Finite Group Databasebeta

← #25064582

Subgroups — #25064582

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#19148558C211yesmaximal, characteristic
2#19143607C211yesmaximal, characteristic, complemented
3#19143024C211yesmaximal, characteristic, complemented
4#19133214C212yesmaximal, complemented
5#19133207C211yesmaximal, characteristic, complemented
6#19133191C212yesmaximal, complemented
7#19133186C211yesmaximal, characteristic, complemented
8#19133183C211yesmaximal, characteristic, complemented
9#19133182C212yesmaximal, complemented
10#329×D43C212yesmaximal, complemented
11C43×#1529C211yesmaximal, characteristic, complemented
12C2×#13063333—21no—
13#14583634C411yescharacteristic
14#14583619C411yescharacteristic
15#14583614—21no—
16#14583574—22no—
17Q8×D172C411yescharacteristic
18#14583559C412yes—
19#14583546C412yes—
20#14583545—21no—
21D4×D172C411yescharacteristic
22#14583520—21no—
23#14583485—22no—
24#14583449C2211yescharacteristic
25#14583434C2212yes—
26#124×D43C2212yes—
27#14583373—21no—
28C4×#10621898C2211yescharacteristic
29#14583026—21no—
30#14582973—22no—
31#14582964—21no—
32#14582954C2212yescomplemented
33#14582857—21no—
34#14582853—22no—
35C4×#10621877C2211yescharacteristic, complemented
36#14582851C2212yescomplemented
37C2×#13063236C2211yescharacteristic, complemented
38#97×D43C2212yescomplemented
39#97×D43C2212yescomplemented
40#14582641C2211yescharacteristic, complemented
41#14582641C2211yescharacteristic, complemented
42#14582639C2211yescharacteristic
43#14582639C2211yescharacteristic
44#14582638C2212yescomplemented
45#14582638C2212yescomplemented
46#14582638C2212yescomplemented
47#14582638C2212yescomplemented
48C43×#529C2211yescharacteristic
49C43×#432C2211yescharacteristic, complemented
50C4×M16×C43C2211yescharacteristic, complemented
51C43×#330C2212yescomplemented
52C43×#329C2212yes—
53C2×#10621898C2×C412yes—
54C2×#10621898D411yescharacteristic
55C2×Q8×D43C2×C412yes—
56C22×D172—21no—
57C2×D4×D43C2×C412yes—
58#13063333—28no—
59C2×#10621877—21no—
60C2×#10621872—22no—
61C22×C43⋊C8—21no—
62C2×C8×D43—22no—
63C2×C8×D43—22no—
64#13063325—21no—
65#13063325C2×C411yescharacteristic
66#13063322C2×C411yescharacteristic
67#13063320—22no—
68#13063318—22no—
69#13063314C2×C412yes—
70#13063313—21no—
71#13063313C2312yes—
72#13063312C2×C412yes—
73#13063311—22no—
74#13063311—22no—
75#13063311—22no—
76#13063310—22no—
77#13063310—22no—
78#13063307—22no—
79#13063305—22no—
80#13063305C2×C412yes—
81#13063304—21no—
82#13063303—22no—
83#13063300C2×C412yes—
84#13063299—21no—
85#13063299—21no—
86#13063299—21no—
87#13063298—22no—
88#13063296—22no—
89#13063295—22no—
90#13063293—22no—
91C4×Dic86C2×C411yescharacteristic
92C4×Dic86D411yescharacteristic
93#13063290C2×C412yes—
94C4×D172—21no—
95C4×D172—21no—
96C4×D172—21no—
97C4×D172—21no—
98C4×D172C2×C411yescharacteristic
99C4×D172D411yescharacteristic
100#13063287—22no—
101#13063287—22no—
102#13063287C2×C412yes—
103C4×C22⋊D43C2×C412yes—
104C4×C22⋊D43D412yes—
105#13063284—21no—
106#13063284D411yescharacteristic
107#13063283—22no—
108#13063282D412yes—
109C22⋊C4×D43—22no—
110C22⋊C4×D43—22no—
111C22⋊C4×D43—22no—
112C42×D43C2312yes—
113Dic43⋊C8—22no—
114(C2×D43)⋊C8—22no—
115#13063236—21no—
116#13063236C2311yescharacteristic
117#13063236C2311yescharacteristic
118#13063236C2311yescharacteristic
119#13063236C2311yescharacteristic
120#13063235—22no—
121#13063235—22no—
122C4×C43⋊C8—21no—
123C8×Dic43—22no—
124C2×M16×C43—21no—
125#126×C43—21no—
126#125×C43C2311yescharacteristic
127#124×C43C2311yescharacteristic
128#123×C43—21no—
129C22⋊Q8×C43C2×C411yescharacteristic
130#121×C43C2×C411yescharacteristic
131C4×Q8×C43C2×C411yescharacteristic
132C4×D4×C43—21no—
133C4×D4×C43C2×C411yescharacteristic
134#117×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138#97×C43C2312yes—
139#97×C43C2312yes—
140C4×C8×C43—21no—
141C23×D43—22no—
142C2×Q8×C43C22×C411yescharacteristic
143C2×D4×C43—21no—
144C2×D4×C43C22×C411yescharacteristic
145C22×C4×C43—21no—
146C22×C4×C43C22×C411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C2×C22⋊D43—22no—
150C2×C22⋊D43—22no—
151C2×C22⋊D43C22⋊C412yes—
152Q8×D43—82no—
153D4×D43—82no—
154#10621898—24no—
155#10621898—82no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—22no—
159C2×D172—44no—
160C2×D172C22⋊C411yescharacteristic
161C2×D172C22×C412yes—
162C2×C4×D43—22no—
163C2×C4×D43—22no—
164C2×C4×D43—22no—
165C2×C4×D43C22×C412yes—
166C2×C4×D43C2×D412yes—
167C2×C4×D43C2×D412yes—
168C2×Dic86—22no—
169C2×Dic86C22⋊C411yescharacteristic
170C2×Dic86C22×C412yes—
171M16×C43—24no—
172C2×C8×C43—22no—
173C2×C8×C43—22no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43C22×C411yescharacteristic
179C4⋊C4×C43C22×C411yescharacteristic
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—21no—
183C22⋊C4×C43—21no—
184C22⋊C4×C43—21no—
185C42×C43—21no—
186C42×C43C22×C411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43C2411yescharacteristic
190C22⋊Dic43—22no—
191C22⋊Dic43—22no—
192C22⋊Dic43C22⋊C412yes—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4—22no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4—22no—
200(C2×D43)⋊C4C22⋊C412yes—
201(C2×D43)⋊C4C22⋊C412yes—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—22no—
205C4⋊Dic43C22⋊C411yescharacteristic
206C4⋊Dic43C22⋊C411yescharacteristic
207Dic43⋊C4—22no—
208Dic43⋊C4C22⋊C412yes—
209Dic43⋊C4C22⋊C412yes—
210C4×Dic43—22no—
211C4×Dic43C22×C412yes—
212C4×Dic43C2×D412yes—
213C4×Dic43C2×D412yes—
214#10621877—42no—
215C2×C43⋊C8—24no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220#10621872—28no—
221C8×D43—28no—
222C8×D43—44no—
223C23×C43—21no—
224C23×C43C2×C22⋊C411yescharacteristic
225C22×D43—22no—
226C22×D43—44no—
227C22×D43—82no—
228C22×D43—82no—
229C22×D43C2×C22⋊C412yes—
230Q8×C43—41no—
231D4×C43—41no—
232D4×C43—81no—
233C2×C4×C43—22no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—42no—
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—82no—
248C22⋊D43—82no—
249C2×Dic43—22no—
250C2×Dic43C2×C22⋊C412yes—
251C2×Dic43C2×C22⋊C412yes—
252C2×Dic43C2×C22⋊C412yes—
253D172—42no—
254D172—44no—
255D172—42no—
256D172—81no—
257D172#10414yes—
258C4×D43—24no—
259C4×D43—42no—
260C4×D43—42no—
261C4×D43—82no—
262C4×D43—82no—
263C4×D43—82no—
264Dic86—22no—
265Dic86—42no—
266Dic86—82no—
267C8×C43—24no—
268C8×C43—42no—
269C43⋊C8—22no—
270C43⋊C8—22no—
271C43⋊C8—22no—
272C43⋊C8—41no—
273#17652—431nomaximal, Sylow
274C22×C43—21no—
275C22×C43—21no—
276C22×C43—21no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43C22×C22⋊C411yescharacteristic
281C2×D43—22no—
282C2×D43—22no—
283C2×D43—42no—
284C2×D43—42no—
285C2×D43—42no—
286C2×D43—164no—
287C2×D43C2×#10414yes—
288C4×C43—21no—
289C4×C43—21no—
290C4×C43—21no—
291C4×C43—21no—
292C4×C43—21no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43—41no—
296C4×C43C2×#10412yes—
297Dic43—22no—
298Dic43—22no—
299Dic43—22no—
300Dic43—42no—
301#3514—431no—
302#2970—431no—
303#2875—431no—
304#1532—432no—
305#1530—431no—
306#1529D4311yescharacteristic, complemented
307#1527—432no—
308#1525—431no—
309#1524—432no—
310#1524—431no—
311C2×#329—432no—
312C2×C43—41no—
313C2×C43—81no—
314C2×C43#288811yescharacteristic
315C2×C43C22×#10411yescharacteristic
316C2×C43#290111yescharacteristic
317D43—24no—
318D43—82no—
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#532—431no—
332#529—432no—
333#529C2×D4311yescharacteristic
334C2×#124—432no—
335#518—861no—
336C4×#41—431no—
337#446—861no—
338#435—862no—
339C8×D4—861no—
340#432—432no—
341#432C2×D4311yescharacteristic, complemented
342#405—862no—
343#405—861no—
344C4×M16—431no—
345C4×M16—432no—
346C4×M16C2×D4311yescharacteristic, complemented
347C2×#97—431no—
348C2×#97—432no—
349C2×#97—432no—
350#330—431no—
351#330—431no—
352#330C2×D4312yescomplemented
353#329—431no—
354#329—431no—
355#329—432no—
356#329—432no—
357#329—432no—
358#329—432no—
359#329C2×D4312yes—
360C43#1765211yescharacteristic, complemented, Sylow
361C2×#41—431no—
362C2×#41—432no—
363C22×Q8—432no—
364C22×D4—432no—
365C22×D4—861no—
366#131—868no—
367C2×M16—21no—
368C2×M16—862no—
369C2×M16—861no—
370C22×C8—862no—
371C22×C8—862no—
372C22×C8—861no—
373C4⋊Q8—431no—
374C4⋊Q8—861no—
375#127—431no—
376#126—21no—
377#126—862no—
378#126—862no—
379#125C22×D4311yescharacteristic
380#124—432no—
381#124—432no—
382#124—432no—
383#124—861no—
384#124—862no—
385#124—862no—
386#124—862no—
387#124C22×D4311yescharacteristic
388#123—21no—
389#123—862no—
390#123—862no—
391#123—862no—
392C22⋊Q8—432no—
393C22⋊Q8—862no—
394C22⋊Q8—862no—
395C22⋊Q8—861no—
396C22⋊Q8C4×D4311yescharacteristic
397#121—432no—
398#121—862no—
399#121—862no—
400#121—861no—
401#121—861no—
402#121—861no—
403#121C4×D4311yescharacteristic
404#120—862no—
405#120—862no—
406C4×Q8—431no—
407C4×Q8—431no—
408C4×Q8—432no—
409C4×Q8C4×D4311yescharacteristic
410C4×D4—21no—
411C4×D4—432no—
412C4×D4—432no—
413C4×D4—432no—
414C4×D4—431no—
415C4×D4—431no—
416C4×D4—861no—
417C4×D4—861no—
418C4×D4—862no—
419C4×D4—862no—
420C4×D4—861no—
421C4×D4—861no—
422C4×D4C4×D4311yescharacteristic
423#117—21no—
424#117—431no—
425#117—432no—
426#117—862no—
427#117—861no—
428C2×C22⋊C4—862no—
429C2×C22⋊C4—862no—
430C2×C22⋊C4—862no—
431C2×C42—432no—
432C2×C42C22×D4311yescharacteristic
433C4⋊C8—21no—
434C4⋊C8—862no—
435C22⋊C8—21no—
436C22⋊C8—862no—
437#97—431no—
438#97—431no—
439#97—431no—
440#97—431no—
441#97—862no—
442#97—862no—
443#97—861no—
444#97C22×D4312yes—
445#97C22×D4312yes—
446C4×C8—21no—
447C4×C8—862no—
448C4×C8—861no—
449C24—862no—
450#41—864no—
451#41—3442no—
452C2×Q8—431no—
453C2×Q8—432no—
454C2×Q8—862no—
455C2×Q8—3442no—
456C2×Q8C2×C4×D4311yescharacteristic
457C2×D4—21no—
458C2×D4—432no—
459C2×D4—431no—
460C2×D4—432no—
461C2×D4—862no—
462C2×D4—862no—
463C2×D4—862no—
464C2×D4—861no—
465C2×D4—861no—
466C2×D4—3442no—
467C2×D4—1724no—
468C2×D4C2×C4×D4311yescharacteristic
469C22×C4—21no—
470C22×C4—432no—
471C22×C4—432no—
472C22×C4—432no—
473C22×C4—862no—
474C22×C4—862no—
475C22×C4—862no—
476C22×C4C2×C4×D4311yescharacteristic
477C22×C4D4×D4311yescharacteristic
478C22×C4D4×D4311yescharacteristic
479M16—24no—
480M16—868no—
481M16—1722no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—868no—
485C2×C8—864no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—1724no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—431no—
496C4⋊C4—431no—
497C4⋊C4—432no—
498C4⋊C4—432no—
499C4⋊C4—862no—
500C4⋊C4—862no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4C2×C4×D4311yescharacteristic
504C4⋊C4C2×C4×D4311yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—432no—
511C22⋊C4—432no—
512C22⋊C4—432no—
513C22⋊C4—862no—
514C22⋊C4—862no—
515C22⋊C4—862no—
516C22⋊C4—862no—
517C22⋊C4—862no—
518C22⋊C4—862no—
519C22⋊C4—862no—
520C22⋊C4—862no—
521C22⋊C4—862no—
522C42—21no—
523C42—432no—
524C42—432no—
525C42—432no—
526C42—862no—
527C42C2×C4×D4311yescharacteristic
528C42D4×D4311yescharacteristic
529C42D4×D4311yescharacteristic
530C42C23×D4311yescharacteristic
531C23—21no—
532C23—432no—
533C23—862no—
534C23—3442no—
535C23—3442no—
536C23—1724no—
537C23C22⋊C4×D4311yescharacteristic
538Q8—41no—
539Q8—862no—
540Q8—3442no—
541Q8—1722no—
542D4—41no—
543D4—81no—
544D4—434no—
545D4—864no—
546D4—3441no—
547D4—3442no—
548D4—3442no—
549D4—1722no—
550D4—1724no—
551D4—1722no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—432no—
560C2×C4—432no—
561C2×C4—432no—
562C2×C4—864no—
563C2×C4—862no—
564C2×C4—3442no—
565C2×C4—3442no—
566C2×C4—3442no—
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—42no—
577C8—862no—
578C8—862no—
579C8—862no—
580C8—1721no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—434no—
588C22—862no—
589C22—862no—
590C22—1722no—
591C22—1722no—
592C22—1722no—
593C22—6884no—
594C22C2×C22⋊C4×D4311yescharacteristic
595C4—21no—
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—862no—
604C4—862no—
605C4—862no—
606C4—1722no—
607C4#104×D4312yes—
608C2—41no—
609C2—81no—
610C2—864no—
611C2—3442no—
612C2#1914307211yescharacteristic
613C2C2×#104×D4311yescharacteristic
614C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1529C2
socleC22×C43C22×C22⋊C4
prime radical#19148558C2
cosocleC42×C43C24
hypercenter#1529D43
hypocenterC43#17652
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1529

Complements

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

NH ≅ G/Ntype
2. #19143607C2semidirect
3. #19143024C2semidirect
4. #19133214C2semidirect
5. #19133207C2semidirect
6. #19133191C2semidirect
7. #19133186C2semidirect
8. #19133183C2semidirect
9. #19133182C2semidirect
10. #329×D43C2semidirect
11. C43×#1529C2semidirect
32. #14582954C22semidirect
35. C4×#10621877C22semidirect
36. #14582851C22semidirect
37. C2×#13063236C22semidirect
38. #97×D43C22semidirect
39. #97×D43C22semidirect
40. #14582641C22semidirect
41. #14582641C22semidirect
44. #14582638C22semidirect
45. #14582638C22semidirect
46. #14582638C22semidirect
47. #14582638C22semidirect
49. C43×#432C22semidirect
50. C4×M16×C43C22semidirect
51. C43×#330C22semidirect
306. #1529D43semidirect
341. #432C2×D43semidirect
346. C4×M16C2×D43semidirect
352. #330C2×D43semidirect
360. C43#17652semidirect

Maximal subgroups

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

subgroupindex
#191485582
#191436072
#191430242
#191332142
#191332072
#191331912
#191331862
#191331832
#191331822
#329×D432
C43×#15292
#1765243