Finite Group Databasebeta

← #25130497

Subgroups — #25130497

Order 11008.

1238 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583614C211yesmaximal, characteristic, complemented
2C2×#14583189C211yesmaximal, characteristic, complemented
3C2×C4×#10621882C211yesmaximal, characteristic, complemented
4#19135784C212yesmaximal, complemented
5#19135591C212yesmaximal, complemented
6#19135555C211yesmaximal, characteristic, complemented
7#19135390C211yesmaximal, characteristic, complemented
8#19134918C212yesmaximal, complemented
9#19134792C212yesmaximal, complemented
10#19134592C211yesmaximal, characteristic, complemented
11C43×#2537C211yesmaximal, characteristic, complemented
12C22×#10621882C2211yescharacteristic
13#14583614—24no—
14#14583614—24no—
15C2×#13063325C2211yescharacteristic
16C2×#13063311—22no—
17C2×#13063299C2212yes—
18C2×#13063296—21no—
19C2×C4×D172C2211yescharacteristic
20C2×#13063284C2212yes—
21C2×#13063283—21no—
22#14583189—24no—
23C4×#10621882—24no—
24C2×#13063258C2211yescharacteristic
25C2×#13063256C2212yes—
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063246C2212yes—
28C2×#13063246C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2212yes—
31C2×C22⋊(C43⋊C8)C2212yes—
32C2×C22⋊(C43⋊C8)C2212yes—
33C2×C4×C43⋊C8C2211yescharacteristic
34#14582661C2212yes—
35#14582661C2212yes—
36#14582661C2212yes—
37C2×#121×C43—21no—
38C2×#121×C43C2212yes—
39C2×C4×D4×C43C2211yescharacteristic
40C2×C4×D4×C43C2211yescharacteristic
41C43×#394—22no—
42C43×#384C2211yescharacteristic
43C43×#380—21no—
44C43×#380C2212yes—
45C22×Dic86—21no—
46C22×D172C2311yescharacteristic
47C22×C22⋊D43—22no—
48C22×C4×D43—21no—
49C2×#10621882—22no—
50C2×#10621882—22no—
51C2×#10621882—22no—
52C22×C43⋊C8C2311yescharacteristic
53C22×C43⋊C8C2312yes—
54C22×C43⋊C8C2311yescharacteristic
55#13063325—22no—
56#13063325D414yescomplemented
57#13063311—216no—
58#13063299—24no—
59#13063299—24no—
60#13063296—28no—
61C4×D172—22no—
62C4×D172D414yescomplemented
63#13063284—24no—
64#13063284—24no—
65#13063283—28no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2312yes—
69C2×C22⋊Dic43—22no—
70C2×(C2×D43)⋊C4—22no—
71C2×(C2×D43)⋊C4—21no—
72C2×C4×Dic43—22no—
73#13063258—22no—
74#13063256—24no—
75C4⋊(C43⋊C8)—22no—
76#13063246—24no—
77#13063246—22no—
78#13063245—22no—
79#13063245—42no—
80C22⋊(C43⋊C8)—24no—
81C22⋊(C43⋊C8)—42no—
82C4×C43⋊C8—22no—
83C22×D4×C43—22no—
84C22×D4×C43D411yescharacteristic
85C22×D4×C43C2311yescharacteristic
86C23×C4×C43—21no—
87C23×C4×C43C2312yes—
88#121×C43—24no—
89#121×C43—42no—
90#121×C43—44no—
91C4×D4×C43—22no—
92C4×D4×C43—22no—
93C4×D4×C43—22no—
94C4×D4×C43—22no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43—21no—
97C2×C4⋊C4×C43D411yescharacteristic
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C4⋊C4×C43C2312yes—
100C2×C22⋊C4×C43—22no—
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43—22no—
103C2×C22⋊C4×C43D412yes—
104C2×C42×C43C2311yescharacteristic
105#95×C43—22no—
106C24×C43—21no—
107C24×C43C2×D412yes—
108C23×D43—21no—
109C2×D4×C43—22no—
110C2×D4×C43—22no—
111C2×D4×C43—22no—
112C2×D4×C43—21no—
113C2×D4×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—21no—
117C2×D4×C43—44no—
118C2×D4×C43—44no—
119C2×D4×C43—82no—
120C2×D4×C43#4112yes—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—21no—
128C22×C4×C43—22no—
129C22×C4×C43—42no—
130C22×C4×C43—42no—
131C22×C4×C43—42no—
132C22×C4×C43C2×D412yes—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2411yescharacteristic
136C2×C22⋊D43—28no—
137C2×C22⋊D43—82no—
138C2×C22⋊D43—82no—
139C22×Dic43—21no—
140C22×Dic43—22no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172C2×D412yes—
147C2×C4×D43—24no—
148C2×C4×D43—42no—
149C2×C4×D43—42no—
150C2×Dic86—24no—
151C2×Dic86—81no—
152C2×Dic86—81no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—22no—
158C4⋊C4×C43—42no—
159C4⋊C4×C43—81no—
160C22⋊C4×C43—24no—
161C22⋊C4×C43—44no—
162C22⋊C4×C43—44no—
163C22⋊C4×C43—42no—
164C42×C43C2×D412yes—
165C42×C43C2×D412yes—
166C22⋊Dic43—28no—
167#10621882—28no—
168(C2×D43)⋊C4—28no—
169(C2×D43)⋊C4—24no—
170C4⋊Dic43—24no—
171C4⋊Dic43—21no—
172C4⋊Dic43—22no—
173C4⋊Dic43C2×D414yes—
174C4⋊Dic43C2×D412yes—
175C4×Dic43—28no—
176C2×C43⋊C8—21no—
177C2×C43⋊C8—21no—
178C2×C43⋊C8—21no—
179C2×C43⋊C8—22no—
180C2×C43⋊C8—22no—
181C2×C43⋊C8—21no—
182C2×C43⋊C8—22no—
183C2×C43⋊C8—21no—
184C2×C43⋊C8#4112yes—
185C23×C43—22no—
186C23×C43—22no—
187C23×C43—22no—
188C23×C43—22no—
189C23×C43—22no—
190C23×C43—22no—
191C23×C43—22no—
192C23×C43—22no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43C22×D411yescharacteristic
200C22×D43—22no—
201C22×D43—41no—
202C22×D43—41no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207D4×C43—22no—
208D4×C43—22no—
209D4×C43—41no—
210D4×C43—41no—
211D4×C43—44no—
212D4×C43—88no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43—41no—
223C2×C4×C43—42no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—42no—
227C2×C4×C43—42no—
228C2×C4×C43—84no—
229C2×C4×C43#12012yes—
230C2×C4×C43#12012yes—
231C2×C4×C43#13512yes—
232C2×C4×C43AGL(1,ℤ/8)12yes—
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43H(5,𝔽2)11yescharacteristic
238C2×C4×C432−1+411yescharacteristic
239C22⋊D43—88no—
240C2×Dic43—22no—
241C2×Dic43—24no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246D172—22no—
247D172—22no—
248D172—41no—
249D172—41no—
250C4×D43—48no—
251Dic86—84no—
252C43⋊C8—22no—
253C43⋊C8—41no—
254C43⋊C8—42no—
255#24117—431nomaximal, Sylow
256C22×C43—42no—
257C22×C43—42no—
258C22×C43—42no—
259C22×C43—42no—
260C22×C43—42no—
261C22×C43—42no—
262C22×C43—42no—
263C22×C43—42no—
264C22×C43—42no—
265C22×C43—42no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43—81no—
270C22×C43C2×#12011yescharacteristic
271C22×C43#54611yescharacteristic
272C22×C43#54711yescharacteristic
273C22×C43C2×#13511yescharacteristic
274C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
275C22×C43#57611yescharacteristic
276C22×C43#57711yescharacteristic
277C2×D43—42no—
278C2×D43—42no—
279C2×D43—42no—
280C2×D43—81no—
281C2×D43—81no—
282C2×D43—81no—
283C2×D43—81no—
284C4×C43—22no—
285C4×C43—42no—
286C4×C43—81no—
287C4×C43—82no—
288C4×C43#44914yes—
289C4×C43#52511yescharacteristic
290C4×C43#53711yescharacteristic
291C4×C43#54811yescharacteristic
292C4×C43#55011yescharacteristic
293Dic43—42no—
294Dic43—44no—
295C2×#555—431no—
296C2×#476—431no—
297C2×C4×D8—431no—
298#2537D4311yescharacteristic, complemented
299#2034—432no—
300#1999—432no—
301#1990—431no—
302#1954—431no—
303#1875—432no—
304#1854—432no—
305#1802—431no—
306C2×C43—82no—
307C2×C43—82no—
308C2×C43#240711yescharacteristic
309C2×C43C2×#44911yescharacteristic
310C2×C43#301211yescharacteristic
311C2×C43#330311yescharacteristic
312C2×C43#332511yescharacteristic
313C2×C43#334111yescharacteristic
314C2×C43#335411yescharacteristic
315D43—82no—
316C22×D8—431no—
317#555—864no—
318#555—864no—
319C2×C4⋊Q8—431no—
320C2×#124—862no—
321C2×#121—21no—
322C2×#121—432no—
323C2×#121—861no—
324C2×#121C2×D4312yes—
325C2×C4×D4—431no—
326C2×C4×D4C2×D4311yescharacteristic
327C2×C4×D4C2×D4311yescharacteristic
328C2×#117—432no—
329C2×#117—861no—
330#476—864no—
331C4×D8—864no—
332C2×#107—431no—
333C2×#106—432no—
334C2×C4⋊C8—431no—
335C2×#102—431no—
336C2×#102—432no—
337C2×#102—431no—
338C2×#102—432no—
339C2×C22⋊C8—432no—
340C2×C22⋊C8—432no—
341C2×C4×C8—431no—
342#394—22no—
343#384C2×D4311yescharacteristic
344#380—21no—
345#380C2×D4312yes—
346#340—432no—
347#340—432no—
348#340—432no—
349C43#2411711yescharacteristic, complemented, Sylow
350C22×Q8—861no—
351C22×D4—22no—
352C22×D4—431no—
353C22×D4—862no—
354C22×D4C22⋊D4311yescharacteristic
355C22×D4C22×D4311yescharacteristic
356C23×C4—21no—
357C23×C4—861no—
358C23×C4C22×D4312yes—
359C2×D8—862no—
360C2×D8—862no—
361C2×D8—862no—
362C22×C8—431no—
363C22×C8—431no—
364C22×C8—432no—
365C4⋊Q8—434no—
366C4⋊Q8—862no—
367#124—8616no—
368#121—24no—
369#121—42no—
370#121—44no—
371#121—864no—
372#121—864no—
373#121—868no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4—434no—
379C4×D4—862no—
380#117—868no—
381#117—864no—
382#117—864no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—431no—
386C2×C4⋊C4—432no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4C22⋊D4311yescharacteristic
389C2×C4⋊C4C22×D4311yescharacteristic
390C2×C4⋊C4C22×D4312yes—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—862no—
395C2×C22⋊C4—862no—
396C2×C22⋊C4—861no—
397C2×C22⋊C4C22⋊D4312yes—
398C2×C42—862no—
399C2×C42C22×D4311yescharacteristic
400#107—862no—
401#106—864no—
402C4⋊C8—862no—
403#102—862no—
404#102—862no—
405#102—864no—
406#102—1722no—
407C22⋊C8—864no—
408C22⋊C8—1722no—
409C4×C8—862no—
410#95—22no—
411C24—21no—
412C24—861no—
413C24C2×C22⋊D4312yes—
414C2×Q8—864no—
415C2×Q8—3441no—
416C2×Q8—3441no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—44no—
426C2×D4—44no—
427C2×D4—82no—
428C2×D4—432no—
429C2×D4—868no—
430C2×D4—861no—
431C2×D4—861no—
432C2×D4—861no—
433C2×D4—861no—
434C2×D4—861no—
435C2×D4—3442no—
436C2×D4—3442no—
437C2×D4#1062190012yes—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—861no—
450C22×C4—862no—
451C22×C4—864no—
452C22×C4—1722no—
453C22×C4—1722no—
454C22×C4C2×C22⋊D4312yes—
455C22×C4C2×C22⋊D4311yescharacteristic
456C22×C4C2×C22⋊D4311yescharacteristic
457C22×C4C23×D4311yescharacteristic
458D8—868no—
459C2×C8—432no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—862no—
464C2×C8—862no—
465C2×C8—861no—
466C2×C8—862no—
467C2×C8—861no—
468C4⋊C4—22no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—42no—
474C4⋊C4—81no—
475C4⋊C4—434no—
476C4⋊C4—432no—
477C4⋊C4—864no—
478C4⋊C4—861no—
479C4⋊C4—862no—
480C22⋊C4—24no—
481C22⋊C4—44no—
482C22⋊C4—44no—
483C22⋊C4—42no—
484C22⋊C4—868no—
485C22⋊C4—868no—
486C22⋊C4—864no—
487C42—868no—
488C42D4×D4312yes—
489C42D4×D4312yes—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—862no—
505C23—1721no—
506C23—1721no—
507C23—1721no—
508C23—1721no—
509C23—1721no—
510C23—1721no—
511C23C22×C22⋊D4311yescharacteristic
512Q8—3444no—
513D4—22no—
514D4—22no—
515D4—44no—
516D4—41no—
517D4—41no—
518D4—88no—
519D4—862no—
520D4—862no—
521D4—3448no—
522D4—1721no—
523D4—1721no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—84no—
540C2×C4—862no—
541C2×C4—864no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1722no—
545C2×C4—1722no—
546C2×C4—1728no—
547C2×C4#1306329312yes—
548C2×C4#1306329312yes—
549C2×C4#1306334512yes—
550C2×C4#1306335112yes—
551C2×C4C2×D4×D4311yescharacteristic
552C2×C4C2×D4×D4311yescharacteristic
553C2×C4#41×D4311yescharacteristic
554C2×C4C2×#1062190011yescharacteristic
555C2×C4#1306337011yescharacteristic
556C2×C4#1306337211yescharacteristic
557C8—862no—
558C8—1722no—
559C8—1721no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—3441no—
575C22—3441no—
576C22—3441no—
577C22—3441no—
578C22—1722no—
579C22—1722no—
580C22—1722no—
581C22C2×#1306329311yescharacteristic
582C22#1458354311yescharacteristic
583C22#1458354811yescharacteristic
584C22C2×#1306334511yescharacteristic
585C22C2×#1306335111yescharacteristic
586C22#1458370211yescharacteristic
587C22#1458370711yescharacteristic
588C4—22no—
589C4—42no—
590C4—82no—
591C4—81no—
592C4—1722no—
593C4—1724no—
594C4#1458304214yes—
595C4#1458340911yescharacteristic
596C4#1458347811yescharacteristic
597C4#1458355511yescharacteristic
598C4#1458356711yescharacteristic
599C2—82no—
600C2—82no—
601C2—3442no—
602C2#1913793611yescharacteristic
603C2C2×#1458304211yescharacteristic
604C2#1914389611yescharacteristic
605C2#1914652311yescharacteristic
606C2#1914683711yescharacteristic
607C2#1914701311yescharacteristic
608C2#1914719011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2537C2
socleC23×C43C22×D4
hypercenter#2537D43
hypocenterC43#24117
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. C2×#14583614C2semidirect
2. C2×#14583189C2semidirect
3. C2×C4×#10621882C2semidirect
4. #19135784C2semidirect
5. #19135591C2semidirect
6. #19135555C2semidirect
7. #19135390C2semidirect
8. #19134918C2semidirect
9. #19134792C2semidirect
10. #19134592C2semidirect
11. C43×#2537C2semidirect
56. #13063325D4semidirect
62. C4×D172D4semidirect
298. #2537D43semidirect
349. C43#24117semidirect

Maximal subgroups

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

subgroupindex
C2×#145836142
C2×#145831892
C2×C4×#106218822
#191357842
#191355912
#191355552
#191353902
#191349182
#191347922
#191345922
C43×#25372
#2411743