Finite Group Databasebeta

← #25070458

Subgroups — #25070458

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
1C2×#14583496C211yesmaximal, characteristic, complemented
2#19145352C211yesmaximal, characteristic, complemented
3#19145343C211yesmaximal, characteristic
4#19133590C214yesmaximal, complemented
5#19133522C214yesmaximal, complemented
6#19133166C211yesmaximal, characteristic, complemented
7#19133162C211yesmaximal, characteristic, complemented
8C2×#14582625C211yesmaximal, characteristic, complemented
9C43×#2618C211yesmaximal, characteristic, complemented
10#14583496—22no—
11#14583496—22no—
12#14583496—22no—
13#14583496C2214yes—
14C2×#13063320—21no—
15C2×#13063315—21no—
16C2×#13063310—21no—
17C2×#13063308—21no—
18C2×#13063304C2211yescharacteristic
19C2×#13063303—21no—
20C2×#13063299C2211yescharacteristic
21C2×C4×C22⋊D43—21no—
22#14583229C2212yescomplemented
23#14583215—21no—
24#14583212C2212yes—
25#14583210—21no—
26#14583133—22no—
27#14583126—22no—
28#14583050C2212yescomplemented
29#14583037—21no—
30#14583033C2212yes—
31#14583032—21no—
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34#14582635C2214yescomplemented
35#14582632C2214yes—
36#14582625C2214yescomplemented
37C2×#123×C43—21no—
38C2×#121×C43C2211yescharacteristic
39C22×C4⋊C4×C43C2211yescharacteristic
40C43×#398C2212yescomplemented
41C43×#396—22no—
42C43×#394C2212yescomplemented
43C43×#386—21no—
44C43×#380C2211yescharacteristic
45C22×Dic86D411yescharacteristic
46C22×D172D411yescharacteristic
47C22×C22⋊D43—21no—
48C22×C4×D43—21no—
49C2×#10621883—22no—
50C2×#10621882—22no—
51C22×C43⋊C8—21no—
52C22×C43⋊C8—21no—
53#13063320—24no—
54#13063320—24no—
55#13063315—24no—
56#13063315—24no—
57#13063310—24no—
58#13063310—24no—
59#13063308—24no—
60#13063308—24no—
61#13063304—21no—
62#13063304—21no—
63#13063304D412yes—
64#13063304C2312yes—
65#13063303—24no—
66#13063303—24no—
67#13063299—21no—
68#13063299—21no—
69#13063299D412yes—
70#13063299C2312yes—
71C4×C22⋊D43—24no—
72C4×C22⋊D43—24no—
73C2×C4⋊Dic43D411yescharacteristic
74C2×C4⋊Dic43D411yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×C22⋊Dic43—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×C4×Dic43—21no—
85#13063258—22no—
86#13063256—22no—
87#13063248—22no—
88#13063246—22no—
89#13063246—22no—
90#13063245—22no—
91C22⋊(C43⋊C8)—21no—
92C22⋊(C43⋊C8)—21no—
93C22⋊(C43⋊C8)C2312yes—
94C22⋊(C43⋊C8)C2312yes—
95C22×D4×C43—21no—
96C22×D4×C43C2311yescharacteristic
97C23×C4×C43D411yescharacteristic
98C23×C4×C43D411yescharacteristic
99C23×C4×C43C2311yescharacteristic
100#123×C43—44no—
101#121×C43—21no—
102#121×C43—21no—
103#121×C43—21no—
104#121×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—22no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43D412yes—
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2312yes—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—22no—
117C2×C22⋊C4×C43—22no—
118#95×C43—22no—
119#95×C43C2312yes—
120C24×C43—21no—
121C24×C43C2×D411yescharacteristic
122C23×D43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—41no—
126C2×D4×C43—41no—
127C2×D4×C43—42no—
128C2×D4×C43—42no—
129C2×D4×C43—81no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—21no—
137C22×C4×C43—22no—
138C22×C4×C43—81no—
139C22×C4×C43—81no—
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D412yes—
145C22×C4×C43C2×D412yes—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C2×C22⋊D43—22no—
149C2×C22⋊D43—22no—
150C2×C22⋊D43—42no—
151C2×C22⋊D43—42no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C2×D172—21no—
156C2×D172—81no—
157C2×D172C2×D412yes—
158C2×C4×D43—24no—
159C2×C4×D43—82no—
160C2×Dic86—21no—
161C2×Dic86—81no—
162C2×Dic86C2×D412yes—
163C4⋊C4×C43—22no—
164C4⋊C4×C43—22no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—44no—
170C4⋊C4×C43—81no—
171C22⋊C4×C43—44no—
172C22⋊C4×C43—41no—
173C22⋊C4×C43—41no—
174C22⋊C4×C43—42no—
175C22⋊C4×C43—82no—
176C22⋊Dic43—22no—
177C22⋊Dic43—22no—
178#10621883—82no—
179#10621882—82no—
180(C2×D43)⋊C4—24no—
181(C2×D43)⋊C4—24no—
182(C2×D43)⋊C4—24no—
183(C2×D43)⋊C4—22no—
184(C2×D43)⋊C4—22no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43C2×D412yes—
188C4⋊Dic43C2×D412yes—
189Dic43⋊C4—24no—
190Dic43⋊C4—24no—
191Dic43⋊C4—24no—
192Dic43⋊C4—22no—
193Dic43⋊C4—22no—
194C4×Dic43—24no—
195C2×C43⋊C8—22no—
196C2×C43⋊C8—22no—
197C2×C43⋊C8—81no—
198C2×C43⋊C8—81no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—42no—
202C23×C43—42no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43—41no—
206C23×C43#12011yescharacteristic
207C23×C43#12011yescharacteristic
208C23×C43#13512yes—
209C23×C43AGL(1,ℤ/8)12yes—
210C23×C43C22×D411yescharacteristic
211C22×D43—22no—
212C22×D43—42no—
213C22×D43—42no—
214C22×D43—42no—
215D4×C43—42no—
216D4×C43—42no—
217D4×C43—82no—
218D4×C43—82no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—42no—
238C2×C4×C43—41no—
239C2×C4×C43—81no—
240C2×C4×C43#12011yescharacteristic
241C2×C4×C43#12011yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C22×D411yescharacteristic
244C22⋊D43—42no—
245C22⋊D43—42no—
246C22⋊D43—44no—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—42no—
251C2×Dic43—42no—
252C2×Dic43—42no—
253D172—42no—
254D172—81no—
255C4×D43—84no—
256Dic86—42no—
257Dic86—81no—
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—82no—
270C22×C43—82no—
271C22×C43—81no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43#44912yes—
275C22×C43#44912yes—
276C22×C43C2×#12011yescharacteristic
277C22×C43C2×#13511yescharacteristic
278C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
279C2×D43—42no—
280C2×D43—42no—
281C2×D43—42no—
282C2×D43—84no—
283C4×C43—21no—
284C4×C43—21no—
285C4×C43—21no—
286C4×C43—21no—
287C4×C43—42no—
288C4×C43—42no—
289C4×C43—82no—
290C4×C43—81no—
291Dic43—42no—
292Dic43—42no—
293Dic43—42no—
294C2×#539—431no—
295#3187—431no—
296#3186—431no—
297#2618D4311yescharacteristic, complemented
298#1609—434no—
299#1597—434no—
300#1520—431no—
301#1519—431no—
302C2×#324—431no—
303C2×C43—21no—
304C2×C43—22no—
305C2×C43—21no—
306C2×C43—22no—
307C2×C43—161no—
308C2×C43C2×#44911yescharacteristic
309C2×C43#302011yescharacteristic
310C2×C43#302611yescharacteristic
311D43—82no—
312#539—434no—
313#539—862no—
314#539—862no—
315#539—862no—
316C2×#126—861no—
317C2×#125—861no—
318C2×#123—21no—
319C2×#123—861no—
320C2×#123—861no—
321C2×C22⋊Q8—431no—
322C2×C22⋊Q8—861no—
323C2×#121—431no—
324C2×#121C2×D4311yescharacteristic
325C2×C4×D4—861no—
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#398C2×D4312yescomplemented
340#396—22no—
341#394C2×D4312yescomplemented
342#386—21no—
343#380C2×D4311yescharacteristic
344#328—434no—
345#327—434no—
346#324—434no—
347C43#1828811yescharacteristic, complemented, Sylow
348C22×Q8—431no—
349C22×D4—21no—
350C22×D4—431no—
351C22×D4—861no—
352C22×D4C22×D4311yescharacteristic
353C23×C4—861no—
354C23×C4C22⋊D4311yescharacteristic
355C23×C4C22⋊D4311yescharacteristic
356C23×C4C22×D4311yescharacteristic
357C2×SD16—862no—
358C2×D8—862no—
359C22×C8—861no—
360C22×C8—861no—
361#126—864no—
362#126—864no—
363#125—864no—
364#125—864no—
365#123—44no—
366#123—864no—
367#123—864no—
368#123—864no—
369#123—864no—
370C22⋊Q8—432no—
371C22⋊Q8—432no—
372C22⋊Q8—864no—
373C22⋊Q8—864no—
374C22⋊Q8—861no—
375C22⋊Q8—861no—
376#121—21no—
377#121—21no—
378#121—21no—
379#121—21no—
380#121—432no—
381#121—432no—
382#121—861no—
383#121—861no—
384C4×D4—864no—
385C4×D4—864no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4C22⋊D4312yes—
399C2×C4⋊C4C22×D4311yescharacteristic
400C2×C4⋊C4C22×D4312yes—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C42—861no—
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—22no—
422#95C22×D4312yes—
423C24—21no—
424C24—861no—
425C24C2×C22⋊D4311yescharacteristic
426C2×Q8—432no—
427C2×Q8—861no—
428C2×Q8—3441no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—41no—
432C2×D4—41no—
433C2×D4—42no—
434C2×D4—42no—
435C2×D4—81no—
436C2×D4—432no—
437C2×D4—862no—
438C2×D4—862no—
439C2×D4—861no—
440C2×D4—3441no—
441C2×D4—1722no—
442C2×D4—1722no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—81no—
452C22×C4—81no—
453C22×C4—864no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—3442no—
458C22×C4D4×D4311yescharacteristic
459C22×C4D4×D4311yescharacteristic
460C22×C4D4×D4311yescharacteristic
461C22×C4D4×D4311yescharacteristic
462C22×C4C2×C22⋊D4312yes—
463C22×C4C2×C22⋊D4312yes—
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—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—44no—
479C4⋊C4—81no—
480C4⋊C4—432no—
481C4⋊C4—432no—
482C4⋊C4—864no—
483C4⋊C4—864no—
484C4⋊C4—864no—
485C4⋊C4—861no—
486C4⋊C4—861no—
487C4⋊C4—862no—
488C4⋊C4—862no—
489C22⋊C4—44no—
490C22⋊C4—42no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—82no—
494C22⋊C4—864no—
495C22⋊C4—864no—
496C22⋊C4—864no—
497C22⋊C4—862no—
498C22⋊C4—862no—
499C22⋊C4—862no—
500C22⋊C4—862no—
501C42—864no—
502C23—41no—
503C23—41no—
504C23—42no—
505C23—42no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—862no—
510C23—1722no—
511C23—1722no—
512C23—1722no—
513C23#1306329311yescharacteristic
514C23#1306329311yescharacteristic
515C23#1306334512yes—
516C23#1306335112yes—
517C23C22×C22⋊D4311yescharacteristic
518Q8—3441no—
519Q8—1722no—
520D4—42no—
521D4—42no—
522D4—82no—
523D4—82no—
524D4—3441no—
525D4—1722no—
526D4—1724no—
527D4—1722no—
528D4—1722no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—41no—
549C2×C4—81no—
550C2×C4—862no—
551C2×C4—862no—
552C2×C4—862no—
553C2×C4—3444no—
554C2×C4—1722no—
555C2×C4—1722no—
556C2×C4—1722no—
557C2×C4#1306329311yescharacteristic
558C2×C4#1306329311yescharacteristic
559C2×C4C2×D4×D4311yescharacteristic
560C2×C4C2×D4×D4311yescharacteristic
561C8—1722no—
562C8—1722no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—42no—
570C22—42no—
571C22—82no—
572C22—82no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—3444no—
577C22—1722no—
578C22—1722no—
579C22—1722no—
580C22#1458304212yes—
581C22#1458304212yes—
582C22C2×#1306329311yescharacteristic
583C22C2×#1306334511yescharacteristic
584C22C2×#1306335111yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—42no—
590C4—42no—
591C4—82no—
592C4—81no—
593C4—1722no—
594C4—1722no—
595C4—1722no—
596C2—21no—
597C2—21no—
598C2—22no—
599C2—22no—
600C2—161no—
601C2—3442no—
602C2C2×#1458304211yescharacteristic
603C2#1914395811yescharacteristic
604C2#1914399111yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2618C2
socleC22×C43C2×#120
prime radical#19145343C2
hypercenter#2618D43
hypocenterC43#18288
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2618

Complements

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

NH ≅ G/Ntype
1. C2×#14583496C2semidirect
2. #19145352C2semidirect
4. #19133590C2semidirect
5. #19133522C2semidirect
6. #19133166C2semidirect
7. #19133162C2semidirect
8. C2×#14582625C2semidirect
9. C43×#2618C2semidirect
22. #14583229C22semidirect
28. #14583050C22semidirect
34. #14582635C22semidirect
36. #14582625C22semidirect
40. C43×#398C22semidirect
42. C43×#394C22semidirect
297. #2618D43semidirect
339. #398C2×D43semidirect
341. #394C2×D43semidirect
347. C43#18288semidirect

Maximal subgroups

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

subgroupindex
C2×#145834962
#191453522
#191453432
#191335902
#191335222
#191331662
#191331622
C2×#145826252
C43×#26182
#1828843