Finite Group Databasebeta

← #14755369

Subgroups — #14755369

Order 2816.

1710 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623347C211yesmaximal, characteristic
2#13081817C211yesmaximal, characteristic
3C2×#10622838C211yesmaximal, characteristic, complemented
4C2×#10622745C211yesmaximal, characteristic
5#13069006C214yesmaximal, complemented
6#13069001C214yesmaximal, complemented
7#13068327C211yesmaximal, characteristic, complemented
8#13068325C211yesmaximal, characteristic, complemented
9C2×C11×#419C211yesmaximal, characteristic, complemented
10C23×Q8×C11C2211yescharacteristic
11C22×#4339C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14#10623347—24no—
15#10623347C418yescomplemented
16C2×#67000C2212yes—
17C2×#66999—22no—
18C2×#66997C2212yes—
19C2×#66982—22no—
20C2×#66979C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23#10623054—22no—
24#10623053—22no—
25#10623052C2212yes—
26D11×#117—22no—
27#10623047C2212yes—
28#10623035—22no—
29#10623017—22no—
30C4×#4339—22no—
31C11×#419—22no—
32C11×#419C2214yes—
33C2×C11×#103—22no—
34#10622838—22no—
35#10622838C2214yes—
36C2×#66899—22no—
37C2×#66888C2212yes—
38#10622745—24no—
39C2×#66887C2212yes—
40#10622193C2214yes—
41#10622170C2214yes—
42C22×Q8×C11—21no—
43C22×Q8×C11—22no—
44C22×Q8×C11—21no—
45C22×Q8×C11—21no—
46C22×Q8×C11—21no—
47C22×Q8×C11—21no—
48C22×Q8×C11—22no—
49C22×Q8×C11—22no—
50C22×Q8×C11C2×C414yescomplemented
51C22×Q8×C11C2312yes—
52C23×C4×C11—21no—
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11D412yes—
55C2×#4339—21no—
56C2×#4339—21no—
57C2×#4339—21no—
58C2×#4339—21no—
59C2×#4339—22no—
60C2×#4339—22no—
61C2×#4339C2×C414yes—
62C2×#4339D414yes—
63C22×D44C2311yescharacteristic
64C22×C4×D11D412yes—
65C22×Dic22C2311yescharacteristic
66C2×C11×M16—21no—
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C2×C11×M16C2312yes—
70C22×C8×C11—21no—
71C11×#117—21no—
72C11×#117—21no—
73C11×#117D412yes—
74C11×#117C2312yes—
75C2×C11×C4⋊C4D412yes—
76C2×C11×C22⋊C4—21no—
77C2×C42×C11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80#67000—24no—
81#67000C2×C418yescomplemented
82#66999—216no—
83#66997—24no—
84#66997C2×C418yescomplemented
85#66982—216no—
86C4×C22⋊D11—28no—
87C2×(C2×D11)⋊C4—24no—
88#66979—21no—
89#66979—21no—
90#66979—22no—
91#66979C2×C414yescomplemented
92#66979D412yes—
93#66979C2312yes—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11D412yes—
96C2×Dic11⋊C4—24no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2312yes—
99C2×#4318—21no—
100C2×#4318—22no—
101C2×#4318—22no—
102C2×#4318C2312yes—
103C22×C11⋊C8—21no—
104#66946—24no—
105#66945—24no—
106C4⋊C4×D11—24no—
107#66940—24no—
108(C22⋊D11)⋊C4—28no—
109C22⋊C4×D11—24no—
110#66930—24no—
111C4×D44—24no—
112#66925—24no—
113C42×D11—24no—
114C4×Dic22—24no—
115C11×#103—28no—
116#66899—28no—
117#66888—24no—
118#66887—24no—
119#20955—111nomaximal, Sylow
120C24×C11C2×D411yescharacteristic
121C23×D11C2×D412yes—
122C2×Q8×C11—24no—
123C2×Q8×C11—22no—
124C2×Q8×C11—24no—
125C2×Q8×C11—24no—
126C2×Q8×C11—24no—
127C2×Q8×C11—24no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11—41no—
133C2×Q8×C11—41no—
134C2×Q8×C11—42no—
135C2×Q8×C11—42no—
136C2×Q8×C11—42no—
137C2×Q8×C11—42no—
138C2×Q8×C11—42no—
139C2×Q8×C11C22×C414yes—
140C22×C4×C11—24no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—41no—
144C22×C4×C11—41no—
145C22×C4×C11—42no—
146C22×C4×C11C22×C412yes—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11#4112yes—
154C22×C4×C11#4112yes—
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—22no—
157C2×C22⋊D11—22no—
158C2×C22⋊D11—24no—
159C2×C22⋊D11C22⋊C418yes—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11C2×D412yes—
163#4339—24no—
164#4339—24no—
165#4339—24no—
166#4339—24no—
167#4339—24no—
168#4339—24no—
169#4339—24no—
170#4339—24no—
171C2×D44—21no—
172C2×D44—21no—
173C2×D44—21no—
174C2×D44—21no—
175C2×D44C22×C412yes—
176C2×D44C2×D412yes—
177C2×C4×D11—28no—
178C2×C4×D11—22no—
179C2×C4×D11—22no—
180C2×C4×D11—24no—
181C2×C4×D11C22⋊C418yes—
182C2×Dic22—21no—
183C2×Dic22—21no—
184C2×Dic22—21no—
185C2×Dic22—21no—
186C2×Dic22C22×C412yes—
187C2×Dic22C2×D412yes—
188C11×M16—22no—
189C11×M16—22no—
190C11×M16—42no—
191C2×C8×C11—22no—
192C2×C8×C11—42no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4C2×D414yes—
195C11×C22⋊C4—22no—
196C11×C22⋊C4—22no—
197C42×C11—22no—
198C42×C11—22no—
199C22⋊Dic11—24no—
200C22⋊Dic11—22no—
201C22⋊Dic11—22no—
202(C2×D11)⋊C4—28no—
203(C2×D11)⋊C4—216no—
204C4⋊Dic11—24no—
205C4⋊Dic11—22no—
206C4⋊Dic11C2×D414yes—
207Dic11⋊C4—28no—
208Dic11⋊C4—216no—
209C4×Dic11—28no—
210C4×Dic11—22no—
211C4×Dic11—22no—
212C4×Dic11—22no—
213C4×Dic11C22×C414yes—
214#4318—22no—
215#4318—22no—
216#4318—42no—
217C2×C11⋊C8—22no—
218C2×C11⋊C8—42no—
219C2×#536—111no—
220#3428—111no—
221C2×#419—111no—
222C2×#419D1111yescharacteristic, complemented
223C2×#413—111no—
224#1886—114no—
225#1885—114no—
226#1733—111no—
227#1733—111no—
228C23×C11—42no—
229C23×C11C2×C22⋊C412yes—
230C23×C11#12011yescharacteristic
231C23×C11#12011yescharacteristic
232C23×C11#12312yes—
233C23×C11C22×D411yescharacteristic
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—44no—
237C22×D11C2×C22⋊C414yes—
238Q8×C11—24no—
239Q8×C11—24no—
240Q8×C11—42no—
241Q8×C11—42no—
242Q8×C11—44no—
243Q8×C11—44no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—44no—
249C2×C4×C11—44no—
250C2×C4×C11—82no—
251C2×C4×C11C2×C22⋊C412yes—
252C2×C4×C11C4×D412yes—
253C2×C4×C11C4×D412yes—
254C2×C4×C11C4×D412yes—
255C2×C4×C11C4×D412yes—
256C2×C4×C11#12011yescharacteristic
257C2×C4×C11#12011yescharacteristic
258C2×C4×C11#12112yes—
259C2×C4×C11#12112yes—
260C2×C4×C11#12112yes—
261C2×C4×C11#12112yes—
262C2×C4×C11#12312yes—
263C2×C4×C11C23×C411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C22⋊D11—28no—
270C22⋊D11—28no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—44no—
276C2×Dic11—82no—
277C2×Dic11C2×C22⋊C414yes—
278D44—22no—
279D44—22no—
280D44—22no—
281D44—22no—
282C4×D11—28no—
283C4×D11—28no—
284C4×D11—88no—
285Dic22—22no—
286Dic22—22no—
287Dic22—22no—
288Dic22—22no—
289C8×C11—42no—
290C11⋊C8—42no—
291C22×#41—111no—
292C23×Q8C2×D1111yescharacteristic
293C22×M16—111no—
294C22×M16C2×D1111yescharacteristic
295#536—118no—
296#536—224no—
297C2×C4⋊Q8—112no—
298C2×#124—112no—
299C2×#123—222no—
300C2×C22⋊Q8—222no—
301#520—222no—
302#520—222no—
303#519—112no—
304#518—112no—
305#518—222no—
306C4×#41—222no—
307C4×#41—222no—
308C2×#117—111no—
309C2×#117—111no—
310C2×#117—222no—
311C2×#117C2×D1111yescharacteristic
312#419—22no—
313#419—114no—
314#419—222no—
315#419C2×D1114yes—
316C2×#103—22no—
317C2×#103—222no—
318#413—224no—
319C2×#101—112no—
320C2×#100—112no—
321#339—114no—
322#339—114no—
323C22×C11—22no—
324C22×C11—22no—
325C22×C11—22no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11#38612yes—
329C22×C11#38612yes—
330C22×C11C22×C22⋊C411yescharacteristic
331C22×C11C2×#12011yescharacteristic
332C22×C11C2×#12311yescharacteristic
333C2×D11—24no—
334C2×D11—44no—
335C2×D11—44no—
336C2×D11—82no—
337C4×C11—44no—
338C4×C11—44no—
339C4×C11#38612yes—
340C4×C11#38612yes—
341C4×C11C2×C4×D411yescharacteristic
342C4×C11C2×C4×D411yescharacteristic
343C4×C11C2×#12111yescharacteristic
344C4×C11C2×#12111yescharacteristic
345Dic11—24no—
346Dic11—44no—
347Dic11—44no—
348C2×#41—114no—
349C2×#41—114no—
350C2×#41—222no—
351C2×#41—221no—
352C2×#41—221no—
353C2×#41—222no—
354C2×#41—221no—
355C2×#41—221no—
356C22×Q8—21no—
357C22×Q8—22no—
358C22×Q8—22no—
359C22×Q8—21no—
360C22×Q8—21no—
361C22×Q8—22no—
362C22×Q8—21no—
363C22×Q8—21no—
364C22×Q8—111no—
365C22×Q8C4×D1114yescomplemented
366C22×Q8C22×D1112yes—
367C22×D4—112no—
368C22×D4—111no—
369C23×C4—21no—
370C23×C4—112no—
371C23×C4C22×D1111yescharacteristic
372C2×M16—21no—
373C2×M16—22no—
374C2×M16—22no—
375C2×M16—112no—
376C2×M16—221no—
377C2×M16—222no—
378C2×M16—222no—
379C2×M16C22×D1112yes—
380C22×C8—21no—
381C22×C8—221no—
382C4⋊Q8—118no—
383C4⋊Q8—224no—
384#124—118no—
385#124—224no—
386#123—2216no—
387C22⋊Q8—2216no—
388C4×Q8—224no—
389C4×Q8—224no—
390C4×D4—224no—
391C4×D4—228no—
392C4×D4—228no—
393C4×D4—224no—
394#117—21no—
395#117—21no—
396#117—114no—
397#117—112no—
398#117—112no—
399#117—224no—
400#117—224no—
401#117—224no—
402#117—221no—
403#117—222no—
404#117—221no—
405#117C22⋊D1112yes—
406#117C22×D1112yes—
407C2×C4⋊C4—112no—
408C2×C4⋊C4—224no—
409C2×C4⋊C4—224no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4C22⋊D1112yes—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—224no—
414C2×C22⋊C4—224no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C42—21no—
418C2×C42—112no—
419C2×C42—224no—
420C2×C42—221no—
421#103—28no—
422#103—228no—
423#101—224no—
424#100—224no—
425C2×C11—21no—
426C2×C11—21no—
427C2×C11—22no—
428C2×C11—22no—
429C2×C11C2×#38611yescharacteristic
430C2×C11#302212yes—
431D11—44no—
432C24—112no—
433C24D4×D1111yescharacteristic
434#41—224no—
435#41—224no—
436#41—224no—
437#41—224no—
438#41—224no—
439#41—224no—
440#41—224no—
441#41—224no—
442C2×Q8—24no—
443C2×Q8—22no—
444C2×Q8—24no—
445C2×Q8—24no—
446C2×Q8—24no—
447C2×Q8—24no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—42no—
453C2×Q8—42no—
454C2×Q8—42no—
455C2×Q8—41no—
456C2×Q8—41no—
457C2×Q8—42no—
458C2×Q8—42no—
459C2×Q8—112no—
460C2×Q8—112no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8C2×C4×D1114yes—
466C2×D4—118no—
467C2×D4—112no—
468C2×D4—112no—
469C2×D4—224no—
470C2×D4—222no—
471C2×D4—222no—
472C2×D4—221no—
473C2×D4—221no—
474C2×D4—221no—
475C2×D4—221no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—42no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—112no—
483C22×C4—118no—
484C22×C4—228no—
485C22×C4—224no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4C2×C4×D1112yes—
491C22×C4#433912yes—
492C22×C4D4×D1111yescharacteristic
493C22×C4D4×D1112yes—
494C22×C4D4×D1111yescharacteristic
495C22×C4D4×D1111yescharacteristic
496C22×C4#434112yes—
497C22×C4C2×C22⋊D1111yescharacteristic
498C22×C4C2×C22⋊D1111yescharacteristic
499C22×C4C23×D1111yescharacteristic
500M16—22no—
501M16—22no—
502M16—42no—
503M16—222no—
504M16—222no—
505M16—442no—
506C2×C8—22no—
507C2×C8—42no—
508C2×C8—222no—
509C2×C8—442no—
510C4⋊C4—22no—
511C4⋊C4—114no—
512C4⋊C4—2216no—
513C4⋊C4—228no—
514C4⋊C4—224no—
515C4⋊C4—222no—
516C4⋊C4C2×C22⋊D1114yes—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—2216no—
520C22⋊C4—228no—
521C22⋊C4—224no—
522C22⋊C4—222no—
523C22⋊C4—222no—
524C42—22no—
525C42—22no—
526C42—114no—
527C42—228no—
528C42—222no—
529C42—222no—
530C42—222no—
531C11#2095511yescharacteristic, complemented, Sylow
532C23—42no—
533C23—114no—
534C23—222no—
535C23—222no—
536C23—444no—
537C23C22⋊C4×D1112yes—
538C23#6693612yes—
539C23#6699011yescharacteristic
540C23#6699011yescharacteristic
541C23C2×D4×D1111yescharacteristic
542Q8—24no—
543Q8—24no—
544Q8—42no—
545Q8—42no—
546Q8—44no—
547Q8—44no—
548Q8—222no—
549Q8—222no—
550Q8—222no—
551Q8—222no—
552D4—228no—
553D4—228no—
554D4—222no—
555D4—222no—
556D4—222no—
557D4—222no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—44no—
563C2×C4—44no—
564C2×C4—82no—
565C2×C4—114no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—228no—
569C2×C4—228no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—444no—
573C2×C4—888no—
574C2×C4—882no—
575C2×C4C22⋊C4×D1112yes—
576C2×C4(C22⋊D11)⋊C412yes—
577C2×C4(C22⋊D11)⋊C412yes—
578C2×C4#6693612yes—
579C2×C4#6693712yes—
580C2×C4#6693712yes—
581C2×C4C4×C22⋊D1112yes—
582C2×C4C4×C22⋊D1112yes—
583C2×C4#6699011yescharacteristic
584C2×C4#6699011yescharacteristic
585C2×C4#6699112yes—
586C2×C4#6699112yes—
587C2×C4C22×C4×D1111yescharacteristic
588C2×C4C2×#433911yescharacteristic
589C2×C4C2×D4×D1111yescharacteristic
590C2×C4C2×D4×D1111yescharacteristic
591C2×C4C2×#434111yescharacteristic
592C2×C4C22×C22⋊D1111yescharacteristic
593C8—42no—
594C8—442no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22—42no—
599C22—42no—
600C22—224no—
601C22—444no—
602C22—444no—
603C22—882no—
604C22#1062256912yes—
605C22#1062256912yes—
606C22C2×C22⋊C4×D1111yescharacteristic
607C22C2×#6693611yescharacteristic
608C22C2×#6699011yescharacteristic
609C4—44no—
610C4—44no—
611C4—224no—
612C4—444no—
613C4—444no—
614C4#1062256912yes—
615C4#1062256912yes—
616C4C2×(C22⋊D11)⋊C411yescharacteristic
617C4C2×#6693711yescharacteristic
618C4C2×C4×C22⋊D1111yescharacteristic
619C4C2×#6699111yescharacteristic
620C2—21no—
621C2—21no—
622C2—22no—
623C2—22no—
624C2—444no—
625C2C2×#1062256911yescharacteristic
626C2#1307799212yes—
subgroupG/H
centerC22C2×#66990
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#419C2
socleC22×C11C2×#120
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenterC2×#419D11
hypocenterC11#20955
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
3. C2×#10622838C2semidirect
5. #13069006C2semidirect
6. #13069001C2semidirect
7. #13068327C2semidirect
8. #13068325C2semidirect
9. C2×C11×#419C2semidirect
15. #10623347C4semidirect
50. C22×Q8×C11C2×C4semidirect
81. #67000C2×C4semidirect
84. #66997C2×C4semidirect
91. #66979C2×C4semidirect
222. C2×#419D11semidirect
365. C22×Q8C4×D11semidirect
531. C11#20955semidirect

Maximal subgroups

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

subgroupindex
C2×#106233472
#130818172
C2×#106228382
C2×#106227452
#130690062
#130690012
#130683272
#130683252
C2×C11×#4192
#2095511