Finite Group Databasebeta

← #15620741

Subgroups — #15620741

Order 2816.

2674 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66995C211yesmaximal, characteristic, complemented
2#13081945C211yesmaximal, characteristic
3C2×#10623343C211yesmaximal, characteristic, complemented
4#13078148C214yesmaximal, complemented
5#13078143C214yesmaximal, complemented
6#13078139C214yesmaximal, complemented
7#13078134C214yesmaximal, complemented
8#13078085C218yesmaximal, complemented
9#13077179C211yesmaximal, characteristic, complemented
10#13077136C211yesmaximal, characteristic, complemented
11#13077135C211yesmaximal, characteristic, complemented
12C22×C11×#137C211yesmaximal, characteristic, complemented
13C22×C11×#41C2211yescharacteristic
14C23×Q8×C11C2211yescharacteristic
15C22×#4339C2211yescharacteristic
16C2×C11×#137—28no—
17C2×C11×#137C2214yes—
18C2×C11×#137C2214yescomplemented
19C22×C11×Q16C2212yescomplemented
20C22×C11×SD16C2212yescomplemented
21C22×C11×M16C2211yescharacteristic
22#10623364—22no—
23#10623363C2214yes—
24#10623361C2212yes—
25#10623359—22no—
26#10623356C2212yes—
27#10623347C2212yes—
28#10623343—22no—
29#10623343—22no—
30#10623343C2214yescomplemented
31#10623343C2214yescomplemented
32C2×Q8×Dic11—22no—
33C2×Q8×Dic11C2214yescomplemented
34C22×#4326C2212yescomplemented
35C2×#66995—28no—
36C2×#66995C2214yes—
37C2×#66995C2214yescomplemented
38C22×#4325C2212yescomplemented
39#10623336C2212yes—
40#10623335—22no—
41#10623322—22no—
42C2×#66979—22no—
43C2×#66979C2211yescharacteristic
44C2×#66979C2211yescharacteristic
45C22×#4318C2211yescharacteristic
46#10622846C2214yes—
47#10622845C2214yescomplemented
48#10622838C2212yescomplemented
49#10622828C2212yescomplemented
50#10622798C22116yescomplemented
51#10622795C22116yescomplemented
52#10622779C22116yescomplemented
53#10622776C22116yescomplemented
54#10622746C2214yescomplemented
55#10622744C2212yescomplemented
56#10622733C2212yescomplemented
57#10622732C2214yescomplemented
58#10622731C2214yescomplemented
59#10622726C2214yes—
60#10622715C2214yescomplemented
61C2×C11×#41—21no—
62C2×C11×#41—21no—
63C2×C11×#41—24no—
64C2×C11×#41—24no—
65C2×C11×#41C2312yes—
66C2×C11×#41C2312yes—
67C22×Q8×C11—21no—
68C22×Q8×C11—21no—
69C22×Q8×C11—21no—
70C22×Q8×C11—24no—
71C22×Q8×C11D418yescomplemented
72C22×Q8×C11C2311yescharacteristic
73C22×Q8×C11C2312yes—
74C22×Q8×C11C2312yes—
75C22×Q8×C11C2312yes—
76C22×D4×C11—21no—
77C22×D4×C11C2311yescharacteristic
78C23×C4×C11—21no—
79C23×C4×C11—21no—
80C23×C4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C2×#4339—21no—
83C2×#4339—21no—
84C2×#4339—24no—
85C2×#4339—24no—
86C2×#4339C2312yes—
87C2×#4339C2312yes—
88C22×D44C2311yescharacteristic
89C22×C4×D11—21no—
90C22×Dic22C2311yescharacteristic
91C11×#137—216no—
92C11×#137—216no—
93C2×C11×Q16—28no—
94C2×C11×Q16C2318yes—
95C2×C11×SD16—28no—
96C2×C11×SD16C2318yes—
97C2×C11×M16—24no—
98C2×C11×M16C2312yes—
99C2×C11×M16C2312yes—
100C22×C8×C11C2312yes—
101#67006—24no—
102C2×C22⋊Dic11—21no—
103C2×C22⋊Dic11D412yes—
104#67000C2314yes—
105#66999—24no—
106Q8×Dic11—28no—
107Q8×Dic11—28no—
108Q8×Dic11—28no—
109Q8×Dic11C23116yes—
110#66997C2314yes—
111C2×#4326—28no—
112C2×#4326C2318yes—
113#66995—216no—
114#66995—216no—
115C2×#4325—28no—
116C2×#4325C2318yes—
117#66993C2314yes—
118#66992—28no—
119#66991—24no—
120#66990—24no—
121#66989C2314yes—
122#66988—24no—
123#66983—24no—
124#66982—24no—
125C4×C22⋊D11—28no—
126#66979—21no—
127#66979—21no—
128#66979—28no—
129#66979—28no—
130#66979D412yes—
131#66979D412yes—
132#66979C2312yes—
133#66979C2312yes—
134#66979C2312yes—
135#66979C2312yes—
136C2×C4⋊Dic11—24no—
137C2×C4⋊Dic11D412yes—
138C2×C4⋊Dic11C2312yes—
139#66977—24no—
140C2×C4×Dic11—21no—
141C2×C4×Dic11—24no—
142C2×C4×Dic11C2312yes—
143C2×#4318—24no—
144C2×#4318C2312yes—
145C2×#4318C2312yes—
146C22×C11⋊C8C2312yes—
147#66899C2318yes—
148#66896C2318yes—
149#66885C2318yes—
150#66880C2318yes—
151Dic11⋊C8C23116yes—
152#60424—111nomaximal, Sylow
153C24×C11—21no—
154C24×C11C2×D411yescharacteristic
155C23×D11—21no—
156C11×#41—24no—
157C11×#41—24no—
158C11×#41—24no—
159C11×#41—24no—
160C11×#41—44no—
161C11×#41—44no—
162C2×Q8×C11—28no—
163C2×Q8×C11—28no—
164C2×Q8×C11—28no—
165C2×Q8×C11—22no—
166C2×Q8×C11—22no—
167C2×Q8×C11—22no—
168C2×Q8×C11—21no—
169C2×Q8×C11—24no—
170C2×Q8×C11—24no—
171C2×Q8×C11—24no—
172C2×Q8×C11—22no—
173C2×Q8×C11—22no—
174C2×Q8×C11C2×D418yes—
175C2×Q8×C11C2×D418yes—
176C2×Q8×C11C2×D418yes—
177C2×Q8×C11C2412yes—
178C2×Q8×C11C2414yes—
179C2×D4×C11—22no—
180C2×D4×C11—22no—
181C2×D4×C11—22no—
182C2×D4×C11—21no—
183C2×D4×C11—22no—
184C2×D4×C11—44no—
185C2×D4×C11C2412yes—
186C22×C4×C11—28no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—22no—
190C22×C4×C11—21no—
191C22×C4×C11—22no—
192C22×C4×C11—22no—
193C22×C4×C11—44no—
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D414yes—
198C22×C4×C11#4114yes—
199C22×C4×C11C2411yescharacteristic
200C22×C4×C11C2411yescharacteristic
201C22×C4×C11C2411yescharacteristic
202C2×C22⋊D11—28no—
203C2×C22⋊D11—22no—
204C2×C22⋊D11—22no—
205C2×C22⋊D11—44no—
206C22×Dic11—22no—
207C22×Dic11—21no—
208C22×Dic11C2×D414yes—
209#4339—24no—
210#4339—24no—
211#4339—24no—
212#4339—24no—
213#4339—44no—
214#4339—44no—
215C2×D44—21no—
216C2×D44—22no—
217C2×D44—22no—
218C2×D44C2412yes—
219C2×C4×D11—22no—
220C2×C4×D11—22no—
221C2×C4×D11—44no—
222C2×Dic22—22no—
223C2×Dic22—21no—
224C2×Dic22—22no—
225C2×Dic22C2412yes—
226C11×Q16—216no—
227C11×SD16—216no—
228C11×M16—24no—
229C11×M16—24no—
230C2×C8×C11—24no—
231C2×C8×C11C2414yes—
232C22⋊Dic11—28no—
233C22⋊Dic11—22no—
234C22⋊Dic11—22no—
235C22⋊Dic11C2×D414yes—
236C22⋊Dic11C2×D414yes—
237#4326—216no—
238#4325—216no—
239(C2×D11)⋊C4—28no—
240C4⋊Dic11—216no—
241C4⋊Dic11—22no—
242C4⋊Dic11C2×D414yes—
243C4⋊Dic11C2×D414yes—
244C4⋊Dic11C2414yes—
245Dic11⋊C4—28no—
246C4×Dic11—216no—
247C4×Dic11—22no—
248C4×Dic11—22no—
249C4×Dic11C2×D414yes—
250C4×Dic11C2414yes—
251#4318—24no—
252#4318—24no—
253C2×C11⋊C8—24no—
254C2×C11⋊C8C2414yes—
255C22×#137—111no—
256C22×#137D1111yescharacteristic, complemented
257#3449—111no—
258C2×#519—111no—
259#3044—114no—
260#3044—114no—
261#3043—114no—
262#3043—114no—
263#3037—118no—
264#2905—111no—
265#2896—111no—
266#2896—111no—
267C23×C11—22no—
268C23×C11—42no—
269C23×C11—42no—
270C23×C11—82no—
271C23×C11#12114yes—
272C23×C11C22×D411yescharacteristic
273C23×C11C22×D411yescharacteristic
274C23×C11C22×D411yescharacteristic
275C22×D11—22no—
276C22×D11—42no—
277C22×D11—82no—
278Q8×C11—28no—
279Q8×C11—28no—
280Q8×C11—28no—
281Q8×C11—24no—
282Q8×C11—22no—
283Q8×C11—22no—
284Q8×C11—42no—
285Q8×C11C22×D418yes—
286D4×C11—22no—
287D4×C11—22no—
288D4×C11—44no—
289D4×C11—44no—
290D4×C11—42no—
291C2×C4×C11—28no—
292C2×C4×C11—28no—
293C2×C4×C11—28no—
294C2×C4×C11—24no—
295C2×C4×C11—22no—
296C2×C4×C11—42no—
297C2×C4×C11—44no—
298C2×C4×C11—44no—
299C2×C4×C11#12114yes—
300C2×C4×C11#12114yes—
301C2×C4×C11#12114yes—
302C2×C4×C11C22×D411yescharacteristic
303C2×C4×C11C22×D411yescharacteristic
304C2×C4×C11C22×D411yescharacteristic
305C2×C4×C11C22×D412yes—
306C2×C4×C11C22×D412yes—
307C2×C4×C11C22×D412yes—
308C2×C4×C11C2×#4112yes—
309C2×C4×C11C2×#4112yes—
310C2×C4×C11C2×#4112yes—
311C2×C4×C11C2511yescharacteristic
312C22⋊D11—44no—
313C22⋊D11—44no—
314C22⋊D11—88no—
315C2×Dic11—24no—
316C2×Dic11—22no—
317C2×Dic11—44no—
318C2×Dic11—44no—
319C2×Dic11—42no—
320C2×Dic11C22×D418yes—
321D44—22no—
322D44—22no—
323D44—42no—
324C4×D11—44no—
325C4×D11—44no—
326Dic22—22no—
327Dic22—22no—
328Dic22—42no—
329C8×C11—24no—
330C11⋊C8—24no—
331C22×#41—111no—
332C22×#41C2×D1111yescharacteristic
333C23×Q8C2×D1111yescharacteristic
334C2×#137—28no—
335C2×#137—114no—
336C2×#137—114no—
337C2×#137—228no—
338C2×#137C2×D1114yes—
339C2×#137C2×D1114yescomplemented
340C22×Q16—112no—
341C22×Q16C2×D1112yescomplemented
342C22×SD16—112no—
343C22×SD16C2×D1112yescomplemented
344C22×M16—111no—
345C22×M16C2×D1111yescharacteristic
346#537—222no—
347#536—112no—
348#536—112no—
349#535—112no—
350#535—112no—
351#534—222no—
352#532—114no—
353#525—222no—
354#525—222no—
355#519—114no—
356#519—114no—
357#519—222no—
358#519—222no—
359C2×C4×Q8—114no—
360C2×C4×Q8—222no—
361C2×#117—111no—
362C2×#117—111no—
363C2×#117—222no—
364#464—1116no—
365#464—1116no—
366#462—1116no—
367#460—1116no—
368#424—114no—
369#424—114no—
370#423—114no—
371#419—112no—
372#419—112no—
373#418—112no—
374#418—112no—
375#417—114no—
376#417—114no—
377#416—114no—
378#416—114no—
379C22×C11—22no—
380C22×C11—22no—
381C22×C11—22no—
382C22×C11—44no—
383C22×C11—44no—
384C22×C11—42no—
385C22×C11—84no—
386C22×C11C2×#12112yes—
387C22×C11C2×#12112yes—
388C22×C11C2×#12112yes—
389C22×C11C23×D411yescharacteristic
390C2×D11—44no—
391C2×D11—42no—
392C2×D11—84no—
393C4×C11—28no—
394C4×C11—42no—
395C4×C11C2×#12112yes—
396C4×C11C2×#12112yes—
397C4×C11C2×#12112yes—
398C4×C11C23×D411yescharacteristic
399C4×C11C22×#4111yescharacteristic
400Dic11—28no—
401Dic11—44no—
402Dic11—42no—
403C2×#41—21no—
404C2×#41—21no—
405C2×#41—24no—
406C2×#41—24no—
407C2×#41—112no—
408C2×#41—112no—
409C2×#41—221no—
410C2×#41—221no—
411C2×#41—224no—
412C2×#41—224no—
413C2×#41C22×D1112yes—
414C2×#41C22×D1112yes—
415C22×Q8—21no—
416C22×Q8—21no—
417C22×Q8—21no—
418C22×Q8—24no—
419C22×Q8—111no—
420C22×Q8C22⋊D1118yescomplemented
421C22×Q8C22×D1111yescharacteristic
422C22×Q8C22×D1112yes—
423C22×Q8C22×D1112yes—
424C22×Q8C22×D1112yes—
425C22×D4—21no—
426C22×D4—111no—
427C22×D4—221no—
428C22×D4C22×D1111yescharacteristic
429C23×C4—21no—
430C23×C4—21no—
431C23×C4—221no—
432C23×C4C22×D1111yescharacteristic
433#137—216no—
434#137—216no—
435#137—2216no—
436#137—2216no—
437C2×Q16—28no—
438C2×Q16—118no—
439C2×Q16—228no—
440C2×Q16C22×D1118yes—
441C2×SD16—28no—
442C2×SD16—118no—
443C2×SD16—228no—
444C2×SD16C22×D1118yes—
445C2×M16—24no—
446C2×M16—112no—
447C2×M16—112no—
448C2×M16—224no—
449C2×M16C22×D1112yes—
450C2×M16C22×D1112yes—
451C22×C8—112no—
452C22×C8C22×D1112yes—
453C4⋊Q8—114no—
454#127—114no—
455#124—114no—
456#124—114no—
457#123—224no—
458#123—224no—
459C22⋊Q8—224no—
460C22⋊Q8—224no—
461#121—224no—
462#121—224no—
463#121—228no—
464#120—224no—
465#120—224no—
466C4×Q8—1116no—
467C4×Q8—228no—
468C4×Q8—228no—
469C4×Q8—228no—
470C4×D4—228no—
471#117—112no—
472#117—112no—
473#117—112no—
474#117—112no—
475#117—112no—
476#117—112no—
477#117—228no—
478#117—228no—
479#117—221no—
480#117—221no—
481C2×C4⋊C4—112no—
482C2×C4⋊C4—112no—
483C2×C4⋊C4—224no—
484C2×C22⋊C4—112no—
485C2×C22⋊C4—221no—
486C2×C42—112no—
487C2×C42—224no—
488C2×C42—221no—
489C4⋊C8—1116no—
490#103—118no—
491#103—118no—
492#102—118no—
493#102—118no—
494C2×C11—22no—
495C2×C11—22no—
496C2×C11—22no—
497C2×C11—82no—
498C2×C11C22×#12111yescharacteristic
499C2×C11#358612yes—
500D11—82no—
501C24—21no—
502C24—221no—
503C24D4×D1111yescharacteristic
504#41—24no—
505#41—24no—
506#41—24no—
507#41—24no—
508#41—44no—
509#41—44no—
510#41—224no—
511#41—224no—
512#41—224no—
513#41—224no—
514#41—444no—
515#41—444no—
516C2×Q8—28no—
517C2×Q8—28no—
518C2×Q8—28no—
519C2×Q8—22no—
520C2×Q8—22no—
521C2×Q8—22no—
522C2×Q8—21no—
523C2×Q8—24no—
524C2×Q8—24no—
525C2×Q8—24no—
526C2×Q8—22no—
527C2×Q8—22no—
528C2×Q8—112no—
529C2×Q8—221no—
530C2×Q8—222no—
531C2×Q8—222no—
532C2×Q8C2×C22⋊D1118yes—
533C2×Q8C2×C22⋊D1118yes—
534C2×Q8C2×C22⋊D1118yes—
535C2×Q8C23×D1112yes—
536C2×Q8C23×D1114yes—
537C2×D4—22no—
538C2×D4—22no—
539C2×D4—21no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—44no—
543C2×D4—112no—
544C2×D4—228no—
545C2×D4—222no—
546C2×D4—222no—
547C2×D4—221no—
548C2×D4—222no—
549C2×D4—222no—
550C2×D4—444no—
551C2×D4C23×D1112yes—
552C22×C4—28no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—44no—
560C22×C4—114no—
561C22×C4—222no—
562C22×C4—221no—
563C22×C4—222no—
564C22×C4—222no—
565C22×C4—444no—
566C22×C4D4×D1111yescharacteristic
567C22×C4D4×D1111yescharacteristic
568C22×C4D4×D1111yescharacteristic
569C22×C4#434114yes—
570C22×C4C2×C22⋊D1114yes—
571C22×C4C23×D1111yescharacteristic
572C22×C4C23×D1111yescharacteristic
573C22×C4C23×D1111yescharacteristic
574Q16—216no—
575Q16—2216no—
576SD16—216no—
577SD16—2216no—
578M16—24no—
579M16—24no—
580M16—224no—
581M16—224no—
582C2×C8—24no—
583C2×C8—114no—
584C2×C8—224no—
585C2×C8C23×D1114yes—
586C4⋊C4—114no—
587C4⋊C4—114no—
588C4⋊C4—114no—
589C4⋊C4—2216no—
590C4⋊C4—228no—
591C4⋊C4—222no—
592C22⋊C4—114no—
593C22⋊C4—114no—
594C22⋊C4—228no—
595C22⋊C4—228no—
596C22⋊C4—222no—
597C22⋊C4—222no—
598C42—114no—
599C42—114no—
600C42—2216no—
601C42—222no—
602C42—222no—
603C11#6042411yescharacteristic, complemented, Sylow
604C23—22no—
605C23—42no—
606C23—42no—
607C23—82no—
608C23—222no—
609C23—442no—
610C23—882no—
611C23#6699214yes—
612C23C2×D4×D1111yescharacteristic
613C23C2×D4×D1111yescharacteristic
614C23C2×D4×D1111yescharacteristic
615Q8—28no—
616Q8—28no—
617Q8—28no—
618Q8—24no—
619Q8—22no—
620Q8—22no—
621Q8—42no—
622Q8—222no—
623Q8—222no—
624Q8—442no—
625Q8C22×C22⋊D1118yes—
626D4—22no—
627D4—22no—
628D4—44no—
629D4—44no—
630D4—42no—
631D4—222no—
632D4—222no—
633D4—444no—
634D4—444no—
635D4—442no—
636D4—888no—
637C2×C4—28no—
638C2×C4—28no—
639C2×C4—28no—
640C2×C4—24no—
641C2×C4—22no—
642C2×C4—42no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—118no—
646C2×C4—224no—
647C2×C4—222no—
648C2×C4—444no—
649C2×C4—444no—
650C2×C4—442no—
651C2×C4—444no—
652C2×C4—444no—
653C2×C4#6699214yes—
654C2×C4#6699214yes—
655C2×C4#6699214yes—
656C2×C4C2×D4×D1111yescharacteristic
657C2×C4C2×D4×D1111yescharacteristic
658C2×C4C2×D4×D1111yescharacteristic
659C2×C4C2×#434112yes—
660C2×C4C2×#434112yes—
661C2×C4C2×#434112yes—
662C2×C4C22×C22⋊D1112yes—
663C2×C4C22×C22⋊D1112yes—
664C2×C4C22×C22⋊D1112yes—
665C2×C4C24×D1111yescharacteristic
666C8—24no—
667C8—224no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—44no—
672C22—44no—
673C22—42no—
674C22—84no—
675C22—444no—
676C22—442no—
677C22—884no—
678C22C2×#6699212yes—
679C22C2×#6699212yes—
680C22C2×#6699212yes—
681C22C22×D4×D1111yescharacteristic
682C4—28no—
683C4—42no—
684C4—228no—
685C4—444no—
686C4—442no—
687C4C2×#6699212yes—
688C4C2×#6699212yes—
689C4C2×#6699212yes—
690C4C22×#434111yescharacteristic
691C4C23×C22⋊D1111yescharacteristic
692C2—22no—
693C2—22no—
694C2—22no—
695C2—82no—
696C2—882no—
697C2C22×#6699211yescharacteristic
698C2#1308339912yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#137C2
socleC22×C11C23×D4
prime radical#13081945C2
hypercenterC22×#137D11
hypocenterC11#60424
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C22×#66995C2semidirect
3. C2×#10623343C2semidirect
4. #13078148C2semidirect
5. #13078143C2semidirect
6. #13078139C2semidirect
7. #13078134C2semidirect
8. #13078085C2semidirect
9. #13077179C2semidirect
10. #13077136C2semidirect
11. #13077135C2semidirect
12. C22×C11×#137C2semidirect
18. C2×C11×#137C22semidirect
19. C22×C11×Q16C22semidirect
20. C22×C11×SD16C22semidirect
30. #10623343C22semidirect
31. #10623343C22semidirect
33. C2×Q8×Dic11C22semidirect
34. C22×#4326C22semidirect
37. C2×#66995C22semidirect
38. C22×#4325C22semidirect
47. #10622845C22semidirect
48. #10622838C22semidirect
49. #10622828C22semidirect
50. #10622798C22semidirect
51. #10622795C22semidirect
52. #10622779C22semidirect
53. #10622776C22semidirect
54. #10622746C22semidirect
55. #10622744C22semidirect
56. #10622733C22semidirect
57. #10622732C22semidirect
58. #10622731C22semidirect
60. #10622715C22semidirect
71. C22×Q8×C11D4semidirect
256. C22×#137D11semidirect
339. C2×#137C2×D11semidirect
341. C22×Q16C2×D11semidirect
343. C22×SD16C2×D11semidirect
420. C22×Q8C22⋊D11semidirect
603. C11#60424semidirect

Maximal subgroups

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

subgroupindex
C22×#669952
#130819452
C2×#106233432
#130781482
#130781432
#130781392
#130781342
#130780852
#130771792
#130771362
#130771352
C22×C11×#1372
#6042411