Finite Group Databasebeta

← #25070460

Subgroups — #25070460

Order 11008.

1034 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145348C211yesmaximal, characteristic, complemented
2#19145343C211yesmaximal, characteristic
3#19140337C211yesmaximal, characteristic, complemented
4#19133592C214yesmaximal, complemented
5#19133524C214yesmaximal, complemented
6#19133167C211yesmaximal, characteristic, complemented
7#19133163C211yesmaximal, characteristic, complemented
8C2×#14582625C211yesmaximal, characteristic, complemented
9C2×C43×#539C211yesmaximal, characteristic, complemented
10C2×#13063308—21no—
11C2×#13063299C2211yescharacteristic
12#14583227C2212yescomplemented
13#14583217—21no—
14#14583212—21no—
15#14583210C2212yes—
16#14583133—22no—
17#14583130—22no—
18#14583049C2212yescomplemented
19#14583038—21no—
20#14583033—21no—
21#14583032C2212yes—
22C2×C22⋊(C43⋊C8)C2211yescharacteristic
23C2×C22⋊(C43⋊C8)C2211yescharacteristic
24#14582829C2212yescomplemented
25#14582821—22no—
26#14582816C2212yescomplemented
27#14582778—21no—
28#14582759C2211yescharacteristic
29#14582636C2214yescomplemented
30#14582633C2214yes—
31#14582625C2214yescomplemented
32C43×#539—22no—
33C43×#539—22no—
34C43×#539—22no—
35C43×#539C2214yes—
36C2×#126×C43—21no—
37C2×#125×C43—21no—
38C2×#123×C43—21no—
39C2×#123×C43—21no—
40C2×C22⋊Q8×C43—21no—
41C2×C22⋊Q8×C43C2211yescharacteristic
42C2×#121×C43C2211yescharacteristic
43C2×C4×D4×C43—21no—
44C22×C4⋊C4×C43C2211yescharacteristic
45C22×D172C2311yescharacteristic
46C22×C22⋊D43—21no—
47C2×#10621884—22no—
48C2×#10621882—22no—
49C22×C43⋊C8—21no—
50C22×C43⋊C8—21no—
51#13063308—44no—
52#13063299—21no—
53#13063299—21no—
54#13063299—21no—
55#13063299—21no—
56C2×C4⋊Dic43—21no—
57C2×C4⋊Dic43C2311yescharacteristic
58C2×Dic43⋊C4—22no—
59C2×C22⋊Dic43—21no—
60C2×(C2×D43)⋊C4—22no—
61C2×(C2×D43)⋊C4—21no—
62C2×(C2×D43)⋊C4—22no—
63#13063258—22no—
64#13063256—22no—
65#13063249—22no—
66#13063246—22no—
67#13063245—22no—
68#13063245—22no—
69C22⋊(C43⋊C8)—21no—
70C22⋊(C43⋊C8)—21no—
71C22⋊(C43⋊C8)C2312yes—
72C22⋊(C43⋊C8)C2312yes—
73C43⋊#95—22no—
74C43⋊#95C2312yes—
75C22×Q8×C43D411yescharacteristic
76C22×D4×C43—21no—
77C22×D4×C43D411yescharacteristic
78C23×C4×C43—21no—
79C23×C4×C43D411yescharacteristic
80C23×C4×C43D411yescharacteristic
81C23×C4×C43C2311yescharacteristic
82#126×C43—24no—
83#126×C43—24no—
84#125×C43—24no—
85#125×C43—24no—
86#123×C43—24no—
87#123×C43—24no—
88#123×C43—24no—
89#123×C43—24no—
90C22⋊Q8×C43—24no—
91C22⋊Q8×C43—24no—
92C22⋊Q8×C43—21no—
93C22⋊Q8×C43—21no—
94C22⋊Q8×C43D412yes—
95C22⋊Q8×C43C2312yes—
96#121×C43—21no—
97#121×C43—21no—
98#121×C43D412yes—
99#121×C43C2312yes—
100C4×D4×C43—24no—
101C4×D4×C43—24no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43D412yes—
111C2×C4⋊C4×C43D411yescharacteristic
112C2×C4⋊C4×C43D411yescharacteristic
113C2×C4⋊C4×C43C2312yes—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43—21no—
119C2×C42×C43—21no—
120C24×C43—21no—
121C24×C43C2×D411yescharacteristic
122C23×D43—21no—
123C2×Q8×C43—21no—
124C2×Q8×C43—81no—
125C2×Q8×C43C2×D412yes—
126C2×D4×C43—21no—
127C2×D4×C43—22no—
128C2×D4×C43—22no—
129C2×D4×C43—42no—
130C2×D4×C43—42no—
131C2×D4×C43—81no—
132C2×D4×C43C2×D412yes—
133C22×C4×C43—24no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—81no—
144C22×C4×C43—81no—
145C22×C4×C43—82no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D412yes—
151C22×C4×C43C2×D412yes—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C2×C22⋊D43—41no—
155C2×C22⋊D43—41no—
156C2×C22⋊D43—42no—
157C2×C22⋊D43—42no—
158C22×Dic43—21no—
159C22×Dic43—22no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—81no—
163C4⋊C4×C43—24no—
164C4⋊C4×C43—24no—
165C4⋊C4×C43—24no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—22no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—22no—
172C4⋊C4×C43—22no—
173C4⋊C4×C43—22no—
174C4⋊C4×C43C2×D412yes—
175C4⋊C4×C43C2×D412yes—
176C22⋊C4×C43—24no—
177C22⋊C4×C43—24no—
178C22⋊C4×C43—24no—
179C22⋊C4×C43—22no—
180C22⋊C4×C43—22no—
181C22⋊C4×C43—22no—
182C22⋊C4×C43—22no—
183C42×C43—24no—
184C22⋊Dic43—42no—
185#10621884—82no—
186#10621882—82no—
187(C2×D43)⋊C4—44no—
188(C2×D43)⋊C4—41no—
189(C2×D43)⋊C4—41no—
190(C2×D43)⋊C4—82no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—81no—
194Dic43⋊C4—44no—
195C2×C43⋊C8—22no—
196C2×C43⋊C8—22no—
197C2×C43⋊C8—81no—
198C2×C43⋊C8—81no—
199C23×C43—22no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—42no—
203C23×C43—42no—
204C23×C43—42no—
205C23×C43#12011yescharacteristic
206C23×C43#12011yescharacteristic
207C23×C43#13512yes—
208C23×C43AGL(1,ℤ/8)12yes—
209C23×C43C22×D411yescharacteristic
210C22×D43—42no—
211C22×D43—42no—
212C22×D43—41no—
213C22×D43—41no—
214C22×D43—41no—
215Q8×C43—42no—
216Q8×C43—81no—
217D4×C43—42no—
218D4×C43—42no—
219D4×C43—42no—
220D4×C43—44no—
221D4×C43—81no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—81no—
243C2×C4×C43—84no—
244C2×C4×C43#12011yescharacteristic
245C2×C4×C43#12011yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C22×D411yescharacteristic
248C22⋊D43—82no—
249C22⋊D43—82no—
250C2×Dic43—42no—
251C2×Dic43—42no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—42no—
256D172—42no—
257D172—42no—
258C43⋊C8—42no—
259C43⋊C8—42no—
260#18288—431nomaximal, Sylow
261C22×C43—21no—
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—42no—
268C22×C43—42no—
269C22×C43—42no—
270C22×C43—42no—
271C22×C43—42no—
272C22×C43—84no—
273C22×C43#44912yes—
274C22×C43#44912yes—
275C22×C43C2×#12011yescharacteristic
276C22×C43C2×#13511yescharacteristic
277C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
278C2×D43—82no—
279C2×D43—82no—
280C2×D43—81no—
281C2×D43—81no—
282C2×D43—81no—
283C4×C43—21no—
284C4×C43—21no—
285C4×C43—21no—
286C4×C43—21no—
287C4×C43—42no—
288C4×C43—42no—
289C4×C43—42no—
290C4×C43—42no—
291C4×C43—42no—
292Dic43—82no—
293Dic43—81no—
294C2×#539D4311yescharacteristic, complemented
295#3187—431no—
296#3186—431no—
297#2618—431no—
298#1609—434no—
299#1597—434no—
300#1520—431no—
301#1519—431no—
302C2×#324—431no—
303C2×C43—21no—
304C2×C43—21no—
305C2×C43—22no—
306C2×C43—22no—
307C2×C43—82no—
308C2×C43C2×#44911yescharacteristic
309C2×C43#302011yescharacteristic
310C2×C43#302611yescharacteristic
311D43—161no—
312#539—22no—
313#539—22no—
314#539—22no—
315#539C2×D4314yes—
316C2×#126—21no—
317C2×#125—21no—
318C2×#123—21no—
319C2×#123—21no—
320C2×#123—861no—
321C2×C22⋊Q8—21no—
322C2×C22⋊Q8C2×D4311yescharacteristic
323C2×#121—431no—
324C2×#121C2×D4311yescharacteristic
325C2×C4×D4—21no—
326C22×C4⋊C4C2×D4311yescharacteristic
327#483—432no—
328#481—861no—
329#480—432no—
330#480—861no—
331#466—862no—
332#465—862no—
333#450—432no—
334#448—861no—
335#447—432no—
336#447—861no—
337C2×C22⋊C8—431no—
338C2×C22⋊C8—431no—
339#398—432no—
340#396—862no—
341#394—432no—
342#386—861no—
343#380—431no—
344#328—434no—
345#327—434no—
346#324—434no—
347C43#1828811yescharacteristic, complemented, Sylow
348C22×Q8C22⋊D4311yescharacteristic
349C22×D4—21no—
350C22×D4—431no—
351C22×D4—861no—
352C22×D4C22⋊D4311yescharacteristic
353C23×C4—21no—
354C23×C4C22⋊D4311yescharacteristic
355C23×C4C22⋊D4311yescharacteristic
356C23×C4C22×D4311yescharacteristic
357C2×SD16—862no—
358C2×D8—862no—
359C22×C8—861no—
360C22×C8—861no—
361#126—24no—
362#126—24no—
363#125—24no—
364#125—24no—
365#123—24no—
366#123—24no—
367#123—24no—
368#123—24no—
369#123—1724no—
370C22⋊Q8—24no—
371C22⋊Q8—24no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8C22⋊D4312yes—
375C22⋊Q8C22×D4312yes—
376#121—21no—
377#121—21no—
378#121—861no—
379#121—861no—
380#121—861no—
381#121—861no—
382#121C22⋊D4312yes—
383#121C22×D4312yes—
384C4×D4—24no—
385C4×D4—24no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—862no—
397C2×C4⋊C4C22⋊D4312yes—
398C2×C4⋊C4C22⋊D4311yescharacteristic
399C2×C4⋊C4C22⋊D4311yescharacteristic
400C2×C4⋊C4C22×D4312yes—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—862no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—862no—
410C2×C42—21no—
411#107—862no—
412#106—862no—
413#103—862no—
414#102—862no—
415#102—862no—
416#102—862no—
417C22⋊C8—432no—
418C22⋊C8—432no—
419C22⋊C8—861no—
420C22⋊C8—861no—
421#95—432no—
422#95—862no—
423C24—21no—
424C24—861no—
425C24C2×C22⋊D4311yescharacteristic
426C2×Q8—21no—
427C2×Q8—81no—
428C2×Q8C2×C22⋊D4312yes—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—21no—
432C2×D4—42no—
433C2×D4—42no—
434C2×D4—81no—
435C2×D4—861no—
436C2×D4—861no—
437C2×D4—3441no—
438C2×D4—1721no—
439C2×D4—1721no—
440C2×D4—1722no—
441C2×D4—1722no—
442C2×D4C2×C22⋊D4312yes—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—24no—
452C22×C4—21no—
453C22×C4—81no—
454C22×C4—81no—
455C22×C4—82no—
456C22×C4—862no—
457C22×C4—861no—
458C22×C4C2×C22⋊D4312yes—
459C22×C4C2×C22⋊D4312yes—
460C22×C4C2×C22⋊D4311yescharacteristic
461C22×C4C2×C22⋊D4311yescharacteristic
462C22×C4C2×C22⋊D4311yescharacteristic
463C22×C4C2×C22⋊D4311yescharacteristic
464C22×C4C2×C22⋊D4311yescharacteristic
465C22×C4C23×D4311yescharacteristic
466SD16—3442no—
467D8—3442no—
468C2×C8—862no—
469C2×C8—862no—
470C2×C8—3441no—
471C2×C8—3441no—
472C4⋊C4—24no—
473C4⋊C4—24no—
474C4⋊C4—24no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—861no—
484C4⋊C4—861no—
485C4⋊C4—3441no—
486C4⋊C4—1724no—
487C4⋊C4C2×C22⋊D4312yes—
488C4⋊C4C2×C22⋊D4312yes—
489C22⋊C4—24no—
490C22⋊C4—24no—
491C22⋊C4—24no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—3442no—
497C22⋊C4—1724no—
498C22⋊C4—1722no—
499C22⋊C4—1721no—
500C22⋊C4—1721no—
501C42—24no—
502C23—22no—
503C23—41no—
504C23—41no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—1722no—
509C23—1722no—
510C23—1721no—
511C23—1721no—
512C23—1721no—
513C23#1306329411yescharacteristic
514C23#1306329411yescharacteristic
515C23#1306334512yes—
516C23#1306335012yes—
517C23C22×C22⋊D4311yescharacteristic
518Q8—42no—
519Q8—81no—
520D4—42no—
521D4—44no—
522D4—42no—
523D4—42no—
524D4—81no—
525D4—3442no—
526D4—3442no—
527D4—1722no—
528D4—1722no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—81no—
550C2×C4—84no—
551C2×C4—1722no—
552C2×C4—1722no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1722no—
556C2×C4—1721no—
557C2×C4#1306329411yescharacteristic
558C2×C4#1306329411yescharacteristic
559C2×C4C22×C22⋊D4311yescharacteristic
560C2×C4C22×C22⋊D4311yescharacteristic
561C8—1722no—
562C8—1722no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22—84no—
575C22—3442no—
576C22—3442no—
577C22—3441no—
578C22—3441no—
579C22—3441no—
580C22#1458304412yes—
581C22#1458304412yes—
582C22C2×#1306329411yescharacteristic
583C22C2×#1306334511yescharacteristic
584C22C2×#1306335011yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—42no—
590C4—42no—
591C4—42no—
592C4—42no—
593C4—42no—
594C4—3442no—
595C4—3441no—
596C2—21no—
597C2—22no—
598C2—21no—
599C2—22no—
600C2—82no—
601C2—6881no—
602C2C2×#1458304411yescharacteristic
603C2#1914395911yescharacteristic
604C2#1914399211yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#539C2
socleC22×C43C2×#120
prime radical#19145343C2
hypercenterC2×#539D43
hypocenterC43#18288
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#539

Complements

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

NH ≅ G/Ntype
1. #19145348C2semidirect
3. #19140337C2semidirect
4. #19133592C2semidirect
5. #19133524C2semidirect
6. #19133167C2semidirect
7. #19133163C2semidirect
8. C2×#14582625C2semidirect
9. C2×C43×#539C2semidirect
12. #14583227C22semidirect
18. #14583049C22semidirect
24. #14582829C22semidirect
26. #14582816C22semidirect
29. #14582636C22semidirect
31. #14582625C22semidirect
294. C2×#539D43semidirect
347. C43#18288semidirect

Maximal subgroups

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

subgroupindex
#191453482
#191453432
#191403372
#191335922
#191335242
#191331672
#191331632
C2×#145826252
C2×C43×#5392
#1828843