Finite Group Databasebeta

← #25079021

Subgroups — #25079021

Order 11008.

672 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145154C211yesmaximal, characteristic, complemented
2#19144385C211yesmaximal, characteristic, complemented
3#19144052C211yesmaximal, characteristic
4C8×#10621898C211yesmaximal, characteristic, complemented
5#19134026C211yesmaximal, characteristic, complemented
6#19134019C211yesmaximal, characteristic, complemented
7#19134012C211yesmaximal, characteristic, complemented
8#19134005C211yesmaximal, characteristic, complemented
9#19133978C211yesmaximal, characteristic, complemented
10#19133971C211yesmaximal, characteristic, complemented
11#19133944C211yesmaximal, characteristic, complemented
12#19133937C211yesmaximal, characteristic, complemented
13#19133253C211yesmaximal, characteristic, complemented
14#19133245C211yesmaximal, characteristic, complemented
15C2×C43×#334C211yesmaximal, characteristic, complemented
16C2×#13063347—21no—
17#14583456C2211yescharacteristic
18#14583449C2211yescharacteristic
19C4×#10621898C2211yescharacteristic
20#14583297C2211yescharacteristic
21#14583272C2211yescharacteristic
22#14583250C2211yescharacteristic
23#14583246C2211yescharacteristic
24#14583207—21no—
25#14583200—21no—
26#14583195C2211yescharacteristic
27#14583190C2211yescharacteristic
28#14583185C2211yescharacteristic
29#14583180C2211yescharacteristic
30#14583128—21no—
31#14583128—21no—
32#14583122—21no—
33#14583115—21no—
34#14583110C2211yescharacteristic
35#14583105C2211yescharacteristic
36#14583100C2211yescharacteristic
37#14583095C2211yescharacteristic
38C8×Dic86C2211yescharacteristic
39C8×Dic86C2211yescharacteristic
40C4×#10621873—21no—
41C4×#10621873—21no—
42C8×D172C2211yescharacteristic
43C8×D172C2211yescharacteristic
44C8×C22⋊D43—21no—
45C8×C22⋊D43—21no—
46#14582952C2211yescharacteristic
47#14582950—21no—
48#14582937—21no—
49#14582896—21no—
50#14582896—21no—
51C4×C8×D43—21no—
52#14582647C2211yescharacteristic
53#14582647C2211yescharacteristic
54#14582646C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582644C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C2×C4⋊C8×C43C2211yescharacteristic
61C2×C4⋊C8×C43C2211yescharacteristic
62C2×C4×C8×C43C2211yescharacteristic
63C43×#334C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#334C2211yescharacteristic
66C43×#334C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621898D411yescharacteristic
69#13063347—44no—
70C2×Dic172—21no—
71C2×#10621873—21no—
72C2×#10621873—21no—
73C2×#10621873—21no—
74C2×#10621873—21no—
75C2×D344—21no—
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063325C2311yescharacteristic
81#13063322C2311yescharacteristic
82#13063317—21no—
83#13063313—21no—
84#13063304—21no—
85#13063304—21no—
86#13063299—21no—
87#13063299—21no—
88C4×Dic86—21no—
89C4×Dic86—21no—
90C4×Dic86D411yescharacteristic
91C4×Dic86C2311yescharacteristic
92C4×D172—21no—
93C4×D172—21no—
94C4×D172D411yescharacteristic
95C4×D172C2311yescharacteristic
96C4×C22⋊D43—21no—
97C4×C22⋊D43—21no—
98#13063284—21no—
99#13063284D411yescharacteristic
100#13063282—21no—
101C42×D43—21no—
102#13063259—21no—
103#13063259—21no—
104#13063257—21no—
105#13063257—21no—
106#13063257—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#13063247—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—
127C4×C43⋊C8—21no—
128C8×Dic43—21no—
129C8×Dic43—21no—
130C22×C8×C43—21no—
131C22×C8×C43—21no—
132C22×C8×C43D411yescharacteristic
133C22×C8×C43D411yescharacteristic
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—21no—
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C4×C8×C43D411yescharacteristic
142C4×C8×C43D411yescharacteristic
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—42no—
152#10621898—42no—
153#10621898SD1614yescomplemented
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
166C2×C8×C43—22no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—41no—
172C2×C8×C43—42no—
173C2×C8×C43—42no—
174C2×C8×C43C2×D411yescharacteristic
175C2×C8×C43C2×D411yescharacteristic
176C2×C8×C43C2×D411yescharacteristic
177C2×C8×C43C2×D411yescharacteristic
178C42×C43C2×D411yescharacteristic
179C42×C43C2×D411yescharacteristic
180C42×C43#4111yescharacteristic
181C42×C43C2411yescharacteristic
182C22⋊Dic43—21no—
183C22⋊Dic43—41no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—41no—
187(C2×D43)⋊C4—41no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43C2×D411yescharacteristic
195C4⋊Dic43C2×D411yescharacteristic
196Dic43⋊C4—21no—
197Dic43⋊C4—21no—
198Dic43⋊C4—41no—
199Dic43⋊C4—41no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43—21no—
203C4×Dic43—41no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206Dic172—42no—
207D344—42no—
208#10621873—42no—
209#10621873—42no—
210#10621873—42no—
211#10621873—42no—
212C8×D43—42no—
213C8×D43—42no—
214C23×C43#12111yescharacteristic
215C22×D43—21no—
216C22×D43—41no—
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×C43C2×SD1612yes—
224C2×C4×C43#13512yes—
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C22⋊D43—24no—
229C22⋊D43—82no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236D172—21no—
237D172—41no—
238D172—41no—
239D172—41no—
240D172—41no—
241D172—81no—
242D172C2×SD1612yes—
243C4×D43—24no—
244C4×D43—42no—
245C4×D43—41no—
246C4×D43—41no—
247C4×D43—82no—
248Dic86—21no—
249Dic86—41no—
250Dic86—41no—
251Dic86—41no—
252Dic86—41no—
253Dic86—81no—
254Dic86C2×SD1612yes—
255C8×C43—21no—
256C8×C43—21no—
257C8×C43—21no—
258C8×C43—41no—
259C8×C43—41no—
260C8×C43—41no—
261C8×C43—41no—
262C8×C43#13512yescomplemented
263C43⋊C8—41no—
264C43⋊C8—41no—
265#19124—431nomaximal, Sylow
266C22×C43—21no—
267C22×C43—21no—
268C22×C43#46512yes—
269C22×C43C2×#12111yescharacteristic
270C2×D43—22no—
271C2×D43—41no—
272C2×D43—41no—
273C2×D43—81no—
274C2×D43—81no—
275C2×D43—81no—
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43#46512yes—
280C4×C43C22×SD1611yescharacteristic
281C4×C43C2×#13511yescharacteristic
282C4×C43C2×#13511yescharacteristic
283C4×C43#57511yescharacteristic
284Dic43—22no—
285Dic43—41no—
286Dic43—41no—
287Dic43—81no—
288Dic43—81no—
289Dic43—81no—
290#3167—431no—
291#3076—431no—
292#3035—431no—
293C8×#41—431no—
294#1680—431no—
295#1679—431no—
296#1678—431no—
297#1677—431no—
298#1672—431no—
299#1671—431no—
300#1666—431no—
301#1665—431no—
302C2×#334D4311yescharacteristic, complemented
303#1542—431no—
304#1540—431no—
305C2×C43—22no—
306C2×C43#303511yescharacteristic
307C2×C43C2×#46511yescharacteristic
308C2×C43#306711yescharacteristic
309D43—42no—
310D43—161no—
311C2×#135—861no—
312#533—431no—
313#532—431no—
314C4×#41—431no—
315#498—431no—
316#492—431no—
317#487—431no—
318#486—431no—
319#479—861no—
320#478—861no—
321#477—431no—
322#476—431no—
323#475—431no—
324#474—431no—
325#465—861no—
326#465—861no—
327#464—861no—
328#463—861no—
329#462—431no—
330#461—431no—
331#460—431no—
332#459—431no—
333C8×Q8—431no—
334C8×Q8—431no—
335C4×SD16—861no—
336C4×SD16—861no—
337C8×D4—431no—
338C8×D4—431no—
339C8×D4—861no—
340C8×D4—861no—
341#431—431no—
342#431—861no—
343#427—861no—
344C2×C4⋊C8C2×D4311yescharacteristic
345C2×C4⋊C8C2×D4311yescharacteristic
346#416—861no—
347#416—861no—
348C2×C4×C8—861no—
349C2×C4×C8C2×D4311yescharacteristic
350#334C2×D4311yescharacteristic
351#334C2×D4311yescharacteristic
352#334C2×D4311yescharacteristic
353#334C2×D4311yescharacteristic
354#333—431no—
355#333—431no—
356#332—431no—
357#332—431no—
358#332—431no—
359#332—431no—
360#331—431no—
361#331—431no—
362C43#1912411yescharacteristic, complemented, Sylow
363C2×#41—431no—
364C2×#41—861no—
365#135—1724no—
366C2×Q16—861no—
367C2×SD16—861no—
368C2×SD16—861no—
369C2×SD16—861no—
370C2×SD16—861no—
371C2×D8—861no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—861no—
375C22×C8—861no—
376C22×C8D17211yescharacteristic
377C22×C8D17211yescharacteristic
378C4⋊Q8—431no—
379C4⋊Q8—431no—
380C4⋊Q8—431no—
381#127—431no—
382#125—861no—
383#124—861no—
384C22⋊Q8—861no—
385C22⋊Q8—861no—
386#121—861no—
387#121—861no—
388C4×Q8—431no—
389C4×Q8—431no—
390C4×Q8—861no—
391C4×Q8—861no—
392C4×D4—431no—
393C4×D4—431no—
394C4×D4—861no—
395C4×D4—861no—
396C4×D4—861no—
397C4×D4—861no—
398#117—431no—
399#117—861no—
400#117—861no—
401C2×C42—861no—
402C2×C42C22×D4311yescharacteristic
403#107—861no—
404#107—861no—
405#106—861no—
406#106—861no—
407#106—861no—
408#106—861no—
409C4⋊C8—21no—
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#102—861no—
426#102—861no—
427#102—861no—
428#102—861no—
429#102—861no—
430#102—861no—
431C22⋊C8—861no—
432C22⋊C8—861no—
433C22⋊C8—861no—
434C4×C8—861no—
435C4×C8—861no—
436C4×C8—861no—
437C4×C8D17211yescharacteristic
438C4×C8D17211yescharacteristic
439C4×C8C22×D4311yescharacteristic
440C4×C8C22×D4311yescharacteristic
441#41—434no—
442#41—862no—
443#41—1722no—
444#41—1722no—
445C2×Q8—431no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×D4—431no—
450C2×D4—861no—
451C2×D4—861no—
452C2×D4—861no—
453C2×D4—861no—
454C2×D4—1721no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—1721no—
459C22×C4C2×D17211yescharacteristic
460C22×C4D4×D4311yescharacteristic
461C22×C4#1062190211yescharacteristic
462Q16—1722no—
463SD16—1722no—
464SD16—1722no—
465SD16—1722no—
466SD16—1722no—
467D8—1722no—
468C2×C8—22no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—41no—
474C2×C8—42no—
475C2×C8—42no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—1722no—
479C2×C8—1722no—
480C2×C8C2×D17211yescharacteristic
481C2×C8C2×D17211yescharacteristic
482C2×C8C2×D17211yescharacteristic
483C2×C8C2×D17211yescharacteristic
484C4⋊C4—431no—
485C4⋊C4—431no—
486C4⋊C4—861no—
487C4⋊C4—861no—
488C4⋊C4—861no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—1721no—
495C4⋊C4—1721no—
496C22⋊C4—861no—
497C22⋊C4—861no—
498C22⋊C4—861no—
499C22⋊C4—1721no—
500C22⋊C4—1721no—
501C22⋊C4—1721no—
502C42—861no—
503C42—861no—
504C42—861no—
505C42—1721no—
506C42C2×D17211yescharacteristic
507C42D4×D4311yescharacteristic
508C42#1062190211yescharacteristic
509C42C23×D4311yescharacteristic
510C23—861no—
511C23—1721no—
512C23#1306330011yescharacteristic
513Q8—432no—
514Q8—861no—
515Q8—3441no—
516Q8—1721no—
517Q8—1721no—
518Q8—1721no—
519Q8—1721no—
520D4—432no—
521D4—864no—
522D4—861no—
523D4—3441no—
524D4—3442no—
525D4—1721no—
526D4—1721no—
527D4—1721no—
528D4—1721no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—861no—
533C2×C4—864no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—3442no—
537C2×C4—1722no—
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×C4SD16×D4312yes—
547C2×C4#1306334612yes—
548C2×C4C2×D4×D4311yescharacteristic
549C2×C4C22×D17211yescharacteristic
550C2×C4C2×#1062190211yescharacteristic
551C8—21no—
552C8—21no—
553C8—21no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—1721no—
559C8—1721no—
560C8#1306334712yescomplemented
561C22—21no—
562C22—21no—
563C22—862no—
564C22—3441no—
565C22—3441no—
566C22—3441no—
567C22—1721no—
568C22—1721no—
569C22#1458312912yes—
570C22C2×#1306330011yescharacteristic
571C4—21no—
572C4—21no—
573C4—21no—
574C4—862no—
575C4—3441no—
576C4—3441no—
577C4—3441no—
578C4—1721no—
579C4—1721no—
580C4#1458312912yes—
581C4C2×SD16×D4311yescharacteristic
582C4C2×#1306334611yescharacteristic
583C4C2×#1306334711yescharacteristic
584C4#1458369911yescharacteristic
585C2—22no—
586C2—1722no—
587C2—6881no—
588C2#1914405211yescharacteristic
589C2C2×#1458312911yescharacteristic
590C2#1914431611yescharacteristic
subgroupG/H
centerC2×C4#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#334C2
socleC22×C43C2×#121
prime radical#19144052C2
hypercenterC2×#334D43
hypocenterC43#19124
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
1. #19145154C2semidirect
2. #19144385C2semidirect
4. C8×#10621898C2semidirect
5. #19134026C2semidirect
6. #19134019C2semidirect
7. #19134012C2semidirect
8. #19134005C2semidirect
9. #19133978C2semidirect
10. #19133971C2semidirect
11. #19133944C2semidirect
12. #19133937C2semidirect
13. #19133253C2semidirect
14. #19133245C2semidirect
15. C2×C43×#334C2semidirect
153. #10621898SD16semidirect
262. C8×C43#135semidirect
302. C2×#334D43semidirect
362. C43#19124semidirect
560. C8#13063347semidirect

Maximal subgroups

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

subgroupindex
#191451542
#191443852
#191440522
C8×#106218982
#191340262
#191340192
#191340122
#191340052
#191339782
#191339712
#191339442
#191339372
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C2×C43×#3342
#1912443