Finite Group Databasebeta

← #25081746

Subgroups — #25081746

Order 11008.

606 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145958C211yesmaximal, characteristic
2#19145624C211yesmaximal, characteristic, complemented
3#19144989C211yesmaximal, characteristic, complemented
4#19143599C211yesmaximal, characteristic, complemented
5#19134164C211yesmaximal, characteristic, complemented
6#19134157C211yesmaximal, characteristic, complemented
7#19134150C211yesmaximal, characteristic, complemented
8#19134143C211yesmaximal, characteristic, complemented
9#19134040C211yesmaximal, characteristic, complemented
10#19134033C211yesmaximal, characteristic, complemented
11#19134026C211yesmaximal, characteristic, complemented
12#19134019C211yesmaximal, characteristic, complemented
13#19133301C211yesmaximal, characteristic, complemented
14#19133268C211yesmaximal, characteristic, complemented
15C43×#1569C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17C2×#13063325C2211yescharacteristic
18#14583433C2211yescharacteristic
19#14583293—21no—
20#14583268—21no—
21#14583259—21no—
22#14583259—21no—
23#14583250C2211yescharacteristic
24#14583250C2211yescharacteristic
25#14583246C2211yescharacteristic
26#14583246C2211yescharacteristic
27#14583200—21no—
28#14583185C2211yescharacteristic
29#14583180C2211yescharacteristic
30#14583152—21no—
31#14583145—21no—
32#14583115—21no—
33#14583110C2211yescharacteristic
34#14583110C2211yescharacteristic
35#14583105C2211yescharacteristic
36#14583105C2211yescharacteristic
37#14583100C2211yescharacteristic
38#14583095C2211yescharacteristic
39#14583057—21no—
40#14583040—21no—
41#14583029C2211yescharacteristic
42C8×Dic86C2211yescharacteristic
43#14582978C2211yescharacteristic
44#14582975—21no—
45#14582968—21no—
46C8×D172C2211yescharacteristic
47#14582961—21no—
48#14582952C2211yescharacteristic
49#14582901—21no—
50#14582901—21no—
51#14582856—21no—
52#14582646C2211yescharacteristic
53#14582646C2211yescharacteristic
54#14582646C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582644C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#432C2211yescharacteristic
61C43×#423C2211yescharacteristic
62C4×M16×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#334C2211yescharacteristic
66C43×#334C2211yescharacteristic
67C2×#10621898—21no—
68C22×Dic86—21no—
69C2×Dic172—21no—
70C2×Dic172—21no—
71C2×#10621873—21no—
72C2×#10621873—21no—
73C2×#10621873—21no—
74C2×D344—21no—
75C2×#10621872—21no—
76C2×C8×D43—21no—
77#13063325—21no—
78#13063325—21no—
79#13063325—21no—
80#13063325C2311yescharacteristic
81#13063325C2311yescharacteristic
82#13063325C2311yescharacteristic
83#13063322C2311yescharacteristic
84#13063319—21no—
85#13063317D411yescharacteristic
86#13063313—21no—
87#13063313D411yescharacteristic
88#13063308—21no—
89#13063304D411yescharacteristic
90#13063299—21no—
91#13063299—21no—
92#13063299D411yescharacteristic
93C4×Dic86C2311yescharacteristic
94C4×D172—21no—
95C4×D172—21no—
96C4×D172C2311yescharacteristic
97C4×C22⋊D43—21no—
98#13063282—21no—
99C2×C4⋊Dic43—21no—
100C2×C4⋊Dic43—21no—
101#13063259—21no—
102#13063257—21no—
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107#13063250—21no—
108#13063250—21no—
109#13063250—21no—
110#13063250—21no—
111#13063250—21no—
112#13063250—21no—
113#13063250—21no—
114#13063250—21no—
115#13063250—21no—
116#13063247—21no—
117#13063247—21no—
118#13063247—21no—
119#13063247—21no—
120#13063247—21no—
121#13063247—21no—
122#13063247—21no—
123C22⋊(C43⋊C8)—21no—
124(C2×D43)⋊C8—21no—
125(C2×D43)⋊C8—21no—
126#13063235—21no—
127C4×C43⋊C8—21no—
128C8×Dic43—21no—
129C2×M16×C43—21no—
130C2×M16×C43D411yescharacteristic
131C2×M16×C43D411yescharacteristic
132C2×C42×C43C2311yescharacteristic
133C4⋊C8×C43—21no—
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C22⋊C8×C43—21no—
139#97×C43—21no—
140#97×C43D411yescharacteristic
141#97×C43D411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43#4111yescharacteristic
147C2×C22⋊D43—21no—
148C2×C22⋊D43—41no—
149C22×Dic43—41no—
150#10621898—42no—
151#10621898—42no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172C2×D411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43—41no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—41no—
162C2×Dic86—81no—
163C2×Dic86—81no—
164C2×Dic86C2×D411yescharacteristic
165M16×C43—41no—
166M16×C43—41no—
167M16×C43—81no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C42×C43C2×D411yescharacteristic
177C42×C43C2×D411yescharacteristic
178C42×C43#4111yescharacteristic
179C42×C43C2411yescharacteristic
180C22⋊Dic43—21no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
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⋊Dic43—41no—
194C4⋊Dic43—41no—
195C4⋊Dic43C2×D411yescharacteristic
196C4⋊Dic43C2×D411yescharacteristic
197Dic43⋊C4—21no—
198Dic43⋊C4—21no—
199Dic43⋊C4—21no—
200Dic43⋊C4—21no—
201C4×Dic43—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204Dic172—81no—
205Dic172—81no—
206D344—81no—
207#10621873—81no—
208#10621873—81no—
209#10621873—81no—
210#10621872—42no—
211C8×D43—42no—
212C23×C43#12111yescharacteristic
213C22×D43—21no—
214C22×D43—41no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—41no—
220C2×C4×C43#12111yescharacteristic
221C2×C4×C43#12111yescharacteristic
222C2×C4×C43#12111yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C22⋊D43—81no—
227C22⋊D43—82no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—82no—
235D172—21no—
236D172—21no—
237D172—41no—
238D172—41no—
239D172—41no—
240D172—41no—
241D172—81no—
242C4×D43—41no—
243C4×D43—41no—
244C4×D43—82no—
245Dic86—21no—
246Dic86—21no—
247Dic86—41no—
248Dic86—41no—
249Dic86—41no—
250Dic86—41no—
251Dic86—41no—
252Dic86—41no—
253Dic86—82no—
254C8×C43—21no—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—41no—
259C8×C43—41no—
260C8×C43—41no—
261C8×C43—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264#19383—431nomaximal, Sylow
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—21no—
268C22×C43C2×#12111yescharacteristic
269C2×D43—41no—
270C2×D43—41no—
271C2×D43—41no—
272C2×D43—81no—
273C2×D43—81no—
274C2×D43—81no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43#57511yescharacteristic
280C4×C43#57511yescharacteristic
281C4×C43#57611yescharacteristic
282C4×C43#57711yescharacteristic
283Dic43—41no—
284Dic43—41no—
285Dic43—41no—
286Dic43—81no—
287Dic43—81no—
288Dic43—81no—
289#3251—431no—
290#3218—431no—
291#3141—431no—
292#2969—431no—
293#1702—431no—
294#1701—431no—
295#1700—431no—
296#1699—431no—
297#1682—431no—
298#1681—431no—
299#1680—431no—
300#1679—431no—
301#1569D4311yescharacteristic, complemented
302#1553—431no—
303#1546—431no—
304C2×C43—41no—
305C2×C43#304011yescharacteristic
306C2×C43#306211yescharacteristic
307C2×C43#306911yescharacteristic
308D43—81no—
309D43—161no—
310#532—431no—
311C2×C4⋊Q8—431no—
312#529—431no—
313#497—861no—
314#491—861no—
315#489—861no—
316#489—861no—
317#487—431no—
318#487—431no—
319#486—431no—
320#486—431no—
321#478—861no—
322#475—431no—
323#474—431no—
324#469—861no—
325#468—861no—
326#463—861no—
327#462—431no—
328#462—431no—
329#461—431no—
330#461—431no—
331#460—431no—
332#459—431no—
333#451—861no—
334#448—861no—
335#446—431no—
336C8×Q8—431no—
337#436—431no—
338#436—861no—
339#435—861no—
340C8×D4—431no—
341#433—861no—
342#432C2×D4311yescharacteristic
343#431—431no—
344#423C2×D4311yescharacteristic
345#417—861no—
346#417—861no—
347#405—861no—
348C4×M16C2×D4311yescharacteristic
349#335C2×D4311yescharacteristic
350#335C2×D4311yescharacteristic
351#334C2×D4311yescharacteristic
352#334C2×D4311yescharacteristic
353#332—431no—
354#332—431no—
355#332—431no—
356#332—431no—
357#332—431no—
358#332—431no—
359#331—431no—
360#331—431no—
361C43#1938311yescharacteristic, complemented, Sylow
362C2×#41—861no—
363C22×Q8—861no—
364C2×Q16—861no—
365C2×Q16—861no—
366C2×SD16—861no—
367C2×SD16—861no—
368C2×SD16—861no—
369C2×D8—861no—
370C2×M16—21no—
371C2×M16—861no—
372C2×M16D17211yescharacteristic
373C2×M16D17211yescharacteristic
374C22×C8—861no—
375C4⋊Q8—431no—
376C4⋊Q8—431no—
377C4⋊Q8—431no—
378C4⋊Q8—861no—
379C4⋊Q8—861no—
380C4⋊Q8—861no—
381#127—431no—
382#126—861no—
383#125—431no—
384#124—431no—
385#124—861no—
386#123—861no—
387C22⋊Q8—431no—
388#121—431no—
389#121—861no—
390#121—861no—
391C4×Q8—431no—
392C4×D4—431no—
393C4×D4—861no—
394C4×D4—861no—
395C4×D4—861no—
396#117—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C42C22×D4311yescharacteristic
400#107—861no—
401#106—861no—
402C4⋊C8—21no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—861no—
406C4⋊C8—861no—
407C4⋊C8C22×D4311yescharacteristic
408C4⋊C8C22×D4311yescharacteristic
409C4⋊C8C22×D4311yescharacteristic
410C4⋊C8C22×D4311yescharacteristic
411#103—861no—
412#103—861no—
413#103—861no—
414#103—861no—
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#103—861no—
420#102—861no—
421#102—861no—
422#102—861no—
423#102—861no—
424#102—861no—
425#102—861no—
426#102—861no—
427C22⋊C8—21no—
428C22⋊C8—861no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431#97—21no—
432#97—861no—
433#97D17211yescharacteristic
434#97D17211yescharacteristic
435C4×C8—861no—
436C4×C8—861no—
437C4×C8C22×D4311yescharacteristic
438C4×C8C22×D4311yescharacteristic
439#41—1722no—
440#41—1722no—
441C2×Q8—431no—
442C2×Q8—861no—
443C2×Q8—861no—
444C2×Q8—861no—
445C2×Q8—3441no—
446C2×Q8—3441no—
447C2×Q8—1721no—
448C2×D4—431no—
449C2×D4—861no—
450C2×D4—861no—
451C2×D4—861no—
452C2×D4—861no—
453C2×D4—1721no—
454C22×C4—861no—
455C22×C4—1721no—
456C22×C4—1721no—
457C22×C4C2×D17211yescharacteristic
458C22×C4D4×D4311yescharacteristic
459C22×C4#1062190211yescharacteristic
460Q16—3441no—
461Q16—3441no—
462SD16—3441no—
463SD16—3441no—
464SD16—3441no—
465D8—3441no—
466M16—41no—
467M16—41no—
468M16—81no—
469M16—1722no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—861no—
475C2×C8—861no—
476C2×C8—1722no—
477C2×C8C2×D17211yescharacteristic
478C2×C8C2×D17211yescharacteristic
479C2×C8C2×D17211yescharacteristic
480C2×C8C2×D17211yescharacteristic
481C4⋊C4—431no—
482C4⋊C4—431no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—1721no—
494C4⋊C4—1721no—
495C22⋊C4—861no—
496C22⋊C4—861no—
497C22⋊C4—861no—
498C22⋊C4—861no—
499C22⋊C4—861no—
500C22⋊C4—1721no—
501C22⋊C4—1721no—
502C42—861no—
503C42C2×D17211yescharacteristic
504C42D4×D4311yescharacteristic
505C42#1062190211yescharacteristic
506C42C23×D4311yescharacteristic
507C23—861no—
508C23—1721no—
509C23#1306330011yescharacteristic
510Q8—861no—
511Q8—861no—
512Q8—3442no—
513Q8—1721no—
514Q8—1721no—
515Q8—1721no—
516Q8—1721no—
517Q8—1721no—
518Q8—1721no—
519D4—861no—
520D4—861no—
521D4—3441no—
522D4—3442no—
523D4—3441no—
524D4—1721no—
525D4—1721no—
526D4—1721no—
527D4—1721no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—3442no—
537C2×C4—3442no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4#1306330011yescharacteristic
544C2×C4#1306330011yescharacteristic
545C2×C4#1306330011yescharacteristic
546C2×C4C2×D4×D4311yescharacteristic
547C2×C4C22×D17211yescharacteristic
548C2×C4C2×#1062190211yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8—1721no—
558C8—1721no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—3441no—
563C22—3441no—
564C22—3441no—
565C22—1721no—
566C22—1721no—
567C22—1721no—
568C22C2×#1306330011yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—3441no—
574C4—3441no—
575C4—3441no—
576C4—1721no—
577C4—1721no—
578C4—1721no—
579C4#1458369911yescharacteristic
580C4#1458369911yescharacteristic
581C4#1458370311yescharacteristic
582C4#1458370811yescharacteristic
583C2—41no—
584C2—3441no—
585C2—6881no—
586C2#1914409011yescharacteristic
587C2#1914427611yescharacteristic
588C2#1914433311yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1569C2
socleC22×C43C2×#121
prime radical#19145958C2
hypercenter#1569D43
hypocenterC43#19383
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1569

Complements

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

NH ≅ G/Ntype
2. #19145624C2semidirect
3. #19144989C2semidirect
4. #19143599C2semidirect
5. #19134164C2semidirect
6. #19134157C2semidirect
7. #19134150C2semidirect
8. #19134143C2semidirect
9. #19134040C2semidirect
10. #19134033C2semidirect
11. #19134026C2semidirect
12. #19134019C2semidirect
13. #19133301C2semidirect
14. #19133268C2semidirect
15. C43×#1569C2semidirect
301. #1569D43semidirect
361. C43#19383semidirect

Maximal subgroups

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

subgroupindex
#191459582
#191456242
#191449892
#191435992
#191341642
#191341572
#191341502
#191341432
#191340402
#191340332
#191340262
#191340192
#191333012
#191332682
C43×#15692
#1938343