Finite Group Databasebeta

← C151×#18712 #50323637

Subgroups — C151×#18712 #50323637

Order 38656.

1084 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3543×C151C211yesmaximal, characteristic, complemented
2#3247×C151C212yesmaximal, complemented
3#3151×C151C211yesmaximal, characteristic, complemented
4#1631×C151C212yesmaximal, complemented
5#1630×C151C211yesmaximal, characteristic, complemented
6#1629×C151C211yesmaximal, characteristic, complemented
7#1621×C151C212yesmaximal, complemented
8#1620×C151C211yesmaximal, characteristic, complemented
9#1619×C151C211yesmaximal, characteristic, complemented
10C2×#331×C151C211yesmaximal, characteristic, complemented
11#1483×C151C212yesmaximal, complemented
12C2×AGL(1,ℤ/8)×C151—22no—
13#560×C151—22no—
14#559×C151C2211yescharacteristic
15#550×C151C2212yes—
16#546×C151—22no—
17D42×C151—22no—
18D42×C151C2211yescharacteristic
19#540×C151—22no—
20#535×C151—22no—
21#534×C151—22no—
22#532×C151C2211yescharacteristic, complemented
23C2×#127×C151C2211yescharacteristic
24#529×C151C2212yes—
25#496×C151—22no—
26#493×C151C2211yescharacteristic
27#493×C151C2211yescharacteristic, complemented
28#492×C151C2211yescharacteristic
29#492×C151C2211yescharacteristic, complemented
30#478×C151—22no—
31#477×C151C2212yescomplemented
32#476×C151C2212yescomplemented
33#466×C151—22no—
34#465×C151—22no—
35#463×C151—22no—
36#460×C151C2212yescomplemented
37#459×C151C2212yescomplemented
38C2×C4⋊C8×C151C2212yescomplemented
39C4×M16×C151C2211yescharacteristic, complemented
40#331×C151C2211yescharacteristic
41#331×C151C2211yescharacteristic
42#331×C151C2212yescomplemented
43Q8⋊C8×C151C2212yescomplemented
44Q8⋊C8×C151C2212yescomplemented
45D4⋊C8×C151C2212yescomplemented
46D4⋊C8×C151C2212yescomplemented
47C2×#41×C151—21no—
48C2×#41×C151—22no—
49C22×D4×C151—22no—
50C22×D4×C151—22no—
51C22×D4×C151—22no—
52C22×D4×C151D412yes—
53AGL(1,ℤ/8)×C151—48no—
54C2×SD16×C151—22no—
55C2×SD16×C151—22no—
56C2×SD16×C151—22no—
57C2×D8×C151—22no—
58C2×D8×C151—22no—
59C2×D8×C151—22no—
60C2×M16×C151—21no—
61C22×C8×C151—22no—
62C4⋊Q8×C151C2311yescharacteristic
63#127×C151—22no—
64#127×C151—22no—
65#127×C151D412yes—
66#127×C151C2311yescharacteristic
67#127×C151C2311yescharacteristic
68#127×C151C2311yescharacteristic
69#126×C151—22no—
70#125×C151D412yes—
71#124×C151—21no—
72#124×C151—22no—
73#124×C151D412yes—
74#123×C151—22no—
75#123×C151—24no—
76#123×C151—22no—
77#123×C151—22no—
78C22⋊Q8×C151D412yes—
79#121×C151—24no—
80#121×C151—24no—
81#121×C151—24no—
82#121×C151—24no—
83#121×C151—22no—
84#121×C151—22no—
85#121×C151—22no—
86#121×C151D412yes—
87#120×C151—22no—
88#120×C151—24no—
89#120×C151—24no—
90#120×C151—22no—
91C4×Q8×C151C2312yes—
92C4×D4×C151—22no—
93C4×D4×C151—22no—
94C4×D4×C151—22no—
95C4×D4×C151—22no—
96C4×D4×C151C2312yes—
97#117×C151—22no—
98C2×C22⋊C4×C151—22no—
99C2×C42×C151C2311yescharacteristic
100#107×C151—22no—
101#106×C151—22no—
102C4⋊C8×C151—22no—
103C4⋊C8×C151C2312yes—
104C4⋊C8×C151C2312yes—
105#103×C151—22no—
106#102×C151—22no—
107#102×C151—22no—
108#102×C151—22no—
109#97×C151—21no—
110C4×C8×C151C2311yescharacteristic
111C4×C8×C151C2311yescharacteristic
112C24×C151—22no—
113C24×C151—22no—
114#41×C151—44no—
115#41×C151—82no—
116#41×C151—82no—
117C2×Q8×C151—21no—
118C2×Q8×C151C2×D412yes—
119C2×D4×C151—22no—
120C2×D4×C151—24no—
121C2×D4×C151—24no—
122C2×D4×C151—24no—
123C2×D4×C151—22no—
124C2×D4×C151—24no—
125C2×D4×C151—22no—
126C2×D4×C151—22no—
127C2×D4×C151—22no—
128C2×D4×C151—21no—
129C2×D4×C151—44no—
130C2×D4×C151—41no—
131C2×D4×C151—82no—
132C2×D4×C151—82no—
133C2×D4×C151—82no—
134C2×D4×C151—82no—
135C2×D4×C151—84no—
136C2×D4×C151C2×D412yes—
137C2×D4×C151C2×D412yes—
138C2×D4×C151C2×D412yes—
139C22×C4×C151—24no—
140C22×C4×C151—22no—
141C22×C4×C151—22no—
142C22×C4×C151—41no—
143C22×C4×C151C2×D412yes—
144C22×C4×C151C2×D411yescharacteristic
145SD16×C151—44no—
146SD16×C151—44no—
147SD16×C151—82no—
148D8×C151—44no—
149D8×C151—44no—
150D8×C151—82no—
151M16×C151—24no—
152C2×C8×C151—21no—
153C2×C8×C151—21no—
154C2×C8×C151—22no—
155C2×C8×C151—22no—
156C2×C8×C151—82no—
157C4⋊C4×C151—22no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—22no—
161C4⋊C4×C151—22no—
162C4⋊C4×C151C2×D412yes—
163C4⋊C4×C151C2×D412yes—
164C22⋊C4×C151—22no—
165C22⋊C4×C151—22no—
166C22⋊C4×C151—24no—
167C22⋊C4×C151—24no—
168C22⋊C4×C151—22no—
169C22⋊C4×C151—22no—
170C22⋊C4×C151—22no—
171C22⋊C4×C151—22no—
172C22⋊C4×C151—22no—
173C22⋊C4×C151—42no—
174C42×C151—22no—
175C42×C151C2×D411yescharacteristic
176C42×C151C2×D412yes—
177C42×C151C2411yescharacteristic
178C23×C151—22no—
179C23×C151—22no—
180C23×C151—22no—
181C23×C151—44no—
182C23×C151—41no—
183C23×C151—84no—
184C23×C151—84no—
185C23×C151—82no—
186C23×C151#12011yescharacteristic
187Q8×C151—22no—
188Q8×C151—22no—
189Q8×C151—42no—
190D4×C151—22no—
191D4×C151—22no—
192D4×C151—42no—
193D4×C151—42no—
194D4×C151—42no—
195D4×C151—44no—
196D4×C151—42no—
197D4×C151—42no—
198D4×C151—42no—
199D4×C151—42no—
200D4×C151—42no—
201D4×C151—42no—
202D4×C151—82no—
203D4×C151—84no—
204D4×C151—84no—
205D4×C151—84no—
206D4×C151—84no—
207D4×C151—82no—
208C2×C4×C151—22no—
209C2×C4×C151—22no—
210C2×C4×C151—22no—
211C2×C4×C151—22no—
212C2×C4×C151—22no—
213C2×C4×C151—22no—
214C2×C4×C151—42no—
215C2×C4×C151—42no—
216C2×C4×C151—41no—
217C2×C4×C151—82no—
218C2×C4×C151—84no—
219C2×C4×C151—82no—
220C2×C4×C151#12012yes—
221C2×C4×C151#12011yescharacteristic
222C2×C4×C151C22×D411yescharacteristic
223C2×C4×C151C22×D412yes—
224C8×C151—22no—
225C8×C151—22no—
226C8×C151—42no—
227C8×C151—42no—
228C22×C151—22no—
229C22×C151—42no—
230C22×C151—44no—
231C22×C151—42no—
232C22×C151—44no—
233C22×C151—42no—
234C22×C151—42no—
235C22×C151—42no—
236C22×C151—82no—
237C22×C151—81no—
238C22×C151—164no—
239C22×C151—164no—
240C22×C151#45312yes—
241C22×C151C2×#12011yescharacteristic
242C4×C151—22no—
243C4×C151—21no—
244C4×C151—21no—
245C4×C151—42no—
246C4×C151—42no—
247C4×C151—42no—
248C4×C151—81no—
249C4×C151#57612yes—
250C4×C151#57712yes—
251C2×C151—22no—
252C2×C151—82no—
253C2×C151—82no—
254C2×C151—82no—
255C2×C151—161no—
256C2×C151#301212yes—
257C2×C151C2×#45311yescharacteristic
258#18712C15111yesmaximal, characteristic, direct product factor, Sylow
259C151#1871211yescharacteristic, direct product factor, Sylow
260#3543C2×C15111yescharacteristic, complemented
261#3247C2×C15112yescomplemented
262#3151C2×C15111yescharacteristic, complemented
263#1631C2×C15112yescomplemented
264#1630C2×C15111yescharacteristic, complemented
265#1629C2×C15111yescharacteristic, complemented
266#1621C2×C15112yescomplemented
267#1620C2×C15111yescharacteristic, complemented
268#1619C2×C15111yescharacteristic, complemented
269C2×#331C2×C15111yescharacteristic, complemented
270#1483C2×C15112yescomplemented
271C2×AGL(1,ℤ/8)—22no—
272#560—22no—
273#559C22×C15111yescharacteristic
274#550C22×C15112yes—
275#546—22no—
276D42—22no—
277D42C22×C15111yescharacteristic
278#540—22no—
279#535—22no—
280#534—22no—
281#532C22×C15111yescharacteristic, complemented
282C2×#127C22×C15111yescharacteristic
283#529C22×C15112yes—
284#496—22no—
285#493C22×C15111yescharacteristic
286#493C22×C15111yescharacteristic, complemented
287#492C22×C15111yescharacteristic
288#492C22×C15111yescharacteristic, complemented
289#478—22no—
290#477C22×C15112yescomplemented
291#476C22×C15112yescomplemented
292#466—22no—
293#465—22no—
294#463—22no—
295#460C22×C15112yescomplemented
296#459C22×C15112yescomplemented
297C2×C4⋊C8C22×C15112yescomplemented
298C4×M16C22×C15111yescharacteristic, complemented
299#331C22×C15111yescharacteristic
300#331C22×C15111yescharacteristic
301#331C22×C15112yescomplemented
302Q8⋊C8C22×C15112yescomplemented
303Q8⋊C8C22×C15112yescomplemented
304D4⋊C8C22×C15112yescomplemented
305D4⋊C8C22×C15112yescomplemented
306C2×#41—22no—
307C2×#41—21no—
308C22×D4—22no—
309C22×D4—22no—
310C22×D4—22no—
311C22×D4D4×C15112yes—
312AGL(1,ℤ/8)—48no—
313C2×SD16—22no—
314C2×SD16—22no—
315C2×SD16—22no—
316C2×D8—22no—
317C2×D8—22no—
318C2×D8—22no—
319C2×M16—21no—
320C22×C8—22no—
321C4⋊Q8C23×C15111yescharacteristic
322#127—22no—
323#127—22no—
324#127D4×C15112yes—
325#127C23×C15111yescharacteristic
326#127C23×C15111yescharacteristic
327#127C23×C15111yescharacteristic
328#126—22no—
329#125D4×C15112yes—
330#124—22no—
331#124—21no—
332#124D4×C15112yes—
333#123—22no—
334#123—24no—
335#123—22no—
336#123—22no—
337C22⋊Q8D4×C15112yes—
338#121—24no—
339#121—24no—
340#121—24no—
341#121—24no—
342#121—22no—
343#121—22no—
344#121—22no—
345#121D4×C15112yes—
346#120—22no—
347#120—24no—
348#120—24no—
349#120—22no—
350C4×Q8C23×C15112yes—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—22no—
355C4×D4C23×C15112yes—
356#117—22no—
357C2×C22⋊C4—22no—
358C2×C42C23×C15111yescharacteristic
359#107—22no—
360#106—22no—
361C4⋊C8—22no—
362C4⋊C8C23×C15112yes—
363C4⋊C8C23×C15112yes—
364#103—22no—
365#102—22no—
366#102—22no—
367#102—22no—
368#97—21no—
369C4×C8C23×C15111yescharacteristic
370C4×C8C23×C15111yescharacteristic
371C24—22no—
372C24—22no—
373#41—44no—
374#41—82no—
375#41—82no—
376C2×Q8—21no—
377C2×Q8C2×D4×C15112yes—
378C2×D4—22no—
379C2×D4—24no—
380C2×D4—24no—
381C2×D4—24no—
382C2×D4—22no—
383C2×D4—24no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—21no—
388C2×D4—44no—
389C2×D4—41no—
390C2×D4—82no—
391C2×D4—82no—
392C2×D4—82no—
393C2×D4—82no—
394C2×D4—84no—
395C2×D4C2×D4×C15112yes—
396C2×D4C2×D4×C15112yes—
397C2×D4C2×D4×C15112yes—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—41no—
402C22×C4C2×D4×C15112yes—
403C22×C4C2×D4×C15111yescharacteristic
404SD16—44no—
405SD16—44no—
406SD16—82no—
407D8—44no—
408D8—44no—
409D8—82no—
410M16—24no—
411C2×C8—21no—
412C2×C8—21no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—82no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4C2×D4×C15112yes—
422C4⋊C4C2×D4×C15112yes—
423C22⋊C4—22no—
424C22⋊C4—22no—
425C22⋊C4—24no—
426C22⋊C4—24no—
427C22⋊C4—22no—
428C22⋊C4—22no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—22no—
432C22⋊C4—42no—
433C42—22no—
434C42C2×D4×C15111yescharacteristic
435C42C2×D4×C15112yes—
436C42C24×C15111yescharacteristic
437C23—22no—
438C23—22no—
439C23—22no—
440C23—44no—
441C23—41no—
442C23—84no—
443C23—84no—
444C23—82no—
445C23#120×C15111yescharacteristic
446Q8—22no—
447Q8—22no—
448Q8—42no—
449D4—22no—
450D4—22no—
451D4—42no—
452D4—42no—
453D4—42no—
454D4—44no—
455D4—42no—
456D4—42no—
457D4—42no—
458D4—42no—
459D4—42no—
460D4—42no—
461D4—82no—
462D4—84no—
463D4—84no—
464D4—84no—
465D4—84no—
466D4—82no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—82no—
477C2×C4—82no—
478C2×C4—84no—
479C2×C4#120×C15112yes—
480C2×C4#120×C15111yescharacteristic
481C2×C4C22×D4×C15111yescharacteristic
482C2×C4C22×D4×C15112yes—
483C8—22no—
484C8—22no—
485C8—42no—
486C8—42no—
487C22—22no—
488C22—42no—
489C22—44no—
490C22—42no—
491C22—44no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—82no—
496C22—81no—
497C22—164no—
498C22—164no—
499C22#453×C15112yes—
500C22C2×#120×C15111yescharacteristic
501C4—22no—
502C4—21no—
503C4—21no—
504C4—42no—
505C4—42no—
506C4—42no—
507C4—81no—
508C4#576×C15112yes—
509C4#577×C15112yes—
510C2—22no—
511C2—82no—
512C2—82no—
513C2—82no—
514C2—161no—
515C2#3012×C15112yes—
516C2C2×#453×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3543×C151C2semidirect
2. #3247×C151C2semidirect
3. #3151×C151C2semidirect
4. #1631×C151C2semidirect
5. #1630×C151C2semidirect
6. #1629×C151C2semidirect
7. #1621×C151C2semidirect
8. #1620×C151C2semidirect
9. #1619×C151C2semidirect
10. C2×#331×C151C2semidirect
11. #1483×C151C2semidirect
22. #532×C151C22semidirect
27. #493×C151C22semidirect
29. #492×C151C22semidirect
31. #477×C151C22semidirect
32. #476×C151C22semidirect
36. #460×C151C22semidirect
37. #459×C151C22semidirect
38. C2×C4⋊C8×C151C22semidirect
39. C4×M16×C151C22semidirect
42. #331×C151C22semidirect
43. Q8⋊C8×C151C22semidirect
44. Q8⋊C8×C151C22semidirect
45. D4⋊C8×C151C22semidirect
46. D4⋊C8×C151C22semidirect
258. #18712C151direct (N × H)
259. C151#18712direct (N × H)
260. #3543C2×C151semidirect
261. #3247C2×C151semidirect
262. #3151C2×C151semidirect
263. #1631C2×C151semidirect
264. #1630C2×C151semidirect
265. #1629C2×C151semidirect
266. #1621C2×C151semidirect
267. #1620C2×C151semidirect
268. #1619C2×C151semidirect
269. C2×#331C2×C151semidirect
270. #1483C2×C151semidirect
281. #532C22×C151semidirect
286. #493C22×C151semidirect
288. #492C22×C151semidirect
290. #477C22×C151semidirect
291. #476C22×C151semidirect
295. #460C22×C151semidirect
296. #459C22×C151semidirect
297. C2×C4⋊C8C22×C151semidirect
298. C4×M16C22×C151semidirect
301. #331C22×C151semidirect
302. Q8⋊C8C22×C151semidirect
303. Q8⋊C8C22×C151semidirect
304. D4⋊C8C22×C151semidirect
305. D4⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3543×C1512
#3247×C1512
#3151×C1512
#1631×C1512
#1630×C1512
#1629×C1512
#1621×C1512
#1620×C1512
#1619×C1512
C2×#331×C1512
#1483×C1512
#18712151