Finite Group Databasebeta

← #25130363

Subgroups — #25130363

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×#14583614C211yesmaximal, characteristic
2C2×#14583217C211yesmaximal, characteristic, complemented
3C2×#14582939C211yesmaximal, characteristic, complemented
4#19135928C212yesmaximal, complemented
5#19135784C212yesmaximal, complemented
6#19135031C211yesmaximal, characteristic, complemented
7#19134893C211yesmaximal, characteristic, complemented
8#19134841C212yesmaximal, complemented
9#19134792C212yesmaximal, complemented
10#19134687C211yesmaximal, characteristic, complemented
11C43×#2486C211yesmaximal, characteristic, complemented
12C22×#10621877C2211yescharacteristic
13#14583614—24no—
14#14583614—24no—
15C2×#13063325C2211yescharacteristic
16C2×#13063311—21no—
17C2×#13063311—21no—
18C2×#13063299C2211yescharacteristic
19C2×#13063299C2211yescharacteristic
20C2×#13063296—21no—
21C2×C4×D172C2211yescharacteristic
22C2×#13063284C2211yescharacteristic
23C2×#13063284C2211yescharacteristic
24C2×#13063283—21no—
25#14583217—24no—
26#14582939—24no—
27C2×#13063258C2212yes—
28C2×#13063256C2212yes—
29C2×#13063256C2212yes—
30C2×#13063245C2212yes—
31C2×#13063245C2212yes—
32C2×C22⋊(C43⋊C8)C2212yes—
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34#14582661C2212yes—
35#14582661C2212yes—
36#14582661C2212yes—
37#14582654C2212yes—
38C2×#123×C43—21no—
39C2×C4×D4×C43C2211yescharacteristic
40C22×C4⋊C4×C43C2211yescharacteristic
41C43×#398—21no—
42C43×#397—21no—
43C43×#389C2212yes—
44C43×#381—21no—
45C43×#380C2212yes—
46C43×#380C2211yescharacteristic
47C22×Dic86—21no—
48C22×D172C2311yescharacteristic
49C22×C22⋊D43—21no—
50C22×C22⋊D43—21no—
51C22×C4×D43—21no—
52C2×#10621877—22no—
53C2×#10621877—24no—
54C22×C43⋊C8C2312yes—
55C22×C43⋊C8C2312yes—
56#13063325—22no—
57#13063325—22no—
58#13063311—28no—
59#13063311—28no—
60#13063299—22no—
61#13063299—22no—
62#13063299—22no—
63#13063299D414yes—
64#13063296—28no—
65C4×D172—22no—
66C4×D172—22no—
67#13063284—22no—
68#13063284—22no—
69#13063284—22no—
70#13063284D414yes—
71#13063283—28no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83#13063258—24no—
84#13063256—24no—
85#13063256—24no—
86#13063245—24no—
87#13063245—24no—
88C22⋊(C43⋊C8)—22no—
89C22⋊(C43⋊C8)—24no—
90C22×D4×C43D411yescharacteristic
91C23×C4×C43—21no—
92C23×C4×C43C2311yescharacteristic
93C23×C4×C43C2311yescharacteristic
94#123×C43—44no—
95C4×D4×C43—22no—
96C4×D4×C43—22no—
97C2×C4⋊C4×C43—22no—
98C2×C4⋊C4×C43—22no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—22no—
101C2×C4⋊C4×C43D411yescharacteristic
102C2×C4⋊C4×C43C2312yes—
103C2×C4⋊C4×C43C2312yes—
104C2×C22⋊C4×C43—21no—
105C2×C22⋊C4×C43—22no—
106C2×C22⋊C4×C43D411yescharacteristic
107C2×C22⋊C4×C43D411yescharacteristic
108C2×C42×C43C2311yescharacteristic
109#95×C43—22no—
110#95×C43—21no—
111#95×C43—22no—
112C24×C43C2×D411yescharacteristic
113C24×C43C2×D411yescharacteristic
114C23×D43—21no—
115C2×D4×C43—22no—
116C2×D4×C43—22no—
117C2×D4×C43—41no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—42no—
127C22×C4×C43—42no—
128C22×C4×C43—42no—
129C22×C4×C43C2×D412yes—
130C22×C4×C43C2×D412yes—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2411yescharacteristic
136C2×C22⋊D43—24no—
137C2×C22⋊D43—24no—
138C2×C22⋊D43—82no—
139C2×C22⋊D43—82no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C2×D172—21no—
144C2×D172—22no—
145C2×D172—22no—
146C2×D172C2×D412yes—
147C2×C4×D43—24no—
148C2×C4×D43—42no—
149C2×C4×D43—42no—
150C2×Dic86—24no—
151C2×Dic86—82no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—42no—
158C4⋊C4×C43—44no—
159C22⋊C4×C43—22no—
160C22⋊C4×C43—22no—
161C22⋊C4×C43—42no—
162C22⋊C4×C43—44no—
163C42×C43—21no—
164C42×C43—21no—
165C22⋊Dic43—24no—
166C22⋊Dic43—24no—
167(C2×D43)⋊C4—24no—
168(C2×D43)⋊C4—24no—
169(C2×D43)⋊C4—24no—
170C4⋊Dic43—24no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43C2×D412yes—
175C4⋊Dic43C2×D412yes—
176C4⋊Dic43C2×D412yes—
177C4×Dic43—24no—
178C4×Dic43—24no—
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—21no—
193C23×C43—21no—
194C23×C43—22no—
195C23×C43#12012yes—
196C23×C43C22×D411yescharacteristic
197C22×D43—22no—
198C22×D43—42no—
199C22×D43—41no—
200C22×D43—41no—
201C22×D43—42no—
202D4×C43—44no—
203C2×C4×C43—21no—
204C2×C4×C43—22no—
205C2×C4×C43—21no—
206C2×C4×C43—22no—
207C2×C4×C43—22no—
208C2×C4×C43—24no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43—84no—
223C2×C4×C43#12012yes—
224C2×C4×C43AGL(1,ℤ/8)12yes—
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C2×#4112yes—
228C2×C4×C432−1+412yes—
229C22⋊D43—84no—
230C22⋊D43—84no—
231C2×Dic43—22no—
232C2×Dic43—22no—
233C2×Dic43—22no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—42no—
237C2×Dic43—42no—
238D172—24no—
239D172—41no—
240D172—41no—
241C4×D43—48no—
242Dic86—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—41no—
255C22×C43—41no—
256C22×C43C2×#12011yescharacteristic
257C22×C43#54712yes—
258C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
259C22×C43#57511yescharacteristic
260C22×C43#57712yes—
261C2×D43—42no—
262C2×D43—42no—
263C2×D43—42no—
264C2×D43—82no—
265C2×D43—82no—
266C4×C43—22no—
267C4×C43—22no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43—82no—
271C4×C43—82no—
272C4×C43#52511yescharacteristic
273C4×C43#53611yescharacteristic
274C4×C43#54712yes—
275Dic43—42no—
276Dic43—42no—
277Dic43—42no—
278C2×#555—431no—
279C2×#481—431no—
280C2×#428—431no—
281#2486D4311yescharacteristic, complemented
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#240611yescharacteristic
292C2×C43#300611yescharacteristic
293C2×C43#300911yescharacteristic
294C2×C43#334812yes—
295C2×C43#335412yes—
296D43—82no—
297C22×M16—431no—
298#555—864no—
299#555—864no—
300C2×C4⋊Q8—431no—
301C2×#124—861no—
302C2×#124—861no—
303C2×#123—21no—
304C2×#121—431no—
305C2×#121—431no—
306C2×#121—861no—
307C2×C4×D4—431no—
308C2×C4×D4C2×D4311yescharacteristic
309C2×#117—431no—
310C2×#117—431no—
311C2×#117—861no—
312C22×C4⋊C4C2×D4311yescharacteristic
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—21no—
323#397—21no—
324#389C2×D4312yes—
325#381—21no—
326#380C2×D4311yescharacteristic
327#380C2×D4312yes—
328#340—432no—
329#340—432no—
330#340—432no—
331#336—432no—
332C43#2410411yescharacteristic, complemented, Sylow
333C22×Q8—861no—
334C22×D4—431no—
335C22×D4—861no—
336C22×D4—861no—
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—862no—
347C4⋊Q8—862no—
348#124—868no—
349#124—868no—
350#123—44no—
351#121—434no—
352#121—862no—
353#121—862no—
354#121—868no—
355#121—862no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—862no—
359C4×D4—862no—
360#117—434no—
361#117—868no—
362#117—862no—
363#117—862no—
364#117—862no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—431no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—861no—
373C2×C4⋊C4C22⋊D4311yescharacteristic
374C2×C4⋊C4C22×D4312yes—
375C2×C4⋊C4C22×D4312yes—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—861no—
379C2×C22⋊C4—861no—
380C2×C22⋊C4—861no—
381C2×C22⋊C4—861no—
382C2×C22⋊C4—861no—
383C2×C22⋊C4C22⋊D4311yescharacteristic
384C2×C22⋊C4C22⋊D4311yescharacteristic
385C2×C42—861no—
386C2×C42—861no—
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—22no—
396#95—21no—
397#95—22no—
398C24—861no—
399C24C2×C22⋊D4311yescharacteristic
400C24C2×C22⋊D4311yescharacteristic
401C2×Q8—864no—
402C2×Q8—3442no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—41no—
406C2×D4—432no—
407C2×D4—864no—
408C2×D4—864no—
409C2×D4—861no—
410C2×D4—862no—
411C2×D4—862no—
412C2×D4—3442no—
413C2×D4—3442no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—864no—
426C22×C4—861no—
427C22×C4—861no—
428C22×C4—861no—
429C22×C4—1722no—
430C22×C4—1722no—
431C22×C4D4×D4312yes—
432C22×C4D4×D4312yes—
433C22×C4C2×C22⋊D4311yescharacteristic
434C22×C4C2×C22⋊D4311yescharacteristic
435C22×C4C2×C22⋊D4311yescharacteristic
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—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—42no—
451C4⋊C4—44no—
452C4⋊C4—432no—
453C4⋊C4—432no—
454C4⋊C4—432no—
455C4⋊C4—864no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—42no—
462C22⋊C4—44no—
463C22⋊C4—864no—
464C22⋊C4—864no—
465C22⋊C4—864no—
466C22⋊C4—864no—
467C22⋊C4—864no—
468C42—21no—
469C42—21no—
470C42—864no—
471C42—864no—
472C23—21no—
473C23—21no—
474C23—22no—
475C23—22no—
476C23—21no—
477C23—21no—
478C23—21no—
479C23—22no—
480C23—22no—
481C23—862no—
482C23—1721no—
483C23—1721no—
484C23—1722no—
485C23—1722no—
486C23#1306329312yes—
487C23C22×C22⋊D4311yescharacteristic
488Q8—3444no—
489D4—44no—
490D4—864no—
491D4—3444no—
492D4—3444no—
493D4—1721no—
494D4—1721no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—84no—
515C2×C4—862no—
516C2×C4—862no—
517C2×C4—862no—
518C2×C4—1728no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4—1722no—
522C2×C4—1722no—
523C2×C4#1306329312yes—
524C2×C4#1306335112yes—
525C2×C4C2×D4×D4311yescharacteristic
526C2×C4C2×D4×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—41no—
539C22—42no—
540C22—41no—
541C22—3442no—
542C22—3442no—
543C22—1722no—
544C22—1722no—
545C22—1722no—
546C22C2×#1306329311yescharacteristic
547C22#1458354812yes—
548C22C2×#1306335111yescharacteristic
549C22#1458369711yescharacteristic
550C22#1458370712yes—
551C4—22no—
552C4—22no—
553C4—41no—
554C4—41no—
555C4—82no—
556C4—82no—
557C4—1722no—
558C4—1722no—
559C4—1722no—
560C4#1458340711yescharacteristic
561C4#1458347111yescharacteristic
562C4#1458354712yes—
563C2—42no—
564C2—81no—
565C2—3442no—
566C2#1913792711yescharacteristic
567C2#1914384511yescharacteristic
568C2#1914387011yescharacteristic
569C2#1914710412yes—
570C2#1914719012yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2486C2
socleC23×C43C22×D4
prime radicalC2×#14583614C2
hypercenter#2486D43
hypocenterC43#24104
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2486

Complements

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

NH ≅ G/Ntype
2. C2×#14583217C2semidirect
3. C2×#14582939C2semidirect
4. #19135928C2semidirect
5. #19135784C2semidirect
6. #19135031C2semidirect
7. #19134893C2semidirect
8. #19134841C2semidirect
9. #19134792C2semidirect
10. #19134687C2semidirect
11. C43×#2486C2semidirect
281. #2486D43semidirect
332. C43#24104semidirect

Maximal subgroups

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

subgroupindex
C2×#145836142
C2×#145832172
C2×#145829392
#191359282
#191357842
#191350312
#191348932
#191348412
#191347922
#191346872
C43×#24862
#2410443