Finite Group Databasebeta

← C151×#19826 #50324751

Subgroups — C151×#19826 #50324751

Order 38656.

600 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3361×C151C211yesmaximal, characteristic, complemented
2#3361×C151C211yesmaximal, characteristic, complemented
3#3335×C151C211yesmaximal, characteristic, complemented
4#3331×C151C211yesmaximal, characteristic, complemented
5#1720×C151C211yesmaximal, characteristic, complemented
6#1697×C151C211yesmaximal, characteristic, complemented
7#1684×C151C211yesmaximal, characteristic, complemented
8#1677×C151C211yesmaximal, characteristic, complemented
9#1672×C151C211yesmaximal, characteristic, complemented
10#1640×C151C211yesmaximal, characteristic, complemented
11#1632×C151C211yesmaximal, characteristic, complemented
12#1632×C151C211yesmaximal, characteristic, complemented
13#1625×C151C211yesmaximal, characteristic
14#1583×C151C211yesmaximal, characteristic, complemented
15SD16⋊C8×C151C211yesmaximal, characteristic, complemented
16#559×C151C2211yescharacteristic
17#554×C151C2211yescharacteristic
18#554×C151C2211yescharacteristic
19#547×C151C2211yescharacteristic
20#498×C151C2211yescharacteristic
21#494×C151C2211yescharacteristic
22#488×C151—21no—
23#488×C151—21no—
24#487×C151C2211yescharacteristic
25#486×C151C2211yescharacteristic
26#486×C151C2211yescharacteristic
27#486×C151C2211yescharacteristic
28#483×C151—21no—
29#483×C151—21no—
30#481×C151—21no—
31#478×C151—21no—
32#478×C151—21no—
33#477×C151C2211yescharacteristic
34#477×C151C2211yescharacteristic
35#476×C151C2211yescharacteristic
36#476×C151C2211yescharacteristic
37#475×C151C2211yescharacteristic
38#470×C151—21no—
39#465×C151—21no—
40#463×C151—21no—
41#463×C151—21no—
42#462×C151C2211yescharacteristic
43#459×C151C2211yescharacteristic
44#459×C151C2211yescharacteristic
45#452×C151—21no—
46C8×Q8×C151C2211yescharacteristic
47C8×Q8×C151C2211yescharacteristic
48C4×SD16×C151C2211yescharacteristic
49C4×SD16×C151C2211yescharacteristic
50C4×D8×C151—21no—
51C4×D8×C151—21no—
52#436×C151C2211yescharacteristic
53C8×D4×C151C2211yescharacteristic
54C2×#106×C151—21no—
55#417×C151—21no—
56#335×C151C2211yescharacteristic
57#334×C151C2211yescharacteristic
58#333×C151C2211yescharacteristic
59#333×C151C2211yescharacteristic
60#332×C151C2211yescharacteristic
61#331×C151C2211yescharacteristic
62Q8⋊C8×C151C2211yescharacteristic
63Q8⋊C8×C151C2211yescharacteristic
64D4⋊C8×C151C2211yescharacteristic
65D4⋊C8×C151C2211yescharacteristic
66#322×C151C2211yescharacteristic
67C2×#41×C151—21no—
68C2×Q16×C151—21no—
69C2×Q16×C151—41no—
70C2×SD16×C151D411yescharacteristic
71C2×SD16×C151D411yescharacteristic
72C2×D8×C151—21no—
73C2×D8×C151—21no—
74C2×M16×C151—21no—
75C22×C8×C151—21no—
76C4⋊Q8×C151C2311yescharacteristic
77C4⋊Q8×C151C2311yescharacteristic
78C4⋊Q8×C151C2311yescharacteristic
79#127×C151C2311yescharacteristic
80#125×C151—21no—
81#125×C151—21no—
82#124×C151—21no—
83#124×C151—21no—
84#123×C151—41no—
85#123×C151—41no—
86C22⋊Q8×C151—21no—
87C22⋊Q8×C151—21no—
88C22⋊Q8×C151—21no—
89C22⋊Q8×C151—41no—
90C22⋊Q8×C151—41no—
91#121×C151—21no—
92C4×Q8×C151C2311yescharacteristic
93C4×Q8×C151C2311yescharacteristic
94C4×D4×C151—21no—
95C4×D4×C151—21no—
96C4×D4×C151—21no—
97C4×D4×C151—21no—
98C4×D4×C151C2311yescharacteristic
99C4×D4×C151C2311yescharacteristic
100C2×C4⋊C4×C151—21no—
101C2×C4⋊C4×C151—21no—
102C2×C4⋊C4×C151—21no—
103#107×C151—21no—
104#107×C151—21no—
105#106×C151—21no—
106#106×C151—21no—
107#106×C151—21no—
108#106×C151—21no—
109#106×C151—21no—
110#106×C151D411yescharacteristic
111#106×C151D411yescharacteristic
112C4⋊C8×C151—21no—
113C4⋊C8×C151—21no—
114C4⋊C8×C151C2311yescharacteristic
115C4⋊C8×C151C2311yescharacteristic
116C4⋊C8×C151C2311yescharacteristic
117C4⋊C8×C151C2311yescharacteristic
118#103×C151—21no—
119#103×C151—21no—
120#103×C151—21no—
121#103×C151—21no—
122#103×C151—21no—
123#103×C151—21no—
124#103×C151D411yescharacteristic
125#103×C151D411yescharacteristic
126#102×C151—21no—
127#102×C151—21no—
128#102×C151—21no—
129#102×C151—21no—
130#102×C151—21no—
131#102×C151—21no—
132#102×C151—21no—
133#102×C151—21no—
134#102×C151—41no—
135#102×C151D411yescharacteristic
136#102×C151D411yescharacteristic
137C22⋊C8×C151—21no—
138C22⋊C8×C151—21no—
139C4×C8×C151—21no—
140C4×C8×C151—21no—
141C4×C8×C151C2311yescharacteristic
142C4×C8×C151C2311yescharacteristic
143C4×C8×C151C2311yescharacteristic
144#41×C151—42no—
145#41×C151—81no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151C2×D411yescharacteristic
150C2×Q8×C151C2×D411yescharacteristic
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—41no—
155C2×D4×C151C2×D411yescharacteristic
156C2×D4×C151C2×D411yescharacteristic
157C22×C4×C151—21no—
158C22×C4×C151—21no—
159C22×C4×C151—41no—
160C22×C4×C151—41no—
161C22×C4×C151—41no—
162C22×C4×C151—41no—
163Q16×C151—81no—
164Q16×C151—82no—
165SD16×C151—22no—
166SD16×C151—41no—
167D8×C151—42no—
168D8×C151—42no—
169M16×C151—81no—
170C2×C8×C151—21no—
171C2×C8×C151—21no—
172C2×C8×C151—21no—
173C2×C8×C151—21no—
174C2×C8×C151—21no—
175C2×C8×C151—42no—
176C2×C8×C151C2×D411yescharacteristic
177C2×C8×C151C2×D411yescharacteristic
178C2×C8×C151C2×D411yescharacteristic
179C2×C8×C151C2×D411yescharacteristic
180C4⋊C4×C151—21no—
181C4⋊C4×C151—21no—
182C4⋊C4×C151—21no—
183C4⋊C4×C151—21no—
184C4⋊C4×C151—21no—
185C4⋊C4×C151—21no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—41no—
189C4⋊C4×C151—41no—
190C4⋊C4×C151—41no—
191C4⋊C4×C151—41no—
192C4⋊C4×C151—41no—
193C4⋊C4×C151C2×D411yescharacteristic
194C4⋊C4×C151C2×D411yescharacteristic
195C4⋊C4×C151C2×D411yescharacteristic
196C4⋊C4×C151C2×D411yescharacteristic
197C22⋊C4×C151—21no—
198C22⋊C4×C151—21no—
199C22⋊C4×C151—41no—
200C22⋊C4×C151—41no—
201C22⋊C4×C151—41no—
202C22⋊C4×C151—41no—
203C22⋊C4×C151—41no—
204C22⋊C4×C151—41no—
205C42×C151—21no—
206C42×C151—21no—
207C42×C151C2411yescharacteristic
208C23×C151—21no—
209C23×C151—21no—
210C23×C151—41no—
211Q8×C151—21no—
212Q8×C151—21no—
213Q8×C151—21no—
214Q8×C151—21no—
215Q8×C151—41no—
216Q8×C151—41no—
217Q8×C151—81no—
218Q8×C151—81no—
219D4×C151—21no—
220D4×C151—21no—
221D4×C151—21no—
222D4×C151—41no—
223D4×C151—41no—
224D4×C151—41no—
225D4×C151—41no—
226D4×C151—81no—
227D4×C151—82no—
228D4×C151#13512yes—
229C2×C4×C151—21no—
230C2×C4×C151—21no—
231C2×C4×C151—21no—
232C2×C4×C151—21no—
233C2×C4×C151—21no—
234C2×C4×C151—21no—
235C2×C4×C151—41no—
236C2×C4×C151—41no—
237C2×C4×C151—41no—
238C2×C4×C151—41no—
239C2×C4×C151—41no—
240C2×C4×C151—41no—
241C2×C4×C151—41no—
242C2×C4×C151—82no—
243C2×C4×C151—161no—
244C2×C4×C151—161no—
245C2×C4×C151—161no—
246C2×C4×C151C22×D411yescharacteristic
247C2×C4×C151C22×D411yescharacteristic
248C2×C4×C151H(5,𝔽2)11yescharacteristic
249C8×C151—21no—
250C8×C151—21no—
251C8×C151—21no—
252C8×C151—21no—
253C8×C151—41no—
254C8×C151—41no—
255C8×C151—41no—
256C8×C151—41no—
257C8×C151—41no—
258C22×C151—22no—
259C22×C151—41no—
260C22×C151—41no—
261C22×C151—41no—
262C22×C151—41no—
263C22×C151—41no—
264C22×C151—81no—
265C22×C151—81no—
266C22×C151—81no—
267C22×C151D4211yescharacteristic
268C4×C151—21no—
269C4×C151—41no—
270C4×C151—41no—
271C4×C151—41no—
272C4×C151—41no—
273C4×C151—41no—
274C4×C151—41no—
275C4×C151—81no—
276C4×C151—81no—
277C4×C151—81no—
278C4×C151C2×#13511yescharacteristic
279C4×C151#57511yescharacteristic
280C4×C151#57711yescharacteristic
281C4×C151#57811yescharacteristic
282C2×C151—42no—
283C2×C151—81no—
284C2×C151—161no—
285C2×C151#326911yescharacteristic
286C2×C151#328211yescharacteristic
287C2×C151#328811yescharacteristic
288#19826C15111yesmaximal, characteristic, direct product factor, Sylow
289C151#1982611yescharacteristic, direct product factor, Sylow
290#3361C2×C15111yescharacteristic, complemented
291#3361C2×C15111yescharacteristic, complemented
292#3335C2×C15111yescharacteristic, complemented
293#3331C2×C15111yescharacteristic, complemented
294#1720C2×C15111yescharacteristic, complemented
295#1697C2×C15111yescharacteristic, complemented
296#1684C2×C15111yescharacteristic, complemented
297#1677C2×C15111yescharacteristic, complemented
298#1672C2×C15111yescharacteristic, complemented
299#1640C2×C15111yescharacteristic, complemented
300#1632C2×C15111yescharacteristic, complemented
301#1632C2×C15111yescharacteristic, complemented
302#1625C2×C15111yescharacteristic
303#1583C2×C15111yescharacteristic, complemented
304SD16⋊C8C2×C15111yescharacteristic, complemented
305#559C22×C15111yescharacteristic
306#554C22×C15111yescharacteristic
307#554C22×C15111yescharacteristic
308#547C22×C15111yescharacteristic
309#498C22×C15111yescharacteristic
310#494C22×C15111yescharacteristic
311#488—21no—
312#488—21no—
313#487C22×C15111yescharacteristic
314#486C22×C15111yescharacteristic
315#486C22×C15111yescharacteristic
316#486C22×C15111yescharacteristic
317#483—21no—
318#483—21no—
319#481—21no—
320#478—21no—
321#478—21no—
322#477C22×C15111yescharacteristic
323#477C22×C15111yescharacteristic
324#476C22×C15111yescharacteristic
325#476C22×C15111yescharacteristic
326#475C22×C15111yescharacteristic
327#470—21no—
328#465—21no—
329#463—21no—
330#463—21no—
331#462C22×C15111yescharacteristic
332#459C22×C15111yescharacteristic
333#459C22×C15111yescharacteristic
334#452—21no—
335C8×Q8C22×C15111yescharacteristic
336C8×Q8C22×C15111yescharacteristic
337C4×SD16C22×C15111yescharacteristic
338C4×SD16C22×C15111yescharacteristic
339C4×D8—21no—
340C4×D8—21no—
341#436C22×C15111yescharacteristic
342C8×D4C22×C15111yescharacteristic
343C2×#106—21no—
344#417—21no—
345#335C22×C15111yescharacteristic
346#334C22×C15111yescharacteristic
347#333C22×C15111yescharacteristic
348#333C22×C15111yescharacteristic
349#332C22×C15111yescharacteristic
350#331C22×C15111yescharacteristic
351Q8⋊C8C22×C15111yescharacteristic
352Q8⋊C8C22×C15111yescharacteristic
353D4⋊C8C22×C15111yescharacteristic
354D4⋊C8C22×C15111yescharacteristic
355#322C22×C15111yescharacteristic
356C2×#41—21no—
357C2×Q16—21no—
358C2×Q16—41no—
359C2×SD16D4×C15111yescharacteristic
360C2×SD16D4×C15111yescharacteristic
361C2×D8—21no—
362C2×D8—21no—
363C2×M16—21no—
364C22×C8—21no—
365C4⋊Q8C23×C15111yescharacteristic
366C4⋊Q8C23×C15111yescharacteristic
367C4⋊Q8C23×C15111yescharacteristic
368#127C23×C15111yescharacteristic
369#125—21no—
370#125—21no—
371#124—21no—
372#124—21no—
373#123—41no—
374#123—41no—
375C22⋊Q8—21no—
376C22⋊Q8—21no—
377C22⋊Q8—21no—
378C22⋊Q8—41no—
379C22⋊Q8—41no—
380#121—21no—
381C4×Q8C23×C15111yescharacteristic
382C4×Q8C23×C15111yescharacteristic
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4C23×C15111yescharacteristic
388C4×D4C23×C15111yescharacteristic
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392#107—21no—
393#107—21no—
394#106—21no—
395#106—21no—
396#106—21no—
397#106—21no—
398#106—21no—
399#106D4×C15111yescharacteristic
400#106D4×C15111yescharacteristic
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8C23×C15111yescharacteristic
404C4⋊C8C23×C15111yescharacteristic
405C4⋊C8C23×C15111yescharacteristic
406C4⋊C8C23×C15111yescharacteristic
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103D4×C15111yescharacteristic
414#103D4×C15111yescharacteristic
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—41no—
424#102D4×C15111yescharacteristic
425#102D4×C15111yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—21no—
428C4×C8—21no—
429C4×C8—21no—
430C4×C8C23×C15111yescharacteristic
431C4×C8C23×C15111yescharacteristic
432C4×C8C23×C15111yescharacteristic
433#41—42no—
434#41—81no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8C2×D4×C15111yescharacteristic
439C2×Q8C2×D4×C15111yescharacteristic
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—41no—
444C2×D4C2×D4×C15111yescharacteristic
445C2×D4C2×D4×C15111yescharacteristic
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452Q16—81no—
453Q16—82no—
454SD16—22no—
455SD16—41no—
456D8—42no—
457D8—42no—
458M16—81no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—42no—
465C2×C8C2×D4×C15111yescharacteristic
466C2×C8C2×D4×C15111yescharacteristic
467C2×C8C2×D4×C15111yescharacteristic
468C2×C8C2×D4×C15111yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4C2×D4×C15111yescharacteristic
483C4⋊C4C2×D4×C15111yescharacteristic
484C4⋊C4C2×D4×C15111yescharacteristic
485C4⋊C4C2×D4×C15111yescharacteristic
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C42—21no—
495C42—21no—
496C42C24×C15111yescharacteristic
497C23—21no—
498C23—21no—
499C23—41no—
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—21no—
504Q8—41no—
505Q8—41no—
506Q8—81no—
507Q8—81no—
508D4—21no—
509D4—21no—
510D4—21no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—81no—
516D4—82no—
517D4#135×C15112yes—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—82no—
532C2×C4—161no—
533C2×C4—161no—
534C2×C4—161no—
535C2×C4C22×D4×C15111yescharacteristic
536C2×C4C22×D4×C15111yescharacteristic
537C2×C4H(5,𝔽2)×C15111yescharacteristic
538C8—21no—
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C22—22no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22D42×C15111yescharacteristic
557C4—21no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—81no—
565C4—81no—
566C4—81no—
567C4C2×#135×C15111yescharacteristic
568C4#575×C15111yescharacteristic
569C4#577×C15111yescharacteristic
570C4#578×C15111yescharacteristic
571C2—42no—
572C2—81no—
573C2—161no—
574C2#3269×C15111yescharacteristic
575C2#3282×C15111yescharacteristic
576C2#3288×C15111yescharacteristic
subgroupG/H
center, socleC22×C151D42
commutator, Frattini, cosocleC42C24×C151
prime radical#1625×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3361×C151C2semidirect
2. #3361×C151C2semidirect
3. #3335×C151C2semidirect
4. #3331×C151C2semidirect
5. #1720×C151C2semidirect
6. #1697×C151C2semidirect
7. #1684×C151C2semidirect
8. #1677×C151C2semidirect
9. #1672×C151C2semidirect
10. #1640×C151C2semidirect
11. #1632×C151C2semidirect
12. #1632×C151C2semidirect
14. #1583×C151C2semidirect
15. SD16⋊C8×C151C2semidirect
288. #19826C151direct (N × H)
289. C151#19826direct (N × H)
290. #3361C2×C151semidirect
291. #3361C2×C151semidirect
292. #3335C2×C151semidirect
293. #3331C2×C151semidirect
294. #1720C2×C151semidirect
295. #1697C2×C151semidirect
296. #1684C2×C151semidirect
297. #1677C2×C151semidirect
298. #1672C2×C151semidirect
299. #1640C2×C151semidirect
300. #1632C2×C151semidirect
301. #1632C2×C151semidirect
303. #1583C2×C151semidirect
304. SD16⋊C8C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3361×C1512
#3335×C1512
#3331×C1512
#1720×C1512
#1697×C1512
#1684×C1512
#1677×C1512
#1672×C1512
#1640×C1512
#1632×C1512
#1625×C1512
#1583×C1512
SD16⋊C8×C1512
#19826151