Finite Group Databasebeta

← #25086585

Subgroups — #25086585

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
1#19147409C211yesmaximal, characteristic, complemented
2#19147253C211yesmaximal, characteristic
3#19146471C211yesmaximal, characteristic, complemented
4#19134253C211yesmaximal, characteristic, complemented
5#19134175C211yesmaximal, characteristic, complemented
6#19134011C211yesmaximal, characteristic, complemented
7#19134006C211yesmaximal, characteristic
8#19133974C211yesmaximal, characteristic, complemented
9#19133780C211yesmaximal, characteristic, complemented
10#19133735C211yesmaximal, characteristic, complemented
11#19133727C211yesmaximal, characteristic, complemented
12#19133698C211yesmaximal, characteristic
13#19133432C211yesmaximal, characteristic, complemented
14#19133412C211yesmaximal, characteristic, complemented
15Q8×SD16×C43C211yesmaximal, characteristic, complemented
16#14583634C2211yescharacteristic
17#14583606C2211yescharacteristic
18#14583278C2211yescharacteristic
19#14583261—21no—
20#14583255—21no—
21#14583249C2211yescharacteristic
22#14583247C2211yescharacteristic
23#14583247C2211yescharacteristic
24#14583246C2211yescharacteristic
25#14583232—21no—
26#14583198—21no—
27#14583194C2211yescharacteristic
28#14583194C2211yescharacteristic
29#14583191C2211yescharacteristic
30#14583176—21no—
31#14583138—21no—
32#14583121—21no—
33#14583116—21no—
34#14583106C2211yescharacteristic
35#14583099C2211yescharacteristic
36#14583094C2211yescharacteristic
37#14583055—21no—
38#14583030C2211yescharacteristic
39C8×Dic86C2211yescharacteristic
40#14582997—21no—
41C4×#10621885C2211yescharacteristic
42#14582979—21no—
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063249—21no—
45#14582650C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582642C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic
56Q82×C43C2211yescharacteristic
57D4×Q8×C43C2211yescharacteristic
58C43×#498—21no—
59C43×#498C2211yescharacteristic
60C43×#476—21no—
61C43×#476C2211yescharacteristic
62C43×#475—21no—
63C43×#475C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×SD16×C43—21no—
66C4×SD16×C43C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621885—41no—
69C2×#10621885D411yescharacteristic
70C2×#10621884—21no—
71C2×#10621882—21no—
72C22×C43⋊C8—21no—
73#13063325C2311yescharacteristic
74#13063322C2311yescharacteristic
75#13063316—21no—
76#13063314—21no—
77#13063313—21no—
78#13063310—41no—
79#13063304—21no—
80#13063302—41no—
81C4×Dic86C2311yescharacteristic
82C4×D172—21no—
83D4×Dic43—21no—
84#13063287—21no—
85C2×C4⋊Dic43—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258D411yescharacteristic
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94Dic43⋊C8—21no—
95#13063249—21no—
96#13063249—21no—
97#13063249—21no—
98#13063249—21no—
99#13063249—21no—
100#13063249D411yescharacteristic
101#13063248—21no—
102#13063248D411yescharacteristic
103#13063247—21no—
104#13063247—21no—
105#13063245—21no—
106#13063245—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245—41no—
110C22⋊(C43⋊C8)—21no—
111#13063236—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C22×Q8×C43—21no—
116C2×SD16×C43D411yescharacteristic
117C4⋊Q8×C43—21no—
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43—41no—
121C4⋊Q8×C43C2311yescharacteristic
122C4⋊Q8×C43C2311yescharacteristic
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—41no—
125C4×Q8×C43—21no—
126C4×Q8×C43—21no—
127C4×Q8×C43C2311yescharacteristic
128C4×Q8×C43C2311yescharacteristic
129C4×D4×C43—21no—
130C4×D4×C43C2311yescharacteristic
131#106×C43—21no—
132#106×C43—21no—
133#106×C43—21no—
134#106×C43—21no—
135#106×C43D411yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43D411yescharacteristic
140#102×C43—21no—
141#102×C43D411yescharacteristic
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43—41no—
148C2×Q8×C43—42no—
149C2×Q8×C43—81no—
150C2×Q8×C43C2×D411yescharacteristic
151C2×Q8×C43C2×D411yescharacteristic
152C2×D4×C43C2×D411yescharacteristic
153C22×C4×C43—21no—
154C22×C4×C43—41no—
155C22×Dic43—41no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×C4×D43—41no—
160C2×Dic86—21no—
161C2×Dic86C2×D411yescharacteristic
162SD16×C43—22no—
163C2×C8×C43—21no—
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43C2×D411yescharacteristic
176C4⋊C4×C43C2×D411yescharacteristic
177C4⋊C4×C43C2×D411yescharacteristic
178C22⋊C4×C43—21no—
179C22⋊C4×C43—41no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—41no—
183C42×C43C2411yescharacteristic
184C22⋊Dic43—41no—
185#10621885—22no—
186#10621885—81no—
187#10621885—82no—
188#10621884—42no—
189#10621882—42no—
190(C2×D43)⋊C4—41no—
191(C2×D43)⋊C4—41no—
192(C2×D43)⋊C4—41no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—41no—
196C4⋊Dic43C2×D411yescharacteristic
197Dic43⋊C4—21no—
198Dic43⋊C4—41no—
199C4×Dic43—21no—
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—
208C22×D43—41no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—82no—
215Q8×C43—81no—
216Q8×C43—161no—
217Q8×C43#13512yes—
218D4×C43—21no—
219D4×C43#13712yes—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—82no—
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43H(5,𝔽2)11yescharacteristic
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—41no—
236C2×Dic43—161no—
237D172—41no—
238D172—41no—
239D172—41no—
240D172—41no—
241D172—81no—
242C4×D43—161no—
243Dic86—21no—
244Dic86—21no—
245Dic86—81no—
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×C43D4211yescharacteristic
260C2×D43—81no—
261C2×D43—81no—
262C2×D43—81no—
263C4×C43—22no—
264C4×C43—21no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—81no—
270C4×C43—81no—
271C4×C43C2×#13511yescharacteristic
272C4×C43C2×#13711yescharacteristic
273C4×C43#57711yescharacteristic
274C4×C43#57811yescharacteristic
275Dic43—41no—
276Dic43—41no—
277Dic43—81no—
278Q8×SD16D4311yescharacteristic, complemented
279#3375—431no—
280#3361—431no—
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#327011yescharacteristic
295C2×C43#328211yescharacteristic
296C2×C43#328811yescharacteristic
297D43—161no—
298#559—431no—
299Q82C2×D4311yescharacteristic
300#554—431no—
301D4×Q8C2×D4311yescharacteristic
302#498—21no—
303#498C2×D4311yescharacteristic
304#494—431no—
305#489—861no—
306#488—861no—
307#487—431no—
308#486—431no—
309#486—431no—
310#486—431no—
311#484—861no—
312#478—861no—
313#477—431no—
314#477—431no—
315#477—431no—
316#476—21no—
317#476C2×D4311yescharacteristic
318#475—21no—
319#475C2×D4311yescharacteristic
320#474—861no—
321#467—861no—
322#464—861no—
323#463—861no—
324#462—431no—
325#460—431no—
326#459—431no—
327#451—861no—
328#446—431no—
329C8×Q8—431no—
330C8×Q8C2×D4311yescharacteristic
331#440—861no—
332C4×Q16—431no—
333C4×SD16—21no—
334C4×SD16C2×D4311yescharacteristic
335C4×D8—861no—
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—21no—
351C2×Q16—431no—
352C2×Q16—861no—
353C2×Q16—1721no—
354C2×SD16—861no—
355C2×SD16C22⋊D4311yescharacteristic
356C2×D8—861no—
357C22×C8—861no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8—21no—
361C4⋊Q8—41no—
362C4⋊Q8—431no—
363C4⋊Q8C22×D4311yescharacteristic
364C4⋊Q8C22×D4311yescharacteristic
365#127—431no—
366#125—861no—
367#124—861no—
368#124—861no—
369#123—1721no—
370C22⋊Q8—21no—
371C22⋊Q8—41no—
372C22⋊Q8—861no—
373C22⋊Q8—1721no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8—431no—
377C4×Q8C22×D4311yescharacteristic
378C4×Q8C22×D4311yescharacteristic
379C4×D4—21no—
380C4×D4—861no—
381C4×D4—861no—
382C4×D4—861no—
383C4×D4C22×D4311yescharacteristic
384C2×C4⋊C4—861no—
385#107—431no—
386#107—861no—
387#107—861no—
388#107—861no—
389#106—21no—
390#106—21no—
391#106—21no—
392#106—21no—
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—861no—
413#102—861no—
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—21no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×Q8—42no—
432C2×Q8—81no—
433C2×Q8—431no—
434C2×Q8—861no—
435C2×Q8D4×D4311yescharacteristic
436C2×Q8C2×C22⋊D4311yescharacteristic
437C2×D4—861no—
438C2×D4—861no—
439C2×D4—861no—
440C2×D4C2×C22⋊D4311yescharacteristic
441C22×C4—21no—
442C22×C4—41no—
443C22×C4—1721no—
444C22×C4—1721no—
445Q16—862no—
446Q16—3441no—
447Q16—3442no—
448SD16—22no—
449SD16—1722no—
450D8—1722no—
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—21no—
466C4⋊C4—21no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—431no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
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—1721no—
482C22⋊C4—1721no—
483C22⋊C4—1721no—
484C22⋊C4—1721no—
485C42—21no—
486C42—21no—
487C42—41no—
488C42—861no—
489C42C23×D4311yescharacteristic
490C23—21no—
491C23—1721no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—41no—
496Q8—41no—
497Q8—82no—
498Q8—81no—
499Q8—161no—
500Q8—861no—
501Q8—861no—
502Q8—3441no—
503Q8#1306334612yes—
504D4—21no—
505D4—3441no—
506D4—1721no—
507D4—1721no—
508D4—1721no—
509D4—1721no—
510D4#1306335612yes—
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—41no—
520C2×C4—82no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—1721no—
524C2×C4—6881no—
525C2×C4—6881no—
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—3441no—
542C22—3441no—
543C22—3441no—
544C22D4×C22⋊D4311yescharacteristic
545C4—22no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—81no—
552C4—81no—
553C4—3441no—
554C4—1721no—
555C4—1721no—
556C4C2×#1306334611yescharacteristic
557C4C2×#1306335611yescharacteristic
558C4#1458370511yescharacteristic
559C4#1458371411yescharacteristic
560C2—42no—
561C2—6881no—
562C2#1914616611yescharacteristic
563C2#1914630211yescharacteristic
564C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingQ8×SD16×C43C2
socleC22×C43D42
prime radical#14583094C22
hypercenterQ8×SD16D43
hypocenterC43#19798
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ Q8×SD16

Complements

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

NH ≅ G/Ntype
1. #19147409C2semidirect
3. #19146471C2semidirect
4. #19134253C2semidirect
5. #19134175C2semidirect
6. #19134011C2semidirect
8. #19133974C2semidirect
9. #19133780C2semidirect
10. #19133735C2semidirect
11. #19133727C2semidirect
13. #19133432C2semidirect
14. #19133412C2semidirect
15. Q8×SD16×C43C2semidirect
278. Q8×SD16D43semidirect
349. C43#19798semidirect

Maximal subgroups

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

subgroupindex
#191474092
#191472532
#191464712
#191342532
#191341752
#191340112
#191340062
#191339742
#191337802
#191337352
#191337272
#191336982
#191334322
#191334122
Q8×SD16×C432
#1979843