Finite Group Databasebeta

← #14765177

Subgroups — #14765177

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#13077832C211yesmaximal, characteristic
2#13077311C211yesmaximal, characteristic, complemented
3C2×#10622742C211yesmaximal, characteristic, complemented
4#13069501C212yesmaximal, complemented
5#13069321C212yesmaximal, complemented
6#13069262C212yesmaximal, complemented
7#13068941C212yesmaximal, complemented
8#13068821C211yesmaximal, characteristic, complemented
9#13068561C211yesmaximal, characteristic, complemented
10C22⋊C4×C11⋊C8C211yesmaximal, characteristic, complemented
11C11×#1871C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C11×#525C2211yescharacteristic
15C2×#67003C2212yes—
16C2×#67001C2211yescharacteristic, complemented
17C23×C11⋊C8C2211yescharacteristic
18C2×C11×#104C2212yescomplemented
19C4×C11×C22⋊C4C2211yescharacteristic
20#10622847C2211yescharacteristic, complemented
21#10622820C2211yescharacteristic
22C2×C22⋊(C11⋊C8)C2211yescharacteristic
23#10622742—21no—
24#10622742—21no—
25#10622742C2212yes—
26#10622742C2212yes—
27C2×#66886C2212yescomplemented
28C2×(C2×D11)⋊C8—21no—
29C2×(C2×D11)⋊C8—21no—
30#10622663C411yescharacteristic, complemented
31#10622660C412yescomplemented
32#10622659C411yescharacteristic, complemented
33#10622653C411yescharacteristic, complemented
34#10622650C412yescomplemented
35#10622649C411yescharacteristic, complemented
36#10622624—21no—
37#10622624—21no—
38D4×C11⋊C8—21no—
39D4×C11⋊C8—21no—
40#10622615C2212yes—
41#10622612C2211yescharacteristic, complemented
42#10622610C2211yescharacteristic, complemented
43C2×#66869C2212yes—
44C2×#66869C2212yes—
45C2×C4×C11⋊C8C2212yescomplemented
46C11×#339C2212yescomplemented
47#10622196C2212yescomplemented
48#10622162C2212yescomplemented
49C2×C11×#41C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C22×C22⋊D11—21no—
52C2×#4339—21no—
53C2×#4339—21no—
54C2×#4339—42no—
55C2×#4339—42no—
56C2×#4339C2×C412yes—
57C2×#4339C2312yes—
58C22×D44C2×C411yescharacteristic
59C22×C4×D11—21no—
60C22×Dic22C2×C411yescharacteristic
61C2×C11×M16—21no—
62C2×C11×M16—42no—
63C2×C11×M16C2312yes—
64C22×C8×C11—21no—
65C11×#123—21no—
66C11×C22⋊Q8C2×C411yescharacteristic
67C11×C22⋊Q8C2×C411yescharacteristic
68C11×#121C2×C411yescharacteristic
69C11×#121C2×C411yescharacteristic
70C11×#120—21no—
71C4×D4×C11—21no—
72C4×D4×C11—21no—
73C11×#117C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C42×C11C2312yes—
76#67003—42no—
77#67003—42no—
78#67001—42no—
79C2×#4326C2×C412yes—
80C2×#4325C2×C412yes—
81C2×#4324C2×C412yes—
82C2×#4323C2×C412yes—
83C2×#4318—21no—
84C2×#4318C2311yescharacteristic
85C2×#4318C2311yescharacteristic
86C22×C11⋊C8—21no—
87C22×C11⋊C8—42no—
88C22×C11⋊C8D411yescharacteristic
89C22×C11⋊C8D411yescharacteristic
90C22×C11⋊C8D411yescharacteristic
91C22×C11⋊C8D411yescharacteristic
92C22×C11⋊C8C2312yes—
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C11×#104—42no—
96C11×#95—21no—
97C22⋊(C11⋊C8)—21no—
98C22⋊(C11⋊C8)—21no—
99C22⋊(C11⋊C8)—21no—
100C22⋊(C11⋊C8)—21no—
101C22⋊(C11⋊C8)C2×C411yescharacteristic
102C22⋊(C11⋊C8)C2×C412yes—
103C22⋊(C11⋊C8)C2×C411yescharacteristic
104#66886—42no—
105(C2×D11)⋊C8—22no—
106(C2×D11)⋊C8—22no—
107(C2×D11)⋊C8—22no—
108(C2×D11)⋊C8—22no—
109#66874C2×C412yes—
110#66874C2×C412yes—
111#66873C2×C412yes—
112#66873C2×C412yes—
113#66869—42no—
114#66869—42no—
115C4⋊(C11⋊C8)—21no—
116C4⋊(C11⋊C8)—21no—
117#66867—21no—
118C4×C11⋊C8—21no—
119C4×C11⋊C8—42no—
120#22060—111nomaximal, Sylow
121C24×C11#4111yescharacteristic
122C23×D11—21no—
123C11×#41—22no—
124C11×#41—22no—
125C2×Q8×C11C22×C411yescharacteristic
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11C22×C411yescharacteristic
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11#4111yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C2×C22⋊D11—22no—
141C2×C22⋊D11—22no—
142C2×C22⋊D11—44no—
143C22×Dic11—21no—
144#4339—22no—
145#4339—22no—
146#4339—22no—
147#4339—22no—
148#4339—42no—
149#4339—42no—
150#4339—44no—
151#4339—42no—
152#4339—42no—
153C2×D44—21no—
154C2×D44—42no—
155C2×D44C22×C412yes—
156C2×C4×D11—22no—
157C2×C4×D11—22no—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×Dic22—21no—
161C2×Dic22—42no—
162C2×Dic22C22×C412yes—
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—42no—
166C2×C8×C11—22no—
167C2×C8×C11—42no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4C22×C411yescharacteristic
171C11×C4⋊C4C22×C411yescharacteristic
172C11×C22⋊C4—24no—
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C42×C11—21no—
179C42×C11—22no—
180C42×C11—22no—
181#4326—42no—
182#4325—42no—
183#4324—42no—
184#4323—42no—
185#4318—22no—
186#4318—22no—
187#4318—42no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—41no—
195C2×C11⋊C8—41no—
196C2×C11⋊C8—41no—
197C2×C11⋊C8—41no—
198C2×C11⋊C8—42no—
199C2×C11⋊C8C22×C412yes—
200C2×C11⋊C8C22×C412yes—
201C2×C11⋊C8C2×D411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203C2×C11⋊C8C2×D411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205#3002—111no—
206#2929—111no—
207C2×#408—111no—
208#1974—112no—
209#1937—112no—
210#1929—112no—
211#1876—112no—
212#1871D1111yescharacteristic, complemented
213#1855—111no—
214#1789—111no—
215C8×C22⋊C4—111no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—21no—
219C23×C11—41no—
220C23×C11C4×D411yescharacteristic
221C23×C11C4×D411yescharacteristic
222C23×C11C2×#4111yescharacteristic
223C22×D11—22no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—42no—
227Q8×C11—22no—
228D4×C11—22no—
229D4×C11—42no—
230D4×C11—42no—
231D4×C11—42no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—24no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—42no—
244C2×C4×C11—42no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11C4×D411yescharacteristic
248C2×C4×C11C4×D411yescharacteristic
249C2×C4×C11C23×C411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11H(5,𝔽2)12yes—
252C2×C4×C11H(5,𝔽2)12yes—
253C22⋊D11—44no—
254C22⋊D11—42no—
255C22⋊D11—42no—
256C2×Dic11—22no—
257C2×Dic11—42no—
258D44—22no—
259D44—22no—
260D44—42no—
261C4×D11—44no—
262C4×D11—42no—
263C4×D11—42no—
264Dic22—22no—
265Dic22—22no—
266Dic22—42no—
267C8×C11—42no—
268C11⋊C8—22no—
269C11⋊C8—22no—
270C11⋊C8—21no—
271C11⋊C8—21no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C22×#41—111no—
277C2×#135—112no—
278C2×#131—111no—
279C22×M16C2×D1111yescharacteristic
280C23×C8—111no—
281#525C2×D1111yescharacteristic
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×#104C2×D1112yescomplemented
297#416—112no—
298#408—111no—
299#408—112no—
300#408—112no—
301#408—221no—
302#408—221no—
303#407—111no—
304C2×C22⋊C8—111no—
305C2×C22⋊C8—221no—
306C2×C22⋊C8—221no—
307#405—111no—
308C2×C4×C8—112no—
309C4×C22⋊C4C2×D1111yescharacteristic
310#341—112no—
311#339C2×D1112yescomplemented
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—41no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11#44312yes—
325C22×C11C2×C4×D411yescharacteristic
326C22×C11#53812yes—
327C2×D11—42no—
328C2×D11—42no—
329C2×D11—42no—
330C2×D11—84no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—44no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11#51812yes—
338C4×C11#53411yescharacteristic
339C4×C11#53511yescharacteristic
340Dic11—42no—
341C2×#41—112no—
342C2×#41—112no—
343C2×#41—221no—
344C2×#41—221no—
345C2×#41—442no—
346C2×#41—442no—
347C2×#41C22×D1111yescharacteristic
348C22×Q8—111no—
349C22×D4—111no—
350C22×D4—221no—
351C23×C4—221no—
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—111no—
368C22×C8—111no—
369C22×C8—112no—
370C22×C8—111no—
371C22×C8—111no—
372C22×C8—111no—
373C22×C8—111no—
374C22×C8—221no—
375C22×C8—442no—
376#123—21no—
377C22⋊Q8C4×D1111yescharacteristic
378C22⋊Q8C4×D1111yescharacteristic
379#121C4×D1111yescharacteristic
380#121C4×D1111yescharacteristic
381#120—21no—
382C4×D4—21no—
383C4×D4—21no—
384#117C22×D1111yescharacteristic
385C2×C22⋊C4—21no—
386C2×C42C22×D1112yes—
387#108—442no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390#104—42no—
391#104—442no—
392#104—442no—
393#103—112no—
394#103—112no—
395#102—112no—
396#102—112no—
397C22⋊C8—111no—
398C22⋊C8—111no—
399C22⋊C8—112no—
400C22⋊C8—222no—
401C22⋊C8—222no—
402C22⋊C8—222no—
403C22⋊C8—222no—
404C22⋊C8—221no—
405C22⋊C8—221no—
406C22⋊C8—221no—
407C22⋊C8—221no—
408#97—221no—
409C4×C8—221no—
410C4×C8—442no—
411#95—21no—
412C2×C11—22no—
413C2×C11—22no—
414C2×C11—41no—
415C2×C11—81no—
416C2×C11#232111yescharacteristic
417C2×C11C2×#44311yescharacteristic
418C2×C11#295511yescharacteristic
419D11—82no—
420C24—221no—
421C24#434111yescharacteristic
422#41—22no—
423#41—22no—
424#41—222no—
425#41—222no—
426#41—222no—
427#41—222no—
428#41—442no—
429#41—442no—
430#41—444no—
431#41—442no—
432#41—442no—
433C2×Q8—112no—
434C2×Q8—221no—
435C2×Q8—442no—
436C2×Q8C2×C4×D1111yescharacteristic
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—112no—
441C2×D4—222no—
442C2×D4—222no—
443C2×D4—221no—
444C2×D4—442no—
445C2×D4—444no—
446C2×D4C2×C4×D1111yescharacteristic
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—221no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—442no—
455C22×C4—442no—
456C22×C4C2×C4×D1111yescharacteristic
457C22×C4C2×C4×D1111yescharacteristic
458C22×C4D4×D1111yescharacteristic
459C22×C4D4×D1111yescharacteristic
460C22×C4#434111yescharacteristic
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—42no—
474C2×C8—112no—
475C2×C8—112no—
476C2×C8—111no—
477C2×C8—111no—
478C2×C8—111no—
479C2×C8—111no—
480C2×C8—222no—
481C2×C8—222no—
482C2×C8—222no—
483C2×C8—222no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—441no—
487C2×C8—441no—
488C2×C8—441no—
489C2×C8—441no—
490C2×C8—442no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4C2×C4×D1111yescharacteristic
494C4⋊C4C2×C4×D1111yescharacteristic
495C22⋊C4—24no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—21no—
501C42—21no—
502C42—22no—
503C42—22no—
504C11#2206011yescharacteristic, complemented, Sylow
505C23—22no—
506C23—22no—
507C23—21no—
508C23—41no—
509C23—222no—
510C23—442no—
511C23—442no—
512C23—442no—
513C23(C22⋊D11)⋊C411yescharacteristic
514C23(C22⋊D11)⋊C411yescharacteristic
515C23C2×#434111yescharacteristic
516Q8—22no—
517Q8—222no—
518Q8—222no—
519Q8—442no—
520D4—22no—
521D4—42no—
522D4—42no—
523D4—42no—
524D4—222no—
525D4—222no—
526D4—442no—
527D4—444no—
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—24no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—222no—
546C2×C4—444no—
547C2×C4—442no—
548C2×C4—442no—
549C2×C4—442no—
550C2×C4(C22⋊D11)⋊C411yescharacteristic
551C2×C4(C22⋊D11)⋊C411yescharacteristic
552C2×C4C22×C4×D1111yescharacteristic
553C2×C4C2×D4×D1111yescharacteristic
554C2×C4#6703712yes—
555C2×C4#6704212yes—
556C8—42no—
557C8—222no—
558C8—222no—
559C8—221no—
560C8—221no—
561C8—221no—
562C8—221no—
563C8—441no—
564C8—441no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—44no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—442no—
577C22—442no—
578C22—442no—
579C22—884no—
580C22#1062243712yes—
581C22C2×(C22⋊D11)⋊C411yescharacteristic
582C22#1062314812yes—
583C4—21no—
584C4—21no—
585C4—44no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—442no—
590C4#1062307612yes—
591C4#1062312311yescharacteristic
592C4#1062318411yescharacteristic
593C2—22no—
594C2—22no—
595C2—41no—
596C2—81no—
597C2—882no—
598C2#1307127911yescharacteristic
599C2C2×#1062243711yescharacteristic
600C2#1307751511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1871C2
socleC22×C11C2×C4×D4
prime radical#13077832C2
cosocleC22×C4×C11C24
hypercenter#1871D11
hypocenterC11#22060
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
2. #13077311C2semidirect
3. C2×#10622742C2semidirect
4. #13069501C2semidirect
5. #13069321C2semidirect
6. #13069262C2semidirect
7. #13068941C2semidirect
8. #13068821C2semidirect
9. #13068561C2semidirect
10. C22⋊C4×C11⋊C8C2semidirect
11. C11×#1871C2semidirect
16. C2×#67001C22semidirect
18. C2×C11×#104C22semidirect
20. #10622847C22semidirect
27. C2×#66886C22semidirect
30. #10622663C4semidirect
31. #10622660C4semidirect
32. #10622659C4semidirect
33. #10622653C4semidirect
34. #10622650C4semidirect
35. #10622649C4semidirect
41. #10622612C22semidirect
42. #10622610C22semidirect
45. C2×C4×C11⋊C8C22semidirect
46. C11×#339C22semidirect
47. #10622196C22semidirect
48. #10622162C22semidirect
212. #1871D11semidirect
296. C2×#104C2×D11semidirect
311. #339C2×D11semidirect
504. C11#22060semidirect

Maximal subgroups

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

subgroupindex
#130778322
#130773112
C2×#106227422
#130695012
#130693212
#130692622
#130689412
#130688212
#130685612
C22⋊C4×C11⋊C82
C11×#18712
#2206011