Finite Group Databasebeta

← #25130356

Subgroups — #25130356

Order 11008.

1146 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583215C211yesmaximal, characteristic, complemented
2C2×#14582942C211yesmaximal, characteristic, complemented
3#19138903C211yesmaximal, characteristic, complemented
4#19135925C212yesmaximal, complemented
5#19135781C212yesmaximal, complemented
6#19135034C211yesmaximal, characteristic, complemented
7#19134893C211yesmaximal, characteristic, complemented
8#19134842C212yesmaximal, complemented
9#19134794C212yesmaximal, complemented
10#19134690C211yesmaximal, characteristic, complemented
11C2×C43×#555C211yesmaximal, characteristic
12C22×#10621877C2211yescharacteristic
13C2×#13063306—21no—
14C22×C4⋊Dic43C2211yescharacteristic
15#14583215—24no—
16#14582942—24no—
17C2×#13063258C2212yes—
18C2×#13063256C2212yes—
19C2×#13063256C2212yes—
20C2×#13063246C2212yes—
21C2×#13063246C2212yes—
22C2×C22⋊(C43⋊C8)C2212yes—
23C2×C22⋊(C43⋊C8)C2211yescharacteristic
24#14582829—21no—
25#14582824—21no—
26#14582797C2212yes—
27#14582760—21no—
28#14582759C2212yes—
29#14582759C2211yescharacteristic
30#14582661C2212yes—
31#14582661C2212yes—
32#14582661C2212yes—
33#14582654C2212yes—
34C43×#555—24no—
35C43×#555—24no—
36C2×C4⋊Q8×C43C2211yescharacteristic
37C2×#124×C43—21no—
38C2×#124×C43—21no—
39C2×#121×C43—21no—
40C2×#121×C43C2211yescharacteristic
41C2×#121×C43C2211yescharacteristic
42C2×C4×D4×C43C2211yescharacteristic
43C2×C4×D4×C43C2211yescharacteristic
44C2×#117×C43—21no—
45C2×#117×C43C2211yescharacteristic
46C2×#117×C43C2211yescharacteristic
47C23×Dic43—21no—
48C2×#10621877—22no—
49C2×#10621877—24no—
50C22×C43⋊C8C2312yes—
51C22×C43⋊C8C2312yes—
52#13063306—44no—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43—22no—
55C2×C4⋊Dic43—21no—
56C2×C4⋊Dic43C2312yes—
57C2×C4⋊Dic43C2312yes—
58C2×Dic43⋊C4—22no—
59C2×C22⋊Dic43—22no—
60C2×C22⋊Dic43—21no—
61#13063258—24no—
62#13063256—24no—
63#13063256—24no—
64#13063246—24no—
65#13063246—24no—
66C22⋊(C43⋊C8)—22no—
67C22⋊(C43⋊C8)—24no—
68C43⋊#95—22no—
69C43⋊#95—21no—
70C43⋊#95—22no—
71C22×Q8×C43—21no—
72C22×D4×C43—21no—
73C22×D4×C43—21no—
74C22×D4×C43D411yescharacteristic
75C22×D4×C43C2311yescharacteristic
76C23×C4×C43—21no—
77C23×C4×C43C2311yescharacteristic
78C23×C4×C43C2311yescharacteristic
79C4⋊Q8×C43—22no—
80C4⋊Q8×C43—22no—
81#124×C43—28no—
82#124×C43—28no—
83#121×C43—28no—
84#121×C43—22no—
85#121×C43—22no—
86#121×C43—22no—
87#121×C43D414yes—
88C4×D4×C43—22no—
89C4×D4×C43—22no—
90C4×D4×C43—22no—
91C4×D4×C43—22no—
92#117×C43—28no—
93#117×C43—22no—
94#117×C43—22no—
95#117×C43—22no—
96#117×C43D414yes—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43D411yescharacteristic
99C2×C4⋊C4×C43C2311yescharacteristic
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C4⋊C4×C43C2311yescharacteristic
102C2×C22⋊C4×C43—21no—
103C2×C22⋊C4×C43—21no—
104C2×C22⋊C4×C43—21no—
105C2×C22⋊C4×C43—21no—
106C2×C22⋊C4×C43—21no—
107C2×C22⋊C4×C43D411yescharacteristic
108C2×C22⋊C4×C43D411yescharacteristic
109C2×C42×C43—21no—
110C2×C42×C43—21no—
111C2×C42×C43C2311yescharacteristic
112C24×C43—21no—
113C24×C43C2×D411yescharacteristic
114C24×C43C2×D411yescharacteristic
115C2×Q8×C43—24no—
116C2×Q8×C43—82no—
117C2×D4×C43—24no—
118C2×D4×C43—22no—
119C2×D4×C43—21no—
120C2×D4×C43—22no—
121C2×D4×C43—24no—
122C2×D4×C43—22no—
123C2×D4×C43—22no—
124C2×D4×C43—41no—
125C2×D4×C43—82no—
126C2×D4×C43—82no—
127C2×D4×C43C2×D412yes—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—24no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—42no—
139C22×C4×C43—42no—
140C22×C4×C43C2×D412yes—
141C22×C4×C43C2×D412yes—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2411yescharacteristic
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—42no—
150C22×Dic43—42no—
151C22×Dic43—42no—
152C4⋊C4×C43—24no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43C2×D412yes—
158C4⋊C4×C43C2×D412yes—
159C4⋊C4×C43C2×D412yes—
160C22⋊C4×C43—24no—
161C22⋊C4×C43—24no—
162C22⋊C4×C43—24no—
163C22⋊C4×C43—24no—
164C22⋊C4×C43—22no—
165C22⋊C4×C43—24no—
166C22⋊C4×C43—22no—
167C42×C43—24no—
168C42×C43—24no—
169C42×C43—21no—
170C42×C43—21no—
171C22⋊Dic43—42no—
172C22⋊Dic43—44no—
173C4⋊Dic43—22no—
174C4⋊Dic43—22no—
175C4⋊Dic43—22no—
176C4⋊Dic43—22no—
177C4⋊Dic43—42no—
178Dic43⋊C4—44no—
179#10621877—28no—
180C2×C43⋊C8—22no—
181C2×C43⋊C8—22no—
182C2×C43⋊C8—22no—
183C2×C43⋊C8—22no—
184C2×C43⋊C8—22no—
185C2×C43⋊C8#4114yes—
186C23×C43—22no—
187C23×C43—21no—
188C23×C43—21no—
189C23×C43—22no—
190C23×C43—21no—
191C23×C43—22no—
192C23×C43—22no—
193C23×C43—21no—
194C23×C43—21no—
195C23×C43—22no—
196C23×C43—42no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43—42no—
200C23×C43#12012yes—
201C23×C43C22×D411yescharacteristic
202Q8×C43—84no—
203D4×C43—24no—
204D4×C43—44no—
205D4×C43—41no—
206D4×C43—41no—
207D4×C43—84no—
208D4×C43—84no—
209C2×C4×C43—21no—
210C2×C4×C43—22no—
211C2×C4×C43—21no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—24no—
215C2×C4×C43—21no—
216C2×C4×C43—22no—
217C2×C4×C43—21no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—48no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—42no—
230C2×C4×C43#12012yes—
231C2×C4×C43AGL(1,ℤ/8)12yes—
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C2×#4112yes—
235C2×C4×C432−1+412yes—
236C2×Dic43—42no—
237C2×Dic43—42no—
238C2×Dic43—42no—
239C2×Dic43—42no—
240C2×Dic43—42no—
241C2×Dic43—42no—
242C2×Dic43—84no—
243C43⋊C8—24no—
244C43⋊C8—42no—
245#24104—431nomaximal, Sylow
246C22×C43—22no—
247C22×C43—22no—
248C22×C43—22no—
249C22×C43—42no—
250C22×C43—42no—
251C22×C43—42no—
252C22×C43—42no—
253C22×C43—41no—
254C22×C43—42no—
255C22×C43—41no—
256C22×C43—42no—
257C22×C43—41no—
258C22×C43—42no—
259C22×C43—82no—
260C22×C43—82no—
261C22×C43C2×#12011yescharacteristic
262C22×C43#54712yes—
263C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
264C22×C43#57511yescharacteristic
265C22×C43#57712yes—
266C4×C43—22no—
267C4×C43—22no—
268C4×C43—41no—
269C4×C43—42no—
270C4×C43—41no—
271C4×C43—42no—
272C4×C43—42no—
273C4×C43#52511yescharacteristic
274C4×C43#53611yescharacteristic
275C4×C43#54712yes—
276Dic43—82no—
277Dic43—82no—
278C2×#555D4311yescharacteristic
279C2×#481—431no—
280C2×#428—431no—
281#2486—431no—
282#2058—432no—
283#2034—432no—
284#1895—431no—
285#1870—431no—
286#1862—432no—
287#1854—432no—
288#1825—431no—
289C2×C43—42no—
290C2×C43—81no—
291C2×C43—82no—
292C2×C43#240611yescharacteristic
293C2×C43#300611yescharacteristic
294C2×C43#300911yescharacteristic
295C2×C43#334812yes—
296C2×C43#335412yes—
297C22×M16—431no—
298#555—24no—
299#555—24no—
300C2×C4⋊Q8C2×D4311yescharacteristic
301C2×#124—21no—
302C2×#124—21no—
303C2×#123—861no—
304C2×#121—21no—
305C2×#121C2×D4311yescharacteristic
306C2×#121C2×D4311yescharacteristic
307C2×C4×D4C2×D4311yescharacteristic
308C2×C4×D4C2×D4311yescharacteristic
309C2×#117—21no—
310C2×#117C2×D4311yescharacteristic
311C2×#117C2×D4311yescharacteristic
312C22×C4⋊C4—431no—
313#481—864no—
314#428—864no—
315C2×#107—432no—
316C2×#106—432no—
317C2×#106—432no—
318C2×#102—432no—
319C2×#102—432no—
320C2×C22⋊C8—431no—
321C2×C22⋊C8—432no—
322#398—861no—
323#397—861no—
324#389—432no—
325#381—861no—
326#380—431no—
327#380—432no—
328#340—432no—
329#340—432no—
330#340—432no—
331#336—432no—
332C43#2410411yescharacteristic, complemented, Sylow
333C22×Q8—21no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4C22⋊D4311yescharacteristic
337C22×D4C22×D4311yescharacteristic
338C23×C4—21no—
339C23×C4—861no—
340C23×C4C22×D4311yescharacteristic
341C23×C4C22×D4311yescharacteristic
342C2×M16—864no—
343C2×M16—862no—
344C22×C8—432no—
345C22×C8—432no—
346C4⋊Q8—22no—
347C4⋊Q8—22no—
348#124—28no—
349#124—28no—
350#123—1724no—
351#121—28no—
352#121—22no—
353#121—22no—
354#121—22no—
355#121C22⋊D4314yes—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—22no—
360#117—28no—
361#117—22no—
362#117—22no—
363#117—22no—
364#117C22⋊D4314yes—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—432no—
367C2×C4⋊C4—432no—
368C2×C4⋊C4—862no—
369C2×C4⋊C4—862no—
370C2×C4⋊C4—861no—
371C2×C4⋊C4—862no—
372C2×C4⋊C4C22⋊D4311yescharacteristic
373C2×C4⋊C4C22×D4311yescharacteristic
374C2×C4⋊C4C22×D4311yescharacteristic
375C2×C4⋊C4C22×D4311yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—861no—
382C2×C22⋊C4—862no—
383C2×C22⋊C4C22⋊D4311yescharacteristic
384C2×C22⋊C4C22⋊D4311yescharacteristic
385C2×C42—21no—
386C2×C42—21no—
387C2×C42C22×D4311yescharacteristic
388#107—864no—
389#106—864no—
390#106—864no—
391#102—864no—
392#102—864no—
393C22⋊C8—864no—
394C22⋊C8—862no—
395#95—862no—
396#95—861no—
397#95—862no—
398C24—21no—
399C24C2×C22⋊D4311yescharacteristic
400C24C2×C22⋊D4311yescharacteristic
401C2×Q8—24no—
402C2×Q8—82no—
403C2×D4—22no—
404C2×D4—24no—
405C2×D4—24no—
406C2×D4—22no—
407C2×D4—21no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—41no—
411C2×D4—82no—
412C2×D4—82no—
413C2×D4C2×C22⋊D4312yes—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—862no—
427C22×C4—862no—
428C22×C4—1722no—
429C22×C4—1722no—
430C22×C4—1722no—
431C22×C4C2×C22⋊D4311yescharacteristic
432C22×C4C2×C22⋊D4311yescharacteristic
433C22×C4C2×C22⋊D4311yescharacteristic
434C22×C4C2×C22⋊D4312yes—
435C22×C4C2×C22⋊D4312yes—
436C22×C4C2×C22⋊D4311yescharacteristic
437C22×C4C23×D4311yescharacteristic
438M16—868no—
439C2×C8—434no—
440C2×C8—862no—
441C2×C8—862no—
442C2×C8—862no—
443C2×C8—862no—
444C2×C8—862no—
445C4⋊C4—24no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—862no—
451C4⋊C4—862no—
452C4⋊C4—862no—
453C4⋊C4—862no—
454C4⋊C4—1722no—
455C4⋊C4—1724no—
456C4⋊C4C2×C22⋊D4312yes—
457C4⋊C4C2×C22⋊D4312yes—
458C4⋊C4C2×C22⋊D4312yes—
459C22⋊C4—24no—
460C22⋊C4—24no—
461C22⋊C4—24no—
462C22⋊C4—24no—
463C22⋊C4—22no—
464C22⋊C4—24no—
465C22⋊C4—22no—
466C22⋊C4—1722no—
467C22⋊C4—1724no—
468C42—24no—
469C42—24no—
470C42—21no—
471C42—21no—
472C23—21no—
473C23—21no—
474C23—22no—
475C23—22no—
476C23—21no—
477C23—22no—
478C23—21no—
479C23—21no—
480C23—22no—
481C23—22no—
482C23—41no—
483C23—41no—
484C23—42no—
485C23—42no—
486C23#1306329412yes—
487C23C22×C22⋊D4311yescharacteristic
488Q8—84no—
489D4—24no—
490D4—44no—
491D4—41no—
492D4—41no—
493D4—84no—
494D4—84no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—48no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—3444no—
517C2×C4—1722no—
518C2×C4—1722no—
519C2×C4—1722no—
520C2×C4—1722no—
521C2×C4—1722no—
522C2×C4—1722no—
523C2×C4#1306329412yes—
524C2×C4#1306335012yes—
525C2×C4C22×C22⋊D4311yescharacteristic
526C2×C4C22×C22⋊D4311yescharacteristic
527C2×C4#41×D4312yes—
528C2×C4#1306337212yes—
529C8—864no—
530C8—1722no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—41no—
538C22—42no—
539C22—42no—
540C22—41no—
541C22—42no—
542C22—41no—
543C22—42no—
544C22—82no—
545C22—82no—
546C22C2×#1306329411yescharacteristic
547C22#1458354812yes—
548C22C2×#1306335011yescharacteristic
549C22#1458369711yescharacteristic
550C22#1458371012yes—
551C4—22no—
552C4—22no—
553C4—41no—
554C4—42no—
555C4—41no—
556C4—42no—
557C4—42no—
558C4—3442no—
559C4—3442no—
560C4#1458340611yescharacteristic
561C4#1458347011yescharacteristic
562C4#1458354812yes—
563C2—42no—
564C2—81no—
565C2—82no—
566C2#1913792611yescharacteristic
567C2#1914384711yescharacteristic
568C2#1914387211yescharacteristic
569C2#1914711012yes—
570C2#1914718412yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#555C2
socleC23×C43C22×D4
hypercenterC2×#555D43
hypocenterC43#24104
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. C2×#14583215C2semidirect
2. C2×#14582942C2semidirect
3. #19138903C2semidirect
4. #19135925C2semidirect
5. #19135781C2semidirect
6. #19135034C2semidirect
7. #19134893C2semidirect
8. #19134842C2semidirect
9. #19134794C2semidirect
10. #19134690C2semidirect
332. C43#24104semidirect

Maximal subgroups

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

subgroupindex
C2×#145832152
C2×#145829422
#191389032
#191359252
#191357812
#191350342
#191348932
#191348422
#191347942
#191346902
C2×C43×#5552
#2410443