Finite Group Databasebeta

← #25067968

Subgroups — #25067968

Order 11008.

606 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144624C211yesmaximal, characteristic
2#19143681C211yesmaximal, characteristic, complemented
3#19143660C211yesmaximal, characteristic
4#19133482C211yesmaximal, characteristic, complemented
5#19133472C211yesmaximal, characteristic, complemented
6#19133453C211yesmaximal, characteristic, complemented
7#19133436C211yesmaximal, characteristic, complemented
8#19133429C211yesmaximal, characteristic, complemented
9#19133409C211yesmaximal, characteristic, complemented
10#19133398C211yesmaximal, characteristic, complemented
11#19133374C211yesmaximal, characteristic, complemented
12#19133062C211yesmaximal, characteristic
13#19132988C211yesmaximal, characteristic, complemented
14#19132896C211yesmaximal, characteristic, complemented
15C43×#1592C211yesmaximal, characteristic, complemented
16#14583446C2211yescharacteristic
17C4×Q8×D43C2211yescharacteristic
18#14583219C411yescharacteristic
19#14583216C411yescharacteristic
20#14583183C411yescharacteristic
21#14583182C411yescharacteristic
22#14583098C411yescharacteristic
23#14583097C411yescharacteristic
24#14583039C411yescharacteristic
25#14583036C411yescharacteristic
26#14583030C2211yescharacteristic
27#14583028—21no—
28#14583027—21no—
29C8×Dic86C2211yescharacteristic
30#14583023C2211yescharacteristic
31C4×#10621873C2211yescharacteristic
32C4×#10621884C2211yescharacteristic
33C4×#10621883C2211yescharacteristic
34#14582976C2211yescharacteristic
35#14582975—21no—
36C8×D172C2211yescharacteristic
37D4×C43⋊C8C2211yescharacteristic
38(C22⋊D43)⋊C8—21no—
39#14582955C2211yescharacteristic
40#14582954—21no—
41#14582951—21no—
42#14582951C2211yescharacteristic
43#14582950C2211yescharacteristic
44#14582950C2211yescharacteristic
45#14582950C2211yescharacteristic
46#14582867—21no—
47#14582864—21no—
48#14582652C2211yescharacteristic
49#14582649C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582631C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54#14582628C2211yescharacteristic
55D4⋊(C43⋊C8)C2211yescharacteristic
56#14582626C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582620C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C43×#446C2211yescharacteristic
61C4×SD16×C43C2211yescharacteristic
62C43×#436C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#10621898—21no—
68C2×Q8×D43C2×C411yescharacteristic
69C2×#10621873C2×C411yescharacteristic
70C2×#10621883C2×C411yescharacteristic
71C2×#10621884C2×C411yescharacteristic
72C2×#10621872—21no—
73C22×C43⋊C8—21no—
74C2×C8×D43—21no—
75#13063324C2×C411yescharacteristic
76#13063321C2×C411yescharacteristic
77#13063311—21no—
78#13063300C2×C411yescharacteristic
79#13063298—21no—
80#13063296C2×C411yescharacteristic
81Q8×Dic43C2×C411yescharacteristic
82C4×Dic86—21no—
83C4×Dic86C2311yescharacteristic
84#13063290—21no—
85#13063290C2×C411yescharacteristic
86C4×D172C2311yescharacteristic
87C4×C22⋊D43—21no—
88C4⋊C4×D43—21no—
89C4⋊C4×D43C2×C411yescharacteristic
90C42×D43—21no—
91C42×D43C2311yescharacteristic
92#13063257C2×C411yescharacteristic
93#13063256C2×C411yescharacteristic
94#13063256C2×C411yescharacteristic
95C4⋊(C43⋊C8)—21no—
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98Dic43⋊C8—21no—
99Dic43⋊C8—21no—
100Dic43⋊C8—21no—
101Dic43⋊C8C2×C411yescharacteristic
102Dic43⋊C8C2×C411yescharacteristic
103Dic43⋊C8D411yescharacteristic
104Dic43⋊C8D411yescharacteristic
105#13063250C2×C411yescharacteristic
106#13063249C2×C411yescharacteristic
107#13063248C2×C411yescharacteristic
108#13063247C2×C411yescharacteristic
109#13063246C2×C411yescharacteristic
110#13063245C2×C411yescharacteristic
111C22⋊(C43⋊C8)—21no—
112(C2×D43)⋊C8—21no—
113(C2×D43)⋊C8—21no—
114(C2×D43)⋊C8—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8—21no—
117(C2×D43)⋊C8C2×C411yescharacteristic
118(C2×D43)⋊C8C2×C411yescharacteristic
119(C2×D43)⋊C8D411yescharacteristic
120(C2×D43)⋊C8D411yescharacteristic
121#13063236—21no—
122#13063235—21no—
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×SD16×C43C2×C411yescharacteristic
130C2×M16×C43—21no—
131C4×Q8×C43C2311yescharacteristic
132C4×D4×C43C2311yescharacteristic
133#106×C43C2×C411yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43C2×C411yescharacteristic
138#102×C43C2×C411yescharacteristic
139C22⋊C8×C43—21no—
140#97×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C22×C411yescharacteristic
145C2×D4×C43C22×C411yescharacteristic
146C22×C4×C43—21no—
147C2×C22⋊D43—21no—
148C2×C22⋊D43—21no—
149C2×C22⋊D43—21no—
150Q8×D43—22no—
151Q8×D43—41no—
152#10621898—81no—
153#10621898—81no—
154C2×D172—21no—
155C2×D172C22×C411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43C22×C411yescharacteristic
160C2×C4×D43C2×D411yescharacteristic
161C2×C4×D43#4111yescharacteristic
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86C22×C411yescharacteristic
165SD16×C43—41no—
166M16×C43—81no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43C22×C411yescharacteristic
171C2×C8×C43C22×C411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C4⋊C4×C43—21no—
175C4⋊C4×C43C22×C411yescharacteristic
176C4⋊C4×C43C22×C411yescharacteristic
177C22⋊C4×C43—21no—
178C42×C43—21no—
179C42×C43C2411yescharacteristic
180C22⋊Dic43—21no—
181#10621884—41no—
182#10621883—22no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43C22×C411yescharacteristic
187C4⋊Dic43C22×C411yescharacteristic
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43C22×C411yescharacteristic
196C4×Dic43C2×D411yescharacteristic
197C4×Dic43#4111yescharacteristic
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—81no—
202C2×C43⋊C8C22×C411yescharacteristic
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206#10621873—22no—
207#10621872—81no—
208C8×D43—81no—
209C23×C43—21no—
210C22×D43—21no—
211C22×D43C4×D411yescharacteristic
212Q8×C43—21no—
213Q8×C43—21no—
214D4×C43—21no—
215D4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43C23×C411yescharacteristic
222C2×C4×C43C22×D411yescharacteristic
223C2×C4×C43C2×#4111yescharacteristic
224C22⋊D43—42no—
225C22⋊D43—81no—
226C22⋊D43—81no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43C4×D411yescharacteristic
231C2×Dic43C4×D411yescharacteristic
232C2×Dic43C4×D411yescharacteristic
233D172—21no—
234D172—21no—
235D172—81no—
236C4×D43—21no—
237C4×D43—21no—
238C4×D43—21no—
239C4×D43—21no—
240C4×D43—41no—
241C4×D43—42no—
242C4×D43—42no—
243C4×D43—41no—
244C4×D43—41no—
245Dic86—21no—
246Dic86—42no—
247Dic86—81no—
248Dic86#13112yes—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—21no—
252C8×C43—21no—
253C8×C43—41no—
254C8×C43—41no—
255C8×C43—41no—
256C43⋊C8—21no—
257C43⋊C8—21no—
258C43⋊C8—21no—
259C43⋊C8—21no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262C43⋊C8—41no—
263#18030—431nomaximal, Sylow
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43C2×C4×D411yescharacteristic
268C2×D43—21no—
269C2×D43—21no—
270C2×D43—21no—
271C2×D43—41no—
272C2×D43—41no—
273C2×D43—41no—
274C4×C43—21no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43C2×#13111yescharacteristic
279C4×C43#56811yescharacteristic
280C4×C43#57711yescharacteristic
281C4×C43#57711yescharacteristic
282Dic43—22no—
283Dic43—21no—
284Dic43—21no—
285Dic43—21no—
286Dic43—41no—
287Dic43—41no—
288#3103—431no—
289#2984—431no—
290#2979—431no—
291#1592D4311yescharacteristic, complemented
292#1590—431no—
293#1588—431no—
294#1585—431no—
295#1583—431no—
296#1582—431no—
297SD16⋊C8—431no—
298C8×SD16—431no—
299#1572—431no—
300#1496—431no—
301#1479—431no—
302#1454—431no—
303C2×C43—81no—
304C2×C43#293311yescharacteristic
305C2×C43#294911yescharacteristic
306C2×C43#295511yescharacteristic
307D43—41no—
308D43—81no—
309#532—431no—
310C2×C4×Q8—431no—
311#481—431no—
312#481—431no—
313#475—431no—
314#475—431no—
315#460—431no—
316#460—431no—
317#448—431no—
318#448—431no—
319#446—431no—
320#446—861no—
321#446—861no—
322#446C2×D4311yescharacteristic
323C8×Q8—431no—
324C8×Q8—431no—
325C4×SD16—431no—
326C4×SD16—431no—
327C4×SD16—431no—
328C4×SD16C2×D4311yescharacteristic
329#436—431no—
330#436—861no—
331#436C2×D4311yescharacteristic
332C8×D4—431no—
333C8×D4—431no—
334C8×D4—861no—
335#432—431no—
336#432—861no—
337#431—431no—
338#431—431no—
339#431—431no—
340#431—431no—
341#431—861no—
342#408—861no—
343#408—861no—
344#335—431no—
345#335C2×D4311yescharacteristic
346#334—431no—
347#334—431no—
348Q8⋊C8—431no—
349Q8⋊C8—431no—
350Q8⋊C8—431no—
351Q8⋊C8C2×D4311yescharacteristic
352D4⋊C8—431no—
353D4⋊C8—431no—
354D4⋊C8—431no—
355D4⋊C8C2×D4311yescharacteristic
356#322—431no—
357#322—431no—
358#322C2×D4311yescharacteristic
359C82—431no—
360C43#1803011yescharacteristic, complemented, Sylow
361C2×#41—861no—
362C22×Q8—431no—
363C2×SD16—431no—
364C2×SD16—431no—
365C2×SD16—431no—
366C2×SD16C4×D4311yescharacteristic
367C2×M16—21no—
368C2×M16—861no—
369C22×C8—861no—
370C22×C8—861no—
371C4⋊Q8—431no—
372#127—431no—
373#124—861no—
374#121—431no—
375#121—431no—
376#121—861no—
377C4×Q8—431no—
378C4×Q8—431no—
379C4×Q8—431no—
380C4×Q8—861no—
381C4×Q8—861no—
382C4×Q8C22×D4311yescharacteristic
383C4×D4—431no—
384C4×D4—861no—
385C4×D4C22×D4311yescharacteristic
386C2×C4⋊C4—431no—
387C2×C4⋊C4—861no—
388C2×C42—431no—
389C2×C42—861no—
390#106—431no—
391#106—431no—
392#106—431no—
393#106C4×D4311yescharacteristic
394C4⋊C8—21no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8—861no—
405C4⋊C8C22×D4311yescharacteristic
406C4⋊C8C22×D4311yescharacteristic
407#103—431no—
408#103—431no—
409#103—431no—
410#103C4×D4311yescharacteristic
411#102—431no—
412#102—431no—
413#102—431no—
414#102C4×D4311yescharacteristic
415C22⋊C8—21no—
416C22⋊C8—431no—
417C22⋊C8—431no—
418C22⋊C8—431no—
419C22⋊C8—431no—
420C22⋊C8—861no—
421C22⋊C8—861no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426#97—21no—
427#97—861no—
428#97—861no—
429C4×C8—431no—
430C4×C8—431no—
431C4×C8—431no—
432C4×C8—861no—
433C4×C8—861no—
434C4×C8—861no—
435C4×C8C22×D4311yescharacteristic
436C4×C8C22×D4311yescharacteristic
437C4×C8C22×D4311yescharacteristic
438#41—3441no—
439#41—3441no—
440C2×Q8—431no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×Q8—862no—
444C2×Q8—1721no—
445C2×Q8C2×C4×D4311yescharacteristic
446C2×D4—431no—
447C2×D4—861no—
448C2×D4—861no—
449C2×D4—861no—
450C2×D4—861no—
451C2×D4C2×C4×D4311yescharacteristic
452C22×C4—21no—
453C22×C4—431no—
454C22×C4—431no—
455C22×C4—431no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459SD16—41no—
460SD16—862no—
461SD16—862no—
462SD16—1721no—
463M16—81no—
464M16—3441no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—431no—
469C2×C8—431no—
470C2×C8—431no—
471C2×C8—431no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—861no—
475C2×C8—3441no—
476C2×C8—3441no—
477C2×C8C2×C4×D4311yescharacteristic
478C2×C8C2×C4×D4311yescharacteristic
479C2×C8D4×D4311yescharacteristic
480C2×C8D4×D4311yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—431no—
483C4⋊C4—431no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4C2×C4×D4311yescharacteristic
490C4⋊C4C2×C4×D4311yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—861no—
493C22⋊C4—861no—
494C22⋊C4—861no—
495C42—21no—
496C42—431no—
497C42—431no—
498C42—431no—
499C42—861no—
500C42—861no—
501C42—861no—
502C42C23×D4311yescharacteristic
503C23—21no—
504C23—431no—
505C23—861no—
506Q8—21no—
507Q8—21no—
508Q8—432no—
509Q8—861no—
510Q8—3441no—
511Q8—1722no—
512D4—21no—
513D4—21no—
514D4—861no—
515D4—861no—
516D4—3441no—
517D4—3441no—
518D4—3441no—
519D4—1722no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—431no—
526C2×C4—431no—
527C2×C4—431no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—1721no—
536C2×C4—1722no—
537C2×C4—1722no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4C22×C4×D4311yescharacteristic
541C2×C4C2×D4×D4311yescharacteristic
542C2×C4#41×D4311yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—21no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—861no—
551C8—861no—
552C8—861no—
553C8—861no—
554C8—1721no—
555C8—1721no—
556C8—1721no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—861no—
561C22—861no—
562C22—861no—
563C22—1721no—
564C22—1721no—
565C22—1721no—
566C22C4×D4×D4311yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—861no—
572C4—861no—
573C4—861no—
574C4—862no—
575C4—1721no—
576C4—1721no—
577C4#131×D4311yescharacteristic
578C4#1458366511yescharacteristic
579C4#1458370811yescharacteristic
580C4#1458370911yescharacteristic
581C2—81no—
582C2—3441no—
583C2—1721no—
584C2#1914332411yescharacteristic
585C2#1914345111yescharacteristic
586C2#1914349511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1592C2
socleC22×C43C2×C4×D4
prime radical#14583446C22
cosocleC42×C43C24
hypercenter#1592D43
hypocenterC43#18030
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1592

Complements

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

NH ≅ G/Ntype
2. #19143681C2semidirect
4. #19133482C2semidirect
5. #19133472C2semidirect
6. #19133453C2semidirect
7. #19133436C2semidirect
8. #19133429C2semidirect
9. #19133409C2semidirect
10. #19133398C2semidirect
11. #19133374C2semidirect
13. #19132988C2semidirect
14. #19132896C2semidirect
15. C43×#1592C2semidirect
291. #1592D43semidirect
360. C43#18030semidirect

Maximal subgroups

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

subgroupindex
#191446242
#191436812
#191436602
#191334822
#191334722
#191334532
#191334362
#191334292
#191334092
#191333982
#191333742
#191330622
#191329882
#191328962
C43×#15922
#1803043