Finite Group Databasebeta

← #24988680

Subgroups — #24988680

Order 11008.

1048 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583554C211yesmaximal, characteristic
2#19135555C211yesmaximal, characteristic, complemented
3#19134592C211yesmaximal, characteristic, complemented
4C2×#14582644C211yesmaximal, characteristic, complemented
5C2×D4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
6C2×#14582626C211yesmaximal, characteristic, complemented
7C43×#1802C211yesmaximal, characteristic, complemented
8C22×#10621898—21no—
9#14583554—22no—
10#14583554—22no—
11#14583554—22no—
12#14583554C414yescomplemented
13C2×#13063325C2211yescharacteristic
14C2×#13063307—22no—
15C2×#13063304—21no—
16C2×#13063296—21no—
17C2×C4×D172C2211yescharacteristic
18C2×C4⋊C4×D43—21no—
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20C2×#13063245—21no—
21C2×C4×C43⋊C8C2211yescharacteristic
22#14582661—22no—
23#14582661—21no—
24#14582644—22no—
25D4⋊(C43⋊C8)—22no—
26#14582626—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×Dic86—21no—
39C22×D172D411yescharacteristic
40C22×C22⋊D43—22no—
41C22×C4×D43—22no—
42C22×C4×D43—21no—
43C22×C43⋊C8—21no—
44C22×C43⋊C8—21no—
45#13063325—21no—
46#13063325—21no—
47#13063325C2×C412yes—
48#13063325D412yes—
49#13063307—28no—
50#13063307—28no—
51#13063304—24no—
52#13063304—24no—
53#13063296—24no—
54#13063296—24no—
55C4×D172—21no—
56C4×D172—21no—
57C4×D172C2×C412yes—
58C4×D172D412yes—
59C2×C4⋊Dic43—21no—
60C2×C4⋊Dic43D411yescharacteristic
61C2×C4⋊Dic43D412yes—
62C2×Dic43⋊C4—22no—
63C4⋊C4×D43—24no—
64C4⋊C4×D43—24no—
65C2×C22⋊Dic43—22no—
66C2×(C2×D43)⋊C4—21no—
67C4⋊(C43⋊C8)—21no—
68C4⋊(C43⋊C8)—21no—
69#13063245—42no—
70C4×C43⋊C8—21no—
71C4×C43⋊C8—21no—
72C22×D4×C43D411yescharacteristic
73C23×C4×C43—21no—
74C22×C8×C43—21no—
75C4×D4×C43—21no—
76C4×D4×C43—21no—
77C4×D4×C43C2×C412yes—
78C4×D4×C43D412yes—
79C2×C4⋊C4×C43—21no—
80C2×C4⋊C4×C43—21no—
81C2×C4⋊C4×C43—21no—
82C2×C4⋊C4×C43D411yescharacteristic
83C2×C22⋊C4×C43—21no—
84C2×C42×C43C2311yescharacteristic
85C4⋊C8×C43—21no—
86C4⋊C8×C43—21no—
87#102×C43—42no—
88C24×C43—21no—
89C23×D43—21no—
90C2×D4×C43—21no—
91C2×D4×C43—21no—
92C2×D4×C43—21no—
93C2×D4×C43—21no—
94C2×D4×C43—21no—
95C2×D4×C43C22⋊C412yes—
96C22×C4×C43—22no—
97C22×C4×C43—22no—
98C22×C4×C43—21no—
99C22×C4×C43—41no—
100C22×C4×C43—41no—
101C22×C4×C43—41no—
102C22×C4×C43—41no—
103C22×C4×C43—41no—
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C2×C22⋊D43—28no—
108C2×C22⋊D43—44no—
109C2×C22⋊D43—44no—
110C22×Dic43—21no—
111C22×Dic43—22no—
112#10621898—48no—
113#10621898—48no—
114#10621898—48no—
115#10621898—48no—
116C2×D172—21no—
117C2×D172—21no—
118C2×D172—21no—
119C2×D172C22⋊C412yes—
120C2×D172D812yes—
121C2×D172SD1612yes—
122C2×C4×D43—28no—
123C2×C4×D43—22no—
124C2×C4×D43—22no—
125C2×C4×D43—44no—
126C2×C4×D43—44no—
127C2×C4×D43—41no—
128C2×C4×D43—41no—
129C2×C4×D43—41no—
130C2×C4×D43—41no—
131C2×Dic86—22no—
132C2×Dic86—22no—
133C2×Dic86—41no—
134C2×Dic86—41no—
135C2×Dic86—41no—
136C2×Dic86—41no—
137C2×C8×C43—41no—
138C2×C8×C43—41no—
139C2×C8×C43—41no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43—42no—
142C4⋊C4×C43—41no—
143C4⋊C4×C43—41no—
144C4⋊C4×C43—41no—
145C4⋊C4×C43—41no—
146C4⋊C4×C43C22⋊C412yes—
147C22⋊C4×C43—22no—
148C22⋊C4×C43—22no—
149C42×C43C22×C411yescharacteristic
150C42×C43C2×D411yescharacteristic
151C42×C43C2×D411yescharacteristic
152C42×C43C2×D411yescharacteristic
153C22⋊Dic43—28no—
154(C2×D43)⋊C4—22no—
155(C2×D43)⋊C4—22no—
156C4⋊Dic43—22no—
157C4⋊Dic43—22no—
158C4⋊Dic43—21no—
159C4⋊Dic43—22no—
160C4⋊Dic43C22⋊C412yes—
161C4⋊Dic43C22⋊C414yes—
162Dic43⋊C4—28no—
163C2×C43⋊C8—22no—
164C2×C43⋊C8—41no—
165C2×C43⋊C8—41no—
166C2×C43⋊C8—41no—
167C2×C43⋊C8—41no—
168C2×C43⋊C8—41no—
169C23×C43—22no—
170C23×C43—41no—
171C23×C43—41no—
172C23×C43—41no—
173C23×C43—41no—
174C23×C43—41no—
175C23×C43—41no—
176C23×C43#12011yescharacteristic
177C22×D43—22no—
178C22×D43—22no—
179C22×D43—22no—
180C22×D43—41no—
181C22×D43—41no—
182C22×D43—41no—
183C22×D43—41no—
184D4×C43—22no—
185D4×C43—22no—
186D4×C43—41no—
187D4×C43—41no—
188C2×C4×C43—21no—
189C2×C4×C43—21no—
190C2×C4×C43—22no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—42no—
194C2×C4×C43—42no—
195C2×C4×C43—42no—
196C2×C4×C43—42no—
197C2×C4×C43—81no—
198C2×C4×C43—81no—
199C2×C4×C43—81no—
200C2×C4×C43C2×C22⋊C411yescharacteristic
201C2×C4×C43C2×C22⋊C411yescharacteristic
202C2×C4×C43C2×C22⋊C411yescharacteristic
203C2×C4×C43#12011yescharacteristic
204C2×C4×C43#12011yescharacteristic
205C2×C4×C43#12011yescharacteristic
206C2×C4×C43C2×D811yescharacteristic
207C2×C4×C43C2×SD1611yescharacteristic
208C2×C4×C43#13511yescharacteristic
209C2×C4×C43#13511yescharacteristic
210C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
211C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
212C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
213C2×C4×C43#13711yescharacteristic
214C22⋊D43—416no—
215C2×Dic43—22no—
216C2×Dic43—24no—
217C2×Dic43—42no—
218C2×Dic43—41no—
219C2×Dic43—42no—
220C2×Dic43—41no—
221D172—22no—
222D172—22no—
223D172—22no—
224D172#10214yescomplemented
225C4×D43—416no—
226C4×D43—42no—
227C4×D43—42no—
228C4×D43—42no—
229C4×D43—42no—
230Dic86—42no—
231Dic86—42no—
232Dic86—42no—
233Dic86—42no—
234C8×C43—81no—
235C43⋊C8—42no—
236C43⋊C8—81no—
237#8446—431nomaximal, Sylow
238C22×C43—42no—
239C22×C43—42no—
240C22×C43—42no—
241C22×C43—81no—
242C22×C43—81no—
243C22×C43—81no—
244C22×C43—81no—
245C22×C43#37911yescharacteristic
246C22×C43#44711yescharacteristic
247C22×C43#44911yescharacteristic
248C22×C43#45011yescharacteristic
249C22×C43#45211yescharacteristic
250C22×C43#45411yescharacteristic
251C22×C43#45611yescharacteristic
252C2×D43—24no—
253C2×D43—42no—
254C2×D43—42no—
255C2×D43—42no—
256C2×D43—42no—
257C2×D43—42no—
258C2×D43—42no—
259C4×C43—21no—
260C4×C43—21no—
261C4×C43—42no—
262C4×C43—161no—
263C4×C43C2×#10211yescharacteristic
264C4×C43#41611yescharacteristic
265C4×C43#41711yescharacteristic
266C4×C43#41811yescharacteristic
267C4×C43#44711yescharacteristic
268C4×C43#44911yescharacteristic
269C4×C43#45011yescharacteristic
270C4×C43#45211yescharacteristic
271Dic43—44no—
272Dic43—42no—
273C2×#547—431no—
274#1990—431no—
275#1802—431no—
276#1802D4311yescharacteristic, complemented
277C2×#332—431no—
278C2×D4⋊C8—431no—
279C2×D4⋊C8—431no—
280C2×C43—82no—
281C2×C43#162511yescharacteristic
282C2×C43#163511yescharacteristic
283C2×C43#164711yescharacteristic
284C2×C43#165411yescharacteristic
285C2×C43#178611yescharacteristic
286C2×C43#178811yescharacteristic
287C2×C43#179311yescharacteristic
288D43—44no—
289C22×#41—861no—
290#547—434no—
291#547—862no—
292#547—862no—
293#547—862no—
294C2×C4⋊Q8—431no—
295C2×#123—862no—
296C2×C22⋊Q8—861no—
297C2×#121—861no—
298C2×C4×D4—431no—
299C2×C4×D4C2×D4311yescharacteristic
300C22×C4⋊C4—861no—
301C2×C4⋊C8—431no—
302C2×C4⋊C8C2×D4311yescharacteristic
303C2×#102—21no—
304C2×#102—861no—
305C2×C4×C8—431no—
306#384C2×D4311yescharacteristic
307#340—21no—
308#340—861no—
309#340—862no—
310#332—862no—
311D4⋊C8—862no—
312D4⋊C8—862no—
313C43#844611yescharacteristic, complemented, Sylow
314C2×#41—864no—
315C2×#41—864no—
316C2×#41—1722no—
317C2×#41—1722no—
318C2×#41—1722no—
319C2×#41—1722no—
320C22×Q8—861no—
321C22×D4—431no—
322C22×D4—862no—
323C22×D4C22⋊D4311yescharacteristic
324C23×C4—21no—
325C23×C4—862no—
326C23×C4—861no—
327C22×C8—21no—
328C22×C8—861no—
329C22×C8—861no—
330C4⋊Q8—432no—
331C4⋊Q8—432no—
332C4⋊Q8—861no—
333C4⋊Q8—861no—
334#123—868no—
335#123—868no—
336C22⋊Q8—864no—
337C22⋊Q8—864no—
338#121—864no—
339#121—864no—
340C4×D4—21no—
341C4×D4—21no—
342C4×D4—432no—
343C4×D4—432no—
344C4×D4—861no—
345C4×D4—861no—
346C4×D4C4×D4312yes—
347C4×D4D17212yes—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—431no—
352C2×C4⋊C4—432no—
353C2×C4⋊C4—864no—
354C2×C4⋊C4—862no—
355C2×C4⋊C4—861no—
356C2×C4⋊C4—864no—
357C2×C4⋊C4C22⋊D4311yescharacteristic
358C2×C22⋊C4—21no—
359C2×C22⋊C4—862no—
360C2×C22⋊C4—861no—
361C2×C42C22×D4311yescharacteristic
362C4⋊C8—21no—
363C4⋊C8—21no—
364C4⋊C8—861no—
365C4⋊C8—861no—
366#102—42no—
367#102—1722no—
368C4×C8—861no—
369C4×C8—861no—
370C24—21no—
371C24—861no—
372#41—1728no—
373#41—1728no—
374#41—1728no—
375#41—1728no—
376C2×Q8—862no—
377C2×Q8—862no—
378C2×Q8—1721no—
379C2×Q8—1721no—
380C2×Q8—1721no—
381C2×Q8—1721no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—432no—
388C2×D4—432no—
389C2×D4—432no—
390C2×D4—868no—
391C2×D4—861no—
392C2×D4—861no—
393C2×D4—861no—
394C2×D4—1724no—
395C2×D4—1724no—
396C2×D4(C2×D43)⋊C412yes—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—868no—
406C22×C4—861no—
407C22×C4—862no—
408C22×C4—862no—
409C22×C4—862no—
410C22×C4—1724no—
411C22×C4—1724no—
412C22×C4—1721no—
413C22×C4—1721no—
414C22×C4—1721no—
415C22×C4—1721no—
416C22×C4D4×D4311yescharacteristic
417C22×C4D4×D4311yescharacteristic
418C22×C4C2×C22⋊D4311yescharacteristic
419C2×C8—41no—
420C2×C8—41no—
421C2×C8—41no—
422C2×C8—862no—
423C2×C8—1721no—
424C2×C8—1721no—
425C2×C8—1721no—
426C2×C8—1721no—
427C2×C8—1721no—
428C4⋊C4—21no—
429C4⋊C4—42no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C4⋊C4—41no—
434C4⋊C4—432no—
435C4⋊C4—434no—
436C4⋊C4—868no—
437C4⋊C4—862no—
438C4⋊C4—862no—
439C4⋊C4—861no—
440C4⋊C4—862no—
441C4⋊C4(C2×D43)⋊C412yes—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—868no—
445C22⋊C4—862no—
446C22⋊C4—862no—
447C42C2×C4×D4311yescharacteristic
448C42C2×D17211yescharacteristic
449C42D4×D4311yescharacteristic
450C42D4×D4311yescharacteristic
451C23—22no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23—862no—
459C23—862no—
460C23—862no—
461C23—1721no—
462C23—1721no—
463C23—1721no—
464C23—1721no—
465C23#1306329311yescharacteristic
466Q8—1722no—
467Q8—1722no—
468Q8—1722no—
469Q8—1722no—
470D4—22no—
471D4—22no—
472D4—41no—
473D4—41no—
474D4—434no—
475D4—862no—
476D4—862no—
477D4—862no—
478D4—17216no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—81no—
489C2×C4—81no—
490C2×C4—81no—
491C2×C4—862no—
492C2×C4—864no—
493C2×C4—17216no—
494C2×C4—1721no—
495C2×C4—1722no—
496C2×C4—1721no—
497C2×C4—1722no—
498C2×C4—1722no—
499C2×C4—1722no—
500C2×C4—1722no—
501C2×C4—1722no—
502C2×C4C22⋊C4×D4311yescharacteristic
503C2×C4C22⋊C4×D4311yescharacteristic
504C2×C4C2×(C2×D43)⋊C411yescharacteristic
505C2×C4#1306329311yescharacteristic
506C2×C4#1306329511yescharacteristic
507C2×C4#1306329511yescharacteristic
508C2×C4D8×D4311yescharacteristic
509C2×C4SD16×D4311yescharacteristic
510C2×C4#1306334511yescharacteristic
511C2×C4#1306334511yescharacteristic
512C2×C4#1306334911yescharacteristic
513C2×C4#1306335111yescharacteristic
514C2×C4#1306335211yescharacteristic
515C2×C4#1306335611yescharacteristic
516C8—81no—
517C8—3441no—
518C8—1722no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22—864no—
527C22—1722no—
528C22—1722no—
529C22—1722no—
530C22—1722no—
531C22—1722no—
532C22—1722no—
533C22#1458275411yescharacteristic
534C22#1458303111yescharacteristic
535C22#1458304211yescharacteristic
536C22#1458304811yescharacteristic
537C22#1458305911yescharacteristic
538C22#1458307011yescharacteristic
539C22#1458308011yescharacteristic
540C4—21no—
541C4—21no—
542C4—42no—
543C4—161no—
544C4—1724no—
545C4—1722no—
546C4#102×D4311yescharacteristic
547C4#1458289311yescharacteristic
548C4#1458289811yescharacteristic
549C4#1458290211yescharacteristic
550C4#1458303411yescharacteristic
551C4#1458304211yescharacteristic
552C4#1458305111yescharacteristic
553C4#1458305911yescharacteristic
554C2—82no—
555C2—1724no—
556C2#1913368311yescharacteristic
557C2#1913374511yescharacteristic
558C2#1913382911yescharacteristic
559C2#1913387711yescharacteristic
560C2#1913452411yescharacteristic
561C2#1913453311yescharacteristic
562C2#1913455211yescharacteristic
subgroupG/H
centerC23#13063293
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1802C2
socleC23×C43#120
prime radicalC2×#14583554C2
cosocleC2×C42×C43C23
hypercenter#1802D43
hypocenterC43#8446
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. #19135555C2semidirect
3. #19134592C2semidirect
4. C2×#14582644C2semidirect
5. C2×D4⋊(C43⋊C8)C2semidirect
6. C2×#14582626C2semidirect
7. C43×#1802C2semidirect
12. #14583554C4semidirect
224. D172#102semidirect
276. #1802D43semidirect
313. C43#8446semidirect

Maximal subgroups

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

subgroupindex
C2×#145835542
#191355552
#191345922
C2×#145826442
C2×D4⋊(C43⋊C8)2
C2×#145826262
C43×#18022
#844643