Finite Group Databasebeta

← #25135319

Subgroups — #25135319

Order 11008.

1188 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583050C211yesmaximal, characteristic
2C2×#14582956C211yesmaximal, characteristic, complemented
3#19142934C211yesmaximal, characteristic, complemented
4#19135983C212yesmaximal, complemented
5#19135912C212yesmaximal, complemented
6#19135475C212yesmaximal, complemented
7#19135295C212yesmaximal, complemented
8#19134902C211yesmaximal, characteristic, complemented
9#19134783C211yesmaximal, characteristic, complemented
10#19134526C211yesmaximal, characteristic
11C2×C43×#390C211yesmaximal, characteristic
12C22×#10621883C2212yes—
13C2×#13063304C2211yescharacteristic
14#14583050—24no—
15#14582956—24no—
16C2×#13063258C2212yescomplemented
17C2×C4⋊(C43⋊C8)C2212yescomplemented
18C2×#13063248C2212yescomplemented
19C2×#13063246C2212yes—
20C2×#13063246C2212yes—
21C2×#13063246C2212yes—
22C2×C22⋊(C43⋊C8)C2211yescharacteristic
23C2×C22⋊(C43⋊C8)C2211yescharacteristic
24C2×#13063236C2212yescomplemented
25#14582805C2211yescharacteristic, complemented
26#14582805C2211yescharacteristic, complemented
27#14582797C2211yescharacteristic, complemented
28#14582797C2211yescharacteristic, complemented
29#14582783—21no—
30#14582783—21no—
31#14582772—21no—
32#14582762—21no—
33#14582759C2211yescharacteristic
34#14582661C2212yescomplemented
35#14582661C2212yescomplemented
36C23×D4×C43C2211yescharacteristic
37C22×C4⋊C4×C43C2211yescharacteristic
38C22×C22⋊C4×C43—21no—
39C22×C22⋊C4×C43—21no—
40C22×C42×C43C2211yescharacteristic
41C43×#390—21no—
42C43×#390—21no—
43C43×#390C2212yes—
44C43×#390C2212yes—
45C22×Dic86C2311yescharacteristic
46C2×#10621883—24no—
47C2×#10621883—24no—
48C2×#10621883—42no—
49C22×C43⋊C8C2312yes—
50C22×C43⋊C8C2312yes—
51#13063304—22no—
52#13063304—22no—
53C2×C4⋊Dic43C2311yescharacteristic
54C2×C4⋊Dic43C2311yescharacteristic
55C2×C4⋊Dic43C2311yescharacteristic
56C2×Dic43⋊C4—21no—
57C2×Dic43⋊C4—21no—
58C2×Dic43⋊C4—21no—
59C2×C22⋊Dic43—21no—
60C2×C22⋊Dic43—21no—
61#13063258—42no—
62C4⋊(C43⋊C8)—24no—
63#13063248—42no—
64#13063246—24no—
65#13063246—24no—
66#13063246—42no—
67C22⋊(C43⋊C8)—22no—
68C22⋊(C43⋊C8)D414yes—
69#13063236—24no—
70C43⋊#95—21no—
71C43⋊#95—21no—
72C43⋊#95—21no—
73C43⋊#95—21no—
74C43⋊#95—21no—
75C43⋊#95—21no—
76C43⋊#95—21no—
77C25×C43—21no—
78C22×D4×C43—24no—
79C22×D4×C43—21no—
80C22×D4×C43—22no—
81C22×D4×C43—22no—
82C22×D4×C43—42no—
83C22×D4×C43C2312yes—
84C23×C4×C43—21no—
85C23×C4×C43D411yescharacteristic
86C23×C4×C43D411yescharacteristic
87C23×C4×C43C2311yescharacteristic
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43—42no—
90C2×C4⋊C4×C43C2312yes—
91C2×C22⋊C4×C43—22no—
92C2×C22⋊C4×C43—22no—
93C2×C22⋊C4×C43—22no—
94C2×C22⋊C4×C43—22no—
95C2×C22⋊C4×C43—44no—
96C2×C22⋊C4×C43—44no—
97C2×C42×C43—22no—
98C2×C42×C43—22no—
99C2×C42×C43D411yescharacteristic
100C2×C42×C43D411yescharacteristic
101C2×C42×C43C2311yescharacteristic
102C2×C42×C43C2311yescharacteristic
103C24×C43—24no—
104C24×C43—22no—
105C24×C43—42no—
106C24×C43—42no—
107C24×C43—42no—
108C24×C43—42no—
109C24×C43—42no—
110C24×C43—42no—
111C24×C43C2×D411yescharacteristic
112C2×D4×C43—24no—
113C2×D4×C43—22no—
114C2×D4×C43—22no—
115C2×D4×C43—22no—
116C2×D4×C43—22no—
117C2×D4×C43—22no—
118C2×D4×C43—48no—
119C2×D4×C43—48no—
120C2×D4×C43—42no—
121C2×D4×C43—42no—
122C2×D4×C43#4114yes—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—41no—
132C22×C4×C43—42no—
133C22×C4×C43—42no—
134C22×C4×C43—42no—
135C22×C4×C43C2×D412yes—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43#4112yes—
142C22×C4×C43C2411yescharacteristic
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86—22no—
150C2×Dic86—22no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—42no—
154C22⋊C4×C43—44no—
155C22⋊C4×C43—44no—
156C22⋊C4×C43—44no—
157C22⋊C4×C43—44no—
158C42×C43—22no—
159C42×C43—22no—
160C42×C43—21no—
161C42×C43—21no—
162C42×C43—21no—
163C42×C43—21no—
164C22⋊Dic43—42no—
165C22⋊Dic43—42no—
166#10621883—48no—
167C4⋊Dic43—21no—
168C4⋊Dic43—22no—
169C4⋊Dic43—21no—
170C4⋊Dic43—22no—
171Dic43⋊C4—42no—
172Dic43⋊C4—42no—
173Dic43⋊C4—42no—
174C2×C43⋊C8—22no—
175C2×C43⋊C8—22no—
176C2×C43⋊C8—22no—
177C2×C43⋊C8—22no—
178C2×C43⋊C8—22no—
179C2×C43⋊C8C2×D414yes—
180C23×C43—21no—
181C23×C43—21no—
182C23×C43—21no—
183C23×C43—21no—
184C23×C43—24no—
185C23×C43—48no—
186C23×C43—48no—
187C23×C43—48no—
188C23×C43—42no—
189C23×C43—42no—
190C23×C43—42no—
191C23×C43—42no—
192C23×C43—42no—
193C23×C43—42no—
194C23×C43—84no—
195C23×C43—84no—
196C23×C43—84no—
197C23×C43—84no—
198C23×C43#12112yes—
199C23×C43AGL(1,ℤ/8)12yes—
200C23×C43#13712yes—
201C23×C43C22×D411yescharacteristic
202D4×C43—24no—
203D4×C43—24no—
204D4×C43—48no—
205D4×C43—42no—
206D4×C43—42no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—24no—
212C2×C4×C43—24no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—44no—
223C2×C4×C43—44no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—84no—
228C2×C4×C43#12112yes—
229C2×C4×C43AGL(1,ℤ/8)12yes—
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4112yes—
233C2×C4×C43H(5,𝔽2)12yes—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246Dic86—42no—
247Dic86—42no—
248C43⋊C8—24no—
249C43⋊C8—42no—
250#24507—431nomaximal, Sylow
251C22×C43—22no—
252C22×C43—22no—
253C22×C43—22no—
254C22×C43—22no—
255C22×C43—22no—
256C22×C43—22no—
257C22×C43—44no—
258C22×C43—44no—
259C22×C43—44no—
260C22×C43—816no—
261C22×C43—82no—
262C22×C43—82no—
263C22×C43—82no—
264C22×C43—82no—
265C22×C43#46814yes—
266C22×C43C2×#12111yescharacteristic
267C22×C43#52511yescharacteristic
268C22×C43#53511yescharacteristic
269C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
271C22×C43C2×#13711yescharacteristic
272C22×C43#57511yescharacteristic
273C4×C43—22no—
274C4×C43—22no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—82no—
279C4×C43#54612yes—
280C4×C43#55112yes—
281Dic43—81no—
282Dic43—81no—
283Dic43—81no—
284Dic43—81no—
285C2×#450—431no—
286C2×#432—431no—
287#2855—431no—
288C2×#390D4311yescharacteristic
289#2067—432no—
290#2055—432no—
291#1973—432no—
292#1936—432no—
293#1872—431no—
294#1852—431no—
295#1786—431no—
296C2×C43—24no—
297C2×C43—84no—
298C2×C43#241111yescharacteristic
299C2×C43C2×#46811yescharacteristic
300C2×C43#305511yescharacteristic
301C2×C43#311011yescharacteristic
302C2×C43#311411yescharacteristic
303C2×C43#321511yescharacteristic
304C2×C43#321711yescharacteristic
305C23×D4C2×D4311yescharacteristic
306C22×SD16—432no—
307C2×C22⋊Q8—431no—
308C22×C4⋊C4C2×D4311yescharacteristic
309C22×C22⋊C4—21no—
310C22×C22⋊C4—21no—
311C22×C42C2×D4311yescharacteristic
312#450—864no—
313#432—864no—
314C2×#107—432no—
315C2×C4⋊C8—432no—
316C2×#103—432no—
317C2×#102—432no—
318C2×#102—432no—
319C2×#102—432no—
320C2×C22⋊C8—431no—
321C2×C22⋊C8—431no—
322C2×#97—432no—
323#391—431no—
324#391—431no—
325#390—21no—
326#390—21no—
327#390C2×D4312yes—
328#390C2×D4312yes—
329#389—431no—
330#389—431no—
331#387—861no—
332#387—861no—
333#385—861no—
334#381—861no—
335#380—431no—
336#340—432no—
337#340—432no—
338C43#2450711yescharacteristic, complemented, Sylow
339C25—21no—
340C22×Q8—431no—
341C22×D4—24no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—21no—
345C22×D4—42no—
346C22×D4C22×D4312yes—
347C23×C4—21no—
348C23×C4C22⋊D4311yescharacteristic
349C23×C4C22⋊D4311yescharacteristic
350C23×C4C22×D4311yescharacteristic
351C2×SD16—864no—
352C2×SD16—864no—
353C2×SD16—1722no—
354C22×C8—432no—
355C22×C8—432no—
356C22⋊Q8—862no—
357C22⋊Q8—862no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—431no—
361C2×C4⋊C4—431no—
362C2×C4⋊C4—431no—
363C2×C4⋊C4—861no—
364C2×C4⋊C4—861no—
365C2×C4⋊C4—861no—
366C2×C4⋊C4C22×D4312yes—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—861no—
374C2×C22⋊C4—861no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42C22⋊D4311yescharacteristic
378C2×C42C22⋊D4311yescharacteristic
379C2×C42C22×D4311yescharacteristic
380C2×C42C22×D4311yescharacteristic
381#107—1722no—
382C4⋊C8—864no—
383#103—1722no—
384#102—864no—
385#102—864no—
386#102—1722no—
387C22⋊C8—434no—
388C22⋊C8—862no—
389#97—864no—
390#95—861no—
391#95—861no—
392#95—861no—
393#95—861no—
394#95—861no—
395#95—861no—
396#95—861no—
397C24—24no—
398C24—22no—
399C24—42no—
400C24—42no—
401C24—42no—
402C24—42no—
403C24—42no—
404C24—42no—
405C24C2×C22⋊D4311yescharacteristic
406C2×Q8—861no—
407C2×Q8—861no—
408C2×Q8—862no—
409C2×Q8—862no—
410C2×D4—24no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—48no—
417C2×D4—48no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4#1062189814yes—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—41no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4D4×D4312yes—
438C22×C4#1062190012yes—
439C22×C4C2×C22⋊D4311yescharacteristic
440C22×C4C2×C22⋊D4311yescharacteristic
441C22×C4C2×C22⋊D4311yescharacteristic
442C22×C4C2×C22⋊D4311yescharacteristic
443C22×C4C2×C22⋊D4311yescharacteristic
444C22×C4C23×D4311yescharacteristic
445SD16—1728no—
446C2×C8—434no—
447C2×C8—862no—
448C2×C8—862no—
449C2×C8—862no—
450C2×C8—862no—
451C2×C8—862no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—42no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—862no—
458C4⋊C4—862no—
459C4⋊C4—1722no—
460C4⋊C4—1722no—
461C4⋊C4—1722no—
462C22⋊C4—44no—
463C22⋊C4—44no—
464C22⋊C4—44no—
465C22⋊C4—44no—
466C22⋊C4—1722no—
467C22⋊C4—1722no—
468C42—22no—
469C42—22no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—21no—
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—24no—
479C23—48no—
480C23—48no—
481C23—48no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—84no—
489C23—84no—
490C23—84no—
491C23—84no—
492C23#1306329712yes—
493C23#1306335112yes—
494C23#1306335512yes—
495C23C22×C22⋊D4311yescharacteristic
496Q8—1722no—
497Q8—1722no—
498D4—24no—
499D4—24no—
500D4—48no—
501D4—42no—
502D4—42no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—44no—
519C2×C4—44no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—84no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4—1721no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4#1306329712yes—
537C2×C4#1306335112yes—
538C2×C4C2×D4×D4311yescharacteristic
539C2×C4C2×#1062190011yescharacteristic
540C2×C4C2×#1062189812yes—
541C2×C4#1306337012yes—
542C8—864no—
543C8—1722no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—44no—
551C22—44no—
552C22—44no—
553C22—816no—
554C22—82no—
555C22—82no—
556C22—82no—
557C22—82no—
558C22#1458314314yes—
559C22C2×#1306329711yescharacteristic
560C22#1458341011yescharacteristic
561C22#1458346611yescharacteristic
562C22C2×#1306335111yescharacteristic
563C22C2×#1306335111yescharacteristic
564C22C2×#1306335511yescharacteristic
565C22#1458369711yescharacteristic
566C4—22no—
567C4—22no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—82no—
572C4—3441no—
573C4—3441no—
574C4—3441no—
575C4—3441no—
576C4#1458353912yes—
577C4#1458357512yes—
578C2—24no—
579C2—84no—
580C2#1913798011yescharacteristic
581C2C2×#1458314311yescharacteristic
582C2#1914421011yescharacteristic
583C2#1914469411yescharacteristic
584C2#1914473311yescharacteristic
585C2#1914559811yescharacteristic
586C2#1914561311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#390C2
socleC23×C43C22×D4
prime radicalC23×D4×C43C22
hypercenterC2×#390D43
hypocenterC43#24507
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#14582956C2semidirect
3. #19142934C2semidirect
4. #19135983C2semidirect
5. #19135912C2semidirect
6. #19135475C2semidirect
7. #19135295C2semidirect
8. #19134902C2semidirect
9. #19134783C2semidirect
16. C2×#13063258C22semidirect
17. C2×C4⋊(C43⋊C8)C22semidirect
18. C2×#13063248C22semidirect
24. C2×#13063236C22semidirect
25. #14582805C22semidirect
26. #14582805C22semidirect
27. #14582797C22semidirect
28. #14582797C22semidirect
34. #14582661C22semidirect
35. #14582661C22semidirect
338. C43#24507semidirect

Maximal subgroups

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

subgroupindex
C2×#145830502
C2×#145829562
#191429342
#191359832
#191359122
#191354752
#191352952
#191349022
#191347832
#191345262
C2×C43×#3902
#2450743