Finite Group Databasebeta

← #25066252

Subgroups — #25066252

Order 11008.

650 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143702C211yesmaximal, characteristic
2#19143677C211yesmaximal, characteristic, complemented
3C4×#13063354C211yesmaximal, characteristic
4#19133465C211yesmaximal, characteristic, complemented
5#19133464C211yesmaximal, characteristic, complemented
6#19133453C211yesmaximal, characteristic, complemented
7#19133452C211yesmaximal, characteristic, complemented
8#19133448C211yesmaximal, characteristic, complemented
9#19133447C211yesmaximal, characteristic, complemented
10#19133428C211yesmaximal, characteristic, complemented
11#19133344C211yesmaximal, characteristic, complemented
12#19132974C211yesmaximal, characteristic
13Q8⋊C8×D43C211yesmaximal, characteristic, complemented
14#19132883C211yesmaximal, characteristic, complemented
15C43×#1582C211yesmaximal, characteristic, complemented
16C2×#13063354C411yescharacteristic
17C4×#10621900C2211yescharacteristic
18C4×Q8×D43C2211yescharacteristic
19#14583030C2211yescharacteristic
20#14583029C2211yescharacteristic
21#14583028—21no—
22#14583027—21no—
23#14583026C2211yescharacteristic
24C8×Dic86C2211yescharacteristic
25#14583023C2211yescharacteristic
26#14583005C411yescharacteristic
27#14583003C411yescharacteristic
28#14583000C411yescharacteristic
29#14582996C411yescharacteristic
30C4×Dic172C2211yescharacteristic
31C4×#10621885C2211yescharacteristic
32C4×#10621883C2211yescharacteristic
33D4×C43⋊C8C2211yescharacteristic
34C8×C22⋊D43—21no—
35(C22⋊D43)⋊C8—21no—
36#14582955—21no—
37#14582954—21no—
38#14582951C2211yescharacteristic
39#14582950C2211yescharacteristic
40#14582949—21no—
41#14582938C411yescharacteristic
42C2×Dic43⋊C8—21no—
43C4⋊C8×D43C2211yescharacteristic
44#14582906C411yescharacteristic
45#14582897C411yescharacteristic
46C4×#10621872C2211yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582652C2211yescharacteristic
49#14582651C2211yescharacteristic
50#14582649C2211yescharacteristic
51#14582631C2211yescharacteristic
52#14582631C2211yescharacteristic
53Q8⋊(C43⋊C8)C2211yescharacteristic
54#14582629C2211yescharacteristic
55#14582629C2211yescharacteristic
56D4⋊(C43⋊C8)C2211yescharacteristic
57#14582621C2211yescharacteristic
58#14582621C2211yescharacteristic
59#14582621C2211yescharacteristic
60C43×#446C2211yescharacteristic
61C4×SD16×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#334C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×#10621900C2×C411yescharacteristic
68C2×Q8×D43C2×C411yescharacteristic
69#13063354—24no—
70C2×Dic172C2×C411yescharacteristic
71C2×#10621885C2×C411yescharacteristic
72C2×#10621883C2×C411yescharacteristic
73C2×#10621872C2×C411yescharacteristic
74C2×#10621872C2×C411yescharacteristic
75C22×C43⋊C8—21no—
76C2×C8×D43—21no—
77C2×C8×D43—21no—
78Q8×Dic43C2×C411yescharacteristic
79C4×Dic86—21no—
80C4×Dic86C2311yescharacteristic
81C4×Dic86C2311yescharacteristic
82#13063290—21no—
83#13063290C2×C411yescharacteristic
84#13063290C2×C411yescharacteristic
85D4×Dic43C2×C411yescharacteristic
86C4×C22⋊D43—21no—
87(C22⋊D43)⋊C4—21no—
88#13063283C2×C411yescharacteristic
89#13063281—21no—
90C4⋊C4×D43—21no—
91C4⋊C4×D43C2×C411yescharacteristic
92C2×C4×Dic43—21no—
93C42×D43—21no—
94C42×D43C2311yescharacteristic
95#13063259C2×C411yescharacteristic
96#13063258C2×C411yescharacteristic
97#13063256C2×C411yescharacteristic
98C4⋊(C43⋊C8)—21no—
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8D411yescharacteristic
107Dic43⋊C8D411yescharacteristic
108#13063250C2×C411yescharacteristic
109#13063250C2×C411yescharacteristic
110#13063249C2×C411yescharacteristic
111#13063248C2×C411yescharacteristic
112#13063248C2×C411yescharacteristic
113#13063246C2×C411yescharacteristic
114C22⋊(C43⋊C8)—21no—
115(C2×D43)⋊C8—21no—
116(C2×D43)⋊C8D411yescharacteristic
117(C2×D43)⋊C8D411yescharacteristic
118#13063236—21no—
119#13063235—21no—
120#13063235—21no—
121#13063235C2×C411yescharacteristic
122#13063235C2×C411yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C8×Dic43—21no—
130C2×SD16×C43C2×C411yescharacteristic
131C22×C8×C43—21no—
132C4×Q8×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#106×C43C2×C411yescharacteristic
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43C2×C411yescharacteristic
139#102×C43C2×C411yescharacteristic
140C22⋊C8×C43—21no—
141#97×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C4×C8×C43C2311yescharacteristic
145C2×Q8×C43C22×C411yescharacteristic
146C2×D4×C43C22×C411yescharacteristic
147C22×C4×C43—21no—
148C2×C22⋊D43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151Q8×D43—22no—
152Q8×D43—22no—
153#10621900—22no—
154#10621900M1614yes—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43C22×C411yescharacteristic
158C2×C4×D43C2×D411yescharacteristic
159C2×C4×D43#4111yescharacteristic
160C2×Dic86—21no—
161C2×Dic86C22×C411yescharacteristic
162C2×Dic86C22×C411yescharacteristic
163SD16×C43—22no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—81no—
168C2×C8×C43C22×C411yescharacteristic
169C2×C8×C43C22×C411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C4⋊C4×C43—21no—
173C4⋊C4×C43C22×C411yescharacteristic
174C4⋊C4×C43C22×C411yescharacteristic
175C22⋊C4×C43—21no—
176C42×C43—21no—
177C42×C43C2411yescharacteristic
178C22⋊Dic43—21no—
179#10621885—22no—
180#10621883—22no—
181(C2×D43)⋊C4—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43C22×C411yescharacteristic
184C4⋊Dic43C22×C411yescharacteristic
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190C4×Dic43—21no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43C22×C411yescharacteristic
197C4×Dic43C2×D411yescharacteristic
198C4×Dic43#4111yescharacteristic
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—81no—
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C22×C411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207Dic172—22no—
208#10621872—22no—
209#10621872—22no—
210C8×D43—42no—
211C8×D43—81no—
212C23×C43—21no—
213C22×D43C4×D411yescharacteristic
214Q8×C43—21no—
215Q8×C43—21no—
216D4×C43—21no—
217D4×C43C2×M1612yes—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43C23×C411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C22⋊D43—24no—
227C2×Dic43—21no—
228C2×Dic43—24no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—81no—
233C2×Dic43C4×D411yescharacteristic
234C2×Dic43C4×D411yescharacteristic
235C2×Dic43C4×D411yescharacteristic
236C4×D43—21no—
237C4×D43—21no—
238C4×D43—41no—
239C4×D43—42no—
240C4×D43—81no—
241C4×D43C2×M1612yes—
242C4×D43#13112yes—
243Dic86—21no—
244Dic86—21no—
245Dic86—21no—
246Dic86—42no—
247Dic86C2×M1612yes—
248C8×C43—21no—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—21no—
252C8×C43—41no—
253C8×C43—41no—
254C8×C43—41no—
255C43⋊C8—22no—
256C43⋊C8—21no—
257C43⋊C8—21no—
258C43⋊C8—21no—
259C43⋊C8—21no—
260C43⋊C8—41no—
261C43⋊C8—41no—
262#17876—431nomaximal, Sylow
263C22×C43—22no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43C2×C4×D411yescharacteristic
267C2×D43—21no—
268C2×D43—21no—
269C2×D43#43512yes—
270C4×C43—21no—
271C4×C43—41no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43C22×M1611yescharacteristic
275C4×C43C2×#13111yescharacteristic
276C4×C43#57711yescharacteristic
277C4×C43#57811yescharacteristic
278Dic43—22no—
279Dic43—21no—
280Dic43—21no—
281Dic43—41no—
282Dic43—41no—
283Dic43—41no—
284Dic43#43512yes—
285#2988—431no—
286#2983—431no—
287C4×#137—431no—
288#1587—431no—
289#1587—431no—
290#1585—431no—
291#1585—431no—
292#1584—431no—
293#1584—431no—
294#1582—431no—
295#1582D4311yescharacteristic, complemented
296#1565—431no—
297#1476—431no—
298C2×Q8⋊C8—431no—
299#1451—431no—
300C2×C43—42no—
301C2×C43C2×#43511yescharacteristic
302C2×C43#294711yescharacteristic
303C2×C43#295611yescharacteristic
304D43—22no—
305C2×#137—431no—
306C4×#41—431no—
307C2×C4×Q8—431no—
308#446—431no—
309#446—431no—
310#446—431no—
311#446—861no—
312#446—861no—
313#446C2×D4311yescharacteristic
314C8×Q8—431no—
315C8×Q8—431no—
316#441—431no—
317#441—431no—
318#440—431no—
319#440—431no—
320C4×Q16—431no—
321C4×Q16—431no—
322C4×SD16—431no—
323C4×SD16C2×D4311yescharacteristic
324C8×D4—431no—
325C8×D4—861no—
326C8×D4—861no—
327C8×D4C2×D4311yescharacteristic
328#432—861no—
329#432—861no—
330#431—431no—
331#431—431no—
332#431—861no—
333#428—431no—
334C2×C4⋊C8—431no—
335C2×C4⋊C8—861no—
336#419—431no—
337#417—431no—
338C4×M16—431no—
339C2×C4×C8—431no—
340#335—431no—
341#335—431no—
342#334—431no—
343#334C2×D4311yescharacteristic
344Q8⋊C8—431no—
345Q8⋊C8—431no—
346Q8⋊C8—431no—
347Q8⋊C8—431no—
348Q8⋊C8—431no—
349Q8⋊C8C2×D4311yescharacteristic
350D4⋊C8—431no—
351D4⋊C8C2×D4311yescharacteristic
352#322—431no—
353#322—431no—
354#322—431no—
355#322C2×D4311yescharacteristic
356C43#1787611yescharacteristic, complemented, Sylow
357C2×#41—431no—
358C22×Q8—431no—
359#137—864no—
360C2×Q16—431no—
361C2×Q16—431no—
362C2×SD16—431no—
363C2×SD16C4×D4311yescharacteristic
364C2×M16—431no—
365C2×M16—431no—
366C22×C8—21no—
367C22×C8—861no—
368C22×C8—861no—
369C22×C8—861no—
370C4×Q8—431no—
371C4×Q8—431no—
372C4×Q8—431no—
373C4×Q8—431no—
374C4×Q8—431no—
375C4×Q8—861no—
376C4×Q8—861no—
377C4×Q8C22×D4311yescharacteristic
378C4×D4—431no—
379C4×D4—861no—
380C4×D4—861no—
381C4×D4C22×D4311yescharacteristic
382#117—431no—
383#117—861no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—861no—
386C2×C42—431no—
387C2×C42—861no—
388C2×C42—861no—
389#107—431no—
390#107—431no—
391#106—431no—
392#106C4×D4311yescharacteristic
393C4⋊C8—21no—
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—861no—
399C4⋊C8—861no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8C22×D4311yescharacteristic
405C4⋊C8C22×D4311yescharacteristic
406#103—431no—
407#103—431no—
408#103—431no—
409#103—431no—
410#103—431no—
411#103C4×D4311yescharacteristic
412#102—431no—
413#102C4×D4311yescharacteristic
414C22⋊C8—21no—
415C22⋊C8—431no—
416C22⋊C8—431no—
417C22⋊C8—861no—
418C22⋊C8—861no—
419#97—21no—
420#97—431no—
421#97—431no—
422#97—861no—
423#97—861no—
424#97—861no—
425C4×C8—431no—
426C4×C8—431no—
427C4×C8—431no—
428C4×C8—861no—
429C4×C8—861no—
430C4×C8—861no—
431C4×C8—861no—
432C4×C8C22×D4311yescharacteristic
433C4×C8C22×D4311yescharacteristic
434C4×C8C22×D4311yescharacteristic
435#41—434no—
436#41—862no—
437C2×Q8—431no—
438C2×Q8—431no—
439C2×Q8—861no—
440C2×Q8—862no—
441C2×Q8—862no—
442C2×Q8C2×C4×D4311yescharacteristic
443C2×D4—861no—
444C2×D4C2×C4×D4311yescharacteristic
445C22×C4—21no—
446C22×C4—431no—
447C22×C4—431no—
448C22×C4—431no—
449C22×C4—861no—
450C22×C4—861no—
451C22×C4—861no—
452C22×C4—861no—
453Q16—862no—
454Q16—862no—
455SD16—22no—
456SD16—862no—
457M16—862no—
458M16—862no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—81no—
463C2×C8—431no—
464C2×C8—431no—
465C2×C8—431no—
466C2×C8—431no—
467C2×C8—861no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—3441no—
471C2×C8—3441no—
472C2×C8—1722no—
473C2×C8C2×C4×D4311yescharacteristic
474C2×C8C2×C4×D4311yescharacteristic
475C2×C8D4×D4311yescharacteristic
476C2×C8D4×D4311yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—431no—
479C4⋊C4—431no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—861no—
486C4⋊C4C2×C4×D4311yescharacteristic
487C4⋊C4C2×C4×D4311yescharacteristic
488C22⋊C4—21no—
489C22⋊C4—861no—
490C22⋊C4—861no—
491C42—21no—
492C42—431no—
493C42—431no—
494C42—431no—
495C42—861no—
496C42—861no—
497C42—861no—
498C42—861no—
499C42—861no—
500C42—861no—
501C42C23×D4311yescharacteristic
502C23—21no—
503C23—431no—
504Q8—21no—
505Q8—21no—
506Q8—432no—
507Q8—861no—
508Q8—861no—
509Q8—861no—
510Q8—1722no—
511D4—21no—
512D4—864no—
513D4M16×D4312yes—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—431no—
520C2×C4—432no—
521C2×C4—432no—
522C2×C4—431no—
523C2×C4—431no—
524C2×C4—864no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—3441no—
532C2×C4—3441no—
533C2×C4—1721no—
534C2×C4—1722no—
535C2×C4C22×C4×D4311yescharacteristic
536C2×C4C2×D4×D4311yescharacteristic
537C2×C4#41×D4311yescharacteristic
538C8—21no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—862no—
546C8—861no—
547C8—861no—
548C8—861no—
549C8—861no—
550C8—1721no—
551C8—1721no—
552C22—22no—
553C22—41no—
554C22—41no—
555C22—432no—
556C22—861no—
557C22—861no—
558C22C4×D4×D4311yescharacteristic
559C4—21no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—432no—
564C4—861no—
565C4—861no—
566C4—862no—
567C4—1721no—
568C4—1721no—
569C4—1721no—
570C4C2×M16×D4311yescharacteristic
571C4#131×D4311yescharacteristic
572C4#1458370511yescharacteristic
573C4#1458371311yescharacteristic
574C2—42no—
575C2—862no—
576C2#435×D4311yescharacteristic
577C2#1914343111yescharacteristic
578C2#1914350311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1582C2
socleC22×C43C2×C4×D4
prime radicalC2×#10621900C2×C4
cosocleC42×C43C24
hypercenter#1582D43
hypocenterC43#17876
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
2. #19143677C2semidirect
4. #19133465C2semidirect
5. #19133464C2semidirect
6. #19133453C2semidirect
7. #19133452C2semidirect
8. #19133448C2semidirect
9. #19133447C2semidirect
10. #19133428C2semidirect
11. #19133344C2semidirect
13. Q8⋊C8×D43C2semidirect
14. #19132883C2semidirect
15. C43×#1582C2semidirect
295. #1582D43semidirect
356. C43#17876semidirect

Maximal subgroups

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

subgroupindex
#191437022
#191436772
C4×#130633542
#191334652
#191334642
#191334532
#191334522
#191334482
#191334472
#191334282
#191333442
#191329742
Q8⋊C8×D432
#191328832
C43×#15822
#1787643