Finite Group Databasebeta

← #14724891

Subgroups — #14724891

Order 2816.

660 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
1#13078672C211yesmaximal, characteristic
2#13077632C211yesmaximal, characteristic, complemented
3#13077361C211yesmaximal, characteristic, complemented
4#13067498C211yesmaximal, characteristic, complemented
5#13067492C211yesmaximal, characteristic, complemented
6#13067478C211yesmaximal, characteristic, complemented
7#13067458C211yesmaximal, characteristic, complemented
8#13067446C211yesmaximal, characteristic, complemented
9#13067430C211yesmaximal, characteristic, complemented
10#13067419C211yesmaximal, characteristic, complemented
11#13067398C211yesmaximal, characteristic, complemented
12#13067083C211yesmaximal, characteristic, complemented
13#13067000C211yesmaximal, characteristic, complemented
14#13066912C211yesmaximal, characteristic, complemented
15C11×#1594C211yesmaximal, characteristic, complemented
16C2×#66960—21no—
17#10623079C2211yescharacteristic
18C4×#4341C2211yescharacteristic
19C4×C11×D8C2211yescharacteristic
20C11×#436C2211yescharacteristic
21C11×#436C2211yescharacteristic
22#10622771C411yescharacteristic
23#10622763C411yescharacteristic
24#10622741—21no—
25#10622740—21no—
26M16×Dic11—21no—
27C4×#4324C2211yescharacteristic
28C4×#4323C2211yescharacteristic
29#10622625C2211yescharacteristic
30D4×C11⋊C8C2211yescharacteristic
31#10622498C411yescharacteristic
32#10622488C411yescharacteristic
33#10622451C2211yescharacteristic
34#10622448C2211yescharacteristic
35D11×C4⋊C8C2211yescharacteristic
36#10622443C2211yescharacteristic
37#10622394C411yescharacteristic
38#10622392C411yescharacteristic
39#10622375C411yescharacteristic
40#10622374C411yescharacteristic
41#10622343—21no—
42#10622342—21no—
43#10622340—21no—
44#10622332—21no—
45C4×#4314C2211yescharacteristic
46C4×#4313C2211yescharacteristic
47C8×D44C2211yescharacteristic
48#10622298C2211yescharacteristic
49#10622298C2211yescharacteristic
50C8×Dic22C2211yescharacteristic
51C11×#334C2211yescharacteristic
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic
54C11×#322C2211yescharacteristic
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic
57#10622122C2211yescharacteristic
58#10622121C2211yescharacteristic
59#10622118C2211yescharacteristic
60#10622117C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622096C2211yescharacteristic
63#10622094C2211yescharacteristic
64#10622092C2211yescharacteristic
65#10622092C2211yescharacteristic
66C8×C11⋊C8C2211yescharacteristic
67C2×#4341C2×C411yescharacteristic
68C2×#4339—21no—
69C2×C11×D8C2×C411yescharacteristic
70C2×C11×M16—21no—
71C2×C11×M16—21no—
72C4×D4×C11C2311yescharacteristic
73C4×D4×C11C2311yescharacteristic
74#66993C2×C411yescharacteristic
75#66991C2×C411yescharacteristic
76D4×Dic11C2×C411yescharacteristic
77C2×#4324C2×C411yescharacteristic
78C2×#4323C2×C411yescharacteristic
79C4×C22⋊D11—21no—
80C4×C22⋊D11—21no—
81C2×C4×Dic11—21no—
82C2×#4318—21no—
83C22×C11⋊C8—21no—
84#66960—44no—
85C2×#4314C2×C411yescharacteristic
86C2×#4313—21no—
87C2×#4313D411yescharacteristic
88C2×#4313D411yescharacteristic
89C2×C8×D11—21no—
90C2×C8×D11—21no—
91#66948C2×C411yescharacteristic
92#66945C2×C411yescharacteristic
93#66941C2×C411yescharacteristic
94#66940C2×C411yescharacteristic
95#66938—21no—
96#66937—21no—
97(C22⋊D11)⋊C4—21no—
98#66930—21no—
99C4×D44C2311yescharacteristic
100C42×D11C2311yescharacteristic
101C4×Dic22C2311yescharacteristic
102C11×#107C2×C411yescharacteristic
103C11×C4⋊C8C2311yescharacteristic
104C11×C4⋊C8C2311yescharacteristic
105C11×#102C2×C411yescharacteristic
106C11×#102C2×C411yescharacteristic
107C11×C22⋊C8—21no—
108C11×C22⋊C8—21no—
109C4×C8×C11C2311yescharacteristic
110C4×C8×C11C2311yescharacteristic
111C4×C8×C11C2311yescharacteristic
112#66896C2×C411yescharacteristic
113#66896C2×C411yescharacteristic
114C22⋊(C11⋊C8)—21no—
115C22⋊(C11⋊C8)—21no—
116#66885C2×C411yescharacteristic
117(C2×D11)⋊C8—21no—
118(C2×D11)⋊C8—21no—
119(C2×D11)⋊C8—21no—
120(C2×D11)⋊C8—21no—
121(C2×D11)⋊C8C2×C411yescharacteristic
122(C2×D11)⋊C8C2×C411yescharacteristic
123#66881C2×C411yescharacteristic
124#66880C2×C411yescharacteristic
125#66879—21no—
126#66879D411yescharacteristic
127#66879D411yescharacteristic
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130Dic11⋊C8—21no—
131Dic11⋊C8—21no—
132Dic11⋊C8C2×C411yescharacteristic
133Dic11⋊C8C2×C411yescharacteristic
134C8×Dic11—21no—
135C8×Dic11—21no—
136#66874C2×C411yescharacteristic
137#66873C2×C411yescharacteristic
138#66872C2×C411yescharacteristic
139#66871C2×C411yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145#18011—111nomaximal, Sylow
146C2×D4×C11C22×C411yescharacteristic
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C2×C22⋊D11—21no—
151C2×C22⋊D11—21no—
152C2×C22⋊D11—21no—
153C2×C22⋊D11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156#4341—22no—
157#4341—41no—
158#4339—42no—
159#4339—42no—
160C2×D44—21no—
161C2×D44C22×C411yescharacteristic
162C2×C4×D11—21no—
163C2×C4×D11C22×C411yescharacteristic
164C2×C4×D11C2×D411yescharacteristic
165C2×C4×D11#4111yescharacteristic
166C2×Dic22—21no—
167C2×Dic22C22×C411yescharacteristic
168C11×D8—41no—
169C11×M16—42no—
170C11×M16—42no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11C22×C411yescharacteristic
175C2×C8×C11C22×C411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C2×C8×C11C2×D411yescharacteristic
178C11×C4⋊C4C22×C411yescharacteristic
179C11×C4⋊C4C22×C411yescharacteristic
180C11×C22⋊C4—21no—
181C11×C22⋊C4—21no—
182C42×C11C2411yescharacteristic
183C22⋊Dic11—21no—
184C22⋊Dic11—21no—
185#4324—22no—
186#4323—41no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190C4⋊Dic11C22×C411yescharacteristic
191C4⋊Dic11C22×C411yescharacteristic
192Dic11⋊C4—21no—
193Dic11⋊C4—21no—
194Dic11⋊C4—21no—
195C4×Dic11—21no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11C22×C411yescharacteristic
199C4×Dic11C2×D411yescharacteristic
200C4×Dic11#4111yescharacteristic
201#4318—42no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—42no—
206C2×C11⋊C8C22×C411yescharacteristic
207C2×C11⋊C8C22×C411yescharacteristic
208C2×C11⋊C8C2×D411yescharacteristic
209C2×C11⋊C8C2×D411yescharacteristic
210#4314—22no—
211#4313—22no—
212#4313—41no—
213#4313—42no—
214C8×D11—42no—
215C8×D11—42no—
216#3106—111no—
217#2971—111no—
218#2935—111no—
219#1594D1111yescharacteristic, complemented
220#1589—111no—
221#1588—111no—
222#1586—111no—
223#1583—111no—
224#1581—111no—
225SD16⋊C8—111no—
226C8×SD16—111no—
227#1573—111no—
228#1496—111no—
229#1477—111no—
230#1453—111no—
231C23×C11—21no—
232C23×C11—21no—
233C22×D11—21no—
234C22×D11C4×D411yescharacteristic
235D4×C11—21no—
236D4×C11—21no—
237D4×C11—21no—
238D4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11C23×C411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C22⋊D11—42no—
249C22⋊D11—42no—
250C22⋊D11—42no—
251C22⋊D11—81no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—42no—
256C2×Dic11—81no—
257C2×Dic11C4×D411yescharacteristic
258C2×Dic11C4×D411yescharacteristic
259C2×Dic11C4×D411yescharacteristic
260D44—21no—
261D44—21no—
262D44—42no—
263C4×D11—21no—
264C4×D11—21no—
265C4×D11—21no—
266C4×D11—21no—
267C4×D11—41no—
268C4×D11—41no—
269C4×D11—41no—
270Dic22—21no—
271Dic22—42no—
272Dic22#13112yescomplemented
273C8×C11—21no—
274C8×C11—21no—
275C8×C11—21no—
276C8×C11—21no—
277C8×C11—41no—
278C8×C11—41no—
279C8×C11—41no—
280C11⋊C8—21no—
281C11⋊C8—21no—
282C11⋊C8—21no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C11⋊C8—41no—
286C11⋊C8AGL(1,ℤ/8)12yes—
287C2×#131—221no—
288#532—111no—
289C4×#41—111no—
290#482—111no—
291#482—111no—
292#477—111no—
293#476—111no—
294#460—111no—
295#459—111no—
296#449—111no—
297#449—111no—
298C8×Q8—111no—
299C8×Q8—111no—
300C4×SD16—111no—
301C4×SD16—111no—
302C4×D8—111no—
303C4×D8C2×D1111yescharacteristic
304#436—111no—
305#436—111no—
306#436—221no—
307#436—221no—
308#436C2×D1111yescharacteristic
309#436C2×D1111yescharacteristic
310#435—221no—
311#435—221no—
312C8×D4—111no—
313C8×D4—111no—
314#432—111no—
315#432—221no—
316#431—111no—
317#431—111no—
318C2×C4⋊C8—111no—
319#408—221no—
320C4×M16—111no—
321C4×M16—221no—
322#335—111no—
323#335—111no—
324#334—111no—
325#334C2×D1111yescharacteristic
326Q8⋊C8—111no—
327Q8⋊C8—111no—
328D4⋊C8—111no—
329D4⋊C8—111no—
330D4⋊C8—111no—
331D4⋊C8—111no—
332D4⋊C8C2×D1111yescharacteristic
333D4⋊C8C2×D1111yescharacteristic
334#322—111no—
335#322—111no—
336#322C2×D1111yescharacteristic
337C82—111no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11C2×C4×D411yescharacteristic
345C2×D11—21no—
346C2×D11—21no—
347C2×D11—21no—
348C2×D11—41no—
349C2×D11—41no—
350C2×D11—41no—
351C4×C11—21no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11C2×#13111yescharacteristic
355C4×C11#56811yescharacteristic
356C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
357C4×C11#57511yescharacteristic
358Dic11—22no—
359Dic11—21no—
360Dic11—21no—
361Dic11—21no—
362Dic11—41no—
363Dic11—41no—
364C2×#41—111no—
365C2×#41—221no—
366C2×SD16—111no—
367C2×SD16—111no—
368C2×D8—111no—
369C2×D8C4×D1111yescharacteristic
370#131—444no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—111no—
374C2×M16—111no—
375C2×M16—221no—
376C2×M16—221no—
377C22×C8—221no—
378C22×C8—221no—
379C22×C8—221no—
380C4⋊Q8—111no—
381#127—111no—
382#124—221no—
383#121—111no—
384#121—111no—
385#121—221no—
386C4×Q8—111no—
387C4×Q8—111no—
388C4×D4—111no—
389C4×D4—111no—
390C4×D4—221no—
391C4×D4—221no—
392C4×D4—221no—
393C4×D4C22×D1111yescharacteristic
394C4×D4C22×D1111yescharacteristic
395#117—111no—
396#117—221no—
397C2×C42—111no—
398C2×C42—221no—
399#107—111no—
400#107C4×D1111yescharacteristic
401#106—111no—
402#106—111no—
403C4⋊C8—111no—
404C4⋊C8—111no—
405C4⋊C8—111no—
406C4⋊C8—111no—
407C4⋊C8—221no—
408C4⋊C8—221no—
409C4⋊C8—221no—
410C4⋊C8—221no—
411C4⋊C8C22×D1111yescharacteristic
412C4⋊C8C22×D1111yescharacteristic
413#103—111no—
414#103—111no—
415#102—111no—
416#102—111no—
417#102—111no—
418#102—111no—
419#102C4×D1111yescharacteristic
420#102C4×D1111yescharacteristic
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—111no—
424C22⋊C8—111no—
425C22⋊C8—221no—
426C22⋊C8—221no—
427C22⋊C8—221no—
428C22⋊C8—221no—
429C22⋊C8—221no—
430C22⋊C8—221no—
431#97—111no—
432#97—111no—
433#97—221no—
434C4×C8—111no—
435C4×C8—111no—
436C4×C8—111no—
437C4×C8—221no—
438C4×C8—221no—
439C4×C8C22×D1111yescharacteristic
440C4×C8C22×D1111yescharacteristic
441C4×C8C22×D1111yescharacteristic
442C2×C11—81no—
443C2×C11—81no—
444C2×C11#293311yescharacteristic
445C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
446C2×C11#295711yescharacteristic
447D11—41no—
448D11—81no—
449#41—222no—
450#41—442no—
451#41—442no—
452#41—441no—
453C2×Q8—111no—
454C2×Q8—221no—
455C2×D4—111no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4C2×C4×D1111yescharacteristic
462C2×D4C2×C4×D1111yescharacteristic
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—221no—
471SD16—222no—
472SD16—222no—
473D8—41no—
474D8—441no—
475M16—42no—
476M16—42no—
477M16—222no—
478M16—441no—
479M16—442no—
480M16—442no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—111no—
485C2×C8—111no—
486C2×C8—111no—
487C2×C8—111no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—442no—
492C2×C8—442no—
493C2×C8—442no—
494C2×C8C2×C4×D1111yescharacteristic
495C2×C8C2×C4×D1111yescharacteristic
496C2×C8D4×D1111yescharacteristic
497C2×C8D4×D1111yescharacteristic
498C4⋊C4—111no—
499C4⋊C4—111no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4C2×C4×D1111yescharacteristic
504C4⋊C4C2×C4×D1111yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—221no—
508C22⋊C4—221no—
509C22⋊C4—221no—
510C22⋊C4—221no—
511C22⋊C4—221no—
512C42—111no—
513C42—111no—
514C42—111no—
515C42—221no—
516C42—221no—
517C42—221no—
518C42C23×D1111yescharacteristic
519C11#1801111yescharacteristic, complemented, Sylow
520C23—21no—
521C23—21no—
522C23—111no—
523C23—221no—
524Q8—112no—
525Q8—221no—
526Q8—442no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—221no—
532D4—221no—
533D4—442no—
534D4—442no—
535D4—442no—
536D4—442no—
537D4—881no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—111no—
545C2×C4—111no—
546C2×C4—111no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—441no—
555C2×C4—442no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—881no—
559C2×C4C22×C4×D1111yescharacteristic
560C2×C4C2×D4×D1111yescharacteristic
561C2×C4#41×D1111yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—41no—
567C8—41no—
568C8—41no—
569C8—112no—
570C8—221no—
571C8—221no—
572C8—221no—
573C8—441no—
574C8—441no—
575C8—441no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—221no—
583C22—221no—
584C22—221no—
585C22—441no—
586C22—441no—
587C22—441no—
588C22C4×D4×D1111yescharacteristic
589C4—21no—
590C4—41no—
591C4—41no—
592C4—221no—
593C4—221no—
594C4—222no—
595C4—221no—
596C4—441no—
597C4—441no—
598C4#1062327611yescharacteristic
599C4D11×#13111yescharacteristic
600C4D11×AGL(1,ℤ/8)11yescharacteristic
601C4#1062330411yescharacteristic
602C2—81no—
603C2—81no—
604C2—441no—
605C2—881no—
606C2#1307734511yescharacteristic
607C2#1307742711yescharacteristic
608C2#1307753011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1594C2
socleC22×C11C2×C4×D4
prime radical#13078672C2
cosocleC42×C11C24
hypercenter#1594D11
hypocenterC11#18011
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1594

Complements

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

NH ≅ G/Ntype
2. #13077632C2semidirect
3. #13077361C2semidirect
4. #13067498C2semidirect
5. #13067492C2semidirect
6. #13067478C2semidirect
7. #13067458C2semidirect
8. #13067446C2semidirect
9. #13067430C2semidirect
10. #13067419C2semidirect
11. #13067398C2semidirect
12. #13067083C2semidirect
13. #13067000C2semidirect
14. #13066912C2semidirect
15. C11×#1594C2semidirect
219. #1594D11semidirect
272. Dic22#131semidirect
519. C11#18011semidirect

Maximal subgroups

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

subgroupindex
#130786722
#130776322
#130773612
#130674982
#130674922
#130674782
#130674582
#130674462
#130674302
#130674192
#130673982
#130670832
#130670002
#130669122
C11×#15942
#1801111