Finite Group Databasebeta

← #25101917

Subgroups — #25101917

Order 11008.

1170 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
1#19147887C211yesmaximal, characteristic
2#19143224C211yesmaximal, characteristic, complemented
3#117×Dic43C211yesmaximal, characteristic, complemented
4#19135570C212yesmaximal, complemented
5#19135421C212yesmaximal, complemented
6#19135044C211yesmaximal, characteristic, complemented
7#19135043C211yesmaximal, characteristic, complemented
8#19135041C211yesmaximal, characteristic, complemented
9#19134407C212yesmaximal, complemented
10#19134404C212yesmaximal, complemented
11C43×#1897C211yesmaximal, characteristic, complemented
12#14583452C2211yescharacteristic
13#14583451C412yescomplemented
14#14583445C2211yescharacteristic
15#14583444C412yescomplemented
16#14583435C412yescomplemented
17#14583430C412yescomplemented
18#14583429—22no—
19#14583426—22no—
20#14583410C2211yescharacteristic
21#14583405—22no—
22#41×Dic43C2211yescharacteristic
23#14583367C2211yescharacteristic
24C4×#10621900—22no—
25C2×#13063284C2211yescharacteristic
26C22×C4×Dic43C2211yescharacteristic
27#14582953—22no—
28#14582949—22no—
29#14582922C2212yes—
30C2×#13063253C2212yes—
31C2×#13063252C2212yes—
32C2×#13063251C2212yes—
33#14582863C2211yescharacteristic
34M16×Dic43C2212yes—
35C4⋊C4×Dic43—22no—
36C22⋊C4×Dic43—22no—
37#14582745C2212yes—
38C42×Dic43C2212yes—
39#14582660C2212yes—
40#14582659C2212yes—
41#14582658C2212yes—
42C43×#525C2211yescharacteristic
43C2×#117×C43C2211yescharacteristic
44C2×#104×C43C2212yes—
45C43×#407C2211yescharacteristic
46C43×#339C2212yes—
47C2×#10621898C2311yescharacteristic
48C2×#10621900—22no—
49C23×Dic43D412yes—
50C2×#10621877C2312yes—
51#13063324C2×C412yes—
52#13063323C2×C411yescharacteristic
53#13063321C2×C411yescharacteristic
54#13063320—22no—
55#13063318—22no—
56#13063316C2×C412yes—
57#13063315—22no—
58#13063314C2×C411yescharacteristic
59#13063312C2×C411yescharacteristic
60#13063311—22no—
61#13063309—22no—
62#13063308—21no—
63#13063306—22no—
64#13063304C2×C412yes—
65#13063302—22no—
66#13063302—22no—
67#13063299C2×C412yes—
68#13063297—22no—
69#13063297—22no—
70#13063294—21no—
71Q8×Dic43C2×C412yes—
72C4×Dic86—22no—
73#13063290—22no—
74#13063290C2×C412yes—
75D4×Dic43—22no—
76D4×Dic43—22no—
77D4×Dic43C2×C412yes—
78#13063287C2×C412yes—
79C4×C22⋊D43—22no—
80C4×C22⋊D43—22no—
81(C22⋊D43)⋊C4—22no—
82(C22⋊D43)⋊C4—22no—
83(C22⋊D43)⋊C4—22no—
84#13063284—21no—
85#13063284—24no—
86#13063284C2311yescharacteristic
87#13063283—22no—
88#13063282—21no—
89#13063281—22no—
90#13063281—22no—
91C2×C4⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—24no—
95C2×C4×Dic43C2×C412yes—
96C2×C4×Dic43C2×C412yes—
97C2×C4×Dic43D412yes—
98C2×C4×Dic43D412yes—
99C2×C4×Dic43D412yes—
100C2×C4×Dic43C2312yes—
101C2×C4×Dic43C2311yescharacteristic
102C2×C4×Dic43C2311yescharacteristic
103C42×D43—21no—
104Dic43⋊C8—24no—
105#13063253—24no—
106#13063252—24no—
107#13063251—24no—
108C22⋊(C43⋊C8)—22no—
109#13063235—22no—
110C8×Dic43—22no—
111C43⋊#95—24no—
112C2×#41×C43C2311yescharacteristic
113C23×C4×C43C2311yescharacteristic
114C2×M16×C43C2312yes—
115#123×C43—21no—
116C22⋊Q8×C43C2×C412yes—
117#121×C43C2×C412yes—
118#120×C43—21no—
119C4×D4×C43—22no—
120#117×C43—24no—
121#117×C43C2311yescharacteristic
122C2×C4⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C42×C43C2312yes—
125#104×C43—24no—
126C22⋊C8×C43—22no—
127C24×C43C2×D411yescharacteristic
128#41×C43—22no—
129#41×C43—22no—
130C2×Q8×C43C22×C411yescharacteristic
131C2×D4×C43—22no—
132C2×D4×C43—21no—
133C2×D4×C43C22×C411yescharacteristic
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—21no—
137C22×C4×C43—22no—
138C22×C4×C43C22×C412yes—
139C22×C4×C43C2×D412yes—
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2411yescharacteristic
142C2×C22⋊D43—22no—
143C2×C22⋊D43—22no—
144C2×C22⋊D43—21no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—44no—
148C22×Dic43C22⋊C412yes—
149C22×Dic43C22⋊C412yes—
150C22×Dic43C22⋊C412yes—
151C22×Dic43C22⋊C412yes—
152C22×Dic43C2×D412yes—
153C22×Dic43C2×D412yes—
154#10621900—48no—
155#10621898—22no—
156#10621898—22no—
157C2×D172C22×C411yescharacteristic
158C2×C4×D43—21no—
159C2×C4×D43—22no—
160C2×Dic86—22no—
161C2×Dic86C22×C411yescharacteristic
162M16×C43—22no—
163M16×C43—22no—
164C2×C8×C43—22no—
165C4⋊C4×C43—24no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43C22×C412yes—
168C22⋊C4×C43—24no—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—21no—
172C42×C43—21no—
173C42×C43—22no—
174C42×C43#4114yescomplemented
175C22⋊Dic43—24no—
176C22⋊Dic43—22no—
177C22⋊Dic43—22no—
178C22⋊Dic43—22no—
179C22⋊Dic43—21no—
180(C2×D43)⋊C4—22no—
181(C2×D43)⋊C4—22no—
182(C2×D43)⋊C4—22no—
183C4⋊Dic43—24no—
184C4⋊Dic43—22no—
185C4⋊Dic43—22no—
186C4⋊Dic43C22×C412yes—
187Dic43⋊C4—22no—
188Dic43⋊C4—22no—
189Dic43⋊C4—22no—
190Dic43⋊C4—22no—
191Dic43⋊C4—22no—
192C4×Dic43—21no—
193C4×Dic43—22no—
194C4×Dic43—22no—
195C4×Dic43—22no—
196C4×Dic43—48no—
197C4×Dic43C22⋊C412yes—
198C4×Dic43C22⋊C412yes—
199C4×Dic43C22⋊C412yes—
200C4×Dic43C22⋊C412yes—
201C4×Dic43C22×C412yes—
202C4×Dic43C22×C411yescharacteristic
203C4×Dic43C22×C411yescharacteristic
204C4×Dic43C2×D411yescharacteristic
205C4×Dic43C2×D411yescharacteristic
206C4×Dic43C2×D412yes—
207C4×Dic43#4114yescomplemented
208#10621877—22no—
209#10621877—22no—
210C2×C43⋊C8—22no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—42no—
215C23×C43C2×C22⋊C412yes—
216C23×C43C22×D411yescharacteristic
217C22×D43—21no—
218Q8×C43—22no—
219D4×C43—22no—
220D4×C43—44no—
221D4×C43—41no—
222D4×C43—41no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—24no—
226C2×C4×C43—24no—
227C2×C4×C43—21no—
228C2×C4×C43—22no—
229C2×C4×C43—24no—
230C2×C4×C43—44no—
231C2×C4×C43—42no—
232C2×C4×C43C2×C22⋊C412yes—
233C2×C4×C43C23×C411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C2×#4112yes—
236C2×C4×C43C2×#4112yes—
237C22⋊D43—44no—
238C22⋊D43—41no—
239C22⋊D43—41no—
240C22⋊D43—44no—
241C2×Dic43—24no—
242C2×Dic43—24no—
243C2×Dic43—24no—
244C2×Dic43—21no—
245C2×Dic43—22no—
246C2×Dic43—24no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249C2×Dic43—42no—
250C2×Dic43—44no—
251C2×Dic43—44no—
252C2×Dic43C2×C22⋊C412yes—
253C2×Dic43C2×C22⋊C412yes—
254C2×Dic43C2×C22⋊C412yes—
255C2×Dic43C2×C22⋊C412yes—
256D172—22no—
257C4×D43—44no—
258C4×D43—42no—
259Dic86—22no—
260Dic86—44no—
261C8×C43—42no—
262C43⋊C8—42no—
263#21418—431nomaximal, Sylow
264C22×C43—22no—
265C22×C43—22no—
266C22×C43—22no—
267C22×C43—22no—
268C22×C43—42no—
269C22×C43—42no—
270C22×C43—42no—
271C22×C43—41no—
272C22×C43C22×C22⋊C411yescharacteristic
273C22×C43#52511yescharacteristic
274C22×C43#52511yescharacteristic
275C2×D43—42no—
276C2×D43—41no—
277C4×C43—22no—
278C4×C43—44no—
279C4×C43—42no—
280C4×C43—41no—
281C4×C43C4×#4112yes—
282C4×C43#53212yes—
283Dic43—22no—
284Dic43—22no—
285Dic43—22no—
286Dic43—44no—
287Dic43—42no—
288Dic43—41no—
289Dic43#42114yes—
290#3444—431no—
291#2920—431no—
292C4×#117—431no—
293#1994—432no—
294#1962—432no—
295#1897—431no—
296#1897—431no—
297#1897—431no—
298#1897D4311yescharacteristic, complemented
299#1759—432no—
300#1759—432no—
301C2×C43—21no—
302C2×C43—21no—
303C2×C43—42no—
304C2×C43—81no—
305C2×C43#229711yescharacteristic
306C2×C43C2×#42112yes—
307D43—81no—
308#533—431no—
309#533—432no—
310#532—432no—
311#532—431no—
312#529—432no—
313#529—432no—
314#529—862no—
315#529—862no—
316#525—431no—
317#525—862no—
318#525C2×D4311yescharacteristic
319C4×#41—431no—
320C4×#41—431no—
321C4×#41—862no—
322C2×#117—431no—
323C2×#117C2×D4311yescharacteristic
324C22×C42—431no—
325#432—862no—
326#431—862no—
327#423—432no—
328C2×#104—432no—
329C2×#104—432no—
330C2×#104—432no—
331C2×#104C2×D4312yes—
332#407—431no—
333#407C2×D4311yescharacteristic
334C4×M16—432no—
335C4×C4⋊C4—862no—
336C4×C22⋊C4—862no—
337#376—432no—
338C43—432no—
339#339—432no—
340#339—432no—
341#339—432no—
342#339C2×D4312yes—
343C43#2141811yescharacteristic, complemented, Sylow
344C2×#41—431no—
345C2×#41—862no—
346C2×#41C22×D4311yescharacteristic
347C23×C4—432no—
348C23×C4C22×D4311yescharacteristic
349C2×M16—432no—
350C2×M16C22×D4312yes—
351C4⋊Q8—432no—
352C4⋊Q8—431no—
353#127—431no—
354#126—862no—
355#126—862no—
356#125—432no—
357#125—862no—
358#124—431no—
359#124—431no—
360#124—862no—
361#123—21no—
362#123—862no—
363#123—862no—
364#123—861no—
365C22⋊Q8—432no—
366C22⋊Q8—862no—
367C22⋊Q8—862no—
368C22⋊Q8C4×D4312yes—
369#121—432no—
370#121—862no—
371#121—862no—
372#121C4×D4312yes—
373#120—21no—
374#120—861no—
375C4×Q8—432no—
376C4×Q8—432no—
377C4×Q8—862no—
378C4×Q8—862no—
379C4×D4—22no—
380C4×D4—432no—
381C4×D4—432no—
382C4×D4—862no—
383C4×D4—862no—
384C4×D4—862no—
385C4×D4—862no—
386C4×D4—862no—
387C4×D4—862no—
388C4×D4—862no—
389#117—24no—
390#117—431no—
391#117—861no—
392#117—862no—
393#117—862no—
394#117—864no—
395#117—861no—
396#117—862no—
397#117C22×D4311yescharacteristic
398C2×C4⋊C4—21no—
399C2×C4⋊C4—861no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—861no—
402C2×C42—432no—
403C2×C42—432no—
404C2×C42—432no—
405C2×C42—432no—
406C2×C42—432no—
407C2×C42—431no—
408C2×C42—431no—
409C2×C42—432no—
410C2×C42—861no—
411C2×C42—861no—
412C2×C42—864no—
413C2×C42C22×D4312yes—
414C4⋊C8—864no—
415#104—24no—
416#104—864no—
417#104—864no—
418#104—864no—
419C22⋊C8—22no—
420C22⋊C8—862no—
421#97—862no—
422C4×C8—862no—
423#95—864no—
424C24D4×D4311yescharacteristic
425#41—22no—
426#41—22no—
427#41—862no—
428#41—862no—
429#41—1728no—
430C2×Q8—431no—
431C2×Q8—862no—
432C2×Q8C2×C4×D4311yescharacteristic
433C2×D4—22no—
434C2×D4—21no—
435C2×D4—431no—
436C2×D4—862no—
437C2×D4—862no—
438C2×D4—861no—
439C2×D4C2×C4×D4311yescharacteristic
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—432no—
445C22×C4—432no—
446C22×C4—432no—
447C22×C4—432no—
448C22×C4—432no—
449C22×C4—432no—
450C22×C4—862no—
451C22×C4—862no—
452C22×C4—862no—
453C22×C4—861no—
454C22×C4—1724no—
455C22×C4C2×C4×D4312yes—
456C22×C4D4×D4311yescharacteristic
457C22×C4D4×D4312yes—
458C22×C4C23×D4311yescharacteristic
459M16—22no—
460M16—22no—
461M16—862no—
462M16—862no—
463C2×C8—22no—
464C2×C8—862no—
465C4⋊C4—24no—
466C4⋊C4—22no—
467C4⋊C4—432no—
468C4⋊C4—862no—
469C4⋊C4—862no—
470C4⋊C4—862no—
471C4⋊C4—862no—
472C4⋊C4—862no—
473C4⋊C4—862no—
474C4⋊C4—864no—
475C4⋊C4—862no—
476C4⋊C4C2×C4×D4312yes—
477C22⋊C4—24no—
478C22⋊C4—22no—
479C22⋊C4—21no—
480C22⋊C4—22no—
481C22⋊C4—862no—
482C22⋊C4—862no—
483C22⋊C4—862no—
484C22⋊C4—862no—
485C22⋊C4—864no—
486C22⋊C4—862no—
487C22⋊C4—861no—
488C22⋊C4—862no—
489C42—21no—
490C42—22no—
491C42—432no—
492C42—432no—
493C42—432no—
494C42—432no—
495C42—432no—
496C42—431no—
497C42—431no—
498C42—431no—
499C42—431no—
500C42—432no—
501C42—434no—
502C42—862no—
503C42—862no—
504C42—861no—
505C42—862no—
506C42—1728no—
507C42#1062190014yescomplemented
508C23—21no—
509C23—21no—
510C23—21no—
511C23—42no—
512C23—861no—
513C23C22⋊C4×D4312yes—
514C23C2×D4×D4311yescharacteristic
515Q8—22no—
516Q8—862no—
517Q8—1724no—
518D4—22no—
519D4—44no—
520D4—41no—
521D4—41no—
522D4—862no—
523D4—1724no—
524D4—1724no—
525D4—1721no—
526D4—1721no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—24no—
534C2×C4—44no—
535C2×C4—42no—
536C2×C4—432no—
537C2×C4—432no—
538C2×C4—432no—
539C2×C4—432no—
540C2×C4—864no—
541C2×C4—864no—
542C2×C4—864no—
543C2×C4—862no—
544C2×C4—861no—
545C2×C4—864no—
546C2×C4—1724no—
547C2×C4—1722no—
548C2×C4—1722no—
549C2×C4—1722no—
550C2×C4—1724no—
551C2×C4—1724no—
552C2×C4—1722no—
553C2×C4C22⋊C4×D4312yes—
554C2×C4C22×C4×D4311yescharacteristic
555C2×C4C2×D4×D4311yescharacteristic
556C2×C4#41×D4312yes—
557C2×C4C2×#1062190012yes—
558C8—42no—
559C8—1722no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—42no—
565C22—42no—
566C22—41no—
567C22—42no—
568C22—1721no—
569C22—1722no—
570C22C2×C22⋊C4×D4311yescharacteristic
571C22#1458340511yescharacteristic
572C22#1458340711yescharacteristic
573C4—22no—
574C4—44no—
575C4—41no—
576C4—42no—
577C4—434no—
578C4—862no—
579C4—862no—
580C4—862no—
581C4—1724no—
582C4—1721no—
583C4—1722no—
584C4C4×#1062190012yes—
585C4#1458344412yes—
586C2—21no—
587C2—21no—
588C2—42no—
589C2—81no—
590C2—3441no—
591C2#1913708011yescharacteristic
592C2#421×D4312yes—
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1897C2
socleC22×C43C22×C22⋊C4
prime radical#19147887C2
cosocleC22×C4×C43C24
hypercenter#1897D43
hypocenterC43#21418
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1897

Complements

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

NH ≅ G/Ntype
2. #19143224C2semidirect
3. #117×Dic43C2semidirect
4. #19135570C2semidirect
5. #19135421C2semidirect
6. #19135044C2semidirect
7. #19135043C2semidirect
8. #19135041C2semidirect
9. #19134407C2semidirect
10. #19134404C2semidirect
11. C43×#1897C2semidirect
13. #14583451C4semidirect
15. #14583444C4semidirect
16. #14583435C4semidirect
17. #14583430C4semidirect
174. C42×C43#41semidirect
207. C4×Dic43#41semidirect
298. #1897D43semidirect
343. C43#21418semidirect
507. C42#10621900semidirect

Maximal subgroups

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

subgroupindex
#191478872
#191432242
#117×Dic432
#191355702
#191354212
#191350442
#191350432
#191350412
#191344072
#191344042
C43×#18972
#2141843