Finite Group Databasebeta

← #25067115

Subgroups — #25067115

Order 11008.

682 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145151C211yesmaximal, characteristic
2#19143524C211yesmaximal, characteristic, complemented
3#19143302C211yesmaximal, characteristic
4#19133488C211yesmaximal, characteristic, complemented
5#19133486C211yesmaximal, characteristic, complemented
6#19133484C211yesmaximal, characteristic, complemented
7#19133482C211yesmaximal, characteristic, complemented
8C8×#10621873C211yesmaximal, characteristic, complemented
9C8×#10621884C211yesmaximal, characteristic, complemented
10C8×#10621883C211yesmaximal, characteristic, complemented
11#19133349C211yesmaximal, characteristic, complemented
12#19133048C211yesmaximal, characteristic, complemented
13#19133044C211yesmaximal, characteristic
14C82×D43C211yesmaximal, characteristic, complemented
15C8×SD16×C43C211yesmaximal, characteristic, complemented
16C2×#13063331—21no—
17#14583453C2211yescharacteristic
18#14583446C2211yescharacteristic
19#14583296C411yescharacteristic
20#14583270C411yescharacteristic
21#14583248C411yescharacteristic
22#14583244C411yescharacteristic
23#14583131C411yescharacteristic
24#14583129C411yescharacteristic
25#14583127C411yescharacteristic
26#14583125C411yescharacteristic
27#14583030C2211yescharacteristic
28#14583028—21no—
29#14583026C2211yescharacteristic
30C8×Dic86—21no—
31C8×Dic86C2211yescharacteristic
32C4×#10621873C2211yescharacteristic
33C4×#10621884C2211yescharacteristic
34C4×#10621883C2211yescharacteristic
35#14582977C2211yescharacteristic
36#14582976C2211yescharacteristic
37#14582974—21no—
38C8×D172C2211yescharacteristic
39C8×C22⋊D43—21no—
40#14582924—21no—
41#14582921C2211yescharacteristic
42#14582921C2211yescharacteristic
43#14582864—21no—
44#14582853—21no—
45C4×C8×D43C2211yescharacteristic
46C4×C8×D43C2211yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582650C2211yescharacteristic
49#14582649C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582631C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54#14582628C2211yescharacteristic
55D4⋊(C43⋊C8)C2211yescharacteristic
56#14582626C2211yescharacteristic
57C8×C43⋊C8C2211yescharacteristic
58C8×C43⋊C8C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C8×Q8×C43C2211yescharacteristic
61C4×SD16×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#334C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C82×C43C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621873C2×C411yescharacteristic
69C2×#10621883C2×C411yescharacteristic
70C2×#10621884C2×C411yescharacteristic
71#13063331—44no—
72C2×#10621877—21no—
73C2×#10621872—21no—
74C2×#10621872—21no—
75C2×#10621872—21no—
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78C2×C8×D43C2×C411yescharacteristic
79C2×C8×D43C2×C411yescharacteristic
80C2×C8×D43D411yescharacteristic
81C2×C8×D43D411yescharacteristic
82#13063324C2×C411yescharacteristic
83#13063324C2×C411yescharacteristic
84#13063323C2×C411yescharacteristic
85#13063321C2×C411yescharacteristic
86#13063315—21no—
87#13063311—21no—
88#13063305C2×C411yescharacteristic
89#13063303—21no—
90#13063301C2×C411yescharacteristic
91#13063300C2×C411yescharacteristic
92#13063298—21no—
93#13063296C2×C411yescharacteristic
94C4×Dic86—21no—
95C4×Dic86C2311yescharacteristic
96C4×D172C2311yescharacteristic
97C4×C22⋊D43—21no—
98#13063282—21no—
99C42×D43C2311yescharacteristic
100#13063257C2×C411yescharacteristic
101#13063256C2×C411yescharacteristic
102#13063256C2×C411yescharacteristic
103C4⋊(C43⋊C8)—21no—
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8—21no—
110#13063250C2×C411yescharacteristic
111#13063249C2×C411yescharacteristic
112#13063248C2×C411yescharacteristic
113#13063247C2×C411yescharacteristic
114#13063246C2×C411yescharacteristic
115#13063245C2×C411yescharacteristic
116C22⋊(C43⋊C8)—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8—21no—
119#13063236—21no—
120#13063235—21no—
121C4×C43⋊C8C2311yescharacteristic
122C4×C43⋊C8C2311yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C8×Dic43—21no—
125C8×Dic43—21no—
126C8×Dic43C2×C411yescharacteristic
127C8×Dic43C2×C411yescharacteristic
128C8×Dic43D411yescharacteristic
129C8×Dic43D411yescharacteristic
130C2×SD16×C43C2×C411yescharacteristic
131C22×C8×C43—21no—
132C4×Q8×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#106×C43C2×C411yescharacteristic
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43C2×C411yescharacteristic
139#102×C43C2×C411yescharacteristic
140C22⋊C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C2×Q8×C43C22×C411yescharacteristic
146C2×D4×C43C22×C411yescharacteristic
147C22×C4×C43—21no—
148C2×C22⋊D43—21no—
149C2×C22⋊D43—21no—
150C2×C22⋊D43—21no—
151#10621898—42no—
152#10621898—42no—
153C2×D172—21no—
154C2×D172C22×C411yescharacteristic
155C2×C4×D43—21no—
156C2×C4×D43C22×C411yescharacteristic
157C2×C4×D43C2×D411yescharacteristic
158C2×C4×D43#4111yescharacteristic
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86C22×C411yescharacteristic
162SD16×C43—22no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—42no—
167C2×C8×C43C22×C411yescharacteristic
168C2×C8×C43C22×C411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C4⋊C4×C43—21no—
172C4⋊C4×C43C22×C411yescharacteristic
173C4⋊C4×C43C22×C411yescharacteristic
174C22⋊C4×C43—21no—
175C42×C43—21no—
176C42×C43C2411yescharacteristic
177C22⋊Dic43—21no—
178#10621884—22no—
179#10621883—22no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43C22×C411yescharacteristic
186C4⋊Dic43C22×C411yescharacteristic
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193C4×Dic43—21no—
194C4×Dic43C22×C411yescharacteristic
195C4×Dic43C2×D411yescharacteristic
196C4×Dic43#4111yescharacteristic
197#10621877—42no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8C22×C411yescharacteristic
202C2×C43⋊C8C22×C411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205#10621873—22no—
206#10621872—42no—
207#10621872—42no—
208#10621872—42no—
209C8×D43—24no—
210C8×D43—22no—
211C8×D43—22no—
212C8×D43—22no—
213C8×D43—42no—
214C8×D43SD1614yescomplemented
215C23×C43—21no—
216C22×D43—21no—
217C22×D43C4×D411yescharacteristic
218Q8×C43—21no—
219Q8×C43—21no—
220D4×C43—21no—
221D4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43C23×C411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C22⋊D43—42no—
231C22⋊D43—42no—
232C22⋊D43—42no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43C4×D411yescharacteristic
237C2×Dic43C4×D411yescharacteristic
238C2×Dic43C4×D411yescharacteristic
239D172—21no—
240D172—21no—
241D172—42no—
242C4×D43—21no—
243C4×D43—21no—
244C4×D43—22no—
245C4×D43—41no—
246C4×D43—41no—
247C4×D43C2×SD1612yes—
248C4×D43#13512yes—
249Dic86—21no—
250Dic86—21no—
251Dic86—42no—
252Dic86—42no—
253C8×C43—22no—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—41no—
257C8×C43—41no—
258C8×C43#13112yescomplemented
259C8×C43C2×SD1612yes—
260C43⋊C8—22no—
261C43⋊C8—21no—
262C43⋊C8—21no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265C43⋊C8#13112yescomplemented
266C43⋊C8C2×SD1612yes—
267#17957—431nomaximal, Sylow
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43C2×C4×D411yescharacteristic
272C2×D43—21no—
273C2×D43—21no—
274C2×D43—41no—
275C2×D43—41no—
276C2×D43—41no—
277C2×D43C4×SD1612yes—
278C4×C43—21no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43C2×#13111yescharacteristic
283C4×C43C2×#13111yescharacteristic
284C4×C43C22×SD1611yescharacteristic
285C4×C43C2×#13511yescharacteristic
286Dic43—21no—
287Dic43—41no—
288Dic43—41no—
289Dic43—41no—
290Dic43C4×SD1612yes—
291Dic43#44312yes—
292#3167—431no—
293#2960—431no—
294#2931—431no—
295#1590—431no—
296#1590—431no—
297#1590—431no—
298#1590—431no—
299C8×SD16—431no—
300C8×SD16—431no—
301C8×SD16—431no—
302C8×SD16D4311yescharacteristic, complemented
303#1566—431no—
304#1493—431no—
305#1492—431no—
306C2×C82—431no—
307C2×C43—81no—
308C2×C43#293111yescharacteristic
309C2×C43C2×C4×SD1611yescharacteristic
310C2×C43C2×#44311yescharacteristic
311D43—22no—
312D43—81no—
313C2×#131—861no—
314#533—431no—
315#532—431no—
316#498—431no—
317#492—431no—
318#487—431no—
319#486—431no—
320#465—431no—
321#465—431no—
322#465—431no—
323#465—431no—
324#446—431no—
325#446—431no—
326#446—861no—
327C8×Q8—431no—
328C8×Q8—861no—
329C8×Q8C2×D4311yescharacteristic
330C4×SD16—431no—
331C4×SD16—431no—
332C4×SD16—431no—
333C4×SD16C2×D4311yescharacteristic
334#436—431no—
335#436—431no—
336#436—861no—
337C8×D4—431no—
338C8×D4—861no—
339C8×D4C2×D4311yescharacteristic
340#424—861no—
341#423—431no—
342#423—431no—
343#408—861no—
344#405—861no—
345C2×C4×C8—431no—
346C2×C4×C8—431no—
347C2×C4×C8—431no—
348#334—431no—
349#334—431no—
350#334—431no—
351#334C2×D4311yescharacteristic
352Q8⋊C8—431no—
353Q8⋊C8—431no—
354Q8⋊C8—431no—
355Q8⋊C8C2×D4311yescharacteristic
356D4⋊C8—431no—
357D4⋊C8—431no—
358D4⋊C8—431no—
359D4⋊C8C2×D4311yescharacteristic
360C82—431no—
361C82—431no—
362C82—431no—
363C82C2×D4311yescharacteristic
364C43#1795711yescharacteristic, complemented, Sylow
365C2×#41—861no—
366C2×SD16—431no—
367C2×SD16—431no—
368C2×SD16—431no—
369C2×SD16C4×D4311yescharacteristic
370#131—1724no—
371C2×M16—861no—
372C2×M16—861no—
373C2×M16—861no—
374C2×M16—861no—
375C22×C8—21no—
376C22×C8—431no—
377C22×C8—431no—
378C22×C8—431no—
379C22×C8—431no—
380C22×C8—861no—
381C22×C8—861no—
382C4⋊Q8—431no—
383C4⋊Q8—431no—
384C4⋊Q8—431no—
385#127—431no—
386#125—861no—
387#124—861no—
388C22⋊Q8—431no—
389C22⋊Q8—431no—
390C22⋊Q8—861no—
391#121—431no—
392#121—431no—
393#121—861no—
394C4×Q8—431no—
395C4×Q8—861no—
396C4×Q8C22×D4311yescharacteristic
397C4×D4—431no—
398C4×D4—861no—
399C4×D4C22×D4311yescharacteristic
400#117—861no—
401C2×C42—431no—
402#106—431no—
403#106—431no—
404#106—431no—
405#106C4×D4311yescharacteristic
406C4⋊C8—21no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—861no—
410C4⋊C8—861no—
411C4⋊C8—861no—
412C4⋊C8—861no—
413C4⋊C8—861no—
414C4⋊C8C22×D4311yescharacteristic
415C4⋊C8C22×D4311yescharacteristic
416#103—431no—
417#103—431no—
418#103—431no—
419#103C4×D4311yescharacteristic
420#102—431no—
421#102—431no—
422#102—431no—
423#102C4×D4311yescharacteristic
424C22⋊C8—21no—
425C22⋊C8—861no—
426C22⋊C8—861no—
427C22⋊C8—861no—
428#97—861no—
429#97—861no—
430C4×C8—21no—
431C4×C8—431no—
432C4×C8—431no—
433C4×C8—431no—
434C4×C8—431no—
435C4×C8—431no—
436C4×C8—431no—
437C4×C8—431no—
438C4×C8—861no—
439C4×C8—861no—
440C4×C8C22×D4311yescharacteristic
441C4×C8C22×D4311yescharacteristic
442C4×C8C22×D4311yescharacteristic
443#41—1722no—
444#41—1722no—
445C2×Q8—431no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8C2×C4×D4311yescharacteristic
449C2×D4—431no—
450C2×D4—861no—
451C2×D4—861no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4C2×C4×D4311yescharacteristic
455C22×C4—21no—
456C22×C4—431no—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—861no—
460SD16—22no—
461SD16—862no—
462SD16—862no—
463SD16—862no—
464M16—1722no—
465M16—1722no—
466M16—1722no—
467M16—1722no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—42no—
472C2×C8—431no—
473C2×C8—431no—
474C2×C8—434no—
475C2×C8—431no—
476C2×C8—431no—
477C2×C8—862no—
478C2×C8—862no—
479C2×C8—864no—
480C2×C8—861no—
481C2×C8—862no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—1722no—
485C2×C8C2×C4×D4311yescharacteristic
486C2×C8C2×C4×D4311yescharacteristic
487C2×C8D4×D4311yescharacteristic
488C2×C8D4×D4311yescharacteristic
489C4⋊C4—21no—
490C4⋊C4—431no—
491C4⋊C4—431no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—861no—
499C4⋊C4C2×C4×D4311yescharacteristic
500C4⋊C4C2×C4×D4311yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—861no—
503C22⋊C4—861no—
504C22⋊C4—861no—
505C22⋊C4—861no—
506C22⋊C4—861no—
507C42—21no—
508C42—431no—
509C42—431no—
510C42—431no—
511C42—861no—
512C42C23×D4311yescharacteristic
513C23—21no—
514C23—431no—
515C23—861no—
516Q8—21no—
517Q8—21no—
518Q8—861no—
519Q8—861no—
520Q8—1722no—
521Q8—1722no—
522D4—21no—
523D4—21no—
524D4—861no—
525D4—861no—
526D4—1722no—
527D4—1722no—
528D4—1722no—
529D4—1722no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—431no—
536C2×C4—431no—
537C2×C4—432no—
538C2×C4—432no—
539C2×C4—431no—
540C2×C4—862no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4C22×C4×D4311yescharacteristic
549C2×C4C2×D4×D4311yescharacteristic
550C2×C4#41×D4311yescharacteristic
551C8—22no—
552C8—21no—
553C8—21no—
554C8—41no—
555C8—41no—
556C8—432no—
557C8—432no—
558C8—862no—
559C8—861no—
560C8—861no—
561C8—1721no—
562C8—1721no—
563C8#1306333112yescomplemented
564C8SD16×D4312yes—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—432no—
569C22—861no—
570C22—861no—
571C22—1721no—
572C22—1721no—
573C22—1721no—
574C22C4×D4×D4311yescharacteristic
575C4—21no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—432no—
580C4—432no—
581C4—861no—
582C4—1721no—
583C4—1721no—
584C4—1721no—
585C4#131×D4311yescharacteristic
586C4C2×#1306333111yescharacteristic
587C4C2×SD16×D4311yescharacteristic
588C4#135×D4311yescharacteristic
589C2—81no—
590C2—862no—
591C2—3441no—
592C2#1914330211yescharacteristic
593C2C4×SD16×D4311yescharacteristic
594C2#443×D4311yescharacteristic
subgroupG/H
centerC2×C8D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC8×SD16×C43C2
socleC22×C43C2×C4×D4
prime radical#14583446C22
cosocleC42×C43C24
hypercenterC8×SD16D43
hypocenterC43#17957
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ C8×SD16

Complements

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

NH ≅ G/Ntype
2. #19143524C2semidirect
4. #19133488C2semidirect
5. #19133486C2semidirect
6. #19133484C2semidirect
7. #19133482C2semidirect
8. C8×#10621873C2semidirect
9. C8×#10621884C2semidirect
10. C8×#10621883C2semidirect
11. #19133349C2semidirect
12. #19133048C2semidirect
14. C82×D43C2semidirect
15. C8×SD16×C43C2semidirect
214. C8×D43SD16semidirect
258. C8×C43#131semidirect
265. C43⋊C8#131semidirect
302. C8×SD16D43semidirect
364. C43#17957semidirect
563. C8#13063331semidirect

Maximal subgroups

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

subgroupindex
#191451512
#191435242
#191433022
#191334882
#191334862
#191334842
#191334822
C8×#106218732
C8×#106218842
C8×#106218832
#191333492
#191330482
#191330442
C82×D432
C8×SD16×C432
#1795743