Finite Group Databasebeta

← C151×#24493 #50329418

Subgroups — C151×#24493 #50329418

Order 38656.

1068 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#485×C151C211yesmaximal, characteristic, complemented
2C2×#418×C151C211yesmaximal, characteristic
3#2435×C151C211yesmaximal, characteristic
4#2347×C151C211yesmaximal, characteristic, complemented
5#2065×C151C212yesmaximal, complemented
6#2042×C151C212yesmaximal, complemented
7#1983×C151C212yesmaximal, complemented
8#1925×C151C212yesmaximal, complemented
9#1894×C151C211yesmaximal, characteristic, complemented
10#1851×C151C211yesmaximal, characteristic, complemented
11#1786×C151C211yesmaximal, characteristic
12C23×D4×C151C2211yescharacteristic
13C22×M16×C151C2211yescharacteristic
14C2×#124×C151C2212yes—
15C2×C22⋊Q8×C151C2211yescharacteristic
16C2×#117×C151C2211yescharacteristic
17#485×C151—24no—
18C2×#107×C151C2211yescharacteristic, complemented
19C2×#106×C151C2211yescharacteristic, complemented
20C2×C4⋊C8×C151C2212yescomplemented
21#418×C151—24no—
22C2×#103×C151C2211yescharacteristic, complemented
23C2×#103×C151C2211yescharacteristic, complemented
24C2×#103×C151C2212yescomplemented
25C2×#102×C151C2212yes—
26C2×#102×C151C2212yes—
27C2×#102×C151C2212yes—
28C2×#102×C151C2212yes—
29C2×C22⋊C8×C151C2211yescharacteristic
30#394×C151—21no—
31#394×C151—21no—
32#390×C151C2212yes—
33#389×C151C2212yescomplemented
34#388×C151—22no—
35#383×C151—21no—
36#380×C151C2211yescharacteristic
37#379×C151—22no—
38C4×C4⋊C4×C151—21no—
39C4×C4⋊C4×C151C2212yescomplemented
40C4×C22⋊C4×C151C2211yescharacteristic
41#340×C151C2212yescomplemented
42#336×C151C2212yescomplemented
43C25×C151—21no—
44C22×Q8×C151C2311yescharacteristic
45C22×D4×C151—21no—
46C22×D4×C151—24no—
47C22×D4×C151—22no—
48C22×D4×C151—22no—
49C22×D4×C151—42no—
50C22×D4×C151C2312yes—
51C23×C4×C151C2311yescharacteristic
52C2×M16×C151—22no—
53C2×M16×C151—42no—
54C22×C8×C151C2311yescharacteristic
55C22×C8×C151C2312yes—
56C22×C8×C151C2311yescharacteristic
57#124×C151—24no—
58#124×C151—42no—
59C22⋊Q8×C151—22no—
60C22⋊Q8×C151—22no—
61#117×C151—22no—
62#117×C151D414yes—
63C2×C4⋊C4×C151—22no—
64C2×C4⋊C4×C151—21no—
65C2×C4⋊C4×C151C2311yescharacteristic
66C2×C4⋊C4×C151C2312yes—
67C2×C4⋊C4×C151C2311yescharacteristic
68C2×C4⋊C4×C151C2311yescharacteristic
69C2×C22⋊C4×C151—22no—
70C2×C22⋊C4×C151—22no—
71C2×C22⋊C4×C151—22no—
72C2×C22⋊C4×C151—22no—
73C2×C22⋊C4×C151—21no—
74C2×C22⋊C4×C151—21no—
75C2×C22⋊C4×C151—21no—
76C2×C22⋊C4×C151D412yes—
77C2×C42×C151—21no—
78C2×C42×C151—22no—
79C2×C42×C151C2312yes—
80#107×C151—22no—
81#106×C151—22no—
82C4⋊C8×C151—42no—
83#103×C151—22no—
84#103×C151—22no—
85#103×C151—42no—
86#102×C151—24no—
87#102×C151—24no—
88#102×C151—24no—
89#102×C151—42no—
90C22⋊C8×C151—22no—
91#95×C151—21no—
92#95×C151—22no—
93#95×C151—22no—
94#95×C151D411yescharacteristic
95#95×C151D411yescharacteristic
96C24×C151—22no—
97C24×C151—44no—
98C24×C151—44no—
99C24×C151—42no—
100C24×C151—81no—
101C24×C151—81no—
102C24×C151C2×D411yescharacteristic
103C2×Q8×C151—21no—
104C2×Q8×C151—21no—
105C2×Q8×C151—22no—
106C2×Q8×C151—22no—
107C2×D4×C151—28no—
108C2×D4×C151—22no—
109C2×D4×C151—22no—
110C2×D4×C151—22no—
111C2×D4×C151—22no—
112C2×D4×C151—22no—
113C2×D4×C151—48no—
114C2×D4×C151—44no—
115C2×D4×C151—44no—
116C2×D4×C151—42no—
117C2×D4×C151#4114yes—
118C22×C4×C151—22no—
119C22×C4×C151—22no—
120C22×C4×C151—21no—
121C22×C4×C151—21no—
122C22×C4×C151—22no—
123C22×C4×C151—21no—
124C22×C4×C151—21no—
125C22×C4×C151C2×D412yes—
126C22×C4×C151C2×D412yes—
127C22×C4×C151C2×D411yescharacteristic
128C22×C4×C151C2×D412yes—
129C22×C4×C151#4112yes—
130C22×C4×C151C2411yescharacteristic
131M16×C151—44no—
132C2×C8×C151—21no—
133C2×C8×C151—21no—
134C2×C8×C151—22no—
135C2×C8×C151—22no—
136C2×C8×C151—22no—
137C2×C8×C151—22no—
138C2×C8×C151—22no—
139C4⋊C4×C151—21no—
140C4⋊C4×C151—21no—
141C4⋊C4×C151—21no—
142C4⋊C4×C151—22no—
143C4⋊C4×C151—21no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—44no—
146C4⋊C4×C151—42no—
147C4⋊C4×C151C2×D412yes—
148C4⋊C4×C151C2×D412yes—
149C22⋊C4×C151—24no—
150C22⋊C4×C151—42no—
151C22⋊C4×C151—44no—
152C22⋊C4×C151—44no—
153C22⋊C4×C151—42no—
154C22⋊C4×C151—82no—
155C22⋊C4×C151—82no—
156C22⋊C4×C151—81no—
157C42×C151—24no—
158C42×C151—22no—
159C42×C151—22no—
160C42×C151—82no—
161C23×C151—22no—
162C23×C151—22no—
163C23×C151—21no—
164C23×C151—21no—
165C23×C151—24no—
166C23×C151—48no—
167C23×C151—42no—
168C23×C151—42no—
169C23×C151—42no—
170C23×C151—42no—
171C23×C151—42no—
172C23×C151—42no—
173C23×C151—84no—
174C23×C151—84no—
175C23×C151—88no—
176C23×C151—88no—
177C23×C151#12112yes—
178C23×C151C22×D411yescharacteristic
179Q8×C151—41no—
180Q8×C151—41no—
181Q8×C151—42no—
182D4×C151—24no—
183D4×C151—24no—
184D4×C151—48no—
185D4×C151—42no—
186D4×C151—42no—
187C2×C4×C151—22no—
188C2×C4×C151—22no—
189C2×C4×C151—22no—
190C2×C4×C151—24no—
191C2×C4×C151—22no—
192C2×C4×C151—22no—
193C2×C4×C151—22no—
194C2×C4×C151—22no—
195C2×C4×C151—22no—
196C2×C4×C151—22no—
197C2×C4×C151—22no—
198C2×C4×C151—22no—
199C2×C4×C151—42no—
200C2×C4×C151—41no—
201C2×C4×C151—41no—
202C2×C4×C151—41no—
203C2×C4×C151—41no—
204C2×C4×C151—42no—
205C2×C4×C151—42no—
206C2×C4×C151—42no—
207C2×C4×C151—42no—
208C2×C4×C151—41no—
209C2×C4×C151—41no—
210C2×C4×C151#12112yes—
211C2×C4×C151C22×D411yescharacteristic
212C2×C4×C151C2×#4112yes—
213C2×C4×C151C2×#4111yescharacteristic
214C2×C4×C151H(5,𝔽2)12yes—
215C8×C151—41no—
216C8×C151—41no—
217C8×C151—42no—
218C22×C151—22no—
219C22×C151—22no—
220C22×C151—22no—
221C22×C151—42no—
222C22×C151—42no—
223C22×C151—44no—
224C22×C151—44no—
225C22×C151—44no—
226C22×C151—816no—
227C22×C151—82no—
228C22×C151—82no—
229C22×C151—82no—
230C22×C151—82no—
231C22×C151C2×#12111yescharacteristic
232C22×C151#54612yes—
233C22×C151#57512yes—
234C22×C151#57611yescharacteristic
235C22×C151#57711yescharacteristic
236C4×C151—22no—
237C4×C151—42no—
238C4×C151—42no—
239C4×C151—42no—
240C4×C151—42no—
241C4×C151—81no—
242C4×C151—81no—
243C4×C151—82no—
244C4×C151#52511yescharacteristic
245C4×C151#53511yescharacteristic
246C4×C151#55112yes—
247C2×C151—42no—
248C2×C151—84no—
249C2×C151#241111yescharacteristic
250C2×C151#304011yescharacteristic
251C2×C151#304511yescharacteristic
252C2×C151#331112yes—
253C2×C151#332212yes—
254#24493C15111yesmaximal, characteristic, direct product factor, Sylow
255C151#2449311yescharacteristic, direct product factor, Sylow
256C2×#485C2×C15111yescharacteristic, complemented
257C2×#418C2×C15111yescharacteristic
258#2435C2×C15111yescharacteristic
259#2347C2×C15111yescharacteristic, complemented
260#2065C2×C15112yescomplemented
261#2042C2×C15112yescomplemented
262#1983C2×C15112yescomplemented
263#1925C2×C15112yescomplemented
264#1894C2×C15111yescharacteristic, complemented
265#1851C2×C15111yescharacteristic, complemented
266#1786C2×C15111yescharacteristic
267C23×D4C22×C15111yescharacteristic
268C22×M16C22×C15111yescharacteristic
269C2×#124C22×C15112yes—
270C2×C22⋊Q8C22×C15111yescharacteristic
271C2×#117C22×C15111yescharacteristic
272#485—24no—
273C2×#107C22×C15111yescharacteristic, complemented
274C2×#106C22×C15111yescharacteristic, complemented
275C2×C4⋊C8C22×C15112yescomplemented
276#418—24no—
277C2×#103C22×C15111yescharacteristic, complemented
278C2×#103C22×C15111yescharacteristic, complemented
279C2×#103C22×C15112yescomplemented
280C2×#102C22×C15112yes—
281C2×#102C22×C15112yes—
282C2×#102C22×C15112yes—
283C2×#102C22×C15112yes—
284C2×C22⋊C8C22×C15111yescharacteristic
285#394—21no—
286#394—21no—
287#390C22×C15112yes—
288#389C22×C15112yescomplemented
289#388—22no—
290#383—21no—
291#380C22×C15111yescharacteristic
292#379—22no—
293C4×C4⋊C4—21no—
294C4×C4⋊C4C22×C15112yescomplemented
295C4×C22⋊C4C22×C15111yescharacteristic
296#340C22×C15112yescomplemented
297#336C22×C15112yescomplemented
298C25—21no—
299C22×Q8C23×C15111yescharacteristic
300C22×D4—24no—
301C22×D4—22no—
302C22×D4—22no—
303C22×D4—21no—
304C22×D4—42no—
305C22×D4C23×C15112yes—
306C23×C4C23×C15111yescharacteristic
307C2×M16—22no—
308C2×M16—42no—
309C22×C8C23×C15112yes—
310C22×C8C23×C15111yescharacteristic
311C22×C8C23×C15111yescharacteristic
312#124—24no—
313#124—42no—
314C22⋊Q8—22no—
315C22⋊Q8—22no—
316#117—22no—
317#117D4×C15114yes—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4C23×C15111yescharacteristic
321C2×C4⋊C4C23×C15112yes—
322C2×C4⋊C4C23×C15111yescharacteristic
323C2×C4⋊C4C23×C15111yescharacteristic
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4D4×C15112yes—
332C2×C42—21no—
333C2×C42—22no—
334C2×C42C23×C15112yes—
335#107—22no—
336#106—22no—
337C4⋊C8—42no—
338#103—22no—
339#103—22no—
340#103—42no—
341#102—24no—
342#102—24no—
343#102—24no—
344#102—42no—
345C22⋊C8—22no—
346#95—21no—
347#95—22no—
348#95—22no—
349#95D4×C15111yescharacteristic
350#95D4×C15111yescharacteristic
351C24—22no—
352C24—44no—
353C24—44no—
354C24—42no—
355C24—81no—
356C24—81no—
357C24C2×D4×C15111yescharacteristic
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×D4—28no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—48no—
369C2×D4—44no—
370C2×D4—44no—
371C2×D4—42no—
372C2×D4#41×C15114yes—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4C2×D4×C15112yes—
381C22×C4C2×D4×C15112yes—
382C22×C4C2×D4×C15111yescharacteristic
383C22×C4C2×D4×C15112yes—
384C22×C4#41×C15112yes—
385C22×C4C24×C15111yescharacteristic
386M16—44no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—22no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—22no—
398C4⋊C4—21no—
399C4⋊C4—22no—
400C4⋊C4—44no—
401C4⋊C4—42no—
402C4⋊C4C2×D4×C15112yes—
403C4⋊C4C2×D4×C15112yes—
404C22⋊C4—24no—
405C22⋊C4—42no—
406C22⋊C4—44no—
407C22⋊C4—44no—
408C22⋊C4—42no—
409C22⋊C4—82no—
410C22⋊C4—82no—
411C22⋊C4—81no—
412C42—24no—
413C42—22no—
414C42—22no—
415C42—82no—
416C23—22no—
417C23—22no—
418C23—21no—
419C23—21no—
420C23—24no—
421C23—48no—
422C23—42no—
423C23—42no—
424C23—42no—
425C23—42no—
426C23—42no—
427C23—42no—
428C23—84no—
429C23—84no—
430C23—88no—
431C23—88no—
432C23#121×C15112yes—
433C23C22×D4×C15111yescharacteristic
434Q8—41no—
435Q8—41no—
436Q8—42no—
437D4—24no—
438D4—24no—
439D4—48no—
440D4—42no—
441D4—42no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—24no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4#121×C15112yes—
466C2×C4C22×D4×C15111yescharacteristic
467C2×C4C2×#41×C15112yes—
468C2×C4C2×#41×C15111yescharacteristic
469C2×C4H(5,𝔽2)×C15112yes—
470C8—41no—
471C8—42no—
472C8—41no—
473C22—22no—
474C22—22no—
475C22—22no—
476C22—42no—
477C22—42no—
478C22—44no—
479C22—44no—
480C22—44no—
481C22—816no—
482C22—82no—
483C22—82no—
484C22—82no—
485C22—82no—
486C22C2×#121×C15111yescharacteristic
487C22#546×C15112yes—
488C22#575×C15112yes—
489C22#576×C15111yescharacteristic
490C22#577×C15111yescharacteristic
491C4—22no—
492C4—42no—
493C4—42no—
494C4—42no—
495C4—42no—
496C4—81no—
497C4—81no—
498C4—82no—
499C4#525×C15111yescharacteristic
500C4#535×C15111yescharacteristic
501C4#551×C15112yes—
502C2—42no—
503C2—84no—
504C2#2411×C15111yescharacteristic
505C2#3040×C15111yescharacteristic
506C2#3045×C15111yescharacteristic
507C2#3311×C15112yes—
508C2#3322×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC23×D4×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C22⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#485×C151C2semidirect
4. #2347×C151C2semidirect
5. #2065×C151C2semidirect
6. #2042×C151C2semidirect
7. #1983×C151C2semidirect
8. #1925×C151C2semidirect
9. #1894×C151C2semidirect
10. #1851×C151C2semidirect
18. C2×#107×C151C22semidirect
19. C2×#106×C151C22semidirect
20. C2×C4⋊C8×C151C22semidirect
22. C2×#103×C151C22semidirect
23. C2×#103×C151C22semidirect
24. C2×#103×C151C22semidirect
33. #389×C151C22semidirect
39. C4×C4⋊C4×C151C22semidirect
41. #340×C151C22semidirect
42. #336×C151C22semidirect
254. #24493C151direct (N × H)
255. C151#24493direct (N × H)
256. C2×#485C2×C151semidirect
259. #2347C2×C151semidirect
260. #2065C2×C151semidirect
261. #2042C2×C151semidirect
262. #1983C2×C151semidirect
263. #1925C2×C151semidirect
264. #1894C2×C151semidirect
265. #1851C2×C151semidirect
273. C2×#107C22×C151semidirect
274. C2×#106C22×C151semidirect
275. C2×C4⋊C8C22×C151semidirect
277. C2×#103C22×C151semidirect
278. C2×#103C22×C151semidirect
279. C2×#103C22×C151semidirect
288. #389C22×C151semidirect
294. C4×C4⋊C4C22×C151semidirect
296. #340C22×C151semidirect
297. #336C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#485×C1512
C2×#418×C1512
#2435×C1512
#2347×C1512
#2065×C1512
#2042×C1512
#1983×C1512
#1925×C1512
#1894×C1512
#1851×C1512
#1786×C1512
#24493151