Finite Group Databasebeta

← #25079010

Subgroups — #25079010

Order 11008.

628 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144919C211yesmaximal, characteristic
2#19144636C211yesmaximal, characteristic, complemented
3#19144628C211yesmaximal, characteristic
4C8×Q8×D43C211yesmaximal, characteristic, complemented
5#19134050C211yesmaximal, characteristic, complemented
6#19134040C211yesmaximal, characteristic, complemented
7#19134039C211yesmaximal, characteristic, complemented
8#19134024C211yesmaximal, characteristic, complemented
9#19134023C211yesmaximal, characteristic, complemented
10#19134014C211yesmaximal, characteristic, complemented
11#19134013C211yesmaximal, characteristic, complemented
12#19133342C211yesmaximal, characteristic, complemented
13#19133249C211yesmaximal, characteristic, complemented
14#19133243C211yesmaximal, characteristic
15C43×#1684C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583450C2211yescharacteristic
18C4×Q8×D43C2211yescharacteristic
19#14583255—21no—
20#14583255—21no—
21#14583249C2211yescharacteristic
22#14583247C2211yescharacteristic
23#14583246C2211yescharacteristic
24#14583236—21no—
25#14583219—21no—
26#14583191C2211yescharacteristic
27#14583181C2211yescharacteristic
28#14583110C2211yescharacteristic
29#14583109C2211yescharacteristic
30#14583100C2211yescharacteristic
31#14583099C2211yescharacteristic
32#14583056—21no—
33#14583039—21no—
34Q8×C43⋊C8C2211yescharacteristic
35C8×Dic86—21no—
36C8×Dic86C2211yescharacteristic
37#14583023—21no—
38#14583023C2211yescharacteristic
39#14582993—21no—
40#14582991—21no—
41#14582986—21no—
42#14582984—21no—
43#14582951C2211yescharacteristic
44#14582951C2211yescharacteristic
45C4⋊C8×D43—21no—
46C4⋊C8×D43C2211yescharacteristic
47#14582894—21no—
48#14582894—21no—
49C4×C8×D43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582649C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582645C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582642C2211yescharacteristic
59#14582642C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#477C2211yescharacteristic
62C43×#475C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621902—21no—
68C2×Q8×D43D411yescharacteristic
69C2×Dic172—21no—
70C2×#10621885—21no—
71C2×#10621873—21no—
72C2×#10621884—21no—
73C2×C8×D43—21no—
74C2×C8×D43D411yescharacteristic
75C2×C8×D43D411yescharacteristic
76#13063325C2311yescharacteristic
77#13063322C2311yescharacteristic
78#13063316—21no—
79#13063314—21no—
80#13063305—21no—
81#13063301—21no—
82#13063300—21no—
83#13063300—21no—
84Q8×Dic43—21no—
85Q8×Dic43D411yescharacteristic
86C4×Dic86—21no—
87C4×Dic86C2311yescharacteristic
88#13063290—21no—
89#13063290—21no—
90#13063290D411yescharacteristic
91#13063287—21no—
92#13063287—21no—
93#13063283—21no—
94C4⋊C4×D43—21no—
95C4⋊C4×D43D411yescharacteristic
96C42×D43—21no—
97C42×D43C2311yescharacteristic
98#13063258—21no—
99#13063256—21no—
100C4⋊(C43⋊C8)—21no—
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104Dic43⋊C8—21no—
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107#13063250—21no—
108#13063249—21no—
109#13063249—21no—
110#13063248—21no—
111#13063248—21no—
112#13063248—21no—
113#13063247—21no—
114#13063247—21no—
115#13063247—21no—
116#13063245—21no—
117#13063245—21no—
118#13063245—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121C4×C43⋊C8—21no—
122C4×C43⋊C8C2311yescharacteristic
123C8×Dic43—21no—
124C8×Dic43—21no—
125C8×Dic43—21no—
126C8×Dic43—21no—
127C8×Dic43D411yescharacteristic
128C8×Dic43D411yescharacteristic
129C4⋊Q8×C43C2311yescharacteristic
130C4⋊Q8×C43C2311yescharacteristic
131C4×Q8×C43C2311yescharacteristic
132#107×C43—21no—
133#106×C43—21no—
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#103×C43—21no—
141#103×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147#10621902—42no—
148#10621902—42no—
149Q8×D43—22no—
150Q8×D43—22no—
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—41no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—41no—
158C2×C4×D43C2×D411yescharacteristic
159C2×C4×D43C2×D411yescharacteristic
160C2×C4×D43#4111yescharacteristic
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86C2×D411yescharacteristic
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43C2×D411yescharacteristic
175C42×C43—21no—
176C42×C43C2411yescharacteristic
177#10621885—42no—
178#10621884—42no—
179(C2×D43)⋊C4—41no—
180(C2×D43)⋊C4—41no—
181(C2×D43)⋊C4—41no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—41no—
186C4⋊Dic43C2×D411yescharacteristic
187Dic43⋊C4—21no—
188Dic43⋊C4—21no—
189Dic43⋊C4—21no—
190Dic43⋊C4—41no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—41no—
195C4×Dic43C2×D411yescharacteristic
196C4×Dic43C2×D411yescharacteristic
197C4×Dic43#4111yescharacteristic
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203Dic172—42no—
204#10621873—42no—
205C8×D43—22no—
206C8×D43—22no—
207C8×D43—42no—
208C22×D43—41no—
209C22×D43#12111yescharacteristic
210Q8×C43—21no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—81no—
214Q8×C43#13512yes—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—41no—
225C2×Dic43#12111yescharacteristic
226C2×Dic43#12111yescharacteristic
227C2×Dic43#12111yescharacteristic
228D172—41no—
229D172—41no—
230D172—41no—
231D172—41no—
232D172—81no—
233D172—82no—
234C4×D43—24no—
235C4×D43—21no—
236C4×D43—21no—
237C4×D43—41no—
238C4×D43—42no—
239C4×D43—82no—
240C4×D43#13512yes—
241C4×D43#13712yes—
242Dic86—24no—
243Dic86—21no—
244Dic86—41no—
245Dic86—41no—
246Dic86#13512yes—
247C8×C43—21no—
248C8×C43—21no—
249C8×C43—41no—
250C8×C43—41no—
251C8×C43—41no—
252C43⋊C8—21no—
253C43⋊C8—21no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257#19123—431nomaximal, Sylow
258C22×C43C2×#12111yescharacteristic
259C2×D43—21no—
260C2×D43—21no—
261C2×D43—81no—
262C2×D43—81no—
263C2×D43—81no—
264C2×D43#46412yes—
265C4×C43—22no—
266C4×C43—21no—
267C4×C43—41no—
268C4×C43—81no—
269C4×C43—81no—
270C4×C43C2×#13511yescharacteristic
271C4×C43C2×#13511yescharacteristic
272C4×C43C2×#13511yescharacteristic
273C4×C43C2×#13711yescharacteristic
274Dic43—21no—
275Dic43—22no—
276Dic43—21no—
277Dic43—41no—
278Dic43—81no—
279Dic43#46412yes—
280#3131—431no—
281#3104—431no—
282#3103—431no—
283C2×C8×Q8—431no—
284#1684—431no—
285#1684D4311yescharacteristic, complemented
286#1682—431no—
287#1682—431no—
288#1680—431no—
289#1680—431no—
290#1678—431no—
291#1678—431no—
292#1564—431no—
293#1542—431no—
294#1540—431no—
295C2×C43C2×#46411yescharacteristic
296C2×C43#305011yescharacteristic
297C2×C43#306711yescharacteristic
298D43—22no—
299D43—161no—
300#533—431no—
301#532—431no—
302C2×C4×Q8—431no—
303#488—861no—
304#488—861no—
305#487—431no—
306#487C2×D4311yescharacteristic
307#486—431no—
308#486—431no—
309#484—861no—
310#481—861no—
311#477—431no—
312#477C2×D4311yescharacteristic
313#475—431no—
314#475C2×D4311yescharacteristic
315#462—431no—
316#462—431no—
317#460—431no—
318#460—431no—
319#451—861no—
320#448—861no—
321C8×Q8—431no—
322C8×Q8—431no—
323C8×Q8—431no—
324C8×Q8—861no—
325C8×Q8—861no—
326C8×Q8C2×D4311yescharacteristic
327C4×Q16—861no—
328C4×Q16—861no—
329C4×SD16—861no—
330C4×SD16—861no—
331#431—431no—
332#431—431no—
333C2×C4⋊C8—431no—
334C2×C4⋊C8—861no—
335#416—861no—
336#416—861no—
337C2×C4×C8—431no—
338C2×C4×C8—861no—
339#335—431no—
340#335C2×D4311yescharacteristic
341#334—431no—
342#334—431no—
343#333—431no—
344#333C2×D4311yescharacteristic
345#332—431no—
346#332—431no—
347#332—431no—
348#332C2×D4311yescharacteristic
349#331—431no—
350#331—431no—
351C43#1912311yescharacteristic, complemented, Sylow
352C2×#41—861no—
353C22×Q8—431no—
354C2×Q16—861no—
355C2×Q16—861no—
356C2×SD16—861no—
357C2×SD16—861no—
358C22×C8—431no—
359C22×C8—431no—
360C22×C8—861no—
361C4⋊Q8—431no—
362C4⋊Q8C22×D4311yescharacteristic
363C4⋊Q8C22×D4311yescharacteristic
364#127—431no—
365#125—861no—
366#124—861no—
367C22⋊Q8—861no—
368C22⋊Q8—861no—
369#121—861no—
370#121—861no—
371C4×Q8—431no—
372C4×Q8—431no—
373C4×Q8—431no—
374C4×Q8—861no—
375C4×Q8—861no—
376C4×Q8—861no—
377C4×Q8—861no—
378C4×Q8C22×D4311yescharacteristic
379C4×D4—861no—
380C4×D4—861no—
381#117—861no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—861no—
384C2×C42—431no—
385C2×C42—861no—
386#107—21no—
387#107—861no—
388#106—21no—
389#106—861no—
390C4⋊C8—21no—
391C4⋊C8—431no—
392C4⋊C8—431no—
393C4⋊C8—431no—
394C4⋊C8—861no—
395C4⋊C8—861no—
396C4⋊C8—861no—
397C4⋊C8—861no—
398C4⋊C8C22×D4311yescharacteristic
399C4⋊C8C22×D4311yescharacteristic
400C4⋊C8C22×D4311yescharacteristic
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#102—861no—
412#102—861no—
413#102—861no—
414#102—861no—
415#102—861no—
416#102—861no—
417C22⋊C8—861no—
418C22⋊C8—861no—
419C4×C8—21no—
420C4×C8—431no—
421C4×C8—431no—
422C4×C8—431no—
423C4×C8—861no—
424C4×C8—861no—
425C4×C8—861no—
426C4×C8—861no—
427C4×C8—861no—
428C4×C8C22×D4311yescharacteristic
429#41—1722no—
430#41—1722no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—431no—
434C2×Q8—861no—
435C2×Q8—862no—
436C2×Q8—862no—
437C2×Q8—861no—
438C2×Q8D4×D4311yescharacteristic
439C2×D4—861no—
440C2×D4—861no—
441C2×D4—861no—
442C2×D4—1721no—
443C22×C4—431no—
444C22×C4—431no—
445C22×C4—431no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—1721no—
449Q16—1722no—
450Q16—1722no—
451SD16—1722no—
452SD16—1722no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—431no—
457C2×C8—431no—
458C2×C8—862no—
459C2×C8—862no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—1722no—
464C2×C8D4×D4311yescharacteristic
465C2×C8D4×D4311yescharacteristic
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—431no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—1721no—
479C4⋊C4—1721no—
480C4⋊C4D4×D4311yescharacteristic
481C22⋊C4—1721no—
482C22⋊C4—1721no—
483C22⋊C4—1721no—
484C42—21no—
485C42—431no—
486C42—431no—
487C42—431no—
488C42—861no—
489C42—861no—
490C42—861no—
491C42—1721no—
492C42C23×D4311yescharacteristic
493C23—431no—
494C23—1721no—
495Q8—21no—
496Q8—41no—
497Q8—41no—
498Q8—81no—
499Q8—432no—
500Q8—864no—
501Q8—861no—
502Q8—1721no—
503Q8—1721no—
504Q8#1306334812yes—
505D4—3441no—
506D4—3442no—
507D4—1721no—
508D4—1721no—
509D4—1721no—
510D4—1721no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—431no—
516C2×C4—432no—
517C2×C4—432no—
518C2×C4—431no—
519C2×C4—431no—
520C2×C4—864no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—3442no—
526C2×C4—1721no—
527C2×C4—1722no—
528C2×C4—1721no—
529C2×C4C2×D4×D4311yescharacteristic
530C2×C4C2×D4×D4311yescharacteristic
531C2×C4#41×D4311yescharacteristic
532C8—21no—
533C8—21no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—861no—
538C8—861no—
539C8—1721no—
540C8—1721no—
541C8—1721no—
542C22—432no—
543C22—861no—
544C22—861no—
545C22—3441no—
546C22—3441no—
547C22—3441no—
548C22#121×D4311yescharacteristic
549C4—21no—
550C4—22no—
551C4—41no—
552C4—81no—
553C4—81no—
554C4—432no—
555C4—861no—
556C4—861no—
557C4—862no—
558C4—3441no—
559C4—1721no—
560C4#135×D4311yescharacteristic
561C4#135×D4311yescharacteristic
562C4C2×#1306334811yescharacteristic
563C4#137×D4311yescharacteristic
564C2—862no—
565C2—6881no—
566C2#464×D4311yescharacteristic
567C2#1914417811yescharacteristic
568C2#1914431011yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1684C2
socleC22×C43C2×#121
prime radical#14583450C22
hypercenter#1684D43
hypocenterC43#19123
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1684

Complements

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

NH ≅ G/Ntype
2. #19144636C2semidirect
4. C8×Q8×D43C2semidirect
5. #19134050C2semidirect
6. #19134040C2semidirect
7. #19134039C2semidirect
8. #19134024C2semidirect
9. #19134023C2semidirect
10. #19134014C2semidirect
11. #19134013C2semidirect
12. #19133342C2semidirect
13. #19133249C2semidirect
15. C43×#1684C2semidirect
285. #1684D43semidirect
351. C43#19123semidirect

Maximal subgroups

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

subgroupindex
#191449192
#191446362
#191446282
C8×Q8×D432
#191340502
#191340402
#191340392
#191340242
#191340232
#191340142
#191340132
#191333422
#191332492
#191332432
C43×#16842
#1912343