Finite Group Databasebeta

← #25080575

Subgroups — #25080575

Order 11008.

638 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#487×D43C211yesmaximal, characteristic, complemented
2#19144409C211yesmaximal, characteristic
3#19144405C211yesmaximal, characteristic
4C8×#10621902C211yesmaximal, characteristic
5#19134055C211yesmaximal, characteristic, complemented
6#19134053C211yesmaximal, characteristic, complemented
7#19134051C211yesmaximal, characteristic, complemented
8#19134049C211yesmaximal, characteristic, complemented
9#19134047C211yesmaximal, characteristic, complemented
10#19134045C211yesmaximal, characteristic, complemented
11#19134043C211yesmaximal, characteristic, complemented
12#19133352C211yesmaximal, characteristic, complemented
13#19133278C211yesmaximal, characteristic, complemented
14#19133274C211yesmaximal, characteristic, complemented
15C43×#1684C211yesmaximal, characteristic, complemented
16C4⋊Q8×D43C2211yescharacteristic
17C4⋊Q8×D43C2211yescharacteristic
18C4×#10621902C2211yescharacteristic
19#14583251C2211yescharacteristic
20#14583250C2211yescharacteristic
21#14583249C2211yescharacteristic
22#14583248—21no—
23#14583248—21no—
24#14583194C2211yescharacteristic
25#14583192—21no—
26#14583190C2211yescharacteristic
27#14583188—21no—
28#14583186C2211yescharacteristic
29#14583184C2211yescharacteristic
30#14583182—21no—
31#14583180C2211yescharacteristic
32#14583178—21no—
33#14583176C2211yescharacteristic
34Q8×C43⋊C8C2211yescharacteristic
35C8×D172—21no—
36C8×D172C2211yescharacteristic
37#14582964—21no—
38#14582964C2211yescharacteristic
39#14582951—21no—
40#14582951C2211yescharacteristic
41#14582940—21no—
42#14582938—21no—
43#14582921C2211yescharacteristic
44#14582921C2211yescharacteristic
45#14582899—21no—
46#14582899—21no—
47#103×D43—21no—
48#103×D43—21no—
49C4×C8×D43—21no—
50C4×C8×D43C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582645C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#477C2211yescharacteristic
62C43×#475C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×#10621902D411yescharacteristic
68C2×Q8×D43—21no—
69C2×Q8×D43—21no—
70C2×#10621872—21no—
71C2×#10621872—21no—
72C2×C8×D43—21no—
73C2×C8×D43—21no—
74C2×C8×D43D411yescharacteristic
75C2×C8×D43D411yescharacteristic
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063324—21no—
79#13063324—21no—
80#13063324—21no—
81#13063324—21no—
82#13063323—21no—
83#13063323—21no—
84Q8×Dic43D411yescharacteristic
85C4×D172—21no—
86C4×D172C2311yescharacteristic
87#13063287—21no—
88#13063287D411yescharacteristic
89#13063283—21no—
90#13063283D411yescharacteristic
91C4⋊C4×D43—21no—
92C4⋊C4×D43—21no—
93C4⋊C4×D43—21no—
94C4⋊C4×D43—21no—
95C42×D43—21no—
96C42×D43C2311yescharacteristic
97#13063259—21no—
98#13063258—21no—
99#13063258—21no—
100#13063257—21no—
101#13063256—21no—
102#13063256—21no—
103C4⋊(C43⋊C8)—21no—
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109#13063250—21no—
110#13063250—21no—
111#13063249—21no—
112#13063249—21no—
113#13063249—21no—
114#13063249—21no—
115#13063248—21no—
116#13063248—21no—
117#13063247—21no—
118#13063247—21no—
119#13063245—21no—
120#13063245—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8—21no—
124C4×C43⋊C8—21no—
125C4×C43⋊C8C2311yescharacteristic
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—22no—
148#10621902Q1614yes—
149Q8×D43—42no—
150Q8×D43—42no—
151Q8×D43—82no—
152C2×D172—21no—
153C2×D172C2×D411yescharacteristic
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—41no—
158C2×C4×D43—41no—
159C2×C4×D43C2×D411yescharacteristic
160C2×C4×D43C2×D411yescharacteristic
161C2×C4×D43#4111yescharacteristic
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—41no—
165C2×Dic86—41no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43C2×D411yescharacteristic
177C42×C43—21no—
178C42×C43C2411yescharacteristic
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43C2×D411yescharacteristic
188Dic43⋊C4—41no—
189Dic43⋊C4—41no—
190Dic43⋊C4—41no—
191Dic43⋊C4—41no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43C2×D411yescharacteristic
195C4×Dic43C2×D411yescharacteristic
196C4×Dic43#4111yescharacteristic
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202#10621872—42no—
203#10621872—42no—
204C8×D43—41no—
205C8×D43—41no—
206C8×D43—42no—
207C8×D43—42no—
208C22×D43—21no—
209C22×D43#12111yescharacteristic
210Q8×C43—21no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—81no—
214Q8×C43C2×Q1612yes—
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—41no—
224C2×Dic43—41no—
225C2×Dic43#12111yescharacteristic
226C2×Dic43#12111yescharacteristic
227C2×Dic43#12111yescharacteristic
228D172—24no—
229D172—21no—
230D172C2×Q1612yes—
231C4×D43—21no—
232C4×D43—21no—
233C4×D43—24no—
234C4×D43—22no—
235C4×D43—41no—
236C4×D43—41no—
237C4×D43—42no—
238C4×D43—82no—
239C4×D43—82no—
240C4×D43C2×Q1612yes—
241C4×D43#13512yes—
242Dic86—41no—
243Dic86—41no—
244Dic86—82no—
245Dic86—82no—
246Dic86—81no—
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#19277—431nomaximal, Sylow
258C22×C43C2×#12111yescharacteristic
259C2×D43—21no—
260C2×D43—21no—
261C2×D43—22no—
262C2×D43—41no—
263C2×D43—41no—
264C2×D43#46712yes—
265C4×C43—22no—
266C4×C43—21no—
267C4×C43—41no—
268C4×C43—81no—
269C4×C43—81no—
270C4×C43C22×Q1611yescharacteristic
271C4×C43C2×#13511yescharacteristic
272C4×C43#57511yescharacteristic
273C4×C43#57511yescharacteristic
274Dic43—21no—
275Dic43—41no—
276Dic43—81no—
277Dic43—81no—
278Dic43#46712yes—
279Dic43#47112yes—
280C2×#487—431no—
281#3079—431no—
282#3079—431no—
283C8×#41—431no—
284#1684—431no—
285#1684—431no—
286#1684—431no—
287#1684D4311yescharacteristic, complemented
288#1683—431no—
289#1683—431no—
290#1683—431no—
291#1683—431no—
292#1567—431no—
293#1549—431no—
294#1548—431no—
295C2×C43#304011yescharacteristic
296C2×C43C2×#46711yescharacteristic
297C2×C43C2×#47111yescharacteristic
298D43—22no—
299D43—42no—
300C2×C4⋊Q8—431no—
301C2×C4⋊Q8—431no—
302C4×#41—431no—
303#487—431no—
304#487—431no—
305#487—431no—
306#487—861no—
307#487—861no—
308#487C2×D4311yescharacteristic
309#477—431no—
310#477—861no—
311#477C2×D4311yescharacteristic
312#476—431no—
313#476—431no—
314#476—861no—
315#475—431no—
316#475—861no—
317#475C2×D4311yescharacteristic
318#474—431no—
319#474—431no—
320#474—861no—
321C8×Q8—431no—
322C8×Q8C2×D4311yescharacteristic
323C8×D4—431no—
324C8×D4—431no—
325C8×D4—861no—
326C8×D4—861no—
327#431—431no—
328#431—861no—
329#428—861no—
330#428—861no—
331#423—431no—
332#423—431no—
333#417—861no—
334#417—861no—
335C2×#103—861no—
336C2×#103—861no—
337C2×C4×C8—431no—
338C2×C4×C8—861no—
339#335—431no—
340#335—431no—
341#335—431no—
342#335C2×D4311yescharacteristic
343#333—431no—
344#333—431no—
345#333—431no—
346#333C2×D4311yescharacteristic
347#332—431no—
348#332—431no—
349#332—431no—
350#332C2×D4311yescharacteristic
351C43#1927711yescharacteristic, complemented, Sylow
352C2×#41—431no—
353C22×Q8—861no—
354C22×Q8—861no—
355C2×M16—861no—
356C2×M16—861no—
357C22×C8—431no—
358C22×C8—431no—
359C22×C8—861no—
360C22×C8—861no—
361C4⋊Q8—431no—
362C4⋊Q8—431no—
363C4⋊Q8—861no—
364C4⋊Q8—861no—
365C4⋊Q8—861no—
366C4⋊Q8—861no—
367C4⋊Q8—861no—
368C4⋊Q8—861no—
369C4⋊Q8C22×D4311yescharacteristic
370C4⋊Q8C22×D4311yescharacteristic
371C4×Q8—431no—
372C4×Q8C22×D4311yescharacteristic
373C4×D4—431no—
374C4×D4—431no—
375C4×D4—861no—
376C4×D4—861no—
377#117—431no—
378#117—861no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C42—431no—
384C2×C42—861no—
385#107—21no—
386#107—861no—
387#107—861no—
388#107—861no—
389#106—21no—
390#106—861no—
391#106—861no—
392#106—861no—
393C4⋊C8—21no—
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—861no—
398C4⋊C8—861no—
399C4⋊C8—861no—
400C4⋊C8C22×D4311yescharacteristic
401C4⋊C8C22×D4311yescharacteristic
402C4⋊C8C22×D4311yescharacteristic
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#103—861no—
414#103—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419C22⋊C8—861no—
420C22⋊C8—861no—
421C22⋊C8—861no—
422C4×C8—21no—
423C4×C8—431no—
424C4×C8—431no—
425C4×C8—431no—
426C4×C8—861no—
427C4×C8—861no—
428C4×C8C22×D4311yescharacteristic
429#41—434no—
430#41—862no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—861no—
434C2×Q8—861no—
435C2×Q8—3442no—
436C2×Q8—1721no—
437C2×Q8—1721no—
438C2×Q8—1722no—
439C2×Q8—1722no—
440C2×Q8D4×D4311yescharacteristic
441C2×D4—431no—
442C2×D4—861no—
443C22×C4—431no—
444C22×C4—431no—
445C22×C4—431no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—1721no—
450C22×C4—1721no—
451M16—1722no—
452M16—1722no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—431no—
457C2×C8—431no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—1721no—
462C2×C8—1721no—
463C2×C8—1722no—
464C2×C8—1722no—
465C2×C8D4×D4311yescharacteristic
466C2×C8D4×D4311yescharacteristic
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—431no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—1721no—
479C4⋊C4—1721no—
480C4⋊C4—1721no—
481C4⋊C4—1721no—
482C4⋊C4D4×D4311yescharacteristic
483C22⋊C4—861no—
484C22⋊C4—861no—
485C22⋊C4—861no—
486C42—21no—
487C42—431no—
488C42—431no—
489C42—431no—
490C42—861no—
491C42—861no—
492C42C23×D4311yescharacteristic
493C23—431no—
494C23—861no—
495Q8—21no—
496Q8—41no—
497Q8—41no—
498Q8—81no—
499Q8—3441no—
500Q8—3442no—
501Q8—3442no—
502Q8—1721no—
503Q8—1721no—
504Q8Q16×D4312yes—
505D4—432no—
506D4—864no—
507D4—861no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—431no—
513C2×C4—431no—
514C2×C4—432no—
515C2×C4—432no—
516C2×C4—431no—
517C2×C4—862no—
518C2×C4—864no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—861no—
522C2×C4—3442no—
523C2×C4—3442no—
524C2×C4—1722no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
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—862no—
546C22—1721no—
547C22—1721no—
548C22#121×D4311yescharacteristic
549C4—21no—
550C4—22no—
551C4—41no—
552C4—81no—
553C4—81no—
554C4—432no—
555C4—432no—
556C4—861no—
557C4—3441no—
558C4—3441no—
559C4—1721no—
560C4C2×Q16×D4311yescharacteristic
561C4#135×D4311yescharacteristic
562C4#1458369611yescharacteristic
563C4#1458369811yescharacteristic
564C2—862no—
565C2—1722no—
566C2#1914408611yescharacteristic
567C2#467×D4311yescharacteristic
568C2#471×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1684C2
socleC22×C43C2×#121
prime radicalC2×#10621902D4
hypercenter#1684D43
hypocenterC43#19277
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1684

Complements

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

NH ≅ G/Ntype
1. #487×D43C2semidirect
5. #19134055C2semidirect
6. #19134053C2semidirect
7. #19134051C2semidirect
8. #19134049C2semidirect
9. #19134047C2semidirect
10. #19134045C2semidirect
11. #19134043C2semidirect
12. #19133352C2semidirect
13. #19133278C2semidirect
14. #19133274C2semidirect
15. C43×#1684C2semidirect
287. #1684D43semidirect
351. C43#19277semidirect

Maximal subgroups

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

subgroupindex
#487×D432
#191444092
#191444052
C8×#106219022
#191340552
#191340532
#191340512
#191340492
#191340472
#191340452
#191340432
#191333522
#191332782
#191332742
C43×#16842
#1927743