Finite Group Databasebeta

← #25063624

Subgroups — #25063624

Order 11008.

1008 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148203C211yesmaximal, characteristic
2#19143725C211yesmaximal, characteristic, complemented
3#19143237C211yesmaximal, characteristic, complemented
4#19133057C212yesmaximal, complemented
5#19133032C211yesmaximal, characteristic, complemented
6#19133018C212yesmaximal, complemented
7#19133012C211yesmaximal, characteristic, complemented
8#19133000C212yesmaximal, complemented
9#19132984C212yesmaximal, complemented
10#19132978C211yesmaximal, characteristic, complemented
11C43×#1492C211yesmaximal, characteristic, complemented
12#14583635C411yescharacteristic
13#14583610C411yescharacteristic
14#14583610C411yescharacteristic
15#14583596—21no—
16#14583596C412yes—
17#14583579—22no—
18#14583546—21no—
19#14583546C412yes—
20#14583534C411yescharacteristic
21#14583431—21no—
22#14583431C2212yes—
23#14583406—22no—
24C4×#10621898C2211yescharacteristic
25C4×#10621898C2211yescharacteristic
26C4×D4×D43—21no—
27C4×D4×D43C2212yes—
28#14583023—21no—
29#14582976—21no—
30#14582975—22no—
31#14582958—22no—
32#14582952C2211yescharacteristic, complemented
33#14582951C2212yescomplemented
34#14582950C2212yescomplemented
35#14582950C2212yescomplemented
36#14582925—21no—
37#14582921C2212yescomplemented
38#14582865—21no—
39C4×#10621877C2211yescharacteristic, complemented
40#14582631C2211yescharacteristic, complemented
41#14582631C2211yescharacteristic, complemented
42#14582629C2212yescomplemented
43#14582628C2211yescharacteristic
44#14582628C2211yescharacteristic
45D4⋊(C43⋊C8)C2212yescomplemented
46D4⋊(C43⋊C8)C2212yescomplemented
47#14582626C2212yes—
48C43×#532C2211yescharacteristic
49C43×#423C2211yescharacteristic, complemented
50C2×C4×C8×C43C2211yescharacteristic, complemented
51C43×D4⋊C8C2212yescomplemented
52C43×D4⋊C8C2212yescomplemented
53C2×#10621898C2×C411yescharacteristic
54C2×#10621898D411yescharacteristic
55C2×D4×D43—21no—
56C2×D4×D43C2×C412yes—
57C22×C4×D43—22no—
58C2×#10621877—21no—
59C2×#10621872—22no—
60#13063318—22no—
61#13063318—22no—
62#13063316—21no—
63#13063316C2×C412yes—
64#13063312—21no—
65#13063312C2×C412yes—
66#13063307—22no—
67#13063307—22no—
68#13063306—22no—
69#13063306—22no—
70#13063305—21no—
71#13063305C2×C412yes—
72#13063301—22no—
73#13063301—22no—
74#13063296—22no—
75#13063296—22no—
76#13063296—21no—
77#13063296C2×C412yes—
78#13063293—22no—
79#13063293—22no—
80C4×Dic86C2×C411yescharacteristic
81C4×Dic86C2×C411yescharacteristic
82C4×Dic86D411yescharacteristic
83C4×Dic86C2311yescharacteristic
84C4×D172C2×C411yescharacteristic
85C4×D172C2×C411yescharacteristic
86C4×D172D411yescharacteristic
87C4×D172C2311yescharacteristic
88D4×Dic43—21no—
89D4×Dic43C2×C412yes—
90#13063287—21no—
91#13063287C2×C412yes—
92C4×C22⋊D43—21no—
93C4×C22⋊D43—21no—
94C4×C22⋊D43—22no—
95C4×C22⋊D43—22no—
96C4×C22⋊D43C2×C412yes—
97C4×C22⋊D43D412yes—
98(C22⋊D43)⋊C4—22no—
99(C22⋊D43)⋊C4—22no—
100#13063284—22no—
101#13063284C2×C411yescharacteristic
102#13063284D411yescharacteristic
103#13063282—21no—
104#13063282D412yes—
105C4⋊C4×D43—21no—
106C4⋊C4×D43C2×C412yes—
107C22⋊C4×D43—22no—
108C22⋊C4×D43—22no—
109C42×D43—21no—
110C42×D43C2312yes—
111C4⋊(C43⋊C8)C2311yescharacteristic
112C4⋊(C43⋊C8)C2311yescharacteristic
113Dic43⋊C8—22no—
114Dic43⋊C8—22no—
115Dic43⋊C8—22no—
116C22⋊(C43⋊C8)—21no—
117(C2×D43)⋊C8—22no—
118(C2×D43)⋊C8—22no—
119(C2×D43)⋊C8—22no—
120#13063236—21no—
121C4×C43⋊C8—21no—
122C4×C43⋊C8C2312yes—
123C8×Dic43—22no—
124C2×#41×C43—21no—
125C2×M16×C43—21no—
126C22×C8×C43—21no—
127C4⋊Q8×C43C2×C411yescharacteristic
128#127×C43C2×C411yescharacteristic
129#124×C43—21no—
130#121×C43—21no—
131#121×C43C2×C412yes—
132C4×D4×C43—21no—
133C4×D4×C43C2312yes—
134C2×C42×C43C2311yescharacteristic
135C4⋊C8×C43—21no—
136C4⋊C8×C43C2312yes—
137C4×C8×C43—21no—
138C4×C8×C43C2311yescharacteristic
139C4×C8×C43C2311yescharacteristic
140C23×D43—22no—
141#41×C43—81no—
142#41×C43—81no—
143C2×Q8×C43—21no—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—22no—
147C2×D4×C43C22×C412yes—
148C22×C4×C43—22no—
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C2×C22⋊D43—22no—
153C2×C22⋊D43—21no—
154C2×C22⋊D43—22no—
155C2×C22⋊D43C22⋊C412yes—
156C22×Dic43—22no—
157D4×D43—24no—
158D4×D43—42no—
159D4×D43—44no—
160#10621898—22no—
161#10621898—41no—
162#10621898—42no—
163C2×D172C22⋊C411yescharacteristic
164C2×D172C22×C411yescharacteristic
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—82no—
171C2×C4×D43—82no—
172C2×C4×D43C22×C412yes—
173C2×C4×D43C2×D412yes—
174C2×C4×D43C2×D412yes—
175C2×Dic86C22⋊C411yescharacteristic
176C2×Dic86C22×C411yescharacteristic
177M16×C43—81no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43—22no—
181C2×C8×C43—42no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43C22×C412yes—
184C22⋊C4×C43—22no—
185C22⋊C4×C43—22no—
186C42×C43C22×C411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43C2411yescharacteristic
190C22⋊Dic43—22no—
191C22⋊Dic43—22no—
192C22⋊Dic43—22no—
193C22⋊Dic43—22no—
194C22⋊Dic43—21no—
195C22⋊Dic43C22⋊C412yes—
196(C2×D43)⋊C4—21no—
197(C2×D43)⋊C4—21no—
198(C2×D43)⋊C4—22no—
199(C2×D43)⋊C4—22no—
200(C2×D43)⋊C4C22⋊C412yes—
201(C2×D43)⋊C4C22⋊C412yes—
202C4⋊Dic43—22no—
203C4⋊Dic43—22no—
204C4⋊Dic43C22⋊C411yescharacteristic
205C4⋊Dic43C22⋊C411yescharacteristic
206C4⋊Dic43C22×C411yescharacteristic
207C4⋊Dic43C22×C411yescharacteristic
208Dic43⋊C4—21no—
209Dic43⋊C4—21no—
210Dic43⋊C4—22no—
211Dic43⋊C4—22no—
212Dic43⋊C4C22⋊C412yes—
213Dic43⋊C4C22⋊C412yes—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—21no—
217C4×Dic43C22×C412yes—
218C4×Dic43C2×D412yes—
219C4×Dic43C2×D412yes—
220#10621877—42no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—22no—
224#10621872—82no—
225C23×C43—22no—
226C23×C43C2×C22⋊C411yescharacteristic
227C22×D43—21no—
228C22×D43—44no—
229C22×D43—44no—
230C22×D43—82no—
231C22×D43C2×C22⋊C412yes—
232Q8×C43—81no—
233D4×C43—22no—
234D4×C43—22no—
235D4×C43—42no—
236D4×C43—81no—
237D4×C43—82no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×C4×C43C2×C22⋊C411yescharacteristic
247C2×C4×C43C2×C22⋊C411yescharacteristic
248C2×C4×C43C2×C22⋊C411yescharacteristic
249C2×C4×C43C23×C411yescharacteristic
250C2×C4×C43C22×D411yescharacteristic
251C2×C4×C43C22×D411yescharacteristic
252C22⋊D43—42no—
253C22⋊D43—44no—
254C22⋊D43—42no—
255C22⋊D43—44no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—82no—
260C2×Dic43C2×C22⋊C412yes—
261C2×Dic43C2×C22⋊C412yes—
262C2×Dic43C2×C22⋊C412yes—
263D172—21no—
264D172—22no—
265D172#13112yes—
266C4×D43—22no—
267C4×D43—22no—
268C4×D43—22no—
269C4×D43—22no—
270C4×D43—42no—
271C4×D43—42no—
272C4×D43—41no—
273C4×D43—41no—
274C4×D43—42no—
275C4×D43—82no—
276C4×D43—82no—
277Dic86—22no—
278Dic86—21no—
279Dic86—21no—
280C8×C43—41no—
281C8×C43—41no—
282C8×C43—42no—
283C43⋊C8—42no—
284C43⋊C8—41no—
285C43⋊C8—41no—
286#17522—431nomaximal, Sylow
287C22×C43—21no—
288C22×C43—21no—
289C22×C43—21no—
290C22×C43—42no—
291C22×C43—42no—
292C22×C43—42no—
293C22×C43C22×C22⋊C411yescharacteristic
294C2×D43—22no—
295C2×D43—22no—
296C2×D43—22no—
297C2×D43—22no—
298C2×D43—41no—
299C2×D43—41no—
300C2×D43—88no—
301C4×C43—21no—
302C4×C43—21no—
303C4×C43—21no—
304C4×C43—42no—
305C4×C43#42112yes—
306C4×C43C2×#13111yescharacteristic
307C4×C43#56811yescharacteristic
308C4×C43#57611yescharacteristic
309C4×C43#57711yescharacteristic
310Dic43—22no—
311Dic43—22no—
312Dic43—22no—
313Dic43—41no—
314Dic43—41no—
315Dic43—41no—
316#3481—431no—
317#2991—431no—
318#2922—431no—
319#1495—432no—
320#1492D4311yescharacteristic, complemented
321#1489—431no—
322#1486—432no—
323#1484—431no—
324#1482—432no—
325#1478—432no—
326#1476—431no—
327C2×C43—41no—
328C2×C43—82no—
329C2×C43#288011yescharacteristic
330C2×C43#289711yescharacteristic
331C2×C43C2×#42111yescharacteristic
332D43—42no—
333D43—42no—
334#559—431no—
335#554—431no—
336#554—431no—
337#553—432no—
338#553—861no—
339#551—862no—
340#546—432no—
341#546—861no—
342D42—431no—
343#532C2×D4311yescharacteristic
344#529—432no—
345#529—861no—
346#525—862no—
347C4×#41—431no—
348C4×#41—431no—
349C2×C4×D4—432no—
350C2×C4×D4—861no—
351C8×Q8—861no—
352#436—861no—
353#436—862no—
354#433—862no—
355#431—432no—
356#431—432no—
357#431—431no—
358#431—432no—
359#424—861no—
360#423—432no—
361#423C2×D4311yescharacteristic, complemented
362#408—861no—
363C4×M16—431no—
364C2×C4×C8C2×D4311yescharacteristic, complemented
365Q8⋊C8—432no—
366Q8⋊C8—431no—
367Q8⋊C8—431no—
368D4⋊C8—432no—
369D4⋊C8—432no—
370D4⋊C8—432no—
371D4⋊C8—431no—
372D4⋊C8—431no—
373D4⋊C8C2×D4312yescomplemented
374D4⋊C8C2×D4312yescomplemented
375C43#1752211yescharacteristic, complemented, Sylow
376C2×#41—21no—
377C2×#41—431no—
378C2×#41—431no—
379C22×D4—432no—
380C22×D4—861no—
381C23×C4—862no—
382C2×M16—21no—
383C2×M16—862no—
384C2×M16—861no—
385C22×C8—21no—
386C4⋊Q8C4×D4311yescharacteristic
387#127C4×D4311yescharacteristic
388#126—862no—
389#126—862no—
390#125—432no—
391#125—861no—
392#124—21no—
393#124—432no—
394#124—861no—
395#123—862no—
396#123—862no—
397#123—862no—
398#123—862no—
399C22⋊Q8—432no—
400C22⋊Q8—862no—
401C22⋊Q8—861no—
402C22⋊Q8—862no—
403#121—21no—
404#121—432no—
405#121—862no—
406#121—861no—
407#121—862no—
408#121C4×D4312yes—
409#120—862no—
410#120—862no—
411C4×Q8—431no—
412C4×Q8—431no—
413C4×Q8—431no—
414C4×Q8—431no—
415C4×D4—21no—
416C4×D4—432no—
417C4×D4—432no—
418C4×D4—432no—
419C4×D4—432no—
420C4×D4—431no—
421C4×D4—431no—
422C4×D4—431no—
423C4×D4—431no—
424C4×D4—862no—
425C4×D4—862no—
426C4×D4—862no—
427C4×D4—861no—
428C4×D4—861no—
429C4×D4—862no—
430C4×D4—861no—
431C4×D4—861no—
432C4×D4C22×D4312yes—
433#117—431no—
434#117—432no—
435#117—431no—
436#117—862no—
437#117—861no—
438C2×C4⋊C4—432no—
439C2×C4⋊C4—861no—
440C2×C22⋊C4—862no—
441C2×C22⋊C4—862no—
442C2×C42—432no—
443C2×C42—861no—
444C2×C42C22×D4311yescharacteristic
445C4⋊C8—21no—
446C4⋊C8—431no—
447C4⋊C8—431no—
448C4⋊C8—862no—
449C4⋊C8—862no—
450C4⋊C8—862no—
451C4⋊C8C22×D4312yes—
452C22⋊C8—862no—
453C22⋊C8—862no—
454C22⋊C8—862no—
455C22⋊C8—861no—
456#97—861no—
457C4×C8—21no—
458C4×C8—432no—
459C4×C8—862no—
460C4×C8—861no—
461C4×C8C22×D4311yescharacteristic
462C4×C8C22×D4311yescharacteristic
463C24—862no—
464#41—81no—
465#41—81no—
466#41—862no—
467#41—1721no—
468#41—1722no—
469C2×Q8—21no—
470C2×Q8—431no—
471C2×Q8—431no—
472C2×D4—22no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—432no—
476C2×D4—431no—
477C2×D4—431no—
478C2×D4—862no—
479C2×D4—864no—
480C2×D4—862no—
481C2×D4—861no—
482C2×D4—1722no—
483C2×D4—1724no—
484C2×D4C2×C4×D4312yes—
485C22×C4—22no—
486C22×C4—432no—
487C22×C4—432no—
488C22×C4—432no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—3442no—
496C22×C4—3442no—
497C22×C4C2×C4×D4311yescharacteristic
498C22×C4D4×D4311yescharacteristic
499C22×C4D4×D4311yescharacteristic
500M16—81no—
501M16—3442no—
502M16—1722no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—22no—
506C2×C8—42no—
507C2×C8—862no—
508C2×C8—861no—
509C2×C8—861no—
510C4⋊C4—21no—
511C4⋊C4—431no—
512C4⋊C4—431no—
513C4⋊C4—432no—
514C4⋊C4—432no—
515C4⋊C4—431no—
516C4⋊C4—431no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—862no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4C2×C4×D4312yes—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—432no—
527C22⋊C4—432no—
528C22⋊C4—432no—
529C22⋊C4—862no—
530C22⋊C4—862no—
531C22⋊C4—862no—
532C22⋊C4—862no—
533C22⋊C4—862no—
534C22⋊C4—862no—
535C22⋊C4—861no—
536C22⋊C4—861no—
537C22⋊C4—861no—
538C42—432no—
539C42—432no—
540C42—432no—
541C42—861no—
542C42—861no—
543C42—861no—
544C42C2×C4×D4311yescharacteristic
545C42D4×D4311yescharacteristic
546C42D4×D4311yescharacteristic
547C42C23×D4311yescharacteristic
548C23—22no—
549C23—432no—
550C23—861no—
551C23—3442no—
552C23—1724no—
553C23—1724no—
554C23C22⋊C4×D4311yescharacteristic
555Q8—81no—
556Q8—862no—
557Q8—861no—
558Q8—861no—
559D4—22no—
560D4—22no—
561D4—42no—
562D4—81no—
563D4—82no—
564D4—432no—
565D4—861no—
566D4—862no—
567D4—1722no—
568D4—1724no—
569D4—1722no—
570D4—1724no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—432no—
580C2×C4—432no—
581C2×C4—432no—
582C2×C4—862no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—3442no—
590C2×C4—3442no—
591C2×C4—3442no—
592C2×C4—1722no—
593C2×C4—1722no—
594C2×C4—1722no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4C22⋊C4×D4311yescharacteristic
598C2×C4C22⋊C4×D4311yescharacteristic
599C2×C4C22⋊C4×D4311yescharacteristic
600C2×C4C22×C4×D4311yescharacteristic
601C2×C4C2×D4×D4311yescharacteristic
602C2×C4C2×D4×D4311yescharacteristic
603C8—41no—
604C8—41no—
605C8—42no—
606C8—1722no—
607C8—1721no—
608C8—1721no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—862no—
616C22—862no—
617C22—862no—
618C22—862no—
619C22—3448no—
620C22—1721no—
621C22—1721no—
622C22C2×C22⋊C4×D4311yescharacteristic
623C4—21no—
624C4—21no—
625C4—21no—
626C4—42no—
627C4—862no—
628C4—862no—
629C4—862no—
630C4—1721no—
631C4—1721no—
632C4—1721no—
633C4#1458291412yes—
634C4#131×D4311yescharacteristic
635C4#1458366411yescharacteristic
636C4#1458370011yescharacteristic
637C4#1458370511yescharacteristic
638C2—41no—
639C2—82no—
640C2—1722no—
641C2—1722no—
642C2#1914304311yescharacteristic
643C2#1914311611yescharacteristic
644C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1492C2
socleC22×C43C22×C22⋊C4
prime radical#19148203C2
cosocleC42×C43C24
hypercenter#1492D43
hypocenterC43#17522
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
2. #19143725C2semidirect
3. #19143237C2semidirect
4. #19133057C2semidirect
5. #19133032C2semidirect
6. #19133018C2semidirect
7. #19133012C2semidirect
8. #19133000C2semidirect
9. #19132984C2semidirect
10. #19132978C2semidirect
11. C43×#1492C2semidirect
32. #14582952C22semidirect
33. #14582951C22semidirect
34. #14582950C22semidirect
35. #14582950C22semidirect
37. #14582921C22semidirect
39. C4×#10621877C22semidirect
40. #14582631C22semidirect
41. #14582631C22semidirect
42. #14582629C22semidirect
45. D4⋊(C43⋊C8)C22semidirect
46. D4⋊(C43⋊C8)C22semidirect
49. C43×#423C22semidirect
50. C2×C4×C8×C43C22semidirect
51. C43×D4⋊C8C22semidirect
52. C43×D4⋊C8C22semidirect
320. #1492D43semidirect
361. #423C2×D43semidirect
364. C2×C4×C8C2×D43semidirect
373. D4⋊C8C2×D43semidirect
374. D4⋊C8C2×D43semidirect
375. C43#17522semidirect

Maximal subgroups

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

subgroupindex
#191482032
#191437252
#191432372
#191330572
#191330322
#191330182
#191330122
#191330002
#191329842
#191329782
C43×#14922
#1752243