Finite Group Databasebeta

← #25082052

Subgroups — #25082052

Order 11008.

628 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#19145553C211yesmaximal, characteristic, complemented
2#19144747C211yesmaximal, characteristic
3#19144667C211yesmaximal, characteristic, complemented
4#19143703C211yesmaximal, characteristic, complemented
5#19134040C211yesmaximal, characteristic, complemented
6#19134033C211yesmaximal, characteristic, complemented
7#19134026C211yesmaximal, characteristic, complemented
8#19134019C211yesmaximal, characteristic, complemented
9#19133966C211yesmaximal, characteristic, complemented
10#19133961C211yesmaximal, characteristic, complemented
11#19133944C211yesmaximal, characteristic, complemented
12#19133937C211yesmaximal, characteristic, complemented
13#19133296C211yesmaximal, characteristic, complemented
14#19133242C211yesmaximal, characteristic, complemented
15C43×#1572C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583449C2211yescharacteristic
18C4×#10621898C2211yescharacteristic
19#14583279C2211yescharacteristic
20#14583272C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583246C2211yescharacteristic
23#14583241—21no—
24#14583224—21no—
25#14583185C2211yescharacteristic
26#14583185C2211yescharacteristic
27#14583180C2211yescharacteristic
28#14583180C2211yescharacteristic
29#14583122—21no—
30#14583122—21no—
31#14583110C2211yescharacteristic
32#14583105C2211yescharacteristic
33#14583100C2211yescharacteristic
34#14583095C2211yescharacteristic
35#14583063—21no—
36#14583063—21no—
37#14583063—21no—
38#14583046—21no—
39C8×Dic86C2211yescharacteristic
40C8×Dic86C2211yescharacteristic
41#14583012—21no—
42#14583001—21no—
43C4×Dic172—21no—
44C4×#10621873—21no—
45C8×D172C2211yescharacteristic
46C8×D172C2211yescharacteristic
47(C22⋊D43)⋊C8—21no—
48(C22⋊D43)⋊C8—21no—
49#14582951—21no—
50C2×C4⋊(C43⋊C8)C2211yescharacteristic
51C4⋊C8×D43—21no—
52#14582646C2211yescharacteristic
53#14582646C2211yescharacteristic
54#14582644C2211yescharacteristic
55#14582644C2211yescharacteristic
56#14582644C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#432C2211yescharacteristic
61C43×#431C2211yescharacteristic
62C43×#431C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#334C2211yescharacteristic
66C43×#334C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621898D411yescharacteristic
69C2×Dic172—21no—
70C2×Dic172—21no—
71C2×Dic172—21no—
72C2×#10621873—21no—
73C2×#10621873—21no—
74C2×#10621873—21no—
75C2×#10621873—21no—
76C2×D344—21no—
77C22×C43⋊C8—21no—
78C2×C8×D43—21no—
79C2×C8×D43—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#13063257—21no—
107#13063257—21no—
108C4⋊(C43⋊C8)—21no—
109C4⋊(C43⋊C8)C2311yescharacteristic
110C4⋊(C43⋊C8)C2311yescharacteristic
111Dic43⋊C8—21no—
112Dic43⋊C8—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—
124#13063247—21no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43D411yescharacteristic
131C4⋊C8×C43D411yescharacteristic
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43D411yescharacteristic
139C22⋊C8×C43D411yescharacteristic
140#97×C43—21no—
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—22no—
150#10621898—22no—
151#10621898—81no—
152#10621898—81no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172C2×D411yescharacteristic
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—41no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86C2×D411yescharacteristic
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C42×C43C2×D411yescharacteristic
174C42×C43C2×D411yescharacteristic
175C42×C43#4111yescharacteristic
176C42×C43C2411yescharacteristic
177C22⋊Dic43—21no—
178C22⋊Dic43—41no—
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—41no—
182(C2×D43)⋊C4—41no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43C2×D411yescharacteristic
190C4⋊Dic43C2×D411yescharacteristic
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—41no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—81no—
202Dic172—42no—
203Dic172—81no—
204Dic172—81no—
205D344—42no—
206#10621873—42no—
207#10621873—42no—
208#10621873—81no—
209#10621873—81no—
210C8×D43—81no—
211C8×D43—81no—
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—24no—
227C22⋊D43—82no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234D172—21no—
235D172—41no—
236D172—41no—
237D172—41no—
238D172—41no—
239D172—81no—
240D172#13512yes—
241C4×D43—24no—
242C4×D43—41no—
243C4×D43—41no—
244C4×D43—81no—
245C4×D43—82no—
246Dic86—21no—
247Dic86—41no—
248Dic86—41no—
249Dic86—41no—
250Dic86—41no—
251Dic86—41no—
252Dic86—41no—
253Dic86#13512yes—
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#19413—431nomaximal, Sylow
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—21no—
268C22×C43C2×#12111yescharacteristic
269C2×D43—22no—
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×C43C2×#13511yescharacteristic
280C4×C43C2×#13511yescharacteristic
281C4×C43#57611yescharacteristic
282C4×C43#57711yescharacteristic
283Dic43—22no—
284Dic43—41no—
285Dic43—41no—
286Dic43—81no—
287Dic43—81no—
288Dic43—81no—
289#3210—431no—
290#3115—431no—
291#3107—431no—
292#2988—431no—
293#1682—431no—
294#1681—431no—
295#1680—431no—
296#1679—431no—
297#1670—431no—
298#1669—431no—
299#1666—431no—
300#1665—431no—
301#1572D4311yescharacteristic, complemented
302#1552—431no—
303#1540—431no—
304C2×C43—41no—
305C2×C43#304511yescharacteristic
306C2×C43#305011yescharacteristic
307C2×C43#306911yescharacteristic
308D43—42no—
309D43—161no—
310#533—431no—
311#532—431no—
312C4×#41—431no—
313#494—431no—
314#492—431no—
315#487—431no—
316#486—431no—
317#485—861no—
318#482—861no—
319#475—431no—
320#475—431no—
321#474—431no—
322#474—431no—
323#464—861no—
324#464—861no—
325#462—431no—
326#461—431no—
327#460—431no—
328#459—431no—
329#452—861no—
330#452—861no—
331#452—861no—
332#449—861no—
333C8×Q8—431no—
334C8×Q8—431no—
335#442—861no—
336#440—861no—
337C4×Q16—861no—
338C4×SD16—861no—
339C8×D4—431no—
340C8×D4—431no—
341C8×D4—861no—
342C8×D4—861no—
343#432C2×D4311yescharacteristic
344#431—861no—
345#431C2×D4311yescharacteristic
346#431C2×D4311yescharacteristic
347C2×C4⋊C8—431no—
348C2×C4⋊C8—861no—
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#1941311yescharacteristic, complemented, Sylow
362C2×#41—431no—
363C2×#41—861no—
364C2×Q16—861no—
365C2×Q16—861no—
366C2×Q16—861no—
367C2×SD16—861no—
368C2×SD16—861no—
369C2×SD16—861no—
370C2×SD16—861no—
371C2×D8—861no—
372C22×C8—861no—
373C22×C8—861no—
374C22×C8—861no—
375C4⋊Q8—431no—
376C4⋊Q8—431no—
377C4⋊Q8—431no—
378#127—431no—
379#125—861no—
380#124—861no—
381C22⋊Q8—861no—
382C22⋊Q8—861no—
383#121—861no—
384#121—861no—
385C4×Q8—431no—
386C4×Q8—431no—
387C4×Q8—861no—
388C4×Q8—861no—
389C4×D4—431no—
390C4×D4—431no—
391C4×D4—861no—
392C4×D4—861no—
393C4×D4—861no—
394C4×D4—861no—
395#117—431no—
396#117—861no—
397#117—861no—
398C2×C42—861no—
399C2×C42C22×D4311yescharacteristic
400#107—861no—
401#107—861no—
402#106—861no—
403#106—861no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—861no—
407C4⋊C8—861no—
408C4⋊C8—861no—
409C4⋊C8D17211yescharacteristic
410C4⋊C8D17211yescharacteristic
411C4⋊C8C22×D4311yescharacteristic
412C4⋊C8C22×D4311yescharacteristic
413C4⋊C8C22×D4311yescharacteristic
414C4⋊C8C22×D4311yescharacteristic
415#103—861no—
416#103—861no—
417#103—861no—
418#103—861no—
419#103—861no—
420#103—861no—
421#102—861no—
422#102—861no—
423#102—861no—
424#102—861no—
425#102—861no—
426#102—861no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—861no—
430C22⋊C8—861no—
431C22⋊C8D17211yescharacteristic
432C22⋊C8D17211yescharacteristic
433#97—21no—
434C4×C8—21no—
435C4×C8—861no—
436C4×C8—861no—
437C4×C8C22×D4311yescharacteristic
438C4×C8C22×D4311yescharacteristic
439#41—862no—
440#41—862no—
441#41—3441no—
442#41—3441no—
443C2×Q8—431no—
444C2×Q8—861no—
445C2×Q8—861no—
446C2×Q8—861no—
447C2×D4—431no—
448C2×D4—861no—
449C2×D4—861no—
450C2×D4—861no—
451C2×D4—861no—
452C2×D4—1721no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—1721no—
457C22×C4C2×D17211yescharacteristic
458C22×C4D4×D4311yescharacteristic
459C22×C4#1062190211yescharacteristic
460Q16—3441no—
461Q16—3441no—
462Q16—1722no—
463SD16—3441no—
464SD16—3441no—
465SD16—1722no—
466SD16—1722no—
467D8—1722no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—861no—
473C2×C8—861no—
474C2×C8—3441no—
475C2×C8—3441no—
476C2×C8—3441no—
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—1721no—
492C4⋊C4—1721no—
493C22⋊C4—861no—
494C22⋊C4—861no—
495C22⋊C4—861no—
496C22⋊C4—1721no—
497C22⋊C4—1721no—
498C22⋊C4—1721no—
499C42—861no—
500C42—861no—
501C42—861no—
502C42—1721no—
503C42C2×D17211yescharacteristic
504C42D4×D4311yescharacteristic
505C42#1062190211yescharacteristic
506C42C23×D4311yescharacteristic
507C23—861no—
508C23—1721no—
509C23#1306330011yescharacteristic
510Q8—432no—
511Q8—861no—
512Q8—1721no—
513Q8—1721no—
514Q8—1721no—
515Q8—1721no—
516Q8—1721no—
517Q8—1721no—
518D4—432no—
519D4—864no—
520D4—861no—
521D4—3441no—
522D4—3442no—
523D4—1721no—
524D4—1721no—
525D4—1721no—
526D4—1721no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—864no—
533C2×C4—861no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—3442no—
537C2×C4—3441no—
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—862no—
563C22—3441no—
564C22—3441no—
565C22—3441no—
566C22—1721no—
567C22—1721no—
568C22C2×#1306330011yescharacteristic
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—862no—
574C4—3441no—
575C4—3441no—
576C4—3441no—
577C4—1721no—
578C4—1721no—
579C4#135×D4311yescharacteristic
580C4#135×D4311yescharacteristic
581C4#1458370411yescharacteristic
582C4#1458371111yescharacteristic
583C2—41no—
584C2—1722no—
585C2—6881no—
586C2#1914413611yescharacteristic
587C2#1914417711yescharacteristic
588C2#1914433311yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1572C2
socleC22×C43C2×#121
prime radical#19144747C2
hypercenter#1572D43
hypocenterC43#19413
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1572

Complements

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

NH ≅ G/Ntype
1. #19145553C2semidirect
3. #19144667C2semidirect
4. #19143703C2semidirect
5. #19134040C2semidirect
6. #19134033C2semidirect
7. #19134026C2semidirect
8. #19134019C2semidirect
9. #19133966C2semidirect
10. #19133961C2semidirect
11. #19133944C2semidirect
12. #19133937C2semidirect
13. #19133296C2semidirect
14. #19133242C2semidirect
15. C43×#1572C2semidirect
301. #1572D43semidirect
361. C43#19413semidirect

Maximal subgroups

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

subgroupindex
#191455532
#191447472
#191446672
#191437032
#191340402
#191340332
#191340262
#191340192
#191339662
#191339612
#191339442
#191339372
#191332962
#191332422
C43×#15722
#1941343