Finite Group Databasebeta

← #25074563

Subgroups — #25074563

Order 11008.

878 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145822C211yesmaximal, characteristic, complemented
2#19145619C211yesmaximal, characteristic, complemented
3C2×#14583295C211yesmaximal, characteristic, complemented
4#19133879C212yesmaximal, complemented
5#19133872C212yesmaximal, complemented
6#19133865C212yesmaximal, complemented
7#19133858C212yesmaximal, complemented
8#19133312C211yesmaximal, characteristic, complemented
9#19133055C211yesmaximal, characteristic, complemented
10#19133055C211yesmaximal, characteristic, complemented
11C43×#3552C211yesmaximal, characteristic
12C2×#13063325C2211yescharacteristic
13#14583309—21no—
14#14583295—22no—
15#14583295C2212yes—
16#14583295C2212yes—
17#14583294—21no—
18#14583269—21no—
19#14583258—21no—
20#14583232—21no—
21#14583215—21no—
22#14583184C2212yes—
23#14583179C2212yes—
24#14583109C2212yes—
25#14583104C2212yes—
26#14583054—21no—
27#14583037—21no—
28#14582956C2211yescharacteristic
29#14582956C2211yescharacteristic
30C2×#13063256—22no—
31C2×C4×C43⋊C8C2211yescharacteristic
32#14582645C2212yes—
33#14582645C2212yes—
34Q8⋊(C43⋊C8)C2212yes—
35Q8⋊(C43⋊C8)C2212yes—
36D4⋊(C43⋊C8)C2212yes—
37D4⋊(C43⋊C8)C2212yes—
38C43×#563—22no—
39C43×#557C2211yescharacteristic
40C43×#556C2211yescharacteristic
41C43×#554—21no—
42C43×#553—21no—
43D4×Q8×C43—21no—
44D4×Q8×C43C2211yescharacteristic
45C43×#548—21no—
46C43×#547C2211yescharacteristic
47C43×#544—21no—
48C43×#542—21no—
49C43×#541—21no—
50C43×#539—22no—
51C43×#536—21no—
52C2×C4⋊Q8×C43C2211yescharacteristic
53C43×#529C2211yescharacteristic
54C43×#529C2211yescharacteristic
55C22×Dic86—21no—
56C2×#10621885—22no—
57C2×#10621883—22no—
58C22×C43⋊C8—21no—
59#13063325—21no—
60#13063325—21no—
61#13063325—21no—
62#13063325C2312yes—
63C2×C4⋊Dic43—21no—
64C2×C4⋊Dic43—21no—
65#13063258—22no—
66#13063256—22no—
67#13063256—24no—
68#13063256—24no—
69C4⋊(C43⋊C8)C2312yes—
70C4⋊(C43⋊C8)C2312yes—
71#13063249—22no—
72#13063248—22no—
73#13063248—22no—
74#13063246—22no—
75C22⋊(C43⋊C8)—21no—
76C22⋊(C43⋊C8)—21no—
77#13063236—21no—
78#13063236—21no—
79C4×C43⋊C8—21no—
80C4×C43⋊C8C2312yes—
81C2×#41×C43—21no—
82C22×Q8×C43—21no—
83C22×Q8×C43—21no—
84C4⋊Q8×C43—22no—
85C4⋊Q8×C43—21no—
86C4⋊Q8×C43—21no—
87C4⋊Q8×C43—21no—
88C4⋊Q8×C43—21no—
89C4⋊Q8×C43D412yes—
90C4⋊Q8×C43C2311yescharacteristic
91C4⋊Q8×C43C2311yescharacteristic
92#126×C43—22no—
93#126×C43—22no—
94#126×C43—22no—
95#126×C43—21no—
96#126×C43—21no—
97#125×C43—22no—
98#125×C43—22no—
99#125×C43—22no—
100#125×C43—21no—
101#125×C43D411yescharacteristic
102#125×C43D411yescharacteristic
103#124×C43—22no—
104#124×C43—21no—
105#124×C43D411yescharacteristic
106#124×C43D411yescharacteristic
107#123×C43—22no—
108#123×C43—22no—
109#123×C43—21no—
110#123×C43—21no—
111#123×C43—22no—
112C22⋊Q8×C43—22no—
113C22⋊Q8×C43—22no—
114C22⋊Q8×C43—22no—
115C22⋊Q8×C43—22no—
116C22⋊Q8×C43—22no—
117C22⋊Q8×C43—21no—
118C22⋊Q8×C43—22no—
119C22⋊Q8×C43—21no—
120C22⋊Q8×C43—21no—
121C22⋊Q8×C43D411yescharacteristic
122C22⋊Q8×C43D411yescharacteristic
123#121×C43—22no—
124#121×C43—21no—
125#121×C43D411yescharacteristic
126#121×C43D411yescharacteristic
127C4×Q8×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43—21no—
130C4×Q8×C43C2311yescharacteristic
131C4×Q8×C43C2311yescharacteristic
132C4×D4×C43—22no—
133C4×D4×C43—22no—
134C4×D4×C43—21no—
135C4×D4×C43—21no—
136C4×D4×C43—21no—
137C4×D4×C43C2311yescharacteristic
138C4×D4×C43C2311yescharacteristic
139#117×C43—21no—
140#117×C43—21no—
141#117×C43—21no—
142C2×C4⋊C4×C43—21no—
143C2×C4⋊C4×C43—21no—
144C2×C4⋊C4×C43D412yes—
145C2×C42×C43C2311yescharacteristic
146#41×C43—82no—
147C2×Q8×C43—22no—
148C2×Q8×C43—22no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—82no—
152C2×Q8×C43—82no—
153C2×Q8×C43C2×D411yescharacteristic
154C2×Q8×C43C2×D411yescharacteristic
155C2×D4×C43—22no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43C2×D411yescharacteristic
159C2×D4×C43C2×D411yescharacteristic
160C22×C4×C43—22no—
161C22×C4×C43—22no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—22no—
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2×D411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×Dic43—41no—
169C2×Dic86—22no—
170C2×Dic86—41no—
171C2×Dic86—82no—
172C4⋊C4×C43—22no—
173C4⋊C4×C43—22no—
174C4⋊C4×C43—22no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—22no—
179C4⋊C4×C43—22no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—21no—
188C4⋊C4×C43—21no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43C2×D411yescharacteristic
191C4⋊C4×C43C2×D412yes—
192C4⋊C4×C43C2×D412yes—
193C4⋊C4×C43C2×D411yescharacteristic
194C4⋊C4×C43C2×D411yescharacteristic
195C4⋊C4×C43C2×D411yescharacteristic
196C22⋊C4×C43—22no—
197C22⋊C4×C43—22no—
198C22⋊C4×C43—22no—
199C22⋊C4×C43—22no—
200C22⋊C4×C43—21no—
201C22⋊C4×C43—21no—
202C22⋊C4×C43—21no—
203C22⋊C4×C43—21no—
204C22⋊C4×C43—21no—
205C22⋊C4×C43—21no—
206C22⋊C4×C43—21no—
207C22⋊C4×C43—21no—
208C22⋊C4×C43—21no—
209C22⋊C4×C43—21no—
210C42×C43—22no—
211C42×C43—22no—
212C42×C43—21no—
213C42×C43—21no—
214C42×C43C2×D411yescharacteristic
215C42×C43C2×D411yescharacteristic
216C42×C43C2×D411yescharacteristic
217C42×C43C2411yescharacteristic
218#10621885—82no—
219#10621883—82no—
220C4⋊Dic43—22no—
221C4⋊Dic43—22no—
222C4⋊Dic43—41no—
223C4⋊Dic43—41no—
224C2×C43⋊C8—24no—
225C2×C43⋊C8—22no—
226C2×C43⋊C8—22no—
227C2×C43⋊C8—22no—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43#12011yescharacteristic
231Q8×C43—22no—
232Q8×C43—22no—
233Q8×C43—42no—
234Q8×C43—42no—
235Q8×C43—82no—
236Q8×C43—82no—
237D4×C43—22no—
238D4×C43—22no—
239D4×C43—42no—
240D4×C43—42no—
241D4×C43—82no—
242C2×C4×C43—22no—
243C2×C4×C43—22no—
244C2×C4×C43—22no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—21no—
253C2×C4×C43—42no—
254C2×C4×C43—42no—
255C2×C4×C43—82no—
256C2×C4×C43—82no—
257C2×C4×C43—82no—
258C2×C4×C43#12011yescharacteristic
259C2×C4×C43#12011yescharacteristic
260C2×C4×C43#12011yescharacteristic
261C2×C4×C43C22×D411yescharacteristic
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43C22×D411yescharacteristic
264C2×Dic43—42no—
265C2×Dic43—82no—
266Dic86—42no—
267Dic86—42no—
268Dic86—82no—
269C43⋊C8—24no—
270C43⋊C8—42no—
271C43⋊C8—42no—
272#18700—431nomaximal, Sylow
273C22×C43—21no—
274C22×C43—21no—
275C22×C43—41no—
276C22×C43—41no—
277C22×C43—41no—
278C22×C43—41no—
279C22×C43—41no—
280C22×C43—41no—
281C22×C43#45612yes—
282C22×C43C2×#12011yescharacteristic
283C4×C43—21no—
284C4×C43—21no—
285C4×C43—21no—
286C4×C43—21no—
287C4×C43—41no—
288C4×C43—42no—
289C4×C43—41no—
290C4×C43—42no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—41no—
294C4×C43—41no—
295C4×C43#57712yes—
296C4×C43#57712yes—
297Dic43—82no—
298#3552D4311yescharacteristic
299#3239—431no—
300#3218—431no—
301C2×#498—431no—
302#1654—432no—
303#1653—432no—
304#1652—432no—
305#1651—432no—
306#1556—431no—
307#1494—431no—
308#1494—431no—
309C2×C43—22no—
310C2×C43—81no—
311C2×C43—81no—
312C2×C43#300911yescharacteristic
313C2×C43#301011yescharacteristic
314C2×C43C2×#45611yescharacteristic
315#563—22no—
316#557C2×D4311yescharacteristic
317#556C2×D4311yescharacteristic
318#554—21no—
319#553—21no—
320D4×Q8—21no—
321D4×Q8C2×D4311yescharacteristic
322#548—21no—
323#547C2×D4311yescharacteristic
324#544—21no—
325#542—21no—
326#541—21no—
327#539—22no—
328#536—21no—
329C2×C4⋊Q8—431no—
330C2×C4⋊Q8C2×D4311yescharacteristic
331#529C2×D4311yescharacteristic
332#529C2×D4311yescharacteristic
333#501—861no—
334#498—432no—
335#498—432no—
336#498—862no—
337#497—861no—
338#491—861no—
339#489—861no—
340#484—861no—
341#481—861no—
342#475—432no—
343#474—432no—
344#462—432no—
345#461—432no—
346#451—861no—
347#448—861no—
348#432—431no—
349#432—431no—
350C2×#106—862no—
351C2×C4×C8—431no—
352#332—432no—
353#332—432no—
354Q8⋊C8—432no—
355Q8⋊C8—432no—
356D4⋊C8—432no—
357D4⋊C8—432no—
358C43#1870011yescharacteristic, complemented, Sylow
359C2×#41—21no—
360C22×Q8—21no—
361C22×Q8—21no—
362C22×Q8—861no—
363C2×Q16—862no—
364C2×SD16—862no—
365C22×C8—861no—
366C4⋊Q8—22no—
367C4⋊Q8—21no—
368C4⋊Q8—21no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371C4⋊Q8—432no—
372C4⋊Q8—861no—
373C4⋊Q8—861no—
374C4⋊Q8—861no—
375C4⋊Q8C22⋊D4312yes—
376C4⋊Q8C22×D4311yescharacteristic
377C4⋊Q8C22×D4311yescharacteristic
378#126—22no—
379#126—22no—
380#126—22no—
381#126—21no—
382#126—21no—
383#125—22no—
384#125—22no—
385#125—22no—
386#125—21no—
387#125C22⋊D4311yescharacteristic
388#125C22⋊D4311yescharacteristic
389#124—22no—
390#124—21no—
391#124C22⋊D4311yescharacteristic
392#124C22⋊D4311yescharacteristic
393#123—22no—
394#123—22no—
395#123—21no—
396#123—21no—
397#123—22no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402C22⋊Q8—22no—
403C22⋊Q8—21no—
404C22⋊Q8—22no—
405C22⋊Q8—21no—
406C22⋊Q8—21no—
407C22⋊Q8C22⋊D4311yescharacteristic
408C22⋊Q8C22⋊D4311yescharacteristic
409#121—22no—
410#121—21no—
411#121C22⋊D4311yescharacteristic
412#121C22⋊D4311yescharacteristic
413C4×Q8—21no—
414C4×Q8—21no—
415C4×Q8—21no—
416C4×Q8C22×D4311yescharacteristic
417C4×Q8C22×D4311yescharacteristic
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4C22×D4311yescharacteristic
424C4×D4C22×D4311yescharacteristic
425#117—21no—
426#117—21no—
427#117—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4C22⋊D4312yes—
433C2×C42C22×D4311yescharacteristic
434#107—862no—
435#106—864no—
436#106—864no—
437#106—862no—
438C4⋊C8—432no—
439C4⋊C8—432no—
440#103—862no—
441#103—862no—
442#103—862no—
443#102—862no—
444C22⋊C8—861no—
445C22⋊C8—861no—
446#97—861no—
447#97—861no—
448C4×C8—432no—
449C4×C8—861no—
450#41—82no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—82no—
456C2×Q8—82no—
457C2×Q8—862no—
458C2×Q8—3442no—
459C2×Q8—1721no—
460C2×Q8C2×C22⋊D4311yescharacteristic
461C2×Q8C2×C22⋊D4311yescharacteristic
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—22no—
465C2×D4C2×C22⋊D4311yescharacteristic
466C2×D4C2×C22⋊D4311yescharacteristic
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—1721no—
473C22×C4C2×C22⋊D4311yescharacteristic
474C22×C4C2×C22⋊D4311yescharacteristic
475C22×C4C2×C22⋊D4311yescharacteristic
476Q16—3442no—
477SD16—3442no—
478C2×C8—864no—
479C2×C8—862no—
480C2×C8—862no—
481C2×C8—862no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—862no—
501C4⋊C4—862no—
502C4⋊C4—1721no—
503C4⋊C4—1721no—
504C4⋊C4C2×C22⋊D4311yescharacteristic
505C4⋊C4C2×C22⋊D4311yescharacteristic
506C4⋊C4C2×C22⋊D4312yes—
507C4⋊C4C2×C22⋊D4312yes—
508C4⋊C4C2×C22⋊D4311yescharacteristic
509C4⋊C4C2×C22⋊D4311yescharacteristic
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C42—22no—
525C42—22no—
526C42—21no—
527C42—21no—
528C42C2×C22⋊D4311yescharacteristic
529C42C2×C22⋊D4311yescharacteristic
530C42C2×C22⋊D4311yescharacteristic
531C42C23×D4311yescharacteristic
532C23—21no—
533C23—21no—
534C23#1306329411yescharacteristic
535Q8—22no—
536Q8—22no—
537Q8—42no—
538Q8—42no—
539Q8—82no—
540Q8—82no—
541Q8—3442no—
542Q8—1722no—
543Q8—1722no—
544D4—22no—
545D4—22no—
546D4—42no—
547D4—42no—
548D4—82no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—82no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4—3442no—
566C2×C4—1722no—
567C2×C4#1306329411yescharacteristic
568C2×C4#1306329411yescharacteristic
569C2×C4#1306329411yescharacteristic
570C2×C4C22×C22⋊D4311yescharacteristic
571C2×C4C22×C22⋊D4311yescharacteristic
572C2×C4C22×C22⋊D4311yescharacteristic
573C8—864no—
574C8—1722no—
575C8—1722no—
576C22—21no—
577C22—21no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22#1458308212yes—
585C22C2×#1306329411yescharacteristic
586C4—21no—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—42no—
594C4—41no—
595C4—42no—
596C4—41no—
597C4—41no—
598C4—3442no—
599C4#1458370712yes—
600C4#1458371012yes—
601C2—22no—
602C2—81no—
603C2—81no—
604C2#1914387211yescharacteristic
605C2#1914388111yescharacteristic
606C2C2×#1458308211yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3552C2
socleC22×C43C2×#120
hypercenter#3552D43
hypocenterC43#18700
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3552

Complements

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

NH ≅ G/Ntype
1. #19145822C2semidirect
2. #19145619C2semidirect
3. C2×#14583295C2semidirect
4. #19133879C2semidirect
5. #19133872C2semidirect
6. #19133865C2semidirect
7. #19133858C2semidirect
8. #19133312C2semidirect
9. #19133055C2semidirect
10. #19133055C2semidirect
358. C43#18700semidirect

Maximal subgroups

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

subgroupindex
#191458222
#191456192
C2×#145832952
#191338792
#191338722
#191338652
#191338582
#191333122
#191330552
C43×#35522
#1870043