Finite Group Databasebeta

← C151×#24421 #50329346

Subgroups — C151×#24421 #50329346

Order 38656.

1310 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3585×C151C211yesmaximal, characteristic
2#3069×C151C212yesmaximal, complemented
3#3022×C151C211yesmaximal, characteristic, complemented
4#3009×C151C211yesmaximal, characteristic, complemented
5#2888×C151C211yesmaximal, characteristic, complemented
6#2048×C151C212yesmaximal, complemented
7#2019×C151C212yesmaximal, complemented
8#1915×C151C211yesmaximal, characteristic, complemented
9#1881×C151C212yesmaximal, complemented
10#1858×C151C211yesmaximal, characteristic, complemented
11#1791×C151C211yesmaximal, characteristic, complemented
12#585×C151C2211yescharacteristic
13C2×H(5,𝔽2)×C151C2211yescharacteristic
14#577×C151—24no—
15#576×C151—24no—
16#575×C151—22no—
17#575×C151C2212yes—
18C2×#137×C151C2211yescharacteristic, complemented
19C2×#137×C151C2212yescomplemented
20C2×AGL(1,ℤ/8)×C151—22no—
21C2×AGL(1,ℤ/8)×C151C2212yes—
22C22×SD16×C151C2211yescharacteristic, complemented
23#568×C151C2211yescharacteristic
24#568×C151C2212yescomplemented
25#536×C151C2211yescharacteristic
26#473×C151—24no—
27#471×C151—24no—
28#456×C151—22no—
29#455×C151—22no—
30#452×C151—22no—
31#450×C151—22no—
32#430×C151C2212yescomplemented
33#421×C151C2212yescomplemented
34#418×C151C2211yescharacteristic, complemented
35#416×C151C2211yescharacteristic, complemented
36#413×C151—22no—
37#413×C151C2211yescharacteristic
38#413×C151C2211yescharacteristic
39#413×C151C2212yescomplemented
40C2×#101×C151C2212yescomplemented
41C2×#100×C151—22no—
42C2×#100×C151C2212yescomplemented
43#408×C151C2211yescharacteristic
44#408×C151C2212yescomplemented
45#344×C151C2212yescomplemented
46#341×C151C2212yescomplemented
472−1+4×C151—22no—
482−1+4×C151—21no—
49H(5,𝔽2)×C151—22no—
50H(5,𝔽2)×C151—24no—
51H(5,𝔽2)×C151—21no—
52H(5,𝔽2)×C151—22no—
53H(5,𝔽2)×C151—42no—
54C2×#41×C151—22no—
55C2×#41×C151—21no—
56C2×#41×C151—42no—
57C2×#41×C151D412yes—
58C2×#41×C151C2312yes—
59C2×#41×C151C2311yescharacteristic
60C2×#41×C151C2311yescharacteristic
61C22×Q8×C151C2311yescharacteristic
62C22×D4×C151—21no—
63C22×D4×C151—22no—
64C22×D4×C151D412yes—
65C22×D4×C151C2311yescharacteristic
66#137×C151—24no—
67#137×C151—24no—
68#137×C151—24no—
69#137×C151—22no—
70#137×C151—42no—
71#137×C151D414yes—
72AGL(1,ℤ/8)×C151—28no—
73AGL(1,ℤ/8)×C151—24no—
74AGL(1,ℤ/8)×C151—22no—
75AGL(1,ℤ/8)×C151—24no—
76AGL(1,ℤ/8)×C151—24no—
77AGL(1,ℤ/8)×C151D414yes—
78#135×C151—28no—
79#135×C151—24no—
80C2×Q16×C151—21no—
81C2×Q16×C151—22no—
82C2×SD16×C151—24no—
83C2×SD16×C151—21no—
84C2×SD16×C151—22no—
85C2×SD16×C151—22no—
86C2×SD16×C151—22no—
87C2×SD16×C151—42no—
88C2×D8×C151—24no—
89C2×D8×C151—22no—
90#131×C151—24no—
91#131×C151—24no—
92#131×C151—42no—
93C2×M16×C151—22no—
94C2×M16×C151—24no—
95C2×M16×C151C2312yes—
96C2×M16×C151C2311yescharacteristic
97C2×M16×C151C2312yes—
98C2×M16×C151C2312yes—
99C22×C8×C151C2311yescharacteristic
100C4⋊Q8×C151—21no—
101#124×C151—21no—
102#123×C151—22no—
103C22⋊Q8×C151—22no—
104#117×C151C2311yescharacteristic
105#108×C151—24no—
106#104×C151—24no—
107#103×C151—21no—
108#102×C151—21no—
109#102×C151—22no—
110#101×C151—24no—
111#101×C151—21no—
112#101×C151—22no—
113#101×C151D412yes—
114#100×C151—21no—
115#100×C151—22no—
116#100×C151—24no—
117#100×C151D412yes—
118C22⋊C8×C151—22no—
119C22⋊C8×C151—42no—
120C24×C151—22no—
121C24×C151—21no—
122#41×C151—22no—
123#41×C151—22no—
124#41×C151—22no—
125#41×C151—24no—
126#41×C151—24no—
127#41×C151—22no—
128#41×C151—22no—
129#41×C151—22no—
130#41×C151—22no—
131#41×C151—42no—
132#41×C151—44no—
133#41×C151—44no—
134#41×C151—42no—
135#41×C151—42no—
136#41×C151—42no—
137#41×C151—42no—
138#41×C151C2×D414yes—
139C2×Q8×C151—22no—
140C2×Q8×C151—22no—
141C2×Q8×C151—21no—
142C2×Q8×C151—21no—
143C2×Q8×C151—22no—
144C2×Q8×C151—42no—
145C2×Q8×C151C2×D412yes—
146C2×Q8×C151C2×D411yescharacteristic
147C2×Q8×C151C2×D411yescharacteristic
148C2×D4×C151—21no—
149C2×D4×C151—22no—
150C2×D4×C151—24no—
151C2×D4×C151—22no—
152C2×D4×C151—22no—
153C2×D4×C151—22no—
154C2×D4×C151—22no—
155C2×D4×C151—21no—
156C2×D4×C151—22no—
157C2×D4×C151—42no—
158C2×D4×C151—44no—
159C2×D4×C151—48no—
160C2×D4×C151—42no—
161C2×D4×C151—44no—
162C2×D4×C151—42no—
163C2×D4×C151C2×D412yes—
164C2×D4×C151C2×D412yes—
165C2×D4×C151C2×D411yescharacteristic
166C2×D4×C151C2×D411yescharacteristic
167C2×D4×C151#4112yes—
168C22×C4×C151—21no—
169C22×C4×C151—22no—
170C22×C4×C151—22no—
171C22×C4×C151—21no—
172C22×C4×C151—42no—
173C22×C4×C151C2×D412yes—
174C22×C4×C151C2411yescharacteristic
175Q16×C151—24no—
176Q16×C151—44no—
177Q16×C151—42no—
178SD16×C151—28no—
179SD16×C151—24no—
180SD16×C151—24no—
181SD16×C151—44no—
182SD16×C151—44no—
183SD16×C151—42no—
184D8×C151—28no—
185D8×C151—24no—
186M16×C151—24no—
187M16×C151—22no—
188M16×C151—22no—
189M16×C151—22no—
190M16×C151—22no—
191M16×C151—22no—
192M16×C151—44no—
193M16×C151C2×D414yes—
194M16×C151C2×D414yes—
195C2×C8×C151—24no—
196C2×C8×C151—22no—
197C2×C8×C151—22no—
198C2×C8×C151—21no—
199C2×C8×C151—21no—
200C2×C8×C151—22no—
201C2×C8×C151—22no—
202C2×C8×C151—44no—
203C4⋊C4×C151—21no—
204C4⋊C4×C151—42no—
205C22⋊C4×C151—21no—
206C22⋊C4×C151—42no—
207C42×C151—21no—
208C23×C151—21no—
209C23×C151—22no—
210C23×C151—22no—
211C23×C151—44no—
212C23×C151—42no—
213C23×C151—42no—
214C23×C151—161no—
215C23×C151—162no—
216C23×C151#12112yes—
217C23×C151C2×#4111yescharacteristic
218Q8×C151—21no—
219Q8×C151—22no—
220Q8×C151—22no—
221Q8×C151—22no—
222Q8×C151—42no—
223Q8×C151—41no—
224Q8×C151—41no—
225Q8×C151—42no—
226Q8×C151#12012yes—
227D4×C151—24no—
228D4×C151—24no—
229D4×C151—22no—
230D4×C151—22no—
231D4×C151—21no—
232D4×C151—22no—
233D4×C151—22no—
234D4×C151—22no—
235D4×C151—44no—
236D4×C151—44no—
237D4×C151—42no—
238D4×C151—44no—
239D4×C151—42no—
240D4×C151—42no—
241D4×C151—42no—
242D4×C151#12012yes—
243C2×C4×C151—21no—
244C2×C4×C151—22no—
245C2×C4×C151—22no—
246C2×C4×C151—24no—
247C2×C4×C151—22no—
248C2×C4×C151—44no—
249C2×C4×C151—44no—
250C2×C4×C151—42no—
251C2×C4×C151—42no—
252C2×C4×C151—42no—
253C2×C4×C151—41no—
254C2×C4×C151—41no—
255C2×C4×C151—42no—
256C2×C4×C151#12112yes—
257C2×C4×C151C22×D411yescharacteristic
258C2×C4×C151C22×D412yes—
259C2×C4×C151C22×D411yescharacteristic
260C2×C4×C151H(5,𝔽2)12yes—
261C8×C151—24no—
262C8×C151—24no—
263C8×C151—41no—
264C8×C151—41no—
265C8×C151—42no—
266C22×C151—22no—
267C22×C151—22no—
268C22×C151—41no—
269C22×C151—42no—
270C22×C151—42no—
271C22×C151—42no—
272C22×C151—81no—
273C22×C151—82no—
274C22×C151—82no—
275C22×C151—162no—
276C22×C151—164no—
277C22×C151—162no—
278C22×C151C2×#12111yescharacteristic
279C22×C151#54612yes—
280C4×C151—22no—
281C4×C151—22no—
282C4×C151—42no—
283C4×C151—81no—
284C4×C151—81no—
285C4×C151C2×#12011yescharacteristic
286C4×C151#53411yescharacteristic
287C4×C151D4212yes—
288C2×C151—21no—
289C2×C151—22no—
290C2×C151—42no—
291C2×C151—42no—
292C2×C151—82no—
293C2×C151—82no—
294C2×C151#241011yescharacteristic
295#24421C15111yesmaximal, characteristic, direct product factor, Sylow
296C151#2442111yescharacteristic, direct product factor, Sylow
297#3585C2×C15111yescharacteristic
298#3069C2×C15112yescomplemented
299#3022C2×C15111yescharacteristic, complemented
300#3009C2×C15111yescharacteristic, complemented
301#2888C2×C15111yescharacteristic, complemented
302#2048C2×C15112yescomplemented
303#2019C2×C15112yescomplemented
304#1915C2×C15111yescharacteristic, complemented
305#1881C2×C15112yescomplemented
306#1858C2×C15111yescharacteristic, complemented
307#1791C2×C15111yescharacteristic, complemented
308#585C22×C15111yescharacteristic
309C2×H(5,𝔽2)C22×C15111yescharacteristic
310#577—24no—
311#576—24no—
312#575—22no—
313#575C22×C15112yes—
314C2×#137C22×C15111yescharacteristic, complemented
315C2×#137C22×C15112yescomplemented
316C2×AGL(1,ℤ/8)—22no—
317C2×AGL(1,ℤ/8)C22×C15112yes—
318C22×SD16C22×C15111yescharacteristic, complemented
319#568C22×C15111yescharacteristic
320#568C22×C15112yescomplemented
321#536C22×C15111yescharacteristic
322#473—24no—
323#471—24no—
324#456—22no—
325#455—22no—
326#452—22no—
327#450—22no—
328#430C22×C15112yescomplemented
329#421C22×C15112yescomplemented
330#418C22×C15111yescharacteristic, complemented
331#416C22×C15111yescharacteristic, complemented
332#413—22no—
333#413C22×C15111yescharacteristic
334#413C22×C15111yescharacteristic
335#413C22×C15112yescomplemented
336C2×#101C22×C15112yescomplemented
337C2×#100—22no—
338C2×#100C22×C15112yescomplemented
339#408C22×C15111yescharacteristic
340#408C22×C15112yescomplemented
341#344C22×C15112yescomplemented
342#341C22×C15112yescomplemented
3432−1+4—22no—
3442−1+4—21no—
345H(5,𝔽2)—24no—
346H(5,𝔽2)—22no—
347H(5,𝔽2)—22no—
348H(5,𝔽2)—21no—
349H(5,𝔽2)—42no—
350C2×#41—21no—
351C2×#41—22no—
352C2×#41—42no—
353C2×#41D4×C15112yes—
354C2×#41C23×C15112yes—
355C2×#41C23×C15111yescharacteristic
356C2×#41C23×C15111yescharacteristic
357C22×Q8C23×C15111yescharacteristic
358C22×D4—22no—
359C22×D4—21no—
360C22×D4D4×C15112yes—
361C22×D4C23×C15111yescharacteristic
362#137—24no—
363#137—22no—
364#137—24no—
365#137—24no—
366#137—42no—
367#137D4×C15114yes—
368AGL(1,ℤ/8)—28no—
369AGL(1,ℤ/8)—24no—
370AGL(1,ℤ/8)—22no—
371AGL(1,ℤ/8)—24no—
372AGL(1,ℤ/8)—24no—
373AGL(1,ℤ/8)D4×C15114yes—
374#135—28no—
375#135—24no—
376C2×Q16—21no—
377C2×Q16—22no—
378C2×SD16—24no—
379C2×SD16—22no—
380C2×SD16—22no—
381C2×SD16—21no—
382C2×SD16—22no—
383C2×SD16—42no—
384C2×D8—24no—
385C2×D8—22no—
386#131—24no—
387#131—24no—
388#131—42no—
389C2×M16—22no—
390C2×M16—24no—
391C2×M16C23×C15112yes—
392C2×M16C23×C15111yescharacteristic
393C2×M16C23×C15112yes—
394C2×M16C23×C15112yes—
395C22×C8C23×C15111yescharacteristic
396C4⋊Q8—21no—
397#124—21no—
398#123—22no—
399C22⋊Q8—22no—
400#117C23×C15111yescharacteristic
401#108—24no—
402#104—24no—
403#103—21no—
404#102—21no—
405#102—22no—
406#101—21no—
407#101—22no—
408#101—24no—
409#101D4×C15112yes—
410#100—21no—
411#100—22no—
412#100—24no—
413#100D4×C15112yes—
414C22⋊C8—22no—
415C22⋊C8—42no—
416C24—22no—
417C24—21no—
418#41—22no—
419#41—22no—
420#41—22no—
421#41—24no—
422#41—24no—
423#41—22no—
424#41—22no—
425#41—22no—
426#41—22no—
427#41—42no—
428#41—44no—
429#41—44no—
430#41—42no—
431#41—42no—
432#41—42no—
433#41—42no—
434#41C2×D4×C15114yes—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—22no—
440C2×Q8—42no—
441C2×Q8C2×D4×C15112yes—
442C2×Q8C2×D4×C15111yescharacteristic
443C2×Q8C2×D4×C15111yescharacteristic
444C2×D4—21no—
445C2×D4—22no—
446C2×D4—24no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—22no—
453C2×D4—42no—
454C2×D4—44no—
455C2×D4—48no—
456C2×D4—42no—
457C2×D4—44no—
458C2×D4—42no—
459C2×D4C2×D4×C15112yes—
460C2×D4C2×D4×C15112yes—
461C2×D4C2×D4×C15111yescharacteristic
462C2×D4C2×D4×C15111yescharacteristic
463C2×D4#41×C15112yes—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—42no—
469C22×C4C2×D4×C15112yes—
470C22×C4C24×C15111yescharacteristic
471Q16—24no—
472Q16—44no—
473Q16—42no—
474SD16—28no—
475SD16—24no—
476SD16—24no—
477SD16—44no—
478SD16—44no—
479SD16—42no—
480D8—28no—
481D8—24no—
482M16—24no—
483M16—22no—
484M16—22no—
485M16—22no—
486M16—22no—
487M16—22no—
488M16—44no—
489M16C2×D4×C15114yes—
490M16C2×D4×C15114yes—
491C2×C8—24no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—44no—
499C4⋊C4—21no—
500C4⋊C4—42no—
501C22⋊C4—21no—
502C22⋊C4—42no—
503C42—21no—
504C23—21no—
505C23—22no—
506C23—22no—
507C23—44no—
508C23—42no—
509C23—42no—
510C23—161no—
511C23—162no—
512C23#121×C15112yes—
513C23C2×#41×C15111yescharacteristic
514Q8—21no—
515Q8—22no—
516Q8—22no—
517Q8—22no—
518Q8—42no—
519Q8—41no—
520Q8—41no—
521Q8—42no—
522Q8#120×C15112yes—
523D4—24no—
524D4—24no—
525D4—22no—
526D4—22no—
527D4—21no—
528D4—22no—
529D4—22no—
530D4—22no—
531D4—44no—
532D4—44no—
533D4—42no—
534D4—44no—
535D4—42no—
536D4—42no—
537D4—42no—
538D4#120×C15112yes—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—44no—
545C2×C4—44no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—42no—
552C2×C4#121×C15112yes—
553C2×C4C22×D4×C15111yescharacteristic
554C2×C4C22×D4×C15112yes—
555C2×C4C22×D4×C15111yescharacteristic
556C2×C4H(5,𝔽2)×C15112yes—
557C8—24no—
558C8—24no—
559C8—41no—
560C8—41no—
561C8—42no—
562C22—22no—
563C22—22no—
564C22—41no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—81no—
569C22—82no—
570C22—82no—
571C22—162no—
572C22—164no—
573C22—162no—
574C22C2×#121×C15111yescharacteristic
575C22#546×C15112yes—
576C4—22no—
577C4—22no—
578C4—42no—
579C4—81no—
580C4—81no—
581C4C2×#120×C15111yescharacteristic
582C4#534×C15111yescharacteristic
583C4D42×C15112yes—
584C2—21no—
585C2—22no—
586C2—42no—
587C2—42no—
588C2—82no—
589C2—82no—
590C2#2410×C15111yescharacteristic
subgroupG/H
center, socleC2×C151#2410
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3585×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C151 ◁ C22×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3069×C151C2semidirect
3. #3022×C151C2semidirect
4. #3009×C151C2semidirect
5. #2888×C151C2semidirect
6. #2048×C151C2semidirect
7. #2019×C151C2semidirect
8. #1915×C151C2semidirect
9. #1881×C151C2semidirect
10. #1858×C151C2semidirect
11. #1791×C151C2semidirect
18. C2×#137×C151C22semidirect
19. C2×#137×C151C22semidirect
22. C22×SD16×C151C22semidirect
24. #568×C151C22semidirect
32. #430×C151C22semidirect
33. #421×C151C22semidirect
34. #418×C151C22semidirect
35. #416×C151C22semidirect
39. #413×C151C22semidirect
40. C2×#101×C151C22semidirect
42. C2×#100×C151C22semidirect
44. #408×C151C22semidirect
45. #344×C151C22semidirect
46. #341×C151C22semidirect
295. #24421C151direct (N × H)
296. C151#24421direct (N × H)
298. #3069C2×C151semidirect
299. #3022C2×C151semidirect
300. #3009C2×C151semidirect
301. #2888C2×C151semidirect
302. #2048C2×C151semidirect
303. #2019C2×C151semidirect
304. #1915C2×C151semidirect
305. #1881C2×C151semidirect
306. #1858C2×C151semidirect
307. #1791C2×C151semidirect
314. C2×#137C22×C151semidirect
315. C2×#137C22×C151semidirect
318. C22×SD16C22×C151semidirect
320. #568C22×C151semidirect
328. #430C22×C151semidirect
329. #421C22×C151semidirect
330. #418C22×C151semidirect
331. #416C22×C151semidirect
335. #413C22×C151semidirect
336. C2×#101C22×C151semidirect
338. C2×#100C22×C151semidirect
340. #408C22×C151semidirect
341. #344C22×C151semidirect
342. #341C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3585×C1512
#3069×C1512
#3022×C1512
#3009×C1512
#2888×C1512
#2048×C1512
#2019×C1512
#1915×C1512
#1881×C1512
#1858×C1512
#1791×C1512
#24421151