Finite Group Databasebeta

← C151×#18864 #50323789

Subgroups — C151×#18864 #50323789

Order 38656.

922 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3506×C151C211yesmaximal, characteristic
2#3255×C151C211yesmaximal, characteristic, complemented
3#3228×C151C211yesmaximal, characteristic, complemented
4#3110×C151C211yesmaximal, characteristic, complemented
5#1652×C151C212yesmaximal, complemented
6#1650×C151C212yesmaximal, complemented
7#1642×C151C212yesmaximal, complemented
8#1641×C151C212yesmaximal, complemented
9#1557×C151C211yesmaximal, characteristic, complemented
10#1497×C151C211yesmaximal, characteristic, complemented
11#1486×C151C211yesmaximal, characteristic, complemented
12#559×C151—22no—
13#556×C151C2212yes—
14#555×C151—21no—
15#553×C151—22no—
16#550×C151C2212yes—
17#547×C151—21no—
18#538×C151—22no—
19#535×C151—21no—
20#533×C151C2211yescharacteristic
21#533×C151C2211yescharacteristic
22#532×C151C2211yescharacteristic
23#525×C151—22no—
24#520×C151—21no—
25C2×C4×D4×C151C2211yescharacteristic
26#500×C151C2211yescharacteristic, complemented
27#498×C151C2211yescharacteristic, complemented
28#486×C151C2211yescharacteristic, complemented
29#486×C151C2211yescharacteristic, complemented
30#484×C151—21no—
31#482×C151—22no—
32#478×C151—22no—
33#475×C151—21no—
34#475×C151C2212yescomplemented
35#474×C151C2212yes—
36#470×C151—22no—
37#462×C151—21no—
38#462×C151C2212yescomplemented
39#461×C151C2212yes—
40#450×C151—21no—
41#440×C151—22no—
42#432×C151C2211yescharacteristic
43#431×C151C2211yescharacteristic
44#423×C151C2211yescharacteristic
45#332×C151C2212yescomplemented
46#331×C151C2212yescomplemented
47Q8⋊C8×C151C2212yescomplemented
48Q8⋊C8×C151C2212yescomplemented
49D4⋊C8×C151C2212yes—
50D4⋊C8×C151C2212yes—
51C2×#41×C151—21no—
52C2×#41×C151—22no—
53C22×D4×C151D411yescharacteristic
54C23×C4×C151—21no—
55C2×Q16×C151—22no—
56C2×SD16×C151—22no—
57C2×M16×C151—21no—
58C4⋊Q8×C151D411yescharacteristic
59C4⋊Q8×C151D411yescharacteristic
60C4⋊Q8×C151C2311yescharacteristic
61C4⋊Q8×C151C2311yescharacteristic
62C4⋊Q8×C151C2311yescharacteristic
63#127×C151—22no—
64#127×C151C2311yescharacteristic
65#126×C151—24no—
66#125×C151—21no—
67#125×C151—21no—
68#124×C151—24no—
69#124×C151—22no—
70#124×C151—21no—
71#123×C151—24no—
72#123×C151—24no—
73C22⋊Q8×C151—21no—
74C22⋊Q8×C151—21no—
75C22⋊Q8×C151—21no—
76C22⋊Q8×C151—22no—
77C22⋊Q8×C151D412yes—
78#121×C151—22no—
79#121×C151—22no—
80#121×C151—24no—
81#121×C151—21no—
82#121×C151—22no—
83#121×C151D412yes—
84#120×C151—24no—
85C4×Q8×C151—22no—
86C4×Q8×C151—21no—
87C4×Q8×C151—21no—
88C4×Q8×C151—21no—
89C4×Q8×C151C2312yes—
90C4×D4×C151—24no—
91C4×D4×C151—24no—
92C4×D4×C151—22no—
93C4×D4×C151—21no—
94C4×D4×C151—21no—
95C4×D4×C151—21no—
96C4×D4×C151D412yes—
97C4×D4×C151D412yes—
98C4×D4×C151C2312yes—
99#117×C151—22no—
100#117×C151—21no—
101#117×C151—22no—
102#117×C151—21no—
103C2×C4⋊C4×C151—22no—
104C2×C4⋊C4×C151D411yescharacteristic
105C2×C22⋊C4×C151—21no—
106C2×C42×C151C2311yescharacteristic
107#107×C151—22no—
108#107×C151—22no—
109#106×C151—22no—
110#106×C151—22no—
111C4⋊C8×C151—21no—
112C4⋊C8×C151—21no—
113C4⋊C8×C151C2312yes—
114C4⋊C8×C151C2312yes—
115#103×C151—22no—
116#103×C151—22no—
117#103×C151—22no—
118#102×C151—22no—
119#102×C151—22no—
120#102×C151—22no—
121C22⋊C8×C151—21no—
122C22⋊C8×C151—21no—
123#97×C151—21no—
124C4×C8×C151C2311yescharacteristic
125C4×C8×C151C2311yescharacteristic
126C24×C151—21no—
127#41×C151—44no—
128#41×C151—82no—
129#41×C151—82no—
130C2×Q8×C151—21no—
131C2×Q8×C151—21no—
132C2×Q8×C151—21no—
133C2×Q8×C151—21no—
134C2×Q8×C151C2×D412yes—
135C2×D4×C151—22no—
136C2×D4×C151—24no—
137C2×D4×C151—24no—
138C2×D4×C151—21no—
139C2×D4×C151—21no—
140C2×D4×C151—21no—
141C2×D4×C151—42no—
142C2×D4×C151C2×D412yes—
143C2×D4×C151C2×D412yes—
144C22×C4×C151—24no—
145C22×C4×C151—21no—
146C22×C4×C151—22no—
147C22×C4×C151—22no—
148C22×C4×C151—22no—
149C22×C4×C151—81no—
150C22×C4×C151—81no—
151C22×C4×C151C2×D411yescharacteristic
152C22×C4×C151C2×D411yescharacteristic
153C22×C4×C151C2×D411yescharacteristic
154Q16×C151—82no—
155SD16×C151—44no—
156M16×C151—81no—
157C2×C8×C151—21no—
158C2×C8×C151—21no—
159C2×C8×C151—22no—
160C2×C8×C151—22no—
161C4⋊C4×C151—24no—
162C4⋊C4×C151—21no—
163C4⋊C4×C151—21no—
164C4⋊C4×C151—21no—
165C4⋊C4×C151—22no—
166C4⋊C4×C151—21no—
167C4⋊C4×C151—21no—
168C4⋊C4×C151—22no—
169C4⋊C4×C151—21no—
170C4⋊C4×C151—21no—
171C4⋊C4×C151—21no—
172C4⋊C4×C151—21no—
173C4⋊C4×C151—41no—
174C4⋊C4×C151—41no—
175C4⋊C4×C151C2×D412yes—
176C4⋊C4×C151C2×D412yes—
177C4⋊C4×C151C2×D412yes—
178C22⋊C4×C151—24no—
179C22⋊C4×C151—24no—
180C22⋊C4×C151—24no—
181C22⋊C4×C151—22no—
182C22⋊C4×C151—22no—
183C22⋊C4×C151—22no—
184C22⋊C4×C151—22no—
185C22⋊C4×C151—22no—
186C22⋊C4×C151—41no—
187C42×C151—24no—
188C42×C151—22no—
189C42×C151—41no—
190C42×C151C2×D411yescharacteristic
191C42×C151C2×D411yescharacteristic
192C42×C151C2×D411yescharacteristic
193C42×C151C2411yescharacteristic
194C23×C151—22no—
195C23×C151—22no—
196C23×C151—42no—
197C23×C151—81no—
198C23×C151—81no—
199C23×C151#12011yescharacteristic
200Q8×C151—22no—
201Q8×C151—22no—
202Q8×C151—42no—
203Q8×C151—42no—
204Q8×C151—41no—
205Q8×C151—41no—
206Q8×C151—81no—
207D4×C151—22no—
208D4×C151—22no—
209D4×C151—42no—
210D4×C151—42no—
211D4×C151—44no—
212D4×C151—42no—
213D4×C151—41no—
214D4×C151—41no—
215D4×C151—84no—
216D4×C151—84no—
217C2×C4×C151—22no—
218C2×C4×C151—21no—
219C2×C4×C151—21no—
220C2×C4×C151—22no—
221C2×C4×C151—22no—
222C2×C4×C151—22no—
223C2×C4×C151—22no—
224C2×C4×C151—41no—
225C2×C4×C151—44no—
226C2×C4×C151—42no—
227C2×C4×C151—42no—
228C2×C4×C151—41no—
229C2×C4×C151—41no—
230C2×C4×C151—82no—
231C2×C4×C151—81no—
232C2×C4×C151—84no—
233C2×C4×C151#12011yescharacteristic
234C2×C4×C151#12011yescharacteristic
235C2×C4×C151#12011yescharacteristic
236C2×C4×C151C22×D411yescharacteristic
237C2×C4×C151C22×D411yescharacteristic
238C2×C4×C151C22×D411yescharacteristic
239C8×C151—41no—
240C8×C151—41no—
241C8×C151—42no—
242C8×C151—42no—
243C22×C151—21no—
244C22×C151—21no—
245C22×C151—21no—
246C22×C151—42no—
247C22×C151—42no—
248C22×C151—42no—
249C22×C151—42no—
250C22×C151—42no—
251C22×C151—42no—
252C22×C151—84no—
253C22×C151C2×#12011yescharacteristic
254C4×C151—21no—
255C4×C151—21no—
256C4×C151—21no—
257C4×C151—21no—
258C4×C151—42no—
259C4×C151—42no—
260C4×C151—42no—
261C4×C151—42no—
262C4×C151—81no—
263C4×C151—81no—
264C4×C151#57512yes—
265C4×C151#57611yescharacteristic
266C4×C151#57711yescharacteristic
267C2×C151—41no—
268C2×C151—82no—
269C2×C151—82no—
270C2×C151#300511yescharacteristic
271C2×C151#301211yescharacteristic
272C2×C151#302211yescharacteristic
273#18864C15111yesmaximal, characteristic, direct product factor, Sylow
274C151#1886411yescharacteristic, direct product factor, Sylow
275#3506C2×C15111yescharacteristic
276#3255C2×C15111yescharacteristic, complemented
277#3228C2×C15111yescharacteristic, complemented
278#3110C2×C15111yescharacteristic, complemented
279#1652C2×C15112yescomplemented
280#1650C2×C15112yescomplemented
281#1642C2×C15112yescomplemented
282#1641C2×C15112yescomplemented
283#1557C2×C15111yescharacteristic, complemented
284#1497C2×C15111yescharacteristic, complemented
285#1486C2×C15111yescharacteristic, complemented
286#559—22no—
287#556C22×C15112yes—
288#555—21no—
289#553—22no—
290#550C22×C15112yes—
291#547—21no—
292#538—22no—
293#535—21no—
294#533C22×C15111yescharacteristic
295#533C22×C15111yescharacteristic
296#532C22×C15111yescharacteristic
297#525—22no—
298#520—21no—
299C2×C4×D4C22×C15111yescharacteristic
300#500C22×C15111yescharacteristic, complemented
301#498C22×C15111yescharacteristic, complemented
302#486C22×C15111yescharacteristic, complemented
303#486C22×C15111yescharacteristic, complemented
304#484—21no—
305#482—22no—
306#478—22no—
307#475—21no—
308#475C22×C15112yescomplemented
309#474C22×C15112yes—
310#470—22no—
311#462—21no—
312#462C22×C15112yescomplemented
313#461C22×C15112yes—
314#450—21no—
315#440—22no—
316#432C22×C15111yescharacteristic
317#431C22×C15111yescharacteristic
318#423C22×C15111yescharacteristic
319#332C22×C15112yescomplemented
320#331C22×C15112yescomplemented
321Q8⋊C8C22×C15112yescomplemented
322Q8⋊C8C22×C15112yescomplemented
323D4⋊C8C22×C15112yes—
324D4⋊C8C22×C15112yes—
325C2×#41—22no—
326C2×#41—21no—
327C22×D4D4×C15111yescharacteristic
328C23×C4—21no—
329C2×Q16—22no—
330C2×SD16—22no—
331C2×M16—21no—
332C4⋊Q8D4×C15111yescharacteristic
333C4⋊Q8D4×C15111yescharacteristic
334C4⋊Q8C23×C15111yescharacteristic
335C4⋊Q8C23×C15111yescharacteristic
336C4⋊Q8C23×C15111yescharacteristic
337#127—22no—
338#127C23×C15111yescharacteristic
339#126—24no—
340#125—21no—
341#125—21no—
342#124—24no—
343#124—22no—
344#124—21no—
345#123—24no—
346#123—24no—
347C22⋊Q8—22no—
348C22⋊Q8—21no—
349C22⋊Q8—21no—
350C22⋊Q8—21no—
351C22⋊Q8D4×C15112yes—
352#121—22no—
353#121—22no—
354#121—24no—
355#121—21no—
356#121—22no—
357#121D4×C15112yes—
358#120—24no—
359C4×Q8—22no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8C23×C15112yes—
364C4×D4—24no—
365C4×D4—24no—
366C4×D4—22no—
367C4×D4—21no—
368C4×D4—21no—
369C4×D4—21no—
370C4×D4D4×C15112yes—
371C4×D4D4×C15112yes—
372C4×D4C23×C15112yes—
373#117—22no—
374#117—21no—
375#117—22no—
376#117—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4D4×C15111yescharacteristic
379C2×C22⋊C4—21no—
380C2×C42C23×C15111yescharacteristic
381#107—22no—
382#107—22no—
383#106—22no—
384#106—22no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8C23×C15112yes—
388C4⋊C8C23×C15112yes—
389#103—22no—
390#103—22no—
391#103—22no—
392#102—22no—
393#102—22no—
394#102—22no—
395C22⋊C8—21no—
396C22⋊C8—21no—
397#97—21no—
398C4×C8C23×C15111yescharacteristic
399C4×C8C23×C15111yescharacteristic
400C24—21no—
401#41—44no—
402#41—82no—
403#41—82no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8C2×D4×C15112yes—
409C2×D4—22no—
410C2×D4—24no—
411C2×D4—24no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—42no—
416C2×D4C2×D4×C15112yes—
417C2×D4C2×D4×C15112yes—
418C22×C4—24no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—81no—
424C22×C4—81no—
425C22×C4C2×D4×C15111yescharacteristic
426C22×C4C2×D4×C15111yescharacteristic
427C22×C4C2×D4×C15111yescharacteristic
428Q16—82no—
429SD16—44no—
430M16—81no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—22no—
434C2×C8—22no—
435C4⋊C4—24no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—41no—
448C4⋊C4—41no—
449C4⋊C4C2×D4×C15112yes—
450C4⋊C4C2×D4×C15112yes—
451C4⋊C4C2×D4×C15112yes—
452C22⋊C4—24no—
453C22⋊C4—24no—
454C22⋊C4—24no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—41no—
461C42—24no—
462C42—22no—
463C42—41no—
464C42C2×D4×C15111yescharacteristic
465C42C2×D4×C15111yescharacteristic
466C42C2×D4×C15111yescharacteristic
467C42C24×C15111yescharacteristic
468C23—22no—
469C23—22no—
470C23—42no—
471C23—81no—
472C23—81no—
473C23#120×C15111yescharacteristic
474Q8—22no—
475Q8—22no—
476Q8—42no—
477Q8—42no—
478Q8—41no—
479Q8—41no—
480Q8—81no—
481D4—22no—
482D4—22no—
483D4—42no—
484D4—42no—
485D4—44no—
486D4—42no—
487D4—41no—
488D4—41no—
489D4—84no—
490D4—84no—
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—41no—
499C2×C4—44no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—82no—
505C2×C4—81no—
506C2×C4—84no—
507C2×C4#120×C15111yescharacteristic
508C2×C4#120×C15111yescharacteristic
509C2×C4#120×C15111yescharacteristic
510C2×C4C22×D4×C15111yescharacteristic
511C2×C4C22×D4×C15111yescharacteristic
512C2×C4C22×D4×C15111yescharacteristic
513C8—41no—
514C8—41no—
515C8—42no—
516C8—42no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—42no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—84no—
527C22C2×#120×C15111yescharacteristic
528C4—21no—
529C4—21no—
530C4—21no—
531C4—21no—
532C4—42no—
533C4—42no—
534C4—42no—
535C4—42no—
536C4—81no—
537C4—81no—
538C4#575×C15112yes—
539C4#576×C15111yescharacteristic
540C4#577×C15111yescharacteristic
541C2—41no—
542C2—82no—
543C2—82no—
544C2#3005×C15111yescharacteristic
545C2#3012×C15111yescharacteristic
546C2#3022×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3506×C151C2
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
2. #3255×C151C2semidirect
3. #3228×C151C2semidirect
4. #3110×C151C2semidirect
5. #1652×C151C2semidirect
6. #1650×C151C2semidirect
7. #1642×C151C2semidirect
8. #1641×C151C2semidirect
9. #1557×C151C2semidirect
10. #1497×C151C2semidirect
11. #1486×C151C2semidirect
26. #500×C151C22semidirect
27. #498×C151C22semidirect
28. #486×C151C22semidirect
29. #486×C151C22semidirect
34. #475×C151C22semidirect
38. #462×C151C22semidirect
45. #332×C151C22semidirect
46. #331×C151C22semidirect
47. Q8⋊C8×C151C22semidirect
48. Q8⋊C8×C151C22semidirect
273. #18864C151direct (N × H)
274. C151#18864direct (N × H)
276. #3255C2×C151semidirect
277. #3228C2×C151semidirect
278. #3110C2×C151semidirect
279. #1652C2×C151semidirect
280. #1650C2×C151semidirect
281. #1642C2×C151semidirect
282. #1641C2×C151semidirect
283. #1557C2×C151semidirect
284. #1497C2×C151semidirect
285. #1486C2×C151semidirect
300. #500C22×C151semidirect
301. #498C22×C151semidirect
302. #486C22×C151semidirect
303. #486C22×C151semidirect
308. #475C22×C151semidirect
312. #462C22×C151semidirect
319. #332C22×C151semidirect
320. #331C22×C151semidirect
321. Q8⋊C8C22×C151semidirect
322. Q8⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3506×C1512
#3255×C1512
#3228×C1512
#3110×C1512
#1652×C1512
#1650×C1512
#1642×C1512
#1641×C1512
#1557×C1512
#1497×C1512
#1486×C1512
#18864151