Finite Group Databasebeta

← #14725631

Subgroups — #14725631

Order 2816.

656 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079211C211yesmaximal, characteristic
2#13077620C211yesmaximal, characteristic, complemented
3#13077362C211yesmaximal, characteristic, complemented
4#13067531C211yesmaximal, characteristic, complemented
5#13067508C211yesmaximal, characteristic, complemented
6#13067496C211yesmaximal, characteristic, complemented
7#13067482C211yesmaximal, characteristic, complemented
8#13067454C211yesmaximal, characteristic, complemented
9#13067447C211yesmaximal, characteristic, complemented
10#13067430C211yesmaximal, characteristic, complemented
11C8×D88C211yesmaximal, characteristic, complemented
12#13067368C211yesmaximal, characteristic, complemented
13#13067034C211yesmaximal, characteristic, complemented
14#13067030C211yesmaximal, characteristic, complemented
15C11×#1455C211yesmaximal, characteristic, complemented
16C2×#66960—21no—
17#10623010C2211yescharacteristic
18#10623008C2211yescharacteristic
19C4×C11×M16C2211yescharacteristic
20C4×C11×M16C2211yescharacteristic
21C4×C11×M16C2211yescharacteristic
22#10622748C411yescharacteristic
23#10622748C411yescharacteristic
24#10622747C411yescharacteristic
25#10622747C411yescharacteristic
26#10622742—21no—
27#10622741—21no—
28#10622740—21no—
29#10622538C2211yescharacteristic
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31#10622327C411yescharacteristic
32#10622326C411yescharacteristic
33#10622325C411yescharacteristic
34#10622322—21no—
35#10622321—21no—
36#10622319—21no—
37#10622319—21no—
38#10622315C411yescharacteristic
39C4×D88C2211yescharacteristic
40C4×D88C2211yescharacteristic
41C4×#4314C2211yescharacteristic
42C4×#4314C2211yescharacteristic
43#10622301C2211yescharacteristic
44#10622301C2211yescharacteristic
45#10622301C2211yescharacteristic
46C8×D44C2211yescharacteristic
47C8×D44C2211yescharacteristic
48C8×D44C2211yescharacteristic
49#10622292C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#322C2211yescharacteristic
52C11×#322C2211yescharacteristic
53C11×#322C2211yescharacteristic
54C82×C11C2211yescharacteristic
55#10622097C2211yescharacteristic
56#10622097C2211yescharacteristic
57#10622097C2211yescharacteristic
58#10622097C2211yescharacteristic
59#10622097C2211yescharacteristic
60#10622097C2211yescharacteristic
61#10622096C2211yescharacteristic
62#10622096C2211yescharacteristic
63#10622095C2211yescharacteristic
64#10622095C2211yescharacteristic
65#10622094C2211yescharacteristic
66#10622094C2211yescharacteristic
67C2×#4339—21no—
68C2×C11×M16—21no—
69C2×C11×M16C2×C411yescharacteristic
70C2×C11×M16C2×C411yescharacteristic
71C2×C11×M16D411yescharacteristic
72C2×C11×M16D411yescharacteristic
73C2×C42×C11C2311yescharacteristic
74#66983—21no—
75#66983C2×C411yescharacteristic
76#66983C2×C411yescharacteristic
77#66983C2×C411yescharacteristic
78#66982—21no—
79C4×C22⋊D11—21no—
80#66977C2×C411yescharacteristic
81C22×C11⋊C8—21no—
82#66960—44no—
83C2×D88C2×C411yescharacteristic
84C2×D88C2×C411yescharacteristic
85C2×#4314C2×C411yescharacteristic
86C2×#4314C2×C411yescharacteristic
87C2×#4313—21no—
88C2×#4313—21no—
89C2×#4313—21no—
90C2×C8×D11—21no—
91C2×C8×D11—21no—
92C2×C8×D11—21no—
93#66929—21no—
94#66928—21no—
95#66928C2×C411yescharacteristic
96#66927C2×C411yescharacteristic
97C4×D44—21no—
98C4×D44C2311yescharacteristic
99C4×D44C2311yescharacteristic
100C4×D44C2311yescharacteristic
101#66925—21no—
102#66923C2×C411yescharacteristic
103#66922C2×C411yescharacteristic
104C4×Dic22C2311yescharacteristic
105C11×#97—21no—
106C11×#97C2×C411yescharacteristic
107C11×#97C2×C411yescharacteristic
108C11×#97D411yescharacteristic
109C11×#97D411yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112C4×C8×C11C2311yescharacteristic
113C4×C8×C11C2311yescharacteristic
114C4×C8×C11C2311yescharacteristic
115C4×C8×C11C2311yescharacteristic
116C22⋊(C11⋊C8)—21no—
117#66885C2×C411yescharacteristic
118#66885C2×C411yescharacteristic
119#66885C2×C411yescharacteristic
120#66885C2×C411yescharacteristic
121#66885C2×C411yescharacteristic
122#66885C2×C411yescharacteristic
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8—21no—
125(C2×D11)⋊C8—21no—
126(C2×D11)⋊C8—21no—
127(C2×D11)⋊C8—21no—
128(C2×D11)⋊C8—21no—
129#66882C2×C411yescharacteristic
130#66882C2×C411yescharacteristic
131#66881C2×C411yescharacteristic
132#66881C2×C411yescharacteristic
133#66880C2×C411yescharacteristic
134#66880C2×C411yescharacteristic
135#66879—21no—
136Dic11⋊C8—21no—
137Dic11⋊C8—21no—
138C8×Dic11—21no—
139C4⋊(C11⋊C8)—21no—
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4⋊(C11⋊C8)C2311yescharacteristic
144C4×C11⋊C8—21no—
145#18076—111nomaximal, Sylow
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11#4111yescharacteristic
149C2×C22⋊D11—21no—
150C2×C22⋊D11—21no—
151C2×C22⋊D11—21no—
152#4339—42no—
153#4339—42no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44C22×C411yescharacteristic
157C2×D44C22×C411yescharacteristic
158C2×D44C22×C411yescharacteristic
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×Dic22—21no—
163C2×Dic22C22×C411yescharacteristic
164C11×M16—22no—
165C11×M16—22no—
166C11×M16—41no—
167C11×M16—41no—
168C11×M16—42no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11C22×C411yescharacteristic
172C2×C8×C11C22×C411yescharacteristic
173C2×C8×C11C22×C411yescharacteristic
174C2×C8×C11C22×C411yescharacteristic
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C2×C8×C11C2×D411yescharacteristic
178C2×C8×C11C2×D411yescharacteristic
179C42×C11C22×C411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11#4111yescharacteristic
182C42×C11C2411yescharacteristic
183C22⋊Dic11—21no—
184(C2×D11)⋊C4—21no—
185(C2×D11)⋊C4—21no—
186(C2×D11)⋊C4—21no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191(C2×D11)⋊C4—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11C22×C411yescharacteristic
194C4⋊Dic11C22×C411yescharacteristic
195C4⋊Dic11C22×C411yescharacteristic
196C4⋊Dic11C22×C411yescharacteristic
197Dic11⋊C4—21no—
198Dic11⋊C4—21no—
199Dic11⋊C4—21no—
200Dic11⋊C4—21no—
201C4×Dic11—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—42no—
207D88—22no—
208D88—41no—
209#4314—22no—
210#4314—41no—
211#4313—42no—
212#4313—42no—
213#4313—42no—
214C8×D11—42no—
215C8×D11—42no—
216C8×D11—42no—
217#3171—111no—
218#2969—111no—
219#2935—111no—
220#1594—111no—
221#1590—111no—
222#1588—111no—
223#1586—111no—
224#1582—111no—
225#1581—111no—
226SD16⋊C8—111no—
227C8×D8—111no—
228#1565—111no—
229#1484—111no—
230#1483—111no—
231#1455D1111yescharacteristic, complemented
232C23×C11C4×D411yescharacteristic
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11C4×D411yescharacteristic
242C2×C4×C11C4×D411yescharacteristic
243C2×C4×C11C4×D411yescharacteristic
244C2×C4×C11C23×C411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C22⋊D11—42no—
248C22⋊D11—42no—
249C22⋊D11—81no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255D44—21no—
256D44—21no—
257D44—21no—
258D44—21no—
259D44—21no—
260D44—21no—
261D44—42no—
262D44—81no—
263C4×D11—41no—
264C4×D11—41no—
265C4×D11—41no—
266C4×D11—41no—
267C4×D11—41no—
268C4×D11—41no—
269Dic22—21no—
270Dic22—21no—
271Dic22—42no—
272C8×C11—22no—
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—21no—
276C8×C11—21no—
277C8×C11—21no—
278C8×C11—21no—
279C8×C11—41no—
280C8×C11#13112yescomplemented
281C8×C11AGL(1,ℤ/8)12yes—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C11⋊C8—41no—
286C2×#131—221no—
287#532—111no—
288#529—111no—
289#501—111no—
290#496—111no—
291#490—111no—
292#489—111no—
293#469—111no—
294#469—111no—
295#468—111no—
296#468—111no—
297#446—111no—
298C8×Q8—111no—
299C4×SD16—111no—
300C4×SD16—111no—
301C4×D8—111no—
302C4×D8—111no—
303#436—111no—
304#436—111no—
305#436—111no—
306#436—221no—
307#435—221no—
308#435—221no—
309#435—221no—
310C8×D4—111no—
311C8×D4—111no—
312C8×D4—111no—
313#433—221no—
314#431—111no—
315C2×C4⋊C8—111no—
316#408—221no—
317#405—221no—
318C4×M16C2×D1111yescharacteristic
319C4×M16C2×D1111yescharacteristic
320C4×M16C2×D1111yescharacteristic
321#335—111no—
322#335—111no—
323#334—111no—
324#334—111no—
325Q8⋊C8—111no—
326Q8⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331D4⋊C8—111no—
332D4⋊C8—111no—
333#322C2×D1111yescharacteristic
334#322C2×D1111yescharacteristic
335#322C2×D1111yescharacteristic
336C82C2×D1111yescharacteristic
337C22×C11—21no—
338C22×C11—21no—
339C22×C11—21no—
340C22×C11C2×C4×D411yescharacteristic
341C2×D11—41no—
342C2×D11—41no—
343C2×D11—41no—
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—41no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11C2×#13111yescharacteristic
355C4×C11#56811yescharacteristic
356C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
357C4×C11#57511yescharacteristic
358Dic11—41no—
359Dic11—41no—
360Dic11—41no—
361Dic11—41no—
362Dic11—41no—
363C2×#41—221no—
364C2×SD16—111no—
365C2×SD16—111no—
366C2×D8—111no—
367C2×D8—111no—
368#131—444no—
369C2×M16—21no—
370C2×M16—221no—
371C2×M16—221no—
372C2×M16—221no—
373C2×M16C4×D1111yescharacteristic
374C2×M16C4×D1111yescharacteristic
375C2×M16D4411yescharacteristic
376C2×M16D4411yescharacteristic
377C22×C8—221no—
378C22×C8—221no—
379C22×C8—221no—
380C22×C8—221no—
381C4⋊Q8—111no—
382#127—111no—
383#126—221no—
384#125—111no—
385#124—111no—
386#124—221no—
387#123—221no—
388C22⋊Q8—111no—
389#121—111no—
390#121—111no—
391#121—111no—
392#121—221no—
393C4×Q8—111no—
394C4×D4—111no—
395C4×D4—111no—
396C4×D4—111no—
397C4×D4—221no—
398C4×D4—221no—
399#117—221no—
400C2×C42C22×D1111yescharacteristic
401#107—111no—
402#107—111no—
403#106—111no—
404#106—111no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—111no—
408C4⋊C8—111no—
409C4⋊C8—221no—
410C4⋊C8—221no—
411C4⋊C8—221no—
412#103—111no—
413#103—111no—
414#102—111no—
415#102—111no—
416#102—111no—
417#102—111no—
418#102—111no—
419#102—111no—
420C22⋊C8—221no—
421C22⋊C8—221no—
422C22⋊C8—221no—
423C22⋊C8—221no—
424C22⋊C8—221no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427#97—21no—
428#97—221no—
429#97C4×D1111yescharacteristic
430#97C4×D1111yescharacteristic
431#97D4411yescharacteristic
432#97D4411yescharacteristic
433C4×C8—221no—
434C4×C8—221no—
435C4×C8C22×D1111yescharacteristic
436C4×C8C22×D1111yescharacteristic
437C4×C8C22×D1111yescharacteristic
438C4×C8C22×D1111yescharacteristic
439C4×C8C22×D1111yescharacteristic
440C4×C8C22×D1111yescharacteristic
441C2×C11—41no—
442C2×C11#293511yescharacteristic
443C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
444C2×C11#295611yescharacteristic
445D11—81no—
446D11—81no—
447D11—81no—
448#41—442no—
449#41—442no—
450C2×Q8—111no—
451C2×Q8—221no—
452C2×D4—111no—
453C2×D4—111no—
454C2×D4—111no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4C2×C4×D1111yescharacteristic
464C22×C4C2×D4411yescharacteristic
465C22×C4#433911yescharacteristic
466SD16—222no—
467SD16—441no—
468D8—222no—
469D8—441no—
470M16—22no—
471M16—22no—
472M16—41no—
473M16—41no—
474M16—42no—
475M16—442no—
476M16—442no—
477M16—442no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—442no—
485C2×C8—442no—
486C2×C8—442no—
487C2×C8—442no—
488C2×C8C2×C4×D1111yescharacteristic
489C2×C8C2×C4×D1111yescharacteristic
490C2×C8C2×C4×D1111yescharacteristic
491C2×C8C2×C4×D1111yescharacteristic
492C2×C8C2×D4411yescharacteristic
493C2×C8C2×D4411yescharacteristic
494C2×C8C2×D4411yescharacteristic
495C2×C8C2×D4411yescharacteristic
496C4⋊C4—111no—
497C4⋊C4—111no—
498C4⋊C4—111no—
499C4⋊C4—111no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C22⋊C4—221no—
506C22⋊C4—221no—
507C22⋊C4—221no—
508C22⋊C4—221no—
509C22⋊C4—221no—
510C22⋊C4—221no—
511C22⋊C4—221no—
512C22⋊C4—221no—
513C22⋊C4—221no—
514C42—221no—
515C42C2×C4×D1111yescharacteristic
516C42C2×D4411yescharacteristic
517C42#433911yescharacteristic
518C42C23×D1111yescharacteristic
519C11#1807611yescharacteristic, complemented, Sylow
520C23—221no—
521C23—221no—
522C23—221no—
523C23C4×D4411yescharacteristic
524Q8—221no—
525Q8—221no—
526Q8—442no—
527D4—221no—
528D4—221no—
529D4—221no—
530D4—221no—
531D4—221no—
532D4—221no—
533D4—442no—
534D4—442no—
535D4—442no—
536D4—881no—
537D4—881no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4C4×D4411yescharacteristic
555C2×C4C4×D4411yescharacteristic
556C2×C4C4×D4411yescharacteristic
557C2×C4C22×C4×D1111yescharacteristic
558C2×C4C22×D4411yescharacteristic
559C2×C4C2×#433911yescharacteristic
560C8—22no—
561C8—21no—
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—41no—
568C8—441no—
569C8—441no—
570C8—441no—
571C8—441no—
572C8#6696012yescomplemented
573C8#6696112yes—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—441no—
578C22—441no—
579C22—441no—
580C22—441no—
581C22—441no—
582C22—441no—
583C22—441no—
584C22—441no—
585C22—441no—
586C22C2×C4×D4411yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—441no—
592C4—441no—
593C4—441no—
594C4—441no—
595C4—441no—
596C4C2×#6696011yescharacteristic
597C4#1062327611yescharacteristic
598C4C2×#6696111yescharacteristic
599C4#1062327911yescharacteristic
600C2—41no—
601C2—881no—
602C2—881no—
603C2—881no—
604C2#1307736211yescharacteristic
605C2C4×#6696111yescharacteristic
606C2#1307752711yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1455C2
socleC22×C11C2×C4×D4
prime radical#13079211C2
cosocleC42×C11C24
hypercenter#1455D11
hypocenterC11#18076
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #1455

Complements

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

NH ≅ G/Ntype
2. #13077620C2semidirect
3. #13077362C2semidirect
4. #13067531C2semidirect
5. #13067508C2semidirect
6. #13067496C2semidirect
7. #13067482C2semidirect
8. #13067454C2semidirect
9. #13067447C2semidirect
10. #13067430C2semidirect
11. C8×D88C2semidirect
12. #13067368C2semidirect
13. #13067034C2semidirect
14. #13067030C2semidirect
15. C11×#1455C2semidirect
231. #1455D11semidirect
280. C8×C11#131semidirect
519. C11#18076semidirect
572. C8#66960semidirect

Maximal subgroups

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

subgroupindex
#130792112
#130776202
#130773622
#130675312
#130675082
#130674962
#130674822
#130674542
#130674472
#130674302
C8×D882
#130673682
#130670342
#130670302
C11×#14552
#1807611