Finite Group Databasebeta

← #25067220

Subgroups — #25067220

Order 11008.

622 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#19145188C211yesmaximal, characteristic
2#19143745C211yesmaximal, characteristic, complemented
3#19143669C211yesmaximal, characteristic, complemented
4#19133509C211yesmaximal, characteristic, complemented
5#19133496C211yesmaximal, characteristic, complemented
6#19133488C211yesmaximal, characteristic, complemented
7#19133477C211yesmaximal, characteristic, complemented
8#19133417C211yesmaximal, characteristic, complemented
9#19133407C211yesmaximal, characteristic, complemented
10C8×#10621873C211yesmaximal, characteristic, complemented
11#19133361C211yesmaximal, characteristic, complemented
12#19133052C211yesmaximal, characteristic, complemented
13#19133044C211yesmaximal, characteristic, complemented
14C8×#10621872C211yesmaximal, characteristic, complemented
15C8×D8×C43C211yesmaximal, characteristic, complemented
16#14583446C2211yescharacteristic
17#14583431C2211yescharacteristic
18#14583307C411yescharacteristic
19#14583287C411yescharacteristic
20#14583262C411yescharacteristic
21#14583257C411yescharacteristic
22#14583151C411yescharacteristic
23#14583149C411yescharacteristic
24#14583146C411yescharacteristic
25#14583144C411yescharacteristic
26#14583026C2211yescharacteristic
27C8×Dic86C2211yescharacteristic
28C4×#10621873C2211yescharacteristic
29C4×#10621883C2211yescharacteristic
30C4×#10621882C2211yescharacteristic
31#14582977C2211yescharacteristic
32#14582977C2211yescharacteristic
33#14582976C2211yescharacteristic
34#14582974—21no—
35#14582973—21no—
36#14582970—21no—
37#14582970—21no—
38C8×D172C2211yescharacteristic
39#14582957—21no—
40#14582955C2211yescharacteristic
41#14582950C2211yescharacteristic
42#14582925—21no—
43#14582921C2211yescharacteristic
44#14582865—21no—
45#14582864—21no—
46C4×#10621872C2211yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582651C2211yescharacteristic
49#14582650C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582631C2211yescharacteristic
52#14582629C2211yescharacteristic
53#14582628C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55D4⋊(C43⋊C8)C2211yescharacteristic
56#14582626C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582620C2211yescharacteristic
59C8×C43⋊C8C2211yescharacteristic
60C4×D8×C43C2211yescharacteristic
61C8×D4×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C82×C43C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621873C2×C411yescharacteristic
69C2×#10621883C2×C411yescharacteristic
70C2×#10621882C2×C411yescharacteristic
71C2×#10621877—21no—
72C2×#10621877—21no—
73C2×#10621872—21no—
74C2×#10621872—21no—
75C2×#10621872C2×C411yescharacteristic
76C2×#10621872C2×C411yescharacteristic
77C2×C8×D43—21no—
78C2×C8×D43—21no—
79#13063324C2×C411yescharacteristic
80#13063321C2×C411yescharacteristic
81#13063318—21no—
82#13063316C2×C411yescharacteristic
83#13063312C2×C411yescharacteristic
84#13063311—21no—
85#13063307—21no—
86#13063305C2×C411yescharacteristic
87#13063300C2×C411yescharacteristic
88#13063298—21no—
89#13063296C2×C411yescharacteristic
90#13063296C2×C411yescharacteristic
91C4×Dic86C2311yescharacteristic
92C4×D172C2311yescharacteristic
93C4×C22⋊D43—21no—
94C4×C22⋊D43—21no—
95#13063284—21no—
96C42×D43C2311yescharacteristic
97#13063258C2×C411yescharacteristic
98#13063257C2×C411yescharacteristic
99#13063256C2×C411yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102Dic43⋊C8—21no—
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8D411yescharacteristic
106Dic43⋊C8D411yescharacteristic
107#13063250C2×C411yescharacteristic
108#13063248C2×C411yescharacteristic
109#13063247C2×C411yescharacteristic
110#13063246C2×C411yescharacteristic
111#13063246C2×C411yescharacteristic
112#13063245C2×C411yescharacteristic
113C22⋊(C43⋊C8)—21no—
114C22⋊(C43⋊C8)—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8—21no—
117(C2×D43)⋊C8—21no—
118(C2×D43)⋊C8D411yescharacteristic
119(C2×D43)⋊C8D411yescharacteristic
120#13063235—21no—
121#13063235—21no—
122#13063235C2×C411yescharacteristic
123#13063235C2×C411yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C4×C43⋊C8C2311yescharacteristic
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×D8×C43C2×C411yescharacteristic
130C22×C8×C43—21no—
131C22×C8×C43—21no—
132C4×D4×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#107×C43C2×C411yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#102×C43C2×C411yescharacteristic
138#102×C43C2×C411yescharacteristic
139C22⋊C8×C43—21no—
140C22⋊C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×D4×C43C22×C411yescharacteristic
145C2×D4×C43C22×C411yescharacteristic
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C2×C22⋊D43—21no—
149C2×C22⋊D43—21no—
150C2×C22⋊D43—21no—
151C2×C22⋊D43—21no—
152#10621898—81no—
153#10621898—81no—
154C2×D172—21no—
155C2×D172C22×C411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43C22×C411yescharacteristic
158C2×C4×D43C2×D411yescharacteristic
159C2×C4×D43#4111yescharacteristic
160C2×Dic86—21no—
161C2×Dic86C22×C411yescharacteristic
162D8×C43—22no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—81no—
167C2×C8×C43—81no—
168C2×C8×C43C22×C411yescharacteristic
169C2×C8×C43C22×C411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C4⋊C4×C43C22×C411yescharacteristic
173C4⋊C4×C43C22×C411yescharacteristic
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C42×C43C2411yescharacteristic
177C22⋊Dic43—21no—
178C22⋊Dic43—21no—
179C22⋊Dic43—21no—
180C22⋊Dic43—21no—
181#10621883—22no—
182#10621882—22no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43C22×C411yescharacteristic
189C4⋊Dic43C22×C411yescharacteristic
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193C4×Dic43—21no—
194C4×Dic43C22×C411yescharacteristic
195C4×Dic43C2×D411yescharacteristic
196C4×Dic43#4111yescharacteristic
197#10621877—81no—
198#10621877—81no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8C22×C411yescharacteristic
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206#10621873—22no—
207#10621872—22no—
208#10621872—22no—
209#10621872—81no—
210#10621872—81no—
211C8×D43—42no—
212C8×D43—81no—
213C23×C43—21no—
214C23×C43—21no—
215C22×D43—21no—
216C22×D43C4×D411yescharacteristic
217D4×C43—21no—
218D4×C43—21no—
219D4×C43—21no—
220D4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43C23×C411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C22⋊D43—81no—
231C22⋊D43—81no—
232C22⋊D43—81no—
233C22⋊D43—81no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43C4×D411yescharacteristic
238C2×Dic43C4×D411yescharacteristic
239C2×Dic43C4×D411yescharacteristic
240D172—21no—
241D172—21no—
242D172—81no—
243C4×D43—21no—
244C4×D43—21no—
245C4×D43—21no—
246C4×D43—21no—
247C4×D43—41no—
248C4×D43—41no—
249C4×D43—41no—
250Dic86—21no—
251Dic86—21no—
252Dic86—81no—
253C8×C43—22no—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—41no—
258C8×C43—41no—
259C8×C43#13112yes—
260C43⋊C8—21no—
261C43⋊C8—21no—
262C43⋊C8—21no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265C43⋊C8—41no—
266C43⋊C8#13112yes—
267#17968—431nomaximal, Sylow
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—41no—
274C22×C43C2×C4×D411yescharacteristic
275C2×D43—21no—
276C2×D43—21no—
277C2×D43—21no—
278C2×D43—41no—
279C2×D43—41no—
280C2×D43—41no—
281C4×C43—21no—
282C4×C43—41no—
283C4×C43—41no—
284C4×C43C2×#13111yescharacteristic
285C4×C43C2×#13111yescharacteristic
286C4×C43#57611yescharacteristic
287C4×C43#57711yescharacteristic
288Dic43—21no—
289Dic43—21no—
290Dic43—21no—
291Dic43—41no—
292Dic43—41no—
293Dic43—41no—
294#3171—431no—
295#2993—431no—
296#2981—431no—
297#1594—431no—
298#1592—431no—
299#1590—431no—
300#1589—431no—
301#1580—431no—
302SD16⋊C8—431no—
303C8×SD16—431no—
304C8×D8D4311yescharacteristic, complemented
305#1569—431no—
306#1494—431no—
307#1492—431no—
308C8×M16—431no—
309C2×C43—81no—
310C2×C43—81no—
311C2×C43#293111yescharacteristic
312C2×C43#294611yescharacteristic
313C2×C43#295611yescharacteristic
314D43—41no—
315D43—81no—
316#532—431no—
317#529—431no—
318#501—431no—
319#496—431no—
320#490—431no—
321#489—431no—
322#469—431no—
323#469—431no—
324#468—431no—
325#468—431no—
326#446—431no—
327C8×Q8—431no—
328C4×SD16—431no—
329C4×SD16—431no—
330C4×D8—431no—
331C4×D8C2×D4311yescharacteristic
332#436—431no—
333#436—431no—
334#436—431no—
335#436—861no—
336#435—861no—
337#435—861no—
338#435—861no—
339C8×D4—431no—
340C8×D4C2×D4311yescharacteristic
341C8×D4C2×D4311yescharacteristic
342#433—861no—
343#432—431no—
344#431—431no—
345#424—861no—
346#423—431no—
347#408—861no—
348#408—861no—
349C4×M16—431no—
350C2×C4×C8—431no—
351#335—431no—
352#335C2×D4311yescharacteristic
353#334—431no—
354#334—431no—
355Q8⋊C8—431no—
356Q8⋊C8—431no—
357D4⋊C8—431no—
358D4⋊C8—431no—
359D4⋊C8—431no—
360D4⋊C8—431no—
361D4⋊C8C2×D4311yescharacteristic
362D4⋊C8C2×D4311yescharacteristic
363#322—431no—
364#322—431no—
365C82—431no—
366C82C2×D4311yescharacteristic
367C43#1796811yescharacteristic, complemented, Sylow
368C2×#41—861no—
369C2×SD16—431no—
370C2×SD16—431no—
371C2×D8—431no—
372C2×D8C4×D4311yescharacteristic
373C2×M16—431no—
374C2×M16—431no—
375C2×M16—861no—
376C2×M16—861no—
377C2×M16—861no—
378C2×M16—861no—
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—861no—
382C22×C8—861no—
383C4⋊Q8—431no—
384#127—431no—
385#126—861no—
386#125—431no—
387#124—431no—
388#124—861no—
389#123—861no—
390C22⋊Q8—431no—
391#121—431no—
392#121—431no—
393#121—431no—
394#121—861no—
395C4×Q8—431no—
396C4×D4—431no—
397C4×D4—861no—
398C4×D4—861no—
399C4×D4C22×D4311yescharacteristic
400C4×D4C22×D4311yescharacteristic
401#117—861no—
402C2×C42—431no—
403#107—431no—
404#107C4×D4311yescharacteristic
405#106—431no—
406#106—431no—
407C4⋊C8—431no—
408C4⋊C8—431no—
409C4⋊C8—431no—
410C4⋊C8—431no—
411C4⋊C8—861no—
412C4⋊C8—861no—
413C4⋊C8—861no—
414C4⋊C8C22×D4311yescharacteristic
415C4⋊C8C22×D4311yescharacteristic
416#103—431no—
417#103—431no—
418#102—431no—
419#102—431no—
420#102—431no—
421#102—431no—
422#102C4×D4311yescharacteristic
423#102C4×D4311yescharacteristic
424C22⋊C8—21no—
425C22⋊C8—21no—
426C22⋊C8—431no—
427C22⋊C8—431no—
428C22⋊C8—861no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433#97—431no—
434#97—431no—
435#97—861no—
436#97—861no—
437C4×C8—431no—
438C4×C8—431no—
439C4×C8—431no—
440C4×C8—861no—
441C4×C8—861no—
442C4×C8C22×D4311yescharacteristic
443C4×C8C22×D4311yescharacteristic
444C4×C8C22×D4311yescharacteristic
445#41—3441no—
446#41—3441no—
447C2×Q8—431no—
448C2×Q8—861no—
449C2×D4—431no—
450C2×D4—861no—
451C2×D4—861no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—861no—
455C2×D4C2×C4×D4311yescharacteristic
456C2×D4C2×C4×D4311yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—431no—
460C22×C4—431no—
461C22×C4—431no—
462C22×C4—861no—
463SD16—862no—
464SD16—862no—
465D8—22no—
466D8—862no—
467M16—862no—
468M16—862no—
469M16—3441no—
470M16—3441no—
471M16—3441no—
472M16—3441no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—81no—
477C2×C8—81no—
478C2×C8—431no—
479C2×C8—431no—
480C2×C8—431no—
481C2×C8—431no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—3441no—
486C2×C8—1722no—
487C2×C8C2×C4×D4311yescharacteristic
488C2×C8C2×C4×D4311yescharacteristic
489C2×C8D4×D4311yescharacteristic
490C2×C8D4×D4311yescharacteristic
491C4⋊C4—431no—
492C4⋊C4—431no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4C2×C4×D4311yescharacteristic
499C4⋊C4C2×C4×D4311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—861no—
503C22⋊C4—861no—
504C22⋊C4—861no—
505C22⋊C4—861no—
506C22⋊C4—861no—
507C22⋊C4—861no—
508C22⋊C4—861no—
509C42—431no—
510C42—431no—
511C42—431no—
512C42—861no—
513C42C23×D4311yescharacteristic
514C23—21no—
515C23—21no—
516C23—431no—
517C23—861no—
518Q8—861no—
519Q8—861no—
520Q8—3441no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—861no—
526D4—861no—
527D4—3441no—
528D4—3441no—
529D4—3441no—
530D4—3441no—
531D4—3441no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—431no—
539C2×C4—431no—
540C2×C4—431no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—861no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4C22×C4×D4311yescharacteristic
552C2×C4C2×D4×D4311yescharacteristic
553C2×C4#41×D4311yescharacteristic
554C8—22no—
555C8—21no—
556C8—21no—
557C8—21no—
558C8—41no—
559C8—41no—
560C8—432no—
561C8—861no—
562C8—861no—
563C8—861no—
564C8—1721no—
565C8—1721no—
566C8—1721no—
567C8#1306333112yes—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—861no—
575C22—861no—
576C22—861no—
577C22—1721no—
578C22—1721no—
579C22—1721no—
580C22C4×D4×D4311yescharacteristic
581C4—21no—
582C4—41no—
583C4—41no—
584C4—861no—
585C4—861no—
586C4—861no—
587C4—1721no—
588C4—1721no—
589C4—1721no—
590C4#131×D4311yescharacteristic
591C4C2×#1306333111yescharacteristic
592C4#1458370011yescharacteristic
593C4#1458370611yescharacteristic
594C2—81no—
595C2—81no—
596C2—3441no—
597C2—1721no—
598C2#1914330211yescharacteristic
599C2#1914342011yescharacteristic
600C2#1914350011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC8×D8×C43C2
socleC22×C43C2×C4×D4
prime radical#19145188C2
cosocleC42×C43C24
hypercenterC8×D8D43
hypocenterC43#17968
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×D8

Complements

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

NH ≅ G/Ntype
2. #19143745C2semidirect
3. #19143669C2semidirect
4. #19133509C2semidirect
5. #19133496C2semidirect
6. #19133488C2semidirect
7. #19133477C2semidirect
8. #19133417C2semidirect
9. #19133407C2semidirect
10. C8×#10621873C2semidirect
11. #19133361C2semidirect
12. #19133052C2semidirect
13. #19133044C2semidirect
14. C8×#10621872C2semidirect
15. C8×D8×C43C2semidirect
304. C8×D8D43semidirect
367. C43#17968semidirect

Maximal subgroups

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

subgroupindex
#191451882
#191437452
#191436692
#191335092
#191334962
#191334882
#191334772
#191334172
#191334072
C8×#106218732
#191333612
#191330522
#191330442
C8×#106218722
C8×D8×C432
#1796843