Finite Group Databasebeta

← #25130638

Subgroups — #25130638

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×#14583554C211yesmaximal, characteristic, complemented
2C2×#14583189C211yesmaximal, characteristic, complemented
3#19139492C211yesmaximal, characteristic, complemented
4#19135782C212yesmaximal, complemented
5#19135590C212yesmaximal, complemented
6#19135568C211yesmaximal, characteristic, complemented
7#19135393C211yesmaximal, characteristic, complemented
8#19134909C212yesmaximal, complemented
9#19134786C212yesmaximal, complemented
10#19134605C211yesmaximal, characteristic, complemented
11C2×C43×#442C211yesmaximal, characteristic, complemented
12C22×#10621898—21no—
13#14583554—24no—
14#14583554—24no—
15C2×#13063325C2211yescharacteristic
16C2×#13063307—22no—
17C2×#13063304—21no—
18C2×#13063296C2212yes—
19C2×#13063296C2212yes—
20C2×C4×D172C2211yescharacteristic
21C2×C4⋊C4×D43C2212yes—
22#14583189—24no—
23C2×#13063256C2212yes—
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×#13063246C2212yes—
26C2×#13063246C2212yes—
27C2×(C2×D43)⋊C8C2212yes—
28C2×(C2×D43)⋊C8C2212yes—
29#14582824—21no—
30#14582808—21no—
31#14582778—22no—
32#14582765C2211yescharacteristic
33#14582756C2212yes—
34#14582662C2212yes—
35#14582662C2212yes—
36#14582661C2212yes—
37C22×D8×C43C2211yescharacteristic
38C2×C4×D4×C43C2211yescharacteristic
39C2×C4×D4×C43C2211yescharacteristic
40C43×#442—24no—
41C2×#106×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×#97×C43C2211yescharacteristic
45C2×#10621898—28no—
46C2×#10621898—48no—
47C22×Dic86—21no—
48C22×D172D411yescharacteristic
49C22×C22⋊D43—22no—
50C22×C22⋊D43—22no—
51C22×C4×D43—22no—
52C22×C4×D43C2312yes—
53C22×C43⋊C8C2312yes—
54#13063325—22no—
55#13063325D414yescomplemented
56#13063307—216no—
57#13063304—28no—
58#13063296—24no—
59#13063296—24no—
60#13063296—24no—
61#13063296—42no—
62C4×D172—22no—
63C4×D172—22no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43D411yescharacteristic
66C2×C4⋊Dic43C2312yes—
67C2×C4⋊Dic43C2312yes—
68C2×Dic43⋊C4—22no—
69C4⋊C4×D43—24no—
70C4⋊C4×D43—24no—
71C2×C22⋊Dic43—22no—
72C2×C22⋊Dic43—22no—
73C2×(C2×D43)⋊C4—22no—
74C2×(C2×D43)⋊C4D412yes—
75#13063256—24no—
76C4⋊(C43⋊C8)—22no—
77#13063246—24no—
78#13063246—42no—
79(C2×D43)⋊C8—24no—
80(C2×D43)⋊C8—42no—
81C43⋊#95—21no—
82C43⋊#95—21no—
83C43⋊#95—22no—
84C22×D4×C43C2311yescharacteristic
85C22×D4×C43C2311yescharacteristic
86C23×C4×C43—21no—
87C23×C4×C43—21no—
88C2×D8×C43—22no—
89C2×D8×C43—22no—
90C2×D8×C43—22no—
91C22×C8×C43C2311yescharacteristic
92C22×C8×C43C2311yescharacteristic
93C4×D4×C43—22no—
94C4×D4×C43—22no—
95C4×D4×C43—22no—
96C4×D4×C43D414yescomplemented
97C2×C4⋊C4×C43C2311yescharacteristic
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C22⋊C4×C43—21no—
100C2×C22⋊C4×C43—21no—
101C2×C42×C43C2311yescharacteristic
102#106×C43—22no—
103#102×C43—22no—
104#102×C43—22no—
105#97×C43—22no—
106C24×C43—21no—
107C24×C43—21no—
108C23×D43C2×D412yes—
109C2×D4×C43—21no—
110C2×D4×C43—21no—
111C2×D4×C43—21no—
112C2×D4×C43—21no—
113C2×D4×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—21no—
119C2×D4×C43C2×D412yes—
120C2×D4×C43#4112yescomplemented
121C22×C4×C43—24no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—44no—
125C22×C4×C43—42no—
126C22×C4×C43—82no—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2411yescharacteristic
130C2×C22⋊D43—28no—
131C2×C22⋊D43—44no—
132C2×C22⋊D43—44no—
133C2×C22⋊D43—44no—
134C2×C22⋊D43—44no—
135C2×C22⋊D43—82no—
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43C2×D412yes—
139#10621898—432no—
140C2×D172—22no—
141C2×D172—24no—
142C2×C4×D43—28no—
143C2×C4×D43—22no—
144C2×C4×D43—22no—
145C2×C4×D43—22no—
146C2×C4×D43—22no—
147C2×C4×D43—22no—
148C2×C4×D43—22no—
149C2×C4×D43—44no—
150C2×C4×D43—44no—
151C2×Dic86—24no—
152C2×Dic86—44no—
153D8×C43—28no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43#4112yescomplemented
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43C2×D412yes—
164C22⋊C4×C43—24no—
165C22⋊C4×C43—42no—
166C42×C43C2×D412yes—
167C42×C43C2×D412yes—
168C22⋊Dic43—28no—
169C22⋊Dic43—44no—
170(C2×D43)⋊C4—24no—
171(C2×D43)⋊C4—82no—
172C4⋊Dic43—24no—
173C4⋊Dic43—22no—
174C4⋊Dic43—22no—
175C4⋊Dic43—22no—
176C4⋊Dic43—22no—
177C4⋊Dic43C2×D414yes—
178Dic43⋊C4—28no—
179C2×C43⋊C8—22no—
180C2×C43⋊C8—22no—
181C2×C43⋊C8—22no—
182C23×C43—22no—
183C23×C43—22no—
184C23×C43—41no—
185C23×C43—41no—
186C23×C43—41no—
187C23×C43—41no—
188C23×C43—42no—
189C23×C43—42no—
190C23×C43—42no—
191C23×C43—42no—
192C23×C43C22×D411yescharacteristic
193C22×D43—22no—
194C22×D43—22no—
195C22×D43—22no—
196C22×D43—22no—
197C22×D43—22no—
198C22×D43—22no—
199C22×D43AGL(1,ℤ/8)14yes—
200D4×C43—22no—
201D4×C43—22no—
202D4×C43—22no—
203D4×C43—22no—
204D4×C43—41no—
205D4×C43—41no—
206D4×C43—41no—
207D4×C43—41no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—48no—
212C2×C4×C43—42no—
213C2×C4×C43—41no—
214C2×C4×C43—42no—
215C2×C4×C43—84no—
216C2×C4×C43#12012yes—
217C2×C4×C43#12012yes—
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C2×C4×C43H(5,𝔽2)11yescharacteristic
223C2×C4×C432−1+411yescharacteristic
224C22⋊D43—416no—
225C22⋊D43—88no—
226C2×Dic43—22no—
227C2×Dic43—24no—
228C2×Dic43—22no—
229C2×Dic43—22no—
230C2×Dic43—42no—
231C2×Dic43—42no—
232C2×Dic43—42no—
233C2×Dic43—42no—
234C2×Dic43—42no—
235D172—28no—
236C4×D43—416no—
237C4×D43—42no—
238C4×D43—42no—
239C4×D43—42no—
240C4×D43—42no—
241Dic86—48no—
242C8×C43—22no—
243C8×C43—41no—
244C43⋊C8—42no—
245#24128—431nomaximal, Sylow
246C22×C43—42no—
247C22×C43—42no—
248C22×C43—42no—
249C22×C43—42no—
250C22×C43—44no—
251C22×C43—82no—
252C22×C43—82no—
253C22×C43—81no—
254C22×C43—81no—
255C22×C43—82no—
256C22×C43C2×#12011yescharacteristic
257C22×C43#54611yescharacteristic
258C22×C43#54711yescharacteristic
259C22×C43C2×AGL(1,ℤ/8)12yes—
260C22×C43#57712yes—
261C2×D43—24no—
262C2×D43—24no—
263C2×D43—24no—
264C2×D43—42no—
265C2×D43—42no—
266C2×D43—42no—
267C2×D43—42no—
268C4×C43—22no—
269C4×C43—22no—
270C4×C43—42no—
271C4×C43—81no—
272C4×C43#52511yescharacteristic
273C4×C43#53711yescharacteristic
274C4×C43#54811yescharacteristic
275C4×C43#55011yescharacteristic
276Dic43—42no—
277Dic43—44no—
278Dic43—82no—
279C2×#547—431no—
280C2×#476—431no—
281C2×#442D4311yescharacteristic, complemented
282#2535—431no—
283#2034—432no—
284#1999—432no—
285#1993—431no—
286#1955—431no—
287#1874—432no—
288#1853—432no—
289#1804—431no—
290C2×C43—82no—
291C2×C43—82no—
292C2×C43#240711yescharacteristic
293C2×C43#300311yescharacteristic
294C2×C43#301011yescharacteristic
295C2×C43#330612yes—
296C2×C43#334512yes—
297D43—44no—
298C22×#41—861no—
299C22×D8C2×D4311yescharacteristic
300#547—864no—
301#547—864no—
302C2×C4⋊Q8—431no—
303C2×#123—862no—
304C2×C22⋊Q8—861no—
305C2×#121—432no—
306C2×#121—432no—
307C2×C4×D4—431no—
308C2×C4×D4C2×D4311yescharacteristic
309C2×C4×D4C2×D4311yescharacteristic
310C22×C4⋊C4—432no—
311#476—864no—
312#442—24no—
313C2×#106—432no—
314C2×#106C2×D4311yescharacteristic
315C2×C4⋊C8—431no—
316C2×#102—432no—
317C2×#102—432no—
318C2×#102C2×D4311yescharacteristic
319C2×#102C2×D4311yescharacteristic
320C2×C22⋊C8—432no—
321C2×C22⋊C8—432no—
322C2×#97C2×D4311yescharacteristic
323#397—861no—
324#392—861no—
325#386—862no—
326#382—431no—
327#380—432no—
328#340—432no—
329#340—432no—
330#340—432no—
331C43#2412811yescharacteristic, complemented, Sylow
332C2×#41—868no—
333C2×#41—1728no—
334C22×Q8—861no—
335C22×D4—431no—
336C22×D4—862no—
337C22×D4—862no—
338C22×D4C22×D4311yescharacteristic
339C22×D4C22×D4311yescharacteristic
340C23×C4—21no—
341C23×C4—21no—
342C23×C4—432no—
343C23×C4—862no—
344C2×D8—22no—
345C2×D8—22no—
346C2×D8—22no—
347C22×C8—432no—
348C22×C8C22×D4311yescharacteristic
349C22×C8C22×D4311yescharacteristic
350C4⋊Q8—434no—
351C4⋊Q8—862no—
352#123—8616no—
353C22⋊Q8—868no—
354#121—864no—
355#121—864no—
356#121—864no—
357#121—1722no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4—862no—
362C4×D4—862no—
363C4×D4C22⋊D4314yescomplemented
364C2×C4⋊C4—432no—
365C2×C4⋊C4—431no—
366C2×C4⋊C4—432no—
367C2×C4⋊C4—864no—
368C2×C4⋊C4—862no—
369C2×C4⋊C4—861no—
370C2×C4⋊C4—864no—
371C2×C4⋊C4C22×D4311yescharacteristic
372C2×C4⋊C4C22×D4311yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—432no—
376C2×C22⋊C4—862no—
377C2×C22⋊C4—862no—
378C2×C22⋊C4—862no—
379C2×C42C22×D4311yescharacteristic
380#106—22no—
381#106—864no—
382C4⋊C8—862no—
383#102—22no—
384#102—22no—
385#102—864no—
386#102—1722no—
387C22⋊C8—864no—
388C22⋊C8—1722no—
389#97—22no—
390#95—862no—
391#95—861no—
392#95—861no—
393C24—21no—
394C24—21no—
395C24—432no—
396#41—17232no—
397C2×Q8—864no—
398C2×Q8—1724no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—864no—
410C2×D4—868no—
411C2×D4—862no—
412C2×D4—3442no—
413C2×D4—1724no—
414C2×D4—1724no—
415C2×D4—1724no—
416C2×D4—1724no—
417C2×D4#1062189812yescomplemented
418C2×D4C2×C22⋊D4312yes—
419C22×C4—21no—
420C22×C4—24no—
421C22×C4—21no—
422C22×C4—44no—
423C22×C4—42no—
424C22×C4—82no—
425C22×C4—432no—
426C22×C4—868no—
427C22×C4—862no—
428C22×C4—862no—
429C22×C4—862no—
430C22×C4—862no—
431C22×C4—862no—
432C22×C4—862no—
433C22×C4—862no—
434C22×C4—862no—
435C22×C4—1724no—
436C22×C4—1724no—
437C22×C4D4×D4311yescharacteristic
438C22×C4D4×D4311yescharacteristic
439C22×C4C23×D4311yescharacteristic
440D8—28no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—862no—
447C2×C8—862no—
448C2×C8—862no—
449C2×C8#1062189812yescomplemented
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—434no—
454C4⋊C4—868no—
455C4⋊C4—862no—
456C4⋊C4—864no—
457C4⋊C4—862no—
458C4⋊C4—862no—
459C4⋊C4—862no—
460C4⋊C4C2×C22⋊D4312yes—
461C22⋊C4—24no—
462C22⋊C4—42no—
463C22⋊C4—868no—
464C22⋊C4—864no—
465C22⋊C4—3442no—
466C22⋊C4—1724no—
467C42D4×D4312yes—
468C42C2×C22⋊D4312yes—
469C23—22no—
470C23—22no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—42no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—41no—
479C23—434no—
480C23—862no—
481C23—862no—
482C23—862no—
483C23—862no—
484C23—862no—
485C23—862no—
486C23C2×D4×D4311yescharacteristic
487Q8—1728no—
488D4—22no—
489D4—22no—
490D4—22no—
491D4—22no—
492D4—41no—
493D4—41no—
494D4—41no—
495D4—41no—
496D4—868no—
497D4—3448no—
498D4—17216no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—48no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—42no—
506C2×C4—84no—
507C2×C4—862no—
508C2×C4—862no—
509C2×C4—864no—
510C2×C4—862no—
511C2×C4—17216no—
512C2×C4—1722no—
513C2×C4—1722no—
514C2×C4—1722no—
515C2×C4—1722no—
516C2×C4—1722no—
517C2×C4—1722no—
518C2×C4—1722no—
519C2×C4—1722no—
520C2×C4—1722no—
521C2×C4#1306329312yes—
522C2×C4#1306329312yes—
523C2×C4C2×D4×D4311yescharacteristic
524C2×C4C22×C22⋊D4311yescharacteristic
525C2×C4C2×#1062189811yescharacteristic
526C2×C4C2×#1062189811yescharacteristic
527C2×C4#1306337111yescharacteristic
528C2×C4#1306337211yescharacteristic
529C8—22no—
530C8—41no—
531C8—1722no—
532C22—44no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—82no—
538C22—82no—
539C22—82no—
540C22—81no—
541C22—81no—
542C22—864no—
543C22—864no—
544C22—864no—
545C22—1722no—
546C22—1722no—
547C22—1722no—
548C22—1722no—
549C22C2×#1306329311yescharacteristic
550C22#1458354511yescharacteristic
551C22#1458355411yescharacteristic
552C22AGL(1,ℤ/8)×D4312yes—
553C22#1458370912yes—
554C4—22no—
555C4—22no—
556C4—42no—
557C4—81no—
558C4—3442no—
559C4—1724no—
560C4—1722no—
561C4#1458341011yescharacteristic
562C4#1458347711yescharacteristic
563C4#1458355811yescharacteristic
564C4#1458357011yescharacteristic
565C2—82no—
566C2—82no—
567C2—1724no—
568C2#1913794011yescharacteristic
569C2#1914382011yescharacteristic
570C2#1914388011yescharacteristic
571C2#1914656112yes—
572C2#1914707012yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#442C2
socleC23×C43C22×D4
hypercenterC2×#442D43
hypocenterC43#24128
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#14583554C2semidirect
2. C2×#14583189C2semidirect
3. #19139492C2semidirect
4. #19135782C2semidirect
5. #19135590C2semidirect
6. #19135568C2semidirect
7. #19135393C2semidirect
8. #19134909C2semidirect
9. #19134786C2semidirect
10. #19134605C2semidirect
11. C2×C43×#442C2semidirect
55. #13063325D4semidirect
96. C4×D4×C43D4semidirect
120. C2×D4×C43#41semidirect
159. C2×C8×C43#41semidirect
281. C2×#442D43semidirect
331. C43#24128semidirect
363. C4×D4C22⋊D43semidirect
417. C2×D4#10621898semidirect
449. C2×C8#10621898semidirect

Maximal subgroups

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

subgroupindex
C2×#145835542
C2×#145831892
#191394922
#191357822
#191355902
#191355682
#191353932
#191349092
#191347862
#191346052
C2×C43×#4422
#2412843