Finite Group Databasebeta

← #14769660

Subgroups — #14769660

Order 2816.

1362 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622810C211yesmaximal, characteristic, complemented
2C2×#10622809C211yesmaximal, characteristic, complemented
3#13077065C212yesmaximal, complemented
4#13069510C211yesmaximal, characteristic, complemented
5#13069505C211yesmaximal, characteristic, complemented
6#13068945C212yesmaximal, complemented
7#13068945C212yesmaximal, complemented
8#13068658C211yesmaximal, characteristic, complemented
9#13068560C212yesmaximal, complemented
10#13068397C211yesmaximal, characteristic, complemented
11C2×C11×#575C211yesmaximal, characteristic
12C22×C11×#41C2212yes—
13C11×#575—24no—
14C11×#575—24no—
15C2×C11×#137C412yescomplemented
16C2×C11×#137C412yescomplemented
17C2×C11×AGL(1,ℤ/8)C412yescomplemented
18C2×C11×AGL(1,ℤ/8)C412yescomplemented
19C2×C11×#135C2212yes—
20C2×C11×#135C2211yescharacteristic
21C2×C11×#135C2211yescharacteristic
22C22×C11×M16C2211yescharacteristic
23C2×#67001C2212yescomplemented
24C2×#67001C2212yescomplemented
25C2×#66901C2212yescomplemented
26C2×#66901C2212yescomplemented
27C2×#66901C2212yescomplemented
28C2×#66901C2212yescomplemented
29#10622847—22no—
30#10622847—22no—
31#10622847C2212yescomplemented
32#10622847C2212yescomplemented
33C4×C22⋊Dic11C2211yescharacteristic
34#10622820—22no—
35#10622820C2212yes—
36C2×C22⋊(C11⋊C8)—22no—
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38#10622810—24no—
39#10622809—24no—
40C2×#66883C2211yescharacteristic, complemented
41C2×#66883C2211yescharacteristic, complemented
42C2×#66879C2211yescharacteristic, complemented
43C2×C8×Dic11C2211yescharacteristic, complemented
44#10622190C2212yescomplemented
45#10622188C2211yescharacteristic, complemented
46#10622188C2211yescharacteristic, complemented
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—24no—
50C2×C11×#41—24no—
51C2×C11×#41—42no—
52C2×C11×#41—42no—
53C2×C11×#41C2×C412yes—
54C2×C11×#41C2×C412yes—
55C2×C11×#41C2312yes—
56C2×C11×#41C2312yes—
57C22×Q8×C11C2×C412yes—
58C22×D4×C11—22no—
59C22×D4×C11C2×C412yes—
60C23×C4×C11—22no—
61C23×C4×C11C2311yescharacteristic
62C11×#137—28no—
63C11×#137—28no—
64C11×AGL(1,ℤ/8)—28no—
65C11×AGL(1,ℤ/8)—28no—
66C11×#135—24no—
67C11×#135—24no—
68C11×#135—22no—
69C11×#135—22no—
70C11×#135D414yes—
71C11×#135D414yes—
72C2×C11×Q16C2×C412yes—
73C2×C11×Q16C2×C411yescharacteristic
74C2×C11×Q16C2×C411yescharacteristic
75C2×C11×SD16C2×C412yes—
76C2×C11×SD16C2×C412yes—
77C2×C11×SD16C2×C412yes—
78C2×C11×SD16C2×C412yes—
79C2×C11×D8C2×C412yes—
80C2×C11×D8C2×C411yescharacteristic
81C2×C11×D8C2×C411yescharacteristic
82C2×C11×M16—22no—
83C2×C11×M16—22no—
84C2×C11×M16C2×C412yes—
85C2×C11×M16C2×C412yes—
86C22×C8×C11C2311yescharacteristic
87C22×C8×C11C2311yescharacteristic
88C2×C22⋊Dic11—21no—
89#67001—24no—
90#67001—24no—
91#67001—42no—
92#67001—42no—
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C2×#4318—22no—
96C2×#4318—22no—
97C2×#4318C2312yes—
98C2×#4318C2312yes—
99C22×C11⋊C8—22no—
100C22×C11⋊C8—22no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66901—24no—
104#66901—24no—
105#66901—42no—
106#66901—42no—
107C11⋊#95—21no—
108C22⋊(C11⋊C8)—22no—
109C22⋊(C11⋊C8)—22no—
110C22⋊(C11⋊C8)—22no—
111C22⋊(C11⋊C8)—22no—
112C22⋊(C11⋊C8)—22no—
113C22⋊(C11⋊C8)—22no—
114C22⋊(C11⋊C8)D412yes—
115C22⋊(C11⋊C8)D412yes—
116#66883—22no—
117#66883—22no—
118#66879—22no—
119C8×Dic11—22no—
120#22453—111nomaximal, Sylow
121C24×C11—22no—
122C24×C11#4111yescharacteristic
123C11×#41—22no—
124C11×#41—22no—
125C11×#41—24no—
126C11×#41—24no—
127C11×#41—22no—
128C11×#41—22no—
129C11×#41—22no—
130C11×#41—22no—
131C11×#41—44no—
132C11×#41—44no—
133C11×#41—42no—
134C11×#41—42no—
135C11×#41—44no—
136C11×#41—44no—
137C11×#41C2×D414yes—
138C11×#41C2×D414yes—
139C2×Q8×C11—22no—
140C2×Q8×C11—24no—
141C2×Q8×C11—42no—
142C2×Q8×C11C22×C412yes—
143C2×Q8×C11C22×C412yes—
144C2×D4×C11—22no—
145C2×D4×C11—24no—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—42no—
151C2×D4×C11—44no—
152C2×D4×C11—44no—
153C2×D4×C11C22×C412yes—
154C2×D4×C11C22×C412yes—
155C22×C4×C11—22no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—44no—
165C22×C4×C11—44no—
166C22×C4×C11C22×C412yes—
167C22×C4×C11C2×D412yes—
168C22×C4×C11#4111yescharacteristic
169C22×C4×C11C2411yescharacteristic
170C22×Dic11—21no—
171C22×Dic11—21no—
172C11×Q16—22no—
173C11×Q16—24no—
174C11×Q16C22⋊C414yescomplemented
175C11×SD16—24no—
176C11×SD16—24no—
177C11×SD16—24no—
178C11×SD16C22⋊C418yescomplemented
179C11×D8—22no—
180C11×D8—24no—
181C11×D8C22⋊C414yescomplemented
182C11×M16—24no—
183C11×M16—24no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11C22×C412yes—
187C2×C8×C11C22×C411yescharacteristic
188C2×C8×C11C22×C411yescharacteristic
189C2×C8×C11C2×D412yes—
190C2×C8×C11C2×D412yes—
191C22⋊Dic11—42no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196#4318—22no—
197#4318—22no—
198#4318—22no—
199#4318—22no—
200#4318—44no—
201#4318—44no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8—22no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—44no—
209C2×C11⋊C8—44no—
210C2×C11⋊C8C2×D411yescharacteristic
211C2×C11⋊C8C2×D412yes—
212C2×C11⋊C8C2×D411yescharacteristic
213C2×#575D1111yescharacteristic
214C2×#444—111no—
215C2×#443—111no—
216#2880—112no—
217#1975—111no—
218#1974—111no—
219#1876—112no—
220#1876—112no—
221#1811—111no—
222#1789—112no—
223#1753—111no—
224C23×C11—22no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—22no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—44no—
231C23×C11—44no—
232C23×C11—82no—
233C23×C11C4×D412yes—
234C23×C11C2×#4111yescharacteristic
235Q8×C11—22no—
236Q8×C11—22no—
237Q8×C11—22no—
238Q8×C11—44no—
239Q8×C11C2×C22⋊C414yes—
240D4×C11—24no—
241D4×C11—24no—
242D4×C11—22no—
243D4×C11—22no—
244D4×C11—22no—
245D4×C11—44no—
246D4×C11—44no—
247D4×C11—44no—
248D4×C11—42no—
249D4×C11—42no—
250D4×C11C2×C22⋊C414yes—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—44no—
262C2×C4×C11—44no—
263C2×C4×C11—44no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11C4×D412yes—
267C2×C4×C11C23×C411yescharacteristic
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11H(5,𝔽2)11yescharacteristic
272C2×C4×C11H(5,𝔽2)11yescharacteristic
273C2×Dic11—22no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C8×C11—22no—
280C8×C11C2×C22⋊C412yes—
281C8×C11C2×C22⋊C412yes—
282C11⋊C8—21no—
283C11⋊C8—22no—
284C11⋊C8—21no—
285C11⋊C8—42no—
286C11⋊C8—42no—
287C22×#41C2×D1112yes—
288#575—24no—
289#575—24no—
290C2×#137Dic1112yescomplemented
291C2×#137Dic1112yescomplemented
292C2×AGL(1,ℤ/8)Dic1112yescomplemented
293C2×AGL(1,ℤ/8)Dic1112yescomplemented
294C2×#135C2×D1112yes—
295C2×#135C2×D1111yescharacteristic
296C2×#135C2×D1111yescharacteristic
297C2×#131—112no—
298C2×#131—112no—
299C22×M16C2×D1111yescharacteristic
300#444—224no—
301#443—224no—
302C2×#108—111no—
303C2×#108—111no—
304C2×#104—112no—
305C2×#104—112no—
306C2×#104—112no—
307C2×#104—112no—
308#408—112no—
309#408—112no—
310#408—222no—
311#408—222no—
312#407—112no—
313#407—222no—
314C2×C22⋊C8—111no—
315C2×C22⋊C8—222no—
316C2×#97—111no—
317C2×C4×C8—111no—
318C4×C22⋊C4—111no—
319#341—112no—
320#336—111no—
321#336—111no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—22no—
325C22×C11—24no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11—81no—
334C22×C11—81no—
335C22×C11—88no—
336C22×C11C2×C4×D411yescharacteristic
337C22×C11#54611yescharacteristic
338C22×C11#54611yescharacteristic
339C4×C11—22no—
340C4×C11—24no—
341C4×C11—42no—
342C4×C11C22×C22⋊C411yescharacteristic
343C4×C11#51811yescharacteristic
344C4×C11D4211yescharacteristic
345C4×C11D4211yescharacteristic
346Dic11—42no—
347Dic11—81no—
348C2×#41—22no—
349C2×#41—22no—
350C2×#41—24no—
351C2×#41—24no—
352C2×#41—42no—
353C2×#41—42no—
354C2×#41C2×Dic1112yes—
355C2×#41C2×Dic1112yes—
356C2×#41C22×D1112yes—
357C2×#41C22×D1112yes—
358C22×Q8C2×Dic1112yes—
359C22×D4—22no—
360C22×D4C2×Dic1112yes—
361C23×C4—22no—
362C23×C4C22×D1111yescharacteristic
363#137—28no—
364#137—28no—
365AGL(1,ℤ/8)—28no—
366AGL(1,ℤ/8)—28no—
367#135—24no—
368#135—24no—
369#135—22no—
370#135—22no—
371#135C22⋊D1114yes—
372#135C22⋊D1114yes—
373C2×Q16C2×Dic1112yes—
374C2×Q16C2×Dic1111yescharacteristic
375C2×Q16C2×Dic1111yescharacteristic
376C2×SD16C2×Dic1112yes—
377C2×SD16C2×Dic1112yes—
378C2×SD16C2×Dic1112yes—
379C2×SD16C2×Dic1112yes—
380C2×D8C2×Dic1112yes—
381C2×D8C2×Dic1111yescharacteristic
382C2×D8C2×Dic1111yescharacteristic
383#131—224no—
384#131—224no—
385#131—442no—
386#131—442no—
387C2×M16—22no—
388C2×M16—22no—
389C2×M16—112no—
390C2×M16—112no—
391C2×M16—222no—
392C2×M16—222no—
393C2×M16C2×Dic1112yes—
394C2×M16C2×Dic1112yes—
395C22×C8—111no—
396C22×C8—111no—
397C22×C8—222no—
398C22×C8—222no—
399C22×C8C22×D1111yescharacteristic
400C22×C8C22×D1111yescharacteristic
401C2×C22⋊C4—221no—
402C2×C42—111no—
403C2×C42—111no—
404#108—222no—
405#108—222no—
406#104—224no—
407#104—224no—
408#104—442no—
409#104—442no—
410C22⋊C8—112no—
411C22⋊C8—112no—
412C22⋊C8—222no—
413C22⋊C8—222no—
414C22⋊C8—222no—
415C22⋊C8—222no—
416C22⋊C8—222no—
417C22⋊C8—222no—
418#97—222no—
419C4×C8—222no—
420#95—221no—
421C2×C11—21no—
422C2×C11—21no—
423C2×C11—42no—
424C2×C11—44no—
425C2×C11—82no—
426C2×C11D4×C22⋊C411yescharacteristic
427C2×C11#295511yescharacteristic
428C2×C11#295611yescharacteristic
429C24—22no—
430C24#434111yescharacteristic
431#41—22no—
432#41—22no—
433#41—24no—
434#41—24no—
435#41—22no—
436#41—22no—
437#41—22no—
438#41—22no—
439#41—44no—
440#41—44no—
441#41—42no—
442#41—42no—
443#41—44no—
444#41—44no—
445#41C2×C22⋊D1114yes—
446#41C2×C22⋊D1114yes—
447C2×Q8—22no—
448C2×Q8—24no—
449C2×Q8—42no—
450C2×Q8C22×Dic1112yes—
451C2×Q8C22×Dic1112yes—
452C2×D4—22no—
453C2×D4—24no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—42no—
459C2×D4—44no—
460C2×D4—44no—
461C2×D4C22×Dic1112yes—
462C2×D4C22×Dic1112yes—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—44no—
473C22×C4—44no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4D4×D1112yes—
477C22×C4#434111yescharacteristic
478C22×C4C22×Dic1112yes—
479C22×C4C23×D1111yescharacteristic
480Q16—24no—
481Q16—22no—
482Q16C22⋊Dic1114yescomplemented
483SD16—24no—
484SD16—24no—
485SD16—24no—
486SD16C22⋊Dic1118yescomplemented
487D8—24no—
488D8—22no—
489D8C22⋊Dic1114yescomplemented
490M16—24no—
491M16—24no—
492M16—222no—
493M16—222no—
494M16—222no—
495M16—222no—
496M16—444no—
497M16—444no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—111no—
501C2×C8—112no—
502C2×C8—111no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—222no—
508C2×C8—222no—
509C2×C8—444no—
510C2×C8—444no—
511C2×C8C22×Dic1112yes—
512C2×C8C22×Dic1111yescharacteristic
513C2×C8C22×Dic1111yescharacteristic
514C2×C8C2×C22⋊D1112yes—
515C2×C8C2×C22⋊D1112yes—
516C22⋊C4—442no—
517C42—221no—
518C42—221no—
519C42—221no—
520C42—221no—
521C11#2245311yescharacteristic, complemented, Sylow
522C23—22no—
523C23—21no—
524C23—21no—
525C23—22no—
526C23—41no—
527C23—41no—
528C23—44no—
529C23—44no—
530C23—82no—
531C23D4×Dic1112yes—
532C23C2×#434111yescharacteristic
533Q8—22no—
534Q8—22no—
535Q8—22no—
536Q8—44no—
537Q8C2×C22⋊Dic1114yes—
538D4—24no—
539D4—24no—
540D4—22no—
541D4—22no—
542D4—22no—
543D4—44no—
544D4—44no—
545D4—44no—
546D4—42no—
547D4—42no—
548D4C2×C22⋊Dic1114yes—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—44no—
560C2×C4—44no—
561C2×C4—44no—
562C2×C4—42no—
563C2×C4—42no—
564C2×C4—222no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4D4×Dic1112yes—
571C2×C4C2×D4×D1111yescharacteristic
572C2×C4#6703711yescharacteristic
573C2×C4#6703711yescharacteristic
574C2×C4C23×Dic1111yescharacteristic
575C2×C4C22×C22⋊D1111yescharacteristic
576C2×C4C22×C22⋊D1111yescharacteristic
577C8—22no—
578C8—221no—
579C8—222no—
580C8—221no—
581C8—442no—
582C8—442no—
583C8C2×C22⋊Dic1112yes—
584C8C2×C22⋊Dic1112yes—
585C22—21no—
586C22—21no—
587C22—22no—
588C22—22no—
589C22—22no—
590C22—24no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—42no—
596C22—81no—
597C22—81no—
598C22—88no—
599C22C2×D4×Dic1111yescharacteristic
600C22#1062333711yescharacteristic
601C22#1062333711yescharacteristic
602C4—22no—
603C4—24no—
604C4—42no—
605C4—442no—
606C4—881no—
607C4#1062332911yescharacteristic
608C4D4×C22⋊D1111yescharacteristic
609C4D4×C22⋊D1111yescharacteristic
610C4C22×C22⋊Dic1111yescharacteristic
611C2—21no—
612C2—21no—
613C2—42no—
614C2—44no—
615C2—82no—
616C2D4×C22⋊Dic1111yescharacteristic
617C2#1307751911yescharacteristic
618C2#1307752611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#575C2
socleC22×C11C2×C4×D4
cosocleC22×C4×C11C24
hypercenterC2×#575D11
hypocenterC11#22453
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#10622810C2semidirect
2. C2×#10622809C2semidirect
3. #13077065C2semidirect
4. #13069510C2semidirect
5. #13069505C2semidirect
6. #13068945C2semidirect
7. #13068945C2semidirect
8. #13068658C2semidirect
9. #13068560C2semidirect
10. #13068397C2semidirect
15. C2×C11×#137C4semidirect
16. C2×C11×#137C4semidirect
17. C2×C11×AGL(1,ℤ/8)C4semidirect
18. C2×C11×AGL(1,ℤ/8)C4semidirect
23. C2×#67001C22semidirect
24. C2×#67001C22semidirect
25. C2×#66901C22semidirect
26. C2×#66901C22semidirect
27. C2×#66901C22semidirect
28. C2×#66901C22semidirect
31. #10622847C22semidirect
32. #10622847C22semidirect
40. C2×#66883C22semidirect
41. C2×#66883C22semidirect
42. C2×#66879C22semidirect
43. C2×C8×Dic11C22semidirect
44. #10622190C22semidirect
45. #10622188C22semidirect
46. #10622188C22semidirect
174. C11×Q16C22⋊C4semidirect
178. C11×SD16C22⋊C4semidirect
181. C11×D8C22⋊C4semidirect
290. C2×#137Dic11semidirect
291. C2×#137Dic11semidirect
292. C2×AGL(1,ℤ/8)Dic11semidirect
293. C2×AGL(1,ℤ/8)Dic11semidirect
482. Q16C22⋊Dic11semidirect
486. SD16C22⋊Dic11semidirect
489. D8C22⋊Dic11semidirect
521. C11#22453semidirect

Maximal subgroups

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

subgroupindex
C2×#106228102
C2×#106228092
#130770652
#130695102
#130695052
#130689452
#130686582
#130685602
#130683972
C2×C11×#5752
#2245311