Finite Group Databasebeta

← #25068380

Subgroups — #25068380

Order 11008.

600 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145159C211yesmaximal, characteristic
2#19143599C211yesmaximal, characteristic, complemented
3#19133490C211yesmaximal, characteristic, complemented
4#19133478C211yesmaximal, characteristic, complemented
5#19133438C211yesmaximal, characteristic, complemented
6#19133436C211yesmaximal, characteristic, complemented
7#19133431C211yesmaximal, characteristic, complemented
8#19133429C211yesmaximal, characteristic, complemented
9C8×#10621885C211yesmaximal, characteristic, complemented
10C8×#10621882C211yesmaximal, characteristic, complemented
11#19133341C211yesmaximal, characteristic, complemented
12#19133003C211yesmaximal, characteristic, complemented
13#19133001C211yesmaximal, characteristic, complemented
14M16×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#2969C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17#14583298C411yescharacteristic
18#14583281C411yescharacteristic
19#14583256C411yescharacteristic
20#14583253C411yescharacteristic
21#14583138C411yescharacteristic
22#14583133C411yescharacteristic
23#14583130C411yescharacteristic
24#14583126C411yescharacteristic
25#14583029C2211yescharacteristic
26C8×Dic86C2211yescharacteristic
27C4×#10621885C2211yescharacteristic
28C4×#10621884C2211yescharacteristic
29C4×#10621883C2211yescharacteristic
30C4×#10621882C2211yescharacteristic
31#14582978C2211yescharacteristic
32#14582975—21no—
33#14582968—21no—
34C8×D172C2211yescharacteristic
35#14582961—21no—
36#14582952C2211yescharacteristic
37#14582952C2211yescharacteristic
38#14582856—21no—
39C2×C4×C43⋊C8C2211yescharacteristic
40#14582651C2211yescharacteristic
41#14582651C2211yescharacteristic
42#14582649C2211yescharacteristic
43#14582649C2211yescharacteristic
44Q8⋊(C43⋊C8)C2211yescharacteristic
45Q8⋊(C43⋊C8)C2211yescharacteristic
46#14582629C2211yescharacteristic
47#14582629C2211yescharacteristic
48D4⋊(C43⋊C8)C2211yescharacteristic
49D4⋊(C43⋊C8)C2211yescharacteristic
50#14582626C2211yescharacteristic
51#14582626C2211yescharacteristic
52#14582620C2211yescharacteristic
53#14582620C2211yescharacteristic
54C8×C43⋊C8C2211yescharacteristic
55C8×C43⋊C8C2211yescharacteristic
56C43×#529C2211yescharacteristic
57C43×#446C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C43×#436—21no—
60C43×#436C2211yescharacteristic
61C43×#435—21no—
62C8×D4×C43C2211yescharacteristic
63C43×#433—21no—
64C43×#431C2211yescharacteristic
65C43×#405—21no—
66C4×M16×C43C2211yescharacteristic
67C2×#10621885C2×C411yescharacteristic
68C2×#10621883C2×C411yescharacteristic
69C2×#10621884C2×C411yescharacteristic
70C2×#10621882C2×C411yescharacteristic
71C2×#10621872—21no—
72C22×C43⋊C8C2×C411yescharacteristic
73C22×C43⋊C8C2×C411yescharacteristic
74C2×C8×D43—21no—
75#13063319—21no—
76#13063317C2×C411yescharacteristic
77#13063313C2×C411yescharacteristic
78#13063308—21no—
79#13063304C2×C411yescharacteristic
80#13063299C2×C411yescharacteristic
81C4×Dic86C2311yescharacteristic
82C4×D172C2311yescharacteristic
83C4×C22⋊D43—21no—
84#13063282—21no—
85#13063258C2×C411yescharacteristic
86#13063258C2×C411yescharacteristic
87#13063256C2×C411yescharacteristic
88#13063256C2×C411yescharacteristic
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)C2311yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92Dic43⋊C8—21no—
93Dic43⋊C8—21no—
94#13063249C2×C411yescharacteristic
95#13063249C2×C411yescharacteristic
96#13063248C2×C411yescharacteristic
97#13063248C2×C411yescharacteristic
98#13063246C2×C411yescharacteristic
99#13063246C2×C411yescharacteristic
100#13063245C2×C411yescharacteristic
101#13063245C2×C411yescharacteristic
102C22⋊(C43⋊C8)—21no—
103C22⋊(C43⋊C8)—21no—
104(C2×D43)⋊C8—21no—
105(C2×D43)⋊C8—21no—
106#13063235—21no—
107C4×C43⋊C8—21no—
108C4×C43⋊C8C2×C411yescharacteristic
109C4×C43⋊C8C2×C411yescharacteristic
110C4×C43⋊C8C2311yescharacteristic
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×M16×C43—21no—
116C2×M16×C43D411yescharacteristic
117C2×M16×C43D411yescharacteristic
118C22×C8×C43—21no—
119#126×C43—21no—
120#125×C43C2×C411yescharacteristic
121#124×C43C2×C411yescharacteristic
122#123×C43—21no—
123C22⋊Q8×C43C2×C411yescharacteristic
124#121×C43C2×C411yescharacteristic
125C4×Q8×C43C2311yescharacteristic
126C4×D4×C43—21no—
127C4×D4×C43C2311yescharacteristic
128#117×C43—21no—
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137#97×C43—21no—
138#97×C43D411yescharacteristic
139#97×C43D411yescharacteristic
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C22×C411yescharacteristic
145C2×D4×C43—21no—
146C2×D4×C43C22×C411yescharacteristic
147C22×C4×C43—21no—
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43#4111yescharacteristic
151C2×C22⋊D43—21no—
152C2×D172C22×C411yescharacteristic
153C2×C4×D43—21no—
154C2×Dic86C22×C411yescharacteristic
155M16×C43—22no—
156M16×C43—22no—
157M16×C43—42no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—42no—
161C2×C8×C43C2×D411yescharacteristic
162C2×C8×C43C2×D411yescharacteristic
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43C22×C411yescharacteristic
170C4⋊C4×C43C22×C411yescharacteristic
171C22⋊C4×C43—21no—
172C22⋊C4×C43—21no—
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C42×C43—21no—
177C42×C43C22×C411yescharacteristic
178C42×C43C2×D411yescharacteristic
179C42×C43#4111yescharacteristic
180C42×C43C2411yescharacteristic
181C22⋊Dic43—21no—
182#10621885—22no—
183#10621884—41no—
184#10621883—41no—
185#10621882—22no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188(C2×D43)⋊C4—21no—
189(C2×D43)⋊C4—21no—
190C4⋊Dic43C22×C411yescharacteristic
191C4⋊Dic43C22×C411yescharacteristic
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196C4×Dic43—21no—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—41no—
203C2×C43⋊C8C22×C411yescharacteristic
204C2×C43⋊C8C22×C411yescharacteristic
205C2×C43⋊C8C22×C411yescharacteristic
206C2×C43⋊C8C22×C411yescharacteristic
207#10621872—42no—
208C8×D43—42no—
209C23×C43—21no—
210C23×C43C4×D411yescharacteristic
211C22×D43—21no—
212Q8×C43—21no—
213Q8×C43—21no—
214D4×C43—21no—
215D4×C43—21no—
216D4×C43—81no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43C4×D411yescharacteristic
228C2×C4×C43C4×D411yescharacteristic
229C2×C4×C43C4×D411yescharacteristic
230C2×C4×C43C23×C411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C22⋊D43—81no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237D172—21no—
238D172—21no—
239C4×D43—41no—
240C4×D43—41no—
241Dic86—21no—
242Dic86—21no—
243C8×C43—21no—
244C8×C43—21no—
245C8×C43—41no—
246C8×C43—41no—
247C8×C43#13512yes—
248C8×C43#13512yes—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8#13112yes—
257#18069—431nomaximal, Sylow
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43C2×C4×D411yescharacteristic
265C2×D43—41no—
266C2×D43—41no—
267C2×D43—41no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43C2×#13111yescharacteristic
276C4×C43#56811yescharacteristic
277C4×C43C2×#13511yescharacteristic
278C4×C43C2×#13511yescharacteristic
279Dic43—41no—
280Dic43—41no—
281Dic43—41no—
282#3168—431no—
283#2969—431no—
284#2969D4311yescharacteristic, complemented
285#1591—431no—
286#1589—431no—
287#1583—431no—
288#1583—431no—
289#1582—431no—
290#1582—431no—
291C8×Q16—431no—
292C8×D8—431no—
293#1564—431no—
294#1482—431no—
295#1482—431no—
296C8×M16—431no—
297C2×C43—41no—
298C2×C43—81no—
299C2×C43#293511yescharacteristic
300C2×C43C4×#13511yescharacteristic
301C2×C43#295711yescharacteristic
302D43—81no—
303#529—431no—
304#529C2×D4311yescharacteristic
305#499—431no—
306#495—431no—
307#488—431no—
308#488—431no—
309#467—431no—
310#466—431no—
311#465—431no—
312#465—431no—
313#446—431no—
314#446C2×D4311yescharacteristic
315C8×Q8—431no—
316C8×Q8C2×D4311yescharacteristic
317C4×Q16—431no—
318C4×SD16—431no—
319C4×SD16—431no—
320C4×D8—431no—
321#436—21no—
322#436—431no—
323#436—861no—
324#436C2×D4311yescharacteristic
325#435—21no—
326#435—861no—
327C8×D4—431no—
328C8×D4C2×D4311yescharacteristic
329#433—21no—
330#433—861no—
331#431—431no—
332#431—431no—
333#431C2×D4311yescharacteristic
334#405—21no—
335#405—861no—
336C4×M16C2×D4311yescharacteristic
337C2×C4×C8—431no—
338#335—431no—
339#335—431no—
340#334—431no—
341#334—431no—
342Q8⋊C8—431no—
343Q8⋊C8—431no—
344Q8⋊C8—431no—
345Q8⋊C8—431no—
346D4⋊C8—431no—
347D4⋊C8—431no—
348D4⋊C8—431no—
349D4⋊C8—431no—
350#322—431no—
351#322—431no—
352C82—431no—
353C82—431no—
354C43#1806911yescharacteristic, complemented, Sylow
355C2×Q16—431no—
356C2×SD16—431no—
357C2×SD16—431no—
358C2×D8—431no—
359C2×M16—21no—
360C2×M16—861no—
361C2×M16C22⋊D4311yescharacteristic
362C2×M16C22⋊D4311yescharacteristic
363C22×C8—21no—
364C22×C8—431no—
365C22×C8—431no—
366C22×C8—861no—
367#126—21no—
368#126—861no—
369#125—431no—
370#125C4×D4311yescharacteristic
371#124—431no—
372#124C4×D4311yescharacteristic
373#123—21no—
374#123—861no—
375C22⋊Q8—431no—
376C22⋊Q8C4×D4311yescharacteristic
377#121—431no—
378#121C4×D4311yescharacteristic
379C4×Q8—431no—
380C4×Q8C22×D4311yescharacteristic
381C4×D4—21no—
382C4×D4—431no—
383C4×D4—861no—
384C4×D4C22×D4311yescharacteristic
385#117—21no—
386#117—861no—
387C2×C42C22×D4311yescharacteristic
388#107—431no—
389#107—431no—
390#106—431no—
391#106—431no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8—861no—
397C4⋊C8—861no—
398C4⋊C8—861no—
399C4⋊C8C22×D4311yescharacteristic
400C4⋊C8C22×D4311yescharacteristic
401#103—431no—
402#103—431no—
403#103—431no—
404#103—431no—
405#102—431no—
406#102—431no—
407#102—431no—
408#102—431no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8—861no—
413C22⋊C8—861no—
414C22⋊C8—861no—
415C22⋊C8—861no—
416#97—21no—
417#97—861no—
418#97C22⋊D4311yescharacteristic
419#97C22⋊D4311yescharacteristic
420C4×C8—21no—
421C4×C8—21no—
422C4×C8—431no—
423C4×C8—431no—
424C4×C8—431no—
425C4×C8—431no—
426C4×C8—431no—
427C4×C8—431no—
428C4×C8—861no—
429C4×C8—861no—
430C4×C8C22×D4311yescharacteristic
431C4×C8C22×D4311yescharacteristic
432C2×Q8—431no—
433C2×Q8C2×C4×D4311yescharacteristic
434C2×D4—21no—
435C2×D4—431no—
436C2×D4—861no—
437C2×D4C2×C4×D4311yescharacteristic
438C22×C4—21no—
439C22×C4—861no—
440C22×C4C2×C4×D4311yescharacteristic
441C22×C4#1062189811yescharacteristic
442C22×C4C2×C22⋊D4311yescharacteristic
443Q16—862no—
444SD16—1721no—
445SD16—1721no—
446D8—862no—
447M16—22no—
448M16—22no—
449M16—42no—
450M16—1722no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—42no—
454C2×C8—431no—
455C2×C8—431no—
456C2×C8—431no—
457C2×C8—431no—
458C2×C8—862no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—1721no—
464C2×C8—1722no—
465C2×C8C2×C22⋊D4311yescharacteristic
466C2×C8C2×C22⋊D4311yescharacteristic
467C2×C8C2×C22⋊D4311yescharacteristic
468C2×C8C2×C22⋊D4311yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—431no—
474C4⋊C4—431no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4C2×C4×D4311yescharacteristic
480C4⋊C4C2×C4×D4311yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—861no—
487C22⋊C4—861no—
488C22⋊C4—861no—
489C22⋊C4—861no—
490C22⋊C4—861no—
491C42—21no—
492C42—861no—
493C42C2×C4×D4311yescharacteristic
494C42#1062189811yescharacteristic
495C42C2×C22⋊D4311yescharacteristic
496C42C23×D4311yescharacteristic
497C23—21no—
498C23—861no—
499C23C4×C22⋊D4311yescharacteristic
500Q8—21no—
501Q8—21no—
502Q8—861no—
503Q8—861no—
504D4—21no—
505D4—21no—
506D4—81no—
507D4—861no—
508D4—861no—
509D4—3441no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4C4×C22⋊D4311yescharacteristic
526C2×C4C4×C22⋊D4311yescharacteristic
527C2×C4C4×C22⋊D4311yescharacteristic
528C2×C4C22×C4×D4311yescharacteristic
529C2×C4C22×C22⋊D4311yescharacteristic
530C2×C4C2×#1062189811yescharacteristic
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—432no—
536C8—861no—
537C8—861no—
538C8—861no—
539C8—1721no—
540C8—1721no—
541C8—1721no—
542C8—1721no—
543C8#1306334512yes—
544C8#1306334512yes—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—1721no—
552C22—1721no—
553C22—1721no—
554C22C2×C4×C22⋊D4311yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—1721no—
563C4—1721no—
564C4—1721no—
565C4#131×D4311yescharacteristic
566C4#1458366411yescharacteristic
567C4C2×#1306334511yescharacteristic
568C4C2×#1306334511yescharacteristic
569C2—41no—
570C2—81no—
571C2—3441no—
572C2#1914333711yescharacteristic
573C2C4×#1306334511yescharacteristic
574C2#1914351011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#2969C2
socleC22×C43C2×C4×D4
prime radical#14583133C4
cosocleC42×C43C24
hypercenter#2969D43
hypocenterC43#18069
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2969

Complements

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

NH ≅ G/Ntype
2. #19143599C2semidirect
3. #19133490C2semidirect
4. #19133478C2semidirect
5. #19133438C2semidirect
6. #19133436C2semidirect
7. #19133431C2semidirect
8. #19133429C2semidirect
9. C8×#10621885C2semidirect
10. C8×#10621882C2semidirect
11. #19133341C2semidirect
12. #19133003C2semidirect
13. #19133001C2semidirect
14. M16×C43⋊C8C2semidirect
15. C43×#2969C2semidirect
284. #2969D43semidirect
354. C43#18069semidirect

Maximal subgroups

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

subgroupindex
#191451592
#191435992
#191334902
#191334782
#191334382
#191334362
#191334312
#191334292
C8×#106218852
C8×#106218822
#191333412
#191330032
#191330012
M16×C43⋊C82
C43×#29692
#1806943