Finite Group Databasebeta

← #25064174

Subgroups — #25064174

Order 11008.

882 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148689C211yesmaximal, characteristic
2#19143685C211yesmaximal, characteristic, complemented
3#19137241C211yesmaximal, characteristic, complemented
4#19133169C212yesmaximal
5#19133157C212yesmaximal, complemented
6#19133144C212yesmaximal, complemented
7#19133130C212yesmaximal
8#19133108C211yesmaximal, characteristic, complemented
9#19133093C211yesmaximal, characteristic, complemented
10#19133081C211yesmaximal, characteristic
11C43×#1509C211yesmaximal, characteristic
12#14583628C411yescharacteristic, complemented
13#14583627C411yescharacteristic, complemented
14#14583626C412yescomplemented
15#14583619C411yescharacteristic, complemented
16#14583618C412yescomplemented
17#14583589—21no—
18#14583586—22no—
19D4×Dic86—21no—
20D4×Dic86C411yescharacteristic, complemented
21#14583511—21no—
22#14583506—22no—
23#14583456C2211yescharacteristic
24#14583451C2212yes—
25#14583430C2212yes—
26#14583376—21no—
27C2×C4×Dic86C2211yescharacteristic
28#14583027—22no—
29#14583026—21no—
30#14583023—21no—
31#14582953C2212yes—
32#14582952C2211yescharacteristic
33#14582949C2212yes—
34#14582804—21no—
35#14582795—21no—
36#14582783—22no—
37#14582766C2212yes—
38#14582763C2212yes—
39#14582745C2211yescharacteristic
40#14582637C2212yes—
41#14582637C2212yes—
42#14582636C2211yescharacteristic
43#14582636C2211yescharacteristic
44#14582635C2212yes—
45#14582635C2212yes—
46#14582633C2211yescharacteristic
47#14582633C2211yescharacteristic
48C43×#529C2211yescharacteristic
49C43×#432C2211yescharacteristic
50C4×C4⋊C4×C43C2211yescharacteristic
51C43×#328C2212yes—
52C43×#327C2212yes—
53C22×Dic86—21no—
54C22×Dic86D411yescharacteristic
55#13063325—21no—
56#13063325C2×C411yescharacteristic
57#13063325C2×C411yescharacteristic
58#13063324—22no—
59#13063324C2×C412yes—
60#13063323C2×C412yes—
61#13063318—22no—
62#13063318—22no—
63#13063318—22no—
64#13063318—22no—
65#13063317—21no—
66#13063317—21no—
67#13063316—22no—
68#13063316C2×C412yes—
69#13063315—22no—
70#13063315—22no—
71#13063315—22no—
72#13063315—22no—
73#13063312C2×C412yes—
74#13063306—22no—
75#13063304—21no—
76#13063304—21no—
77#13063304—21no—
78#13063304C2312yes—
79#13063302—22no—
80#13063302—22no—
81#13063302—22no—
82Q8×Dic43C2×C412yes—
83C4×Dic86—21no—
84C4×Dic86—21no—
85C4×Dic86—21no—
86C4×Dic86C2×C412yes—
87C4×Dic86C2×C411yescharacteristic
88C4×Dic86C2×C412yes—
89C4×Dic86C2×C411yescharacteristic
90C4×Dic86D411yescharacteristic
91C4×Dic86D412yes—
92C4×Dic86D411yescharacteristic
93#13063290—22no—
94#13063290—22no—
95#13063290C2×C412yes—
96#13063290C2×C412yes—
97D4×Dic43—22no—
98D4×Dic43C2×C412yes—
99#13063284—21no—
100#13063284—21no—
101#13063281—22no—
102#13063281—22no—
103#13063281—22no—
104C2×C4⋊Dic43D411yescharacteristic
105C2×Dic43⋊C4—22no—
106C2×Dic43⋊C4D412yes—
107C2×C4×Dic43—21no—
108C2×C4×Dic43C2312yes—
109C4⋊(C43⋊C8)—21no—
110Dic43⋊C8—22no—
111Dic43⋊C8—22no—
112C22⋊(C43⋊C8)C2311yescharacteristic
113C22⋊(C43⋊C8)C2311yescharacteristic
114#13063235—22no—
115C4×C43⋊C8—21no—
116C8×Dic43—22no—
117C43⋊#95—21no—
118C43⋊#95—22no—
119C43⋊#95—22no—
120C43⋊#95—22no—
121C43⋊#95C2311yescharacteristic
122C43⋊#95C2311yescharacteristic
123#126×C43—21no—
124#125×C43C2×C411yescharacteristic
125#124×C43C2×C411yescharacteristic
126#123×C43—21no—
127C22⋊Q8×C43C2311yescharacteristic
128#121×C43C2311yescharacteristic
129C4×Q8×C43C2×C411yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43C2×C411yescharacteristic
132#117×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C42×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43—21no—
137C22⋊C8×C43C2312yes—
138#97×C43—21no—
139#95×C43C2312yes—
140C2×Q8×C43C22×C411yescharacteristic
141C2×D4×C43—21no—
142C2×D4×C43C22×C411yescharacteristic
143C22×C4×C43—21no—
144C22×C4×C43—22no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C22×Dic43—22no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43C2×D412yes—
152C22×Dic43C2×D412yes—
153C2×Dic86—21no—
154C2×Dic86—22no—
155C2×Dic86—42no—
156C2×Dic86—44no—
157C2×Dic86C22⋊C411yescharacteristic
158C2×Dic86C22⋊C411yescharacteristic
159C2×Dic86C22⋊C412yes—
160C2×Dic86C22×C412yes—
161C2×C8×C43—22no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—42no—
167C4⋊C4×C43C22×C411yescharacteristic
168C4⋊C4×C43C22×C411yescharacteristic
169C22⋊C4×C43—21no—
170C22⋊C4×C43—21no—
171C22⋊C4×C43—21no—
172C22⋊C4×C43—21no—
173C22⋊C4×C43—21no—
174C42×C43—21no—
175C42×C43—81no—
176C42×C43C22×C411yescharacteristic
177C42×C43C22×C411yescharacteristic
178C42×C43C2×D411yescharacteristic
179C42×C43C2×D411yescharacteristic
180C22⋊Dic43—22no—
181C22⋊Dic43—22no—
182C22⋊Dic43—22no—
183C22⋊Dic43—22no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—22no—
188C4⋊Dic43—22no—
189C4⋊Dic43C22⋊C411yescharacteristic
190C4⋊Dic43C22⋊C411yescharacteristic
191C4⋊Dic43C22⋊C412yes—
192C4⋊Dic43C22×C412yes—
193Dic43⋊C4—22no—
194Dic43⋊C4—22no—
195Dic43⋊C4—22no—
196Dic43⋊C4—22no—
197Dic43⋊C4—22no—
198Dic43⋊C4—22no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—82no—
202Dic43⋊C4C22⋊C412yes—
203Dic43⋊C4C22⋊C412yes—
204Dic43⋊C4C22⋊C412yes—
205Dic43⋊C4C22⋊C412yes—
206C4×Dic43—22no—
207C4×Dic43—22no—
208C4×Dic43—22no—
209C4×Dic43—22no—
210C4×Dic43—42no—
211C4×Dic43C22×C412yes—
212C4×Dic43C22×C412yes—
213C4×Dic43C2×D412yes—
214C4×Dic43C2×D412yes—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C23×C43—21no—
218C23×C43C22×D411yescharacteristic
219Q8×C43—41no—
220D4×C43—41no—
221D4×C43—41no—
222D4×C43—41no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—22no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—41no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43C2×C22⋊C411yescharacteristic
235C2×C4×C43C2×C22⋊C411yescharacteristic
236C2×C4×C43C2×C22⋊C411yescharacteristic
237C2×C4×C43C2×C22⋊C411yescharacteristic
238C2×C4×C43C23×C411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—42no—
245C2×Dic43—44no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43C2×C22⋊C412yes—
253C2×Dic43C2×C22⋊C412yes—
254C2×Dic43C2×C22⋊C412yes—
255C2×Dic43C2×C22⋊C412yes—
256Dic86—22no—
257Dic86—22no—
258Dic86—42no—
259Dic86—44no—
260Dic86—42no—
261Dic86—42no—
262C8×C43—42no—
263C43⋊C8—41no—
264C43⋊C8—41no—
265#17601—431nomaximal, Sylow
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—41no—
269C22×C43—41no—
270C22×C43—41no—
271C22×C43C22×C22⋊C411yescharacteristic
272C22×C43#57711yescharacteristic
273C22×C43#57811yescharacteristic
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—21no—
279C4×C43—41no—
280C4×C43—41no—
281C4×C43—41no—
282C4×C43—82no—
283C4×C43#42112yes—
284Dic43—22no—
285Dic43—22no—
286Dic43—22no—
287Dic43—22no—
288Dic43—42no—
289Dic43—42no—
290Dic43—81no—
291Dic43—81no—
292#3523—431no—
293#2984—431no—
294#2320—431no—
295#1521—432no—
296#1518—432no—
297#1515—432no—
298#1512—432no—
299#1509D4311yescharacteristic
300#1506—431no—
301#1503—431no—
302#1500—431no—
303C2×C43—21no—
304C2×C43—21no—
305C2×C43—81no—
306C2×C43#288411yescharacteristic
307C2×C43#289811yescharacteristic
308C2×C43C2×#42111yescharacteristic
309#557—432no—
310#557—431no—
311#557—431no—
312#556—432no—
313#556—431no—
314#552—861no—
315#552—862no—
316D4×Q8—431no—
317D4×Q8—861no—
318#541—861no—
319#541—862no—
320#533—432no—
321#533—431no—
322#529—432no—
323#529C2×D4311yescharacteristic
324#519—861no—
325C2×C4×Q8—431no—
326#446—862no—
327#446—861no—
328C8×Q8—861no—
329#432—432no—
330#432C2×D4311yescharacteristic
331#431—431no—
332#431—432no—
333#391—861no—
334#389—861no—
335#387—862no—
336#383—432no—
337#382—432no—
338C4×C4⋊C4C2×D4311yescharacteristic
339#376—431no—
340#328—431no—
341#328—431no—
342#328—432no—
343#328—432no—
344#328—432no—
345#328—432no—
346#328C2×D4312yes—
347#327—431no—
348#327—431no—
349#327C2×D4312yes—
350C43#1760111yescharacteristic, complemented, Sylow
351C22×Q8—431no—
352C22×Q8—861no—
353C4⋊Q8—432no—
354C4⋊Q8—432no—
355C4⋊Q8—431no—
356C4⋊Q8—431no—
357C4⋊Q8—861no—
358C4⋊Q8—862no—
359#126—21no—
360#126—862no—
361#126—862no—
362#126—862no—
363#126—862no—
364#125—432no—
365#125—861no—
366#125—862no—
367#125—862no—
368#125—862no—
369#125—862no—
370#125—862no—
371#125—861no—
372#125C4×D4311yescharacteristic
373#124—432no—
374#124C4×D4311yescharacteristic
375#123—21no—
376#123—862no—
377C22⋊Q8—432no—
378C22⋊Q8—862no—
379C22⋊Q8—862no—
380C22⋊Q8—862no—
381C22⋊Q8—861no—
382C22⋊Q8—861no—
383C22⋊Q8—861no—
384C22⋊Q8C22×D4311yescharacteristic
385#121C22×D4311yescharacteristic
386C4×Q8—431no—
387C4×Q8—432no—
388C4×Q8—431no—
389C4×Q8—431no—
390C4×Q8—431no—
391C4×Q8—432no—
392C4×Q8—432no—
393C4×Q8—432no—
394C4×Q8—432no—
395C4×Q8—432no—
396C4×Q8—861no—
397C4×Q8—861no—
398C4×Q8—862no—
399C4×Q8—862no—
400C4×Q8—861no—
401C4×Q8C4×D4311yescharacteristic
402C4×D4—21no—
403C4×D4—432no—
404C4×D4—862no—
405C4×D4C4×D4311yescharacteristic
406#117—21no—
407#117—862no—
408#117—862no—
409#117—862no—
410#117—861no—
411#117—861no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—432no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—862no—
416C2×C42—21no—
417C2×C42—432no—
418C2×C42—861no—
419C2×C42C22×D4311yescharacteristic
420C4⋊C8—21no—
421C4⋊C8—862no—
422C4⋊C8—862no—
423C4⋊C8—861no—
424C22⋊C8—431no—
425C22⋊C8—431no—
426C22⋊C8C22×D4312yes—
427#97—21no—
428#97—862no—
429C4×C8—862no—
430C4×C8—861no—
431#95—431no—
432#95—431no—
433#95—862no—
434#95—862no—
435#95—862no—
436#95—861no—
437#95C22×D4312yes—
438C2×Q8—431no—
439C2×Q8—431no—
440C2×Q8—432no—
441C2×Q8—432no—
442C2×Q8—862no—
443C2×Q8—861no—
444C2×Q8—1722no—
445C2×Q8—1724no—
446C2×Q8C2×C4×D4311yescharacteristic
447C2×D4—21no—
448C2×D4C2×C4×D4311yescharacteristic
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—432no—
452C22×C4—432no—
453C22×C4—862no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4D4×D4311yescharacteristic
457C22×C4D4×D4311yescharacteristic
458C22×C4C23×D4311yescharacteristic
459C2×C8—22no—
460C2×C8—861no—
461C2×C8—861no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—42no—
467C4⋊C4—432no—
468C4⋊C4—431no—
469C4⋊C4—432no—
470C4⋊C4—431no—
471C4⋊C4—432no—
472C4⋊C4—432no—
473C4⋊C4—432no—
474C4⋊C4—432no—
475C4⋊C4—862no—
476C4⋊C4—862no—
477C4⋊C4—862no—
478C4⋊C4—862no—
479C4⋊C4—862no—
480C4⋊C4—862no—
481C4⋊C4—862no—
482C4⋊C4—862no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4—862no—
487C4⋊C4—862no—
488C4⋊C4—3442no—
489C4⋊C4C2×C4×D4311yescharacteristic
490C4⋊C4C2×C4×D4311yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—862no—
497C22⋊C4—862no—
498C22⋊C4—862no—
499C22⋊C4—862no—
500C42—21no—
501C42—81no—
502C42—432no—
503C42—432no—
504C42—432no—
505C42—432no—
506C42—862no—
507C42—862no—
508C42—862no—
509C42—862no—
510C42—1722no—
511C42C2×C4×D4311yescharacteristic
512C42C2×C4×D4311yescharacteristic
513C42D4×D4311yescharacteristic
514C42D4×D4311yescharacteristic
515C23—21no—
516C23C2×D4×D4311yescharacteristic
517Q8—41no—
518Q8—862no—
519Q8—862no—
520Q8—1722no—
521Q8—1722no—
522Q8—1724no—
523Q8—1722no—
524D4—41no—
525D4—41no—
526D4—41no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—432no—
539C2×C4—432no—
540C2×C4—432no—
541C2×C4—432no—
542C2×C4—862no—
543C2×C4—862no—
544C2×C4—862no—
545C2×C4—862no—
546C2×C4—1722no—
547C2×C4—1724no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4C22⋊C4×D4311yescharacteristic
555C2×C4C22⋊C4×D4311yescharacteristic
556C2×C4C22⋊C4×D4311yescharacteristic
557C2×C4C22⋊C4×D4311yescharacteristic
558C2×C4C22×C4×D4311yescharacteristic
559C2×C4C2×D4×D4311yescharacteristic
560C8—42no—
561C8—1721no—
562C8—1721no—
563C22—21no—
564C22—21no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22C2×C22⋊C4×D4311yescharacteristic
569C22#1458370911yescharacteristic
570C22#1458371511yescharacteristic
571C4—21no—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—21no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—82no—
580C4—862no—
581C4—862no—
582C4—862no—
583C4—862no—
584C4—3441no—
585C4—3441no—
586C4—1722no—
587C4—1722no—
588C4#1458291412yes—
589C2—21no—
590C2—21no—
591C2—81no—
592C2#1914305711yescharacteristic
593C2#1914312611yescharacteristic
594C2C2×#1458291411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1509C2
socleC22×C43C22×C22⋊C4
prime radical#121×C43C23
cosocleC22×C4×C43C24
hypercenter#1509D43
hypocenterC43#17601
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1509

Complements

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

NH ≅ G/Ntype
2. #19143685C2semidirect
3. #19137241C2semidirect
5. #19133157C2semidirect
6. #19133144C2semidirect
8. #19133108C2semidirect
9. #19133093C2semidirect
12. #14583628C4semidirect
13. #14583627C4semidirect
14. #14583626C4semidirect
15. #14583619C4semidirect
16. #14583618C4semidirect
20. D4×Dic86C4semidirect
350. C43#17601semidirect

Maximal subgroups

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

subgroupindex
#191486892
#191436852
#191372412
#191331692
#191331572
#191331442
#191331302
#191331082
#191330932
#191330812
C43×#15092
#1760143