Finite Group Databasebeta

← #24988493

Subgroups — #24988493

Order 11008.

772 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135540C211yesmaximal, characteristic, complemented
2#19134420C211yesmaximal, characteristic, complemented
3#19133210C211yesmaximal, characteristic, complemented
4#19133183C211yesmaximal, characteristic, complemented
5#19133120C211yesmaximal, characteristic, complemented
6#19133038C211yesmaximal, characteristic, complemented
7C43×#3520C211yesmaximal, characteristic
8#14582956C2211yescharacteristic
9C2×#13063246—21no—
10C4×#10621877C2211yescharacteristic
11C2×#13063236C2211yescharacteristic
12C4×C4⋊Dic43C2211yescharacteristic
13#14582661—21no—
14#14582658—22no—
15#14582641—22no—
16#14582641—21no—
17#14582639—21no—
18#14582636—21no—
19#14582633—21no—
20D4⋊(C43⋊C8)—21no—
21D4⋊(C43⋊C8)—21no—
22C43×#556C411yescharacteristic, complemented
23C43×#554—21no—
24C43×#552—21no—
25C43×#551—22no—
26D4×Q8×C43C411yescharacteristic, complemented
27C43×#548—21no—
28C43×#547C411yescharacteristic, complemented
29C43×#547C411yescharacteristic, complemented
30C43×#546—21no—
31C43×#542—21no—
32C43×#539—22no—
33C43×#533C2211yescharacteristic
34C43×#529C2211yescharacteristic
35C43×#525—21no—
36C2×C22⋊Q8×C43—21no—
37C43×#520—21no—
38C2×C4×D4×C43C2211yescharacteristic
39C2×#10621877—21no—
40C22×C43⋊C8—21no—
41C2×C4⋊Dic43—21no—
42C2×C4×Dic43—21no—
43C4⋊(C43⋊C8)—21no—
44#13063246—24no—
45C22⋊(C43⋊C8)—21no—
46#13063236—21no—
47#13063236—21no—
48#13063236—21no—
49#13063236—21no—
50C4×C43⋊C8—21no—
51C43⋊#95—21no—
52C2×#41×C43—21no—
53C2×#41×C43—21no—
54C22×Q8×C43—21no—
55C22×D4×C43D411yescharacteristic
56C23×C4×C43—21no—
57C4⋊Q8×C43—21no—
58C4⋊Q8×C43C2×C411yescharacteristic
59C4⋊Q8×C43C2×C411yescharacteristic
60#126×C43—22no—
61#126×C43—22no—
62#126×C43—21no—
63#125×C43—22no—
64#125×C43D411yescharacteristic
65#125×C43D412yes—
66#124×C43—22no—
67#124×C43—21no—
68#124×C43D411yescharacteristic
69#123×C43—22no—
70#123×C43—22no—
71#123×C43—21no—
72#123×C43—22no—
73#123×C43—22no—
74C22⋊Q8×C43—22no—
75C22⋊Q8×C43—22no—
76C22⋊Q8×C43—22no—
77C22⋊Q8×C43—21no—
78C22⋊Q8×C43—21no—
79C22⋊Q8×C43—21no—
80C22⋊Q8×C43—21no—
81C22⋊Q8×C43—21no—
82C22⋊Q8×C43—22no—
83C22⋊Q8×C43—21no—
84C22⋊Q8×C43D411yescharacteristic
85#121×C43—22no—
86#121×C43—21no—
87#121×C43—21no—
88#121×C43D411yescharacteristic
89#120×C43—22no—
90C4×Q8×C43—21no—
91C4×Q8×C43—21no—
92C4×Q8×C43—21no—
93C4×Q8×C43C2×C411yescharacteristic
94C4×D4×C43—22no—
95C4×D4×C43—22no—
96C4×D4×C43—22no—
97C4×D4×C43—21no—
98C4×D4×C43—21no—
99C4×D4×C43—21no—
100C4×D4×C43—21no—
101C4×D4×C43C2×C411yescharacteristic
102C4×D4×C43C2×C411yescharacteristic
103C4×D4×C43C2×C411yescharacteristic
104C4×D4×C43D411yescharacteristic
105C4×D4×C43D411yescharacteristic
106#117×C43—22no—
107#117×C43—21no—
108#117×C43—21no—
109#117×C43D412yes—
110C2×C4⋊C4×C43—22no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43D411yescharacteristic
114C2×C22⋊C4×C43—22no—
115C2×C22⋊C4×C43—21no—
116C2×C42×C43C2311yescharacteristic
117C24×C43—21no—
118#41×C43—42no—
119#41×C43—42no—
120#41×C43—82no—
121C2×Q8×C43—22no—
122C2×Q8×C43—21no—
123C2×Q8×C43—21no—
124C2×Q8×C43—82no—
125C2×Q8×C43C22⋊C411yescharacteristic
126C2×D4×C43—22no—
127C2×D4×C43—22no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—22no—
131C2×D4×C43—41no—
132C2×D4×C43C22⋊C411yescharacteristic
133C2×D4×C43C22⋊C411yescharacteristic
134C2×D4×C43C22⋊C411yescharacteristic
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—82no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×Dic43—41no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—22no—
162C4⋊C4×C43C22⋊C411yescharacteristic
163C4⋊C4×C43C22⋊C411yescharacteristic
164C4⋊C4×C43C22⋊C411yescharacteristic
165C4⋊C4×C43C22⋊C411yescharacteristic
166C4⋊C4×C43C22⋊C412yes—
167C4⋊C4×C43C22⋊C412yes—
168C22⋊C4×C43—22no—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—22no—
172C22⋊C4×C43—22no—
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—21no—
182C22⋊C4×C43—22no—
183C42×C43—22no—
184C42×C43—21no—
185C42×C43—22no—
186C42×C43C22×C411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C4⋊Dic43—22no—
191C4⋊Dic43—41no—
192C4×Dic43—42no—
193#10621877—22no—
194#10621877—41no—
195C2×C43⋊C8—22no—
196C2×C43⋊C8—41no—
197C2×C43⋊C8—41no—
198C2×C43⋊C8—41no—
199C2×C43⋊C8—41no—
200C23×C43—21no—
201C23×C43—21no—
202C23×C43—21no—
203C23×C43—42no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43—81no—
207C23×C43#12011yescharacteristic
208Q8×C43—41no—
209Q8×C43—42no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—82no—
213D4×C43—21no—
214D4×C43—21no—
215D4×C43—21no—
216D4×C43—42no—
217D4×C43—41no—
218D4×C43—44no—
219D4×C43—41no—
220D4×C43—41no—
221D4×C43—82no—
222D4×C43#10412yes—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—22no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—22no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—41no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—44no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—81no—
241C2×C4×C43—81no—
242C2×C4×C43—81no—
243C2×C4×C43—82no—
244C2×C4×C43—82no—
245C2×C4×C43C2×C22⋊C411yescharacteristic
246C2×C4×C43C2×C22⋊C411yescharacteristic
247C2×C4×C43C2×C22⋊C411yescharacteristic
248C2×C4×C43#12011yescharacteristic
249C2×C4×C43#12011yescharacteristic
250C2×C4×C43#12011yescharacteristic
251C2×Dic43—42no—
252C2×Dic43—81no—
253C2×Dic43—81no—
254C43⋊C8—42no—
255C43⋊C8—42no—
256C43⋊C8—81no—
257#8418—431nomaximal, Sylow
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—22no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43—41no—
269C22×C43—82no—
270C22×C43—82no—
271C22×C43#37911yescharacteristic
272C22×C43#45411yescharacteristic
273C22×C43#45611yescharacteristic
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—42no—
283C4×C43—41no—
284C4×C43—41no—
285C4×C43—42no—
286C4×C43C2×#10411yescharacteristic
287C4×C43#42111yescharacteristic
288Dic43—82no—
289#3520D4311yescharacteristic
290#1986—431no—
291#1762—431no—
292#1531—431no—
293#1524—431no—
294#1509—431no—
295#1490—431no—
296C2×C43—21no—
297C2×C43—21no—
298C2×C43—42no—
299C2×C43—81no—
300C2×C43—81no—
301C2×C43#178911yescharacteristic
302C2×C43#179311yescharacteristic
303C2×C43#179511yescharacteristic
304#556Dic4311yescharacteristic, complemented
305#554—21no—
306#552—21no—
307#551—22no—
308D4×Q8Dic4311yescharacteristic, complemented
309#548—21no—
310#547Dic4311yescharacteristic, complemented
311#547Dic4311yescharacteristic, complemented
312#546—21no—
313#542—21no—
314#539—22no—
315#533C2×D4311yescharacteristic
316#529C2×D4311yescharacteristic
317#525—21no—
318C2×C22⋊Q8—21no—
319#520—21no—
320C2×C4×D4C2×D4311yescharacteristic
321#432—431no—
322C2×#102—861no—
323C4×M16—431no—
324C2×#97—431no—
325C4×C4⋊C4—431no—
326#340—861no—
327#339—862no—
328#330—861no—
329#330—862no—
330#329—861no—
331#328—861no—
332#327—861no—
333D4⋊C8—861no—
334D4⋊C8—861no—
335C43#841811yescharacteristic, complemented, Sylow
336C2×#41—21no—
337C2×#41—21no—
338C22×Q8—21no—
339C22×D4C22⋊D4311yescharacteristic
340C23×C4—21no—
341C2×M16—861no—
342C22×C8—861no—
343C4⋊Q8—21no—
344C4⋊Q8C2×Dic4311yescharacteristic
345C4⋊Q8C2×Dic4311yescharacteristic
346#126—22no—
347#126—22no—
348#126—21no—
349#125—22no—
350#125C22⋊D4311yescharacteristic
351#125C22⋊D4312yes—
352#124—22no—
353#124—21no—
354#124C22⋊D4311yescharacteristic
355#123—22no—
356#123—22no—
357#123—21no—
358#123—22no—
359#123—22no—
360C22⋊Q8—22no—
361C22⋊Q8—22no—
362C22⋊Q8—22no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—22no—
369C22⋊Q8—21no—
370C22⋊Q8C22⋊D4311yescharacteristic
371#121—22no—
372#121—21no—
373#121—21no—
374#121C22⋊D4311yescharacteristic
375#120—22no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8C2×Dic4311yescharacteristic
380C4×D4—22no—
381C4×D4—22no—
382C4×D4—22no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4C2×Dic4311yescharacteristic
388C4×D4C2×Dic4311yescharacteristic
389C4×D4C2×Dic4311yescharacteristic
390C4×D4C22⋊D4311yescharacteristic
391C4×D4C22⋊D4311yescharacteristic
392#117—22no—
393#117—21no—
394#117—21no—
395#117C22⋊D4312yes—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4C22⋊D4311yescharacteristic
401C2×C22⋊C4—22no—
402C2×C22⋊C4—21no—
403C2×C42—861no—
404C2×C42C22×D4311yescharacteristic
405C4⋊C8—861no—
406#102—864no—
407C22⋊C8—861no—
408#97—861no—
409#97—861no—
410#97—861no—
411#97—861no—
412C4×C8—861no—
413#95—861no—
414C24—21no—
415#41—42no—
416#41—42no—
417#41—82no—
418C2×Q8—22no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—82no—
422C2×Q8C22⋊Dic4311yescharacteristic
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—21no—
426C2×D4—22no—
427C2×D4—21no—
428C2×D4—41no—
429C2×D4C22⋊Dic4311yescharacteristic
430C2×D4C22⋊Dic4311yescharacteristic
431C2×D4C22⋊Dic4311yescharacteristic
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—82no—
442C22×C4—1721no—
443C22×C4C2×C22⋊D4311yescharacteristic
444C22×C4C2×C22⋊D4311yescharacteristic
445C22×C4C2×C22⋊D4311yescharacteristic
446M16—862no—
447M16—1721no—
448C2×C8—862no—
449C2×C8—1721no—
450C2×C8—1721no—
451C2×C8—1721no—
452C2×C8—1721no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—22no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—862no—
467C4⋊C4—1721no—
468C4⋊C4C22⋊Dic4311yescharacteristic
469C4⋊C4C22⋊Dic4311yescharacteristic
470C4⋊C4C22⋊Dic4311yescharacteristic
471C4⋊C4C22⋊Dic4311yescharacteristic
472C4⋊C4C22⋊Dic4312yes—
473C4⋊C4C22⋊Dic4312yes—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—21no—
480C22⋊C4—22no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C42—22no—
490C42—21no—
491C42—22no—
492C42—1722no—
493C42C22×Dic4311yescharacteristic
494C42C2×C22⋊D4311yescharacteristic
495C42C2×C22⋊D4311yescharacteristic
496C42C2×C22⋊D4311yescharacteristic
497C23—21no—
498C23—21no—
499C23—21no—
500C23—42no—
501C23—41no—
502C23—41no—
503C23—81no—
504C23#1306329411yescharacteristic
505Q8—41no—
506Q8—42no—
507Q8—41no—
508Q8—41no—
509Q8—82no—
510D4—21no—
511D4—21no—
512D4—21no—
513D4—42no—
514D4—41no—
515D4—44no—
516D4—41no—
517D4—41no—
518D4—82no—
519D4#1306325212yes—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—44no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—81no—
538C2×C4—81no—
539C2×C4—81no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4—3441no—
543C2×C4—3441no—
544C2×C4—1722no—
545C2×C4C2×C22⋊Dic4311yescharacteristic
546C2×C4C2×C22⋊Dic4311yescharacteristic
547C2×C4C2×C22⋊Dic4311yescharacteristic
548C2×C4#1306329411yescharacteristic
549C2×C4#1306329411yescharacteristic
550C2×C4#1306329411yescharacteristic
551C8—3441no—
552C8—1722no—
553C8—1722no—
554C22—21no—
555C22—21no—
556C22—22no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—82no—
566C22—82no—
567C22#1458275511yescharacteristic
568C22#1458307211yescharacteristic
569C22#1458308211yescharacteristic
570C4—21no—
571C4—21no—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—41no—
576C4—42no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—42no—
581C4—41no—
582C4—3442no—
583C4C2×#1306325211yescharacteristic
584C4#1458291611yescharacteristic
585C2—21no—
586C2—21no—
587C2—42no—
588C2—81no—
589C2—81no—
590C2#1913453911yescharacteristic
591C2#1913455411yescharacteristic
592C2#1913456511yescharacteristic
subgroupG/H
centerC22#14582755
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3520C2
socleC22×C43#379
cosocleC2×C42×C43C23
hypercenter#3520D43
hypocenterC43#8418
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3520

Complements

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

NH ≅ G/Ntype
1. #19135540C2semidirect
2. #19134420C2semidirect
3. #19133210C2semidirect
4. #19133183C2semidirect
5. #19133120C2semidirect
6. #19133038C2semidirect
22. C43×#556C4semidirect
26. D4×Q8×C43C4semidirect
28. C43×#547C4semidirect
29. C43×#547C4semidirect
304. #556Dic43semidirect
308. D4×Q8Dic43semidirect
310. #547Dic43semidirect
311. #547Dic43semidirect
335. C43#8418semidirect

Maximal subgroups

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

subgroupindex
#191355402
#191344202
#191332102
#191331832
#191331202
#191330382
C43×#35202
#841843