Finite Group Databasebeta

← #25064585

Subgroups — #25064585

Order 11008.

1028 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148551C211yesmaximal, characteristic
2#19143610C211yesmaximal, characteristic, complemented
3#19143024C211yesmaximal, characteristic, complemented
4#19133212C212yesmaximal, complemented
5#19133206C211yesmaximal, characteristic, complemented
6#19133200C211yesmaximal, characteristic, complemented
7#19133191C212yesmaximal, complemented
8#19133184C211yesmaximal, characteristic, complemented
9#19133180C212yesmaximal, complemented
10#329×D43C212yesmaximal, complemented
11C43×#1525C211yesmaximal, characteristic, complemented
12C2×#13063333—21no—
13#14583635C411yescharacteristic
14#14583623C411yescharacteristic
15#14583613—21no—
16#14583578—22no—
17#14583564C411yescharacteristic
18#14583556C412yes—
19#14583546—21no—
20#14583537C412yes—
21#14583534C411yescharacteristic
22#14583514—21no—
23#14583481—22no—
24#14583433C2211yescharacteristic
25#14583428C2212yes—
26#124×D43C2212yes—
27#14583371—21no—
28C4×#10621898C2211yescharacteristic
29#14583029—21no—
30#14582968—22no—
31C8×D172—21no—
32#14582956C2211yescharacteristic, complemented
33#14582954C2212yescomplemented
34#14582857—21no—
35#14582853—22no—
36#14582851C2212yescomplemented
37C2×#13063236C2211yescharacteristic, complemented
38#97×D43C2212yescomplemented
39#97×D43C2212yescomplemented
40#14582640C2211yescharacteristic, complemented
41#14582640C2211yescharacteristic, complemented
42#14582640C2212yescomplemented
43#14582639C2212yescomplemented
44#14582639C2212yescomplemented
45#14582638C2211yescharacteristic
46#14582638C2211yescharacteristic
47#14582638C2212yes—
48C43×#532C2211yescharacteristic
49C4×M16×C43C2211yescharacteristic, complemented
50C4×M16×C43C2211yescharacteristic, complemented
51C43×#329C2212yescomplemented
52C43×#329C2212yescomplemented
53C2×#10621898D411yescharacteristic
54C2×Q8×D43C2×C412yes—
55C2×D4×D43—21no—
56C2×D4×D43C2×C412yes—
57#13063333—28no—
58C2×#10621872—22no—
59C22×C43⋊C8—21no—
60C2×C8×D43—22no—
61C2×C8×D43—22no—
62#13063324—21no—
63#13063320—22no—
64#13063319—21no—
65#13063318—22no—
66#13063317C2311yescharacteristic
67#13063314C2×C412yes—
68#13063313C2311yescharacteristic
69#13063312—21no—
70#13063312—22no—
71#13063312C2×C412yes—
72#13063311—22no—
73#13063311—22no—
74#13063308—21no—
75#13063308—22no—
76#13063307—22no—
77#13063306—22no—
78#13063305—21no—
79#13063304—22no—
80#13063304C2×C411yescharacteristic
81#13063303—22no—
82#13063301C2×C412yes—
83#13063299C2×C411yescharacteristic
84#13063297—22no—
85#13063296—22no—
86#13063296—21no—
87#13063296C2×C412yes—
88#13063293—22no—
89#13063293—22no—
90Q8×Dic43C2×C412yes—
91C4×Dic86C2×C411yescharacteristic
92C4×Dic86C2×C411yescharacteristic
93C4×Dic86D411yescharacteristic
94C4×D172C2×C411yescharacteristic
95C4×D172C2×C411yescharacteristic
96C4×D172D411yescharacteristic
97D4×Dic43—21no—
98D4×Dic43C2×C412yes—
99#13063287—21no—
100C4×C22⋊D43—21no—
101C4×C22⋊D43—22no—
102C4×C22⋊D43C2×C412yes—
103C4×C22⋊D43D412yes—
104(C22⋊D43)⋊C4—22no—
105#13063284D411yescharacteristic
106#13063283—21no—
107#13063282—21no—
108#13063282D412yes—
109#13063281—22no—
110C2×(C2×D43)⋊C4—22no—
111C22⋊C4×D43—22no—
112C22⋊C4×D43—22no—
113C42×D43C2312yes—
114C4⋊(C43⋊C8)—21no—
115Dic43⋊C8—22no—
116C22⋊(C43⋊C8)—21no—
117(C2×D43)⋊C8—22no—
118#13063236—21no—
119#13063236C2311yescharacteristic
120#13063236C2312yes—
121#13063236C2311yescharacteristic
122#13063235—22no—
123#13063235—22no—
124C8×Dic43—22no—
125C2×#41×C43C2×C412yes—
126C2×M16×C43—21no—
127C2×M16×C43—21no—
128C4⋊Q8×C43C2×C411yescharacteristic
129#127×C43C2×C411yescharacteristic
130#124×C43C2312yes—
131#121×C43—21no—
132#121×C43—21no—
133C4×D4×C43—21no—
134C4×D4×C43—21no—
135C2×C42×C43C2311yescharacteristic
136#97×C43C2311yescharacteristic
137#97×C43C2312yes—
138#97×C43C2311yescharacteristic
139C4×C8×C43—21no—
140C4×C8×C43—21no—
141C23×D43—22no—
142#41×C43—82no—
143C2×Q8×C43C22×C412yes—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—22no—
147C2×D4×C43C22×C412yes—
148C22×C4×C43—22no—
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C2×C22⋊D43—22no—
153C2×C22⋊D43—21no—
154C2×C22⋊D43—22no—
155C2×C22⋊D43C22⋊C412yes—
156C22×Dic43—22no—
157Q8×D43—82no—
158D4×D43—44no—
159D4×D43—82no—
160#10621898—24no—
161C2×D172C22⋊C411yescharacteristic
162C2×D172C22×C411yescharacteristic
163C2×C4×D43—21no—
164C2×C4×D43—22no—
165C2×C4×D43C22×C412yes—
166C2×C4×D43C2×D412yes—
167C2×C4×D43C2×D412yes—
168C2×Dic86—22no—
169C2×Dic86C22⋊C411yescharacteristic
170C2×Dic86C22×C411yescharacteristic
171M16×C43—24no—
172M16×C43—42no—
173C2×C8×C43—22no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C22⋊C4×C43—22no—
179C22⋊C4×C43—22no—
180C42×C43C22×C411yescharacteristic
181C42×C43C2×D411yescharacteristic
182C42×C43C2×D411yescharacteristic
183C42×C43C2411yescharacteristic
184C22⋊Dic43—22no—
185C22⋊Dic43—22no—
186C22⋊Dic43—22no—
187C22⋊Dic43—22no—
188C22⋊Dic43—21no—
189C22⋊Dic43C22⋊C412yes—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—21no—
192(C2×D43)⋊C4—21no—
193(C2×D43)⋊C4—21no—
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4C22⋊C412yes—
198(C2×D43)⋊C4C22⋊C412yes—
199C4⋊Dic43—22no—
200C4⋊Dic43C22⋊C411yescharacteristic
201C4⋊Dic43C22⋊C411yescharacteristic
202C4⋊Dic43C22×C411yescharacteristic
203C4⋊Dic43C22×C411yescharacteristic
204Dic43⋊C4—21no—
205Dic43⋊C4—21no—
206Dic43⋊C4—21no—
207Dic43⋊C4—21no—
208Dic43⋊C4—22no—
209Dic43⋊C4C22⋊C412yes—
210Dic43⋊C4C22⋊C412yes—
211C4×Dic43—21no—
212C4×Dic43—22no—
213C4×Dic43C22×C412yes—
214C4×Dic43C2×D412yes—
215C4×Dic43C2×D412yes—
216C2×C43⋊C8—24no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—22no—
220#10621872—28no—
221C8×D43—28no—
222C8×D43—44no—
223C23×C43—22no—
224C23×C43C2×C22⋊C411yescharacteristic
225C22×D43—21no—
226C22×D43—44no—
227C22×D43—82no—
228C22×D43—82no—
229C22×D43C2×C22⋊C412yes—
230Q8×C43—42no—
231D4×C43—42no—
232D4×C43—42no—
233D4×C43—81no—
234D4×C43—82no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—82no—
240C2×C4×C43C2×C22⋊C411yescharacteristic
241C2×C4×C43C2×C22⋊C411yescharacteristic
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43C23×C411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C22×D411yescharacteristic
246C22⋊D43—24no—
247C22⋊D43—44no—
248C22⋊D43—82no—
249C22⋊D43—81no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—82no—
254C2×Dic43C2×C22⋊C412yes—
255C2×Dic43C2×C22⋊C412yes—
256C2×Dic43C2×C22⋊C412yes—
257D172—41no—
258D172#10414yes—
259C4×D43—24no—
260C4×D43—42no—
261C4×D43—42no—
262C4×D43—42no—
263C4×D43—82no—
264Dic86—22no—
265Dic86—41no—
266Dic86—82no—
267C8×C43—24no—
268C8×C43—22no—
269C8×C43—41no—
270C43⋊C8—22no—
271C43⋊C8—22no—
272C43⋊C8—42no—
273#17652—431nomaximal, Sylow
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—21no—
277C22×C43—42no—
278C22×C43—42no—
279C22×C43—42no—
280C22×C43C22×C22⋊C411yescharacteristic
281C2×D43—22no—
282C2×D43—22no—
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—41no—
286C2×D43—164no—
287C2×D43C2×#10414yes—
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—21no—
291C4×C43—21no—
292C4×C43—21no—
293C4×C43—42no—
294C4×C43C2×#10412yes—
295Dic43—22no—
296Dic43—22no—
297Dic43—22no—
298Dic43—41no—
299Dic43—41no—
300Dic43—41no—
301#3514—431no—
302#2970—431no—
303#2875—431no—
304#1532—432no—
305#1530—431no—
306#1529—431no—
307#1527—432no—
308#1525D4311yescharacteristic, complemented
309#1524—431no—
310#1524—432no—
311C2×#329—432no—
312C2×C43—41no—
313C2×C43—82no—
314C2×C43#288811yescharacteristic
315C2×C43C22×#10411yescharacteristic
316C2×C43#290111yescharacteristic
317D43—24no—
318D43—81no—
319C2×#131—861no—
320#559—431no—
321#556—431no—
322#555—861no—
323#551—862no—
324D4×Q8—431no—
325#548—432no—
326#546—432no—
327#546—861no—
328D42—431no—
329#542—861no—
330#538—862no—
331#532C2×D4311yescharacteristic
332#529—432no—
333#529—431no—
334C2×#124—432no—
335#518—861no—
336C4×#41—431no—
337#446—861no—
338#435—862no—
339C8×D4—861no—
340#432—431no—
341#432—432no—
342#405—862no—
343#405—861no—
344C4×M16—432no—
345C4×M16C2×D4311yescharacteristic, complemented
346C4×M16C2×D4311yescharacteristic, complemented
347C2×#97—431no—
348C2×#97—432no—
349C2×#97—432no—
350#330—431no—
351#330—432no—
352#330—431no—
353#329—432no—
354#329—432no—
355#329—431no—
356#329—432no—
357#329—431no—
358#329C2×D4312yescomplemented
359#329C2×D4312yescomplemented
360C43#1765211yescharacteristic, complemented, Sylow
361C2×#41—431no—
362C2×#41C4×D4312yes—
363C22×Q8—432no—
364C22×D4—432no—
365C22×D4—861no—
366#131—868no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—862no—
370C22×C8—862no—
371C22×C8—862no—
372C22×C8—861no—
373C4⋊Q8—861no—
374C4⋊Q8C4×D4311yescharacteristic
375#127C4×D4311yescharacteristic
376#126—862no—
377#126—862no—
378#126—861no—
379#125—431no—
380#124—432no—
381#124—432no—
382#124—431no—
383#124—862no—
384#124—862no—
385#124—862no—
386#124—861no—
387#124C22×D4312yes—
388#123—862no—
389#123—862no—
390#123—862no—
391#123—861no—
392C22⋊Q8—432no—
393C22⋊Q8—431no—
394C22⋊Q8—862no—
395C22⋊Q8—861no—
396C22⋊Q8—862no—
397#121—21no—
398#121—21no—
399#121—432no—
400#121—431no—
401#121—862no—
402#121—861no—
403#121—862no—
404#120—862no—
405#120—862no—
406C4×Q8—431no—
407C4×Q8—431no—
408C4×Q8—432no—
409C4×Q8—431no—
410C4×D4—21no—
411C4×D4—21no—
412C4×D4—432no—
413C4×D4—432no—
414C4×D4—432no—
415C4×D4—431no—
416C4×D4—431no—
417C4×D4—431no—
418C4×D4—862no—
419C4×D4—862no—
420C4×D4—861no—
421C4×D4—861no—
422C4×D4—861no—
423#117—431no—
424#117—432no—
425#117—862no—
426#117—861no—
427#117—861no—
428C2×C22⋊C4—862no—
429C2×C22⋊C4—862no—
430C2×C22⋊C4—862no—
431C2×C42—432no—
432C2×C42C22×D4311yescharacteristic
433C4⋊C8—862no—
434C4⋊C8—861no—
435C22⋊C8—862no—
436C22⋊C8—861no—
437#97—431no—
438#97—431no—
439#97—432no—
440#97—862no—
441#97—862no—
442#97—861no—
443#97C22×D4311yescharacteristic
444#97C22×D4312yes—
445#97C22×D4311yescharacteristic
446C4×C8—21no—
447C4×C8—21no—
448C4×C8—862no—
449C24—862no—
450#41—82no—
451#41—864no—
452C2×Q8—431no—
453C2×Q8—431no—
454C2×Q8—862no—
455C2×Q8—3442no—
456C2×Q8C2×C4×D4312yes—
457C2×D4—22no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—432no—
461C2×D4—431no—
462C2×D4—431no—
463C2×D4—862no—
464C2×D4—861no—
465C2×D4—862no—
466C2×D4—3442no—
467C2×D4—1724no—
468C2×D4C2×C4×D4312yes—
469C22×C4—22no—
470C22×C4—432no—
471C22×C4—432no—
472C22×C4—432no—
473C22×C4—862no—
474C22×C4—862no—
475C22×C4—861no—
476C22×C4C2×C4×D4311yescharacteristic
477C22×C4D4×D4311yescharacteristic
478C22×C4D4×D4311yescharacteristic
479M16—24no—
480M16—42no—
481M16—868no—
482C2×C8—22no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—868no—
486C2×C8—864no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—862no—
490C2×C8—1724no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—431no—
494C4⋊C4—431no—
495C4⋊C4—432no—
496C4⋊C4—432no—
497C4⋊C4—431no—
498C4⋊C4—431no—
499C4⋊C4—862no—
500C4⋊C4—862no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—861no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—432no—
508C22⋊C4—432no—
509C22⋊C4—432no—
510C22⋊C4—862no—
511C22⋊C4—862no—
512C22⋊C4—862no—
513C22⋊C4—862no—
514C22⋊C4—862no—
515C22⋊C4—862no—
516C22⋊C4—862no—
517C22⋊C4—861no—
518C22⋊C4—861no—
519C22⋊C4—861no—
520C22⋊C4—861no—
521C22⋊C4—861no—
522C42—432no—
523C42—432no—
524C42—432no—
525C42—862no—
526C42—861no—
527C42C2×C4×D4311yescharacteristic
528C42D4×D4311yescharacteristic
529C42D4×D4311yescharacteristic
530C42C23×D4311yescharacteristic
531C23—22no—
532C23—432no—
533C23—861no—
534C23—3442no—
535C23—3442no—
536C23—1724no—
537C23C22⋊C4×D4311yescharacteristic
538Q8—42no—
539Q8—862no—
540Q8—3442no—
541Q8—1721no—
542D4—42no—
543D4—42no—
544D4—81no—
545D4—82no—
546D4—434no—
547D4—864no—
548D4—3442no—
549D4—3441no—
550D4—1721no—
551D4—1724no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—82no—
557C2×C4—432no—
558C2×C4—432no—
559C2×C4—432no—
560C2×C4—864no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—3442no—
565C2×C4—3442no—
566C2×C4—1722no—
567C2×C4—1722no—
568C2×C4—1722no—
569C2×C4C22⋊C4×D4311yescharacteristic
570C2×C4C22⋊C4×D4311yescharacteristic
571C2×C4C22⋊C4×D4311yescharacteristic
572C2×C4C22×C4×D4311yescharacteristic
573C2×C4C2×D4×D4311yescharacteristic
574C2×C4C2×D4×D4311yescharacteristic
575C8—24no—
576C8—22no—
577C8—41no—
578C8—862no—
579C8—862no—
580C8—1722no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—434no—
588C22—862no—
589C22—862no—
590C22—1721no—
591C22—1721no—
592C22—1721no—
593C22—6884no—
594C22C2×C22⋊C4×D4311yescharacteristic
595C4—21no—
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—42no—
601C4—862no—
602C4—862no—
603C4—862no—
604C4—1721no—
605C4—1721no—
606C4—1721no—
607C4#104×D4312yes—
608C2—41no—
609C2—82no—
610C2—864no—
611C2—3441no—
612C2#1914307111yescharacteristic
613C2C2×#104×D4311yescharacteristic
614C2#1914313911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1525C2
socleC22×C43C22×C22⋊C4
prime radical#19148551C2
cosocleC42×C43C24
hypercenter#1525D43
hypocenterC43#17652
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1525

Complements

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

NH ≅ G/Ntype
2. #19143610C2semidirect
3. #19143024C2semidirect
4. #19133212C2semidirect
5. #19133206C2semidirect
6. #19133200C2semidirect
7. #19133191C2semidirect
8. #19133184C2semidirect
9. #19133180C2semidirect
10. #329×D43C2semidirect
11. C43×#1525C2semidirect
32. #14582956C22semidirect
33. #14582954C22semidirect
36. #14582851C22semidirect
37. C2×#13063236C22semidirect
38. #97×D43C22semidirect
39. #97×D43C22semidirect
40. #14582640C22semidirect
41. #14582640C22semidirect
42. #14582640C22semidirect
43. #14582639C22semidirect
44. #14582639C22semidirect
49. C4×M16×C43C22semidirect
50. C4×M16×C43C22semidirect
51. C43×#329C22semidirect
52. C43×#329C22semidirect
308. #1525D43semidirect
345. C4×M16C2×D43semidirect
346. C4×M16C2×D43semidirect
358. #329C2×D43semidirect
359. #329C2×D43semidirect
360. C43#17652semidirect

Maximal subgroups

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

subgroupindex
#191485512
#191436102
#191430242
#191332122
#191332062
#191332002
#191331912
#191331842
#191331802
#329×D432
C43×#15252
#1765243