Finite Group Databasebeta

← C151×#18935 #50323860

Subgroups — C151×#18935 #50323860

Order 38656.

986 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3549×C151C211yesmaximal, characteristic
2#3246×C151C211yesmaximal, characteristic, complemented
3#3235×C151C211yesmaximal, characteristic, complemented
4#3210×C151C211yesmaximal, characteristic, complemented
5#1646×C151C212yesmaximal, complemented
6#1639×C151C212yesmaximal, complemented
7#1634×C151C212yesmaximal, complemented
8#1629×C151C212yesmaximal, complemented
9#1551×C151C211yesmaximal, characteristic, complemented
10#1496×C151C211yesmaximal, characteristic, complemented
11#1480×C151C211yesmaximal, characteristic, complemented
12H(3,𝔽4)×C151—22no—
13#555×C151—21no—
14#555×C151—21no—
15#555×C151C2212yes—
16D42×C151—21no—
17D42×C151—21no—
18D42×C151C2212yes—
19#535×C151—22no—
20#535×C151—22no—
21#535×C151—22no—
22#533×C151C2211yescharacteristic, complemented
23#532×C151C2211yescharacteristic
24#532×C151C2211yescharacteristic
25#532×C151C2211yescharacteristic
26#501×C151—21no—
27#494×C151C2211yescharacteristic, complemented
28#492×C151C2211yescharacteristic
29#490×C151—21no—
30#487×C151C2211yescharacteristic, complemented
31#486×C151C2211yescharacteristic
32#482×C151—22no—
33#476×C151C2212yescomplemented
34#476×C151C2212yescomplemented
35#475×C151—21no—
36#474×C151C2212yescomplemented
37#465×C151—22no—
38#464×C151—22no—
39#461×C151C2212yescomplemented
40#460×C151—21no—
41#452×C151—22no—
42#432×C151C2211yescharacteristic, complemented
43#431×C151C2211yescharacteristic, complemented
44C2×C4⋊C8×C151C2211yescharacteristic, complemented
45#333×C151C2212yescomplemented
46#331×C151C2212yes—
47D4⋊C8×C151C2212yescomplemented
48D4⋊C8×C151C2212yescomplemented
49D4⋊C8×C151C2212yescomplemented
50D4⋊C8×C151C2212yescomplemented
51C2×#41×C151—21no—
52C2×#41×C151—21no—
53C2×#41×C151D412yes—
54C22×D4×C151—22no—
55C22×D4×C151—22no—
56C22×D4×C151—22no—
57C2×Q16×C151—22no—
58C2×SD16×C151—22no—
59C2×SD16×C151—22no—
60C22×C8×C151—21no—
61C4⋊Q8×C151D411yescharacteristic
62C4⋊Q8×C151D411yescharacteristic
63C4⋊Q8×C151C2311yescharacteristic
64C4⋊Q8×C151C2311yescharacteristic
65C4⋊Q8×C151C2311yescharacteristic
66#127×C151—24no—
67#127×C151D411yescharacteristic
68#127×C151D411yescharacteristic
69#127×C151C2311yescharacteristic
70#125×C151—21no—
71#124×C151—24no—
72#124×C151—24no—
73#124×C151—21no—
74#124×C151—21no—
75#124×C151—24no—
76#124×C151D412yes—
77C22⋊Q8×C151—21no—
78C22⋊Q8×C151—21no—
79#121×C151—22no—
80#121×C151—22no—
81#121×C151—22no—
82#121×C151—22no—
83#121×C151—21no—
84#121×C151—21no—
85#121×C151—21no—
86#121×C151—21no—
87#121×C151—22no—
88#121×C151—22no—
89#121×C151D412yes—
90#121×C151D412yes—
91#120×C151—24no—
92#120×C151—24no—
93#120×C151—24no—
94#120×C151—24no—
95C4×Q8×C151—21no—
96C4×Q8×C151—21no—
97C4×D4×C151—21no—
98C4×D4×C151—21no—
99C4×D4×C151—21no—
100C4×D4×C151—21no—
101C4×D4×C151C2312yes—
102C4×D4×C151C2312yes—
103#117×C151—22no—
104#117×C151—22no—
105#117×C151—22no—
106#117×C151—21no—
107C2×C42×C151C2311yescharacteristic
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#102×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—24no—
127#41×C151—81no—
128#41×C151—82no—
129#41×C151—81no—
130#41×C151—82no—
131C2×Q8×C151—21no—
132C2×Q8×C151—21no—
133C2×Q8×C151—21no—
134C2×Q8×C151—21no—
135C2×Q8×C151C2×D412yes—
136C2×D4×C151—24no—
137C2×D4×C151—24no—
138C2×D4×C151—24no—
139C2×D4×C151—22no—
140C2×D4×C151—22no—
141C2×D4×C151—22no—
142C2×D4×C151—21no—
143C2×D4×C151—21no—
144C2×D4×C151—21no—
145C2×D4×C151—21no—
146C2×D4×C151—21no—
147C2×D4×C151—21no—
148C2×D4×C151—82no—
149C2×D4×C151—84no—
150C2×D4×C151—82no—
151C2×D4×C151—84no—
152C2×D4×C151C2×D412yes—
153C2×D4×C151C2×D412yes—
154C2×D4×C151C2×D412yes—
155C22×C4×C151—22no—
156C22×C4×C151—22no—
157C22×C4×C151—22no—
158C22×C4×C151C2×D411yescharacteristic
159C22×C4×C151C2×D411yescharacteristic
160C22×C4×C151C2×D411yescharacteristic
161Q16×C151—82no—
162SD16×C151—82no—
163SD16×C151—82no—
164C2×C8×C151—21no—
165C2×C8×C151—21no—
166C2×C8×C151—22no—
167C2×C8×C151—22no—
168C2×C8×C151—81no—
169C4⋊C4×C151—21no—
170C4⋊C4×C151—21no—
171C4⋊C4×C151—21no—
172C4⋊C4×C151—21no—
173C4⋊C4×C151—21no—
174C4⋊C4×C151—21no—
175C4⋊C4×C151—21no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—41no—
178C4⋊C4×C151—41no—
179C4⋊C4×C151C2×D412yes—
180C4⋊C4×C151C2×D412yes—
181C22⋊C4×C151—24no—
182C22⋊C4×C151—24no—
183C22⋊C4×C151—24no—
184C22⋊C4×C151—22no—
185C22⋊C4×C151—22no—
186C22⋊C4×C151—22no—
187C22⋊C4×C151—22no—
188C22⋊C4×C151—22no—
189C22⋊C4×C151—22no—
190C22⋊C4×C151—41no—
191C42×C151—24no—
192C42×C151—41no—
193C42×C151C2×D411yescharacteristic
194C42×C151C2×D411yescharacteristic
195C42×C151C2×D411yescharacteristic
196C42×C151C2411yescharacteristic
197C23×C151—22no—
198C23×C151—22no—
199C23×C151—22no—
200C23×C151—84no—
201C23×C151—84no—
202C23×C151—84no—
203C23×C151#12011yescharacteristic
204Q8×C151—42no—
205Q8×C151—42no—
206Q8×C151—41no—
207Q8×C151—41no—
208Q8×C151—81no—
209Q8×C151—81no—
210D4×C151—22no—
211D4×C151—24no—
212D4×C151—22no—
213D4×C151—42no—
214D4×C151—42no—
215D4×C151—42no—
216D4×C151—41no—
217D4×C151—42no—
218D4×C151—41no—
219D4×C151—81no—
220D4×C151—81no—
221D4×C151—82no—
222D4×C151—82no—
223D4×C151—82no—
224D4×C151—84no—
225D4×C151—84no—
226D4×C151—84no—
227C2×C4×C151—21no—
228C2×C4×C151—22no—
229C2×C4×C151—21no—
230C2×C4×C151—22no—
231C2×C4×C151—22no—
232C2×C4×C151—22no—
233C2×C4×C151—41no—
234C2×C4×C151—44no—
235C2×C4×C151—42no—
236C2×C4×C151—44no—
237C2×C4×C151—42no—
238C2×C4×C151—41no—
239C2×C4×C151—41no—
240C2×C4×C151#12011yescharacteristic
241C2×C4×C151#12011yescharacteristic
242C2×C4×C151#12011yescharacteristic
243C2×C4×C151C22×D411yescharacteristic
244C2×C4×C151C22×D411yescharacteristic
245C2×C4×C151C22×D411yescharacteristic
246C8×C151—41no—
247C8×C151—41no—
248C8×C151—42no—
249C8×C151—42no—
250C22×C151—21no—
251C22×C151—21no—
252C22×C151—21no—
253C22×C151—42no—
254C22×C151—42no—
255C22×C151—42no—
256C22×C151—42no—
257C22×C151—42no—
258C22×C151—42no—
259C22×C151—42no—
260C22×C151—42no—
261C22×C151—42no—
262C22×C151—168no—
263C22×C151C2×#12011yescharacteristic
264C4×C151—21no—
265C4×C151—21no—
266C4×C151—21no—
267C4×C151—21no—
268C4×C151—42no—
269C4×C151—42no—
270C4×C151—42no—
271C4×C151—81no—
272C4×C151—81no—
273C4×C151#57611yescharacteristic
274C4×C151#57712yes—
275C4×C151#57711yescharacteristic
276C2×C151—41no—
277C2×C151—82no—
278C2×C151—82no—
279C2×C151—82no—
280C2×C151#300911yescharacteristic
281C2×C151#301211yescharacteristic
282C2×C151#301911yescharacteristic
283#18935C15111yesmaximal, characteristic, direct product factor, Sylow
284C151#1893511yescharacteristic, direct product factor, Sylow
285#3549C2×C15111yescharacteristic
286#3246C2×C15111yescharacteristic, complemented
287#3235C2×C15111yescharacteristic, complemented
288#3210C2×C15111yescharacteristic, complemented
289#1646C2×C15112yescomplemented
290#1639C2×C15112yescomplemented
291#1634C2×C15112yescomplemented
292#1629C2×C15112yescomplemented
293#1551C2×C15111yescharacteristic, complemented
294#1496C2×C15111yescharacteristic, complemented
295#1480C2×C15111yescharacteristic, complemented
296H(3,𝔽4)—22no—
297#555—21no—
298#555—21no—
299#555C22×C15112yes—
300D42—21no—
301D42—21no—
302D42C22×C15112yes—
303#535—22no—
304#535—22no—
305#535—22no—
306#533C22×C15111yescharacteristic, complemented
307#532C22×C15111yescharacteristic
308#532C22×C15111yescharacteristic
309#532C22×C15111yescharacteristic
310#501—21no—
311#494C22×C15111yescharacteristic, complemented
312#492C22×C15111yescharacteristic
313#490—21no—
314#487C22×C15111yescharacteristic, complemented
315#486C22×C15111yescharacteristic
316#482—22no—
317#476C22×C15112yescomplemented
318#476C22×C15112yescomplemented
319#475—21no—
320#474C22×C15112yescomplemented
321#465—22no—
322#464—22no—
323#461C22×C15112yescomplemented
324#460—21no—
325#452—22no—
326#432C22×C15111yescharacteristic, complemented
327#431C22×C15111yescharacteristic, complemented
328C2×C4⋊C8C22×C15111yescharacteristic, complemented
329#333C22×C15112yescomplemented
330#331C22×C15112yes—
331D4⋊C8C22×C15112yescomplemented
332D4⋊C8C22×C15112yescomplemented
333D4⋊C8C22×C15112yescomplemented
334D4⋊C8C22×C15112yescomplemented
335C2×#41—21no—
336C2×#41—21no—
337C2×#41D4×C15112yes—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C2×Q16—22no—
342C2×SD16—22no—
343C2×SD16—22no—
344C22×C8—21no—
345C4⋊Q8D4×C15111yescharacteristic
346C4⋊Q8D4×C15111yescharacteristic
347C4⋊Q8C23×C15111yescharacteristic
348C4⋊Q8C23×C15111yescharacteristic
349C4⋊Q8C23×C15111yescharacteristic
350#127—24no—
351#127D4×C15111yescharacteristic
352#127D4×C15111yescharacteristic
353#127C23×C15111yescharacteristic
354#125—21no—
355#124—24no—
356#124—24no—
357#124—24no—
358#124—21no—
359#124—21no—
360#124D4×C15112yes—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363#121—22no—
364#121—22no—
365#121—22no—
366#121—22no—
367#121—21no—
368#121—21no—
369#121—21no—
370#121—21no—
371#121—22no—
372#121—22no—
373#121D4×C15112yes—
374#121D4×C15112yes—
375#120—24no—
376#120—24no—
377#120—24no—
378#120—24no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4C23×C15112yes—
386C4×D4C23×C15112yes—
387#117—22no—
388#117—22no—
389#117—22no—
390#117—21no—
391C2×C42C23×C15111yescharacteristic
392#107—22no—
393#106—22no—
394#106—22no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8C23×C15112yes—
398C4⋊C8C23×C15112yes—
399#103—22no—
400#103—22no—
401#102—22no—
402#102—22no—
403#102—22no—
404#102—22no—
405C22⋊C8—21no—
406C22⋊C8—21no—
407#97—21no—
408C4×C8C23×C15111yescharacteristic
409C4×C8C23×C15111yescharacteristic
410C24—24no—
411#41—81no—
412#41—82no—
413#41—81no—
414#41—82no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8C2×D4×C15112yes—
420C2×D4—24no—
421C2×D4—24no—
422C2×D4—24no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—82no—
433C2×D4—84no—
434C2×D4—82no—
435C2×D4—84no—
436C2×D4C2×D4×C15112yes—
437C2×D4C2×D4×C15112yes—
438C2×D4C2×D4×C15112yes—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4C2×D4×C15111yescharacteristic
443C22×C4C2×D4×C15111yescharacteristic
444C22×C4C2×D4×C15111yescharacteristic
445Q16—82no—
446SD16—82no—
447SD16—82no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—81no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4C2×D4×C15112yes—
464C4⋊C4C2×D4×C15112yes—
465C22⋊C4—24no—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—41no—
475C42—24no—
476C42—41no—
477C42C2×D4×C15111yescharacteristic
478C42C2×D4×C15111yescharacteristic
479C42C2×D4×C15111yescharacteristic
480C42C24×C15111yescharacteristic
481C23—22no—
482C23—22no—
483C23—22no—
484C23—84no—
485C23—84no—
486C23—84no—
487C23#120×C15111yescharacteristic
488Q8—42no—
489Q8—42no—
490Q8—41no—
491Q8—41no—
492Q8—81no—
493Q8—81no—
494D4—22no—
495D4—24no—
496D4—22no—
497D4—42no—
498D4—42no—
499D4—42no—
500D4—41no—
501D4—42no—
502D4—41no—
503D4—81no—
504D4—81no—
505D4—82no—
506D4—82no—
507D4—82no—
508D4—84no—
509D4—84no—
510D4—84no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—41no—
518C2×C4—44no—
519C2×C4—42no—
520C2×C4—44no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4#120×C15111yescharacteristic
525C2×C4#120×C15111yescharacteristic
526C2×C4#120×C15111yescharacteristic
527C2×C4C22×D4×C15111yescharacteristic
528C2×C4C22×D4×C15111yescharacteristic
529C2×C4C22×D4×C15111yescharacteristic
530C8—41no—
531C8—41no—
532C8—42no—
533C8—42no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—42no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—168no—
547C22C2×#120×C15111yescharacteristic
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—42no—
553C4—42no—
554C4—42no—
555C4—81no—
556C4—81no—
557C4#576×C15111yescharacteristic
558C4#577×C15112yes—
559C4#577×C15111yescharacteristic
560C2—41no—
561C2—82no—
562C2—82no—
563C2—82no—
564C2#3009×C15111yescharacteristic
565C2#3012×C15111yescharacteristic
566C2#3019×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3549×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. #3246×C151C2semidirect
3. #3235×C151C2semidirect
4. #3210×C151C2semidirect
5. #1646×C151C2semidirect
6. #1639×C151C2semidirect
7. #1634×C151C2semidirect
8. #1629×C151C2semidirect
9. #1551×C151C2semidirect
10. #1496×C151C2semidirect
11. #1480×C151C2semidirect
22. #533×C151C22semidirect
27. #494×C151C22semidirect
30. #487×C151C22semidirect
33. #476×C151C22semidirect
34. #476×C151C22semidirect
36. #474×C151C22semidirect
39. #461×C151C22semidirect
42. #432×C151C22semidirect
43. #431×C151C22semidirect
44. C2×C4⋊C8×C151C22semidirect
45. #333×C151C22semidirect
47. D4⋊C8×C151C22semidirect
48. D4⋊C8×C151C22semidirect
49. D4⋊C8×C151C22semidirect
50. D4⋊C8×C151C22semidirect
283. #18935C151direct (N × H)
284. C151#18935direct (N × H)
286. #3246C2×C151semidirect
287. #3235C2×C151semidirect
288. #3210C2×C151semidirect
289. #1646C2×C151semidirect
290. #1639C2×C151semidirect
291. #1634C2×C151semidirect
292. #1629C2×C151semidirect
293. #1551C2×C151semidirect
294. #1496C2×C151semidirect
295. #1480C2×C151semidirect
306. #533C22×C151semidirect
311. #494C22×C151semidirect
314. #487C22×C151semidirect
317. #476C22×C151semidirect
318. #476C22×C151semidirect
320. #474C22×C151semidirect
323. #461C22×C151semidirect
326. #432C22×C151semidirect
327. #431C22×C151semidirect
328. C2×C4⋊C8C22×C151semidirect
329. #333C22×C151semidirect
331. D4⋊C8C22×C151semidirect
332. D4⋊C8C22×C151semidirect
333. D4⋊C8C22×C151semidirect
334. D4⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3549×C1512
#3246×C1512
#3235×C1512
#3210×C1512
#1646×C1512
#1639×C1512
#1634×C1512
#1629×C1512
#1551×C1512
#1496×C1512
#1480×C1512
#18935151