Finite Group Databasebeta

← #25130530

Subgroups — #25130530

Order 11008.

1350 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583553C211yesmaximal, characteristic
2C2×#14583184C211yesmaximal, characteristic, complemented
3C2×C4×#10621884C211yesmaximal, characteristic, complemented
4#19135784C212yesmaximal, complemented
5#19135596C212yesmaximal, complemented
6#19135555C211yesmaximal, characteristic, complemented
7#19135390C211yesmaximal, characteristic, complemented
8#19134903C212yesmaximal, complemented
9#19134787C212yesmaximal, complemented
10#19134592C211yesmaximal, characteristic, complemented
11C43×#2538C211yesmaximal, characteristic, complemented
12C22×#10621900—21no—
13C22×#10621884C2211yescharacteristic
14#14583553—24no—
15#14583553—24no—
16C2×#13063325C2211yescharacteristic
17C2×#13063309—22no—
18C2×#13063305—21no—
19C2×#13063299C2212yes—
20C2×C4×D172C2211yescharacteristic
21C22×C4⋊Dic43C2212yes—
22#14583184—24no—
23C4×#10621884—24no—
24C2×#13063256C2212yes—
25C2×#13063256C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063249C2212yes—
28C2×#13063249C2211yescharacteristic
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×C22⋊Q8×C43C2212yes—
38C2×C4×Q8×C43C2211yescharacteristic
39C2×C4×D4×C43C2211yescharacteristic
40C43×#396—22no—
41C43×#390—21no—
42C43×#389—21no—
43C43×#384C2211yescharacteristic
44C43×#380C2212yes—
45C2×#10621900—28no—
46C2×#10621900—44no—
47C2×#10621900—44no—
48C22×Dic86—21no—
49C22×D172C2311yescharacteristic
50C22×C22⋊D43—22no—
51C23×Dic43—22no—
52C22×C4×D43—21no—
53C2×#10621884—22no—
54C2×#10621884—22no—
55C2×#10621884—22no—
56C22×C43⋊C8C2311yescharacteristic
57C22×C43⋊C8C2312yes—
58C22×C43⋊C8C2311yescharacteristic
59#13063325—22no—
60#13063325D414yes—
61#13063309—216no—
62#13063305—28no—
63#13063299—24no—
64#13063299—24no—
65C4×D172—22no—
66C4×D172D414yes—
67C2×C4⋊Dic43—22no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—24no—
70C2×C4⋊Dic43—24no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2312yes—
73C2×(C2×D43)⋊C4—21no—
74C2×(C2×D43)⋊C4—22no—
75#13063256—24no—
76#13063256—22no—
77C4⋊(C43⋊C8)—22no—
78#13063249—24no—
79#13063249—22no—
80#13063245—22no—
81#13063245—42no—
82C22⋊(C43⋊C8)—24no—
83C22⋊(C43⋊C8)—42no—
84C4×C43⋊C8—22no—
85C22×Q8×C43C2311yescharacteristic
86C22×D4×C43D411yescharacteristic
87C23×C4×C43C2312yes—
88C22⋊Q8×C43—24no—
89C22⋊Q8×C43—42no—
90C4×Q8×C43—22no—
91C4×Q8×C43—22no—
92C4×D4×C43—22no—
93C4×D4×C43—22no—
94C2×C4⋊C4×C43—21no—
95C2×C4⋊C4×C43—22no—
96C2×C4⋊C4×C43—21no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43D411yescharacteristic
99C2×C4⋊C4×C43C2311yescharacteristic
100C2×C4⋊C4×C43C2312yes—
101C2×C22⋊C4×C43—22no—
102C2×C22⋊C4×C43—22no—
103C2×C22⋊C4×C43D412yes—
104C2×C42×C43—21no—
105C2×C42×C43C2311yescharacteristic
106#95×C43—22no—
107C24×C43C2×D412yes—
108C23×D43—21no—
109C2×Q8×C43—21no—
110C2×Q8×C43—21no—
111C2×Q8×C43—21no—
112C2×Q8×C43—21no—
113C2×Q8×C43—21no—
114C2×Q8×C43#4112yescomplemented
115C2×D4×C43—22no—
116C2×D4×C43—22no—
117C2×D4×C43SD1614yescomplemented
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—22no—
127C22×C4×C43C2×D412yes—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2411yescharacteristic
131C2×C22⋊D43—28no—
132C2×C22⋊D43—44no—
133C2×C22⋊D43—44no—
134C22×Dic43—28no—
135C22×Dic43—21no—
136C22×Dic43—22no—
137C22×Dic43—44no—
138C22×Dic43—44no—
139#10621900—432no—
140C2×D172—21no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172C2×D412yes—
146C2×C4×D43—24no—
147C2×C4×D43—42no—
148C2×C4×D43—42no—
149C2×Dic86—24no—
150C2×Dic86—42no—
151C2×Dic86—42no—
152C4⋊C4×C43—22no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—44no—
158C4⋊C4×C43—42no—
159C4⋊C4×C43—42no—
160C4⋊C4×C43—81no—
161C22⋊C4×C43—24no—
162C22⋊C4×C43—44no—
163C22⋊C4×C43—82no—
164C42×C43—42no—
165C42×C43C2×D412yes—
166C42×C43C2×D412yes—
167#10621884—28no—
168(C2×D43)⋊C4—28no—
169(C2×D43)⋊C4—24no—
170C4⋊Dic43—28no—
171C4⋊Dic43—24no—
172C4⋊Dic43—21no—
173C4⋊Dic43—22no—
174C4⋊Dic43C2×D412yes—
175C4⋊Dic43C2×D414yes—
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#4112yescomplemented
185C23×C43—22no—
186C23×C43—22no—
187C23×C43—22no—
188C23×C43—22no—
189C23×C43—22no—
190C23×C43—22no—
191C23×C43C2×SD1614yes—
192C23×C43C22×D411yescharacteristic
193C22×D43—22no—
194C22×D43—41no—
195C22×D43—41no—
196C22×D43—41no—
197C22×D43—41no—
198C22×D43—41no—
199C22×D43—41no—
200Q8×C43—22no—
201Q8×C43—22no—
202Q8×C43—41no—
203Q8×C43—41no—
204D4×C43—28no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43—41no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—41no—
221C2×C4×C43—42no—
222C2×C4×C43—41no—
223C2×C4×C43#12012yes—
224C2×C4×C43#12012yes—
225C2×C4×C43C2×SD1612yes—
226C2×C4×C43AGL(1,ℤ/8)12yes—
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43H(5,𝔽2)11yescharacteristic
232C2×C4×C432−1+411yescharacteristic
233C22⋊D43—416no—
234C2×Dic43—24no—
235C2×Dic43—22no—
236C2×Dic43—416no—
237C2×Dic43—42no—
238C2×Dic43—41no—
239C2×Dic43—42no—
240C2×Dic43—41no—
241D172—22no—
242D172—22no—
243D172—41no—
244D172—41no—
245C4×D43—48no—
246Dic86—48no—
247C43⋊C8—22no—
248C43⋊C8—41no—
249C43⋊C8—42no—
250#24120—431nomaximal, Sylow
251C22×C43—24no—
252C22×C43—24no—
253C22×C43—24no—
254C22×C43—42no—
255C22×C43—42no—
256C22×C43—42no—
257C22×C43—42no—
258C22×C43C2×#12011yescharacteristic
259C22×C43#54611yescharacteristic
260C22×C43#54711yescharacteristic
261C22×C43C22×SD1611yescharacteristic
262C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
263C22×C43#57711yescharacteristic
264C22×C43#57811yescharacteristic
265C2×D43—42no—
266C2×D43—42no—
267C2×D43—42no—
268C2×D43—81no—
269C2×D43—81no—
270C2×D43—81no—
271C2×D43—81no—
272C4×C43—22no—
273C4×C43—42no—
274C4×C43—42no—
275C4×C43—82no—
276C4×C43—81no—
277C4×C43#45014yes—
278C4×C43#52511yescharacteristic
279C4×C43#53711yescharacteristic
280C4×C43#54811yescharacteristic
281C4×C43#55011yescharacteristic
282Dic43—44no—
283Dic43—42no—
284C2×#547—431no—
285C2×#475—431no—
286C2×C4×SD16—431no—
287#2538D4311yescharacteristic, complemented
288#2034—432no—
289#2000—432no—
290#1990—431no—
291#1954—431no—
292#1872—432no—
293#1853—432no—
294#1802—431no—
295C2×C43—44no—
296C2×C43#240711yescharacteristic
297C2×C43C2×#45011yescharacteristic
298C2×C43#301311yescharacteristic
299C2×C43#329811yescharacteristic
300C2×C43#333211yescharacteristic
301C2×C43#333511yescharacteristic
302C2×C43#335311yescharacteristic
303D43—82no—
304C22×#41—861no—
305C22×SD16—431no—
306#547—864no—
307#547—864no—
308C2×C4⋊Q8—431no—
309C2×#123—862no—
310C2×C22⋊Q8—861no—
311C2×C22⋊Q8C2×D4312yes—
312C2×#121—432no—
313C2×C4×Q8C2×D4311yescharacteristic
314C2×C4×D4—431no—
315C2×C4×D4C2×D4311yescharacteristic
316C22×C4⋊C4—432no—
317#475—864no—
318C4×SD16—864no—
319C2×#106—432no—
320C2×#106—431no—
321C2×C4⋊C8—431no—
322C2×#103—432no—
323C2×#103—431no—
324C2×#102—431no—
325C2×#102—432no—
326C2×C22⋊C8—432no—
327C2×C22⋊C8—432no—
328C2×C4×C8—431no—
329#396—22no—
330#390—21no—
331#389—21no—
332#384C2×D4311yescharacteristic
333#380C2×D4312yes—
334#340—432no—
335#340—432no—
336#340—432no—
337C43#2412011yescharacteristic, complemented, Sylow
338C2×#41—868no—
339C2×#41—1724no—
340C2×#41—1724no—
341C22×Q8—861no—
342C22×Q8C22×D4311yescharacteristic
343C22×D4—431no—
344C22×D4—862no—
345C22×D4C22⋊D4311yescharacteristic
346C23×C4—862no—
347C23×C4—861no—
348C23×C4C22×D4312yes—
349C2×SD16—862no—
350C2×SD16—862no—
351C2×SD16—862no—
352C22×C8—431no—
353C22×C8—431no—
354C22×C8—432no—
355C4⋊Q8—434no—
356C4⋊Q8—862no—
357#123—8616no—
358C22⋊Q8—24no—
359C22⋊Q8—42no—
360C22⋊Q8—868no—
361#121—864no—
362#121—864no—
363C4×Q8—22no—
364C4×Q8—22no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4—434no—
368C4×D4—862no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—432no—
375C2×C4⋊C4—864no—
376C2×C4⋊C4—864no—
377C2×C4⋊C4—862no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4C22⋊D4311yescharacteristic
380C2×C4⋊C4C22×D4311yescharacteristic
381C2×C4⋊C4C22×D4312yes—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—861no—
385C2×C22⋊C4—862no—
386C2×C22⋊C4C22⋊D4312yes—
387C2×C42—21no—
388C2×C42C22×D4311yescharacteristic
389#106—862no—
390#106—864no—
391C4⋊C8—862no—
392#103—862no—
393#103—864no—
394#102—862no—
395#102—1722no—
396C22⋊C8—864no—
397C22⋊C8—1722no—
398C4×C8—862no—
399#95—22no—
400C24—861no—
401C24C2×C22⋊D4312yes—
402#41—17232no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—864no—
409C2×Q8—1722no—
410C2×Q8—1722no—
411C2×Q8#1062190012yescomplemented
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—432no—
415C2×D4—868no—
416C2×D4—861no—
417C2×D4—861no—
418C2×D4—861no—
419C2×D4—861no—
420C2×D4—861no—
421C2×D4—1724no—
422C2×D4—1724no—
423C2×D4#1062188414yescomplemented
424C22×C4—21no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—868no—
434C22×C4—861no—
435C22×C4—862no—
436C22×C4—864no—
437C22×C4—1724no—
438C22×C4—1724no—
439C22×C4—1722no—
440C22×C4—1722no—
441C22×C4C2×C22⋊D4312yes—
442C22×C4C2×C22⋊D4311yescharacteristic
443C22×C4C2×C22⋊D4311yescharacteristic
444C22×C4C23×D4311yescharacteristic
445SD16—868no—
446C2×C8—432no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—862no—
451C2×C8—862no—
452C2×C8—861no—
453C2×C8—862no—
454C2×C8—861no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—44no—
461C4⋊C4—42no—
462C4⋊C4—42no—
463C4⋊C4—81no—
464C4⋊C4—432no—
465C4⋊C4—434no—
466C4⋊C4—868no—
467C4⋊C4—864no—
468C4⋊C4—861no—
469C4⋊C4—862no—
470C22⋊C4—24no—
471C22⋊C4—44no—
472C22⋊C4—82no—
473C22⋊C4—868no—
474C22⋊C4—864no—
475C42—42no—
476C42D4×D4312yes—
477C42D4×D4312yes—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—862no—
485C23—1721no—
486C23—1721no—
487C23—1721no—
488C23—1721no—
489C23—1721no—
490C23—1721no—
491C23C2×#1062188414yes—
492C23C22×C22⋊D4311yescharacteristic
493Q8—22no—
494Q8—22no—
495Q8—41no—
496Q8—41no—
497Q8—1728no—
498D4—28no—
499D4—862no—
500D4—862no—
501D4—17216no—
502D4—1721no—
503D4—1721no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—862no—
523C2×C4—864no—
524C2×C4—17216no—
525C2×C4—1721no—
526C2×C4—1722no—
527C2×C4—1721no—
528C2×C4—1722no—
529C2×C4—1728no—
530C2×C4#1306329312yes—
531C2×C4#1306329312yes—
532C2×C4C2×#1062188412yes—
533C2×C4#1306335012yes—
534C2×C4C2×D4×D4311yescharacteristic
535C2×C4C2×D4×D4311yescharacteristic
536C2×C4#41×D4311yescharacteristic
537C2×C4C2×#1062190011yescharacteristic
538C2×C4#1306337011yescharacteristic
539C2×C4#1306337211yescharacteristic
540C8—862no—
541C8—1722no—
542C8—1721no—
543C22—24no—
544C22—24no—
545C22—24no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—3441no—
551C22—3441no—
552C22—3441no—
553C22—3441no—
554C22—1722no—
555C22—1722no—
556C22—1722no—
557C22C2×#1306329311yescharacteristic
558C22#1458354311yescharacteristic
559C22#1458354811yescharacteristic
560C22C22×#1062188411yescharacteristic
561C22C2×#1306335011yescharacteristic
562C22#1458371011yescharacteristic
563C22#1458371411yescharacteristic
564C4—22no—
565C4—42no—
566C4—42no—
567C4—82no—
568C4—81no—
569C4—1722no—
570C4—1724no—
571C4#1458304914yes—
572C4#1458340911yescharacteristic
573C4#1458347811yescharacteristic
574C4#1458355511yescharacteristic
575C4#1458356711yescharacteristic
576C2—44no—
577C2—3442no—
578C2#1913793611yescharacteristic
579C2C2×#1458304911yescharacteristic
580C2#1914390711yescharacteristic
581C2#1914646011yescharacteristic
582C2#1914692211yescharacteristic
583C2#1914694611yescharacteristic
584C2#1914717311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2538C2
socleC23×C43C22×D4
prime radicalC2×#14583553C2
hypercenter#2538D43
hypocenterC43#24120
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2538

Complements

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

NH ≅ G/Ntype
2. C2×#14583184C2semidirect
3. C2×C4×#10621884C2semidirect
4. #19135784C2semidirect
5. #19135596C2semidirect
6. #19135555C2semidirect
7. #19135390C2semidirect
8. #19134903C2semidirect
9. #19134787C2semidirect
10. #19134592C2semidirect
11. C43×#2538C2semidirect
114. C2×Q8×C43#41semidirect
117. C2×D4×C43SD16semidirect
184. C2×C43⋊C8#41semidirect
287. #2538D43semidirect
337. C43#24120semidirect
411. C2×Q8#10621900semidirect
423. C2×D4#10621884semidirect

Maximal subgroups

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

subgroupindex
C2×#145835532
C2×#145831842
C2×C4×#106218842
#191357842
#191355962
#191355552
#191353902
#191349032
#191347872
#191345922
C43×#25382
#2412043