Finite Group Databasebeta

← C151×#18747 #50323672

Subgroups — C151×#18747 #50323672

Order 38656.

1634 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C151C211yesmaximal, characteristic
2#3208×C151C211yesmaximal, characteristic, complemented
3#3101×C151C211yesmaximal, characteristic, complemented
4#3077×C151C211yesmaximal, characteristic, complemented
5#1639×C151C214yesmaximal, complemented
6#1629×C151C214yesmaximal, complemented
7#1545×C151C211yesmaximal, characteristic, complemented
8#1486×C151C211yesmaximal, characteristic, complemented
9#1478×C151C211yesmaximal, characteristic, complemented
10C23×D4×C151—21no—
11C23×D4×C151—21no—
12D42×C151—22no—
13D42×C151—22no—
14D42×C151—22no—
15D42×C151C2214yes—
16#533×C151C2211yescharacteristic, complemented
17C2×#127×C151C2211yescharacteristic
18C2×#121×C151—21no—
19C2×#121×C151—21no—
20C2×#120×C151—22no—
21C2×C4×D4×C151C2211yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic
23#492×C151C2212yescomplemented
24#486×C151C2212yescomplemented
25#483×C151—21no—
26#478×C151—22no—
27#476×C151C2212yescomplemented
28#476×C151C2212yescomplemented
29#474×C151C2212yescomplemented
30#461×C151C2212yescomplemented
31#460×C151—22no—
32#450×C151—21no—
33#450×C151—22no—
34C4×SD16×C151—22no—
35#431×C151C2211yescharacteristic, complemented
36#431×C151C2211yescharacteristic, complemented
37#428×C151—21no—
38#423×C151C2211yescharacteristic, complemented
39#418×C151—21no—
40#331×C151C2214yescomplemented
41D4⋊C8×C151C2214yescomplemented
42D4⋊C8×C151C2214yescomplemented
43C25×C151—22no—
44C22×D4×C151—22no—
45C22×D4×C151—22no—
46C22×D4×C151—24no—
47C22×D4×C151—24no—
48C22×D4×C151—24no—
49C22×D4×C151—24no—
50C22×D4×C151—21no—
51C22×D4×C151—21no—
52C22×D4×C151—48no—
53C22×D4×C151—44no—
54C22×D4×C151—44no—
55C22×D4×C151D411yescharacteristic
56C22×D4×C151D411yescharacteristic
57C22×D4×C151D412yes—
58C23×C4×C151—21no—
59C23×C4×C151—21no—
60C2×SD16×C151—22no—
61C2×SD16×C151—24no—
62C2×M16×C151—21no—
63C4⋊Q8×C151C2311yescharacteristic, complemented
64C4⋊Q8×C151C2311yescharacteristic, complemented
65#127×C151—21no—
66#127×C151—21no—
67#127×C151D412yes—
68#127×C151C2312yes—
69#125×C151—21no—
70C22⋊Q8×C151—21no—
71C22⋊Q8×C151—21no—
72#121×C151—24no—
73#121×C151—24no—
74#121×C151—24no—
75#121×C151—24no—
76#120×C151—28no—
77#120×C151—28no—
78C4×Q8×C151—21no—
79C4×Q8×C151—21no—
80C4×D4×C151—21no—
81C4×D4×C151—21no—
82C4×D4×C151—21no—
83C4×D4×C151—21no—
84C4×D4×C151D412yes—
85C4×D4×C151D412yes—
86C4×D4×C151C2312yes—
87C4×D4×C151C2312yes—
88#117×C151—21no—
89C2×C4⋊C4×C151D411yescharacteristic
90C2×C4⋊C4×C151D411yescharacteristic
91C2×C22⋊C4×C151—22no—
92C2×C22⋊C4×C151—21no—
93C2×C22⋊C4×C151—21no—
94C2×C42×C151C2311yescharacteristic
95#107×C151—22no—
96#106×C151—22no—
97#106×C151—22no—
98C4⋊C8×C151—21no—
99C4⋊C8×C151—21no—
100C4⋊C8×C151C2312yescomplemented
101C4⋊C8×C151C2312yescomplemented
102#103×C151—22no—
103#102×C151—22no—
104#102×C151—22no—
105#102×C151—22no—
106#102×C151—24no—
107C22⋊C8×C151—21no—
108C22⋊C8×C151—21no—
109C4×C8×C151—21no—
110C4×C8×C151C2312yescomplemented
111C24×C151—21no—
112C24×C151—21no—
113C24×C151—28no—
114C24×C151—22no—
115C24×C151—48no—
116C24×C151—48no—
117C24×C151—84no—
118C2×Q8×C151—21no—
119C2×Q8×C151—21no—
120C2×D4×C151—24no—
121C2×D4×C151—28no—
122C2×D4×C151—28no—
123C2×D4×C151—21no—
124C2×D4×C151—21no—
125C2×D4×C151—22no—
126C2×D4×C151—22no—
127C2×D4×C151—22no—
128C2×D4×C151—22no—
129C2×D4×C151—22no—
130C2×D4×C151—22no—
131C2×D4×C151—44no—
132C2×D4×C151—416no—
133C2×D4×C151—48no—
134C2×D4×C151—48no—
135C2×D4×C151—416no—
136C2×D4×C151—48no—
137C2×D4×C151—48no—
138C2×D4×C151—48no—
139C2×D4×C151—48no—
140C2×D4×C151—42no—
141C2×D4×C151—42no—
142C2×D4×C151—82no—
143C2×D4×C151SD1614yescomplemented
144C2×D4×C151C2×D412yes—
145C2×D4×C151C2×D412yes—
146C2×D4×C151C2×D414yes—
147C22×C4×C151—21no—
148C22×C4×C151—21no—
149C22×C4×C151—22no—
150C22×C4×C151—22no—
151C22×C4×C151—22no—
152C22×C4×C151—22no—
153C22×C4×C151—44no—
154C22×C4×C151—42no—
155C22×C4×C151—42no—
156C22×C4×C151C2×D411yescharacteristic
157C22×C4×C151C2×D411yescharacteristic
158C22×C4×C151C2×D411yescharacteristic
159SD16×C151—44no—
160SD16×C151—84no—
161M16×C151—42no—
162C2×C8×C151—22no—
163C2×C8×C151—22no—
164C2×C8×C151—22no—
165C4⋊C4×C151—21no—
166C4⋊C4×C151—21no—
167C4⋊C4×C151—21no—
168C4⋊C4×C151—21no—
169C4⋊C4×C151—21no—
170C4⋊C4×C151—21no—
171C4⋊C4×C151—41no—
172C4⋊C4×C151—41no—
173C4⋊C4×C151C2×D412yes—
174C4⋊C4×C151C2×D412yes—
175C22⋊C4×C151—28no—
176C22⋊C4×C151—22no—
177C22⋊C4×C151—22no—
178C22⋊C4×C151—22no—
179C22⋊C4×C151—22no—
180C22⋊C4×C151—41no—
181C42×C151—41no—
182C42×C151C2×D411yescharacteristic
183C42×C151C2×D411yescharacteristic
184C42×C151C2×D411yescharacteristic
185C42×C151C2411yescharacteristic
186C23×C151—24no—
187C23×C151—22no—
188C23×C151—22no—
189C23×C151—24no—
190C23×C151—24no—
191C23×C151—42no—
192C23×C151—42no—
193C23×C151—42no—
194C23×C151—44no—
195C23×C151—416no—
196C23×C151—416no—
197C23×C151—44no—
198C23×C151—42no—
199C23×C151—44no—
200C23×C151—88no—
201C23×C151—832no—
202C23×C151#12011yescharacteristic
203Q8×C151—42no—
204Q8×C151—42no—
205D4×C151—24no—
206D4×C151—22no—
207D4×C151—22no—
208D4×C151—24no—
209D4×C151—44no—
210D4×C151—44no—
211D4×C151—416no—
212D4×C151—416no—
213D4×C151—42no—
214D4×C151—42no—
215D4×C151—44no—
216D4×C151—44no—
217D4×C151—82no—
218D4×C151C2×SD1614yes—
219D4×C151AGL(1,ℤ/8)14yes—
220C2×C4×C151—22no—
221C2×C4×C151—22no—
222C2×C4×C151—22no—
223C2×C4×C151—41no—
224C2×C4×C151—44no—
225C2×C4×C151—42no—
226C2×C4×C151—42no—
227C2×C4×C151—42no—
228C2×C4×C151—42no—
229C2×C4×C151—44no—
230C2×C4×C151—44no—
231C2×C4×C151—41no—
232C2×C4×C151—41no—
233C2×C4×C151#12011yescharacteristic
234C2×C4×C151#12011yescharacteristic
235C2×C4×C151#12011yescharacteristic
236C2×C4×C151C2×SD1612yes—
237C2×C4×C151AGL(1,ℤ/8)12yes—
238C2×C4×C151C22×D411yescharacteristic
239C2×C4×C151C22×D411yescharacteristic
240C2×C4×C151C22×D411yescharacteristic
241C8×C151—42no—
242C8×C151—42no—
243C8×C151—42no—
244C22×C151—21no—
245C22×C151—21no—
246C22×C151—24no—
247C22×C151—24no—
248C22×C151—48no—
249C22×C151—48no—
250C22×C151—42no—
251C22×C151—42no—
252C22×C151—42no—
253C22×C151—42no—
254C22×C151—44no—
255C22×C151—44no—
256C22×C151—44no—
257C22×C151—88no—
258C22×C151—832no—
259C22×C151#45012yes—
260C22×C151C2×#12011yescharacteristic
261C4×C151—21no—
262C4×C151—21no—
263C4×C151—21no—
264C4×C151—42no—
265C4×C151—42no—
266C4×C151—81no—
267C4×C151—81no—
268C4×C151#45012yes—
269C4×C151C22×SD1611yescharacteristic
270C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
271C4×C151C2×AGL(1,ℤ/8)12yes—
272C2×C151—22no—
273C2×C151—44no—
274C2×C151—44no—
275C2×C151—84no—
276C2×C151C2×#45011yescharacteristic
277C2×C151#300311yescharacteristic
278C2×C151#301911yescharacteristic
279#18747C15111yesmaximal, characteristic, direct product factor, Sylow
280C151#1874711yescharacteristic, direct product factor, Sylow
281C2×D42C2×C15111yescharacteristic
282#3208C2×C15111yescharacteristic, complemented
283#3101C2×C15111yescharacteristic, complemented
284#3077C2×C15111yescharacteristic, complemented
285#1639C2×C15114yescomplemented
286#1629C2×C15114yescomplemented
287#1545C2×C15111yescharacteristic, complemented
288#1486C2×C15111yescharacteristic, complemented
289#1478C2×C15111yescharacteristic, complemented
290C23×D4—21no—
291C23×D4—21no—
292D42—22no—
293D42—22no—
294D42—22no—
295D42C22×C15114yes—
296#533C22×C15111yescharacteristic, complemented
297C2×#127C22×C15111yescharacteristic
298C2×#121—21no—
299C2×#121—21no—
300C2×#120—22no—
301C2×C4×D4C22×C15111yescharacteristic
302C2×C4×D4C22×C15111yescharacteristic
303#492C22×C15112yescomplemented
304#486C22×C15112yescomplemented
305#483—21no—
306#478—22no—
307#476C22×C15112yescomplemented
308#476C22×C15112yescomplemented
309#474C22×C15112yescomplemented
310#461C22×C15112yescomplemented
311#460—22no—
312#450—21no—
313#450—22no—
314C4×SD16—22no—
315#431C22×C15111yescharacteristic, complemented
316#431C22×C15111yescharacteristic, complemented
317#428—21no—
318#423C22×C15111yescharacteristic, complemented
319#418—21no—
320#331C22×C15114yescomplemented
321D4⋊C8C22×C15114yescomplemented
322D4⋊C8C22×C15114yescomplemented
323C25—22no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—24no—
327C22×D4—24no—
328C22×D4—24no—
329C22×D4—24no—
330C22×D4—21no—
331C22×D4—21no—
332C22×D4—48no—
333C22×D4—44no—
334C22×D4—44no—
335C22×D4D4×C15111yescharacteristic
336C22×D4D4×C15111yescharacteristic
337C22×D4D4×C15112yes—
338C23×C4—21no—
339C23×C4—21no—
340C2×SD16—22no—
341C2×SD16—24no—
342C2×M16—21no—
343C4⋊Q8C23×C15111yescharacteristic, complemented
344C4⋊Q8C23×C15111yescharacteristic, complemented
345#127—21no—
346#127—21no—
347#127D4×C15112yes—
348#127C23×C15112yes—
349#125—21no—
350C22⋊Q8—21no—
351C22⋊Q8—21no—
352#121—24no—
353#121—24no—
354#121—24no—
355#121—24no—
356#120—28no—
357#120—28no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4D4×C15112yes—
365C4×D4D4×C15112yes—
366C4×D4C23×C15112yes—
367C4×D4C23×C15112yes—
368#117—21no—
369C2×C4⋊C4D4×C15111yescharacteristic
370C2×C4⋊C4D4×C15111yescharacteristic
371C2×C22⋊C4—22no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C42C23×C15111yescharacteristic
375#107—22no—
376#106—22no—
377#106—22no—
378C4⋊C8—21no—
379C4⋊C8—21no—
380C4⋊C8C23×C15112yescomplemented
381C4⋊C8C23×C15112yescomplemented
382#103—22no—
383#102—22no—
384#102—22no—
385#102—22no—
386#102—24no—
387C22⋊C8—21no—
388C22⋊C8—21no—
389C4×C8—21no—
390C4×C8C23×C15112yescomplemented
391C24—21no—
392C24—21no—
393C24—28no—
394C24—22no—
395C24—48no—
396C24—48no—
397C24—84no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×D4—24no—
401C2×D4—28no—
402C2×D4—28no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—44no—
412C2×D4—416no—
413C2×D4—416no—
414C2×D4—48no—
415C2×D4—48no—
416C2×D4—48no—
417C2×D4—48no—
418C2×D4—48no—
419C2×D4—48no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4—82no—
423C2×D4SD16×C15114yescomplemented
424C2×D4C2×D4×C15112yes—
425C2×D4C2×D4×C15112yes—
426C2×D4C2×D4×C15114yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—44no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4C2×D4×C15111yescharacteristic
437C22×C4C2×D4×C15111yescharacteristic
438C22×C4C2×D4×C15111yescharacteristic
439SD16—44no—
440SD16—84no—
441M16—42no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8—22no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—41no—
452C4⋊C4—41no—
453C4⋊C4C2×D4×C15112yes—
454C4⋊C4C2×D4×C15112yes—
455C22⋊C4—28no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—41no—
461C42—41no—
462C42C2×D4×C15111yescharacteristic
463C42C2×D4×C15111yescharacteristic
464C42C2×D4×C15111yescharacteristic
465C42C24×C15111yescharacteristic
466C23—24no—
467C23—24no—
468C23—22no—
469C23—22no—
470C23—24no—
471C23—42no—
472C23—42no—
473C23—42no—
474C23—44no—
475C23—416no—
476C23—416no—
477C23—44no—
478C23—42no—
479C23—44no—
480C23—88no—
481C23—832no—
482C23#120×C15111yescharacteristic
483Q8—42no—
484Q8—42no—
485D4—24no—
486D4—24no—
487D4—22no—
488D4—22no—
489D4—44no—
490D4—44no—
491D4—416no—
492D4—416no—
493D4—44no—
494D4—42no—
495D4—42no—
496D4—44no—
497D4—82no—
498D4C2×SD16×C15114yes—
499D4AGL(1,ℤ/8)×C15114yes—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—41no—
504C2×C4—44no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—44no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—44no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4#120×C15111yescharacteristic
514C2×C4#120×C15111yescharacteristic
515C2×C4#120×C15111yescharacteristic
516C2×C4C2×SD16×C15112yes—
517C2×C4AGL(1,ℤ/8)×C15112yes—
518C2×C4C22×D4×C15111yescharacteristic
519C2×C4C22×D4×C15111yescharacteristic
520C2×C4C22×D4×C15111yescharacteristic
521C8—42no—
522C8—42no—
523C8—42no—
524C22—21no—
525C22—21no—
526C22—24no—
527C22—24no—
528C22—48no—
529C22—48no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—44no—
535C22—44no—
536C22—44no—
537C22—88no—
538C22—832no—
539C22#450×C15112yes—
540C22C2×#120×C15111yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—42no—
545C4—42no—
546C4—81no—
547C4—81no—
548C4#450×C15112yes—
549C4C22×SD16×C15111yescharacteristic
550C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
551C4C2×AGL(1,ℤ/8)×C15112yes—
552C2—22no—
553C2—44no—
554C2—44no—
555C2—84no—
556C2C2×#450×C15111yescharacteristic
557C2#3003×C15111yescharacteristic
558C2#3019×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radicalC2×D42×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. #3208×C151C2semidirect
3. #3101×C151C2semidirect
4. #3077×C151C2semidirect
5. #1639×C151C2semidirect
6. #1629×C151C2semidirect
7. #1545×C151C2semidirect
8. #1486×C151C2semidirect
9. #1478×C151C2semidirect
16. #533×C151C22semidirect
23. #492×C151C22semidirect
24. #486×C151C22semidirect
27. #476×C151C22semidirect
28. #476×C151C22semidirect
29. #474×C151C22semidirect
30. #461×C151C22semidirect
35. #431×C151C22semidirect
36. #431×C151C22semidirect
38. #423×C151C22semidirect
40. #331×C151C22semidirect
41. D4⋊C8×C151C22semidirect
42. D4⋊C8×C151C22semidirect
63. C4⋊Q8×C151C23semidirect
64. C4⋊Q8×C151C23semidirect
100. C4⋊C8×C151C23semidirect
101. C4⋊C8×C151C23semidirect
110. C4×C8×C151C23semidirect
143. C2×D4×C151SD16semidirect
279. #18747C151direct (N × H)
280. C151#18747direct (N × H)
282. #3208C2×C151semidirect
283. #3101C2×C151semidirect
284. #3077C2×C151semidirect
285. #1639C2×C151semidirect
286. #1629C2×C151semidirect
287. #1545C2×C151semidirect
288. #1486C2×C151semidirect
289. #1478C2×C151semidirect
296. #533C22×C151semidirect
303. #492C22×C151semidirect
304. #486C22×C151semidirect
307. #476C22×C151semidirect
308. #476C22×C151semidirect
309. #474C22×C151semidirect
310. #461C22×C151semidirect
315. #431C22×C151semidirect
316. #431C22×C151semidirect
318. #423C22×C151semidirect
320. #331C22×C151semidirect
321. D4⋊C8C22×C151semidirect
322. D4⋊C8C22×C151semidirect
343. C4⋊Q8C23×C151semidirect
344. C4⋊Q8C23×C151semidirect
380. C4⋊C8C23×C151semidirect
381. C4⋊C8C23×C151semidirect
390. C4×C8C23×C151semidirect
423. C2×D4SD16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C1512
#3208×C1512
#3101×C1512
#3077×C1512
#1639×C1512
#1629×C1512
#1545×C1512
#1486×C1512
#1478×C1512
#18747151