Finite Group Databasebeta

← #25080349

Subgroups — #25080349

Order 11008.

602 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145933C211yesmaximal, characteristic, complemented
2#19145573C211yesmaximal, characteristic
3#19145313C211yesmaximal, characteristic, complemented
4#19143599C211yesmaximal, characteristic, complemented
5#19134164C211yesmaximal, characteristic, complemented
6#19134150C211yesmaximal, characteristic, complemented
7#19134109C211yesmaximal, characteristic, complemented
8#19134061C211yesmaximal, characteristic, complemented
9#19134033C211yesmaximal, characteristic, complemented
10#19134019C211yesmaximal, characteristic, complemented
11#19133990C211yesmaximal, characteristic, complemented
12#19133944C211yesmaximal, characteristic, complemented
13#19133259C211yesmaximal, characteristic, complemented
14#19133245C211yesmaximal, characteristic, complemented
15C43×#1565C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583449C2211yescharacteristic
18#14583433C2211yescharacteristic
19#14583304C2211yescharacteristic
20#14583283—21no—
21#14583272C2211yescharacteristic
22#14583254—21no—
23#14583250C2211yescharacteristic
24#14583246C2211yescharacteristic
25#14583207—21no—
26#14583185C2211yescharacteristic
27#14583180C2211yescharacteristic
28#14583145—21no—
29#14583145—21no—
30#14583140—21no—
31#14583128—21no—
32#14583122—21no—
33#14583110C2211yescharacteristic
34#14583110C2211yescharacteristic
35#14583105C2211yescharacteristic
36#14583105C2211yescharacteristic
37#14583100C2211yescharacteristic
38#14583095C2211yescharacteristic
39#14583063—21no—
40#14583046—21no—
41#14583029C2211yescharacteristic
42C8×Dic86C2211yescharacteristic
43#14583001—21no—
44#14583001—21no—
45#14582978C2211yescharacteristic
46#14582975—21no—
47#14582968—21no—
48C8×D172C2211yescharacteristic
49#14582961—21no—
50#14582952C2211yescharacteristic
51#14582856—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×Dic172—21no—
69C2×Dic172—21no—
70C2×#10621873—21no—
71C2×#10621873—21no—
72C2×#10621873—21no—
73C2×#10621873—21no—
74C2×#10621873—21no—
75C2×D344—21no—
76C2×#10621872—21no—
77C2×C8×D43—21no—
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063325C2311yescharacteristic
81#13063322C2311yescharacteristic
82#13063319—21no—
83#13063317—21no—
84#13063317D411yescharacteristic
85#13063313—21no—
86#13063313D411yescharacteristic
87#13063308—21no—
88#13063304—21no—
89#13063304—21no—
90#13063304D411yescharacteristic
91#13063299—21no—
92#13063299—21no—
93#13063299D411yescharacteristic
94C4×Dic86—21no—
95C4×Dic86—21no—
96C4×Dic86C2311yescharacteristic
97C4×D172—21no—
98C4×D172—21no—
99C4×D172C2311yescharacteristic
100C4×C22⋊D43—21no—
101#13063284—21no—
102#13063282—21no—
103#13063259—21no—
104#13063259—21no—
105#13063259—21no—
106#13063257—21no—
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111#13063250—21no—
112#13063250—21no—
113#13063250—21no—
114#13063250—21no—
115#13063250—21no—
116#13063250—21no—
117#13063250—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×C43D411yescharacteristic
130C2×M16×C43D411yescharacteristic
131C22×C8×C43—21no—
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×C43D411yescharacteristic
140#97×C43D411yescharacteristic
141C4×C8×C43—21no—
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—
149#10621898—81no—
150#10621898—81no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172C2×D411yescharacteristic
155C2×C4×D43—21no—
156C2×C4×D43—41no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86C2×D411yescharacteristic
161M16×C43—22no—
162M16×C43—41no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—81no—
168C2×C8×C43C2×D411yescharacteristic
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C42×C43C2×D411yescharacteristic
173C42×C43C2×D411yescharacteristic
174C42×C43#4111yescharacteristic
175C42×C43C2411yescharacteristic
176C22⋊Dic43—21no—
177C22⋊Dic43—41no—
178(C2×D43)⋊C4—21no—
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—41no—
183(C2×D43)⋊C4—41no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43C2×D411yescharacteristic
191C4⋊Dic43C2×D411yescharacteristic
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198C4×Dic43—21no—
199C4×Dic43—41no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202Dic172—81no—
203Dic172—81no—
204D344—81no—
205#10621873—42no—
206#10621873—42no—
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—
234D172—21no—
235D172—21no—
236D172—41no—
237D172—41no—
238D172—41no—
239D172—41no—
240D172—81no—
241C4×D43—41no—
242C4×D43—41no—
243C4×D43—82no—
244Dic86—21no—
245Dic86—21no—
246Dic86—41no—
247Dic86—41no—
248Dic86—41no—
249Dic86—41no—
250Dic86—41no—
251Dic86—41no—
252C8×C43—21no—
253C8×C43—21no—
254C8×C43—21no—
255C8×C43—41no—
256C8×C43—41no—
257C8×C43—41no—
258C8×C43—41no—
259C8×C43#13512yes—
260C43⋊C8—41no—
261C43⋊C8—41no—
262#19252—431nomaximal, Sylow
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—21no—
266C22×C43C2×#12111yescharacteristic
267C2×D43—41no—
268C2×D43—41no—
269C2×D43—41no—
270C2×D43—81no—
271C2×D43—81no—
272C2×D43—81no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43C2×#13511yescharacteristic
278C4×C43#57511yescharacteristic
279C4×C43#57611yescharacteristic
280C4×C43#57711yescharacteristic
281Dic43—41no—
282Dic43—41no—
283Dic43—41no—
284Dic43—81no—
285Dic43—81no—
286Dic43—81no—
287#3248—431no—
288#3212—431no—
289#3182—431no—
290#2969—431no—
291#1702—431no—
292#1700—431no—
293#1693—431no—
294#1685—431no—
295#1681—431no—
296#1679—431no—
297#1674—431no—
298#1666—431no—
299#1565D4311yescharacteristic, complemented
300#1544—431no—
301#1540—431no—
302C2×C43—41no—
303C2×C43#303511yescharacteristic
304C2×C43#306211yescharacteristic
305C2×C43#306911yescharacteristic
306D43—81no—
307D43—161no—
308#533—431no—
309#532—431no—
310#529—431no—
311#500—431no—
312#495—861no—
313#492—431no—
314#488—861no—
315#487—431no—
316#486—431no—
317#479—861no—
318#475—431no—
319#474—431no—
320#468—861no—
321#468—861no—
322#467—861no—
323#465—861no—
324#464—861no—
325#462—431no—
326#462—431no—
327#461—431no—
328#461—431no—
329#460—431no—
330#459—431no—
331#452—861no—
332#449—861no—
333#446—431no—
334C8×Q8—431no—
335#440—861no—
336#440—861no—
337#436—431no—
338#436—861no—
339#435—861no—
340C8×D4—431no—
341#433—861no—
342#431—431no—
343#431C2×D4311yescharacteristic
344C2×C4⋊C8C2×D4311yescharacteristic
345#405—861no—
346C4×M16C2×D4311yescharacteristic
347#335C2×D4311yescharacteristic
348#335C2×D4311yescharacteristic
349#334C2×D4311yescharacteristic
350#334C2×D4311yescharacteristic
351#332—431no—
352#332—431no—
353#332—431no—
354#332—431no—
355#332—431no—
356#332—431no—
357#331—431no—
358#331—431no—
359C43#1925211yescharacteristic, complemented, Sylow
360C2×#41—861no—
361C2×Q16—861no—
362C2×Q16—861no—
363C2×SD16—861no—
364C2×SD16—861no—
365C2×SD16—861no—
366C2×SD16—861no—
367C2×SD16—861no—
368C2×D8—861no—
369C2×M16—861no—
370C2×M16D17211yescharacteristic
371C2×M16D17211yescharacteristic
372C22×C8—21no—
373C22×C8—861no—
374C4⋊Q8—431no—
375C4⋊Q8—431no—
376C4⋊Q8—431no—
377#127—431no—
378#126—861no—
379#125—431no—
380#125—861no—
381#124—431no—
382#124—861no—
383#123—861no—
384C22⋊Q8—431no—
385C22⋊Q8—861no—
386C22⋊Q8—861no—
387#121—431no—
388#121—861no—
389#121—861no—
390C4×Q8—431no—
391C4×Q8—861no—
392C4×Q8—861no—
393C4×D4—431no—
394C4×D4—861no—
395C4×D4—861no—
396C4×D4—861no—
397#117—861no—
398#117—861no—
399C2×C42C22×D4311yescharacteristic
400#107—861no—
401#107—861no—
402#107—861no—
403#106—861no—
404C4⋊C8—21no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—861no—
408C4⋊C8—861no—
409C4⋊C8C22×D4311yescharacteristic
410C4⋊C8C22×D4311yescharacteristic
411C4⋊C8C22×D4311yescharacteristic
412C4⋊C8C22×D4311yescharacteristic
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—
425C22⋊C8—21no—
426C22⋊C8—861no—
427C22⋊C8—861no—
428C22⋊C8—861no—
429#97—861no—
430#97D17211yescharacteristic
431#97D17211yescharacteristic
432C4×C8—21no—
433C4×C8—861no—
434C4×C8—861no—
435C4×C8C22×D4311yescharacteristic
436C4×C8C22×D4311yescharacteristic
437#41—3441no—
438#41—3441no—
439C2×Q8—431no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8—861no—
443C2×D4—431no—
444C2×D4—861no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—861no—
448C2×D4—1721no—
449C22×C4—861no—
450C22×C4—1721no—
451C22×C4C2×D17211yescharacteristic
452C22×C4D4×D4311yescharacteristic
453C22×C4#1062190211yescharacteristic
454Q16—3441no—
455Q16—3441no—
456SD16—3441no—
457SD16—3441no—
458SD16—3441no—
459SD16—1722no—
460SD16—1722no—
461D8—3441no—
462M16—22no—
463M16—41no—
464M16—1722no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—81no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—1722no—
473C2×C8C2×D17211yescharacteristic
474C2×C8C2×D17211yescharacteristic
475C2×C8C2×D17211yescharacteristic
476C2×C8C2×D17211yescharacteristic
477C4⋊C4—431no—
478C4⋊C4—431no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—1721no—
490C4⋊C4—1721no—
491C22⋊C4—861no—
492C22⋊C4—861no—
493C22⋊C4—861no—
494C22⋊C4—861no—
495C22⋊C4—861no—
496C22⋊C4—1721no—
497C22⋊C4—1721no—
498C22⋊C4—1721no—
499C42—861no—
500C42—1721no—
501C42C2×D17211yescharacteristic
502C42D4×D4311yescharacteristic
503C42#1062190211yescharacteristic
504C42C23×D4311yescharacteristic
505C23—861no—
506C23—1721no—
507C23#1306330011yescharacteristic
508Q8—861no—
509Q8—861no—
510Q8—1721no—
511Q8—1721no—
512Q8—1721no—
513Q8—1721no—
514Q8—1721no—
515Q8—1721no—
516D4—861no—
517D4—861no—
518D4—3441no—
519D4—3442no—
520D4—3441no—
521D4—1721no—
522D4—1721no—
523D4—1721no—
524D4—1721no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—41no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—3442no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4#1306330011yescharacteristic
540C2×C4#1306330011yescharacteristic
541C2×C4#1306330011yescharacteristic
542C2×C4C2×D4×D4311yescharacteristic
543C2×C4C22×D17211yescharacteristic
544C2×C4C2×#1062190211yescharacteristic
545C8—21no—
546C8—21no—
547C8—21no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—1721no—
553C8—1721no—
554C8#1306334712yes—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—3441no—
559C22—3441no—
560C22—3441no—
561C22—1721no—
562C22—1721no—
563C22—1721no—
564C22C2×#1306330011yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—3441no—
570C4—3441no—
571C4—3441no—
572C4—1721no—
573C4—1721no—
574C4—1721no—
575C4C2×#1306334711yescharacteristic
576C4#1458369911yescharacteristic
577C4#1458370311yescharacteristic
578C4#1458370811yescharacteristic
579C2—41no—
580C2—3441no—
581C2—6881no—
582C2#1914405211yescharacteristic
583C2#1914427611yescharacteristic
584C2#1914433311yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1565C2
socleC22×C43C2×#121
prime radical#19145573C2
hypercenter#1565D43
hypocenterC43#19252
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. #19145933C2semidirect
3. #19145313C2semidirect
4. #19143599C2semidirect
5. #19134164C2semidirect
6. #19134150C2semidirect
7. #19134109C2semidirect
8. #19134061C2semidirect
9. #19134033C2semidirect
10. #19134019C2semidirect
11. #19133990C2semidirect
12. #19133944C2semidirect
13. #19133259C2semidirect
14. #19133245C2semidirect
15. C43×#1565C2semidirect
299. #1565D43semidirect
359. C43#19252semidirect

Maximal subgroups

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

subgroupindex
#191459332
#191455732
#191453132
#191435992
#191341642
#191341502
#191341092
#191340612
#191340332
#191340192
#191339902
#191339442
#191332592
#191332452
C43×#15652
#1925243