Finite Group Databasebeta

← #14762880

Subgroups — #14762880

Order 2816.

1326 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622847C211yesmaximal, characteristic
2#13071208C211yesmaximal, characteristic
3#13069050C212yesmaximal, complemented
4#13069040C212yesmaximal, complemented
5#13068929C212yesmaximal, complemented
6#13068924C212yesmaximal, complemented
7#13068711C212yesmaximal, complemented
8#13068551C212yesmaximal, complemented
9C2×C11×#536C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C23×Q8×C11C2211yescharacteristic
12C11×#536—24no—
13C11×#536C418yescomplemented
14C2×C11×C4⋊Q8—21no—
15C2×C11×#124—21no—
16C2×C11×#123—21no—
17C2×C11×#123—21no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C11×C22⋊Q8C2212yes—
20C2×C11×#117C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C23×C11⋊C8C2211yescharacteristic
25#10622847—24no—
26#10622843—21no—
27C2×#66899C2212yes—
28C2×#66899C2212yes—
29C2×#66899C2212yes—
30C2×#66899C2212yes—
31#10622834—21no—
32#10622833—21no—
33#10622833—21no—
34#10622825C2212yes—
35#10622825C2212yes—
36C2×C22⋊(C11⋊C8)C2212yes—
37C2×C22⋊(C11⋊C8)C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C2×C11×#41—41no—
43C2×C11×#41—41no—
44C2×C11×#41—41no—
45C2×C11×#41—41no—
46C2×C11×#41C2×C414yes—
47C2×C11×#41D414yes—
48C22×Q8×C11—21no—
49C22×Q8×C11—22no—
50C22×Q8×C11—41no—
51C22×Q8×C11—41no—
52C22×Q8×C11—41no—
53C22×Q8×C11—41no—
54C22×Q8×C11C2×C414yescomplemented
55C22×Q8×C11D411yescharacteristic
56C22×Q8×C11C2312yes—
57C22×D4×C11D411yescharacteristic
58C22×D4×C11D411yescharacteristic
59C22×D4×C11D411yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11—21no—
65C11×C4⋊Q8—28no—
66C11×#124—28no—
67C11×#123—28no—
68C11×#123—28no—
69C11×C22⋊Q8—24no—
70C11×C22⋊Q8—24no—
71C11×C22⋊Q8C2×C418yes—
72C11×C22⋊Q8C2×C418yescomplemented
73C11×#117—22no—
74C11×#117C2×C414yescomplemented
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4C2312yes—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C42×C11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11—22no—
85#66979—41no—
86#66979—41no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—41no—
89C2×C4⋊Dic11—41no—
90C2×C4⋊Dic11C2312yes—
91C2×C4⋊Dic11C2312yes—
92C2×C4×Dic11—21no—
93C2×#4318—22no—
94C2×#4318—41no—
95C2×#4318—41no—
96C22×C11⋊C8—22no—
97C22×C11⋊C8—41no—
98C22×C11⋊C8—41no—
99C22×C11⋊C8C2312yes—
100C22×C11⋊C8C2312yes—
101#66899—42no—
102#66899—42no—
103#66899—42no—
104#66899—42no—
105C11⋊#95—22no—
106C11⋊#95—22no—
107C22⋊(C11⋊C8)—24no—
108C22⋊(C11⋊C8)—24no—
109#21771—111nomaximal, Sylow
110C24×C11C2×D411yescharacteristic
111C24×C11C2×D411yescharacteristic
112C24×C11C2×D411yescharacteristic
113C11×#41—44no—
114C11×#41—44no—
115C11×#41—44no—
116C11×#41—44no—
117C2×Q8×C11—24no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11—41no—
124C2×Q8×C11—41no—
125C2×Q8×C11—44no—
126C2×Q8×C11—44no—
127C2×Q8×C11—42no—
128C2×Q8×C11—42no—
129C2×Q8×C11—44no—
130C2×Q8×C11—44no—
131C2×Q8×C11C22⋊C414yes—
132C2×Q8×C11C22×C414yes—
133C2×D4×C11—41no—
134C2×D4×C11—41no—
135C2×D4×C11—41no—
136C2×D4×C11—41no—
137C2×D4×C11—41no—
138C2×D4×C11—41no—
139C2×D4×C11C22⋊C414yes—
140C2×D4×C11C22⋊C414yes—
141C2×D4×C11C22⋊C414yes—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—24no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—42no—
158C22×C4×C11—42no—
159C22×C4×C11C22×C412yes—
160C22×C4×C11C22×C412yes—
161C22×C4×C11C22×C412yes—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2411yescharacteristic
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—42no—
172C22×Dic11—82no—
173C11×C4⋊C4—28no—
174C11×C4⋊C4—28no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4C22×C414yes—
177C11×C22⋊C4—24no—
178C11×C22⋊C4—28no—
179C11×C22⋊C4—28no—
180C42×C11—24no—
181C22⋊Dic11—42no—
182C22⋊Dic11—82no—
183C22⋊Dic11—82no—
184C4⋊Dic11—22no—
185C4⋊Dic11—22no—
186C4⋊Dic11—22no—
187C4⋊Dic11—22no—
188C4⋊Dic11—42no—
189C4×Dic11—42no—
190#4318—44no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—44no—
198C2×#536D1111yescharacteristic
199C2×#408—111no—
200#2311—111no—
201#1894—112no—
202#1892—112no—
203#1873—112no—
204#1872—112no—
205#1825—112no—
206#1787—112no—
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11C2×C22⋊C412yes—
220C23×C11C2×C22⋊C412yes—
221C23×C11C2×C22⋊C412yes—
222C23×C11C22×D411yescharacteristic
223Q8×C11—24no—
224Q8×C11—24no—
225Q8×C11—44no—
226Q8×C11—48no—
227Q8×C11—42no—
228Q8×C11—42no—
229D4×C11—44no—
230D4×C11—44no—
231D4×C11—44no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—48no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11C2×C22⋊C412yes—
258C2×C4×C11C2×C22⋊C412yes—
259C2×C4×C11C2×C22⋊C412yes—
260C2×C4×C11C23×C411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11H(5,𝔽2)11yescharacteristic
263C2×C4×C11H(5,𝔽2)11yescharacteristic
264C2×C4×C11H(5,𝔽2)11yescharacteristic
265C2×C4×C11H(5,𝔽2)11yescharacteristic
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—84no—
273C11⋊C8—42no—
274C11⋊C8—42no—
275C22×#41C2×D1111yescharacteristic
276C23×Q8C2×D1111yescharacteristic
277C22×M16—111no—
278C23×C8—111no—
279#536—24no—
280#536Dic1118yescomplemented
281C2×C4⋊Q8—21no—
282C2×#124—21no—
283C2×#123—21no—
284C2×#123—21no—
285C2×C22⋊Q8C2×D1112yes—
286C2×C22⋊Q8C2×D1112yes—
287C2×#117—111no—
288C2×#117C2×D1111yescharacteristic
289C22×C4⋊C4—111no—
290C2×#103—112no—
291C2×#103—112no—
292C2×#103—112no—
293C2×#103—112no—
294#408—224no—
295C2×C22⋊C8—112no—
296C2×C22⋊C8—112no—
297#391—221no—
298#390—221no—
299#386—221no—
300#386—221no—
301#380—112no—
302#380—112no—
303#340—112no—
304#340—112no—
305#340—112no—
306#340—112no—
307C22×C11—22no—
308C22×C11—22no—
309C22×C11—22no—
310C22×C11—24no—
311C22×C11—24no—
312C22×C11—24no—
313C22×C11—41no—
314C22×C11—41no—
315C22×C11—41no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11C22×C22⋊C411yescharacteristic
323C22×C11#53411yescharacteristic
324C22×C11#53411yescharacteristic
325C22×C11#57712yes—
326C22×C11#57812yes—
327C4×C11—22no—
328C4×C11—22no—
329C4×C11—22no—
330C4×C11—44no—
331C4×C11—44no—
332C4×C11#51811yescharacteristic
333C4×C11#51811yescharacteristic
334C4×C11#53411yescharacteristic
335C4×C11#53411yescharacteristic
336Dic11—82no—
337Dic11—82no—
338C2×#41—41no—
339C2×#41—41no—
340C2×#41—41no—
341C2×#41—41no—
342C2×#41C2×Dic1114yes—
343C2×#41C22⋊D1114yes—
344C22×Q8—21no—
345C22×Q8—22no—
346C22×Q8—41no—
347C22×Q8—41no—
348C22×Q8—41no—
349C22×Q8—41no—
350C22×Q8C2×Dic1114yescomplemented
351C22×Q8C22⋊D1111yescharacteristic
352C22×Q8C22×D1112yes—
353C22×D4C22⋊D1111yescharacteristic
354C22×D4C22⋊D1111yescharacteristic
355C22×D4C22⋊D1111yescharacteristic
356C23×C4—21no—
357C23×C4—221no—
358C23×C4C22×D1111yescharacteristic
359C23×C4C22×D1111yescharacteristic
360C23×C4C22×D1111yescharacteristic
361C2×M16—222no—
362C2×M16—441no—
363C2×M16—441no—
364C22×C8—112no—
365C22×C8—112no—
366C22×C8—222no—
367C22×C8—441no—
368C22×C8—441no—
369C4⋊Q8—28no—
370#124—28no—
371#123—28no—
372#123—28no—
373C22⋊Q8—24no—
374C22⋊Q8—24no—
375C22⋊Q8C2×Dic1118yes—
376C22⋊Q8C2×Dic1118yescomplemented
377#117—22no—
378#117—441no—
379#117—441no—
380#117C2×Dic1114yescomplemented
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—112no—
384C2×C4⋊C4—112no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4—441no—
387C2×C4⋊C4—441no—
388C2×C4⋊C4C22×D1112yes—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—222no—
394C2×C22⋊C4—222no—
395C2×C42—21no—
396C2×C42—221no—
397#103—442no—
398#103—442no—
399#103—442no—
400#103—442no—
401C22⋊C8—224no—
402C22⋊C8—224no—
403#95—222no—
404#95—222no—
405C2×C11—42no—
406C2×C11—42no—
407C2×C11—42no—
408C2×C11#230811yescharacteristic
409C2×C11#289812yes—
410C2×C11#320011yescharacteristic
411C2×C11#320112yes—
412C2×C11#320211yescharacteristic
413C24C2×C22⋊D1111yescharacteristic
414C24C2×C22⋊D1111yescharacteristic
415C24C2×C22⋊D1111yescharacteristic
416#41—44no—
417#41—44no—
418#41—44no—
419#41—44no—
420C2×Q8—24no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—41no—
427C2×Q8—41no—
428C2×Q8—44no—
429C2×Q8—44no—
430C2×Q8—42no—
431C2×Q8—42no—
432C2×Q8—44no—
433C2×Q8—44no—
434C2×Q8C22⋊Dic1114yes—
435C2×Q8C22×Dic1114yes—
436C2×D4—41no—
437C2×D4—41no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4C22⋊Dic1114yes—
443C2×D4C22⋊Dic1114yes—
444C2×D4C22⋊Dic1114yes—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—442no—
465C22×C4—882no—
466C22×C4C22×Dic1112yes—
467C22×C4C22×Dic1112yes—
468C22×C4C22×Dic1112yes—
469C22×C4C2×C22⋊D1111yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C2×C22⋊D1112yes—
473C22×C4C2×C22⋊D1112yes—
474C22×C4C2×C22⋊D1112yes—
475C22×C4C23×D1111yescharacteristic
476M16—444no—
477C2×C8—222no—
478C2×C8—222no—
479C2×C8—222no—
480C2×C8—222no—
481C2×C8—222no—
482C2×C8—222no—
483C2×C8—444no—
484C4⋊C4—28no—
485C4⋊C4—28no—
486C4⋊C4—22no—
487C4⋊C4—222no—
488C4⋊C4—222no—
489C4⋊C4—222no—
490C4⋊C4—222no—
491C4⋊C4—442no—
492C4⋊C4C22×Dic1114yes—
493C22⋊C4—24no—
494C22⋊C4—28no—
495C22⋊C4—28no—
496C22⋊C4—442no—
497C22⋊C4—882no—
498C22⋊C4—882no—
499C42—24no—
500C42—442no—
501C11#2177111yescharacteristic, complemented, Sylow
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—21no—
507C23—21no—
508C23—22no—
509C23—22no—
510C23—22no—
511C23—22no—
512C23—22no—
513C23—22no—
514C23C2×C22⋊Dic1112yes—
515C23C2×C22⋊Dic1112yes—
516C23C2×C22⋊Dic1112yes—
517C23C22×C22⋊D1111yescharacteristic
518Q8—24no—
519Q8—24no—
520Q8—44no—
521Q8—48no—
522Q8—42no—
523Q8—42no—
524D4—44no—
525D4—44no—
526D4—44no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—48no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—442no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—884no—
559C2×C4C2×C22⋊Dic1112yes—
560C2×C4C2×C22⋊Dic1112yes—
561C2×C4C2×C22⋊Dic1112yes—
562C2×C4#6703711yescharacteristic
563C2×C4#6703711yescharacteristic
564C2×C4#6703711yescharacteristic
565C2×C4#6703711yescharacteristic
566C2×C4C23×Dic1111yescharacteristic
567C2×C4C22×C22⋊D1111yescharacteristic
568C8—442no—
569C8—442no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—24no—
574C22—24no—
575C22—24no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—42no—
580C22—42no—
581C22—42no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22#1062333511yescharacteristic
586C22#1062333511yescharacteristic
587C22#1062336812yes—
588C22#1062336912yes—
589C22C22×C22⋊Dic1111yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—44no—
594C4—44no—
595C4—882no—
596C4—882no—
597C4#1062332911yescharacteristic
598C4#1062332911yescharacteristic
599C4#1062333511yescharacteristic
600C4#1062333511yescharacteristic
601C2—42no—
602C2—42no—
603C2—42no—
604C2#1307119411yescharacteristic
605C2#1307714912yes—
606C2#1307948311yescharacteristic
607C2#1307949812yes—
608C2#1307950711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#536C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenterC2×#536D11
hypocenterC11#21771
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
3. #13069050C2semidirect
4. #13069040C2semidirect
5. #13068929C2semidirect
6. #13068924C2semidirect
7. #13068711C2semidirect
8. #13068551C2semidirect
13. C11×#536C4semidirect
54. C22×Q8×C11C2×C4semidirect
72. C11×C22⋊Q8C2×C4semidirect
74. C11×#117C2×C4semidirect
280. #536Dic11semidirect
350. C22×Q8C2×Dic11semidirect
376. C22⋊Q8C2×Dic11semidirect
380. #117C2×Dic11semidirect
501. C11#21771semidirect

Maximal subgroups

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

subgroupindex
C2×#106228472
#130712082
#130690502
#130690402
#130689292
#130689242
#130687112
#130685512
C2×C11×#5362
#2177111