Finite Group Databasebeta

← #25064866

Subgroups — #25064866

Order 11008.

900 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#19148493C211yesmaximal, characteristic
2#19143612C211yesmaximal, characteristic, complemented
3#19143607C211yesmaximal, characteristic, complemented
4#19133225C212yesmaximal, complemented
5#19133214C212yesmaximal, complemented
6#19133201C212yesmaximal, complemented
7#19133194C211yesmaximal, characteristic, complemented
8#19133194C211yesmaximal, characteristic, complemented
9#19133190C211yesmaximal, characteristic, complemented
10#19133182C212yesmaximal, complemented
11C43×#1537C211yesmaximal, characteristic, complemented
12#14583634—21no—
13#14583634—21no—
14#14583622—21no—
15#14583622—21no—
16#14583576—22no—
17#14583576—22no—
18#14583523C412yes—
19#14583523C412yes—
20#14583475C411yescharacteristic
21#14583468C411yescharacteristic
22#14583434C2212yes—
23#14583434C2212yes—
24C2×#13063313C2211yescharacteristic
25#14583376C411yescharacteristic
26#14583373C411yescharacteristic
27C4×#10621898C2211yescharacteristic
28#14583026—21no—
29#14583023—21no—
30#14582976—21no—
31#14582974—22no—
32#14582973—22no—
33#14582964—21no—
34#14582954C2212yescomplemented
35#14582954C2212yescomplemented
36C4×#10621877C2211yescharacteristic
37C4×#10621877C2211yescharacteristic
38#14582851C2212yescomplemented
39#97×D43C2212yescomplemented
40#14582641C2211yescharacteristic, complemented
41#14582641C2211yescharacteristic, complemented
42#14582641C2211yescharacteristic, complemented
43#14582641C2211yescharacteristic, complemented
44#14582638C2212yes—
45#14582638C2212yes—
46#14582638C2212yes—
47#14582638C2212yes—
48C43×#533C2211yescharacteristic
49C43×#432C2211yescharacteristic
50C43×#432C2211yescharacteristic
51C43×#330C2212yescomplemented
52C43×#330C2212yescomplemented
53C2×#10621898C2×C411yescharacteristic
54C22×Dic86C2×C411yescharacteristic
55C22×D172C2×C411yescharacteristic
56C2×#10621877—21no—
57C2×#10621877—21no—
58C2×#10621872—22no—
59C2×C8×D43—22no—
60#13063325—21no—
61#13063322—21no—
62#13063320—22no—
63#13063320—22no—
64#13063320—22no—
65#13063320—22no—
66#13063314—22no—
67#13063314—22no—
68#13063313—21no—
69#13063313—21no—
70#13063313—21no—
71#13063313—21no—
72#13063313C2×C412yes—
73#13063313C2312yes—
74#13063310—22no—
75#13063310—22no—
76#13063310—22no—
77#13063310—22no—
78#13063309—22no—
79#13063305C2×C412yes—
80#13063305C2×C412yes—
81#13063301—22no—
82#13063301—22no—
83#13063300C2×C412yes—
84#13063300C2×C412yes—
85#13063295—22no—
86C4×Dic86—21no—
87C4×Dic86—21no—
88C4×Dic86D411yescharacteristic
89C4×Dic86D411yescharacteristic
90#13063290C2×C412yes—
91#13063290C2×C412yes—
92C4×D172—21no—
93C4×D172—21no—
94C4×D172D411yescharacteristic
95C4×D172D411yescharacteristic
96#13063287—22no—
97#13063287—22no—
98#13063287C2×C412yes—
99#13063287C2×C412yes—
100C4×C22⋊D43D412yes—
101C4×C22⋊D43D412yes—
102#13063284C2×C411yescharacteristic
103#13063283—22no—
104#13063283—22no—
105#13063282C2×C412yes—
106#13063281—22no—
107C2×(C2×D43)⋊C4—21no—
108C2×(C2×D43)⋊C4—21no—
109C22⋊C4×D43—22no—
110C42×D43C2312yes—
111Dic43⋊C8—22no—
112Dic43⋊C8—22no—
113(C2×D43)⋊C8—22no—
114(C2×D43)⋊C8—22no—
115#13063236C2311yescharacteristic
116#13063236C2311yescharacteristic
117#13063236C2311yescharacteristic
118#13063236C2311yescharacteristic
119#13063235—22no—
120C4×C43⋊C8—21no—
121C4×C43⋊C8—21no—
122C8×Dic43—22no—
123C4⋊Q8×C43C2×C411yescharacteristic
124C4⋊Q8×C43C2×C411yescharacteristic
125#125×C43C2311yescharacteristic
126#125×C43C2311yescharacteristic
127C22⋊Q8×C43—21no—
128C22⋊Q8×C43—21no—
129C4×Q8×C43—21no—
130C4×Q8×C43—21no—
131#117×C43C2×C411yescharacteristic
132#117×C43C2×C411yescharacteristic
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138#97×C43C2312yes—
139#97×C43C2312yes—
140C23×D43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C22×C4×C43C22×C411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C2×C22⋊D43C22⋊C412yes—
147C22×Dic43—21no—
148#10621898—42no—
149C2×D172—21no—
150C2×D172—22no—
151C2×D172—22no—
152C2×D172—42no—
153C2×D172C22⋊C411yescharacteristic
154C2×D172C22×C412yes—
155C2×C4×D43—22no—
156C2×C4×D43—22no—
157C2×C4×D43C22×C412yes—
158C2×C4×D43C2×D412yes—
159C2×C4×D43C2×D412yes—
160C2×Dic86—21no—
161C2×Dic86—42no—
162C2×Dic86C22⋊C411yescharacteristic
163C2×Dic86C22×C412yes—
164C2×C8×C43—22no—
165C2×C8×C43—22no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43C22×C411yescharacteristic
173C4⋊C4×C43C22×C411yescharacteristic
174C4⋊C4×C43C22×C411yescharacteristic
175C4⋊C4×C43C22×C411yescharacteristic
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43C22×C411yescharacteristic
181C42×C43C2×D411yescharacteristic
182C42×C43C2×D411yescharacteristic
183C42×C43C2411yescharacteristic
184C22⋊Dic43C22⋊C412yes—
185(C2×D43)⋊C4—22no—
186(C2×D43)⋊C4—22no—
187(C2×D43)⋊C4—22no—
188(C2×D43)⋊C4—22no—
189(C2×D43)⋊C4—22no—
190(C2×D43)⋊C4—22no—
191(C2×D43)⋊C4—22no—
192(C2×D43)⋊C4—22no—
193(C2×D43)⋊C4—22no—
194(C2×D43)⋊C4—22no—
195(C2×D43)⋊C4C22⋊C412yes—
196(C2×D43)⋊C4C22⋊C412yes—
197C4⋊Dic43—22no—
198C4⋊Dic43—22no—
199C4⋊Dic43C22⋊C411yescharacteristic
200C4⋊Dic43C22⋊C411yescharacteristic
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4C22⋊C412yes—
204Dic43⋊C4C22⋊C412yes—
205C4×Dic43—22no—
206C4×Dic43—22no—
207C4×Dic43C22×C412yes—
208C4×Dic43C2×D412yes—
209C4×Dic43C2×D412yes—
210#10621877—42no—
211#10621877—42no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216#10621872—44no—
217C8×D43—44no—
218C23×C43C2×C22⋊C411yescharacteristic
219C22×D43—22no—
220C22×D43—42no—
221C22×D43—81no—
222C22×D43—81no—
223C22×D43C2×C22⋊C412yes—
224Q8×C43—81no—
225Q8×C43—81no—
226C2×C4×C43—22no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43C2×C22⋊C411yescharacteristic
234C2×C4×C43C2×C22⋊C411yescharacteristic
235C2×C4×C43C2×C22⋊C411yescharacteristic
236C2×C4×C43C23×C411yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C22⋊D43—42no—
240C2×Dic43—22no—
241C2×Dic43—42no—
242C2×Dic43C2×C22⋊C412yes—
243C2×Dic43C2×C22⋊C412yes—
244C2×Dic43C2×C22⋊C412yes—
245D172—22no—
246D172—42no—
247D172—42no—
248D172—82no—
249D172—82no—
250C4×D43—42no—
251C4×D43—42no—
252C4×D43—42no—
253C4×D43—82no—
254C4×D43—82no—
255Dic86—22no—
256Dic86—42no—
257Dic86—42no—
258C8×C43—42no—
259C8×C43—42no—
260C43⋊C8—22no—
261C43⋊C8—22no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264#17691—431nomaximal, Sylow
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—21no—
268C22×C43C22×C22⋊C411yescharacteristic
269C2×D43—22no—
270C2×D43—22no—
271C2×D43—22no—
272C2×D43—42no—
273C2×D43—42no—
274C2×D43—42no—
275C2×D43—162no—
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—21no—
280C4×C43—21no—
281C4×C43—41no—
282C4×C43—41no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43#41312yes—
286Dic43—22no—
287Dic43—22no—
288Dic43—22no—
289Dic43—42no—
290#3510—431no—
291#2971—431no—
292#2970—431no—
293#1537D4311yescharacteristic, complemented
294#1535—432no—
295#1532—432no—
296#1529—432no—
297#1527—431no—
298#1527—431no—
299#1526—431no—
300#1524—432no—
301C2×C43—41no—
302C2×C43C2×#41311yescharacteristic
303C2×C43#290111yescharacteristic
304C2×C43#290111yescharacteristic
305D43—42no—
306D43—82no—
307#559—861no—
308#559—861no—
309#556—861no—
310#556—861no—
311#551—862no—
312#551—862no—
313#542—432no—
314#542—432no—
315#536—431no—
316#535—431no—
317#533C2×D4311yescharacteristic
318#529—432no—
319#529—432no—
320C2×#124—431no—
321#519—431no—
322#518—431no—
323C4×#41—431no—
324#446—861no—
325C8×Q8—861no—
326#436—862no—
327#436—861no—
328#435—862no—
329C8×D4—861no—
330#432—432no—
331#432—432no—
332#432C2×D4311yescharacteristic
333#432C2×D4311yescharacteristic
334C4×M16—431no—
335C4×M16—431no—
336C4×M16—432no—
337C2×#97—432no—
338#330—431no—
339#330—431no—
340#330—431no—
341#330—431no—
342#330C2×D4312yescomplemented
343#330C2×D4312yescomplemented
344#329—432no—
345#329—432no—
346#329—432no—
347#329—432no—
348C43#1769111yescharacteristic, complemented, Sylow
349C2×#41—431no—
350C22×Q8—431no—
351C22×D4—431no—
352C2×M16—862no—
353C2×M16—861no—
354C2×M16—861no—
355C22×C8—862no—
356C4⋊Q8—861no—
357C4⋊Q8C4×D4311yescharacteristic
358C4⋊Q8C4×D4311yescharacteristic
359#127—861no—
360#126—862no—
361#126—862no—
362#126—862no—
363#126—862no—
364#125C22×D4311yescharacteristic
365#125C22×D4311yescharacteristic
366#124—432no—
367#124—432no—
368#124—861no—
369#124—861no—
370#124—862no—
371#124—862no—
372#124—861no—
373#124—861no—
374#123—862no—
375#123—862no—
376#123—862no—
377#123—862no—
378#123—862no—
379C22⋊Q8—21no—
380C22⋊Q8—21no—
381C22⋊Q8—432no—
382C22⋊Q8—432no—
383C22⋊Q8—862no—
384C22⋊Q8—862no—
385#121—432no—
386#121—432no—
387#120—862no—
388C4×Q8—21no—
389C4×Q8—21no—
390C4×Q8—431no—
391C4×Q8—431no—
392C4×Q8—432no—
393C4×Q8—432no—
394C4×Q8—861no—
395C4×Q8—861no—
396C4×D4—432no—
397C4×D4—432no—
398C4×D4—432no—
399C4×D4—432no—
400C4×D4—431no—
401C4×D4—431no—
402C4×D4—861no—
403C4×D4—861no—
404C4×D4—862no—
405C4×D4—862no—
406#117—431no—
407#117—432no—
408#117—862no—
409#117—862no—
410#117—862no—
411#117C4×D4311yescharacteristic
412#117C4×D4311yescharacteristic
413C2×C22⋊C4—862no—
414C2×C22⋊C4—861no—
415C2×C22⋊C4—861no—
416C2×C42—432no—
417C2×C42C22×D4311yescharacteristic
418C4⋊C8—21no—
419C4⋊C8—21no—
420C4⋊C8—862no—
421C4⋊C8—862no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—862no—
425C22⋊C8—862no—
426#97—431no—
427#97—431no—
428#97—431no—
429#97—431no—
430#97—862no—
431#97C22×D4312yes—
432#97C22×D4312yes—
433C4×C8—862no—
434C4×C8—861no—
435C4×C8—861no—
436C24—861no—
437#41—1722no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—431no—
441C2×Q8—432no—
442C2×Q8—861no—
443C2×Q8—1722no—
444C2×D4—432no—
445C2×D4—431no—
446C2×D4—432no—
447C2×D4—862no—
448C2×D4—862no—
449C2×D4—861no—
450C2×D4—1722no—
451C22×C4—432no—
452C22×C4—432no—
453C22×C4—432no—
454C22×C4—862no—
455C22×C4—862no—
456C22×C4—861no—
457C22×C4C2×C4×D4311yescharacteristic
458C22×C4D4×D4311yescharacteristic
459C22×C4D4×D4311yescharacteristic
460M16—1724no—
461M16—1722no—
462M16—1722no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—1724no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—431no—
477C4⋊C4—431no—
478C4⋊C4—432no—
479C4⋊C4—432no—
480C4⋊C4—862no—
481C4⋊C4—862no—
482C4⋊C4—862no—
483C4⋊C4—862no—
484C4⋊C4C2×C4×D4311yescharacteristic
485C4⋊C4C2×C4×D4311yescharacteristic
486C4⋊C4C2×C4×D4311yescharacteristic
487C4⋊C4C2×C4×D4311yescharacteristic
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—432no—
491C22⋊C4—432no—
492C22⋊C4—432no—
493C22⋊C4—862no—
494C22⋊C4—862no—
495C22⋊C4—862no—
496C22⋊C4—862no—
497C22⋊C4—862no—
498C22⋊C4—862no—
499C22⋊C4—862no—
500C22⋊C4—862no—
501C22⋊C4—862no—
502C22⋊C4—862no—
503C42—21no—
504C42—21no—
505C42—432no—
506C42—432no—
507C42—432no—
508C42—862no—
509C42—862no—
510C42C2×C4×D4311yescharacteristic
511C42D4×D4311yescharacteristic
512C42D4×D4311yescharacteristic
513C42C23×D4311yescharacteristic
514C23—432no—
515C23—862no—
516C23—3441no—
517C23—3441no—
518C23—1722no—
519C23C22⋊C4×D4311yescharacteristic
520Q8—81no—
521Q8—81no—
522Q8—862no—
523Q8—1722no—
524Q8—1722no—
525D4—862no—
526D4—3442no—
527D4—3442no—
528D4—1722no—
529D4—1722no—
530D4—1722no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—432no—
539C2×C4—432no—
540C2×C4—432no—
541C2×C4—862no—
542C2×C4—3442no—
543C2×C4—3442no—
544C2×C4—1722no—
545C2×C4—1722no—
546C2×C4—1722no—
547C2×C4—1722no—
548C2×C4C22⋊C4×D4311yescharacteristic
549C2×C4C22⋊C4×D4311yescharacteristic
550C2×C4C22⋊C4×D4311yescharacteristic
551C2×C4C22×C4×D4311yescharacteristic
552C2×C4C2×D4×D4311yescharacteristic
553C2×C4C2×D4×D4311yescharacteristic
554C8—42no—
555C8—42no—
556C8—862no—
557C8—862no—
558C8—1721no—
559C8—1721no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—862no—
564C22—862no—
565C22—862no—
566C22—1722no—
567C22—1722no—
568C22—1722no—
569C22—6882no—
570C22C2×C22⋊C4×D4311yescharacteristic
571C4—21no—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—21no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—862no—
581C4—862no—
582C4—862no—
583C4—1722no—
584C4#1458288212yes—
585C2—41no—
586C2—3442no—
587C2—1722no—
588C2C2×#1458288211yescharacteristic
589C2#1914314111yescharacteristic
590C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1537C2
socleC22×C43C22×C22⋊C4
prime radical#14583468C4
cosocleC42×C43C24
hypercenter#1537D43
hypocenterC43#17691
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1537

Complements

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

NH ≅ G/Ntype
2. #19143612C2semidirect
3. #19143607C2semidirect
4. #19133225C2semidirect
5. #19133214C2semidirect
6. #19133201C2semidirect
7. #19133194C2semidirect
8. #19133194C2semidirect
9. #19133190C2semidirect
10. #19133182C2semidirect
11. C43×#1537C2semidirect
34. #14582954C22semidirect
35. #14582954C22semidirect
38. #14582851C22semidirect
39. #97×D43C22semidirect
40. #14582641C22semidirect
41. #14582641C22semidirect
42. #14582641C22semidirect
43. #14582641C22semidirect
51. C43×#330C22semidirect
52. C43×#330C22semidirect
293. #1537D43semidirect
342. #330C2×D43semidirect
343. #330C2×D43semidirect
348. C43#17691semidirect

Maximal subgroups

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

subgroupindex
#191484932
#191436122
#191436072
#191332252
#191332142
#191332012
#191331942
#191331902
#191331822
C43×#15372
#1769143