Finite Group Databasebeta

← #25079370

Subgroups — #25079370

Order 11008.

760 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144591C211yesmaximal, characteristic
2C2×#14583176C211yesmaximal, characteristic, complemented
3M16×D172C211yesmaximal, characteristic, complemented
4#19134081C212yesmaximal, complemented
5#19134057C212yesmaximal, complemented
6#19133957C212yesmaximal, complemented
7#19133933C212yesmaximal, complemented
8#19133347C211yesmaximal, characteristic, complemented
9#19133272C211yesmaximal, characteristic, complemented
10#19133267C211yesmaximal, characteristic, complemented
11C43×#3152C211yesmaximal, characteristic, complemented
12C2×M16×D43—21no—
13C2×C4×D172C2211yescharacteristic
14#14583210—21no—
15#14583176—21no—
16#14583176—21no—
17#14583176C2211yescharacteristic
18#14583176C2212yes—
19#14583176C2212yes—
20#14583176C2211yescharacteristic
21#14583091C2211yescharacteristic
22#14583091C2211yescharacteristic
23#14583032—21no—
24C4×#10621882—21no—
25C4×#10621882—21no—
26#14582978C2212yes—
27#14582972—22no—
28C8×D172C2212yes—
29#14582952C2211yescharacteristic
30C2×#13063258—21no—
31#14582923C2211yescharacteristic
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33C2×#13063245—21no—
34#14582862—21no—
35#14582652C2212yescomplemented
36#14582650C2212yescomplemented
37#14582645C2212yescomplemented
38#14582645C2212yescomplemented
39#14582645C2212yescomplemented
40#14582643C2212yescomplemented
41C2×#137×C43—21no—
42C2×#137×C43—21no—
43C43×#532C2211yescharacteristic
44C2×C4⋊Q8×C43C2211yescharacteristic
45C43×#497—22no—
46C43×#494C2212yescomplemented
47C43×#492C2212yescomplemented
48C4×M16×C43C2211yescharacteristic
49C22×D172D411yescharacteristic
50C22×C4×D43—21no—
51C2×#10621882—21no—
52C2×#10621882—21no—
53C2×#10621877—21no—
54C2×#10621872—22no—
55M16×D43—44no—
56C22×C43⋊C8—21no—
57C2×C8×D43—22no—
58C4×D172—21no—
59C4×D172—21no—
60C4×D172D411yescharacteristic
61C4×D172D411yescharacteristic
62C4×D172C2311yescharacteristic
63C4×D172C2311yescharacteristic
64C2×C4⋊Dic43D411yescharacteristic
65C2×(C2×D43)⋊C4—21no—
66#13063258—22no—
67#13063258—22no—
68#13063258—21no—
69#13063258—21no—
70C4⋊(C43⋊C8)—21no—
71C4⋊(C43⋊C8)—21no—
72C4⋊(C43⋊C8)C2311yescharacteristic
73C4⋊(C43⋊C8)C2311yescharacteristic
74C4⋊(C43⋊C8)C2312yes—
75C4⋊(C43⋊C8)C2312yes—
76#13063246—21no—
77#13063246—21no—
78#13063245—22no—
79#13063245—22no—
80#13063245—21no—
81#13063245—21no—
82C22⋊(C43⋊C8)—21no—
83(C2×D43)⋊C8—22no—
84(C2×D43)⋊C8—22no—
85C4×C43⋊C8—21no—
86C2×#41×C43—21no—
87C22×Q8×C43—21no—
88#137×C43—44no—
89#137×C43—44no—
90C2×Q16×C43—22no—
91C2×Q16×C43—22no—
92C2×SD16×C43—22no—
93C2×SD16×C43—22no—
94C2×M16×C43D411yescharacteristic
95C2×M16×C43D411yescharacteristic
96C4⋊Q8×C43—21no—
97C4⋊Q8×C43—21no—
98C4⋊Q8×C43—21no—
99C4⋊Q8×C43C2312yes—
100C4⋊Q8×C43C2311yescharacteristic
101#127×C43C2311yescharacteristic
102#124×C43—21no—
103#121×C43—21no—
104#121×C43—21no—
105C4×D4×C43—21no—
106C4×D4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C42×C43C2311yescharacteristic
110#97×C43D412yes—
111C4×C8×C43C2312yes—
112C23×D43—21no—
113#41×C43—42no—
114#41×C43—42no—
115C2×Q8×C43—21no—
116C2×Q8×C43—22no—
117C2×Q8×C43—41no—
118C2×Q8×C43—42no—
119C2×Q8×C43—42no—
120C2×D4×C43—21no—
121C2×D4×C43—21no—
122C2×D4×C43—21no—
123C2×D4×C43—41no—
124C22×C4×C43—41no—
125C22×C4×C43—41no—
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43#4111yescharacteristic
129C22×Dic43—21no—
130C2×D172—21no—
131C2×D172—22no—
132C2×D172—41no—
133C2×D172C2×D411yescharacteristic
134C2×D172C2×D411yescharacteristic
135C2×C4×D43—21no—
136C2×C4×D43—21no—
137C2×C4×D43—21no—
138C2×C4×D43—21no—
139C2×C4×D43—42no—
140C2×C4×D43—42no—
141Q16×C43—44no—
142Q16×C43—44no—
143SD16×C43—44no—
144SD16×C43—44no—
145M16×C43—22no—
146M16×C43D814yescomplemented
147C2×C8×C43C2×D412yes—
148C2×C8×C43C2×D412yes—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—41no—
154C4⋊C4×C43—41no—
155C22⋊C4×C43—41no—
156C22⋊C4×C43—41no—
157C42×C43C2×D411yescharacteristic
158C42×C43C2×D411yescharacteristic
159C42×C43#4111yescharacteristic
160C42×C43C2411yescharacteristic
161#10621882—42no—
162#10621882—42no—
163(C2×D43)⋊C4—21no—
164(C2×D43)⋊C4—21no—
165(C2×D43)⋊C4—21no—
166(C2×D43)⋊C4—21no—
167C4⋊Dic43—21no—
168C4⋊Dic43C2×D411yescharacteristic
169C4⋊Dic43C2×D411yescharacteristic
170#10621877—42no—
171C2×C43⋊C8—21no—
172C2×C43⋊C8—21no—
173C2×C43⋊C8—22no—
174C2×C43⋊C8—22no—
175C2×C43⋊C8—42no—
176#10621872—44no—
177C8×D43—44no—
178C23×C43—41no—
179C23×C43#12111yescharacteristic
180C22×D43—21no—
181C22×D43—21no—
182C22×D43—42no—
183C22×D43—42no—
184C22×D43—81no—
185Q8×C43—42no—
186Q8×C43—41no—
187Q8×C43—42no—
188Q8×C43—41no—
189Q8×C43—82no—
190D4×C43—41no—
191D4×C43—41no—
192D4×C43—41no—
193D4×C43—41no—
194D4×C43—81no—
195D4×C43—82no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—42no—
201C2×C4×C43—82no—
202C2×C4×C43—82no—
203C2×C4×C43#12111yescharacteristic
204C2×C4×C43#12111yescharacteristic
205C2×C4×C43#12111yescharacteristic
206C2×C4×C43C2×D812yes—
207C2×C4×C43AGL(1,ℤ/8)12yes—
208C2×C4×C43C22×D411yescharacteristic
209C2×C4×C43C22×D411yescharacteristic
210C2×C4×C43C2×#4111yescharacteristic
211C2×Dic43—21no—
212C2×Dic43—21no—
213C2×Dic43—42no—
214D172—21no—
215D172—21no—
216D172—21no—
217D172—42no—
218D172#13712yescomplemented
219C4×D43—41no—
220C4×D43—41no—
221C4×D43—41no—
222C4×D43—41no—
223C4×D43—42no—
224C4×D43—42no—
225C8×C43—22no—
226C8×C43C2×D814yes—
227C43⋊C8—42no—
228C43⋊C8—41no—
229C43⋊C8—42no—
230C43⋊C8—41no—
231#19163—431nomaximal, Sylow
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—81no—
235C22×C43—81no—
236C22×C43—81no—
237C22×C43#45912yes—
238C22×C43C2×#12111yescharacteristic
239C2×D43—22no—
240C2×D43—41no—
241C2×D43—41no—
242C2×D43—41no—
243C2×D43—41no—
244C2×D43—41no—
245C2×D43—84no—
246C4×C43—21no—
247C4×C43—21no—
248C4×C43—21no—
249C4×C43—81no—
250C4×C43—82no—
251C4×C43#45912yes—
252C4×C43C22×D811yescharacteristic
253C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
254C4×C43C2×#13711yescharacteristic
255C4×C43#57511yescharacteristic
256Dic43—41no—
257Dic43—41no—
258#3152D4311yescharacteristic, complemented
259#3100—431no—
260C2×#474—431no—
261D4×M16—431no—
262#1689—432no—
263#1685—432no—
264#1669—432no—
265#1665—432no—
266#1565—431no—
267#1547—431no—
268#1546—431no—
269C2×C43—22no—
270C2×C43—161no—
271C2×C43C2×#45911yescharacteristic
272C2×C43#305611yescharacteristic
273C2×C43#306911yescharacteristic
274D43—42no—
275D43—81no—
276C2×#137—21no—
277C2×#137—21no—
278C22×M16—861no—
279#532C2×D4311yescharacteristic
280C2×C4⋊Q8C2×D4311yescharacteristic
281C2×C4×D4—431no—
282#497—22no—
283#494C2×D4312yescomplemented
284#492C2×D4312yescomplemented
285#480—861no—
286#474—431no—
287#474—431no—
288#474—432no—
289#474—432no—
290#474—861no—
291#474—861no—
292#459—431no—
293#459—431no—
294#447—861no—
295C4×D8—861no—
296C4×D8—861no—
297#436—432no—
298#435—862no—
299C8×D4—432no—
300#431—431no—
301C2×#107—861no—
302#423—431no—
303C2×C4⋊C8—431no—
304C2×#102—861no—
305#407—861no—
306C4×M16C2×D4311yescharacteristic
307#335—432no—
308#334—432no—
309#332—432no—
310#332—432no—
311#332—432no—
312#331—432no—
313C43#1916311yescharacteristic, complemented, Sylow
314C2×#41—21no—
315C22×Q8—21no—
316C22×D4—431no—
317C23×C4—861no—
318#137—44no—
319#137—44no—
320C2×Q16—22no—
321C2×Q16—22no—
322C2×SD16—22no—
323C2×SD16—22no—
324C2×D8—861no—
325C2×D8—861no—
326C2×M16—861no—
327C2×M16—862no—
328C2×M16—1724no—
329C2×M16C22⋊D4311yescharacteristic
330C2×M16C22⋊D4311yescharacteristic
331C22×C8—861no—
332C22×C8—862no—
333C4⋊Q8—21no—
334C4⋊Q8—21no—
335C4⋊Q8—21no—
336C4⋊Q8C22×D4312yes—
337C4⋊Q8C22×D4311yescharacteristic
338#127C22×D4311yescharacteristic
339#124—21no—
340#121—21no—
341#121—21no—
342C4×D4—21no—
343C4×D4—21no—
344C4×D4—431no—
345C4×D4—431no—
346C4×D4—431no—
347C4×D4—431no—
348C4×D4—861no—
349C4×D4—861no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—431no—
353C2×C22⋊C4—861no—
354C2×C42C22×D4311yescharacteristic
355#107—862no—
356#107—862no—
357#107—861no—
358#107—861no—
359C4⋊C8—432no—
360C4⋊C8—432no—
361C4⋊C8—431no—
362C4⋊C8—431no—
363C4⋊C8—861no—
364C4⋊C8—861no—
365#102—862no—
366#102—862no—
367#102—861no—
368#102—861no—
369#102—861no—
370#102—861no—
371C22⋊C8—861no—
372C22⋊C8—862no—
373C22⋊C8—862no—
374#97C22⋊D4312yes—
375C4×C8—861no—
376C4×C8C22×D4312yes—
377C24—861no—
378#41—42no—
379#41—42no—
380C2×Q8—21no—
381C2×Q8—22no—
382C2×Q8—41no—
383C2×Q8—42no—
384C2×Q8—42no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—41no—
389C2×D4—431no—
390C2×D4—431no—
391C2×D4—862no—
392C2×D4—861no—
393C2×D4—1721no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—861no—
397C22×C4—861no—
398C22×C4—861no—
399C22×C4—861no—
400C22×C4—861no—
401C22×C4—1722no—
402C22×C4—1722no—
403C22×C4D4×D4311yescharacteristic
404C22×C4#1062190011yescharacteristic
405C22×C4C2×C22⋊D4311yescharacteristic
406Q16—44no—
407Q16—44no—
408SD16—44no—
409SD16—44no—
410D8—1722no—
411D8—1722no—
412M16—22no—
413M16—1722no—
414M16—1724no—
415M16#1062188214yescomplemented
416C2×C8—861no—
417C2×C8—861no—
418C2×C8—862no—
419C2×C8—862no—
420C2×C8—1722no—
421C2×C8—1724no—
422C2×C8C2×C22⋊D4312yes—
423C2×C8C2×C22⋊D4312yes—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—21no—
428C4⋊C4—41no—
429C4⋊C4—41no—
430C4⋊C4—431no—
431C4⋊C4—431no—
432C4⋊C4—861no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—861no—
436C22⋊C4—861no—
437C22⋊C4—861no—
438C22⋊C4—861no—
439C42D4×D4311yescharacteristic
440C42#1062190011yescharacteristic
441C42C2×C22⋊D4311yescharacteristic
442C42C23×D4311yescharacteristic
443C23—41no—
444C23—861no—
445C23—861no—
446C23—3441no—
447C23—1722no—
448C23—1722no—
449C23#1306329611yescharacteristic
450Q8—42no—
451Q8—41no—
452Q8—42no—
453Q8—41no—
454Q8—82no—
455D4—41no—
456D4—41no—
457D4—41no—
458D4—41no—
459D4—81no—
460D4—82no—
461D4—432no—
462D4—861no—
463D4—861no—
464D4—861no—
465D4—1722no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—82no—
472C2×C4—82no—
473C2×C4—861no—
474C2×C4—861no—
475C2×C4—1722no—
476C2×C4—1722no—
477C2×C4—1722no—
478C2×C4—1721no—
479C2×C4—1721no—
480C2×C4—1721no—
481C2×C4—1721no—
482C2×C4#1306329611yescharacteristic
483C2×C4#1306329611yescharacteristic
484C2×C4#1306329611yescharacteristic
485C2×C4C2×#1062188212yes—
486C2×C4#1306335112yes—
487C2×C4C2×D4×D4311yescharacteristic
488C2×C4C22×C22⋊D4311yescharacteristic
489C2×C4C2×#1062190011yescharacteristic
490C8—22no—
491C8—1722no—
492C8—1721no—
493C8—1722no—
494C8—1721no—
495C8C2×#1062188214yes—
496C22—21no—
497C22—21no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—862no—
502C22—3444no—
503C22—1721no—
504C22—1721no—
505C22—1721no—
506C22—1721no—
507C22—1721no—
508C22#1458309112yes—
509C22C2×#1306329611yescharacteristic
510C4—21no—
511C4—21no—
512C4—21no—
513C4—81no—
514C4—82no—
515C4—1721no—
516C4—1721no—
517C4#1458309112yes—
518C4C22×#1062188211yescharacteristic
519C4C2×#1306335111yescharacteristic
520C4#137×D4311yescharacteristic
521C4#1458369811yescharacteristic
522C2—22no—
523C2—161no—
524C2—3441no—
525C2—1722no—
526C2C2×#1458309111yescharacteristic
527C2#1914421911yescharacteristic
528C2#1914432811yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3152C2
socleC22×C43C2×#121
prime radical#19144591C2
hypercenter#3152D43
hypocenterC43#19163
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3152

Complements

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

NH ≅ G/Ntype
2. C2×#14583176C2semidirect
3. M16×D172C2semidirect
4. #19134081C2semidirect
5. #19134057C2semidirect
6. #19133957C2semidirect
7. #19133933C2semidirect
8. #19133347C2semidirect
9. #19133272C2semidirect
10. #19133267C2semidirect
11. C43×#3152C2semidirect
35. #14582652C22semidirect
36. #14582650C22semidirect
37. #14582645C22semidirect
38. #14582645C22semidirect
39. #14582645C22semidirect
40. #14582643C22semidirect
46. C43×#494C22semidirect
47. C43×#492C22semidirect
146. M16×C43D8semidirect
218. D172#137semidirect
258. #3152D43semidirect
283. #494C2×D43semidirect
284. #492C2×D43semidirect
313. C43#19163semidirect
415. M16#10621882semidirect

Maximal subgroups

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

subgroupindex
#191445912
C2×#145831762
M16×D1722
#191340812
#191340572
#191339572
#191339332
#191333472
#191332722
#191332672
C43×#31522
#1916343