Finite Group Databasebeta

← #25086583

Subgroups — #25086583

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
1Q8×#10621884C211yesmaximal, characteristic, complemented
2#19147251C211yesmaximal, characteristic
3#19146473C211yesmaximal, characteristic, complemented
4#19134256C211yesmaximal, characteristic, complemented
5#19134177C211yesmaximal, characteristic, complemented
6#19134009C211yesmaximal, characteristic, complemented
7#19134001C211yesmaximal, characteristic
8#19133979C211yesmaximal, characteristic, complemented
9#19133781C211yesmaximal, characteristic, complemented
10#19133735C211yesmaximal, characteristic, complemented
11#19133728C211yesmaximal, characteristic, complemented
12#19133696C211yesmaximal, characteristic
13#19133429C211yesmaximal, characteristic, complemented
14#19133414C211yesmaximal, characteristic, complemented
15C43×#3375C211yesmaximal, characteristic, complemented
16#14583609C2211yescharacteristic
17Q8×D172C2211yescharacteristic
18#14583295—21no—
19#14583295C2211yescharacteristic
20#14583278C2211yescharacteristic
21#14583253—21no—
22#14583250C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583245C2211yescharacteristic
25#14583236—21no—
26#14583199—21no—
27#14583194C2211yescharacteristic
28#14583194C2211yescharacteristic
29#14583186—21no—
30#14583186C2211yescharacteristic
31#14583184—21no—
32#14583184C2211yescharacteristic
33#14583139—21no—
34#14583111—21no—
35#14583109C2211yescharacteristic
36#14583091C2211yescharacteristic
37#14583053—21no—
38Q8×C43⋊C8C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40C4×#10621884—21no—
41C4×#10621884C2211yescharacteristic
42C4×#10621882—21no—
43C8×D172C2211yescharacteristic
44#103×D43—21no—
45#14582650C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582646C2211yescharacteristic
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53Q8⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582620C2211yescharacteristic
56C43×#559C2211yescharacteristic
57Q82×C43C2211yescharacteristic
58C43×#489—21no—
59C43×#486C2211yescharacteristic
60C43×#477C2211yescharacteristic
61C43×#474—21no—
62C43×#464—21no—
63C43×#460C2211yescharacteristic
64C43×#446C2211yescharacteristic
65C43×#440—21no—
66C4×Q16×C43C2211yescharacteristic
67C2×Q8×D43—21no—
68C2×#10621885—21no—
69C2×#10621885—41no—
70C2×#10621884D411yescharacteristic
71C2×#10621882—21no—
72C2×C8×D43—21no—
73#13063325—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063317—21no—
77#13063305—21no—
78#13063305—41no—
79#13063303—41no—
80#13063301—21no—
81C4×D172—21no—
82C4×D172—21no—
83C4×D172C2311yescharacteristic
84C4⋊C4×D43—21no—
85#13063258—21no—
86#13063258—21no—
87#13063256—21no—
88#13063256—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256D411yescharacteristic
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97#13063250—21no—
98#13063250—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249—21no—
102#13063249D411yescharacteristic
103#13063248—21no—
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—41no—
108#13063245—21no—
109#13063245D411yescharacteristic
110(C2×D43)⋊C8—21no—
111C4×C43⋊C8—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×Q16×C43D411yescharacteristic
116C2×SD16×C43—21no—
117C4⋊Q8×C43—21no—
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43—41no—
120C4⋊Q8×C43C2311yescharacteristic
121#127×C43C2311yescharacteristic
122#124×C43—21no—
123#124×C43—21no—
124#123×C43—41no—
125C4×Q8×C43—21no—
126C4×Q8×C43—21no—
127C4×Q8×C43C2311yescharacteristic
128C4×Q8×C43C2311yescharacteristic
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43—21no—
132#107×C43—21no—
133#107×C43D411yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43D411yescharacteristic
138#103×C43D411yescharacteristic
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142#97×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—41no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×Q8×C43C2×D411yescharacteristic
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C22×C4×C43—41no—
153Q8×D43—42no—
154Q8×D43—81no—
155C2×D172C2×D411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43—41no—
158C2×C4×D43—41no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86—41no—
162Q16×C43—22no—
163SD16×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—21no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43C2×D411yescharacteristic
175C4⋊C4×C43C2×D411yescharacteristic
176C4⋊C4×C43C2×D411yescharacteristic
177C22⋊C4×C43—41no—
178C22⋊C4×C43—41no—
179C22⋊C4×C43—41no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—41no—
184C42×C43C2411yescharacteristic
185#10621885—81no—
186#10621885—82no—
187#10621884—22no—
188#10621882—42no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—41no—
191(C2×D43)⋊C4—41no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—41no—
197C4⋊Dic43C2×D411yescharacteristic
198Dic43⋊C4—41no—
199Dic43⋊C4—41no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C8×D43—81no—
207C23×C43—41no—
208C22×D43—21no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—21no—
214Q8×C43—81no—
215Q8×C43—161no—
216Q8×C43#13512yes—
217D4×C43—41no—
218D4×C43—41no—
219D4×C43—41no—
220D4×C43—41no—
221D4×C43—81no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—41no—
229C2×C4×C43—161no—
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43H(5,𝔽2)11yescharacteristic
233C2×Dic43—21no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236D172—21no—
237D172#13712yes—
238C4×D43—41no—
239C4×D43—41no—
240C4×D43—82no—
241C4×D43—161no—
242Dic86—41no—
243Dic86—41no—
244Dic86—82no—
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—81no—
257C22×C43—81no—
258C22×C43—81no—
259C22×C43D4211yescharacteristic
260C2×D43—22no—
261C2×D43—41no—
262C2×D43—41no—
263C4×C43—22no—
264C4×C43—21no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43—81no—
271C4×C43C2×#13511yescharacteristic
272C4×C43C2×#13711yescharacteristic
273C4×C43#57711yescharacteristic
274C4×C43#57811yescharacteristic
275Dic43—41no—
276Dic43—81no—
277Dic43—81no—
278Q8×SD16—431no—
279#3375D4311yescharacteristic, complemented
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—161no—
294C2×C43#327011yescharacteristic
295C2×C43#328211yescharacteristic
296C2×C43#328811yescharacteristic
297D43—42no—
298#559C2×D4311yescharacteristic
299Q82C2×D4311yescharacteristic
300#554—431no—
301D4×Q8—431no—
302#498—431no—
303#498—861no—
304#494—431no—
305#489—21no—
306#488—861no—
307#487—431no—
308#486—431no—
309#486—431no—
310#486C2×D4311yescharacteristic
311#484—861no—
312#478—861no—
313#477—431no—
314#477—431no—
315#477C2×D4311yescharacteristic
316#476—431no—
317#476—861no—
318#475—431no—
319#475—861no—
320#474—21no—
321#467—861no—
322#464—21no—
323#463—861no—
324#462—431no—
325#460C2×D4311yescharacteristic
326#459—431no—
327#451—861no—
328#446C2×D4311yescharacteristic
329C8×Q8—431no—
330C8×Q8—431no—
331#440—21no—
332C4×Q16C2×D4311yescharacteristic
333C4×SD16—431no—
334C4×SD16—861no—
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—861no—
351C2×Q16—861no—
352C2×Q16—1721no—
353C2×Q16C22⋊D4311yescharacteristic
354C2×SD16—21no—
355C2×SD16—431no—
356C2×D8—861no—
357C22×C8—861no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8—41no—
361C4⋊Q8—431no—
362C4⋊Q8—431no—
363C4⋊Q8—861no—
364C4⋊Q8C22×D4311yescharacteristic
365#127C22×D4311yescharacteristic
366#125—861no—
367#124—21no—
368#124—21no—
369#123—41no—
370C22⋊Q8—861no—
371C22⋊Q8—861no—
372C22⋊Q8—1721no—
373C22⋊Q8—1721no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8C22×D4311yescharacteristic
377C4×Q8C22×D4311yescharacteristic
378C4×Q8C22×D4311yescharacteristic
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—431no—
382C4×D4—861no—
383C4×D4—861no—
384C2×C4⋊C4—861no—
385#107—21no—
386#107—861no—
387#107—861no—
388#107C22⋊D4311yescharacteristic
389#106—431no—
390#106—861no—
391#106—861no—
392#106—861no—
393#106—861no—
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—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103C22⋊D4311yescharacteristic
410#103C22⋊D4311yescharacteristic
411#102—21no—
412#102—21no—
413#102—21no—
414#102—431no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419#102—1721no—
420C22⋊C8—861no—
421#97—21no—
422C4×C8—431no—
423C4×C8—431no—
424C4×C8—861no—
425C4×C8—861no—
426C4×C8C22×D4311yescharacteristic
427C2×Q8—21no—
428C2×Q8—41no—
429C2×Q8—861no—
430C2×Q8—861no—
431C2×Q8—3441no—
432C2×Q8—1721no—
433C2×Q8—1722no—
434C2×Q8D4×D4311yescharacteristic
435C2×Q8C2×C22⋊D4311yescharacteristic
436C2×Q8C2×C22⋊D4311yescharacteristic
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—431no—
441C22×C4—41no—
442C22×C4—861no—
443C22×C4—1721no—
444C22×C4—1721no—
445Q16—22no—
446Q16—3441no—
447Q16—3442no—
448SD16—42no—
449SD16—862no—
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—41no—
467C4⋊C4—41no—
468C4⋊C4—431no—
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—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—861no—
483C22⋊C4—1721no—
484C22⋊C4—1721no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—41no—
489C42C23×D4311yescharacteristic
490C23—41no—
491C23—861no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—81no—
498Q8—161no—
499Q8—3441no—
500Q8—3442no—
501Q8—1721no—
502Q8—1721no—
503Q8#1306334512yes—
504D4—41no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—81no—
509D4—432no—
510D4—861no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—161no—
519C2×C4—861no—
520C2×C4—3442no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1721no—
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—81no—
539C22—81no—
540C22—81no—
541C22—862no—
542C22—1721no—
543C22—1721no—
544C22D4×C22⋊D4311yescharacteristic
545C4—22no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—81no—
553C4—3441no—
554C4—3441no—
555C4—1721no—
556C4C2×#1306334511yescharacteristic
557C4#137×D4311yescharacteristic
558C4#1458370711yescharacteristic
559C4#1458371511yescharacteristic
560C2—161no—
561C2—1722no—
562C2#1914615911yescharacteristic
563C2#1914630311yescharacteristic
564C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3375C2
socleC22×C43D42
prime radical#14583091C22
hypercenter#3375D43
hypocenterC43#19798
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3375

Complements

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

NH ≅ G/Ntype
1. Q8×#10621884C2semidirect
3. #19146473C2semidirect
4. #19134256C2semidirect
5. #19134177C2semidirect
6. #19134009C2semidirect
8. #19133979C2semidirect
9. #19133781C2semidirect
10. #19133735C2semidirect
11. #19133728C2semidirect
13. #19133429C2semidirect
14. #19133414C2semidirect
15. C43×#3375C2semidirect
279. #3375D43semidirect
349. C43#19798semidirect

Maximal subgroups

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

subgroupindex
Q8×#106218842
#191472512
#191464732
#191342562
#191341772
#191340092
#191340012
#191339792
#191337812
#191337352
#191337282
#191336962
#191334292
#191334142
C43×#33752
#1979843