Finite Group Databasebeta

← #25105917

Subgroups — #25105917

Order 11008.

1450 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#124×D43C211yesmaximal, characteristic
2C2×#14582950C211yesmaximal, characteristic, complemented
3#19136988C211yesmaximal, characteristic, complemented
4#19135526C212yesmaximal, complemented
5#19135524C212yesmaximal, complemented
6#19135407C211yesmaximal, characteristic, complemented
7#19135406C211yesmaximal, characteristic, complemented
8#19135404C211yesmaximal, characteristic, complemented
9#19134528C212yesmaximal, complemented
10#19134524C212yesmaximal
11C43×#1958C211yesmaximal, characteristic, complemented
12C22×Q8×D43C2211yescharacteristic
13C22×D4×D43C2211yescharacteristic
14C2×#13063314C2211yescharacteristic
15C2×#13063313C2211yescharacteristic
16C2×#13063312C2211yescharacteristic
17C2×#13063311—21no—
18C2×#13063311—21no—
19#124×D43—24no—
20#124×D43C418yescomplemented
21C2×C22⋊C4×D43—21no—
22C2×C22⋊C4×D43—21no—
23C2×C42×D43C2211yescharacteristic
24#14582950—24no—
25C2×Dic43⋊C8C2212yescomplemented
26C2×#13063250C2212yescomplemented
27C2×#13063249C2212yescomplemented
28C2×#13063248C2212yescomplemented
29C2×#13063247C2212yes—
30C2×#13063246C2212yes—
31C2×#13063245C2212yes—
32C2×(C2×D43)⋊C8C2212yes—
33C2×C4×C43⋊C8C2211yescharacteristic, complemented
34#14582766—21no—
35#14582765C2211yescharacteristic, complemented
36#14582761—21no—
37#14582756C2212yes—
38C4⋊C4×Dic43C2212yescomplemented
39#14582746—21no—
40#14582744—21no—
41C2×#124×C43C2211yescharacteristic
42C2×#103×C43C2212yescomplemented
43C2×#102×C43C2212yes—
44C2×C4×C8×C43C2211yescharacteristic, complemented
45C43×#382C2211yescharacteristic, complemented
46C24×D43—21no—
47C22×Dic86—21no—
48C22×Dic86C2311yescharacteristic
49C2×Q8×D43—22no—
50C2×Q8×D43—42no—
51C2×Q8×D43—42no—
52C2×Q8×D43C2×C414yes—
53C22×D172C2311yescharacteristic
54C22×C22⋊D43—21no—
55C2×D4×D43—22no—
56C2×D4×D43—42no—
57C2×D4×D43—42no—
58C2×D4×D43C2×C414yes—
59C22×C4×D43—21no—
60C22×C4×D43D411yescharacteristic
61C22×C4×D43D411yescharacteristic
62C22×C4×D43C2311yescharacteristic
63C22×C43⋊C8C2312yes—
64#13063314—22no—
65#13063314C2×C414yes—
66#13063313—22no—
67#13063313C2×C414yes—
68#13063312—22no—
69#13063312C2×C414yes—
70#13063311—28no—
71#13063311—28no—
72C2×C4⋊Dic43C2312yes—
73C2×C22⋊Dic43—21no—
74C2×C22⋊Dic43—21no—
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—22no—
80C22⋊C4×D43—28no—
81C22⋊C4×D43—28no—
82C2×C4×Dic43—22no—
83C2×C4×Dic43D411yescharacteristic
84C2×C4×Dic43D411yescharacteristic
85C2×C4×Dic43C2311yescharacteristic
86C42×D43C2×C414yes—
87C42×D43D414yes—
88Dic43⋊C8—24no—
89#13063250—42no—
90#13063249—42no—
91#13063248—42no—
92#13063247—42no—
93#13063246—42no—
94#13063245—42no—
95(C2×D43)⋊C8—24no—
96C4×C43⋊C8—22no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—22no—
100C43⋊#95—22no—
101C22×Q8×C43C2311yescharacteristic
102C22×D4×C43C2311yescharacteristic
103C22×C8×C43C2312yes—
104#124×C43—22no—
105#124×C43C2×C414yes—
106C2×C4⋊C4×C43C2312yes—
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C42×C43C2311yescharacteristic
110#103×C43—42no—
111#102×C43—42no—
112C4×C8×C43—22no—
113#95×C43—21no—
114#95×C43—21no—
115C24×C43—21no—
116C23×D43—21no—
117C23×D43—24no—
118C23×D43—42no—
119C23×D43—42no—
120C23×D43—44no—
121C23×D43—44no—
122C23×D43C2×D411yescharacteristic
123C2×Q8×C43—21no—
124C2×Q8×C43—22no—
125C2×Q8×C43—22no—
126C2×Q8×C43C22×C412yes—
127C2×D4×C43—21no—
128C2×D4×C43—22no—
129C2×D4×C43—22no—
130C2×D4×C43C22×C412yes—
131C22×C4×C43—21no—
132C22×C4×C43—22no—
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2411yescharacteristic
136C2×C22⋊D43—24no—
137C2×C22⋊D43—42no—
138C2×C22⋊D43—42no—
139C22×Dic43—21no—
140C22×Dic43—22no—
141C22×Dic43C2×D411yescharacteristic
142C22×Dic43C2×D411yescharacteristic
143C22×Dic43C2×D411yescharacteristic
144Q8×D43—48no—
145Q8×D43—48no—
146D4×D43—48no—
147D4×D43—48no—
148C2×D172—21no—
149C2×D172—22no—
150C2×D172—22no—
151C2×D172C22×C412yes—
152C2×C4×D43—22no—
153C2×C4×D43—22no—
154C2×C4×D43—24no—
155C2×C4×D43—24no—
156C2×C4×D43—42no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43C22⋊C414yes—
160C2×C4×D43C22⋊C414yes—
161C2×C4×D43C22×C412yes—
162C2×C4×D43C2×D412yes—
163C2×Dic86—22no—
164C2×Dic86—22no—
165C2×Dic86—21no—
166C2×Dic86—24no—
167C2×Dic86—42no—
168C2×Dic86—42no—
169C2×Dic86C22×C412yes—
170C2×C8×C43—22no—
171C2×C8×C43—22no—
172C2×C8×C43—22no—
173C4⋊C4×C43—22no—
174C4⋊C4×C43—22no—
175C22⋊C4×C43—24no—
176C22⋊C4×C43—24no—
177C42×C43C22×C412yes—
178C42×C43C2×D412yes—
179C22⋊Dic43—24no—
180C22⋊Dic43—24no—
181(C2×D43)⋊C4—24no—
182(C2×D43)⋊C4—24no—
183(C2×D43)⋊C4—24no—
184(C2×D43)⋊C4—24no—
185(C2×D43)⋊C4—44no—
186C4⋊Dic43—22no—
187C4⋊Dic43—22no—
188C4×Dic43—44no—
189C4×Dic43C22⋊C414yes—
190C4×Dic43C22⋊C414yes—
191C4×Dic43C22×C412yes—
192C4×Dic43C2×D412yes—
193C2×C43⋊C8—22no—
194C2×C43⋊C8—22no—
195C2×C43⋊C8—22no—
196C23×C43—22no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43—42no—
200C23×C43—42no—
201C23×C43C22×D411yescharacteristic
202C22×D43—21no—
203C22×D43—21no—
204C22×D43—22no—
205C22×D43—22no—
206C22×D43—48no—
207C22×D43—48no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—42no—
211C22×D43—42no—
212C22×D43—48no—
213C22×D43—88no—
214C22×D43—88no—
215C22×D43C2×C22⋊C412yes—
216C22×D43#13514yes—
217Q8×C43—24no—
218Q8×C43—42no—
219D4×C43—24no—
220D4×C43—42no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—42no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43C2×C22⋊C412yes—
230C2×C4×C43C2×C22⋊C412yes—
231C2×C4×C43C23×C411yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43H(5,𝔽2)12yes—
234C2×C4×C43H(5,𝔽2)12yes—
235C22⋊D43—48no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—22no—
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43C2×C22⋊C412yes—
247C2×Dic43C2×C22⋊C412yes—
248C2×Dic43C2×C22⋊C412yes—
249D172—24no—
250D172—42no—
251C4×D43—28no—
252C4×D43—24no—
253C4×D43—24no—
254C4×D43—44no—
255C4×D43—48no—
256Dic86—24no—
257Dic86—48no—
258Dic86—42no—
259C8×C43—42no—
260C43⋊C8—42no—
261#21806—431nomaximal, Sylow
262C22×C43—42no—
263C22×C43—42no—
264C22×C43—42no—
265C22×C43—82no—
266C22×C43—82no—
267C22×C43C22×C22⋊C411yescharacteristic
268C22×C43#53511yescharacteristic
269C22×C43#53511yescharacteristic
270C22×C43C2×#13512yes—
271C22×C43#57512yes—
272C2×D43—22no—
273C2×D43—22no—
274C2×D43—24no—
275C2×D43—24no—
276C2×D43—42no—
277C2×D43—42no—
278C2×D43—42no—
279C2×D43—816no—
280C2×D43—82no—
281C2×D43—82no—
282C2×D43#41614yes—
283C4×C43—22no—
284C4×C43—22no—
285C4×C43—42no—
286C4×C43—82no—
287C4×C43#51812yes—
288C4×C43#53512yes—
289Dic43—22no—
290Dic43—22no—
291Dic43—22no—
292Dic43—42no—
293Dic43—82no—
294C22×#124—431no—
295C2×#431—431no—
296#2283—431no—
297#1983—432no—
298#1983—432no—
299#1958—431no—
300#1958—431no—
301#1958—431no—
302#1958D4311yescharacteristic, complemented
303#1787—432no—
304#1786—432no—
305C2×C43—82no—
306C2×C43#230911yescharacteristic
307C2×C43C2×#41611yescharacteristic
308C2×C43#289611yescharacteristic
309C2×C43#321112yes—
310C2×C43#321112yes—
311D43—24no—
312D43—82no—
313C23×Q8—431no—
314C23×D4—431no—
315C2×#124—431no—
316C2×#124—431no—
317C2×#124—438no—
318C2×#124—431no—
319C2×#124—861no—
320C2×#124—861no—
321C2×#124—864no—
322C2×#124C2×D4311yescharacteristic
323C22×C22⋊C4—861no—
324C22×C22⋊C4—861no—
325C22×C42—431no—
326#431—864no—
327C2×C4⋊C8—432no—
328C2×#103—432no—
329C2×#103—432no—
330C2×#103—432no—
331C2×#103C2×D4312yescomplemented
332C2×#102—432no—
333C2×#102—432no—
334C2×#102—432no—
335C2×#102C2×D4312yes—
336C2×C22⋊C8—432no—
337C2×C4×C8—431no—
338C2×C4×C8C2×D4311yescharacteristic, complemented
339#383—861no—
340#382—431no—
341#382C2×D4311yescharacteristic, complemented
342#381—861no—
343#380—432no—
344C4×C4⋊C4—432no—
345C4×C22⋊C4—861no—
346#376—861no—
347C43#2180611yescharacteristic, complemented, Sylow
348C25—861no—
349C22×Q8—434no—
350C22×Q8—431no—
351C22×Q8—861no—
352C22×Q8—862no—
353C22×Q8—1722no—
354C22×Q8—1722no—
355C22×Q8C22×D4311yescharacteristic
356C22×D4—434no—
357C22×D4—431no—
358C22×D4—862no—
359C22×D4—861no—
360C22×D4—1722no—
361C22×D4—1722no—
362C22×D4C22×D4311yescharacteristic
363C23×C4—431no—
364C23×C4—431no—
365C23×C4—431no—
366C23×C4—861no—
367C22×C8—432no—
368C22×C8C22×D4312yes—
369#124—22no—
370#124—434no—
371#124—434no—
372#124—434no—
373#124—868no—
374#124—868no—
375#124—862no—
376#124—862no—
377#124—862no—
378#124C4×D4314yes—
379C2×C4⋊C4—432no—
380C2×C4⋊C4C22×D4312yes—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—868no—
384C2×C22⋊C4—868no—
385C2×C22⋊C4—861no—
386C2×C22⋊C4—861no—
387C2×C22⋊C4—861no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—862no—
392C2×C42—431no—
393C2×C42—431no—
394C2×C42—431no—
395C2×C42—434no—
396C2×C42—434no—
397C2×C42—862no—
398C2×C42C22×D4311yescharacteristic
399C4⋊C8—864no—
400#103—42no—
401#103—1722no—
402#103—1722no—
403#103—1722no—
404#102—42no—
405#102—1722no—
406#102—1722no—
407#102—1722no—
408C22⋊C8—864no—
409C4×C8—22no—
410C4×C8—862no—
411#95—21no—
412#95—21no—
413#95—862no—
414#95—862no—
415#95—861no—
416#95—861no—
417C24—21no—
418C24—431no—
419C24—864no—
420C24—861no—
421C24—1724no—
422C24—1722no—
423C24—1722no—
424C24—1724no—
425C2×Q8—21no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—432no—
429C2×Q8—864no—
430C2×Q8—861no—
431C2×Q8—862no—
432C2×Q8—862no—
433C2×Q8—1722no—
434C2×Q8—1722no—
435C2×Q8—1728no—
436C2×Q8—1728no—
437C2×Q8C2×C4×D4312yes—
438C2×D4—21no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—432no—
442C2×D4—864no—
443C2×D4—861no—
444C2×D4—862no—
445C2×D4—862no—
446C2×D4—1728no—
447C2×D4—1728no—
448C2×D4—1722no—
449C2×D4—1722no—
450C2×D4C2×C4×D4312yes—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—431no—
454C22×C4—431no—
455C22×C4—431no—
456C22×C4—434no—
457C22×C4—432no—
458C22×C4—432no—
459C22×C4—434no—
460C22×C4—864no—
461C22×C4—864no—
462C22×C4—862no—
463C22×C4—862no—
464C22×C4—861no—
465C22×C4—862no—
466C22×C4—1722no—
467C22×C4—1722no—
468C22×C4—1722no—
469C22×C4D4×D4311yescharacteristic
470C22×C4D4×D4311yescharacteristic
471C22×C4C23×D4311yescharacteristic
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—862no—
476C2×C8—862no—
477C2×C8—862no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—862no—
481C4⋊C4—862no—
482C22⋊C4—24no—
483C22⋊C4—24no—
484C22⋊C4—864no—
485C22⋊C4—864no—
486C22⋊C4—864no—
487C22⋊C4—864no—
488C22⋊C4—864no—
489C22⋊C4—864no—
490C22⋊C4—1724no—
491C42—434no—
492C42—434no—
493C42—432no—
494C42—432no—
495C42—1724no—
496C42C2×C4×D4312yes—
497C42D4×D4312yes—
498C23—22no—
499C23—42no—
500C23—42no—
501C23—41no—
502C23—41no—
503C23—432no—
504C23—434no—
505C23—862no—
506C23—861no—
507C23—861no—
508C23—862no—
509C23—3448no—
510C23—3448no—
511C23—1728no—
512C23—1728no—
513C23—1728no—
514C23—1722no—
515C23—1722no—
516C23—1721no—
517C23—1721no—
518C23C2×D4×D4311yescharacteristic
519Q8—24no—
520Q8—42no—
521Q8—864no—
522Q8—1728no—
523Q8—1722no—
524D4—24no—
525D4—42no—
526D4—864no—
527D4—1728no—
528D4—1722no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—432no—
538C2×C4—432no—
539C2×C4—432no—
540C2×C4—868no—
541C2×C4—862no—
542C2×C4—862no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—864no—
546C2×C4—864no—
547C2×C4—862no—
548C2×C4—1724no—
549C2×C4—1728no—
550C2×C4—1722no—
551C2×C4—1722no—
552C2×C4—1722no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4C22⋊C4×D4312yes—
556C2×C4C22⋊C4×D4312yes—
557C2×C4C22×C4×D4311yescharacteristic
558C2×C4C2×D4×D4311yescharacteristic
559C2×C4#1306337012yes—
560C2×C4#1306337112yes—
561C8—42no—
562C8—1722no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—82no—
567C22—82no—
568C22—434no—
569C22—864no—
570C22—864no—
571C22—862no—
572C22—862no—
573C22—34416no—
574C22—3442no—
575C22—3442no—
576C22—1722no—
577C22—1722no—
578C22—1722no—
579C22C2×C22⋊C4×D4311yescharacteristic
580C22#1458346211yescharacteristic
581C22#1458346711yescharacteristic
582C22#135×D4312yes—
583C22#1458369612yes—
584C4—22no—
585C4—22no—
586C4—42no—
587C4—82no—
588C4—862no—
589C4—862no—
590C4—862no—
591C4—3442no—
592C4—1722no—
593C4#1458337112yes—
594C4#1458346512yes—
595C2—82no—
596C2—864no—
597C2—3442no—
598C2#1913717411yescharacteristic
599C2#416×D4311yescharacteristic
600C2#1914311011yescharacteristic
601C2#1914555512yes—
602C2#1914556112yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1958C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenter#1958D43
hypocenterC43#21806
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1958

Complements

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

NH ≅ G/Ntype
2. C2×#14582950C2semidirect
3. #19136988C2semidirect
4. #19135526C2semidirect
5. #19135524C2semidirect
6. #19135407C2semidirect
7. #19135406C2semidirect
8. #19135404C2semidirect
9. #19134528C2semidirect
11. C43×#1958C2semidirect
20. #124×D43C4semidirect
25. C2×Dic43⋊C8C22semidirect
26. C2×#13063250C22semidirect
27. C2×#13063249C22semidirect
28. C2×#13063248C22semidirect
33. C2×C4×C43⋊C8C22semidirect
35. #14582765C22semidirect
38. C4⋊C4×Dic43C22semidirect
42. C2×#103×C43C22semidirect
44. C2×C4×C8×C43C22semidirect
45. C43×#382C22semidirect
302. #1958D43semidirect
331. C2×#103C2×D43semidirect
338. C2×C4×C8C2×D43semidirect
341. #382C2×D43semidirect
347. C43#21806semidirect

Maximal subgroups

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

subgroupindex
C2×#124×D432
C2×#145829502
#191369882
#191355262
#191355242
#191354072
#191354062
#191354042
#191345282
#191345242
C43×#19582
#2180643