Finite Group Databasebeta

← #25245398

Subgroups — #25245398

Order 11008.

1576 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063290C211yesmaximal, characteristic, complemented
2C2×#14583098C212yesmaximal, complemented
3C2×#14583040C211yesmaximal, characteristic, complemented
4C2×#14583037C211yesmaximal, characteristic, complemented
5#19142938C211yesmaximal, characteristic
6#19134951C212yesmaximal, complemented
7#19134947C212yesmaximal, complemented
8#19134912C211yesmaximal, characteristic, complemented
9#19134599C212yesmaximal, complemented
10#19134573C211yesmaximal, characteristic, complemented
11C43×#1874C211yesmaximal, characteristic, complemented
12C23×Dic86C2211yescharacteristic
13C22×#10621873C2212yes—
14C22×#10621883C2212yes—
15C2×#13063321C2211yescharacteristic
16C2×#13063299C2211yescharacteristic
17C2×#13063297—21no—
18C2×#13063297—21no—
19C2×#13063290—28no—
20C2×#13063290—21no—
21C2×#13063290—21no—
22C2×#13063290C2212yes—
23C2×#13063290C2212yes—
24C22×Dic43⋊C4—21no—
25C22×C4×Dic43—21no—
26C22×C4×Dic43C2211yescharacteristic
27#14583098—28no—
28#14583040—24no—
29#14583037—24no—
30C2×Dic43⋊C8C2212yes—
31C2×#13063250C2212yes—
32C2×#13063248C2212yes—
33C2×#13063245C2212yes—
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35#14582802C2211yescharacteristic
36#14582800C2211yescharacteristic
37#14582799—21no—
38#14582799—21no—
39#14582768C2211yescharacteristic
40#14582661C2212yes—
41#14582653C2212yes—
42C2×#121×C43C2211yescharacteristic
43C22×C4⋊C4×C43C2211yescharacteristic
44C2×#102×C43C2212yes—
45C2×C22⋊C8×C43C2211yescharacteristic
46C43×#340C2212yes—
47C22×Dic86—21no—
48C22×Dic86—22no—
49C22×Dic86—24no—
50C22×Dic86—24no—
51C22×Dic86D414yescomplemented
52C22×Dic86C2312yes—
53C22×D172C2311yescharacteristic
54C22×C22⋊D43—21no—
55C22×C22⋊D43—21no—
56C22×C22⋊D43—21no—
57C23×Dic43—21no—
58C23×Dic43D411yescharacteristic
59C23×Dic43D411yescharacteristic
60C2×#10621873—24no—
61C2×#10621873—24no—
62C2×#10621873—24no—
63C2×#10621883—24no—
64C2×#10621883—24no—
65C2×#10621883—24no—
66C22×C43⋊C8C2312yes—
67#13063321—24no—
68#13063299—22no—
69#13063299—22no—
70#13063297—44no—
71#13063297—44no—
72#13063290—28no—
73#13063290—28no—
74#13063290—24no—
75#13063290—24no—
76#13063290—24no—
77#13063290D418yescomplemented
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—28no—
80C2×Dic43⋊C4—22no—
81C2×Dic43⋊C4—22no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×C4×Dic43—28no—
90C2×C4×Dic43—22no—
91C2×C4×Dic43—22no—
92C2×C4×Dic43—24no—
93C2×C4×Dic43D411yescharacteristic
94C2×C4×Dic43D411yescharacteristic
95C2×C4×Dic43C2311yescharacteristic
96C2×C4×Dic43C2311yescharacteristic
97Dic43⋊C8—24no—
98#13063250—24no—
99#13063248—24no—
100#13063245—24no—
101C22⋊(C43⋊C8)—22no—
102C22×D4×C43—21no—
103C22×D4×C43C2311yescharacteristic
104C23×C4×C43—21no—
105C23×C4×C43C2311yescharacteristic
106C22×C8×C43C2312yes—
107#121×C43—22no—
108#121×C43—22no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—24no—
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2312yes—
113C2×C22⋊C4×C43—21no—
114#102×C43—24no—
115C22⋊C8×C43—22no—
116C24×C43—21no—
117C24×C43C2×D411yescharacteristic
118C23×D43—21no—
119C2×D4×C43—22no—
120C2×D4×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—22no—
123C2×D4×C43—42no—
124C2×D4×C43—42no—
125C2×D4×C43—42no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—24no—
129C22×C4×C43—22no—
130C22×C4×C43—21no—
131C22×C4×C43—42no—
132C22×C4×C43—42no—
133C22×C4×C43C2×D412yes—
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43#4112yes—
136C22×C4×C43C2411yescharacteristic
137C2×C22⋊D43—42no—
138C2×C22⋊D43—42no—
139C2×C22⋊D43—42no—
140C2×C22⋊D43—42no—
141C2×C22⋊D43—42no—
142C2×C22⋊D43—42no—
143C2×C22⋊D43—42no—
144C2×C22⋊D43—42no—
145C2×C22⋊D43—42no—
146C22×Dic43—24no—
147C22×Dic43—24no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—24no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—21no—
155C22×Dic43—41no—
156C22×Dic43SD1614yescomplemented
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C2×D172—22no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—22no—
165C2×Dic86—24no—
166C2×Dic86—24no—
167C2×Dic86—216no—
168C2×Dic86—24no—
169C2×Dic86—22no—
170C2×Dic86—22no—
171C2×Dic86—22no—
172C2×Dic86—216no—
173C2×Dic86C2×D414yes—
174C2×Dic86C2×D414yes—
175C2×Dic86#4114yes—
176C2×C8×C43—22no—
177C2×C8×C43—22no—
178C2×C8×C43—22no—
179C4⋊C4×C43—24no—
180C4⋊C4×C43—22no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43C2×D414yes—
184C22⋊C4×C43—42no—
185C22⋊Dic43—42no—
186C22⋊Dic43—42no—
187#10621883—48no—
188(C2×D43)⋊C4—42no—
189(C2×D43)⋊C4—42no—
190(C2×D43)⋊C4—42no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193Dic43⋊C4—28no—
194Dic43⋊C4—28no—
195Dic43⋊C4—42no—
196Dic43⋊C4—42no—
197C4×Dic43—28no—
198C4×Dic43—22no—
199C4×Dic43—28no—
200C4×Dic43—22no—
201C4×Dic43—22no—
202C4×Dic43C2×D414yes—
203C2×C43⋊C8—22no—
204C2×C43⋊C8—22no—
205C2×C43⋊C8—22no—
206#10621873—48no—
207C23×C43—21no—
208C23×C43—21no—
209C23×C43—21no—
210C23×C43—21no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43#12112yes—
219C23×C43C2×SD1612yes—
220C23×C43AGL(1,ℤ/8)12yes—
221C23×C43C22×D411yescharacteristic
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229D4×C43—42no—
230D4×C43—42no—
231D4×C43—84no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—24no—
235C2×C4×C43—24no—
236C2×C4×C43—24no—
237C2×C4×C43—48no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43#12112yes—
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C22×D412yes—
246C2×C4×C43C2×#4112yes—
247C2×C4×C43C2×#4111yescharacteristic
248C22⋊D43—84no—
249C22⋊D43—84no—
250C22⋊D43—84no—
251C2×Dic43—216no—
252C2×Dic43—21no—
253C2×Dic43—24no—
254C2×Dic43—24no—
255C2×Dic43—24no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—28no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—44no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43#12012yes—
268C2×Dic43#12012yes—
269C2×Dic43C2×SD1612yes—
270C2×Dic43C2×SD1612yes—
271C2×Dic43#13712yes—
272D172—42no—
273D172—42no—
274Dic86—216no—
275Dic86—24no—
276Dic86—24no—
277Dic86—24no—
278Dic86#12118yescomplemented
279C8×C43—42no—
280C43⋊C8—42no—
281#32903—431nomaximal, Sylow
282C22×C43—22no—
283C22×C43—22no—
284C22×C43—22no—
285C22×C43—22no—
286C22×C43—22no—
287C22×C43—22no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43—81no—
293C22×C43—81no—
294C22×C43—81no—
295C22×C43#46014yescomplemented
296C22×C43C2×#12011yescharacteristic
297C22×C43C2×#12111yescharacteristic
298C22×C43#52511yescharacteristic
299C22×C43C22×SD1611yescharacteristic
300C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
301C22×C43C2×#13711yescharacteristic
302C22×C43#57511yescharacteristic
303C2×D43—81no—
304C2×D43—81no—
305C2×D43—81no—
306C2×D43—81no—
307C2×D43—81no—
308C2×D43—81no—
309C2×D43—81no—
310C4×C43—22no—
311C4×C43—44no—
312C4×C43—81no—
313C4×C43C2×#12112yes—
314C4×C43#52512yes—
315Dic43—28no—
316Dic43—22no—
317Dic43—22no—
318Dic43—41no—
319Dic43—81no—
320Dic43#44814yescomplemented
321C22×C4×Q8—431no—
322C2×#460—432no—
323C2×#448—431no—
324C2×#448—431no—
325#2856—431no—
326#1880—432no—
327#1880—432no—
328#1874—431no—
329#1874D4311yescharacteristic, complemented
330#1803—432no—
331#1797—431no—
332C2×C43—24no—
333C2×C43—161no—
334C2×C43#284711yescharacteristic
335C2×C43C2×#44811yescharacteristic
336C2×C43#300611yescharacteristic
337C2×C43C2×#46011yescharacteristic
338C2×C43#303711yescharacteristic
339C2×C43#310311yescharacteristic
340C2×C43#311211yescharacteristic
341D43—161no—
342C23×Q8—431no—
343C22×SD16—432no—
344C22×SD16—432no—
345C2×#127—431no—
346C2×#121—431no—
347C2×#121—861no—
348C2×#121—861no—
349C2×#121C2×D4311yescharacteristic
350C2×C4×Q8—432no—
351C2×C4×Q8—432no—
352C2×C4×Q8—861no—
353C2×C4×Q8—861no—
354C2×C4×Q8—868no—
355C22×C4⋊C4—861no—
356C22×C4⋊C4C2×D4311yescharacteristic
357C22×C42—431no—
358C22×C42—861no—
359#460—868no—
360#448—864no—
361#448—864no—
362C2×C4⋊C8—432no—
363C2×#103—432no—
364C2×#103—432no—
365C2×#102—432no—
366C2×#102C2×D4312yes—
367C2×C22⋊C8—431no—
368C2×C22⋊C8C2×D4311yescharacteristic
369#390—431no—
370#390—431no—
371#390—861no—
372#390—861no—
373#384—431no—
374#340—432no—
375#340C2×D4312yes—
376#336—432no—
377C43#3290311yescharacteristic, complemented, Sylow
378C22×Q8—434no—
379C22×Q8—432no—
380C22×Q8—864no—
381C22×Q8—864no—
382C22×Q8—862no—
383C22×Q8—861no—
384C22×D4—21no—
385C22×D4—431no—
386C22×D4—861no—
387C22×D4—861no—
388C22×D4—861no—
389C22×D4C22×D4311yescharacteristic
390C23×C4—21no—
391C23×C4—431no—
392C23×C4—431no—
393C23×C4—861no—
394C23×C4C22×D4311yescharacteristic
395C2×SD16—864no—
396C2×SD16—864no—
397C2×SD16—864no—
398C2×SD16—864no—
399C2×SD16—864no—
400C2×SD16—864no—
401C22×C8—432no—
402C22×C8C22×D4312yes—
403#127—864no—
404#121—22no—
405#121—22no—
406#121—862no—
407#121—862no—
408#121—1724no—
409#121—1724no—
410C4×Q8—438no—
411C4×Q8—864no—
412C4×Q8—864no—
413C4×Q8—868no—
414C4×Q8—868no—
415C4×Q8—864no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—862no—
420C2×C4⋊C4—862no—
421C2×C4⋊C4—868no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C4⋊C4C22×D4312yes—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C42—431no—
433C2×C42—431no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—864no—
437C2×C42—862no—
438C2×C42—862no—
439C2×C42—868no—
440C4⋊C8—864no—
441#103—864no—
442#103—864no—
443#102—24no—
444#102—864no—
445C22⋊C8—22no—
446C22⋊C8—862no—
447C24—21no—
448C24—861no—
449C24D4×D4311yescharacteristic
450C2×Q8—434no—
451C2×Q8—434no—
452C2×Q8—434no—
453C2×Q8—8616no—
454C2×Q8—864no—
455C2×Q8—864no—
456C2×Q8—8616no—
457C2×Q8—864no—
458C2×Q8—862no—
459C2×Q8—862no—
460C2×Q8—862no—
461C2×D4—22no—
462C2×D4—21no—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—42no—
468C2×D4—862no—
469C2×D4—861no—
470C2×D4—862no—
471C2×D4—861no—
472C2×D4—1722no—
473C2×D4—1722no—
474C2×D4—1722no—
475C2×D4—1722no—
476C2×D4—1722no—
477C2×D4—1722no—
478C2×D4—1722no—
479C2×D4—1722no—
480C2×D4—1722no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—431no—
489C22×C4—434no—
490C22×C4—431no—
491C22×C4—431no—
492C22×C4—431no—
493C22×C4—862no—
494C22×C4—862no—
495C22×C4—862no—
496C22×C4—864no—
497C22×C4—864no—
498C22×C4—864no—
499C22×C4—862no—
500C22×C4—862no—
501C22×C4—861no—
502C22×C4—1721no—
503C22×C4#1062189812yes—
504C22×C4D4×D4311yescharacteristic
505C22×C4D4×D4312yes—
506C22×C4C23×D4311yescharacteristic
507SD16—1728no—
508SD16—1728no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—862no—
513C2×C8—862no—
514C2×C8—862no—
515C4⋊C4—24no—
516C4⋊C4—22no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—868no—
520C4⋊C4—868no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—1722no—
524C4⋊C4—1722no—
525C4⋊C4D4×D4314yes—
526C22⋊C4—42no—
527C22⋊C4—1722no—
528C22⋊C4—1722no—
529C22⋊C4—1722no—
530C22⋊C4—1722no—
531C22⋊C4—1722no—
532C42—434no—
533C42—862no—
534C42—862no—
535C42—868no—
536C42—868no—
537C42—862no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—1721no—
550C23—1721no—
551C23—1721no—
552C23—1721no—
553C23—1721no—
554C23—1721no—
555C23—1721no—
556C23#1306329812yes—
557C23SD16×D4312yes—
558C23#1306334912yes—
559C23C2×D4×D4311yescharacteristic
560Q8—438no—
561Q8—8616no—
562Q8—864no—
563Q8—864no—
564Q8—864no—
565D4—42no—
566D4—42no—
567D4—84no—
568D4—3444no—
569D4—3444no—
570D4—3444no—
571D4—1722no—
572D4—1722no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—48no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—432no—
585C2×C4—432no—
586C2×C4—432no—
587C2×C4—432no—
588C2×C4—432no—
589C2×C4—868no—
590C2×C4—8616no—
591C2×C4—861no—
592C2×C4—864no—
593C2×C4—864no—
594C2×C4—864no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—861no—
601C2×C4—1724no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4#1306329812yes—
606C2×C4C2×D4×D4311yescharacteristic
607C2×C4C2×D4×D4312yes—
608C2×C4#41×D4312yes—
609C2×C4C2×#1062189811yescharacteristic
610C8—42no—
611C8—1722no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22—3441no—
626C22—3441no—
627C22—3441no—
628C22—3441no—
629C22—3441no—
630C22—3441no—
631C22—3441no—
632C22#1458309814yescomplemented
633C22#120×D4311yescharacteristic
634C22C2×#1306329811yescharacteristic
635C22#1458340711yescharacteristic
636C22C2×SD16×D4311yescharacteristic
637C22C2×#1306334911yescharacteristic
638C22#137×D4311yescharacteristic
639C22#1458369511yescharacteristic
640C4—22no—
641C4—44no—
642C4—81no—
643C4—434no—
644C4—862no—
645C4—862no—
646C4—868no—
647C4—3441no—
648C4—1721no—
649C4#121×D4312yes—
650C4#1458340812yes—
651C2—24no—
652C2—161no—
653C2—6881no—
654C2#1914287611yescharacteristic
655C2#448×D4311yescharacteristic
656C2#1914384211yescharacteristic
657C2C2×#1458309811yescharacteristic
658C2#1914406611yescharacteristic
659C2#1914462311yescharacteristic
660C2#1914471411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1874C2
socleC23×C43C22×D4
prime radical#19142938C2
hypercenter#1874D43
hypocenterC43#32903
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
1. C22×#13063290C2semidirect
2. C2×#14583098C2semidirect
3. C2×#14583040C2semidirect
4. C2×#14583037C2semidirect
6. #19134951C2semidirect
7. #19134947C2semidirect
8. #19134912C2semidirect
9. #19134599C2semidirect
10. #19134573C2semidirect
11. C43×#1874C2semidirect
51. C22×Dic86D4semidirect
77. #13063290D4semidirect
156. C22×Dic43SD16semidirect
278. Dic86#121semidirect
295. C22×C43#460semidirect
320. Dic43#448semidirect
329. #1874D43semidirect
377. C43#32903semidirect
632. C22#14583098semidirect

Maximal subgroups

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

subgroupindex
C22×#130632902
C2×#145830982
C2×#145830402
C2×#145830372
#191429382
#191349512
#191349472
#191349122
#191345992
#191345732
C43×#18742
#3290343