Finite Group Databasebeta

← #25128583

Subgroups — #25128583

Order 11008.

1382 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583520C211yesmaximal, characteristic, complemented
2C2×#14583050C211yesmaximal, characteristic, complemented
3C2×#14583033C211yesmaximal, characteristic
4#19135731C212yesmaximal, complemented
5#19135671C212yesmaximal, complemented
6#19134953C212yesmaximal, complemented
7#19134946C212yesmaximal, complemented
8#19134917C211yesmaximal, characteristic, complemented
9#19134907C211yesmaximal, characteristic, complemented
10#19134666C211yesmaximal, characteristic, complemented
11C43×#2309C211yesmaximal, characteristic, complemented
12C22×#10621883C2212yes—
13C22×#10621882C2212yes—
14#14583520—24no—
15#14583520—24no—
16C2×#13063325C2211yescharacteristic, complemented
17C2×#13063320—21no—
18C2×#13063313C2211yescharacteristic, complemented
19C2×#13063311—21no—
20C2×#13063307—21no—
21C2×#13063304C2211yescharacteristic
22C2×#13063303—21no—
23C2×#13063299C2211yescharacteristic
24C2×C4×Dic86C2211yescharacteristic, complemented
25C2×C4×D172C2211yescharacteristic, complemented
26#14583050—24no—
27#14583033—24no—
28C2×#13063248C2212yescomplemented
29C2×#13063246C2212yes—
30C2×#13063246C2212yes—
31C2×#13063245C2212yescomplemented
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34#14582661C2212yescomplemented
35#14582661C2212yescomplemented
36#14582654C2212yescomplemented
37#14582654C2212yescomplemented
38C23×D4×C43C2211yescharacteristic
39C2×#117×C43C2211yescharacteristic
40C2×#117×C43C2211yescharacteristic
41C43×#390—21no—
42C43×#390—21no—
43C43×#390C2212yes—
44C43×#390C2212yes—
45C43×#379—21no—
46C43×#379—21no—
47C22×Dic86—21no—
48C22×Dic86C2311yescharacteristic
49C22×D172C2311yescharacteristic
50C22×C22⋊D43—21no—
51C22×C4×D43—21no—
52C2×#10621883—24no—
53C2×#10621883—24no—
54C2×#10621883—42no—
55C2×#10621882—24no—
56C2×#10621882—24no—
57C2×#10621882—42no—
58C22×C43⋊C8C2312yes—
59C22×C43⋊C8C2312yes—
60#13063325—22no—
61#13063325—22no—
62#13063320—28no—
63#13063313—22no—
64#13063313—22no—
65#13063311—28no—
66#13063307—28no—
67#13063304—22no—
68#13063304D414yes—
69#13063303—28no—
70#13063299—22no—
71#13063299D414yes—
72C4×Dic86—22no—
73C4×Dic86—22no—
74C4×D172—22no—
75C4×D172—22no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×C22⋊Dic43—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×C4×Dic43—21no—
87#13063248—42no—
88#13063246—24no—
89#13063246—24no—
90#13063245—42no—
91C22⋊(C43⋊C8)—22no—
92C22⋊(C43⋊C8)—22no—
93C25×C43—21no—
94C22×D4×C43—24no—
95C22×D4×C43—21no—
96C22×D4×C43—22no—
97C22×D4×C43—22no—
98C22×D4×C43—42no—
99C22×D4×C43C2312yes—
100C23×C4×C43C2311yescharacteristic
101#117×C43—22no—
102#117×C43—22no—
103#117×C43—42no—
104C2×C4⋊C4×C43D411yescharacteristic
105C2×C4⋊C4×C43D411yescharacteristic
106C2×C4⋊C4×C43C2312yes—
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—22no—
109C2×C22⋊C4×C43—22no—
110C2×C22⋊C4×C43—22no—
111C2×C22⋊C4×C43—22no—
112C2×C22⋊C4×C43D411yescharacteristic
113C2×C22⋊C4×C43D411yescharacteristic
114C2×C42×C43—21no—
115C2×C42×C43C2311yescharacteristic
116C2×C42×C43C2311yescharacteristic
117C24×C43—24no—
118C24×C43—22no—
119C24×C43—42no—
120C24×C43—42no—
121C24×C43—82no—
122C24×C43—82no—
123C24×C43C2×D411yescharacteristic
124C23×D43—21no—
125C2×D4×C43—24no—
126C2×D4×C43—22no—
127C2×D4×C43—22no—
128C2×D4×C43—22no—
129C2×D4×C43—22no—
130C2×D4×C43—22no—
131C2×D4×C43—48no—
132C2×D4×C43—48no—
133C2×D4×C43—42no—
134C2×D4×C43—42no—
135C2×D4×C43#4114yes—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43C2×D412yes—
140C22×C4×C43C2×D412yes—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2411yescharacteristic
147C2×C22⋊D43—24no—
148C2×C22⋊D43—82no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C2×D172—21no—
153C2×D172—22no—
154C2×D172—22no—
155C2×D172C2×D412yes—
156C2×C4×D43—24no—
157C2×C4×D43—82no—
158C2×Dic86—22no—
159C2×Dic86—22no—
160C2×Dic86—21no—
161C2×Dic86—24no—
162C2×Dic86—82no—
163C2×Dic86C2×D412yes—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—22no—
168C22⋊C4×C43—22no—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—42no—
171C22⋊C4×C43—82no—
172C22⋊C4×C43—82no—
173C22⋊C4×C43—82no—
174C22⋊C4×C43—82no—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—42no—
180C22⋊Dic43—24no—
181#10621883—48no—
182#10621882—48no—
183(C2×D43)⋊C4—24no—
184(C2×D43)⋊C4—24no—
185(C2×D43)⋊C4—24no—
186(C2×D43)⋊C4—24no—
187C4⋊Dic43—24no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43C2×D412yes—
191C4⋊Dic43C2×D412yes—
192Dic43⋊C4—24no—
193Dic43⋊C4—24no—
194C4×Dic43—24no—
195C2×C43⋊C8—22no—
196C2×C43⋊C8—22no—
197C2×C43⋊C8—22no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—22no—
200C2×C43⋊C8—22no—
201C23×C43—21no—
202C23×C43—21no—
203C23×C43—22no—
204C23×C43—22no—
205C23×C43—24no—
206C23×C43—48no—
207C23×C43—42no—
208C23×C43—42no—
209C23×C43—42no—
210C23×C43—42no—
211C23×C43—42no—
212C23×C43—42no—
213C23×C43—84no—
214C23×C43—84no—
215C23×C43—88no—
216C23×C43—88no—
217C23×C43#12012yes—
218C23×C43C22×D411yescharacteristic
219C22×D43—22no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—42no—
223C22×D43—42no—
224D4×C43—24no—
225D4×C43—24no—
226D4×C43—48no—
227D4×C43—42no—
228D4×C43—42no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—24no—
232C2×C4×C43—24no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43#12012yes—
245C2×C4×C43C22×D411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C2×#4112yes—
248C2×C4×C43H(5,𝔽2)12yes—
249C22⋊D43—84no—
250C2×Dic43—22no—
251C2×Dic43—22no—
252C2×Dic43—22no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257D172—24no—
258D172—42no—
259C4×D43—84no—
260Dic86—24no—
261Dic86—42no—
262Dic86—84no—
263C43⋊C8—42no—
264C43⋊C8—42no—
265#23945—431nomaximal, Sylow
266C22×C43—22no—
267C22×C43—22no—
268C22×C43—22no—
269C22×C43—42no—
270C22×C43—42no—
271C22×C43—44no—
272C22×C43—44no—
273C22×C43—44no—
274C22×C43—816no—
275C22×C43—82no—
276C22×C43—82no—
277C22×C43—82no—
278C22×C43—82no—
279C22×C43C2×#12011yescharacteristic
280C22×C43#52511yescharacteristic
281C22×C43#53511yescharacteristic
282C22×C43#57612yes—
283C22×C43#57712yes—
284C2×D43—42no—
285C2×D43—42no—
286C2×D43—42no—
287C2×D43—82no—
288C2×D43—82no—
289C4×C43—22no—
290C4×C43—41no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—82no—
295C4×C43#54612yes—
296C4×C43#54612yes—
297Dic43—42no—
298Dic43—42no—
299Dic43—42no—
300C2×#542—431no—
301C2×#450—431no—
302C2×#447—431no—
303#2309D4311yescharacteristic, complemented
304#2023—432no—
305#2012—432no—
306#1880—432no—
307#1879—432no—
308#1875—431no—
309#1873—431no—
310#1818—431no—
311C2×C43—42no—
312C2×C43—84no—
313C2×C43#240411yescharacteristic
314C2×C43#300811yescharacteristic
315C2×C43#301011yescharacteristic
316C2×C43#311812yes—
317C2×C43#322412yes—
318D43—82no—
319C23×D4C2×D4311yescharacteristic
320C22×SD16—432no—
321C22×D8—432no—
322#542—864no—
323#542—864no—
324C2×C4⋊Q8—431no—
325C2×#126—861no—
326C2×#124—431no—
327C2×#124—861no—
328C2×#123—861no—
329C2×C22⋊Q8—431no—
330C2×C22⋊Q8—861no—
331C2×#121—431no—
332C2×C4×Q8—431no—
333C2×C4×D4—431no—
334C2×#117C2×D4311yescharacteristic
335C2×#117C2×D4311yescharacteristic
336#450—864no—
337#447—864no—
338C2×#103—432no—
339C2×#102—432no—
340C2×#102—432no—
341C2×#102—432no—
342C2×C22⋊C8—431no—
343C2×C22⋊C8—431no—
344#390—21no—
345#390—21no—
346#390C2×D4312yes—
347#390C2×D4312yes—
348#379—21no—
349#379—21no—
350#340—432no—
351#340—432no—
352#336—432no—
353#336—432no—
354C43#2394511yescharacteristic, complemented, Sylow
355C25—21no—
356C22×Q8—431no—
357C22×Q8—861no—
358C22×D4—24no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—21no—
362C22×D4—42no—
363C22×D4—431no—
364C22×D4—861no—
365C22×D4C22×D4312yes—
366C23×C4—861no—
367C23×C4C22×D4311yescharacteristic
368C2×SD16—864no—
369C2×SD16—864no—
370C2×SD16—1722no—
371C2×D8—864no—
372C2×D8—864no—
373C2×D8—1722no—
374C22×C8—432no—
375C22×C8—432no—
376C4⋊Q8—862no—
377C4⋊Q8—862no—
378#126—868no—
379#124—862no—
380#124—862no—
381#124—868no—
382#123—868no—
383C22⋊Q8—434no—
384C22⋊Q8—868no—
385C22⋊Q8—862no—
386#121—434no—
387#121—862no—
388C4×Q8—862no—
389C4×Q8—862no—
390C4×D4—862no—
391C4×D4—862no—
392#117—22no—
393#117—22no—
394#117—42no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4C22⋊D4311yescharacteristic
401C2×C4⋊C4C22⋊D4311yescharacteristic
402C2×C4⋊C4C22×D4312yes—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—22no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4C22⋊D4311yescharacteristic
414C2×C22⋊C4C22⋊D4311yescharacteristic
415C2×C42—21no—
416C2×C42—861no—
417C2×C42C22×D4311yescharacteristic
418C2×C42C22×D4311yescharacteristic
419#103—1722no—
420#102—864no—
421#102—864no—
422#102—1722no—
423C22⋊C8—862no—
424C22⋊C8—862no—
425C24—24no—
426C24—22no—
427C24—42no—
428C24—42no—
429C24—82no—
430C24—82no—
431C24—861no—
432C24C2×C22⋊D4311yescharacteristic
433C2×Q8—432no—
434C2×Q8—864no—
435C2×Q8—861no—
436C2×Q8—862no—
437C2×Q8—862no—
438C2×Q8—3442no—
439C2×D4—24no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—48no—
446C2×D4—48no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—432no—
450C2×D4—864no—
451C2×D4—861no—
452C2×D4—862no—
453C2×D4—862no—
454C2×D4—3442no—
455C2×D4#1062189814yes—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—864no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—3442no—
464C22×C4D4×D4312yes—
465C22×C4D4×D4312yes—
466C22×C4C2×C22⋊D4311yescharacteristic
467C22×C4C2×C22⋊D4311yescharacteristic
468C22×C4C2×C22⋊D4311yescharacteristic
469C22×C4C2×C22⋊D4311yescharacteristic
470C22×C4C2×C22⋊D4311yescharacteristic
471C22×C4C23×D4311yescharacteristic
472SD16—1728no—
473D8—1728no—
474C2×C8—862no—
475C2×C8—862no—
476C2×C8—862no—
477C2×C8—862no—
478C2×C8—862no—
479C2×C8—862no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—432no—
485C4⋊C4—432no—
486C4⋊C4—864no—
487C4⋊C4—864no—
488C4⋊C4—864no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—42no—
494C22⋊C4—82no—
495C22⋊C4—82no—
496C22⋊C4—82no—
497C22⋊C4—82no—
498C22⋊C4—864no—
499C22⋊C4—864no—
500C22⋊C4—864no—
501C22⋊C4—864no—
502C22⋊C4—864no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—42no—
508C42—864no—
509C23—21no—
510C23—22no—
511C23—22no—
512C23—21no—
513C23—24no—
514C23—48no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—84no—
522C23—84no—
523C23—88no—
524C23—88no—
525C23—862no—
526C23—1721no—
527C23—1722no—
528C23—1722no—
529C23—1721no—
530C23#1306329312yes—
531C23C22×C22⋊D4311yescharacteristic
532Q8—864no—
533Q8—3444no—
534Q8—1722no—
535D4—24no—
536D4—24no—
537D4—48no—
538D4—42no—
539D4—42no—
540D4—864no—
541D4—3444no—
542D4—1722no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—24no—
546C2×C4—24no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—862no—
559C2×C4—862no—
560C2×C4—862no—
561C2×C4—3444no—
562C2×C4—1721no—
563C2×C4—1722no—
564C2×C4—1722no—
565C2×C4—1721no—
566C2×C4#1306329312yes—
567C2×C4C2×D4×D4311yescharacteristic
568C2×C4C2×D4×D4311yescharacteristic
569C2×C4C2×#1062189812yes—
570C2×C4#1306337012yes—
571C8—1722no—
572C8—1722no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—42no—
577C22—42no—
578C22—44no—
579C22—44no—
580C22—44no—
581C22—816no—
582C22—82no—
583C22—82no—
584C22—82no—
585C22—82no—
586C22—3442no—
587C22—3442no—
588C22—1722no—
589C22—1722no—
590C22—1722no—
591C22C2×#1306329311yescharacteristic
592C22#1458341011yescharacteristic
593C22#1458346611yescharacteristic
594C22#1458370212yes—
595C22#1458371012yes—
596C4—22no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—82no—
602C4—1722no—
603C4—1722no—
604C4—1722no—
605C4#1458353912yes—
606C4#1458353912yes—
607C2—42no—
608C2—84no—
609C2—3442no—
610C2#1913791411yescharacteristic
611C2#1914386111yescharacteristic
612C2#1914387911yescharacteristic
613C2#1914477912yes—
614C2#1914568912yes—
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2309C2
socleC23×C43C22×D4
prime radicalC2×#14583033C2
hypercenter#2309D43
hypocenterC43#23945
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2309

Complements

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

NH ≅ G/Ntype
1. C2×#14583520C2semidirect
2. C2×#14583050C2semidirect
4. #19135731C2semidirect
5. #19135671C2semidirect
6. #19134953C2semidirect
7. #19134946C2semidirect
8. #19134917C2semidirect
9. #19134907C2semidirect
10. #19134666C2semidirect
11. C43×#2309C2semidirect
16. C2×#13063325C22semidirect
18. C2×#13063313C22semidirect
24. C2×C4×Dic86C22semidirect
25. C2×C4×D172C22semidirect
28. C2×#13063248C22semidirect
31. C2×#13063245C22semidirect
34. #14582661C22semidirect
35. #14582661C22semidirect
36. #14582654C22semidirect
37. #14582654C22semidirect
303. #2309D43semidirect
354. C43#23945semidirect

Maximal subgroups

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

subgroupindex
C2×#145835202
C2×#145830502
C2×#145830332
#191357312
#191356712
#191349532
#191349462
#191349172
#191349072
#191346662
C43×#23092
#2394543