Finite Group Databasebeta

← #25079603

Subgroups — #25079603

Order 11008.

646 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#19145313C211yesmaximal, characteristic, complemented
2#19144667C211yesmaximal, characteristic, complemented
3#19144052C211yesmaximal, characteristic
4#19143613C211yesmaximal, characteristic, complemented
5#19134157C211yesmaximal, characteristic, complemented
6#19134143C211yesmaximal, characteristic, complemented
7#19134109C211yesmaximal, characteristic, complemented
8#19134061C211yesmaximal, characteristic, complemented
9#19134040C211yesmaximal, characteristic, complemented
10#19134026C211yesmaximal, characteristic, complemented
11#19133990C211yesmaximal, characteristic, complemented
12#19133944C211yesmaximal, characteristic, complemented
13#19133298C211yesmaximal, characteristic, complemented
14#19133293C211yesmaximal, characteristic, complemented
15C43×#1565C211yesmaximal, characteristic, complemented
16C2×#13063347—21no—
17#14583456C2211yescharacteristic
18#14583449C2211yescharacteristic
19C4×#10621898C2211yescharacteristic
20#14583304C2211yescharacteristic
21#14583272C2211yescharacteristic
22#14583250C2211yescharacteristic
23#14583246C2211yescharacteristic
24#14583241—21no—
25#14583185C2211yescharacteristic
26#14583180C2211yescharacteristic
27#14583145—21no—
28#14583145—21no—
29#14583122—21no—
30#14583115—21no—
31#14583110C2211yescharacteristic
32#14583110C2211yescharacteristic
33#14583105C2211yescharacteristic
34#14583105C2211yescharacteristic
35#14583100C2211yescharacteristic
36#14583095C2211yescharacteristic
37#14583063—21no—
38C8×Dic86C2211yescharacteristic
39C8×Dic86C2211yescharacteristic
40#14583001—21no—
41#14583001—21no—
42C4×Dic172—21no—
43C4×#10621873—21no—
44#14582978C2211yescharacteristic
45#14582978C2211yescharacteristic
46#14582975—21no—
47#14582975—21no—
48#14582956C2211yescharacteristic
49#14582954—21no—
50#14582896—21no—
51#14582851—21no—
52#14582646C2211yescharacteristic
53#14582646C2211yescharacteristic
54#14582646C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582644C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#431C2211yescharacteristic
61C2×C4⋊C8×C43C2211yescharacteristic
62C4×M16×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#334C2211yescharacteristic
66C43×#334C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621898D411yescharacteristic
69#13063347—44no—
70C2×Dic172—21no—
71C2×Dic172—21no—
72C2×#10621873—21no—
73C2×#10621873—21no—
74C2×#10621873—21no—
75C2×#10621873—21no—
76C2×#10621873—21no—
77C2×D344—21no—
78C2×#10621872—21no—
79C2×#10621872—21no—
80#13063325C2311yescharacteristic
81#13063325C2311yescharacteristic
82#13063325C2311yescharacteristic
83#13063322C2311yescharacteristic
84#13063317—21no—
85#13063313—21no—
86#13063304—21no—
87#13063304—21no—
88#13063299—21no—
89#13063299—21no—
90C4×Dic86—21no—
91C4×Dic86—21no—
92C4×Dic86D411yescharacteristic
93C4×Dic86C2311yescharacteristic
94C4×D172—21no—
95C4×D172—21no—
96C4×D172D411yescharacteristic
97C4×D172C2311yescharacteristic
98C4×C22⋊D43—21no—
99C4×C22⋊D43—21no—
100#13063284—21no—
101#13063284D411yescharacteristic
102#13063282—21no—
103C42×D43—21no—
104#13063259—21no—
105#13063259—21no—
106#13063259—21no—
107#13063257—21no—
108C4⋊(C43⋊C8)C2311yescharacteristic
109C4⋊(C43⋊C8)C2311yescharacteristic
110Dic43⋊C8—21no—
111Dic43⋊C8—21no—
112#13063250—21no—
113#13063250—21no—
114#13063250—21no—
115#13063250—21no—
116#13063250—21no—
117#13063250—21no—
118#13063250—21no—
119#13063247—21no—
120#13063247—21no—
121#13063247—21no—
122#13063247—21no—
123#13063247—21no—
124C22⋊(C43⋊C8)—21no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8—21no—
127#13063236—21no—
128C8×Dic43—21no—
129C8×Dic43—21no—
130C2×M16×C43D411yescharacteristic
131C2×M16×C43D411yescharacteristic
132C22×C8×C43—21no—
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C22⋊C8×C43—21no—
140#97×C43D411yescharacteristic
141#97×C43D411yescharacteristic
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43#4111yescharacteristic
148C2×C22⋊D43—21no—
149C2×C22⋊D43—41no—
150#10621898—22no—
151#10621898—41no—
152#10621898—42no—
153#10621898—42no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172C2×D411yescharacteristic
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—41no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86C2×D411yescharacteristic
166M16×C43—22no—
167M16×C43—41no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—42no—
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C42×C43C2×D411yescharacteristic
178C42×C43C2×D411yescharacteristic
179C42×C43#4111yescharacteristic
180C42×C43C2411yescharacteristic
181C22⋊Dic43—21no—
182C22⋊Dic43—41no—
183(C2×D43)⋊C4—21no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—41no—
186(C2×D43)⋊C4—41no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43C2×D411yescharacteristic
194C4⋊Dic43C2×D411yescharacteristic
195Dic43⋊C4—21no—
196Dic43⋊C4—21no—
197Dic43⋊C4—41no—
198Dic43⋊C4—41no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43—41no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205Dic172—42no—
206Dic172—42no—
207D344—42no—
208#10621873—42no—
209#10621873—42no—
210#10621873—42no—
211#10621873—42no—
212#10621873—42no—
213#10621872—42no—
214#10621872—42no—
215C23×C43#12111yescharacteristic
216C22×D43—21no—
217C22×D43—41no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—41no—
223C2×C4×C43#12111yescharacteristic
224C2×C4×C43#12111yescharacteristic
225C2×C4×C43#12111yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C2×#4111yescharacteristic
229C22⋊D43—42no—
230C22⋊D43—82no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237D172—21no—
238D172—21no—
239D172—41no—
240D172—41no—
241D172—41no—
242D172—41no—
243D172—81no—
244C4×D43—42no—
245C4×D43—41no—
246C4×D43—41no—
247C4×D43—81no—
248C4×D43—82no—
249Dic86—21no—
250Dic86—41no—
251Dic86—41no—
252Dic86—41no—
253Dic86—41no—
254Dic86—41no—
255Dic86—41no—
256Dic86AGL(1,ℤ/8)12yes—
257C8×C43—21no—
258C8×C43—21no—
259C8×C43—21no—
260C8×C43—41no—
261C8×C43—41no—
262C8×C43—41no—
263C8×C43—41no—
264C8×C43#13512yescomplemented
265C43⋊C8—41no—
266C43⋊C8—41no—
267#19182—431nomaximal, Sylow
268C22×C43—21no—
269C22×C43—21no—
270C22×C43—21no—
271C22×C43C2×#12111yescharacteristic
272C2×D43—41no—
273C2×D43—41no—
274C2×D43—41no—
275C2×D43—81no—
276C2×D43—81no—
277C2×D43—81no—
278C4×C43—21no—
279C4×C43—21no—
280C4×C43—21no—
281C4×C43—21no—
282C4×C43C2×#13511yescharacteristic
283C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
284C4×C43#57511yescharacteristic
285C4×C43#57511yescharacteristic
286Dic43—22no—
287Dic43—41no—
288Dic43—41no—
289Dic43—81no—
290Dic43—81no—
291Dic43—81no—
292#3182—431no—
293#3107—431no—
294#3035—431no—
295#2971—431no—
296#1701—431no—
297#1699—431no—
298#1693—431no—
299#1685—431no—
300#1682—431no—
301#1680—431no—
302#1674—431no—
303#1666—431no—
304#1565D4311yescharacteristic, complemented
305#1553—431no—
306#1552—431no—
307C2×C43—41no—
308C2×C43#303511yescharacteristic
309C2×C43#305511yescharacteristic
310C2×C43#306911yescharacteristic
311D43—81no—
312D43—161no—
313C2×#135—861no—
314#533—431no—
315#532—431no—
316C4×#41—431no—
317#500—431no—
318#492—431no—
319#487—431no—
320#486—431no—
321#485—861no—
322#475—431no—
323#474—431no—
324#468—861no—
325#468—861no—
326#464—861no—
327#463—861no—
328#462—431no—
329#462—431no—
330#461—431no—
331#461—431no—
332#460—431no—
333#459—431no—
334#452—861no—
335C8×Q8—431no—
336C8×Q8—431no—
337#440—861no—
338#440—861no—
339C4×Q16—861no—
340C4×SD16—861no—
341#436—431no—
342#436—431no—
343#436—861no—
344#436—861no—
345#432—431no—
346#432—861no—
347#431C2×D4311yescharacteristic
348C2×C4⋊C8C2×D4311yescharacteristic
349#416—861no—
350C4×M16—861no—
351C4×M16C2×D4311yescharacteristic
352#335C2×D4311yescharacteristic
353#335C2×D4311yescharacteristic
354#334C2×D4311yescharacteristic
355#334C2×D4311yescharacteristic
356#332—431no—
357#332—431no—
358#332—431no—
359#332—431no—
360#332—431no—
361#332—431no—
362#331—431no—
363#331—431no—
364C43#1918211yescharacteristic, complemented, Sylow
365C2×#41—431no—
366C2×#41—861no—
367#135—1724no—
368C2×Q16—861no—
369C2×Q16—861no—
370C2×SD16—861no—
371C2×SD16—861no—
372C2×SD16—861no—
373C2×SD16—861no—
374C2×SD16—861no—
375C2×D8—861no—
376C2×M16—861no—
377C2×M16—861no—
378C2×M16D17211yescharacteristic
379C2×M16D17211yescharacteristic
380C22×C8—21no—
381C4⋊Q8—431no—
382C4⋊Q8—431no—
383C4⋊Q8—431no—
384#127—431no—
385#125—861no—
386#124—861no—
387C22⋊Q8—861no—
388C22⋊Q8—861no—
389#121—861no—
390#121—861no—
391C4×Q8—431no—
392C4×Q8—431no—
393C4×Q8—861no—
394C4×Q8—861no—
395C4×D4—431no—
396C4×D4—431no—
397C4×D4—861no—
398C4×D4—861no—
399C4×D4—861no—
400C4×D4—861no—
401#117—431no—
402#117—861no—
403#117—861no—
404C2×C42—861no—
405C2×C42C22×D4311yescharacteristic
406#107—861no—
407#107—861no—
408#107—861no—
409#106—861no—
410C4⋊C8—21no—
411C4⋊C8—431no—
412C4⋊C8—431no—
413C4⋊C8—861no—
414C4⋊C8—861no—
415C4⋊C8C22×D4311yescharacteristic
416C4⋊C8C22×D4311yescharacteristic
417C4⋊C8C22×D4311yescharacteristic
418C4⋊C8C22×D4311yescharacteristic
419#103—861no—
420#103—861no—
421#103—861no—
422#103—861no—
423#103—861no—
424#103—861no—
425#103—861no—
426#102—861no—
427#102—861no—
428#102—861no—
429#102—861no—
430#102—861no—
431C22⋊C8—21no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C22⋊C8—861no—
435#97—861no—
436#97D17211yescharacteristic
437#97D17211yescharacteristic
438C4×C8—21no—
439C4×C8—861no—
440C4×C8—861no—
441C4×C8C22×D4311yescharacteristic
442C4×C8C22×D4311yescharacteristic
443#41—862no—
444#41—1722no—
445#41—1722no—
446#41—1721no—
447C2×Q8—431no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×Q8—861no—
451C2×D4—431no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—1721no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—1721no—
461C22×C4C2×D17211yescharacteristic
462C22×C4D4×D4311yescharacteristic
463C22×C4#1062190211yescharacteristic
464Q16—1722no—
465Q16—1722no—
466SD16—1722no—
467SD16—1722no—
468SD16—1722no—
469SD16—1722no—
470SD16—1722no—
471D8—1722no—
472M16—22no—
473M16—41no—
474M16—1722no—
475M16—1722no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—42no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8C2×D17211yescharacteristic
484C2×C8C2×D17211yescharacteristic
485C2×C8C2×D17211yescharacteristic
486C2×C8C2×D17211yescharacteristic
487C4⋊C4—431no—
488C4⋊C4—431no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—1721no—
498C4⋊C4—1721no—
499C22⋊C4—861no—
500C22⋊C4—861no—
501C22⋊C4—861no—
502C22⋊C4—1721no—
503C22⋊C4—1721no—
504C22⋊C4—1721no—
505C42—861no—
506C42—861no—
507C42—861no—
508C42—1721no—
509C42C2×D17211yescharacteristic
510C42D4×D4311yescharacteristic
511C42#1062190211yescharacteristic
512C42C23×D4311yescharacteristic
513C23—861no—
514C23—1721no—
515C23#1306330011yescharacteristic
516Q8—432no—
517Q8—861no—
518Q8—1721no—
519Q8—1721no—
520Q8—1721no—
521Q8—1721no—
522Q8—1721no—
523Q8—1721no—
524D4—861no—
525D4—861no—
526D4—3441no—
527D4—3442no—
528D4—1722no—
529D4—1721no—
530D4—1721no—
531D4—1721no—
532D4—1721no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—3442no—
542C2×C4—3441no—
543C2×C4—1722no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4#1306330011yescharacteristic
550C2×C4#1306330011yescharacteristic
551C2×C4#1306330011yescharacteristic
552C2×C4C2×D4×D4311yescharacteristic
553C2×C4C22×D17211yescharacteristic
554C2×C4C2×#1062190211yescharacteristic
555C8—21no—
556C8—21no—
557C8—21no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—41no—
562C8—1721no—
563C8—1721no—
564C8#1306334712yescomplemented
565C22—21no—
566C22—21no—
567C22—21no—
568C22—3441no—
569C22—3441no—
570C22—3441no—
571C22—1721no—
572C22—1721no—
573C22—1721no—
574C22C2×#1306330011yescharacteristic
575C4—21no—
576C4—21no—
577C4—21no—
578C4—21no—
579C4—862no—
580C4—3441no—
581C4—3441no—
582C4—3441no—
583C4—1721no—
584C4—1721no—
585C4C2×#1306334711yescharacteristic
586C4AGL(1,ℤ/8)×D4311yescharacteristic
587C4#1458369811yescharacteristic
588C4#1458369911yescharacteristic
589C2—41no—
590C2—3441no—
591C2—6881no—
592C2#1914405211yescharacteristic
593C2#1914421511yescharacteristic
594C2#1914433311yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1565C2
socleC22×C43C2×#121
prime radical#19144052C2
hypercenter#1565D43
hypocenterC43#19182
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
1. #19145313C2semidirect
2. #19144667C2semidirect
4. #19143613C2semidirect
5. #19134157C2semidirect
6. #19134143C2semidirect
7. #19134109C2semidirect
8. #19134061C2semidirect
9. #19134040C2semidirect
10. #19134026C2semidirect
11. #19133990C2semidirect
12. #19133944C2semidirect
13. #19133298C2semidirect
14. #19133293C2semidirect
15. C43×#1565C2semidirect
264. C8×C43#135semidirect
304. #1565D43semidirect
364. C43#19182semidirect
564. C8#13063347semidirect

Maximal subgroups

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

subgroupindex
#191453132
#191446672
#191440522
#191436132
#191341572
#191341432
#191341092
#191340612
#191340402
#191340262
#191339902
#191339442
#191332982
#191332932
C43×#15652
#1918243