Finite Group Databasebeta

← #14757489

Subgroups — #14757489

Order 2816.

1718 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622845C211yesmaximal, characteristic, complemented
2C2×#10622828C211yesmaximal, characteristic, complemented
3C2×#10622846C211yesmaximal, characteristic, complemented
4C22×#66896C211yesmaximal, characteristic, complemented
5C2×#10622610C211yesmaximal, characteristic, complemented
6#13071239C211yesmaximal, characteristic, complemented
7#13069441C212yesmaximal, complemented
8#13069433C212yesmaximal, complemented
9#13069428C212yesmaximal, complemented
10#13069423C212yesmaximal, complemented
11C2×C11×#535C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C23×D4×C11C2211yescharacteristic
14C11×#535—24no—
15C11×#535C418yescomplemented
16C2×C11×#127C2212yes—
17C2×C11×#124C2212yes—
18C2×C11×#121—22no—
19C2×C11×#120—22no—
20C2×C11×#117C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C23×C11⋊C8C2211yescharacteristic
25#10622846—24no—
26#10622845—24no—
27C2×#66899C2211yescharacteristic, complemented
28C2×#66899C2212yescomplemented
29C2×#66899C2211yescharacteristic, complemented
30#10622828—24no—
31C2×#66896—24no—
32C2×#66896C2212yes—
33C2×#66896C2212yes—
34C2×#66896C2212yes—
35C2×#66896C2212yes—
36C2×#66896C2211yescharacteristic, complemented
37C2×#66896C2212yescomplemented
38C2×#66896C2211yescharacteristic, complemented
39#10622610—24no—
40#10622598—22no—
41#10622563—22no—
42#10622549C2212yescomplemented
43#10622548C2212yescomplemented
44C2×#66867C2212yescomplemented
45C2×C4×C11⋊C8C2212yescomplemented
46C25×C11—21no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C2×C11×#41—22no—
51C2×C11×#41—22no—
52C2×C11×#41C2×C414yes—
53C22×Q8×C11C2311yescharacteristic
54C22×D4×C11—21no—
55C22×D4×C11—22no—
56C22×D4×C11—22no—
57C22×D4×C11—21no—
58C22×D4×C11—22no—
59C22×D4×C11—24no—
60C22×D4×C11—22no—
61C22×D4×C11—22no—
62C22×D4×C11C2×C414yes—
63C22×D4×C11C2312yes—
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C23×Dic11—21no—
68C11×#127—24no—
69C11×#127C2×C418yescomplemented
70C11×#124—24no—
71C11×#124C2×C418yescomplemented
72C11×#121—216no—
73C11×#120—216no—
74C11×#117C2×C414yes—
75C11×#117D414yes—
76C2×C11×C4⋊C4D412yes—
77C2×C11×C22⋊C4—24no—
78C2×C11×C22⋊C4D412yes—
79C2×C42×C11C2312yes—
80C2×C22⋊Dic11—21no—
81#66979—22no—
82#66979—22no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—24no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2312yes—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4×Dic11—21no—
91C2×#4318—22no—
92C2×#4318—22no—
93C2×#4318D414yescomplemented
94C22×C11⋊C8—22no—
95C22×C11⋊C8—22no—
96C22×C11⋊C8D414yescomplemented
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2312yes—
99C22×C11⋊C8C2311yescharacteristic
100#66899—24no—
101#66899—22no—
102#66899—22no—
103#66896—24no—
104#66896—24no—
105#66896—24no—
106#66896—24no—
107#66896—24no—
108#66896—22no—
109#66896—22no—
110C11⋊#95—24no—
111#66867—24no—
112C4×C11⋊C8—24no—
113#21206—111nomaximal, Sylow
114C24×C11—22no—
115C24×C11—21no—
116C24×C11—24no—
117C24×C11—42no—
118C24×C11—42no—
119C24×C11—82no—
120C24×C11—82no—
121C24×C11C2×D411yescharacteristic
122C11×#41—28no—
123C11×#41—28no—
124C11×#41—44no—
125C11×#41—44no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11C22×C412yes—
132C2×D4×C11—24no—
133C2×D4×C11—24no—
134C2×D4×C11—216no—
135C2×D4×C11—28no—
136C2×D4×C11—28no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—22no—
142C2×D4×C11—21no—
143C2×D4×C11—22no—
144C2×D4×C11—22no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—42no—
148C2×D4×C11—42no—
149C2×D4×C11—44no—
150C2×D4×C11—44no—
151C2×D4×C11—42no—
152C2×D4×C11—42no—
153C2×D4×C11—84no—
154C2×D4×C11—84no—
155C2×D4×C11C22×C414yes—
156C2×D4×C11C22×C412yes—
157C22×C4×C11—21no—
158C22×C4×C11—24no—
159C22×C4×C11—42no—
160C22×C4×C11—42no—
161C22×C4×C11C22×C412yes—
162C22×C4×C11C2×D414yes—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D412yes—
167C22×C4×C11#4112yes—
168C22×C4×C11#4112yes—
169C22×C4×C11C2411yescharacteristic
170C22×Dic11—21no—
171C22×Dic11—22no—
172C22×Dic11—21no—
173C22×Dic11—42no—
174C22×Dic11—82no—
175C11×C4⋊C4C22⋊C418yes—
176C11×C22⋊C4—216no—
177C11×C22⋊C4C22⋊C418yes—
178C42×C11C22×C414yes—
179C42×C11C2×D414yes—
180C22⋊Dic11—42no—
181C4⋊Dic11—22no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—22no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—42no—
188C4⋊Dic11—84no—
189C4×Dic11—42no—
190#4318—28no—
191C2×C11⋊C8—28no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8C2×D412yes—
199C2×C11⋊C8C2×D412yes—
200C2×C11⋊C8C2×D414yes—
201C2×#535D1111yescharacteristic
202C2×#417—111no—
203C2×#418—111no—
204C2×#416—111no—
205C22×#102—111no—
206C2×#405—111no—
207#2317—111no—
208#1961—112no—
209#1959—112no—
210#1958—112no—
211#1957—112no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—24no—
215C23×C11—22no—
216C23×C11—41no—
217C23×C11—42no—
218C23×C11—41no—
219C23×C11—42no—
220C23×C11—42no—
221C23×C11—44no—
222C23×C11—42no—
223C23×C11—44no—
224C23×C11—48no—
225C23×C11—88no—
226C23×C11—88no—
227C23×C11—84no—
228C23×C11—84no—
229C23×C11C2×C22⋊C412yes—
230C23×C11#12412yes—
231C23×C11#12712yes—
232C23×C11C22×D411yescharacteristic
233Q8×C11—22no—
234Q8×C11—22no—
235Q8×C11—41no—
236Q8×C11—41no—
237D4×C11—24no—
238D4×C11—24no—
239D4×C11—22no—
240D4×C11—22no—
241D4×C11—48no—
242D4×C11—42no—
243D4×C11—42no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—48no—
247D4×C11—816no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—48no—
254C2×C4×C11C2×C22⋊C418yes—
255C2×C4×C11C2×C22⋊C412yes—
256C2×C4×C11C4×D414yes—
257C2×C4×C11C4×D414yes—
258C2×C4×C11#12114yes—
259C2×C4×C11#12114yes—
260C2×C4×C11#12412yes—
261C2×C4×C11#12712yes—
262C2×C4×C11C23×C411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—44no—
273C2×Dic11—42no—
274C2×Dic11—84no—
275C11⋊C8—22no—
276C11⋊C8—22no—
277C11⋊C8—24no—
278C22×#41C2×D1111yescharacteristic
279C23×D4C2×D1111yescharacteristic
280C22×M16—111no—
281C23×C8—111no—
282#535—24no—
283#535Dic1118yescomplemented
284C2×#127C2×D1112yes—
285C2×#124C2×D1112yes—
286C2×#121—22no—
287C2×#120—22no—
288C2×#117—111no—
289C2×#117C2×D1111yescharacteristic
290C22×C4⋊C4—111no—
291#418—224no—
292#417—224no—
293#416—224no—
294C2×#103—111no—
295C2×#103—111no—
296C2×#103—112no—
297C2×#102—112no—
298C2×#102—112no—
299C2×#102—111no—
300C2×#102—111no—
301C2×#102—112no—
302C2×#102—112no—
303C2×#102—112no—
304C2×#102—224no—
305#405—224no—
306C2×#97—112no—
307C2×C4×C8—112no—
308#389—222no—
309#385—222no—
310#384—112no—
311#382—112no—
312C22×C11—24no—
313C22×C11—24no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—44no—
317C22×C11—48no—
318C22×C11—42no—
319C22×C11—44no—
320C22×C11—816no—
321C22×C11—82no—
322C22×C11—84no—
323C22×C11—81no—
324C22×C11—82no—
325C22×C11—81no—
326C22×C11—82no—
327C22×C11#39014yes—
328C22×C11C22×C22⋊C411yescharacteristic
329C22×C11C2×#12411yescharacteristic
330C22×C11C2×#12711yescharacteristic
331C22×C11#57612yes—
332C22×C11#57712yes—
333C4×C11—28no—
334C4×C11—42no—
335C4×C11#39014yes—
336C4×C11C2×C4×D411yescharacteristic
337C4×C11C2×C4×D411yescharacteristic
338C4×C11C2×#12111yescharacteristic
339C4×C11C2×#12111yescharacteristic
340Dic11—81no—
341Dic11—81no—
342Dic11—82no—
343C25—21no—
344C2×#41—22no—
345C2×#41—22no—
346C2×#41—22no—
347C2×#41—22no—
348C2×#41—22no—
349C2×#41C2×Dic1114yes—
350C22×Q8C22×D1111yescharacteristic
351C22×D4—21no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—21no—
357C22×D4—22no—
358C22×D4—24no—
359C22×D4C2×Dic1114yes—
360C22×D4C22×D1112yes—
361C22×D4C22×D1111yescharacteristic
362C23×C4—21no—
363C23×C4—221no—
364C23×C4C22×D1111yescharacteristic
365C2×M16—114no—
366C2×M16—222no—
367C2×M16—222no—
368C22×C8—114no—
369C22×C8—111no—
370C22×C8—111no—
371C22×C8—112no—
372C22×C8—222no—
373C22×C8—222no—
374#127—24no—
375#127C2×Dic1118yescomplemented
376#124—24no—
377#124C2×Dic1118yescomplemented
378#121—216no—
379#120—216no—
380#117—222no—
381#117—222no—
382#117C2×Dic1114yes—
383#117C22⋊D1114yes—
384C2×C4⋊C4—112no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—222no—
388C2×C4⋊C4—222no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—224no—
391C2×C4⋊C4C22⋊D1112yes—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—221no—
394C2×C22⋊C4C22⋊D1112yes—
395C2×C42—221no—
396C2×C42C22×D1112yes—
397#103—222no—
398#103—222no—
399#103—224no—
400#102—224no—
401#102—224no—
402#102—222no—
403#102—222no—
404#102—224no—
405#102—224no—
406#102—224no—
407#97—224no—
408C4×C8—224no—
409#95—224no—
410C2×C11—24no—
411C2×C11—82no—
412C2×C11—84no—
413C2×C11C2×#39011yescharacteristic
414C2×C11#289712yes—
415C2×C11#313612yes—
416C2×C11#315411yescharacteristic
417C2×C11#315511yescharacteristic
418C24—22no—
419C24—21no—
420C24—24no—
421C24—42no—
422C24—42no—
423C24—82no—
424C24—82no—
425C24C2×C22⋊D1111yescharacteristic
426#41—28no—
427#41—28no—
428#41—44no—
429#41—44no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8C22×Dic1112yes—
436C2×D4—24no—
437C2×D4—28no—
438C2×D4—28no—
439C2×D4—24no—
440C2×D4—216no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—22no—
450C2×D4—21no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—44no—
455C2×D4—44no—
456C2×D4—42no—
457C2×D4—84no—
458C2×D4—84no—
459C2×D4C22×Dic1114yes—
460C2×D4C22×Dic1112yes—
461C22×C4—21no—
462C22×C4—24no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—221no—
466C22×C4—222no—
467C22×C4—221no—
468C22×C4—442no—
469C22×C4—882no—
470C22×C4D4×D1112yes—
471C22×C4D4×D1112yes—
472C22×C4#434112yes—
473C22×C4#434112yes—
474C22×C4C22×Dic1112yes—
475C22×C4C2×C22⋊D1114yes—
476C22×C4C2×C22⋊D1111yescharacteristic
477C22×C4C2×C22⋊D1112yes—
478C22×C4C23×D1111yescharacteristic
479M16—228no—
480C2×C8—112no—
481C2×C8—112no—
482C2×C8—114no—
483C2×C8—228no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—222no—
487C2×C8—221no—
488C2×C8—222no—
489C2×C8—221no—
490C4⋊C4—222no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—222no—
494C4⋊C4—221no—
495C4⋊C4—221no—
496C4⋊C4—442no—
497C4⋊C4—884no—
498C4⋊C4C22⋊Dic1118yes—
499C22⋊C4—216no—
500C22⋊C4—442no—
501C22⋊C4C22⋊Dic1118yes—
502C42—442no—
503C42C22×Dic1114yes—
504C42C2×C22⋊D1114yes—
505C11#2120611yescharacteristic, complemented, Sylow
506C23—22no—
507C23—22no—
508C23—24no—
509C23—22no—
510C23—41no—
511C23—42no—
512C23—41no—
513C23—42no—
514C23—48no—
515C23—42no—
516C23—44no—
517C23—42no—
518C23—44no—
519C23—88no—
520C23—84no—
521C23—84no—
522C23—88no—
523C23#6698912yes—
524C23#6699312yes—
525C23C2×C22⋊Dic1112yes—
526C23C22×C22⋊D1111yescharacteristic
527Q8—22no—
528Q8—22no—
529Q8—41no—
530Q8—41no—
531D4—24no—
532D4—24no—
533D4—22no—
534D4—22no—
535D4—48no—
536D4—42no—
537D4—42no—
538D4—41no—
539D4—41no—
540D4—48no—
541D4—816no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—48no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—442no—
551C2×C4—442no—
552C2×C4—444no—
553C2×C4—442no—
554C2×C4—884no—
555C2×C4D4×Dic1114yes—
556C2×C4D4×Dic1114yes—
557C2×C4#6698912yes—
558C2×C4#6699114yes—
559C2×C4#6699114yes—
560C2×C4#6699312yes—
561C2×C4C2×C22⋊Dic1118yes—
562C2×C4C2×C22⋊Dic1112yes—
563C2×C4C2×D4×D1111yescharacteristic
564C2×C4C2×D4×D1111yescharacteristic
565C2×C4C2×#434111yescharacteristic
566C2×C4C2×#434111yescharacteristic
567C2×C4C23×Dic1111yescharacteristic
568C2×C4C22×C22⋊D1111yescharacteristic
569C8—222no—
570C8—222no—
571C8—224no—
572C22—22no—
573C22—22no—
574C22—24no—
575C22—24no—
576C22—44no—
577C22—48no—
578C22—42no—
579C22—44no—
580C22—816no—
581C22—82no—
582C22—81no—
583C22—82no—
584C22—81no—
585C22—84no—
586C22—82no—
587C22#1062283414yes—
588C22C2×#6698911yescharacteristic
589C22C2×#6699311yescharacteristic
590C22#1062336612yes—
591C22#1062336712yes—
592C22C22×C22⋊Dic1111yescharacteristic
593C4—28no—
594C4—42no—
595C4—881no—
596C4—882no—
597C4—881no—
598C4#1062283414yes—
599C4C2×D4×Dic1111yescharacteristic
600C4C2×D4×Dic1111yescharacteristic
601C4C2×#6699111yescharacteristic
602C4C2×#6699111yescharacteristic
603C2—24no—
604C2—84no—
605C2—82no—
606C2C2×#1062283411yescharacteristic
607C2#1307714212yes—
608C2#1307897012yes—
609C2#1307908811yescharacteristic
610C2#1307909911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#535C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#535D11
hypocenterC11#21206
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C2×#10622845C2semidirect
2. C2×#10622828C2semidirect
3. C2×#10622846C2semidirect
4. C22×#66896C2semidirect
5. C2×#10622610C2semidirect
6. #13071239C2semidirect
7. #13069441C2semidirect
8. #13069433C2semidirect
9. #13069428C2semidirect
10. #13069423C2semidirect
15. C11×#535C4semidirect
27. C2×#66899C22semidirect
28. C2×#66899C22semidirect
29. C2×#66899C22semidirect
36. C2×#66896C22semidirect
37. C2×#66896C22semidirect
38. C2×#66896C22semidirect
42. #10622549C22semidirect
43. #10622548C22semidirect
44. C2×#66867C22semidirect
45. C2×C4×C11⋊C8C22semidirect
69. C11×#127C2×C4semidirect
71. C11×#124C2×C4semidirect
93. C2×#4318D4semidirect
96. C22×C11⋊C8D4semidirect
283. #535Dic11semidirect
375. #127C2×Dic11semidirect
377. #124C2×Dic11semidirect
505. C11#21206semidirect

Maximal subgroups

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

subgroupindex
C2×#106228452
C2×#106228282
C2×#106228462
C22×#668962
C2×#106226102
#130712392
#130694412
#130694332
#130694282
#130694232
C2×C11×#5352
#2120611