×Dic11—21no—
122C22×Dic11—22no—
123C22×Dic11—21no—
124C22×Dic11—42no—
125C22×Dic11—42no—
126C22×Dic11—42no—
127C22×Dic11C2×D411yescharacteristic
128C22×Dic11C2×D411yescharacteristic
129C22×Dic11C2×D411yescharacteristic
130Q8×D11—432no—
131C2×C4×D11—22no—
132C2×C4×D11—22no—
133C2×C4×D11—22no—
134C2×C4×D11—28no—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—44no—
140C2×C4×D11—44no—
141C2×C4×D11D814yes—
142C2×C4×D11C2×Q812yes—
143C2×C4×D11#4112yes—
144C2×Dic22—24no—
145C2×Dic22—28no—
146C2×Dic22—42no—
147C2×Dic22—44no—
148C2×Dic22—44no—
149C2×Dic22—42no—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4C2×D414yes—
157C11×C22⋊C4—42no—
158C11×C22⋊C4—42no—
159C42×C11—22no—
160C22⋊Dic11—24no—
161C22⋊Dic11—42no—
162(C2×D11)⋊C4—42no—
163C4⋊Dic11—24no—
164C4⋊Dic11—22no—
165C4⋊Dic11—22no—
166C4⋊Dic11—21no—
167C4⋊Dic11C2×D414yes—
168C4⋊Dic11C2×Q812yescomplemented
169Dic11⋊C4—28no—
170Dic11⋊C4—28no—
171Dic11⋊C4—42no—
172C4×Dic11—22no—
173C4×Dic11—22no—
174C4×Dic11—42no—
175C4×Dic11C2×D414yes—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C22×C4⋊Q8—111no—
180C2×#474—112no—
181C4×#121—111no—
182#2057—111no—
183#2057—111no—
184#2023—111no—
185#2023D1111yescharacteristic, complemented
186#1988—112no—
187#1874—112no—
188#1852—112no—
189#1797—111no—
190C23×C11—22no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11C22×D411yescharacteristic
198C22×D11—21no—
199C22×D11—21no—
200C22×D11—21no—
201C22×D11—21no—
202C22×D11C22⋊Q812yes—
203C22×D11C2×D812yes—
204C22×D11#13712yes—
205Q8×C11—48no—
206D4×C11—24no—
207D4×C11—42no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—24no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11C2×D812yes—
219C2×C4×C11#13712yes—
220C2×C4×C11C22×D412yes—
221C2×C4×C11C22×Q811yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C112−1+412yes—
224C22⋊D11—48no—
225C2×Dic11—21no—
226C2×Dic11—21no—
227C2×Dic11—21no—
228C2×Dic11—21no—
229C2×Dic11—24no—
230C2×Dic11—22no—
231C2×Dic11—41no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—41no—
235C2×Dic11—41no—
236C2×Dic11—41no—
237C2×Dic11—41no—
238C2×Dic11—84no—
239C2×Dic11#12012yes—
240C2×Dic11#12012yes—
241C2×Dic11C22⋊Q812yes—
242C2×Dic11C2×D812yes—
243C2×Dic11AGL(1,ℤ/8)12yes—
244C4×D11—28no—
245C4×D11—24no—
246C4×D11—24no—
247C4×D11—28no—
248C4×D11—416no—
249Dic22—48no—
250Dic22—416no—
251C8×C11—42no—
252C11⋊C8—42no—
253C23×Q8—221no—
254C2×C4⋊Q8—112no—
255C2×C4⋊Q8—111no—
256C2×C4⋊Q8—221no—
257C2×C4⋊Q8—221no—
258C2×C4⋊Q8—228no—
259C2×C4⋊Q8C2×D1111yescharacteristic
260C2×#121—111no—
261C2×C4×D4—111no—
262C2×C4×D4—221no—
263C22×C4⋊C4—112no—
264C22×C4⋊C4—221no—
265C22×C42—111no—
266#474—228no—
267C2×#107—112no—
268C2×#107—112no—
269C2×C4⋊C8—112no—
270C2×#102—112no—
271C2×#102C2×D1112yes—
272C2×C22⋊C8—112no—
273#390C2×D1111yescharacteristic
274#389—111no—
275#388—221no—
276#386—221no—
277#380—111no—
278C4×C4⋊C4—111no—
279C4×C22⋊C4—221no—
280#340—112no—
281#340—112no—
282#340—112no—
283#340C2×D1112yes—
284#336—111no—
285#336C2×D1111yescharacteristic
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—81no—
290C22×C11—81no—
291C22×C11—81no—
292C22×C11—81no—
293C22×C11C2×#12011yescharacteristic
294C22×C11C2×C22⋊Q811yescharacteristic
295C22×C11#53611yescharacteristic
296C22×C11C22×D811yescharacteristic
297C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
298C22×C11C2×#13711yescharacteristic
299C22×C11C2×#13711yescharacteristic
300C2×D11—22no—
301C2×D11—22no—
302C2×D11—22no—
303C2×D11—22no—
304C2×D11—22no—
305C2×D11—22no—
306C2×D11#47414yescomplemented
307C4×C11—22no—
308C4×C11—22no—
309C4×C11—44no—
310C4×C11—81no—
311C4×C11#54812yes—
312C4×C11D4×Q812yes—
313Dic11—22no—
314Dic11—22no—
315Dic11—44no—
316Dic11—42no—
317Dic11—81no—
318Dic11#44714yes—
319C22×Q8—21no—
320C22×Q8—222no—
321C22×Q8—228no—
322C22×Q8—221no—
323C22×Q8—444no—
324C22×Q8—444no—
325C22×D4—221no—
326C22×D4C22×D1111yescharacteristic
327C23×C4—111no—
328C23×C4—111no—
329C23×C4—111no—
330C23×C4—222no—
331C23×C4—221no—
332C22×C8—112no—
333C22×C8C22×D1112yes—
334C4⋊Q8—24no—
335C4⋊Q8—118no—
336C4⋊Q8—224no—
337C4⋊Q8—224no—
338C4⋊Q8—228no—
339C4⋊Q8—228no—
340#121—114no—
341#121—222no—
342C4×D4—224no—
343C4×D4—444no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—112no—
346C2×C4⋊C4—111no—
347C2×C4⋊C4—111no—
348C2×C4⋊C4—224no—
349C2×C4⋊C4—228no—
350C2×C4⋊C4—222no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4—221no—
353C2×C4⋊C4—224no—
354C2×C4⋊C4—221no—
355C2×C4⋊C4C22×D1111yescharacteristic
356C2×C4⋊C4C22×D1112yes—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—221no—
360C2×C22⋊C4—221no—
361C2×C22⋊C4—221no—
362C2×C42—111no—
363C2×C42—111no—
364C2×C42—111no—
365C2×C42—224no—
366C2×C42—221no—
367C2×C42C22×D1111yescharacteristic
368#107—224no—
369#107—224no—
370C4⋊C8—224no—
371#102—24no—
372#102—224no—
373C22⋊C8—224no—
374#95—221no—
375#95—221no—
376#95—221no—
377C2×C11—82no—
378C2×C11#240911yescharacteristic
379C2×C11C2×#44711yescharacteristic
380C2×C11#300411yescharacteristic
381C2×C11C2×#47411yescharacteristic
382C2×C11#307911yescharacteristic
383C2×C11#322611yescharacteristic
384C2×C11#323911yescharacteristic
385D11—24no—
386C24—21no—
387C24—111no—
388C2×Q8—24no—
389C2×Q8—42no—
390C2×Q8—42no—
391C2×Q8—228no—
392C2×Q8—224no—
393C2×Q8—442no—
394C2×Q8—444no—
395C2×Q8—444no—
396C2×Q8—4432no—
397C2×Q8—442no—
398C2×D4—22no—
399C2×D4—21no—
400C2×D4—22no—
401C2×D4—224no—
402C2×D4—442no—
403C2×D4—442no—
404C2×D4Q8×D1112yescomplemented
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—111no—
408C22×C4—111no—
409C22×C4—111no—
410C22×C4—114no—
411C22×C4—112no—
412C22×C4—112no—
413C22×C4—222no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—228no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—221no—
422C22×C4—222no—
423C22×C4—221no—
424C22×C4—444no—
425C22×C4—444no—
426C22×C4—442no—
427C22×C4—442no—
428C22×C4—442no—
429C22×C4D4×D1111yescharacteristic
430C22×C4D4×D1111yescharacteristic
431C22×C4C23×D1111yescharacteristic
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—222no—
436C2×C8—222no—
437C2×C8—222no—
438C4⋊C4—24no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—114no—
442C4⋊C4—112no—
443C4⋊C4—228no—
444C4⋊C4—228no—
445C4⋊C4—224no—
446C4⋊C4—222no—
447C4⋊C4—221no—
448C4⋊C4—222no—
449C4⋊C4—442no—
450C4⋊C4D4×D1114yes—
451C22⋊C4—42no—
452C22⋊C4—42no—
453C22⋊C4—224no—
454C22⋊C4—442no—
455C22⋊C4—442no—
456C42—22no—
457C42—114no—
458C42—222no—
459C42—222no—
460C42—442no—
461C11#2429811yescharacteristic, complemented, Sylow
462C23—22no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—112no—
470C23—112no—
471C23—112no—
472C23—221no—
473C23—221no—
474C23—221no—
475C23—221no—
476C23C2×D4×D1111yescharacteristic
477Q8—48no—
478Q8—448no—
479Q8—4416no—
480D4—24no—
481D4—42no—
482D4—448no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—24no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—112no—
494C2×C4—112no—
495C2×C4—112no—
496C2×C4—112no—
497C2×C4—112no—
498C2×C4—228no—
499C2×C4—228no—
500C2×C4—221no—
501C2×C4—221no—
502C2×C4—221no—
503C2×C4—221no—
504C2×C4—224no—
505C2×C4—224no—
506C2×C4—224no—
507C2×C4—222no—
508C2×C4—4416no—
509C2×C4—441no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—441no—
513C2×C4—441no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4—884no—
517C2×C4D8×D1112yes—
518C2×C4#6696812yes—
519C2×C4C2×D4×D1112yes—
520C2×C4C2×Q8×D1111yescharacteristic
521C2×C4#41×D1111yescharacteristic
522C2×C4#6704312yes—
523C8—42no—
524C8—442no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—81no—
529C22—81no—
530C22—81no—
531C22—81no—
532C22—114no—
533C22—222no—
534C22—222no—
535C22—222no—
536C22—222no—
537C22—222no—
538C22—222no—
539C22D11×#12011yescharacteristic
540C22D11×C22⋊Q811yescharacteristic
541C22#1062320611yescharacteristic
542C22C2×D8×D1111yescharacteristic
543C22C2×#6696811yescharacteristic
544C22D11×AGL(1,ℤ/8)11yescharacteristic
545C22D11×#13711yescharacteristic
546C4—22no—
547C4—22no—
548C4—44no—
549C4—81no—
550C4—114no—
551C4—222no—
552C4—222no—
553C4—444no—
554C4—442no—
555C4—881no—
556C4#1062316312yes—
557C4#1062320812yes—
558C2—82no—
559C2—224no—
560C2#1307197411yescharacteristic
561C2D11×#44711yescharacteristic
562C2#1307784711yescharacteristic
563C2D11×#47411yescharacteristic
564C2#1307842811yescharacteristic
565C2#1307973311yescharacteristic
566C2#1307984211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2023C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenter#2023D11
hypocenterC11#24298
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2023

Complements

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

NH ≅ G/Ntype
1. C2×D11×C4⋊Q8C2semidirect
2. C2×#10622372C2semidirect
4. #13069945C2semidirect
5. #13069941C2semidirect
6. #13069752C2semidirect
7. #13069566C2semidirect
9. #13068805C2semidirect
10. #13068595C2semidirect
11. C11×#2023C2semidirect
70. #66991Q8semidirect
90. #66941D4semidirect
112. C2×D4×C11C2×Q8semidirect
168. C4⋊Dic11C2×Q8semidirect
185. #2023D11semidirect
306. C2×D11#474semidirect
404. C2×D4Q8×D11semidirect
461. 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×#106223722
#130711322
#130699452
#130699412
#130697522
#130695662
#130689302
#130688052
#130685952
C11×#20232
#2429811