Finite Group Databasebeta

← #14753296

Subgroups — #14753296

Order 2816.

1462 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623054C211yesmaximal, characteristic
2C2×#10622612C211yesmaximal, characteristic, complemented
3C2×#10622579C211yesmaximal, characteristic
4C2×#10622615C211yesmaximal, characteristic
5#13068628C212yesmaximal, complemented
6#13068623C212yesmaximal, complemented
7#13068618C212yesmaximal, complemented
8#13068613C212yesmaximal, complemented
9#13068337C211yesmaximal, characteristic, complemented
10C2×#10622167C211yesmaximal, characteristic, complemented
11C11×#2317C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×#4318C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19#10623054—24no—
20#10623054C418yescomplemented
21C2×#66945—21no—
22C2×C4⋊C4×D11—21no—
23C2×(C22⋊D11)⋊C4—22no—
24C2×C4×D44C2212yes—
25C2×C4×Dic22C2212yes—
26C11×#389—21no—
27C11×#389—21no—
28C11×#385—22no—
29C11×#384C2212yes—
30C11×#382C2212yes—
31#10622615—24no—
32#10622612—24no—
33C2×#66874C2211yescharacteristic
34C2×#66874C2212yes—
35C2×#66874C2211yescharacteristic
36#10622579—24no—
37C2×#66873C2211yescharacteristic
38C2×#66873C2212yes—
39C2×#66873C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2212yes—
41C2×C4⋊(C11⋊C8)C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C23×C4×C11—21no—
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11—21no—
49C23×Dic11—21no—
50C2×#4339—22no—
51C2×#4339—22no—
52C2×#4339—22no—
53C2×#4339C2×C414yes—
54C2×#4339D414yes—
55C2×#4339Q814yes—
56C22×D44C2311yescharacteristic
57C22×C4×D11—21no—
58C22×C4×D11—22no—
59C22×Dic22C2311yescharacteristic
60C11×#117—22no—
61C11×#117—22no—
62C11×#117C2×C414yes—
63C11×#117D414yes—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4D412yes—
76C2×C42×C11—21no—
77C2×C42×C11C2312yes—
78C2×(C2×D11)⋊C4—22no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11C2×C414yes—
82C2×C4⋊Dic11C2312yes—
83C2×Dic11⋊C4—22no—
84C2×C4×Dic11—22no—
85C2×#4318—22no—
86C2×#4318—22no—
87C2×#4318—22no—
88C22×C11⋊C8—22no—
89C22×C11⋊C8—22no—
90C22×C11⋊C8—22no—
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2312yes—
94#66945—28no—
95C4⋊C4×D11—28no—
96(C22⋊D11)⋊C4—216no—
97C4×D44—24no—
98C4×D44C2×C418yescomplemented
99C4×Dic22—24no—
100C4×Dic22C2×C418yescomplemented
101C11×#95—22no—
102C11×#95—22no—
103#66874—24no—
104#66874—22no—
105#66874—22no—
106#66873—24no—
107#66873—22no—
108#66873—22no—
109C4⋊(C11⋊C8)—24no—
110C4⋊(C11⋊C8)—24no—
111#20652—111nomaximal, Sylow
112C24×C11C2×D411yescharacteristic
113C23×D11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—42no—
118C22×C4×C11—81no—
119C22×C4×C11—81no—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×Q812yes—
127C22×C4×C11#4112yes—
128C22×C4×C11#4112yes—
129C22×C4×C11C2411yescharacteristic
130C2×C22⋊D11—24no—
131C2×C22⋊D11—24no—
132C2×C22⋊D11—24no—
133C22×Dic11—24no—
134C22×Dic11—21no—
135C22×Dic11—22no—
136C22×Dic11—81no—
137C22×Dic11—81no—
138#4339—28no—
139#4339—28no—
140#4339—28no—
141#4339C4⋊C4116yescomplemented
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44C22×C412yes—
146C2×D44C2×D412yes—
147C2×D44C2×Q812yes—
148C2×C4×D11—24no—
149C2×C4×D11—28no—
150C2×C4×D11—24no—
151C2×C4×D11—24no—
152C2×C4×D11—82no—
153C2×C4×D11—82no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22C22×C412yes—
158C2×Dic22C2×D412yes—
159C2×Dic22C2×Q812yes—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—42no—
167C11×C4⋊C4—82no—
168C11×C4⋊C4—82no—
169C11×C4⋊C4C22⋊C414yes—
170C11×C4⋊C4C22⋊C414yes—
171C11×C22⋊C4—42no—
172C11×C22⋊C4C22⋊C418yes—
173C42×C11—42no—
174C42×C11C22×C414yes—
175C42×C11C2×D414yes—
176(C2×D11)⋊C4—28no—
177C4⋊Dic11—24no—
178C4⋊Dic11—22no—
179C4⋊Dic11C22×C414yes—
180Dic11⋊C4—28no—
181C4×Dic11—28no—
182#4318—44no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—44no—
193C2×#520—111no—
194C2×#424—111no—
195C2×#417—111no—
196C2×#416—111no—
197#2317D1111yescharacteristic, complemented
198#1805—112no—
199#1804—112no—
200#1803—112no—
201#1802—112no—
202#1736—111no—
203C2×#340—111no—
204C23×C11—21no—
205C23×C11—21no—
206C23×C11—21no—
207C23×C11—21no—
208C23×C11C2×C22⋊C412yes—
209C23×C11#12112yes—
210C23×C11C22⋊Q812yes—
211C23×C11C22×D411yescharacteristic
212C22×D11—22no—
213C22×D11—22no—
214C22×D11—22no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—41no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—42no—
226C2×C4×C11—41no—
227C2×C4×C11—42no—
228C2×C4×C11—41no—
229C2×C4×C11—42no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—84no—
233C2×C4×C11C2×C22⋊C414yes—
234C2×C4×C11C2×C22⋊C414yes—
235C2×C4×C11C2×C22⋊C412yes—
236C2×C4×C11C2×C4⋊C414yes—
237C2×C4×C11#11714yes—
238C2×C4×C11#12114yes—
239C2×C4×C11#12112yes—
240C2×C4×C11C22⋊Q814yes—
241C2×C4×C11C22⋊Q812yes—
242C2×C4×C11C23×C411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×Q811yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C22⋊D11—216no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—84no—
256D44—22no—
257D44—22no—
258D44—22no—
259D44C2×C4⋊C414yes—
260C4×D11—216no—
261C4×D11—88no—
262Dic22—22no—
263Dic22—22no—
264Dic22—22no—
265Dic22C2×C4⋊C414yes—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C11⋊C8—42no—
269C22×#41—111no—
270C22×M16—111no—
271C23×C8—111no—
272#520—118no—
273#520—224no—
274C2×C4×Q8—112no—
275C2×C4×D4—112no—
276C2×C4×D4—222no—
277C2×#117—221no—
278C2×#117C2×D1111yescharacteristic
279C2×#117C2×D1111yescharacteristic
280C22×C4⋊C4—111no—
281C22×C4⋊C4—221no—
282C22×C4⋊C4C2×D1111yescharacteristic
283#424—224no—
284C2×C4⋊C8—112no—
285C2×C4⋊C8—112no—
286#417—224no—
287#416—224no—
288C2×#103—111no—
289C2×#103—112no—
290C2×#103—111no—
291C2×#102—111no—
292C2×#102—112no—
293C2×#102—111no—
294#389—21no—
295#389—21no—
296#385—22no—
297#384C2×D1112yes—
298#382C2×D1112yes—
299#340—112no—
300#340—112no—
301#340—112no—
302#340—112no—
303C22×C11—22no—
304C22×C11—22no—
305C22×C11—22no—
306C22×C11—22no—
307C22×C11—22no—
308C22×C11—22no—
309C22×C11#38014yes—
310C22×C11C22×C22⋊C411yescharacteristic
311C22×C11C2×#12111yescharacteristic
312C22×C11C2×C22⋊Q811yescharacteristic
313C22×C11#57611yescharacteristic
314C22×C11#57711yescharacteristic
315C22×C11#57711yescharacteristic
316C22×C11#57811yescharacteristic
317C2×D11—24no—
318C2×D11—42no—
319C2×D11—42no—
320C2×D11—42no—
321C2×D11—42no—
322C2×D11—42no—
323C2×D11—42no—
324C4×C11—24no—
325C4×C11—24no—
326C4×C11—81no—
327C4×C11—82no—
328C4×C11—81no—
329C4×C11#38014yes—
330C4×C11C22×C4⋊C411yescharacteristic
331C4×C11C2×#11711yescharacteristic
332C4×C11C2×#12111yescharacteristic
333C4×C11C2×C22⋊Q811yescharacteristic
334Dic11—24no—
335Dic11—44no—
336C2×#41—114no—
337C2×#41—114no—
338C2×#41—114no—
339C2×#41—222no—
340C2×#41—222no—
341C2×#41—222no—
342C22×Q8—111no—
343C22×D4—111no—
344C22×D4—221no—
345C23×C4—21no—
346C23×C4—221no—
347C23×C4—221no—
348C23×C4—222no—
349C23×C4C22×D1111yescharacteristic
350C2×M16—222no—
351C2×M16—222no—
352C2×M16—222no—
353C22×C8—111no—
354C22×C8—111no—
355C22×C8—112no—
356C22×C8—222no—
357C22×C8—222no—
358C22×C8—222no—
359C4×Q8—118no—
360C4×Q8—224no—
361C4×D4—118no—
362C4×D4—2216no—
363C4×D4—224no—
364#117—22no—
365#117—22no—
366#117—228no—
367#117C4×D1114yes—
368#117D4414yes—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—114no—
375C2×C4⋊C4—112no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—222no—
379C2×C4⋊C4—228no—
380C2×C4⋊C4C22⋊D1111yescharacteristic
381C2×C4⋊C4C22⋊D1111yescharacteristic
382C2×C4⋊C4C22×D1112yes—
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C4⋊C4C22×D1111yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—222no—
387C2×C22⋊C4C22⋊D1112yes—
388C2×C42—21no—
389C2×C42—222no—
390C2×C42C22×D1112yes—
391C4⋊C8—224no—
392C4⋊C8—224no—
393#103—222no—
394#103—222no—
395#103—224no—
396#102—222no—
397#102—222no—
398#102—224no—
399#95—22no—
400#95—22no—
401C2×C11—24no—
402C2×C11C2×#38011yescharacteristic
403C2×C11#289711yescharacteristic
404C2×C11#289811yescharacteristic
405C2×C11#304511yescharacteristic
406C2×C11#304611yescharacteristic
407C2×C11#308311yescharacteristic
408C2×C11#308411yescharacteristic
409D11—44no—
410C24—221no—
411C24C2×C22⋊D1111yescharacteristic
412#41—1116no—
413#41—228no—
414#41—228no—
415#41—228no—
416C2×Q8—112no—
417C2×Q8—112no—
418C2×Q8—112no—
419C2×Q8—221no—
420C2×Q8—221no—
421C2×Q8—221no—
422C2×D4—112no—
423C2×D4—112no—
424C2×D4—112no—
425C2×D4—224no—
426C2×D4—224no—
427C2×D4—224no—
428C2×D4—221no—
429C2×D4—221no—
430C2×D4—221no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—42no—
435C22×C4—81no—
436C22×C4—81no—
437C22×C4—221no—
438C22×C4—224no—
439C22×C4—224no—
440C22×C4—224no—
441C22×C4—222no—
442C22×C4—224no—
443C22×C4—228no—
444C22×C4—882no—
445C22×C4—882no—
446C22×C4—881no—
447C22×C4—881no—
448C22×C4C2×C4×D1112yes—
449C22×C4C2×D4412yes—
450C22×C4D4×D1112yes—
451C22×C4#434112yes—
452C22×C4Q8×D1112yes—
453C22×C4#434312yes—
454C22×C4C2×C22⋊D1112yes—
455C22×C4C2×C22⋊D1112yes—
456C22×C4C2×C22⋊D1111yescharacteristic
457C22×C4C23×D1111yescharacteristic
458M16—444no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—222no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—222no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—222no—
468C2×C8—444no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—42no—
476C4⋊C4—82no—
477C4⋊C4—82no—
478C4⋊C4—114no—
479C4⋊C4—224no—
480C4⋊C4—228no—
481C4⋊C4—222no—
482C4⋊C4(C2×D11)⋊C414yes—
483C4⋊C4(C2×D11)⋊C414yes—
484C22⋊C4—42no—
485C22⋊C4—228no—
486C22⋊C4(C2×D11)⋊C418yes—
487C42—42no—
488C42—228no—
489C42C2×C4×D1114yes—
490C42C2×D4414yes—
491C11#2065211yescharacteristic, complemented, Sylow
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—222no—
497C23—222no—
498C23—222no—
499C23—441no—
500C23—441no—
501C23—441no—
502C23—441no—
503C23C2×(C2×D11)⋊C412yes—
504C23#6699112yes—
505C23#6699912yes—
506C23C22×C22⋊D1111yescharacteristic
507Q8—114no—
508Q8—222no—
509Q8—222no—
510Q8—222no—
511D4—114no—
512D4—2216no—
513D4—222no—
514D4—222no—
515D4—222no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—84no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—2216no—
534C2×C4—224no—
535C2×C4—442no—
536C2×C4—442no—
537C2×C4—888no—
538C2×C4—884no—
539C2×C4C4⋊C4×D1114yes—
540C2×C4#6694514yes—
541C2×C4#6694814yes—
542C2×C4#6695014yes—
543C2×C4C2×(C2×D11)⋊C414yes—
544C2×C4C2×(C2×D11)⋊C414yes—
545C2×C4C2×(C2×D11)⋊C412yes—
546C2×C4#6699112yes—
547C2×C4#6699912yes—
548C2×C4C22×C4×D1111yescharacteristic
549C2×C4C22×D4411yescharacteristic
550C2×C4C2×D4×D1111yescharacteristic
551C2×C4C2×#434111yescharacteristic
552C2×C4C2×Q8×D1111yescharacteristic
553C2×C4C2×#434311yescharacteristic
554C8—441no—
555C8—441no—
556C8—442no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—224no—
564C22—442no—
565C22—442no—
566C22—442no—
567C22—442no—
568C22—442no—
569C22—442no—
570C22#1062260014yes—
571C22C22×(C2×D11)⋊C411yescharacteristic
572C22C2×#6699111yescharacteristic
573C22C2×#6699911yescharacteristic
574C22#1062336611yescharacteristic
575C22#1062336711yescharacteristic
576C22#1062336811yescharacteristic
577C22#1062336911yescharacteristic
578C4—24no—
579C4—24no—
580C4—82no—
581C4—81no—
582C4—81no—
583C4—224no—
584C4—444no—
585C4#1062260014yes—
586C4C2×C4⋊C4×D1111yescharacteristic
587C4C2×#6694511yescharacteristic
588C4C2×#6694811yescharacteristic
589C4C2×#6695011yescharacteristic
590C2—24no—
591C2—444no—
592C2C2×#1062260011yescharacteristic
593C2#1307713911yescharacteristic
594C2#1307714611yescharacteristic
595C2#1307815111yescharacteristic
596C2#1307816211yescharacteristic
597C2#1307846311yescharacteristic
598C2#1307847411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2317C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#2317D11
hypocenterC11#20652
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2317

Complements

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

NH ≅ G/Ntype
2. C2×#10622612C2semidirect
5. #13068628C2semidirect
6. #13068623C2semidirect
7. #13068618C2semidirect
8. #13068613C2semidirect
9. #13068337C2semidirect
10. C2×#10622167C2semidirect
11. C11×#2317C2semidirect
20. #10623054C4semidirect
98. C4×D44C2×C4semidirect
100. C4×Dic22C2×C4semidirect
141. #4339C4⋊C4semidirect
197. #2317D11semidirect
491. C11#20652semidirect

Maximal subgroups

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

subgroupindex
C2×#106230542
C2×#106226122
C2×#106225792
C2×#106226152
#130686282
#130686232
#130686182
#130686132
#130683372
C2×#106221672
C11×#23172
#2065211