Finite Group Databasebeta

← C151×#24479 #50329404

Subgroups — C151×#24479 #50329404

Order 38656.

1102 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#484×C151C211yesmaximal, characteristic, complemented
2C22×#102×C151C211yesmaximal, characteristic
3#2435×C151C211yesmaximal, characteristic
4#2345×C151C211yesmaximal, characteristic, complemented
5#2067×C151C212yesmaximal, complemented
6#2042×C151C212yesmaximal, complemented
7#1983×C151C212yesmaximal, complemented
8#1925×C151C212yesmaximal, complemented
9#1892×C151C211yesmaximal, characteristic, complemented
10#1850×C151C211yesmaximal, characteristic, complemented
11#1786×C151C211yesmaximal, characteristic
12C23×D4×C151C2211yescharacteristic
13C23×C8×C151C2211yescharacteristic
14C2×#124×C151C2212yes—
15C2×C22⋊Q8×C151C2211yescharacteristic
16C22×C4⋊C4×C151C2211yescharacteristic
17#484×C151—24no—
18C2×#107×C151C2211yescharacteristic, complemented
19C2×#107×C151C2211yescharacteristic, complemented
20C2×C4⋊C8×C151C2212yescomplemented
21C2×#103×C151C2211yescharacteristic, complemented
22C2×#103×C151C2211yescharacteristic, complemented
23C2×#103×C151C2212yescomplemented
24C2×#102×C151—24no—
25C2×#102×C151C2212yes—
26C2×#102×C151C2212yes—
27C2×#102×C151C2212yes—
28C2×#102×C151C2212yes—
29C2×C22⋊C8×C151C2211yescharacteristic
30#394×C151—22no—
31#390×C151C2212yes—
32#389×C151C2212yescomplemented
33#387×C151—22no—
34#380×C151—21no—
35#380×C151C2211yescharacteristic
36#379×C151—21no—
37#379×C151—21no—
38C4×C4⋊C4×C151C2212yescomplemented
39C4×C22⋊C4×C151—21no—
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×C151—21no—
52C23×C4×C151C2311yescharacteristic
53C22×C8×C151—22no—
54C22×C8×C151—42no—
55C22×C8×C151C2311yescharacteristic
56C22×C8×C151C2312yes—
57C22×C8×C151C2311yescharacteristic
58#124×C151—24no—
59#124×C151—42no—
60C22⋊Q8×C151—22no—
61C22⋊Q8×C151—22no—
62C2×C4⋊C4×C151—21no—
63C2×C4⋊C4×C151—22no—
64C2×C4⋊C4×C151—21no—
65C2×C4⋊C4×C151—22no—
66C2×C4⋊C4×C151D414yes—
67C2×C4⋊C4×C151C2311yescharacteristic
68C2×C4⋊C4×C151C2312yes—
69C2×C4⋊C4×C151C2311yescharacteristic
70C2×C4⋊C4×C151C2311yescharacteristic
71C2×C22⋊C4×C151—22no—
72C2×C22⋊C4×C151—22no—
73C2×C22⋊C4×C151—22no—
74C2×C22⋊C4×C151—22no—
75C2×C22⋊C4×C151—21no—
76C2×C22⋊C4×C151—21no—
77C2×C22⋊C4×C151D411yescharacteristic
78C2×C22⋊C4×C151D411yescharacteristic
79C2×C42×C151—22no—
80C2×C42×C151C2312yes—
81#107×C151—22no—
82#107×C151—22no—
83C4⋊C8×C151—42no—
84#103×C151—22no—
85#103×C151—22no—
86#103×C151—42no—
87#102×C151—24no—
88#102×C151—24no—
89#102×C151—24no—
90#102×C151—42no—
91C22⋊C8×C151—22no—
92#95×C151—22no—
93#95×C151—22no—
94#95×C151—21no—
95#95×C151D412yes—
96C24×C151—22no—
97C24×C151—44no—
98C24×C151—42no—
99C24×C151—42no—
100C24×C151—42no—
101C24×C151—82no—
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—24no—
123C22×C4×C151—22no—
124C22×C4×C151—21no—
125C22×C4×C151—21no—
126C22×C4×C151—82no—
127C22×C4×C151C2×D412yes—
128C22×C4×C151C2×D412yes—
129C22×C4×C151C2×D411yescharacteristic
130C22×C4×C151C2×D412yes—
131C22×C4×C151#4112yes—
132C22×C4×C151C2411yescharacteristic
133C2×C8×C151—21no—
134C2×C8×C151—21no—
135C2×C8×C151—22no—
136C2×C8×C151—22no—
137C2×C8×C151—22no—
138C2×C8×C151—22no—
139C2×C8×C151—22no—
140C2×C8×C151—44no—
141C4⋊C4×C151—24no—
142C4⋊C4×C151—21no—
143C4⋊C4×C151—21no—
144C4⋊C4×C151—21no—
145C4⋊C4×C151—22no—
146C4⋊C4×C151—21no—
147C4⋊C4×C151—22no—
148C4⋊C4×C151—42no—
149C4⋊C4×C151—82no—
150C4⋊C4×C151C2×D412yes—
151C4⋊C4×C151C2×D412yes—
152C22⋊C4×C151—22no—
153C22⋊C4×C151—22no—
154C22⋊C4×C151—44no—
155C22⋊C4×C151—44no—
156C22⋊C4×C151—42no—
157C22⋊C4×C151—42no—
158C22⋊C4×C151—82no—
159C22⋊C4×C151—82no—
160C42×C151—22no—
161C42×C151—22no—
162C42×C151—82no—
163C23×C151—22no—
164C23×C151—22no—
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—88no—
174C23×C151—88no—
175C23×C151—84no—
176C23×C151—84no—
177C23×C151#12112yes—
178C23×C151#13512yes—
179C23×C151#13712yes—
180C23×C151C22×D411yescharacteristic
181Q8×C151—41no—
182Q8×C151—41no—
183Q8×C151—42no—
184D4×C151—24no—
185D4×C151—24no—
186D4×C151—48no—
187D4×C151—42no—
188D4×C151—42no—
189C2×C4×C151—22no—
190C2×C4×C151—22no—
191C2×C4×C151—22no—
192C2×C4×C151—24no—
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—22no—
200C2×C4×C151—22no—
201C2×C4×C151—42no—
202C2×C4×C151—42no—
203C2×C4×C151—41no—
204C2×C4×C151—41no—
205C2×C4×C151—42no—
206C2×C4×C151—42no—
207C2×C4×C151—42no—
208C2×C4×C151—42no—
209C2×C4×C151—42no—
210C2×C4×C151—84no—
211C2×C4×C151#12112yes—
212C2×C4×C151C22×D411yescharacteristic
213C2×C4×C151C2×#4112yes—
214C2×C4×C151C2×#4111yescharacteristic
215C2×C4×C151H(5,𝔽2)12yes—
216C8×C151—41no—
217C8×C151—41no—
218C8×C151—42no—
219C22×C151—22no—
220C22×C151—22no—
221C22×C151—24no—
222C22×C151—24no—
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×C151#46414yes—
232C22×C151C2×#12111yescharacteristic
233C22×C151#54612yes—
234C22×C151C2×#13511yescharacteristic
235C22×C151C2×#13711yescharacteristic
236C22×C151#57612yes—
237C4×C151—22no—
238C4×C151—42no—
239C4×C151—42no—
240C4×C151—42no—
241C4×C151—42no—
242C4×C151—81no—
243C4×C151—81no—
244C4×C151—82no—
245C4×C151#52511yescharacteristic
246C4×C151#53511yescharacteristic
247C4×C151#55112yes—
248C2×C151—24no—
249C2×C151—84no—
250C2×C151#241111yescharacteristic
251C2×C151C2×#46411yescharacteristic
252C2×C151#304111yescharacteristic
253C2×C151#329712yes—
254C2×C151#331412yes—
255#24479C15111yesmaximal, characteristic, direct product factor, Sylow
256C151#2447911yescharacteristic, direct product factor, Sylow
257C2×#484C2×C15111yescharacteristic, complemented
258C22×#102C2×C15111yescharacteristic
259#2435C2×C15111yescharacteristic
260#2345C2×C15111yescharacteristic, complemented
261#2067C2×C15112yescomplemented
262#2042C2×C15112yescomplemented
263#1983C2×C15112yescomplemented
264#1925C2×C15112yescomplemented
265#1892C2×C15111yescharacteristic, complemented
266#1850C2×C15111yescharacteristic, complemented
267#1786C2×C15111yescharacteristic
268C23×D4C22×C15111yescharacteristic
269C23×C8C22×C15111yescharacteristic
270C2×#124C22×C15112yes—
271C2×C22⋊Q8C22×C15111yescharacteristic
272C22×C4⋊C4C22×C15111yescharacteristic
273#484—24no—
274C2×#107C22×C15111yescharacteristic, complemented
275C2×#107C22×C15111yescharacteristic, complemented
276C2×C4⋊C8C22×C15112yescomplemented
277C2×#103C22×C15111yescharacteristic, complemented
278C2×#103C22×C15111yescharacteristic, complemented
279C2×#103C22×C15112yescomplemented
280C2×#102—24no—
281C2×#102C22×C15112yes—
282C2×#102C22×C15112yes—
283C2×#102C22×C15112yes—
284C2×#102C22×C15112yes—
285C2×C22⋊C8C22×C15111yescharacteristic
286#394—22no—
287#390C22×C15112yes—
288#389C22×C15112yescomplemented
289#387—22no—
290#380—21no—
291#380C22×C15111yescharacteristic
292#379—21no—
293#379—21no—
294C4×C4⋊C4C22×C15112yescomplemented
295C4×C22⋊C4—21no—
296C4×C22⋊C4C22×C15111yescharacteristic
297#340C22×C15112yescomplemented
298#336C22×C15112yescomplemented
299C25—21no—
300C22×Q8C23×C15111yescharacteristic
301C22×D4—24no—
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—21no—
305C22×D4—42no—
306C22×D4C23×C15112yes—
307C23×C4—21no—
308C23×C4C23×C15111yescharacteristic
309C22×C8—22no—
310C22×C8—42no—
311C22×C8C23×C15112yes—
312C22×C8C23×C15111yescharacteristic
313C22×C8C23×C15111yescharacteristic
314#124—24no—
315#124—42no—
316C22⋊Q8—22no—
317C22⋊Q8—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4D4×C15114yes—
323C2×C4⋊C4C23×C15111yescharacteristic
324C2×C4⋊C4C23×C15112yes—
325C2×C4⋊C4C23×C15111yescharacteristic
326C2×C4⋊C4C23×C15111yescharacteristic
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4D4×C15111yescharacteristic
334C2×C22⋊C4D4×C15111yescharacteristic
335C2×C42—22no—
336C2×C42C23×C15112yes—
337#107—22no—
338#107—22no—
339C4⋊C8—42no—
340#103—22no—
341#103—22no—
342#103—42no—
343#102—24no—
344#102—24no—
345#102—24no—
346#102—42no—
347C22⋊C8—22no—
348#95—22no—
349#95—22no—
350#95—21no—
351#95D4×C15112yes—
352C24—22no—
353C24—44no—
354C24—42no—
355C24—42no—
356C24—42no—
357C24—82no—
358C24C2×D4×C15111yescharacteristic
359C2×Q8—21no—
360C2×Q8—21no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×D4—28no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—48no—
370C2×D4—44no—
371C2×D4—44no—
372C2×D4—42no—
373C2×D4#41×C15114yes—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—24no—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—82no—
383C22×C4C2×D4×C15112yes—
384C22×C4C2×D4×C15112yes—
385C22×C4C2×D4×C15111yescharacteristic
386C22×C4C2×D4×C15112yes—
387C22×C4#41×C15112yes—
388C22×C4C24×C15111yescharacteristic
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—44no—
397C4⋊C4—24no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—42no—
405C4⋊C4—82no—
406C4⋊C4C2×D4×C15112yes—
407C4⋊C4C2×D4×C15112yes—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—44no—
411C22⋊C4—44no—
412C22⋊C4—42no—
413C22⋊C4—42no—
414C22⋊C4—82no—
415C22⋊C4—82no—
416C42—22no—
417C42—22no—
418C42—82no—
419C23—22no—
420C23—22no—
421C23—24no—
422C23—48no—
423C23—42no—
424C23—42no—
425C23—42no—
426C23—42no—
427C23—42no—
428C23—42no—
429C23—88no—
430C23—88no—
431C23—84no—
432C23—84no—
433C23#121×C15112yes—
434C23#135×C15112yes—
435C23#137×C15112yes—
436C23C22×D4×C15111yescharacteristic
437Q8—41no—
438Q8—41no—
439Q8—42no—
440D4—24no—
441D4—24no—
442D4—48no—
443D4—42no—
444D4—42no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—24no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—84no—
467C2×C4#121×C15112yes—
468C2×C4C22×D4×C15111yescharacteristic
469C2×C4C2×#41×C15112yes—
470C2×C4C2×#41×C15111yescharacteristic
471C2×C4H(5,𝔽2)×C15112yes—
472C8—41no—
473C8—42no—
474C8—41no—
475C22—22no—
476C22—22no—
477C22—24no—
478C22—24no—
479C22—44no—
480C22—44no—
481C22—44no—
482C22—816no—
483C22—82no—
484C22—82no—
485C22—82no—
486C22—82no—
487C22#464×C15114yes—
488C22C2×#121×C15111yescharacteristic
489C22#546×C15112yes—
490C22C2×#135×C15111yescharacteristic
491C22C2×#137×C15111yescharacteristic
492C22#576×C15112yes—
493C4—22no—
494C4—42no—
495C4—42no—
496C4—42no—
497C4—42no—
498C4—81no—
499C4—81no—
500C4—82no—
501C4#525×C15111yescharacteristic
502C4#535×C15111yescharacteristic
503C4#551×C15112yes—
504C2—24no—
505C2—84no—
506C2#2411×C15111yescharacteristic
507C2C2×#464×C15111yescharacteristic
508C2#3041×C15111yescharacteristic
509C2#3297×C15112yes—
510C2#3314×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×#484×C151C2semidirect
4. #2345×C151C2semidirect
5. #2067×C151C2semidirect
6. #2042×C151C2semidirect
7. #1983×C151C2semidirect
8. #1925×C151C2semidirect
9. #1892×C151C2semidirect
10. #1850×C151C2semidirect
18. C2×#107×C151C22semidirect
19. C2×#107×C151C22semidirect
20. C2×C4⋊C8×C151C22semidirect
21. C2×#103×C151C22semidirect
22. C2×#103×C151C22semidirect
23. C2×#103×C151C22semidirect
32. #389×C151C22semidirect
38. C4×C4⋊C4×C151C22semidirect
41. #340×C151C22semidirect
42. #336×C151C22semidirect
255. #24479C151direct (N × H)
256. C151#24479direct (N × H)
257. C2×#484C2×C151semidirect
260. #2345C2×C151semidirect
261. #2067C2×C151semidirect
262. #2042C2×C151semidirect
263. #1983C2×C151semidirect
264. #1925C2×C151semidirect
265. #1892C2×C151semidirect
266. #1850C2×C151semidirect
274. C2×#107C22×C151semidirect
275. C2×#107C22×C151semidirect
276. C2×C4⋊C8C22×C151semidirect
277. C2×#103C22×C151semidirect
278. C2×#103C22×C151semidirect
279. C2×#103C22×C151semidirect
288. #389C22×C151semidirect
294. C4×C4⋊C4C22×C151semidirect
297. #340C22×C151semidirect
298. #336C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#484×C1512
C22×#102×C1512
#2435×C1512
#2345×C1512
#2067×C1512
#2042×C1512
#1983×C1512
#1925×C1512
#1892×C1512
#1850×C1512
#1786×C1512
#24479151