Finite Group Databasebeta

← #25106504

Subgroups — #25106504

Order 11008.

1398 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583444C211yesmaximal, characteristic
2C22×Dic43⋊C8C211yesmaximal, characteristic, complemented
3#19136990C211yesmaximal, characteristic, complemented
4#19135541C212yesmaximal, complemented
5#19135520C212yesmaximal, complemented
6#19135024C211yesmaximal, characteristic, complemented
7#19135023C211yesmaximal, characteristic, complemented
8#19135021C211yesmaximal, characteristic, complemented
9#19134604C212yesmaximal, complemented
10#19134603C212yesmaximal, complemented
11C43×#1893C211yesmaximal, characteristic, complemented
12C22×#10621900—21no—
13C23×C43⋊C8C2211yescharacteristic
14#14583444—24no—
15#14583444C418yescomplemented
16C2×#13063324C2211yescharacteristic
17C2×#13063321C2211yescharacteristic
18C2×#13063311—21no—
19C2×#13063299C2211yescharacteristic
20C2×#13063297—21no—
21C2×D4×Dic43C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23C2×(C22⋊D43)⋊C4—21no—
24C22×C4×Dic43C2211yescharacteristic
25C2×Dic43⋊C8—24no—
26C2×Dic43⋊C8C2212yes—
27C2×Dic43⋊C8C2212yes—
28C2×#13063247C2212yes—
29C2×#13063246C2212yes—
30C2×#13063245C2212yes—
31#14582766—21no—
32#14582764C2212yes—
33#14582760—21no—
34#14582759C2211yescharacteristic
35C4⋊C4×Dic43C2212yes—
36C22⋊C4×Dic43—21no—
37#14582744—21no—
38#14582662C2212yes—
39#14582661C2212yes—
40#14582661C2212yes—
41C23×C8×C43C2211yescharacteristic
42C2×#121×C43C2211yescharacteristic
43C2×#102×C43C2212yes—
44C43×#380C2211yescharacteristic
45C43×#340C2212yes—
46C2×#10621900—28no—
47C2×#10621900—44no—
48C2×#10621900—44no—
49C22×Dic86—21no—
50C22×D172C2311yescharacteristic
51C22×C22⋊D43—21no—
52C22×C22⋊D43—21no—
53C22×C22⋊D43—21no—
54C23×Dic43—21no—
55C23×Dic43D411yescharacteristic
56C23×Dic43D411yescharacteristic
57C22×C4×D43—21no—
58C22×C43⋊C8—22no—
59C22×C43⋊C8—42no—
60C22×C43⋊C8C2312yes—
61#13063324—22no—
62#13063324C2×C414yes—
63#13063321—22no—
64#13063321C2×C414yes—
65#13063311—28no—
66#13063299—22no—
67#13063299C2×C414yes—
68#13063297—28no—
69D4×Dic43—22no—
70D4×Dic43C2×C414yes—
71#13063287—22no—
72#13063287C2×C414yes—
73(C22⋊D43)⋊C4—28no—
74C2×C4⋊Dic43C2312yes—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×C4×Dic43—22no—
82C2×C4×Dic43C2×C414yes—
83C2×C4×Dic43D411yescharacteristic
84C2×C4×Dic43D411yescharacteristic
85C2×C4×Dic43D414yes—
86C2×C4×Dic43C2311yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88Dic43⋊C8—24no—
89Dic43⋊C8—24no—
90#13063247—42no—
91#13063246—42no—
92#13063245—42no—
93C43⋊#95—21no—
94C43⋊#95—22no—
95C43⋊#95—22no—
96C43⋊#95—22no—
97C22×D4×C43—21no—
98C22×D4×C43C2311yescharacteristic
99C23×C4×C43C2311yescharacteristic
100C22×C8×C43—22no—
101C22×C8×C43—42no—
102C22×C8×C43C2312yes—
103#121×C43—22no—
104#121×C43C2×C414yes—
105C2×C4⋊C4×C43C2312yes—
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109#102×C43—42no—
110#95×C43—21no—
111C24×C43—21no—
112C24×C43C2×D411yescharacteristic
113C23×D43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—24no—
116C2×D4×C43—22no—
117C2×D4×C43—22no—
118C2×D4×C43—42no—
119C2×D4×C43—42no—
120C2×D4×C43C22×C412yes—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—21no—
124C22×C4×C43—22no—
125C22×C4×C43C22×C412yes—
126C22×C4×C43C2×D412yes—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2411yescharacteristic
129C2×C22⋊D43—24no—
130C2×C22⋊D43—24no—
131C2×C22⋊D43—24no—
132C2×C22⋊D43—42no—
133C2×C22⋊D43—42no—
134C2×C22⋊D43—44no—
135C2×C22⋊D43—42no—
136C2×C22⋊D43—42no—
137C22×Dic43—24no—
138C22×Dic43—24no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—21no—
142C22×Dic43—22no—
143C22×Dic43—42no—
144C22×Dic43—42no—
145C22×Dic43C22⋊C414yes—
146C22×Dic43C22⋊C414yes—
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151#10621900—432no—
152C2×D172—21no—
153C2×D172—22no—
154C2×D172—22no—
155C2×D172C22×C412yes—
156C2×C4×D43—24no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×Dic86—24no—
160C2×Dic86—42no—
161C2×Dic86—42no—
162C2×C8×C43—22no—
163C2×C8×C43—22no—
164C2×C8×C43—22no—
165C2×C8×C43—44no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—22no—
169C4⋊C4×C43C22×C412yes—
170C22⋊C4×C43—24no—
171C22⋊C4×C43—42no—
172C22⋊Dic43—24no—
173C22⋊Dic43—42no—
174(C2×D43)⋊C4—24no—
175(C2×D43)⋊C4—24no—
176C4⋊Dic43—21no—
177C4⋊Dic43—22no—
178C4⋊Dic43—22no—
179C4⋊Dic43C22×C412yes—
180Dic43⋊C4—24no—
181C4×Dic43—44no—
182C4×Dic43C22⋊C414yes—
183C4×Dic43C22⋊C414yes—
184C4×Dic43C22×C412yes—
185C4×Dic43C22×C412yes—
186C4×Dic43C2×D412yes—
187C4×Dic43C2×D412yes—
188C2×C43⋊C8—22no—
189C2×C43⋊C8—22no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—44no—
192C23×C43—22no—
193C23×C43—22no—
194C23×C43—22no—
195C23×C43—42no—
196C23×C43—42no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43C2×C22⋊C412yes—
200C23×C43AGL(1,ℤ/8)12yes—
201C23×C43AGL(1,ℤ/8)12yes—
202C23×C43C22×D411yescharacteristic
203C22×D43—22no—
204C22×D43—42no—
205C22×D43—42no—
206C22×D43—41no—
207C22×D43—41no—
208D4×C43—24no—
209D4×C43—48no—
210D4×C43—41no—
211D4×C43—41no—
212C2×C4×C43—22no—
213C2×C4×C43—24no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43C2×C22⋊C412yes—
223C2×C4×C43C23×C411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43H(5,𝔽2)12yes—
226C2×C4×C432−1+412yes—
227C22⋊D43—48no—
228C22⋊D43—48no—
229C22⋊D43—48no—
230C2×Dic43—22no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—28no—
236C2×Dic43—28no—
237C2×Dic43—22no—
238C2×Dic43—48no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43C2×C22⋊C412yes—
245C2×Dic43C2×C22⋊C412yes—
246C2×Dic43C2×C22⋊C412yes—
247C2×Dic43C2×C22⋊C412yes—
248C2×Dic43#13514yes—
249D172—24no—
250D172—41no—
251D172—41no—
252C4×D43—48no—
253Dic86—48no—
254C8×C43—42no—
255C43⋊C8—42no—
256#21888—431nomaximal, Sylow
257C22×C43—22no—
258C22×C43—22no—
259C22×C43—24no—
260C22×C43—24no—
261C22×C43—42no—
262C22×C43—42no—
263C22×C43—42no—
264C22×C43—82no—
265C22×C43—82no—
266C22×C43#41814yes—
267C22×C43C22×C22⋊C411yescharacteristic
268C22×C43#53712yes—
269C22×C43C2×#13512yes—
270C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
271C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
272C2×D43—42no—
273C2×D43—42no—
274C2×D43—42no—
275C2×D43—82no—
276C2×D43—82no—
277C4×C43—22no—
278C4×C43—42no—
279C4×C43—82no—
280C4×C43#52012yes—
281C4×C43#53511yescharacteristic
282C4×C43#53611yescharacteristic
283Dic43—22no—
284Dic43—22no—
285Dic43—22no—
286Dic43—42no—
287Dic43—82no—
288Dic43#41614yes—
289C2×#532—431no—
290C22×C4⋊C8—431no—
291#2283—431no—
292#1987—432no—
293#1982—432no—
294#1893—431no—
295#1893—431no—
296#1893—431no—
297#1893D4311yescharacteristic, complemented
298#1804—432no—
299#1804—432no—
300C2×C43—24no—
301C2×C43—82no—
302C2×C43#231111yescharacteristic
303C2×C43C2×#41611yescharacteristic
304C2×C43C2×#41811yescharacteristic
305C2×C43#324712yes—
306C2×C43#324712yes—
307D43—82no—
308C22×#41—861no—
309C23×C8—431no—
310C23×C8C2×D4311yescharacteristic
311#532—438no—
312#532—864no—
313C2×C4⋊Q8—431no—
314C2×#127—431no—
315C2×#124—861no—
316C2×#121—431no—
317C2×#121—861no—
318C2×#121C2×D4311yescharacteristic
319C2×C4×D4—431no—
320C2×C4×D4—431no—
321C2×C4×D4—861no—
322C22×C42—431no—
323C2×C4⋊C8—432no—
324C2×C4⋊C8—432no—
325C2×C4⋊C8—864no—
326C2×#102—432no—
327C2×#102—432no—
328C2×#102—432no—
329C2×#102C2×D4312yes—
330#383—861no—
331#382—432no—
332#381—861no—
333#380—431no—
334#380C2×D4311yescharacteristic
335C4×C4⋊C4—432no—
336C4×C22⋊C4—861no—
337#376—861no—
338#340—432no—
339#340—432no—
340#340—432no—
341#340C2×D4312yes—
342C43#2188811yescharacteristic, complemented, Sylow
343C2×#41—868no—
344C2×#41—1724no—
345C2×#41—1724no—
346C22×Q8—861no—
347C22×D4—21no—
348C22×D4—431no—
349C22×D4—861no—
350C22×D4—861no—
351C22×D4—861no—
352C22×D4C22×D4311yescharacteristic
353C23×C4—431no—
354C23×C4—431no—
355C23×C4—861no—
356C23×C4—861no—
357C23×C4C22×D4311yescharacteristic
358C22×C8—22no—
359C22×C8—42no—
360C22×C8—432no—
361C22×C8—862no—
362C22×C8—1722no—
363C22×C8C22×D4312yes—
364C4⋊Q8—434no—
365C4⋊Q8—862no—
366#127—434no—
367#127—862no—
368#124—868no—
369#121—22no—
370#121—434no—
371#121—868no—
372#121—862no—
373#121C4×D4314yes—
374C4×D4—434no—
375C4×D4—434no—
376C4×D4—868no—
377C4×D4—862no—
378C4×D4—862no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—432no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4C22×D4312yes—
383C2×C4⋊C4C22×D4311yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—861no—
387C2×C22⋊C4—861no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C42—434no—
391C2×C42—431no—
392C2×C42—431no—
393C2×C42—434no—
394C2×C42—431no—
395C2×C42—431no—
396C2×C42—862no—
397C4⋊C8—864no—
398C4⋊C8—864no—
399#102—42no—
400#102—1722no—
401#102—1722no—
402#102—1722no—
403#95—21no—
404#95—862no—
405#95—862no—
406#95—862no—
407#95—861no—
408C24—21no—
409C24—861no—
410C24D4×D4311yescharacteristic
411#41—17232no—
412C2×Q8—864no—
413C2×Q8—1722no—
414C2×Q8—1722no—
415C2×D4—24no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4—432no—
422C2×D4—864no—
423C2×D4—864no—
424C2×D4—864no—
425C2×D4—861no—
426C2×D4—862no—
427C2×D4—862no—
428C2×D4—1724no—
429C2×D4—1722no—
430C2×D4—1722no—
431C2×D4—1722no—
432C2×D4—1722no—
433C2×D4C2×C4×D4312yes—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—431no—
439C22×C4—434no—
440C22×C4—434no—
441C22×C4—431no—
442C22×C4—431no—
443C22×C4—431no—
444C22×C4—864no—
445C22×C4—864no—
446C22×C4—864no—
447C22×C4—862no—
448C22×C4—862no—
449C22×C4—861no—
450C22×C4—862no—
451C22×C4—1722no—
452C22×C4—1722no—
453C22×C4—1722no—
454C22×C4—1722no—
455C22×C4C2×C4×D4312yes—
456C22×C4D4×D4311yescharacteristic
457C22×C4D4×D4312yes—
458C22×C4C23×D4311yescharacteristic
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—44no—
463C2×C8—862no—
464C2×C8—862no—
465C2×C8—862no—
466C2×C8—1724no—
467C4⋊C4—21no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—432no—
471C4⋊C4—864no—
472C4⋊C4—861no—
473C4⋊C4—862no—
474C4⋊C4—862no—
475C4⋊C4C2×C4×D4312yes—
476C22⋊C4—24no—
477C22⋊C4—42no—
478C22⋊C4—864no—
479C22⋊C4—864no—
480C22⋊C4—864no—
481C22⋊C4—1722no—
482C42—434no—
483C42—434no—
484C42—432no—
485C42—432no—
486C42—432no—
487C42—432no—
488C42—1724no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—42no—
493C23—41no—
494C23—41no—
495C23—42no—
496C23—862no—
497C23—1722no—
498C23—1721no—
499C23—1721no—
500C23—1722no—
501C23C22⋊C4×D4312yes—
502C23#1306334912yes—
503C23#1306335212yes—
504C23C2×D4×D4311yescharacteristic
505Q8—1728no—
506D4—24no—
507D4—48no—
508D4—41no—
509D4—41no—
510D4—864no—
511D4—1728no—
512D4—1728no—
513D4—1728no—
514D4—1721no—
515D4—1721no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—432no—
527C2×C4—434no—
528C2×C4—432no—
529C2×C4—432no—
530C2×C4—432no—
531C2×C4—868no—
532C2×C4—868no—
533C2×C4—862no—
534C2×C4—861no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—862no—
539C2×C4—1728no—
540C2×C4—1728no—
541C2×C4—1722no—
542C2×C4—1722no—
543C2×C4—1722no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4C22⋊C4×D4312yes—
547C2×C4C22×C4×D4311yescharacteristic
548C2×C4C2×D4×D4311yescharacteristic
549C2×C4#1306337012yes—
550C2×C4#1306337212yes—
551C8—42no—
552C8—1722no—
553C22—22no—
554C22—22no—
555C22—24no—
556C22—24no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—82no—
561C22—82no—
562C22—3442no—
563C22—3442no—
564C22—1722no—
565C22—1722no—
566C22—1722no—
567C22#1458290214yes—
568C22C2×C22⋊C4×D4311yescharacteristic
569C22#1458347612yes—
570C22#135×D4312yes—
571C22C2×#1306334911yescharacteristic
572C22C2×#1306335211yescharacteristic
573C4—22no—
574C4—42no—
575C4—82no—
576C4—434no—
577C4—862no—
578C4—862no—
579C4—862no—
580C4—3442no—
581C4—1722no—
582C4#1458337812yes—
583C4#1458346411yescharacteristic
584C4#1458347111yescharacteristic
585C2—24no—
586C2—82no—
587C2—3442no—
588C2#1913718211yescharacteristic
589C2#416×D4311yescharacteristic
590C2C2×#1458290211yescharacteristic
591C2#1914591412yes—
592C2#1914591612yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1893C2
socleC23×C43C22×D4
prime radicalC2×#14583444C2
cosocleC22×C4×C43C24
hypercenter#1893D43
hypocenterC43#21888
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. C22×Dic43⋊C8C2semidirect
3. #19136990C2semidirect
4. #19135541C2semidirect
5. #19135520C2semidirect
6. #19135024C2semidirect
7. #19135023C2semidirect
8. #19135021C2semidirect
9. #19134604C2semidirect
10. #19134603C2semidirect
11. C43×#1893C2semidirect
15. #14583444C4semidirect
297. #1893D43semidirect
342. C43#21888semidirect

Maximal subgroups

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

subgroupindex
C2×#145834442
C22×Dic43⋊C82
#191369902
#191355412
#191355202
#191350242
#191350232
#191350212
#191346042
#191346032
C43×#18932
#2188843