Finite Group Databasebeta

← #14765172

Subgroups — #14765172

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077834C211yesmaximal, characteristic
2#13077310C211yesmaximal, characteristic, complemented
3#13069503C212yesmaximal, complemented
4#13069323C212yesmaximal, complemented
5#13069261C212yesmaximal, complemented
6#13068946C212yesmaximal, complemented
7#13068918C211yesmaximal, characteristic, complemented
8#13068821C211yesmaximal, characteristic, complemented
9#13068560C211yesmaximal, characteristic, complemented
10C8×C22⋊Dic11C211yesmaximal, characteristic, complemented
11C2×C11×#408C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C23×C8×C11C2211yescharacteristic
15C2×#67003C2212yes—
16#10623322C2211yescharacteristic
17C2×#66954C2211yescharacteristic, complemented
18C11×#408—21no—
19C11×#408—21no—
20C11×#408C2212yes—
21C11×#408C2212yes—
22C2×C11×C22⋊C8—21no—
23C2×C11×C22⋊C8—21no—
24#10622852C412yescomplemented
25#10622851C412yescomplemented
26C2×#66901C2212yes—
27C2×#66901C2212yes—
28#10622846C2212yes—
29#10622841C411yescharacteristic, complemented
30#10622840C411yescharacteristic, complemented
31#10622831C411yescharacteristic, complemented
32#10622830C411yescharacteristic, complemented
33C4×C22⋊Dic11C2211yescharacteristic
34#10622820C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×#66889C2212yescomplemented
37C2×#66886C2212yescomplemented
38#10622724—21no—
39#10622724—21no—
40#10622723C2211yescharacteristic, complemented
41C8×C22⋊D11—21no—
42C8×C22⋊D11—21no—
43#10622715C2211yescharacteristic, complemented
44#10622714C2211yescharacteristic, complemented
45C2×C8×Dic11C2212yescomplemented
46#10622196C2212yescomplemented
47#10622193C2212yescomplemented
48#10622188C2212yescomplemented
49C2×C11×#41—21no—
50C2×C11×#41—21no—
51C2×C11×#41—42no—
52C2×C11×#41—42no—
53C2×C11×#41C2×C412yes—
54C2×C11×#41C2312yes—
55C22×Q8×C11C2×C411yescharacteristic
56C22×D4×C11—21no—
57C22×D4×C11C2×C411yescharacteristic
58C23×C4×C11—21no—
59C23×C4×C11C2311yescharacteristic
60C2×#4339C2311yescharacteristic
61C2×C11×M16—21no—
62C2×C11×M16—42no—
63C2×C11×M16C2312yes—
64C22×C8×C11—21no—
65C22×C8×C11—42no—
66C22×C8×C11D411yescharacteristic
67C22×C8×C11D411yescharacteristic
68C22×C8×C11D411yescharacteristic
69C22×C8×C11D411yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72#67006—21no—
73C2×C22⋊Dic11—21no—
74#67003—42no—
75#67003—42no—
76C2×#4326C2×C412yes—
77C2×#4325C2×C412yes—
78C2×#4324C2×C412yes—
79C2×#4323C2×C412yes—
80#66983C2×C411yescharacteristic
81#66983C2×C411yescharacteristic
82#66982—21no—
83C4×C22⋊D11—21no—
84C4×C22⋊D11—21no—
85#66979C2311yescharacteristic
86#66977C2×C411yescharacteristic
87#66977C2×C411yescharacteristic
88C2×C4×Dic11C2312yes—
89C2×#4318C2311yescharacteristic
90C2×#4318C2311yescharacteristic
91C22×C11⋊C8C2312yes—
92#66954—42no—
93C2×#4313—21no—
94C2×C8×D11—21no—
95C11×C22⋊C8—22no—
96C11×C22⋊C8—22no—
97C11×C22⋊C8—22no—
98C11×C22⋊C8—22no—
99#66901—42no—
100#66901—42no—
101#66899C2×C412yes—
102#66899C2×C412yes—
103#66896C2×C412yes—
104#66896C2×C412yes—
105C11⋊#95—21no—
106C22⋊(C11⋊C8)—21no—
107C22⋊(C11⋊C8)—21no—
108C22⋊(C11⋊C8)C2×C411yescharacteristic
109C22⋊(C11⋊C8)C2×C411yescharacteristic
110C22⋊(C11⋊C8)C2×C412yes—
111#66889—42no—
112#66886—42no—
113(C2×D11)⋊C8—21no—
114(C2×D11)⋊C8—21no—
115#66879—21no—
116Dic11⋊C8—21no—
117Dic11⋊C8—21no—
118C8×Dic11—21no—
119C8×Dic11—42no—
120#22060—111nomaximal, Sylow
121C24×C11—21no—
122C24×C11#4111yescharacteristic
123C11×#41—22no—
124C11×#41—22no—
125C11×#41—22no—
126C11×#41—22no—
127C11×#41—42no—
128C11×#41—42no—
129C11×#41—44no—
130C11×#41—42no—
131C11×#41—42no—
132C2×Q8×C11—21no—
133C2×Q8×C11—42no—
134C2×Q8×C11C22×C412yes—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—21no—
138C2×D4×C11—42no—
139C2×D4×C11—44no—
140C2×D4×C11C22×C412yes—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—21no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11#4111yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C2×C22⋊D11—21no—
155C2×C22⋊D11—21no—
156C2×C22⋊D11—21no—
157C22×Dic11—22no—
158#4339—22no—
159#4339—22no—
160C2×D44C22×C411yescharacteristic
161C2×C4×D11—21no—
162C2×Dic22C22×C411yescharacteristic
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—42no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—41no—
170C2×C8×C11—41no—
171C2×C8×C11—41no—
172C2×C8×C11—41no—
173C2×C8×C11—42no—
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C2×C8×C11C2×D411yescharacteristic
178C22⋊Dic11—24no—
179C22⋊Dic11—21no—
180C22⋊Dic11—21no—
181C22⋊Dic11—21no—
182#4326—42no—
183#4325—42no—
184#4324—42no—
185#4323—42no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188C4⋊Dic11C22×C411yescharacteristic
189C4⋊Dic11C22×C411yescharacteristic
190Dic11⋊C4—21no—
191Dic11⋊C4—21no—
192C4×Dic11—21no—
193C4×Dic11—22no—
194C4×Dic11—22no—
195#4318—22no—
196#4318—22no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8C22×C412yes—
202C2×C11⋊C8C22×C412yes—
203#4313—42no—
204C8×D11—42no—
205#3002—111no—
206#2929—111no—
207C2×#408D1111yescharacteristic, complemented
208#1974—112no—
209#1937—112no—
210#1929—112no—
211#1876—112no—
212#1871—111no—
213#1855—111no—
214#1789—111no—
215C8×C22⋊C4—111no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—41no—
220C23×C11—42no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11C4×D411yescharacteristic
224C23×C11C4×D411yescharacteristic
225C23×C11C2×#4111yescharacteristic
226C22×D11—21no—
227Q8×C11—22no—
228Q8×C11—22no—
229Q8×C11—42no—
230D4×C11—22no—
231D4×C11—22no—
232D4×C11—42no—
233D4×C11—44no—
234D4×C11—42no—
235D4×C11—42no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—44no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11C4×D411yescharacteristic
249C2×C4×C11C4×D411yescharacteristic
250C2×C4×C11C23×C411yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C2×C4×C11H(5,𝔽2)12yes—
253C2×C4×C11H(5,𝔽2)12yes—
254C22⋊D11—42no—
255C22⋊D11—42no—
256C22⋊D11—42no—
257C2×Dic11—24no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263D44—22no—
264C4×D11—41no—
265C4×D11—41no—
266Dic22—22no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—21no—
270C8×C11—21no—
271C8×C11—42no—
272C11⋊C8—22no—
273C11⋊C8—22no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C22×#41C2×D1111yescharacteristic
277C2×#135—112no—
278C2×#131—111no—
279C22×M16C2×D1111yescharacteristic
280C23×C8C2×D1111yescharacteristic
281#525—111no—
282#452—112no—
283#451—111no—
284#450—111no—
285#449—112no—
286#448—111no—
287#447—111no—
288#435—221no—
289#435—221no—
290C8×D4—221no—
291C8×D4—221no—
292C2×#108—112no—
293#424—111no—
294C2×#104—112no—
295C2×#104—112no—
296C2×#104—112no—
297#416—112no—
298#408—21no—
299#408—21no—
300#408—111no—
301#408C2×D1112yes—
302#408C2×D1112yes—
303#407—111no—
304C2×C22⋊C8—21no—
305C2×C22⋊C8—21no—
306C2×C22⋊C8—111no—
307#405—111no—
308C2×C4×C8—112no—
309C4×C22⋊C4—111no—
310#341—112no—
311#339—112no—
312#336—112no—
313C22×C11—21no—
314C22×C11—21no—
315C22×C11—21no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—44no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—84no—
325C22×C11#44312yes—
326C22×C11C2×C4×D411yescharacteristic
327C22×C11#53812yes—
328C2×D11—41no—
329C2×D11—41no—
330C2×D11—41no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—42no—
334C4×C11#51812yes—
335C4×C11#53411yescharacteristic
336C4×C11#53511yescharacteristic
337Dic11—44no—
338Dic11—41no—
339Dic11—41no—
340Dic11—41no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41—42no—
344C2×#41—42no—
345C2×#41—111no—
346C2×#41C4×D1112yes—
347C2×#41C22×D1112yes—
348C22×Q8C4×D1111yescharacteristic
349C22×D4—21no—
350C22×D4C4×D1111yescharacteristic
351C23×C4—21no—
352C23×C4C22×D1111yescharacteristic
353#135—442no—
354#135—442no—
355C2×Q16—112no—
356C2×SD16—112no—
357C2×SD16—112no—
358C2×D8—112no—
359#131—442no—
360C2×M16—21no—
361C2×M16—42no—
362C2×M16—111no—
363C2×M16—111no—
364C2×M16—221no—
365C2×M16C22×D1112yes—
366C22×C8—21no—
367C22×C8—42no—
368C22×C8—112no—
369C22×C8—221no—
370C22×C8C22⋊D1111yescharacteristic
371C22×C8C22⋊D1111yescharacteristic
372C22×C8C22⋊D1111yescharacteristic
373C22×C8C22⋊D1111yescharacteristic
374C22×C8C22×D1111yescharacteristic
375C22×C8C22×D1111yescharacteristic
376#123—221no—
377C22⋊Q8—111no—
378C22⋊Q8—111no—
379#121—111no—
380#121—111no—
381#120—221no—
382C4×D4—221no—
383C4×D4—221no—
384#117—111no—
385C2×C22⋊C4—221no—
386C2×C42—112no—
387#108—442no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390#104—442no—
391#104—442no—
392#104—442no—
393#103—112no—
394#103—112no—
395#102—112no—
396#102—112no—
397C22⋊C8—22no—
398C22⋊C8—22no—
399C22⋊C8—22no—
400C22⋊C8—22no—
401C22⋊C8—111no—
402C22⋊C8—111no—
403C22⋊C8—112no—
404C22⋊C8—221no—
405C22⋊C8—221no—
406C22⋊C8—221no—
407C22⋊C8—221no—
408#97—221no—
409C4×C8—221no—
410C4×C8—442no—
411#95—221no—
412C2×C11—22no—
413C2×C11—22no—
414C2×C11—41no—
415C2×C11—82no—
416C2×C11#232111yescharacteristic
417C2×C11C2×#44311yescharacteristic
418C2×C11#295511yescharacteristic
419D11—81no—
420C24—21no—
421C24#433911yescharacteristic
422#41—22no—
423#41—22no—
424#41—22no—
425#41—22no—
426#41—42no—
427#41—42no—
428#41—44no—
429#41—42no—
430#41—42no—
431#41—222no—
432#41—222no—
433C2×Q8—21no—
434C2×Q8—42no—
435C2×Q8—111no—
436C2×Q8C2×C4×D1112yes—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—21no—
440C2×D4—42no—
441C2×D4—44no—
442C2×D4—111no—
443C2×D4—221no—
444C2×D4—221no—
445C2×D4—221no—
446C2×D4C2×C4×D1112yes—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—222no—
455C22×C4—221no—
456C22×C4C2×C4×D1111yescharacteristic
457C22×C4C2×C4×D1111yescharacteristic
458C22×C4#433911yescharacteristic
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461C22×C4C23×D1111yescharacteristic
462Q16—442no—
463SD16—442no—
464SD16—442no—
465D8—442no—
466M16—22no—
467M16—22no—
468M16—42no—
469M16—222no—
470M16—222no—
471M16—442no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—42no—
480C2×C8—112no—
481C2×C8—112no—
482C2×C8—222no—
483C2×C8—222no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—442no—
487C2×C8C2×C22⋊D1111yescharacteristic
488C2×C8C2×C22⋊D1111yescharacteristic
489C2×C8C2×C22⋊D1111yescharacteristic
490C2×C8C2×C22⋊D1111yescharacteristic
491C4⋊C4—111no—
492C4⋊C4—111no—
493C4⋊C4—221no—
494C4⋊C4—221no—
495C22⋊C4—224no—
496C22⋊C4—221no—
497C22⋊C4—221no—
498C22⋊C4—221no—
499C22⋊C4—221no—
500C22⋊C4—221no—
501C42—221no—
502C42—222no—
503C42—222no—
504C11#2206011yescharacteristic, complemented, Sylow
505C23—22no—
506C23—22no—
507C23—22no—
508C23—41no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—221no—
513C23C4×C22⋊D1111yescharacteristic
514C23C4×C22⋊D1111yescharacteristic
515C23C2×#433911yescharacteristic
516Q8—22no—
517Q8—22no—
518Q8—42no—
519Q8—222no—
520D4—22no—
521D4—22no—
522D4—42no—
523D4—44no—
524D4—42no—
525D4—42no—
526D4—222no—
527D4—442no—
528D4—442no—
529D4—442no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—44no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—224no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—442no—
547C2×C4—442no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4C4×C22⋊D1111yescharacteristic
551C2×C4C4×C22⋊D1111yescharacteristic
552C2×C4C22×C4×D1111yescharacteristic
553C2×C4#6703712yes—
554C2×C4#6703712yes—
555C2×C4C22×C22⋊D1111yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—42no—
561C8—222no—
562C8—222no—
563C8—441no—
564C8—441no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—44no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—84no—
577C22—441no—
578C22—441no—
579C22—441no—
580C22#1062275712yes—
581C22#1062302512yes—
582C22C2×C4×C22⋊D1111yescharacteristic
583C4—21no—
584C4—21no—
585C4—42no—
586C4—444no—
587C4—441no—
588C4—441no—
589C4—441no—
590C4#1062301712yes—
591C4#1062333511yescharacteristic
592C4#1062333611yescharacteristic
593C2—22no—
594C2—22no—
595C2—41no—
596C2—82no—
597C2—881no—
598C2#1307127411yescharacteristic
599C2C2×#1062275711yescharacteristic
600C2#1307751711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#408C2
socleC22×C11C2×C4×D4
prime radical#13077834C2
cosocleC22×C4×C11C24
hypercenterC2×#408D11
hypocenterC11#22060
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C8 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
2. #13077310C2semidirect
3. #13069503C2semidirect
4. #13069323C2semidirect
5. #13069261C2semidirect
6. #13068946C2semidirect
7. #13068918C2semidirect
8. #13068821C2semidirect
9. #13068560C2semidirect
10. C8×C22⋊Dic11C2semidirect
11. C2×C11×#408C2semidirect
17. C2×#66954C22semidirect
24. #10622852C4semidirect
25. #10622851C4semidirect
29. #10622841C4semidirect
30. #10622840C4semidirect
31. #10622831C4semidirect
32. #10622830C4semidirect
36. C2×#66889C22semidirect
37. C2×#66886C22semidirect
40. #10622723C22semidirect
43. #10622715C22semidirect
44. #10622714C22semidirect
45. C2×C8×Dic11C22semidirect
46. #10622196C22semidirect
47. #10622193C22semidirect
48. #10622188C22semidirect
207. C2×#408D11semidirect
504. C11#22060semidirect

Maximal subgroups

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

subgroupindex
#130778342
#130773102
#130695032
#130693232
#130692612
#130689462
#130689182
#130688212
#130685602
C8×C22⋊Dic112
C2×C11×#4082
#2206011