Finite Group Databasebeta

← #14781461

Subgroups — #14781461

Order 2816.

1522 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623363C211yesmaximal, characteristic
2C2×#10622726C211yesmaximal, characteristic, complemented
3C2×#10622846C211yesmaximal, characteristic, complemented
4C2×#10622615C211yesmaximal, characteristic, complemented
5#13071100C211yesmaximal, characteristic, complemented
6#13069861C212yesmaximal, complemented
7#13069856C212yesmaximal, complemented
8#13069854C212yesmaximal, complemented
9#13069849C212yesmaximal, complemented
10C2×#10622188C211yesmaximal, characteristic, complemented
11C2×C11×#416C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×#4339C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16#10623363—24no—
17#10623363—24no—
18C2×#67000C2211yescharacteristic
19C2×#66997C2211yescharacteristic
20C2×#66993C2211yescharacteristic
21C2×#66992—22no—
22C2×#66989C2211yescharacteristic
23C2×C4×C22⋊D11—22no—
24C2×#66979C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27C11×#416—24no—
28C2×C11×#103C2212yes—
29C2×C11×#102C2212yes—
30#10622846—24no—
31C2×#66899C2212yes—
32C2×#66896C2212yes—
33#10622726—24no—
34C2×#66885C2212yes—
35C2×#66880C2212yes—
36#10622615—24no—
37#10622598C2212yes—
38#10622598C2212yes—
39C2×#66874C2212yes—
40C2×#66873C2212yes—
41#10622563—22no—
42C4×C4⋊Dic11—22no—
43#10622188C2212yes—
44#10622188C2212yes—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41D414yes—
51C22×Q8×C11C2311yescharacteristic
52C22×D4×C11—21no—
53C22×D4×C11C2311yescharacteristic
54C23×C4×C11—21no—
55C23×C4×C11C2311yescharacteristic
56C22×C22⋊D11—21no—
57C22×C22⋊D11—22no—
58C23×Dic11D412yes—
59C2×#4339—22no—
60C2×#4339—22no—
61C2×#4339—22no—
62C2×#4339—22no—
63C2×#4339—22no—
64C2×#4339D414yes—
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C22×Dic22C2311yescharacteristic
68C22×C8×C11—22no—
69C22×C8×C11—22no—
70C22×C8×C11—22no—
71C22×C8×C11C2312yes—
72C11×#117—22no—
73C11×#117D414yescomplemented
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11—21no—
77C2×C22⋊Dic11—22no—
78C2×C22⋊Dic11—21no—
79#67000—22no—
80#67000—22no—
81#66997—22no—
82#66997—22no—
83#66993—22no—
84#66993—22no—
85#66992—216no—
86#66989—22no—
87#66989—22no—
88C4×C22⋊D11—216no—
89C2×(C2×D11)⋊C4—22no—
90#66979—22no—
91#66979—22no—
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11C2312yes—
95C2×Dic11⋊C4—22no—
96C2×C4×Dic11—22no—
97C2×C4×Dic11—22no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11D412yes—
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8—22no—
103C22×C11⋊C8—22no—
104C22×C11⋊C8—22no—
105C22×C11⋊C8C2312yes—
106C11×#103—24no—
107C11×#102—24no—
108#66899—24no—
109#66896—24no—
110C11⋊#95—22no—
111C11⋊#95—22no—
112#66885—24no—
113#66880—24no—
114#66874—24no—
115#66873—24no—
116#23504—111nomaximal, Sylow
117C24×C11—21no—
118C24×C11C2×D411yescharacteristic
119C23×D11—21no—
120C11×#41—28no—
121C11×#41—28no—
122C11×#41—44no—
123C11×#41—44no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11C2×D412yes—
130C2×D4×C11—24no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11C2×D412yes—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—24no—
142C22×C4×C11—42no—
143C22×C4×C11—42no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11#4112yes—
149C22×C4×C11#4112yes—
150C22×C4×C11#4112yes—
151C22×C4×C11C2411yescharacteristic
152C2×C22⋊D11—28no—
153C2×C22⋊D11—24no—
154C2×C22⋊D11—44no—
155C2×C22⋊D11—44no—
156C2×C22⋊D11—42no—
157C2×C22⋊D11—42no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11—21no—
161C22×Dic11—22no—
162C22×Dic11—42no—
163C22×Dic11C2×D412yes—
164C22×Dic11C2×D412yes—
165#4339—28no—
166#4339—28no—
167#4339—44no—
168#4339—44no—
169C2×D44—21no—
170C2×D44—21no—
171C2×D44—21no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44C2×D412yes—
175C2×C4×D11—24no—
176C2×C4×D11—42no—
177C2×C4×D11—42no—
178C2×Dic22—21no—
179C2×Dic22—21no—
180C2×Dic22—21no—
181C2×Dic22—21no—
182C2×Dic22—21no—
183C2×Dic22C2×D412yes—
184C2×C8×C11—22no—
185C2×C8×C11—22no—
186C2×C8×C11—22no—
187C2×C8×C11—44no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4C2×D414yes—
190C11×C22⋊C4—24no—
191C42×C11—24no—
192C22⋊Dic11—28no—
193C22⋊Dic11—42no—
194(C2×D11)⋊C4—28no—
195C4⋊Dic11—22no—
196C4⋊Dic11—22no—
197C4⋊Dic11—44no—
198C4⋊Dic11—44no—
199Dic11⋊C4—28no—
200C4×Dic11—24no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—42no—
206C2×C11⋊C8—22no—
207C2×C11⋊C8—22no—
208C2×C11⋊C8—22no—
209C2×C11⋊C8—44no—
210C2×#532—111no—
211C2×#416—111no—
212C2×#416—111no—
213C2×#416—111no—
214C2×#416D1111yescharacteristic, complemented
215#2296—111no—
216#2043—112no—
217#2042—112no—
218#2042—112no—
219#2041—112no—
220C2×#336—111no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11#12012yes—
229C23×C11#12112yes—
230C23×C11#12412yes—
231C23×C11C22×D411yescharacteristic
232C22×D11—22no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—42no—
236C22×D11—42no—
237Q8×C11—22no—
238Q8×C11—22no—
239Q8×C11—41no—
240Q8×C11—41no—
241D4×C11—22no—
242D4×C11—22no—
243D4×C11—48no—
244D4×C11—41no—
245D4×C11—41no—
246C2×C4×C11—22no—
247C2×C4×C11—24no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—48no—
253C2×C4×C11#12012yes—
254C2×C4×C11#12114yes—
255C2×C4×C11#12114yes—
256C2×C4×C11#12112yes—
257C2×C4×C11#12314yes—
258C2×C4×C11#12314yes—
259C2×C4×C11#12412yes—
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C22⋊D11—416no—
267C22⋊D11—48no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—48no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11#13514yes—
281D44—22no—
282D44—22no—
283D44—41no—
284D44—41no—
285C4×D11—48no—
286Dic22—22no—
287Dic22—22no—
288Dic22—41no—
289Dic22—41no—
290C8×C11—42no—
291C11⋊C8—42no—
292C22×#41—111no—
293C22×#41C2×D1111yescharacteristic
294C23×C8—111no—
295C23×C8C2×D1111yescharacteristic
296#532—224no—
297#532—224no—
298C2×C4⋊Q8—111no—
299C2×#127—111no—
300C2×#124—111no—
301C2×#124—111no—
302C2×#121—222no—
303C2×C4×D4—222no—
304C2×#117—111no—
305C2×#117C2×D1111yescharacteristic
306C22×C42—111no—
307#416—24no—
308#416—224no—
309#416—224no—
310#416—224no—
311C2×#103—112no—
312C2×#103—112no—
313C2×#103—112no—
314C2×#103C2×D1112yes—
315C2×#102—112no—
316C2×#102—112no—
317C2×#102—112no—
318C2×#102C2×D1112yes—
319#389—112no—
320#389—112no—
321#385—222no—
322C4×C4⋊C4—222no—
323#336—112no—
324#336—112no—
325C22×C11—22no—
326C22×C11—22no—
327C22×C11—24no—
328C22×C11—24no—
329C22×C11—42no—
330C22×C11—44no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11—82no—
334C22×C11#39414yes—
335C22×C11C2×#12011yescharacteristic
336C22×C11C2×#12111yescharacteristic
337C22×C11C2×#12411yescharacteristic
338C22×C11C2×#13512yes—
339C22×C11#57512yes—
340C2×D11—42no—
341C2×D11—44no—
342C2×D11—81no—
343C2×D11—81no—
344C2×D11—82no—
345C4×C11—42no—
346C4×C11—44no—
347C4×C11#39414yes—
348C4×C11C2×#12111yescharacteristic
349C4×C11C2×#12111yescharacteristic
350C4×C11C2×#12311yescharacteristic
351C4×C11C2×#12311yescharacteristic
352Dic11—24no—
353Dic11—42no—
354Dic11—42no—
355Dic11—82no—
356C2×#41—22no—
357C2×#41—22no—
358C2×#41—22no—
359C2×#41—22no—
360C2×#41—22no—
361C2×#41—114no—
362C2×#41—222no—
363C2×#41—222no—
364C2×#41—222no—
365C2×#41—222no—
366C2×#41—222no—
367C2×#41D4414yes—
368C22×Q8—111no—
369C22×Q8C22×D1111yescharacteristic
370C22×D4—21no—
371C22×D4—111no—
372C22×D4—222no—
373C22×D4—221no—
374C22×D4C22×D1111yescharacteristic
375C23×C4—21no—
376C23×C4—112no—
377C23×C4—221no—
378C23×C4C22×D1111yescharacteristic
379C22×C8—22no—
380C22×C8—22no—
381C22×C8—22no—
382C22×C8—112no—
383C22×C8—222no—
384C22×C8—222no—
385C22×C8—222no—
386C22×C8C22×D1112yes—
387C4⋊Q8—222no—
388C4⋊Q8—222no—
389#127—222no—
390#127—222no—
391#124—222no—
392#124—222no—
393#124—222no—
394#124—222no—
395#121—2216no—
396C4×D4—2216no—
397#117—22no—
398#117—222no—
399#117—222no—
400#117C22⋊D1114yescomplemented
401C2×C4⋊C4—112no—
402C2×C4⋊C4—222no—
403C2×C4⋊C4—222no—
404C2×C4⋊C4—222no—
405C2×C4⋊C4C22×D1112yes—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—222no—
408C2×C22⋊C4—222no—
409C2×C22⋊C4—221no—
410C2×C42—21no—
411C2×C42—112no—
412C2×C42—111no—
413C2×C42—111no—
414C2×C42—222no—
415C2×C42—222no—
416C2×C42—221no—
417#103—24no—
418#103—224no—
419#103—224no—
420#103—224no—
421#102—24no—
422#102—224no—
423#102—224no—
424#102—224no—
425#95—222no—
426#95—222no—
427C2×C11—24no—
428C2×C11—82no—
429C2×C11C2×#39411yescharacteristic
430C2×C11#300212yes—
431C2×C11#303512yes—
432C2×C11#313111yescharacteristic
433C2×C11#313511yescharacteristic
434D11—82no—
435C24—21no—
436C24—221no—
437C24D4×D1111yescharacteristic
438#41—28no—
439#41—28no—
440#41—44no—
441#41—44no—
442#41—228no—
443#41—228no—
444#41—444no—
445#41—444no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—112no—
452C2×Q8—221no—
453C2×Q8—221no—
454C2×Q8—221no—
455C2×Q8—221no—
456C2×Q8—221no—
457C2×Q8C2×D4412yes—
458C2×D4—24no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—42no—
465C2×D4—42no—
466C2×D4—112no—
467C2×D4—228no—
468C2×D4—224no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—444no—
475C2×D4—444no—
476C2×D4—442no—
477C2×D4—442no—
478C2×D4C2×D4412yes—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—24no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—112no—
485C22×C4—112no—
486C22×C4—224no—
487C22×C4—224no—
488C22×C4—221no—
489C22×C4—224no—
490C22×C4—222no—
491C22×C4—442no—
492C22×C4—442no—
493C22×C4—442no—
494C22×C4C2×D4412yes—
495C22×C4#433912yes—
496C22×C4D4×D1112yes—
497C22×C4D4×D1111yescharacteristic
498C22×C4#434112yes—
499C22×C4#434112yes—
500C22×C4C2×C22⋊D1112yes—
501C22×C4C23×D1111yescharacteristic
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—44no—
506C2×C8—222no—
507C2×C8—222no—
508C2×C8—222no—
509C2×C8—444no—
510C4⋊C4—22no—
511C4⋊C4—228no—
512C4⋊C4—222no—
513C4⋊C4—222no—
514C4⋊C4—444no—
515C4⋊C4—444no—
516C4⋊C4C2×C22⋊D1114yes—
517C22⋊C4—24no—
518C22⋊C4—228no—
519C22⋊C4—228no—
520C22⋊C4—442no—
521C42—24no—
522C42—224no—
523C42—221no—
524C42—221no—
525C42—221no—
526C42—221no—
527C42—442no—
528C11#2350411yescharacteristic, complemented, Sylow
529C23—22no—
530C23—22no—
531C23—22no—
532C23—41no—
533C23—42no—
534C23—42no—
535C23—41no—
536C23—222no—
537C23—441no—
538C23—442no—
539C23—442no—
540C23—441no—
541C23#6693512yes—
542C23#6693812yes—
543C23#6699212yes—
544C23C2×D4×D1111yescharacteristic
545Q8—22no—
546Q8—22no—
547Q8—41no—
548Q8—41no—
549Q8—222no—
550Q8—222no—
551Q8—441no—
552Q8—441no—
553D4—22no—
554D4—22no—
555D4—48no—
556D4—41no—
557D4—41no—
558D4—222no—
559D4—222no—
560D4—4416no—
561D4—448no—
562D4—441no—
563D4—441no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—41no—
570C2×C4—48no—
571C2×C4—114no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—448no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—448no—
582C2×C4—442no—
583C2×C4—442no—
584C2×C4—442no—
585C2×C4#6693512yes—
586C2×C4#6693614yes—
587C2×C4#6693812yes—
588C2×C4#6693914yes—
589C2×C4#6698314yes—
590C2×C4#6699114yes—
591C2×C4#6699212yes—
592C2×C4C22×D4411yescharacteristic
593C2×C4C2×#433911yescharacteristic
594C2×C4C2×D4×D1111yescharacteristic
595C2×C4C2×#434111yescharacteristic
596C2×C4C2×#434111yescharacteristic
597C2×C4C22×C22⋊D1111yescharacteristic
598C8—42no—
599C8—442no—
600C22—24no—
601C22—24no—
602C22—22no—
603C22—22no—
604C22—44no—
605C22—42no—
606C22—82no—
607C22—81no—
608C22—81no—
609C22—444no—
610C22—442no—
611C22—882no—
612C22—881no—
613C22—881no—
614C22#1062257414yes—
615C22C2×#6693511yescharacteristic
616C22C2×#6693811yescharacteristic
617C22D11×#13512yes—
618C22#1062329912yes—
619C22C2×#6699211yescharacteristic
620C4—44no—
621C4—42no—
622C4—224no—
623C4—442no—
624C4—442no—
625C4—882no—
626C4#1062257414yes—
627C4C2×#6693611yescharacteristic
628C4C2×#6693911yescharacteristic
629C4C2×#6698311yescharacteristic
630C4C2×#6699111yescharacteristic
631C2—24no—
632C2—82no—
633C2—882no—
634C2C2×#1062257411yescharacteristic
635C2#1307783612yes—
636C2#1307806712yes—
637C2#1307893611yescharacteristic
638C2#1307895911yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#416C2
socleC23×C11C22×D4
prime radicalC2×#10623363C2
hypercenterC2×#416D11
hypocenterC11#23504
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×#10622726C2semidirect
3. C2×#10622846C2semidirect
4. C2×#10622615C2semidirect
5. #13071100C2semidirect
6. #13069861C2semidirect
7. #13069856C2semidirect
8. #13069854C2semidirect
9. #13069849C2semidirect
10. C2×#10622188C2semidirect
11. C2×C11×#416C2semidirect
73. C11×#117D4semidirect
214. C2×#416D11semidirect
400. #117C22⋊D11semidirect
528. C11#23504semidirect

Maximal subgroups

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

subgroupindex
C2×#106233632
C2×#106227262
C2×#106228462
C2×#106226152
#130711002
#130698612
#130698562
#130698542
#130698492
C2×#106221882
C2×C11×#4162
#2350411