Finite Group Databasebeta

← #24988668

Subgroups — #24988668

Order 11008.

1116 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
1C2×#14583570C211yesmaximal, characteristic
2#19135400C211yesmaximal, characteristic, complemented
3#19134597C211yesmaximal, characteristic, complemented
4C2×#14582642C211yesmaximal, characteristic, complemented
5C2×#14582629C211yesmaximal, characteristic, complemented
6C2×D4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
7C43×#1802C211yesmaximal, characteristic, complemented
8C22×#10621898—21no—
9#14583570—22no—
10#14583570—22no—
11#14583570—22no—
12#14583570C414yescomplemented
13C2×#13063322C2211yescharacteristic
14C2×#13063321—21no—
15C2×#13063299—21no—
16C2×#13063298—22no—
17C2×C4×Dic86C2211yescharacteristic
18C2×#13063287—21no—
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20C2×#13063248—21no—
21C2×#13063245—22no—
22C2×C4×C43⋊C8C2211yescharacteristic
23#14582661—21no—
24#14582642—22no—
25#14582629—22no—
26D4⋊(C43⋊C8)—22no—
27C2×C4×D4×C43C2211yescharacteristic
28C2×C4⋊C8×C43C2211yescharacteristic
29C2×#102×C43—21no—
30C43×#384C2211yescharacteristic
31C43×#340—21no—
32C2×#10621898—24no—
33C2×#10621898—24no—
34C2×#10621898—42no—
35C2×#10621898—42no—
36C2×#10621898—42no—
37C2×#10621898—42no—
38C22×Dic86D411yescharacteristic
39C22×D172—21no—
40C22×D172—21no—
41C22×D172D412yes—
42C22×C22⋊D43—22no—
43C22×C22⋊D43—22no—
44C22×C4×D43—22no—
45C22×C43⋊C8—21no—
46C22×C43⋊C8—21no—
47#13063322—21no—
48#13063322—21no—
49#13063322C2×C412yes—
50#13063322D412yes—
51#13063321—24no—
52#13063321—24no—
53#13063299—24no—
54#13063299—24no—
55#13063298—28no—
56#13063298—28no—
57C4×Dic86—21no—
58C4×Dic86—21no—
59C4×Dic86C2×C412yes—
60C4×Dic86D412yes—
61#13063287—24no—
62#13063287—24no—
63C2×C4⋊Dic43D411yescharacteristic
64C2×Dic43⋊C4—21no—
65C2×(C2×D43)⋊C4—22no—
66C2×C4×Dic43—21no—
67C4⋊(C43⋊C8)—21no—
68C4⋊(C43⋊C8)—21no—
69#13063248—42no—
70#13063245—44no—
71C4×C43⋊C8—21no—
72C4×C43⋊C8—21no—
73C22×D4×C43D411yescharacteristic
74C23×C4×C43—21no—
75C22×C8×C43—21no—
76C4×D4×C43—21no—
77C4×D4×C43—21no—
78C4×D4×C43C2×C412yes—
79C4×D4×C43D412yes—
80C2×C4⋊C4×C43—21no—
81C2×C4⋊C4×C43—21no—
82C2×C4⋊C4×C43—21no—
83C2×C4⋊C4×C43D411yescharacteristic
84C2×C22⋊C4×C43—21no—
85C2×C42×C43C2311yescharacteristic
86C4⋊C8×C43—21no—
87C4⋊C8×C43—21no—
88#102×C43—42no—
89C24×C43—21no—
90C23×D43—22no—
91C2×D4×C43—21no—
92C2×D4×C43—21no—
93C2×D4×C43—21no—
94C2×D4×C43—21no—
95C2×D4×C43—21no—
96C2×D4×C43C22⋊C412yes—
97C22×C4×C43—22no—
98C22×C4×C43—22no—
99C22×C4×C43—21no—
100C22×C4×C43—41no—
101C22×C4×C43—41no—
102C22×C4×C43—41no—
103C22×C4×C43—41no—
104C22×C4×C43—41no—
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C2×C22⋊D43—28no—
109C2×C22⋊D43—28no—
110C2×C22⋊D43—44no—
111C2×C22⋊D43—44no—
112C2×C22⋊D43—82no—
113C2×C22⋊D43—82no—
114C22×Dic43—21no—
115C22×Dic43—21no—
116#10621898—48no—
117#10621898—48no—
118#10621898—48no—
119#10621898—48no—
120C2×D172—22no—
121C2×D172—22no—
122C2×D172—22no—
123C2×D172—22no—
124C2×D172—22no—
125C2×D172—41no—
126C2×D172—41no—
127C2×D172—41no—
128C2×D172—41no—
129C2×D172—41no—
130C2×D172—41no—
131C2×D172—41no—
132C2×D172—41no—
133C2×D172—42no—
134C2×D172—42no—
135C2×D172C22⋊C414yes—
136C2×C4×D43—28no—
137C2×C4×D43—44no—
138C2×C4×D43—44no—
139C2×Dic86—21no—
140C2×Dic86—21no—
141C2×Dic86—21no—
142C2×Dic86C22⋊C412yes—
143C2×Dic86D812yes—
144C2×Dic86SD1612yes—
145C2×C8×C43—41no—
146C2×C8×C43—41no—
147C2×C8×C43—41no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—42no—
150C4⋊C4×C43—41no—
151C4⋊C4×C43—41no—
152C4⋊C4×C43—41no—
153C4⋊C4×C43—41no—
154C4⋊C4×C43C22⋊C412yes—
155C22⋊C4×C43—22no—
156C22⋊C4×C43—22no—
157C42×C43C22×C411yescharacteristic
158C42×C43C2×D411yescharacteristic
159C42×C43C2×D411yescharacteristic
160C42×C43C2×D411yescharacteristic
161(C2×D43)⋊C4—28no—
162C4⋊Dic43—21no—
163C4⋊Dic43C22⋊C412yes—
164Dic43⋊C4—22no—
165Dic43⋊C4—22no—
166C4×Dic43—22no—
167C4×Dic43—22no—
168C2×C43⋊C8—22no—
169C2×C43⋊C8—41no—
170C2×C43⋊C8—41no—
171C2×C43⋊C8—41no—
172C2×C43⋊C8—41no—
173C2×C43⋊C8—41no—
174C23×C43—22no—
175C23×C43—41no—
176C23×C43—41no—
177C23×C43—41no—
178C23×C43—41no—
179C23×C43—41no—
180C23×C43—41no—
181C23×C43#12011yescharacteristic
182C22×D43—24no—
183C22×D43—42no—
184C22×D43—42no—
185C22×D43—42no—
186C22×D43—42no—
187C22×D43—42no—
188C22×D43—42no—
189D4×C43—22no—
190D4×C43—22no—
191D4×C43—41no—
192D4×C43—41no—
193C2×C4×C43—21no—
194C2×C4×C43—21no—
195C2×C4×C43—22no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—42no—
199C2×C4×C43—42no—
200C2×C4×C43—42no—
201C2×C4×C43—42no—
202C2×C4×C43—81no—
203C2×C4×C43—81no—
204C2×C4×C43—81no—
205C2×C4×C43C2×C22⋊C411yescharacteristic
206C2×C4×C43C2×C22⋊C411yescharacteristic
207C2×C4×C43C2×C22⋊C411yescharacteristic
208C2×C4×C43#12011yescharacteristic
209C2×C4×C43#12011yescharacteristic
210C2×C4×C43#12011yescharacteristic
211C2×C4×C43C2×D811yescharacteristic
212C2×C4×C43C2×SD1611yescharacteristic
213C2×C4×C43#13511yescharacteristic
214C2×C4×C43#13511yescharacteristic
215C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
216C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
217C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
218C2×C4×C43#13711yescharacteristic
219C22⋊D43—416no—
220C22⋊D43—88no—
221C2×Dic43—22no—
222C2×Dic43—22no—
223C2×Dic43—22no—
224C2×Dic43—22no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227D172—44no—
228D172—42no—
229D172—42no—
230D172—42no—
231D172—42no—
232D172—42no—
233D172—42no—
234D172—42no—
235D172—42no—
236D172—82no—
237C4×D43—416no—
238Dic86—22no—
239Dic86—22no—
240Dic86—22no—
241Dic86#10214yescomplemented
242C8×C43—81no—
243C43⋊C8—42no—
244C43⋊C8—81no—
245#8444—431nomaximal, Sylow
246C22×C43—42no—
247C22×C43—42no—
248C22×C43—42no—
249C22×C43—81no—
250C22×C43—81no—
251C22×C43—81no—
252C22×C43—81no—
253C22×C43#37911yescharacteristic
254C22×C43#44711yescharacteristic
255C22×C43#44911yescharacteristic
256C22×C43#45011yescharacteristic
257C22×C43#45211yescharacteristic
258C22×C43#45311yescharacteristic
259C22×C43#45511yescharacteristic
260C2×D43—44no—
261C2×D43—44no—
262C2×D43—44no—
263C2×D43—82no—
264C2×D43—82no—
265C2×D43—82no—
266C2×D43—82no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—42no—
270C4×C43—161no—
271C4×C43C2×#10211yescharacteristic
272C4×C43#41611yescharacteristic
273C4×C43#41711yescharacteristic
274C4×C43#41811yescharacteristic
275C4×C43#44711yescharacteristic
276C4×C43#44911yescharacteristic
277C4×C43#45011yescharacteristic
278C4×C43#45211yescharacteristic
279Dic43—24no—
280Dic43—42no—
281C2×#550—431no—
282#1957—431no—
283#1803—431no—
284#1802D4311yescharacteristic, complemented
285C2×#331—431no—
286C2×Q8⋊C8—431no—
287C2×D4⋊C8—431no—
288C2×C43—82no—
289C2×C43#162111yescharacteristic
290C2×C43#163111yescharacteristic
291C2×C43#164111yescharacteristic
292C2×C43#164211yescharacteristic
293C2×C43#178611yescharacteristic
294C2×C43#178811yescharacteristic
295C2×C43#179211yescharacteristic
296D43—84no—
297C22×#41—861no—
298#550—434no—
299#550—862no—
300#550—862no—
301#550—862no—
302C2×#127—431no—
303C2×#127—861no—
304C2×#121—862no—
305C2×#121—861no—
306C2×C4×Q8—431no—
307C2×C4×D4—861no—
308C2×C4×D4C2×D4311yescharacteristic
309C2×C4⋊C8—431no—
310C2×C4⋊C8C2×D4311yescharacteristic
311C2×#103—861no—
312C2×#102—21no—
313C2×#102—862no—
314C2×C4×C8—431no—
315#384C2×D4311yescharacteristic
316#340—21no—
317#340—861no—
318#331—862no—
319Q8⋊C8—862no—
320D4⋊C8—862no—
321C43#844411yescharacteristic, complemented, Sylow
322C2×#41—864no—
323C2×#41—864no—
324C2×#41—1722no—
325C2×#41—1722no—
326C2×#41—1722no—
327C2×#41—1722no—
328C22×Q8—431no—
329C22×D4—432no—
330C22×D4—862no—
331C22×D4—862no—
332C22×D4—861no—
333C22×D4—861no—
334C22×D4C22⋊D4311yescharacteristic
335C23×C4—21no—
336C23×C4—862no—
337C22×C8—21no—
338C22×C8—861no—
339C22×C8—861no—
340#127—432no—
341#127—432no—
342#127—864no—
343#127—864no—
344#127—861no—
345#127—861no—
346#121—868no—
347#121—868no—
348#121—864no—
349#121—864no—
350C4×Q8—432no—
351C4×Q8—432no—
352C4×Q8—861no—
353C4×Q8—861no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—864no—
357C4×D4—864no—
358C4×D4C4×D4312yes—
359C4×D4D17212yes—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—431no—
364C2×C4⋊C4—861no—
365C2×C4⋊C4C22⋊D4311yescharacteristic
366C2×C22⋊C4—21no—
367C2×C22⋊C4—862no—
368C2×C42—861no—
369C2×C42C22×D4311yescharacteristic
370C4⋊C8—21no—
371C4⋊C8—21no—
372C4⋊C8—861no—
373C4⋊C8—861no—
374#103—1722no—
375#102—42no—
376#102—1724no—
377C4×C8—861no—
378C4×C8—861no—
379C24—21no—
380C24—862no—
381#41—1728no—
382#41—1728no—
383#41—1728no—
384#41—1728no—
385C2×Q8—432no—
386C2×Q8—432no—
387C2×Q8—432no—
388C2×Q8—861no—
389C2×Q8—861no—
390C2×Q8—861no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—434no—
397C2×D4—868no—
398C2×D4—868no—
399C2×D4—862no—
400C2×D4—862no—
401C2×D4—862no—
402C2×D4—862no—
403C2×D4—862no—
404C2×D4—3442no—
405C2×D4—3442no—
406C2×D4—1722no—
407C2×D4—1722no—
408C2×D4—1724no—
409C2×D4—1724no—
410C2×D4—1721no—
411C2×D4—1721no—
412C2×D4—1721no—
413C2×D4—1721no—
414C2×D4—1721no—
415C2×D4—1721no—
416C2×D4—1721no—
417C2×D4—1721no—
418C2×D4(C2×D43)⋊C412yes—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—868no—
428C22×C4—861no—
429C22×C4—861no—
430C22×C4—1724no—
431C22×C4—1724no—
432C22×C4D4×D4311yescharacteristic
433C22×C4D4×D4311yescharacteristic
434C22×C4C2×C22⋊D4311yescharacteristic
435C2×C8—41no—
436C2×C8—41no—
437C2×C8—41no—
438C2×C8—862no—
439C2×C8—1721no—
440C2×C8—1721no—
441C2×C8—1721no—
442C2×C8—1721no—
443C2×C8—1721no—
444C4⋊C4—21no—
445C4⋊C4—42no—
446C4⋊C4—41no—
447C4⋊C4—41no—
448C4⋊C4—41no—
449C4⋊C4—41no—
450C4⋊C4—432no—
451C4⋊C4—862no—
452C4⋊C4—861no—
453C4⋊C4—862no—
454C4⋊C4(C2×D43)⋊C412yes—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—868no—
458C42—862no—
459C42—862no—
460C42C2×C4×D4311yescharacteristic
461C42C2×D17211yescharacteristic
462C42D4×D4311yescharacteristic
463C42D4×D4311yescharacteristic
464C23—22no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—864no—
472C23—1722no—
473C23—1722no—
474C23—1722no—
475C23—1722no—
476C23—1722no—
477C23—1722no—
478C23#1306329311yescharacteristic
479Q8—434no—
480Q8—862no—
481Q8—862no—
482Q8—862no—
483D4—22no—
484D4—22no—
485D4—41no—
486D4—41no—
487D4—3442no—
488D4—3448no—
489D4—1724no—
490D4—17216no—
491D4—1722no—
492D4—1722no—
493D4—1722no—
494D4—1722no—
495D4—1722no—
496D4—1722no—
497D4—1722no—
498D4—1722no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—81no—
509C2×C4—81no—
510C2×C4—81no—
511C2×C4—862no—
512C2×C4—862no—
513C2×C4—862no—
514C2×C4—862no—
515C2×C4—17216no—
516C2×C4—1721no—
517C2×C4—1721no—
518C2×C4C22⋊C4×D4311yescharacteristic
519C2×C4C22⋊C4×D4311yescharacteristic
520C2×C4C2×(C2×D43)⋊C411yescharacteristic
521C2×C4#1306329311yescharacteristic
522C2×C4#1306329511yescharacteristic
523C2×C4#1306329511yescharacteristic
524C2×C4D8×D4311yescharacteristic
525C2×C4SD16×D4311yescharacteristic
526C2×C4#1306334511yescharacteristic
527C2×C4#1306334511yescharacteristic
528C2×C4#1306334911yescharacteristic
529C2×C4#1306335111yescharacteristic
530C2×C4#1306335211yescharacteristic
531C2×C4#1306335611yescharacteristic
532C8—81no—
533C8—3441no—
534C8—1722no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—3442no—
543C22—3442no—
544C22—3442no—
545C22—3442no—
546C22—1724no—
547C22—1724no—
548C22—1724no—
549C22#1458275411yescharacteristic
550C22#1458303111yescharacteristic
551C22#1458304211yescharacteristic
552C22#1458304811yescharacteristic
553C22#1458305911yescharacteristic
554C22#1458306511yescharacteristic
555C22#1458307511yescharacteristic
556C4—21no—
557C4—21no—
558C4—42no—
559C4—161no—
560C4—864no—
561C4—1722no—
562C4#102×D4311yescharacteristic
563C4#1458289311yescharacteristic
564C4#1458289811yescharacteristic
565C4#1458290211yescharacteristic
566C4#1458303411yescharacteristic
567C4#1458304211yescharacteristic
568C4#1458305111yescharacteristic
569C4#1458305911yescharacteristic
570C2—82no—
571C2—3444no—
572C2#1913365911yescharacteristic
573C2#1913372111yescharacteristic
574C2#1913378711yescharacteristic
575C2#1913379311yescharacteristic
576C2#1913452411yescharacteristic
577C2#1913453311yescharacteristic
578C2#1913454711yescharacteristic
subgroupG/H
centerC23#13063293
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1802C2
socleC23×C43#120
prime radicalC2×#14583570C2
cosocleC2×C42×C43C23
hypercenter#1802D43
hypocenterC43#8444
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. #19135400C2semidirect
3. #19134597C2semidirect
4. C2×#14582642C2semidirect
5. C2×#14582629C2semidirect
6. C2×D4⋊(C43⋊C8)C2semidirect
7. C43×#1802C2semidirect
12. #14583570C4semidirect
241. Dic86#102semidirect
284. #1802D43semidirect
321. C43#8444semidirect

Maximal subgroups

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

subgroupindex
C2×#145835702
#191354002
#191345972
C2×#145826422
C2×#145826292
C2×D4⋊(C43⋊C8)2
C43×#18022
#844443