Finite Group Databasebeta

← #25101807

Subgroups — #25101807

Order 11008.

1422 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583446C211yesmaximal, characteristic
2C2×C4×#10621872C211yesmaximal, characteristic, complemented
3#19136991C211yesmaximal, characteristic, complemented
4#19135566C212yesmaximal, complemented
5#19135417C212yesmaximal, complemented
6#19135032C212yesmaximal, complemented
7#19135030C212yesmaximal, complemented
8C4×#13063245C211yesmaximal, characteristic, complemented
9C4×#13063247C211yesmaximal, characteristic, complemented
10C4×#13063246C211yesmaximal, characteristic, complemented
11C4×#102×C43C211yesmaximal, characteristic, complemented
12C22×#10621898—21no—
13C22×#10621872C2212yes—
14#14583446—24no—
15#14583446C418yescomplemented
16C2×#13063324C2211yescharacteristic
17C2×#13063321C2211yescharacteristic
18C2×#13063311—21no—
19C2×#13063300C2211yescharacteristic
20C2×#13063298—21no—
21C2×#13063296C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23C2×C4×C22⋊D43—21no—
24C2×C42×D43C2211yescharacteristic
25C2×#13063247C2212yes—
26C2×#13063246C2212yes—
27C2×#13063245C2212yes—
28C4×#10621872—24no—
29C2×#13063235C2212yes—
30C2×C4×C43⋊C8C2211yescharacteristic
31#14582766—21no—
32#14582764C2212yes—
33#14582761—21no—
34#14582756C2212yes—
35C4×C4⋊Dic43C2211yescharacteristic
36C4×(C2×D43)⋊C4—21no—
37#14582745—21no—
38#14582662C2212yes—
39#14582661C2212yes—
40#14582661C2212yes—
41C2×C4×D4×C43C2211yescharacteristic
42C2×#102×C43C2212yes—
43C2×C4×C8×C43C2211yescharacteristic
44C4×C4⋊C4×C43C2211yescharacteristic
45C43×#340C2212yes—
46C2×#10621898—28no—
47C2×#10621898—44no—
48C2×#10621898—44no—
49C22×Dic86—21no—
50C22×D172—21no—
51C22×D172C2311yescharacteristic
52C22×C22⋊D43—21no—
53C22×C22⋊D43—21no—
54C22×C22⋊D43—21no—
55C22×C4×D43—21no—
56C22×C4×D43D411yescharacteristic
57C22×C4×D43D411yescharacteristic
58C22×C4×D43C2311yescharacteristic
59C2×#10621872—24no—
60C2×#10621872—24no—
61C2×#10621872—24no—
62C22×C43⋊C8C2312yes—
63#13063324—22no—
64#13063324C2×C414yes—
65#13063321—22no—
66#13063321C2×C414yes—
67#13063311—28no—
68#13063300—22no—
69#13063300C2×C414yes—
70#13063298—28no—
71#13063296—22no—
72#13063296C2×C414yes—
73C4×D172—22no—
74C4×D172C2×C414yes—
75C4×C22⋊D43—28no—
76C2×C4⋊Dic43C2312yes—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×C22⋊Dic43—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—22no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43D411yescharacteristic
85C2×C4×Dic43D411yescharacteristic
86C2×C4×Dic43C2311yescharacteristic
87C42×D43C2×C414yes—
88C42×D43D414yes—
89#13063247—24no—
90#13063246—24no—
91#13063245—24no—
92#13063235—24no—
93C4×C43⋊C8—22no—
94C43⋊#95—21no—
95C43⋊#95—22no—
96C43⋊#95—22no—
97C43⋊#95—22no—
98C22×D4×C43C2311yescharacteristic
99C23×C4×C43—21no—
100C22×C8×C43C2312yes—
101C4×D4×C43—22no—
102C4×D4×C43C2×C414yes—
103C2×C4⋊C4×C43C2312yes—
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C22⋊C4×C43—21no—
106C2×C42×C43—21no—
107C2×C42×C43C2311yescharacteristic
108#102×C43—24no—
109C4×C8×C43—22no—
110#95×C43—21no—
111C24×C43—21no—
112C23×D43—21no—
113C23×D43C2×D411yescharacteristic
114C2×D4×C43—21no—
115C2×D4×C43—22no—
116C2×D4×C43—22no—
117C2×D4×C43C22×C412yes—
118C22×C4×C43—24no—
119C22×C4×C43—21no—
120C22×C4×C43—22no—
121C22×C4×C43—42no—
122C22×C4×C43—42no—
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2411yescharacteristic
126C2×C22⋊D43—24no—
127C2×C22⋊D43—24no—
128C2×C22⋊D43—24no—
129C2×C22⋊D43—42no—
130C2×C22⋊D43—42no—
131C2×C22⋊D43—44no—
132C2×C22⋊D43—42no—
133C2×C22⋊D43—42no—
134C22×Dic43—21no—
135C22×Dic43—22no—
136C22×Dic43C2×D411yescharacteristic
137C22×Dic43C2×D411yescharacteristic
138C22×Dic43C2×D411yescharacteristic
139#10621898—432no—
140C2×D172—21no—
141C2×D172—24no—
142C2×D172—22no—
143C2×D172—22no—
144C2×D172—42no—
145C2×D172—42no—
146C2×D172C22×C412yes—
147C2×C4×D43—22no—
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×C4×D43—22no—
151C2×C4×D43—24no—
152C2×C4×D43—42no—
153C2×C4×D43—42no—
154C2×C4×D43—42no—
155C2×C4×D43C22⋊C414yes—
156C2×C4×D43C22⋊C414yes—
157C2×C4×D43C22×C412yes—
158C2×C4×D43C2×D412yes—
159C2×Dic86—24no—
160C2×Dic86—42no—
161C2×Dic86—42no—
162C2×C8×C43—22no—
163C2×C8×C43—22no—
164C2×C8×C43#4114yescomplemented
165C4⋊C4×C43—21no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43C22×C412yes—
169C22⋊C4×C43—24no—
170C42×C43—42no—
171C42×C43C22×C412yes—
172C42×C43C2×D412yes—
173C22⋊Dic43—24no—
174(C2×D43)⋊C4—24no—
175(C2×D43)⋊C4—24no—
176(C2×D43)⋊C4—44no—
177C4⋊Dic43—21no—
178C4⋊Dic43—22no—
179C4⋊Dic43—22no—
180C4⋊Dic43C22×C412yes—
181Dic43⋊C4—24no—
182C4×Dic43—42no—
183C4×Dic43C22⋊C414yes—
184C4×Dic43C22⋊C414yes—
185C4×Dic43C22×C412yes—
186C4×Dic43C2×D412yes—
187C2×C43⋊C8—22no—
188C2×C43⋊C8—22no—
189C2×C43⋊C8#4114yescomplemented
190#10621872—216no—
191C23×C43—22no—
192C23×C43—42no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43—42no—
196C23×C43C22×D411yescharacteristic
197C22×D43—22no—
198C22×D43—21no—
199C22×D43—21no—
200C22×D43—22no—
201C22×D43—22no—
202C22×D43—42no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—42no—
206C22×D43C2×C22⋊C412yes—
207D4×C43—22no—
208D4×C43—22no—
209D4×C43—42no—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—48no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43C2×C22⋊C412yes—
219C2×C4×C43C2×C22⋊C412yes—
220C2×C4×C43AGL(1,ℤ/8)12yes—
221C2×C4×C43AGL(1,ℤ/8)12yes—
222C2×C4×C43C23×C411yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C2×#4112yes—
225C2×C4×C43C2×#4112yes—
226C22⋊D43—48no—
227C22⋊D43—48no—
228C22⋊D43—48no—
229C2×Dic43—22no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—22no—
233C2×Dic43—22no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—42no—
237C2×Dic43—42no—
238C2×Dic43—42no—
239C2×Dic43C2×C22⋊C412yes—
240C2×Dic43C2×C22⋊C412yes—
241C2×Dic43C2×C22⋊C412yes—
242D172—22no—
243D172—22no—
244D172—48no—
245D172—42no—
246C4×D43—22no—
247C4×D43—22no—
248C4×D43—24no—
249C4×D43—28no—
250C4×D43—44no—
251C4×D43—48no—
252Dic86—48no—
253C8×C43—24no—
254C43⋊C8—24no—
255#21405—431nomaximal, Sylow
256C22×C43—42no—
257C22×C43—42no—
258C22×C43—42no—
259C22×C43—82no—
260C22×C43—82no—
261C22×C43C22×C22⋊C411yescharacteristic
262C22×C43#53212yes—
263C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
264C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
265C22×C43#57512yes—
266C2×D43—22no—
267C2×D43—22no—
268C2×D43—22no—
269C2×D43—42no—
270C2×D43—42no—
271C2×D43—42no—
272C2×D43—42no—
273C2×D43—42no—
274C2×D43—82no—
275C2×D43—82no—
276C4×C43—22no—
277C4×C43—42no—
278C4×C43—82no—
279C4×C43#41814yes—
280C4×C43C4×#4111yescharacteristic
281C4×C43C4×#4111yescharacteristic
282C4×C43#52512yes—
283Dic43—22no—
284Dic43—22no—
285Dic43—22no—
286Dic43—42no—
287Dic43—82no—
288C2×#532—431no—
289C2×C4×M16—431no—
290#2283—431no—
291#1993—432no—
292#1961—432no—
293#1895—432no—
294#1895—432no—
295C4×#102—431no—
296C4×#102—431no—
297C4×#102—431no—
298C4×#102D4311yescharacteristic, complemented
299C2×C43—82no—
300C2×C43#229711yescharacteristic
301C2×C43C2×#41811yescharacteristic
302C2×C43#289611yescharacteristic
303C2×C43#317112yes—
304C2×C43#317112yes—
305D43—42no—
306D43—82no—
307C22×#41—861no—
308C22×M16—432no—
309#532—438no—
310#532—864no—
311C2×C4⋊Q8—431no—
312C2×#127—431no—
313C2×#124—861no—
314C2×#121—431no—
315C2×#121—431no—
316C2×#121—861no—
317C2×C4×D4—431no—
318C2×C4×D4—861no—
319C2×C4×D4C2×D4311yescharacteristic
320C22×C42—431no—
321C2×#102—432no—
322C2×#102—432no—
323C2×#102—432no—
324C2×#102C2×D4312yes—
325C4×M16—864no—
326C2×#97—432no—
327C2×C4×C8—431no—
328C2×C4×C8C2×D4311yescharacteristic
329#383—861no—
330#382—432no—
331#381—861no—
332#380—432no—
333C4×C4⋊C4—431no—
334C4×C4⋊C4C2×D4311yescharacteristic
335C4×C22⋊C4—861no—
336#376—861no—
337#340—432no—
338#340—432no—
339#340—432no—
340#340C2×D4312yes—
341C43#2140511yescharacteristic, complemented, Sylow
342C2×#41—868no—
343C2×#41—1724no—
344C2×#41—1724no—
345C22×Q8—861no—
346C22×D4—431no—
347C22×D4—861no—
348C22×D4—861no—
349C22×D4—861no—
350C22×D4—861no—
351C22×D4C22×D4311yescharacteristic
352C23×C4—21no—
353C23×C4—431no—
354C23×C4—431no—
355C23×C4—431no—
356C23×C4—861no—
357C2×M16—864no—
358C2×M16—864no—
359C2×M16—864no—
360C22×C8—432no—
361C22×C8C22×D4312yes—
362C4⋊Q8—434no—
363C4⋊Q8—862no—
364#127—434no—
365#127—862no—
366#124—868no—
367#121—434no—
368#121—434no—
369#121—868no—
370#121—862no—
371#121—862no—
372C4×D4—22no—
373C4×D4—434no—
374C4×D4—868no—
375C4×D4—862no—
376C4×D4C4×D4314yes—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—432no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4C22×D4312yes—
381C2×C4⋊C4C22×D4311yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—861no—
384C2×C22⋊C4—861no—
385C2×C22⋊C4—861no—
386C2×C22⋊C4—862no—
387C2×C42—21no—
388C2×C42—431no—
389C2×C42—431no—
390C2×C42—431no—
391C2×C42—434no—
392C2×C42—434no—
393C2×C42—861no—
394C2×C42C22×D4311yescharacteristic
395#102—24no—
396#102—864no—
397#102—864no—
398#102—864no—
399#97—864no—
400C4×C8—22no—
401C4×C8—862no—
402#95—21no—
403#95—862no—
404#95—862no—
405#95—862no—
406#95—861no—
407C24—21no—
408C24—431no—
409C24—861no—
410#41—17232no—
411C2×Q8—864no—
412C2×Q8—1722no—
413C2×Q8—1722no—
414C2×D4—21no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—432no—
418C2×D4—864no—
419C2×D4—864no—
420C2×D4—864no—
421C2×D4—864no—
422C2×D4—861no—
423C2×D4—862no—
424C2×D4—862no—
425C2×D4—1722no—
426C2×D4—1722no—
427C2×D4—1722no—
428C2×D4—1722no—
429C2×D4—1724no—
430C2×D4—1722no—
431C2×D4—1722no—
432C2×D4C2×C4×D4312yes—
433C22×C4—21no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—431no—
439C22×C4—431no—
440C22×C4—431no—
441C22×C4—434no—
442C22×C4—432no—
443C22×C4—432no—
444C22×C4—434no—
445C22×C4—862no—
446C22×C4—862no—
447C22×C4—862no—
448C22×C4—862no—
449C22×C4—861no—
450C22×C4—864no—
451C22×C4—862no—
452C22×C4—1722no—
453C22×C4—1722no—
454C22×C4—1722no—
455C22×C4D4×D4311yescharacteristic
456C22×C4D4×D4311yescharacteristic
457C22×C4C23×D4311yescharacteristic
458M16—8616no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—434no—
462C2×C8—862no—
463C2×C8—862no—
464C2×C8#1062189814yescomplemented
465C4⋊C4—21no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—432no—
469C4⋊C4—864no—
470C4⋊C4—861no—
471C4⋊C4—862no—
472C4⋊C4—862no—
473C4⋊C4C2×C4×D4312yes—
474C22⋊C4—24no—
475C22⋊C4—864no—
476C22⋊C4—864no—
477C22⋊C4—864no—
478C22⋊C4—1724no—
479C42—42no—
480C42—434no—
481C42—434no—
482C42—432no—
483C42—432no—
484C42—1722no—
485C42C2×C4×D4312yes—
486C42D4×D4312yes—
487C23—22no—
488C23—41no—
489C23—41no—
490C23—42no—
491C23—42no—
492C23—432no—
493C23—861no—
494C23—861no—
495C23—862no—
496C23—862no—
497C23—862no—
498C23—1721no—
499C23—1721no—
500C23—1722no—
501C23—1722no—
502C23C2×D4×D4311yescharacteristic
503Q8—1728no—
504D4—22no—
505D4—22no—
506D4—42no—
507D4—862no—
508D4—862no—
509D4—1728no—
510D4—1728no—
511D4—1728no—
512D4—1728no—
513D4—1722no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—48no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—432no—
523C2×C4—432no—
524C2×C4—432no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—862no—
528C2×C4—862no—
529C2×C4—862no—
530C2×C4—862no—
531C2×C4—864no—
532C2×C4—868no—
533C2×C4—862no—
534C2×C4—1724no—
535C2×C4—1722no—
536C2×C4—1722no—
537C2×C4—1722no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1728no—
541C2×C4C22⋊C4×D4312yes—
542C2×C4C22⋊C4×D4312yes—
543C2×C4#1306334912yes—
544C2×C4#1306335212yes—
545C2×C4C22×C4×D4311yescharacteristic
546C2×C4C2×D4×D4311yescharacteristic
547C2×C4#41×D4312yes—
548C2×C4C2×#1062189812yes—
549C8—24no—
550C8—864no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—82no—
555C22—82no—
556C22—862no—
557C22—862no—
558C22—862no—
559C22—3442no—
560C22—3442no—
561C22—1722no—
562C22—1722no—
563C22—1722no—
564C22—1722no—
565C22—1722no—
566C22C2×C22⋊C4×D4311yescharacteristic
567C22#1458344612yes—
568C22C2×#1306334911yescharacteristic
569C22C2×#1306335211yescharacteristic
570C22#1458369612yes—
571C4—22no—
572C4—42no—
573C4—82no—
574C4—862no—
575C4—862no—
576C4—862no—
577C4—3442no—
578C4—1722no—
579C4#1458290214yes—
580C4#1458336711yescharacteristic
581C4C4×#1062189811yescharacteristic
582C4#1458340812yes—
583C2—82no—
584C2—3442no—
585C2—1722no—
586C2#1913708111yescharacteristic
587C2C2×#1458290211yescharacteristic
588C2#1914311011yescharacteristic
589C2#1914518612yes—
590C2#1914518812yes—
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#102×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583446C2
cosocleC22×C4×C43C24
hypercenterC4×#102D43
hypocenterC43#21405
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621872C2semidirect
3. #19136991C2semidirect
4. #19135566C2semidirect
5. #19135417C2semidirect
6. #19135032C2semidirect
7. #19135030C2semidirect
8. C4×#13063245C2semidirect
9. C4×#13063247C2semidirect
10. C4×#13063246C2semidirect
11. C4×#102×C43C2semidirect
15. #14583446C4semidirect
164. C2×C8×C43#41semidirect
189. C2×C43⋊C8#41semidirect
298. C4×#102D43semidirect
341. C43#21405semidirect
464. C2×C8#10621898semidirect

Maximal subgroups

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

subgroupindex
C2×#145834462
C2×C4×#106218722
#191369912
#191355662
#191354172
#191350322
#191350302
C4×#130632452
C4×#130632472
C4×#130632462
C4×#102×C432
#2140543