Finite Group Databasebeta

← C151×#18576 #50323501

Subgroups — C151×#18576 #50323501

Order 38656.

980 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3508×C151C211yesmaximal, characteristic
2#3255×C151C211yesmaximal, characteristic, complemented
3#3138×C151C211yesmaximal, characteristic, complemented
4#3107×C151C211yesmaximal, characteristic, complemented
5#1642×C151C212yesmaximal, complemented
6#1641×C151C212yesmaximal, complemented
7#1640×C151C212yesmaximal, complemented
8#1640×C151C212yesmaximal, complemented
9#1545×C151C211yesmaximal, characteristic, complemented
10#1489×C151C211yesmaximal, characteristic, complemented
11#1485×C151C211yesmaximal, characteristic, complemented
12#559×C151—21no—
13#559×C151C2212yes—
14#550×C151—21no—
15#550×C151C2212yes—
16#546×C151—22no—
17#546×C151—22no—
18#540×C151—22no—
19#535×C151—21no—
20#533×C151C2211yescharacteristic
21#533×C151C2211yescharacteristic
22#532×C151—21no—
23#532×C151—21no—
24C2×#127×C151C2211yescharacteristic
25#518×C151—21no—
26C4×#41×C151C2211yescharacteristic
27#490×C151—22no—
28#486×C151C2212yes—
29#486×C151C2212yes—
30#485×C151—21no—
31#475×C151—21no—
32#475×C151C2211yescharacteristic, complemented
33#475×C151C2212yescomplemented
34#474×C151C2211yescharacteristic, complemented
35#470×C151—22no—
36#462×C151—21no—
37#462×C151C2211yescharacteristic, complemented
38#462×C151C2212yescomplemented
39#461×C151C2211yescharacteristic, complemented
40#452×C151—21no—
41C4×Q16×C151—21no—
42C4×SD16×C151—21no—
43#431×C151C2211yescharacteristic
44#423×C151C2211yescharacteristic
45#418×C151—22no—
46C4×M16×C151C2211yescharacteristic
47#331×C151C2212yes—
48#331×C151C2212yes—
49Q8⋊C8×C151C2212yescomplemented
50Q8⋊C8×C151C2212yescomplemented
51Q8⋊C8×C151C2212yescomplemented
52D4⋊C8×C151C2212yescomplemented
53C2×#41×C151—22no—
54C2×#41×C151—22no—
55C2×#41×C151D411yescharacteristic
56C22×D4×C151—21no—
57C22×D4×C151—21no—
58C22×D4×C151D412yes—
59C2×Q16×C151—21no—
60C2×Q16×C151—22no—
61C2×SD16×C151—21no—
62C2×M16×C151—21no—
63C2×M16×C151—21no—
64C4⋊Q8×C151D411yescharacteristic
65C4⋊Q8×C151D411yescharacteristic
66C4⋊Q8×C151C2311yescharacteristic
67C4⋊Q8×C151C2311yescharacteristic
68#127×C151—22no—
69#127×C151—21no—
70#127×C151—21no—
71#127×C151D412yes—
72#127×C151C2312yes—
73#125×C151—21no—
74#125×C151—21no—
75#124×C151—22no—
76#124×C151—22no—
77#124×C151—22no—
78#123×C151—24no—
79#123×C151—24no—
80C22⋊Q8×C151—21no—
81C22⋊Q8×C151—21no—
82C22⋊Q8×C151—21no—
83C22⋊Q8×C151D412yes—
84#121×C151—22no—
85#121×C151—22no—
86#121×C151—22no—
87#121×C151—24no—
88#121×C151—24no—
89#121×C151—22no—
90#120×C151—24no—
91C4×Q8×C151—21no—
92C4×Q8×C151—21no—
93C4×Q8×C151—21no—
94C4×Q8×C151D411yescharacteristic
95C4×Q8×C151C2311yescharacteristic
96C4×Q8×C151C2312yes—
97C4×D4×C151—22no—
98C4×D4×C151—22no—
99C4×D4×C151—22no—
100C4×D4×C151—21no—
101C4×D4×C151—21no—
102C4×D4×C151—22no—
103C4×D4×C151—22no—
104C4×D4×C151—22no—
105C4×D4×C151D411yescharacteristic
106C4×D4×C151C2311yescharacteristic
107#117×C151—21no—
108#117×C151—21no—
109#117×C151—21no—
110#117×C151D411yescharacteristic
111C2×C22⋊C4×C151—24no—
112C2×C42×C151—21no—
113C2×C42×C151C2311yescharacteristic
114#107×C151—21no—
115#106×C151—21no—
116#106×C151—22no—
117C4⋊C8×C151—21no—
118C4⋊C8×C151C2312yes—
119C4⋊C8×C151C2311yescharacteristic
120C4⋊C8×C151C2311yescharacteristic
121#103×C151—21no—
122#103×C151—21no—
123#103×C151—22no—
124#103×C151—21no—
125#103×C151—22no—
126#102×C151—24no—
127#102×C151—24no—
128#102×C151—21no—
129C22⋊C8×C151—21no—
130#97×C151—21no—
131C4×C8×C151—21no—
132C4×C8×C151C2312yes—
133C24×C151—22no—
134#41×C151—41no—
135#41×C151—41no—
136#41×C151—82no—
137#41×C151—82no—
138#41×C151—84no—
139C2×Q8×C151—21no—
140C2×Q8×C151—21no—
141C2×Q8×C151—21no—
142C2×Q8×C151C2×D411yescharacteristic
143C2×Q8×C151C2×D412yes—
144C2×D4×C151—21no—
145C2×D4×C151—24no—
146C2×D4×C151—24no—
147C2×D4×C151—22no—
148C2×D4×C151—22no—
149C2×D4×C151—22no—
150C2×D4×C151—22no—
151C2×D4×C151—22no—
152C2×D4×C151—42no—
153C2×D4×C151—42no—
154C2×D4×C151—44no—
155C2×D4×C151—81no—
156C2×D4×C151—81no—
157C2×D4×C151C2×D411yescharacteristic
158C2×D4×C151C2×D414yes—
159C22×C4×C151—24no—
160C22×C4×C151—24no—
161C22×C4×C151—21no—
162C22×C4×C151—21no—
163C22×C4×C151—21no—
164C22×C4×C151C2×D411yescharacteristic
165C22×C4×C151C2×D411yescharacteristic
166C22×C4×C151C2×D411yescharacteristic
167Q16×C151—42no—
168Q16×C151—82no—
169SD16×C151—42no—
170M16×C151—42no—
171M16×C151—81no—
172C2×C8×C151—21no—
173C2×C8×C151—21no—
174C2×C8×C151—22no—
175C2×C8×C151—22no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151—21no—
180C4⋊C4×C151—22no—
181C4⋊C4×C151—21no—
182C4⋊C4×C151—22no—
183C4⋊C4×C151—21no—
184C4⋊C4×C151—21no—
185C4⋊C4×C151—21no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—41no—
188C4⋊C4×C151—41no—
189C4⋊C4×C151C2×D411yescharacteristic
190C4⋊C4×C151C2×D412yes—
191C4⋊C4×C151C2×D411yescharacteristic
192C22⋊C4×C151—24no—
193C22⋊C4×C151—24no—
194C22⋊C4×C151—24no—
195C22⋊C4×C151—24no—
196C22⋊C4×C151—21no—
197C22⋊C4×C151—22no—
198C22⋊C4×C151—21no—
199C22⋊C4×C151—21no—
200C22⋊C4×C151—41no—
201C42×C151—21no—
202C42×C151—21no—
203C42×C151—21no—
204C42×C151—22no—
205C42×C151—41no—
206C42×C151C2×D411yescharacteristic
207C42×C151C2×D411yescharacteristic
208C42×C151C2×D411yescharacteristic
209C42×C151C2411yescharacteristic
210C23×C151—24no—
211C23×C151—21no—
212C23×C151—44no—
213C23×C151—82no—
214C23×C151—82no—
215C23×C151#12011yescharacteristic
216Q8×C151—21no—
217Q8×C151—21no—
218Q8×C151—22no—
219Q8×C151—22no—
220Q8×C151—42no—
221Q8×C151—41no—
222Q8×C151—41no—
223Q8×C151—41no—
224Q8×C151—41no—
225D4×C151—21no—
226D4×C151—21no—
227D4×C151—44no—
228D4×C151—44no—
229D4×C151—42no—
230D4×C151—42no—
231D4×C151—42no—
232D4×C151—42no—
233D4×C151—42no—
234D4×C151—44no—
235D4×C151—82no—
236D4×C151—84no—
237D4×C151—84no—
238C2×C4×C151—21no—
239C2×C4×C151—21no—
240C2×C4×C151—21no—
241C2×C4×C151—21no—
242C2×C4×C151—22no—
243C2×C4×C151—22no—
244C2×C4×C151—21no—
245C2×C4×C151—22no—
246C2×C4×C151—21no—
247C2×C4×C151—21no—
248C2×C4×C151—42no—
249C2×C4×C151—41no—
250C2×C4×C151—41no—
251C2×C4×C151—42no—
252C2×C4×C151—41no—
253C2×C4×C151—41no—
254C2×C4×C151—84no—
255C2×C4×C151—84no—
256C2×C4×C151#12011yescharacteristic
257C2×C4×C151#12011yescharacteristic
258C2×C4×C151#12011yescharacteristic
259C2×C4×C151C22×D411yescharacteristic
260C2×C4×C151C22×D411yescharacteristic
261C2×C4×C151C22×D411yescharacteristic
262C8×C151—42no—
263C8×C151—41no—
264C8×C151—41no—
265C8×C151—42no—
266C22×C151—21no—
267C22×C151—21no—
268C22×C151—21no—
269C22×C151—41no—
270C22×C151—44no—
271C22×C151—41no—
272C22×C151—44no—
273C22×C151—41no—
274C22×C151—44no—
275C22×C151—164no—
276C22×C151C2×#12011yescharacteristic
277C4×C151—21no—
278C4×C151—21no—
279C4×C151—21no—
280C4×C151—41no—
281C4×C151—41no—
282C4×C151—42no—
283C4×C151—41no—
284C4×C151—42no—
285C4×C151—81no—
286C4×C151—81no—
287C4×C151#45512yes—
288C4×C151#57511yescharacteristic
289C4×C151#57511yescharacteristic
290C4×C151#57611yescharacteristic
291C4×C151#57711yescharacteristic
292C2×C151—41no—
293C2×C151—81no—
294C2×C151—84no—
295C2×C151#300511yescharacteristic
296C2×C151#301211yescharacteristic
297C2×C151C2×#45511yescharacteristic
298#18576C15111yesmaximal, characteristic, direct product factor, Sylow
299C151#1857611yescharacteristic, direct product factor, Sylow
300#3508C2×C15111yescharacteristic
301#3255C2×C15111yescharacteristic, complemented
302#3138C2×C15111yescharacteristic, complemented
303#3107C2×C15111yescharacteristic, complemented
304#1642C2×C15112yescomplemented
305#1641C2×C15112yescomplemented
306#1640C2×C15112yescomplemented
307#1640C2×C15112yescomplemented
308#1545C2×C15111yescharacteristic, complemented
309#1489C2×C15111yescharacteristic, complemented
310#1485C2×C15111yescharacteristic, complemented
311#559—21no—
312#559C22×C15112yes—
313#550—21no—
314#550C22×C15112yes—
315#546—22no—
316#546—22no—
317#540—22no—
318#535—21no—
319#533C22×C15111yescharacteristic
320#533C22×C15111yescharacteristic
321#532—21no—
322#532—21no—
323C2×#127C22×C15111yescharacteristic
324#518—21no—
325C4×#41C22×C15111yescharacteristic
326#490—22no—
327#486C22×C15112yes—
328#486C22×C15112yes—
329#485—21no—
330#475—21no—
331#475C22×C15111yescharacteristic, complemented
332#475C22×C15112yescomplemented
333#474C22×C15111yescharacteristic, complemented
334#470—22no—
335#462—21no—
336#462C22×C15111yescharacteristic, complemented
337#462C22×C15112yescomplemented
338#461C22×C15111yescharacteristic, complemented
339#452—21no—
340C4×Q16—21no—
341C4×SD16—21no—
342#431C22×C15111yescharacteristic
343#423C22×C15111yescharacteristic
344#418—22no—
345C4×M16C22×C15111yescharacteristic
346#331C22×C15112yes—
347#331C22×C15112yes—
348Q8⋊C8C22×C15112yescomplemented
349Q8⋊C8C22×C15112yescomplemented
350Q8⋊C8C22×C15112yescomplemented
351D4⋊C8C22×C15112yescomplemented
352C2×#41—22no—
353C2×#41—22no—
354C2×#41D4×C15111yescharacteristic
355C22×D4—21no—
356C22×D4—21no—
357C22×D4D4×C15112yes—
358C2×Q16—21no—
359C2×Q16—22no—
360C2×SD16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C4⋊Q8D4×C15111yescharacteristic
364C4⋊Q8D4×C15111yescharacteristic
365C4⋊Q8C23×C15111yescharacteristic
366C4⋊Q8C23×C15111yescharacteristic
367#127—22no—
368#127—21no—
369#127—21no—
370#127D4×C15112yes—
371#127C23×C15112yes—
372#125—21no—
373#125—21no—
374#124—22no—
375#124—22no—
376#124—22no—
377#123—24no—
378#123—24no—
379C22⋊Q8—21no—
380C22⋊Q8—21no—
381C22⋊Q8—21no—
382C22⋊Q8D4×C15112yes—
383#121—22no—
384#121—22no—
385#121—22no—
386#121—24no—
387#121—24no—
388#121—22no—
389#120—24no—
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8—21no—
393C4×Q8D4×C15111yescharacteristic
394C4×Q8C23×C15111yescharacteristic
395C4×Q8C23×C15112yes—
396C4×D4—22no—
397C4×D4—22no—
398C4×D4—22no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—22no—
402C4×D4—22no—
403C4×D4—22no—
404C4×D4D4×C15111yescharacteristic
405C4×D4C23×C15111yescharacteristic
406#117—21no—
407#117—21no—
408#117—21no—
409#117D4×C15111yescharacteristic
410C2×C22⋊C4—24no—
411C2×C42—21no—
412C2×C42C23×C15111yescharacteristic
413#107—21no—
414#106—21no—
415#106—22no—
416C4⋊C8—21no—
417C4⋊C8C23×C15112yes—
418C4⋊C8C23×C15111yescharacteristic
419C4⋊C8C23×C15111yescharacteristic
420#103—21no—
421#103—22no—
422#103—21no—
423#103—21no—
424#103—22no—
425#102—24no—
426#102—24no—
427#102—21no—
428C22⋊C8—21no—
429#97—21no—
430C4×C8—21no—
431C4×C8C23×C15112yes—
432C24—22no—
433#41—41no—
434#41—41no—
435#41—82no—
436#41—82no—
437#41—84no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8C2×D4×C15111yescharacteristic
442C2×Q8C2×D4×C15112yes—
443C2×D4—21no—
444C2×D4—24no—
445C2×D4—24no—
446C2×D4—22no—
447C2×D4—22no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4—44no—
454C2×D4—81no—
455C2×D4—81no—
456C2×D4C2×D4×C15111yescharacteristic
457C2×D4C2×D4×C15114yes—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4C2×D4×C15111yescharacteristic
464C22×C4C2×D4×C15111yescharacteristic
465C22×C4C2×D4×C15111yescharacteristic
466Q16—42no—
467Q16—82no—
468SD16—42no—
469M16—42no—
470M16—81no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—22no—
474C2×C8—22no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—22no—
480C4⋊C4—21no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4C2×D4×C15111yescharacteristic
489C4⋊C4C2×D4×C15112yes—
490C4⋊C4C2×D4×C15111yescharacteristic
491C22⋊C4—24no—
492C22⋊C4—24no—
493C22⋊C4—24no—
494C22⋊C4—24no—
495C22⋊C4—21no—
496C22⋊C4—22no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—41no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—22no—
504C42—41no—
505C42C2×D4×C15111yescharacteristic
506C42C2×D4×C15111yescharacteristic
507C42C2×D4×C15111yescharacteristic
508C42C24×C15111yescharacteristic
509C23—24no—
510C23—21no—
511C23—44no—
512C23—82no—
513C23—82no—
514C23#120×C15111yescharacteristic
515Q8—21no—
516Q8—21no—
517Q8—22no—
518Q8—22no—
519Q8—42no—
520Q8—41no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524D4—21no—
525D4—21no—
526D4—44no—
527D4—44no—
528D4—42no—
529D4—44no—
530D4—42no—
531D4—42no—
532D4—42no—
533D4—42no—
534D4—82no—
535D4—84no—
536D4—84no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—84no—
554C2×C4—84no—
555C2×C4#120×C15111yescharacteristic
556C2×C4#120×C15111yescharacteristic
557C2×C4#120×C15111yescharacteristic
558C2×C4C22×D4×C15111yescharacteristic
559C2×C4C22×D4×C15111yescharacteristic
560C2×C4C22×D4×C15111yescharacteristic
561C8—42no—
562C8—41no—
563C8—41no—
564C8—42no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—41no—
569C22—44no—
570C22—41no—
571C22—44no—
572C22—41no—
573C22—44no—
574C22—164no—
575C22C2×#120×C15111yescharacteristic
576C4—21no—
577C4—21no—
578C4—21no—
579C4—41no—
580C4—41no—
581C4—42no—
582C4—41no—
583C4—42no—
584C4—81no—
585C4—81no—
586C4#455×C15112yes—
587C4#575×C15111yescharacteristic
588C4#575×C15111yescharacteristic
589C4#576×C15111yescharacteristic
590C4#577×C15111yescharacteristic
591C2—41no—
592C2—84no—
593C2—81no—
594C2#3005×C15111yescharacteristic
595C2#3012×C15111yescharacteristic
596C2C2×#455×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3508×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. #3138×C151C2semidirect
4. #3107×C151C2semidirect
5. #1642×C151C2semidirect
6. #1641×C151C2semidirect
7. #1640×C151C2semidirect
8. #1640×C151C2semidirect
9. #1545×C151C2semidirect
10. #1489×C151C2semidirect
11. #1485×C151C2semidirect
32. #475×C151C22semidirect
33. #475×C151C22semidirect
34. #474×C151C22semidirect
37. #462×C151C22semidirect
38. #462×C151C22semidirect
39. #461×C151C22semidirect
49. Q8⋊C8×C151C22semidirect
50. Q8⋊C8×C151C22semidirect
51. Q8⋊C8×C151C22semidirect
52. D4⋊C8×C151C22semidirect
298. #18576C151direct (N × H)
299. C151#18576direct (N × H)
301. #3255C2×C151semidirect
302. #3138C2×C151semidirect
303. #3107C2×C151semidirect
304. #1642C2×C151semidirect
305. #1641C2×C151semidirect
306. #1640C2×C151semidirect
307. #1640C2×C151semidirect
308. #1545C2×C151semidirect
309. #1489C2×C151semidirect
310. #1485C2×C151semidirect
331. #475C22×C151semidirect
332. #475C22×C151semidirect
333. #474C22×C151semidirect
336. #462C22×C151semidirect
337. #462C22×C151semidirect
338. #461C22×C151semidirect
348. Q8⋊C8C22×C151semidirect
349. Q8⋊C8C22×C151semidirect
350. Q8⋊C8C22×C151semidirect
351. D4⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3508×C1512
#3255×C1512
#3138×C1512
#3107×C1512
#1642×C1512
#1641×C1512
#1640×C1512
#1545×C1512
#1489×C1512
#1485×C1512
#18576151