Finite Group Databasebeta

← #25130634

Subgroups — #25130634

Order 11008.

1400 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583553C211yesmaximal, characteristic, complemented
2C2×#14583189C211yesmaximal, characteristic, complemented
3C2×#14583009C211yesmaximal, characteristic, complemented
4#19135784C212yesmaximal, complemented
5#19135591C212yesmaximal, complemented
6#19135567C211yesmaximal, characteristic, complemented
7#19135394C211yesmaximal, characteristic, complemented
8#19134913C212yesmaximal, complemented
9#19134787C212yesmaximal, complemented
10#19134602C211yesmaximal, characteristic, complemented
11C43×#2535C211yesmaximal, characteristic, complemented
12C22×#10621900—21no—
13C22×#10621882C2211yescharacteristic
14#14583553—24no—
15#14583553—24no—
16C2×#13063325C2211yescharacteristic
17C2×#13063309—22no—
18C2×#13063305—21no—
19C2×#13063299C2212yes—
20C2×C4×D172C2211yescharacteristic
21C22×C4⋊Dic43C2212yes—
22#14583189—24no—
23#14583009—24no—
24C2×#13063256C2212yes—
25C2×#13063256C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063246C2212yes—
28C2×#13063246C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2212yes—
31C2×C22⋊(C43⋊C8)C2212yes—
32C2×C22⋊(C43⋊C8)C2212yes—
33C2×#13063236C2211yescharacteristic
34#14582661C2212yes—
35#14582661C2212yes—
36#14582661C2212yes—
37C2×#121×C43C2212yes—
38C2×C4×D4×C43C2211yescharacteristic
39C2×C4×D4×C43C2211yescharacteristic
40C43×#397—21no—
41C43×#392—21no—
42C43×#386—22no—
43C43×#382C2211yescharacteristic
44C43×#380C2212yes—
45C2×#10621900—28no—
46C2×#10621900—48no—
47C22×Dic86—21no—
48C22×D172C2311yescharacteristic
49C22×C22⋊D43—22no—
50C23×Dic43—22no—
51C22×C4×D43—21no—
52C2×#10621882—22no—
53C2×#10621882—22no—
54C2×#10621882—22no—
55C22×C43⋊C8C2311yescharacteristic
56C22×C43⋊C8C2312yes—
57C22×C43⋊C8C2311yescharacteristic
58#13063325—22no—
59#13063325D414yescomplemented
60#13063309—216no—
61#13063305—28no—
62#13063299—24no—
63#13063299—24no—
64C4×D172—22no—
65C4×D172D414yescomplemented
66C2×C4⋊Dic43—22no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—24no—
69C2×C4⋊Dic43—24no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2312yes—
72C2×(C2×D43)⋊C4—21no—
73C2×(C2×D43)⋊C4—22no—
74#13063256—24no—
75#13063256—22no—
76C4⋊(C43⋊C8)—22no—
77#13063246—24no—
78#13063246—22no—
79#13063245—22no—
80#13063245—42no—
81C22⋊(C43⋊C8)—24no—
82C22⋊(C43⋊C8)—42no—
83#13063236—22no—
84C22×D4×C43—22no—
85C22×D4×C43D411yescharacteristic
86C22×D4×C43C2311yescharacteristic
87C23×C4×C43—21no—
88C23×C4×C43C2312yes—
89#121×C43—24no—
90#121×C43—42no—
91C4×D4×C43—22no—
92C4×D4×C43—22no—
93C4×D4×C43—22no—
94C4×D4×C43—22no—
95C2×C4⋊C4×C43D411yescharacteristic
96C2×C4⋊C4×C43C2311yescharacteristic
97C2×C4⋊C4×C43C2312yes—
98C2×C22⋊C4×C43—21no—
99C2×C22⋊C4×C43—22no—
100C2×C22⋊C4×C43—22no—
101C2×C22⋊C4×C43D412yes—
102C2×C42×C43C2311yescharacteristic
103#95×C43—22no—
104#95×C43—21no—
105#95×C43—21no—
106C24×C43—21no—
107C24×C43C2×D412yes—
108C23×D43—21no—
109C2×D4×C43—22no—
110C2×D4×C43—21no—
111C2×D4×C43—24no—
112C2×D4×C43—21no—
113C2×D4×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—44no—
117C2×D4×C43—44no—
118C2×D4×C43—82no—
119C2×D4×C43#4112yescomplemented
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—21no—
128C22×C4×C43—42no—
129C22×C4×C43—82no—
130C22×C4×C43C2×D412yes—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2411yescharacteristic
134C2×C22⋊D43—28no—
135C2×C22⋊D43—44no—
136C2×C22⋊D43—44no—
137C22×Dic43—28no—
138C22×Dic43—21no—
139C22×Dic43—22no—
140C22×Dic43—44no—
141C22×Dic43—44no—
142#10621900—432no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172C2×D412yes—
149C2×C4×D43—24no—
150C2×C4×D43—44no—
151C2×Dic86—24no—
152C2×Dic86—44no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—22no—
158C22⋊C4×C43—24no—
159C22⋊C4×C43—44no—
160C22⋊C4×C43—42no—
161C22⋊C4×C43—82no—
162C42×C43C2×D412yes—
163C42×C43C2×D412yes—
164#10621882—28no—
165(C2×D43)⋊C4—28no—
166(C2×D43)⋊C4—24no—
167C4⋊Dic43—28no—
168C4⋊Dic43—24no—
169C4⋊Dic43—21no—
170C4⋊Dic43—22no—
171C4⋊Dic43C2×D412yes—
172C4⋊Dic43C2×D414yes—
173C2×C43⋊C8—21no—
174C2×C43⋊C8—21no—
175C2×C43⋊C8—21no—
176C2×C43⋊C8—22no—
177C2×C43⋊C8—22no—
178C2×C43⋊C8—21no—
179C2×C43⋊C8—22no—
180C2×C43⋊C8—21no—
181C2×C43⋊C8#4112yescomplemented
182C23×C43—22no—
183C23×C43—22no—
184C23×C43—22no—
185C23×C43—22no—
186C23×C43—22no—
187C23×C43—22no—
188C23×C43—22no—
189C23×C43—41no—
190C23×C43—41no—
191C23×C43—42no—
192C23×C43—42no—
193C23×C43AGL(1,ℤ/8)14yes—
194C23×C43C22×D411yescharacteristic
195C22×D43—22no—
196C22×D43—41no—
197C22×D43—41no—
198C22×D43—42no—
199C22×D43—42no—
200D4×C43—28no—
201D4×C43—22no—
202D4×C43—22no—
203D4×C43—41no—
204D4×C43—41no—
205D4×C43—88no—
206C2×C4×C43—22no—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—41no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—84no—
221C2×C4×C43#12012yes—
222C2×C4×C43#12012yes—
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C2×#4111yescharacteristic
226C2×C4×C43C2×#4111yescharacteristic
227C2×C4×C43H(5,𝔽2)11yescharacteristic
228C2×C4×C432−1+411yescharacteristic
229C22⋊D43—416no—
230C2×Dic43—24no—
231C2×Dic43—22no—
232C2×Dic43—416no—
233C2×Dic43—42no—
234C2×Dic43—42no—
235C2×Dic43—42no—
236D172—22no—
237D172—22no—
238D172—41no—
239D172—41no—
240C4×D43—48no—
241Dic86—48no—
242C43⋊C8—22no—
243C43⋊C8—41no—
244C43⋊C8—42no—
245#24128—431nomaximal, Sylow
246C22×C43—24no—
247C22×C43—24no—
248C22×C43—24no—
249C22×C43—42no—
250C22×C43—42no—
251C22×C43—42no—
252C22×C43—42no—
253C22×C43—42no—
254C22×C43—44no—
255C22×C43—82no—
256C22×C43—81no—
257C22×C43—81no—
258C22×C43C2×#12011yescharacteristic
259C22×C43#54611yescharacteristic
260C22×C43#54711yescharacteristic
261C22×C43C2×AGL(1,ℤ/8)12yes—
262C22×C43#57712yes—
263C2×D43—42no—
264C2×D43—42no—
265C2×D43—42no—
266C2×D43—82no—
267C2×D43—82no—
268C4×C43—22no—
269C4×C43—22no—
270C4×C43—42no—
271C4×C43—81no—
272C4×C43—82no—
273C4×C43#52511yescharacteristic
274C4×C43#53711yescharacteristic
275C4×C43#54811yescharacteristic
276C4×C43#55011yescharacteristic
277Dic43—44no—
278Dic43—42no—
279C2×#547—431no—
280C2×#476—431no—
281C2×#442—431no—
282#2535D4311yescharacteristic, complemented
283#2034—432no—
284#1999—432no—
285#1993—431no—
286#1955—431no—
287#1874—432no—
288#1853—432no—
289#1804—431no—
290C2×C43—44no—
291C2×C43—82no—
292C2×C43#240711yescharacteristic
293C2×C43#300311yescharacteristic
294C2×C43#301011yescharacteristic
295C2×C43#330612yes—
296C2×C43#334512yes—
297D43—82no—
298C22×#41—861no—
299C22×D8—431no—
300#547—864no—
301#547—864no—
302C2×C4⋊Q8—431no—
303C2×#123—862no—
304C2×C22⋊Q8—861no—
305C2×#121—432no—
306C2×#121C2×D4312yes—
307C2×C4×D4—431no—
308C2×C4×D4C2×D4311yescharacteristic
309C2×C4×D4C2×D4311yescharacteristic
310C22×C4⋊C4—432no—
311#476—864no—
312#442—864no—
313C2×#106—431no—
314C2×#106—432no—
315C2×C4⋊C8—431no—
316C2×#102—431no—
317C2×#102—432no—
318C2×#102—431no—
319C2×#102—432no—
320C2×C22⋊C8—432no—
321C2×C22⋊C8—432no—
322C2×#97—431no—
323#397—21no—
324#392—21no—
325#386—22no—
326#382C2×D4311yescharacteristic
327#380C2×D4312yes—
328#340—432no—
329#340—432no—
330#340—432no—
331C43#2412811yescharacteristic, complemented, Sylow
332C2×#41—868no—
333C2×#41—1728no—
334C22×Q8—861no—
335C22×D4—22no—
336C22×D4—431no—
337C22×D4—862no—
338C22×D4C22⋊D4311yescharacteristic
339C22×D4C22×D4311yescharacteristic
340C23×C4—21no—
341C23×C4—862no—
342C23×C4—861no—
343C23×C4C22×D4312yes—
344C2×D8—862no—
345C2×D8—862no—
346C2×D8—862no—
347C22×C8—431no—
348C22×C8—431no—
349C22×C8—432no—
350C4⋊Q8—434no—
351C4⋊Q8—862no—
352#123—8616no—
353C22⋊Q8—868no—
354#121—24no—
355#121—42no—
356#121—864no—
357#121—864no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—22no—
362C4×D4—434no—
363C4×D4—862no—
364C2×C4⋊C4—431no—
365C2×C4⋊C4—432no—
366C2×C4⋊C4—864no—
367C2×C4⋊C4—864no—
368C2×C4⋊C4—862no—
369C2×C4⋊C4—861no—
370C2×C4⋊C4C22⋊D4311yescharacteristic
371C2×C4⋊C4C22×D4311yescharacteristic
372C2×C4⋊C4C22×D4312yes—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—861no—
377C2×C22⋊C4—862no—
378C2×C22⋊C4C22⋊D4312yes—
379C2×C42C22×D4311yescharacteristic
380#106—862no—
381#106—864no—
382C4⋊C8—862no—
383#102—862no—
384#102—862no—
385#102—864no—
386#102—1722no—
387C22⋊C8—864no—
388C22⋊C8—1722no—
389#97—862no—
390#95—22no—
391#95—21no—
392#95—21no—
393C24—21no—
394C24—861no—
395C24C2×C22⋊D4312yes—
396#41—17232no—
397C2×Q8—864no—
398C2×Q8—1724no—
399C2×D4—24no—
400C2×D4—22no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—44no—
407C2×D4—44no—
408C2×D4—82no—
409C2×D4—432no—
410C2×D4—868no—
411C2×D4—861no—
412C2×D4—861no—
413C2×D4—861no—
414C2×D4—861no—
415C2×D4—861no—
416C2×D4—1724no—
417C2×D4—1724no—
418C2×D4#1062190012yescomplemented
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—42no—
428C22×C4—82no—
429C22×C4—868no—
430C22×C4—861no—
431C22×C4—862no—
432C22×C4—864no—
433C22×C4—1724no—
434C22×C4—1724no—
435C22×C4—1724no—
436C22×C4C2×C22⋊D4312yes—
437C22×C4C2×C22⋊D4311yescharacteristic
438C22×C4C2×C22⋊D4311yescharacteristic
439C22×C4C23×D4311yescharacteristic
440D8—868no—
441C2×C8—432no—
442C2×C8—861no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—862no—
446C2×C8—862no—
447C2×C8—861no—
448C2×C8—862no—
449C2×C8—861no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—432no—
456C4⋊C4—434no—
457C4⋊C4—868no—
458C4⋊C4—864no—
459C4⋊C4—861no—
460C4⋊C4—862no—
461C22⋊C4—24no—
462C22⋊C4—44no—
463C22⋊C4—42no—
464C22⋊C4—82no—
465C22⋊C4—868no—
466C22⋊C4—864no—
467C42D4×D4312yes—
468C42D4×D4312yes—
469C23—22no—
470C23—22no—
471C23—22no—
472C23—22no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—41no—
477C23—42no—
478C23—42no—
479C23—41no—
480C23—862no—
481C23—1722no—
482C23—1722no—
483C23—1721no—
484C23—1721no—
485C23#1306335014yes—
486C23C22×C22⋊D4311yescharacteristic
487Q8—1728no—
488D4—28no—
489D4—22no—
490D4—22no—
491D4—41no—
492D4—41no—
493D4—88no—
494D4—862no—
495D4—862no—
496D4—17216no—
497D4—1721no—
498D4—1721no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—84no—
514C2×C4—862no—
515C2×C4—864no—
516C2×C4—1728no—
517C2×C4—17216no—
518C2×C4—1722no—
519C2×C4—1722no—
520C2×C4—1722no—
521C2×C4#1306329312yes—
522C2×C4#1306329312yes—
523C2×C4C2×D4×D4311yescharacteristic
524C2×C4C2×D4×D4311yescharacteristic
525C2×C4#41×D4311yescharacteristic
526C2×C4C2×#1062190011yescharacteristic
527C2×C4#1306337011yescharacteristic
528C2×C4#1306337211yescharacteristic
529C8—862no—
530C8—1722no—
531C8—1721no—
532C22—24no—
533C22—24no—
534C22—24no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—44no—
540C22—42no—
541C22—82no—
542C22—81no—
543C22—81no—
544C22—3442no—
545C22—3442no—
546C22—1722no—
547C22—1722no—
548C22—1722no—
549C22C2×#1306329311yescharacteristic
550C22#1458354311yescharacteristic
551C22#1458354811yescharacteristic
552C22C2×#1306335012yes—
553C22#1458371012yes—
554C4—22no—
555C4—22no—
556C4—42no—
557C4—82no—
558C4—81no—
559C4—1722no—
560C4—1724no—
561C4#1458340911yescharacteristic
562C4#1458347811yescharacteristic
563C4#1458355511yescharacteristic
564C4#1458356711yescharacteristic
565C2—44no—
566C2—82no—
567C2—3442no—
568C2#1913793611yescharacteristic
569C2#1914382111yescharacteristic
570C2#1914387911yescharacteristic
571C2#1914655612yes—
572C2#1914705912yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2535C2
socleC23×C43C22×D4
hypercenter#2535D43
hypocenterC43#24128
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. C2×#14583553C2semidirect
2. C2×#14583189C2semidirect
3. C2×#14583009C2semidirect
4. #19135784C2semidirect
5. #19135591C2semidirect
6. #19135567C2semidirect
7. #19135394C2semidirect
8. #19134913C2semidirect
9. #19134787C2semidirect
10. #19134602C2semidirect
11. C43×#2535C2semidirect
59. #13063325D4semidirect
65. C4×D172D4semidirect
119. C2×D4×C43#41semidirect
181. C2×C43⋊C8#41semidirect
282. #2535D43semidirect
331. C43#24128semidirect
418. C2×D4#10621900semidirect

Maximal subgroups

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

subgroupindex
C2×#145835532
C2×#145831892
C2×#145830092
#191357842
#191355912
#191355672
#191353942
#191349132
#191347872
#191346022
C43×#25352
#2412843