Finite Group Databasebeta

← #25086590

Subgroups — #25086590

Order 11008.

592 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1SD16×Dic86C211yesmaximal, characteristic, complemented
2#19147405C211yesmaximal, characteristic, complemented
3#19146465C211yesmaximal, characteristic, complemented
4#19134257C211yesmaximal, characteristic, complemented
5#19134179C211yesmaximal, characteristic, complemented
6#19134008C211yesmaximal, characteristic, complemented
7#19134002C211yesmaximal, characteristic
8#19133977C211yesmaximal, characteristic, complemented
9#19133781C211yesmaximal, characteristic, complemented
10#19133734C211yesmaximal, characteristic, complemented
11#19133729C211yesmaximal, characteristic, complemented
12#19133697C211yesmaximal, characteristic
13#19133432C211yesmaximal, characteristic, complemented
14#19133412C211yesmaximal, characteristic, complemented
15C43×#3361C211yesmaximal, characteristic
16Q8×Dic86C2211yescharacteristic
17D4×Dic86C2211yescharacteristic
18#14583297C2211yescharacteristic
19#14583296—21no—
20#14583278C2211yescharacteristic
21#14583258—21no—
22#14583251C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583245C2211yescharacteristic
25#14583234—21no—
26#14583194C2211yescharacteristic
27#14583191C2211yescharacteristic
28#14583189C2211yescharacteristic
29#14583187—21no—
30#14583184C2211yescharacteristic
31#14583182—21no—
32#14583179—21no—
33#14583138—21no—
34#14583118—21no—
35#14583109C2211yescharacteristic
36#14583096C2211yescharacteristic
37#14583054—21no—
38#14583030C2211yescharacteristic
39C8×Dic86C2211yescharacteristic
40#14582999—21no—
41C4×#10621885C2211yescharacteristic
42SD16×Dic43—21no—
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063248—21no—
45#14582650C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582644C2211yescharacteristic
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic
56C43×#559C2211yescharacteristic
57C43×#554C2211yescharacteristic
58C43×#488—21no—
59C43×#486C2211yescharacteristic
60C43×#478—21no—
61C43×#477C2211yescharacteristic
62C43×#463—21no—
63C43×#459C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×SD16×C43C2211yescharacteristic
66C4×D8×C43—21no—
67C22×Dic86—21no—
68C2×#10621885—21no—
69C2×#10621885—41no—
70C2×#10621885D411yescharacteristic
71C2×#10621883—21no—
72C22×C43⋊C8—21no—
73#13063325—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063324—21no—
77#13063324—21no—
78#13063324—41no—
79#13063304—21no—
80#13063302—41no—
81Q8×Dic43—21no—
82C4×Dic86—21no—
83C4×Dic86C2311yescharacteristic
84D4×Dic43—21no—
85#13063258—21no—
86#13063258—21no—
87#13063258D411yescharacteristic
88#13063257—21no—
89#13063257—21no—
90#13063256—21no—
91#13063256—21no—
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96Dic43⋊C8—21no—
97#13063249—21no—
98#13063249—21no—
99#13063249D411yescharacteristic
100#13063248—21no—
101#13063248—21no—
102#13063248—21no—
103#13063248—21no—
104#13063248D411yescharacteristic
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108#13063246—21no—
109#13063246—41no—
110C22⋊(C43⋊C8)—21no—
111#13063236—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×SD16×C43D411yescharacteristic
116C2×D8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118#127×C43C2311yescharacteristic
119#125×C43—21no—
120#124×C43—21no—
121#124×C43—21no—
122#123×C43—41no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—41no—
125C4×Q8×C43C2311yescharacteristic
126C4×Q8×C43C2311yescharacteristic
127C4×D4×C43—21no—
128C4×D4×C43—21no—
129C4×D4×C43—21no—
130C4×D4×C43C2311yescharacteristic
131C2×C4⋊C4×C43—21no—
132#107×C43—21no—
133#106×C43D411yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43D411yescharacteristic
138#102×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43D411yescharacteristic
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43C2×D411yescharacteristic
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C22×C4×C43—41no—
153C22×C4×C43—41no—
154C22×Dic43—41no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—42no—
158C2×Dic86—41no—
159C2×Dic86—41no—
160C2×Dic86—81no—
161C2×Dic86C2×D411yescharacteristic
162SD16×C43—22no—
163D8×C43—42no—
164C2×C8×C43—21no—
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—41no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43C2×D411yescharacteristic
174C4⋊C4×C43C2×D411yescharacteristic
175C4⋊C4×C43C2×D411yescharacteristic
176C22⋊C4×C43—21no—
177C22⋊C4×C43—41no—
178C22⋊C4×C43—41no—
179C22⋊C4×C43—41no—
180C22⋊C4×C43—41no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43C2411yescharacteristic
184C22⋊Dic43—41no—
185#10621885—22no—
186#10621885—81no—
187#10621885—82no—
188#10621883—42no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—41no—
194C4⋊Dic43C2×D411yescharacteristic
195Dic43⋊C4—21no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198C4×Dic43—21no—
199C4×Dic43—41no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—81no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C23×C43—21no—
208C23×C43—41no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—81no—
214D4×C43—21no—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—41no—
219D4×C43—81no—
220D4×C43#13712yes—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—161no—
230C2×C4×C43—161no—
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43H(5,𝔽2)11yescharacteristic
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—82no—
239Dic86—21no—
240Dic86—41no—
241Dic86—41no—
242Dic86—82no—
243Dic86—81no—
244Dic86—161no—
245Dic86#13512yes—
246C8×C43—21no—
247C8×C43—21no—
248C8×C43—41no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255#19798—431nomaximal, Sylow
256C22×C43—22no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43D4211yescharacteristic
263C4×C43—21no—
264C4×C43—41no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—81no—
270C4×C43C2×#13511yescharacteristic
271C4×C43C2×#13711yescharacteristic
272C4×C43#57711yescharacteristic
273C4×C43#57811yescharacteristic
274Dic43—22no—
275Dic43—41no—
276Dic43—81no—
277Dic43—81no—
278Q8×SD16—431no—
279#3375—431no—
280#3361D4311yescharacteristic
281#3299—431no—
282#1720—431no—
283#1704—431no—
284#1678—431no—
285#1677—431no—
286#1672—431no—
287#1640—431no—
288#1633—431no—
289#1632—431no—
290#1627—431no—
291#1582—431no—
292#1579—431no—
293C2×C43—42no—
294C2×C43—161no—
295C2×C43#327011yescharacteristic
296C2×C43#328211yescharacteristic
297C2×C43#328811yescharacteristic
298#559C2×D4311yescharacteristic
299Q82—431no—
300#554C2×D4311yescharacteristic
301D4×Q8—431no—
302#498—431no—
303#498—861no—
304#494—431no—
305#489—861no—
306#488—21no—
307#487—431no—
308#486—431no—
309#486—431no—
310#486C2×D4311yescharacteristic
311#484—861no—
312#478—21no—
313#477—431no—
314#477—431no—
315#477C2×D4311yescharacteristic
316#476—431no—
317#476—861no—
318#475—431no—
319#475—861no—
320#474—861no—
321#467—861no—
322#464—861no—
323#463—21no—
324#462—431no—
325#460—431no—
326#459C2×D4311yescharacteristic
327#451—861no—
328#446—431no—
329C8×Q8—431no—
330C8×Q8C2×D4311yescharacteristic
331#440—861no—
332C4×Q16—431no—
333C4×SD16—861no—
334C4×SD16C2×D4311yescharacteristic
335C4×D8—21no—
336C8×D4—431no—
337C2×#103—861no—
338#334—431no—
339#334—431no—
340#333—431no—
341#333—431no—
342#332—431no—
343#331—431no—
344Q8⋊C8—431no—
345Q8⋊C8—431no—
346Q8⋊C8—431no—
347D4⋊C8—431no—
348#322—431no—
349C43#1979811yescharacteristic, complemented, Sylow
350C22×Q8—861no—
351C2×Q16—431no—
352C2×Q16—861no—
353C2×Q16—1721no—
354C2×SD16—861no—
355C2×SD16C22⋊D4311yescharacteristic
356C2×D8—21no—
357C22×C8—861no—
358C4⋊Q8—431no—
359C4⋊Q8—431no—
360C4⋊Q8—861no—
361C4⋊Q8—861no—
362C4⋊Q8—861no—
363C4⋊Q8—1721no—
364C4⋊Q8C22×D4311yescharacteristic
365#127C22×D4311yescharacteristic
366#125—21no—
367#124—21no—
368#124—21no—
369#123—41no—
370C22⋊Q8—21no—
371C22⋊Q8—41no—
372C22⋊Q8—861no—
373C22⋊Q8—1721no—
374C4×Q8—431no—
375C4×Q8—861no—
376C4×Q8—861no—
377C4×Q8C22×D4311yescharacteristic
378C4×Q8C22×D4311yescharacteristic
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—861no—
383C4×D4C22×D4311yescharacteristic
384C2×C4⋊C4—21no—
385#107—21no—
386#107—431no—
387#107—861no—
388#107—861no—
389#106—861no—
390#106—861no—
391#106—861no—
392#106—861no—
393#106C22⋊D4311yescharacteristic
394C4⋊C8—21no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—861no—
399C4⋊C8—861no—
400C4⋊C8C22×D4311yescharacteristic
401#103—21no—
402#103—431no—
403#103—431no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103C22⋊D4311yescharacteristic
411#102—21no—
412#102—21no—
413#102—21no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—1721no—
419#102C22⋊D4311yescharacteristic
420C22⋊C8—861no—
421#97—861no—
422C4×C8—21no—
423C4×C8—431no—
424C4×C8—431no—
425C4×C8—861no—
426C4×C8C22×D4311yescharacteristic
427C2×Q8—21no—
428C2×Q8—431no—
429C2×Q8—861no—
430C2×Q8—861no—
431C2×Q8—3441no—
432C2×Q8—1721no—
433C2×Q8—1721no—
434C2×Q8—1722no—
435C2×Q8D4×D4311yescharacteristic
436C2×Q8C2×C22⋊D4311yescharacteristic
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4C2×C22⋊D4311yescharacteristic
441C22×C4—21no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—1721no—
445Q16—862no—
446Q16—3441no—
447Q16—3442no—
448SD16—22no—
449SD16—1722no—
450D8—42no—
451C2×C8—21no—
452C2×C8—431no—
453C2×C8—431no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—3441no—
459C2×C8C2×C22⋊D4311yescharacteristic
460C2×C8C2×C22⋊D4311yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—431no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—1721no—
474C4⋊C4—1721no—
475C4⋊C4—1721no—
476C4⋊C4D4×D4311yescharacteristic
477C4⋊C4C2×C22⋊D4311yescharacteristic
478C4⋊C4C2×C22⋊D4311yescharacteristic
479C22⋊C4—21no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—1721no—
485C42—21no—
486C42—21no—
487C42—861no—
488C42—1721no—
489C42C23×D4311yescharacteristic
490C23—21no—
491C23—41no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—81no—
497Q8—432no—
498Q8—861no—
499Q8—3441no—
500Q8—3442no—
501Q8—1721no—
502Q8—1721no—
503Q8—6881no—
504D4—21no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—81no—
510D4#1306335512yes—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—161no—
520C2×C4—161no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—3442no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4C2×D4×D4311yescharacteristic
527C2×C4C22×C22⋊D4311yescharacteristic
528C2×C4#1306337011yescharacteristic
529C8—21no—
530C8—21no—
531C8—41no—
532C8—861no—
533C8—861no—
534C8—1721no—
535C8—1721no—
536C8—1721no—
537C8—1721no—
538C22—22no—
539C22—41no—
540C22—41no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22D4×C22⋊D4311yescharacteristic
545C4—21no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—81no—
552C4—862no—
553C4—3441no—
554C4—3441no—
555C4—1721no—
556C4#135×D4311yescharacteristic
557C4C2×#1306335511yescharacteristic
558C4#1458370611yescharacteristic
559C4#1458371411yescharacteristic
560C2—42no—
561C2—161no—
562C2#1914616111yescharacteristic
563C2#1914629611yescharacteristic
564C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3361C2
socleC22×C43D42
prime radicalC43×#459C22
hypercenter#3361D43
hypocenterC43#19798
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3361

Complements

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

NH ≅ G/Ntype
1. SD16×Dic86C2semidirect
2. #19147405C2semidirect
3. #19146465C2semidirect
4. #19134257C2semidirect
5. #19134179C2semidirect
6. #19134008C2semidirect
8. #19133977C2semidirect
9. #19133781C2semidirect
10. #19133734C2semidirect
11. #19133729C2semidirect
13. #19133432C2semidirect
14. #19133412C2semidirect
349. C43#19798semidirect

Maximal subgroups

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

subgroupindex
SD16×Dic862
#191474052
#191464652
#191342572
#191341792
#191340082
#191340022
#191339772
#191337812
#191337342
#191337292
#191336972
#191334322
#191334122
C43×#33612
#1979843