Finite Group Databasebeta

← C151×#19246 #50324171

Subgroups — C151×#19246 #50324171

Order 38656.

602 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3248×C151C211yesmaximal, characteristic, complemented
2#3212×C151C211yesmaximal, characteristic
3#3182×C151C211yesmaximal, characteristic, complemented
4#2969×C151C211yesmaximal, characteristic, complemented
5#1701×C151C211yesmaximal, characteristic, complemented
6#1699×C151C211yesmaximal, characteristic, complemented
7#1694×C151C211yesmaximal, characteristic, complemented
8#1686×C151C211yesmaximal, characteristic, complemented
9#1682×C151C211yesmaximal, characteristic, complemented
10#1680×C151C211yesmaximal, characteristic, complemented
11#1673×C151C211yesmaximal, characteristic, complemented
12#1665×C151C211yesmaximal, characteristic, complemented
13#1565×C151C211yesmaximal, characteristic, complemented
14#1544×C151C211yesmaximal, characteristic, complemented
15#1540×C151C211yesmaximal, characteristic, complemented
16#533×C151C2211yescharacteristic
17#532×C151C2211yescharacteristic
18#529×C151C2211yescharacteristic
19#500×C151C2211yescharacteristic
20#495×C151—21no—
21#492×C151C2211yescharacteristic
22#488×C151—21no—
23#487×C151C2211yescharacteristic
24#486×C151C2211yescharacteristic
25#479×C151—21no—
26#475×C151C2211yescharacteristic
27#474×C151C2211yescharacteristic
28#468×C151—21no—
29#468×C151—21no—
30#467×C151—21no—
31#465×C151—21no—
32#464×C151—21no—
33#462×C151C2211yescharacteristic
34#462×C151C2211yescharacteristic
35#461×C151C2211yescharacteristic
36#461×C151C2211yescharacteristic
37#460×C151C2211yescharacteristic
38#459×C151C2211yescharacteristic
39#452×C151—21no—
40#449×C151—21no—
41#446×C151C2211yescharacteristic
42C8×Q8×C151C2211yescharacteristic
43#440×C151—21no—
44#440×C151—21no—
45#436×C151—21no—
46#436×C151C2211yescharacteristic
47#435×C151—21no—
48C8×D4×C151C2211yescharacteristic
49#433×C151—21no—
50#431×C151C2211yescharacteristic
51#431×C151C2211yescharacteristic
52C2×C4⋊C8×C151C2211yescharacteristic
53#405×C151—21no—
54C4×M16×C151C2211yescharacteristic
55#335×C151C2211yescharacteristic
56#335×C151C2211yescharacteristic
57#334×C151C2211yescharacteristic
58#334×C151C2211yescharacteristic
59#332×C151C2211yescharacteristic
60#332×C151C2211yescharacteristic
61#332×C151C2211yescharacteristic
62#332×C151C2211yescharacteristic
63#332×C151C2211yescharacteristic
64#332×C151C2211yescharacteristic
65#331×C151C2211yescharacteristic
66#331×C151C2211yescharacteristic
67C2×#41×C151—21no—
68C2×Q16×C151—21no—
69C2×Q16×C151—21no—
70C2×SD16×C151—21no—
71C2×SD16×C151—21no—
72C2×SD16×C151—21no—
73C2×SD16×C151—21no—
74C2×SD16×C151—21no—
75C2×D8×C151—21no—
76C2×M16×C151—21no—
77C2×M16×C151D411yescharacteristic
78C2×M16×C151D411yescharacteristic
79C22×C8×C151—21no—
80C22×C8×C151—21no—
81C4⋊Q8×C151C2311yescharacteristic
82C4⋊Q8×C151C2311yescharacteristic
83C4⋊Q8×C151C2311yescharacteristic
84#127×C151C2311yescharacteristic
85#126×C151—21no—
86#125×C151—21no—
87#125×C151D411yescharacteristic
88#124×C151—21no—
89#124×C151D411yescharacteristic
90#123×C151—21no—
91C22⋊Q8×C151—21no—
92C22⋊Q8×C151—21no—
93C22⋊Q8×C151D411yescharacteristic
94#121×C151—21no—
95#121×C151—21no—
96#121×C151D411yescharacteristic
97C4×Q8×C151—21no—
98C4×Q8×C151—21no—
99C4×Q8×C151C2311yescharacteristic
100C4×D4×C151—21no—
101C4×D4×C151—21no—
102C4×D4×C151—21no—
103C4×D4×C151C2311yescharacteristic
104#117×C151—21no—
105#117×C151—21no—
106C2×C42×C151C2311yescharacteristic
107#107×C151—21no—
108#107×C151—21no—
109#107×C151—21no—
110#106×C151—21no—
111C4⋊C8×C151—21no—
112C4⋊C8×C151—21no—
113C4⋊C8×C151—21no—
114C4⋊C8×C151C2311yescharacteristic
115C4⋊C8×C151C2311yescharacteristic
116C4⋊C8×C151C2311yescharacteristic
117C4⋊C8×C151C2311yescharacteristic
118C4⋊C8×C151C2311yescharacteristic
119C4⋊C8×C151C2311yescharacteristic
120#103×C151—21no—
121#103×C151—21no—
122#103×C151—21no—
123#103×C151—21no—
124#103×C151—21no—
125#103×C151—21no—
126#103×C151—21no—
127#102×C151—21no—
128#102×C151—21no—
129#102×C151—21no—
130#102×C151—21no—
131#102×C151—21no—
132C22⋊C8×C151—21no—
133C22⋊C8×C151—21no—
134C22⋊C8×C151—21no—
135C22⋊C8×C151—21no—
136#97×C151—21no—
137#97×C151D411yescharacteristic
138#97×C151D411yescharacteristic
139C4×C8×C151—21no—
140C4×C8×C151—21no—
141C4×C8×C151—21no—
142C4×C8×C151C2311yescharacteristic
143C4×C8×C151C2311yescharacteristic
144#41×C151—81no—
145#41×C151—81no—
146C2×Q8×C151—21no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151C2×D411yescharacteristic
150C2×D4×C151—21no—
151C2×D4×C151—21no—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—41no—
155C2×D4×C151C2×D411yescharacteristic
156C22×C4×C151—21no—
157C22×C4×C151—41no—
158C22×C4×C151C2×D411yescharacteristic
159C22×C4×C151C2×D411yescharacteristic
160C22×C4×C151#4111yescharacteristic
161Q16×C151—81no—
162Q16×C151—81no—
163SD16×C151—42no—
164SD16×C151—42no—
165SD16×C151—81no—
166SD16×C151—81no—
167SD16×C151—81no—
168D8×C151—81no—
169M16×C151—22no—
170M16×C151—41no—
171M16×C151—42no—
172C2×C8×C151—21no—
173C2×C8×C151—21no—
174C2×C8×C151—21no—
175C2×C8×C151—21no—
176C2×C8×C151—21no—
177C2×C8×C151—21no—
178C2×C8×C151—42no—
179C2×C8×C151—81no—
180C2×C8×C151C2×D411yescharacteristic
181C2×C8×C151C2×D411yescharacteristic
182C2×C8×C151C2×D411yescharacteristic
183C2×C8×C151C2×D411yescharacteristic
184C4⋊C4×C151—21no—
185C4⋊C4×C151—21no—
186C4⋊C4×C151—21no—
187C4⋊C4×C151—21no—
188C4⋊C4×C151—21no—
189C4⋊C4×C151—21no—
190C4⋊C4×C151—21no—
191C4⋊C4×C151—21no—
192C4⋊C4×C151—21no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—41no—
195C4⋊C4×C151—41no—
196C4⋊C4×C151C2×D411yescharacteristic
197C4⋊C4×C151C2×D411yescharacteristic
198C22⋊C4×C151—21no—
199C22⋊C4×C151—21no—
200C22⋊C4×C151—21no—
201C22⋊C4×C151—21no—
202C22⋊C4×C151—21no—
203C22⋊C4×C151—41no—
204C22⋊C4×C151—41no—
205C22⋊C4×C151—41no—
206C42×C151—21no—
207C42×C151—41no—
208C42×C151C2×D411yescharacteristic
209C42×C151C2×D411yescharacteristic
210C42×C151#4111yescharacteristic
211C42×C151C2411yescharacteristic
212C23×C151—21no—
213C23×C151—41no—
214C23×C151#12111yescharacteristic
215Q8×C151—21no—
216Q8×C151—21no—
217Q8×C151—41no—
218Q8×C151—41no—
219Q8×C151—41no—
220Q8×C151—41no—
221Q8×C151—41no—
222Q8×C151—41no—
223D4×C151—21no—
224D4×C151—21no—
225D4×C151—41no—
226D4×C151—41no—
227D4×C151—41no—
228D4×C151—41no—
229D4×C151—81no—
230D4×C151—81no—
231D4×C151—82no—
232C2×C4×C151—21no—
233C2×C4×C151—21no—
234C2×C4×C151—21no—
235C2×C4×C151—21no—
236C2×C4×C151—21no—
237C2×C4×C151—21no—
238C2×C4×C151—21no—
239C2×C4×C151—41no—
240C2×C4×C151—41no—
241C2×C4×C151—41no—
242C2×C4×C151—41no—
243C2×C4×C151—41no—
244C2×C4×C151—41no—
245C2×C4×C151—82no—
246C2×C4×C151#12111yescharacteristic
247C2×C4×C151#12111yescharacteristic
248C2×C4×C151#12111yescharacteristic
249C2×C4×C151C22×D411yescharacteristic
250C2×C4×C151C22×D411yescharacteristic
251C2×C4×C151C2×#4111yescharacteristic
252C8×C151—21no—
253C8×C151—21no—
254C8×C151—21no—
255C8×C151—41no—
256C8×C151—41no—
257C8×C151—41no—
258C8×C151—41no—
259C8×C151—41no—
260C8×C151—41no—
261C8×C151#13512yes—
262C22×C151—21no—
263C22×C151—21no—
264C22×C151—21no—
265C22×C151—41no—
266C22×C151—41no—
267C22×C151—41no—
268C22×C151—81no—
269C22×C151—81no—
270C22×C151—81no—
271C22×C151C2×#12111yescharacteristic
272C4×C151—21no—
273C4×C151—21no—
274C4×C151—21no—
275C4×C151—21no—
276C4×C151—41no—
277C4×C151—41no—
278C4×C151—41no—
279C4×C151—81no—
280C4×C151—81no—
281C4×C151—81no—
282C4×C151C2×#13511yescharacteristic
283C4×C151#57511yescharacteristic
284C4×C151#57611yescharacteristic
285C4×C151#57711yescharacteristic
286C2×C151—41no—
287C2×C151—81no—
288C2×C151—161no—
289C2×C151#303511yescharacteristic
290C2×C151#306211yescharacteristic
291C2×C151#306911yescharacteristic
292#19246C15111yesmaximal, characteristic, direct product factor, Sylow
293C151#1924611yescharacteristic, direct product factor, Sylow
294#3248C2×C15111yescharacteristic, complemented
295#3212C2×C15111yescharacteristic
296#3182C2×C15111yescharacteristic, complemented
297#2969C2×C15111yescharacteristic, complemented
298#1701C2×C15111yescharacteristic, complemented
299#1699C2×C15111yescharacteristic, complemented
300#1694C2×C15111yescharacteristic, complemented
301#1686C2×C15111yescharacteristic, complemented
302#1682C2×C15111yescharacteristic, complemented
303#1680C2×C15111yescharacteristic, complemented
304#1673C2×C15111yescharacteristic, complemented
305#1665C2×C15111yescharacteristic, complemented
306#1565C2×C15111yescharacteristic, complemented
307#1544C2×C15111yescharacteristic, complemented
308#1540C2×C15111yescharacteristic, complemented
309#533C22×C15111yescharacteristic
310#532C22×C15111yescharacteristic
311#529C22×C15111yescharacteristic
312#500C22×C15111yescharacteristic
313#495—21no—
314#492C22×C15111yescharacteristic
315#488—21no—
316#487C22×C15111yescharacteristic
317#486C22×C15111yescharacteristic
318#479—21no—
319#475C22×C15111yescharacteristic
320#474C22×C15111yescharacteristic
321#468—21no—
322#468—21no—
323#467—21no—
324#465—21no—
325#464—21no—
326#462C22×C15111yescharacteristic
327#462C22×C15111yescharacteristic
328#461C22×C15111yescharacteristic
329#461C22×C15111yescharacteristic
330#460C22×C15111yescharacteristic
331#459C22×C15111yescharacteristic
332#452—21no—
333#449—21no—
334#446C22×C15111yescharacteristic
335C8×Q8C22×C15111yescharacteristic
336#440—21no—
337#440—21no—
338#436—21no—
339#436C22×C15111yescharacteristic
340#435—21no—
341C8×D4C22×C15111yescharacteristic
342#433—21no—
343#431C22×C15111yescharacteristic
344#431C22×C15111yescharacteristic
345C2×C4⋊C8C22×C15111yescharacteristic
346#405—21no—
347C4×M16C22×C15111yescharacteristic
348#335C22×C15111yescharacteristic
349#335C22×C15111yescharacteristic
350#334C22×C15111yescharacteristic
351#334C22×C15111yescharacteristic
352#332C22×C15111yescharacteristic
353#332C22×C15111yescharacteristic
354#332C22×C15111yescharacteristic
355#332C22×C15111yescharacteristic
356#332C22×C15111yescharacteristic
357#332C22×C15111yescharacteristic
358#331C22×C15111yescharacteristic
359#331C22×C15111yescharacteristic
360C2×#41—21no—
361C2×Q16—21no—
362C2×Q16—21no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×D8—21no—
369C2×M16—21no—
370C2×M16D4×C15111yescharacteristic
371C2×M16D4×C15111yescharacteristic
372C22×C8—21no—
373C22×C8—21no—
374C4⋊Q8C23×C15111yescharacteristic
375C4⋊Q8C23×C15111yescharacteristic
376C4⋊Q8C23×C15111yescharacteristic
377#127C23×C15111yescharacteristic
378#126—21no—
379#125—21no—
380#125D4×C15111yescharacteristic
381#124—21no—
382#124D4×C15111yescharacteristic
383#123—21no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8D4×C15111yescharacteristic
387#121—21no—
388#121—21no—
389#121D4×C15111yescharacteristic
390C4×Q8—21no—
391C4×Q8—21no—
392C4×Q8C23×C15111yescharacteristic
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4C23×C15111yescharacteristic
397#117—21no—
398#117—21no—
399C2×C42C23×C15111yescharacteristic
400#107—21no—
401#107—21no—
402#107—21no—
403#106—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8C23×C15111yescharacteristic
408C4⋊C8C23×C15111yescharacteristic
409C4⋊C8C23×C15111yescharacteristic
410C4⋊C8C23×C15111yescharacteristic
411C4⋊C8C23×C15111yescharacteristic
412C4⋊C8C23×C15111yescharacteristic
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429#97—21no—
430#97D4×C15111yescharacteristic
431#97D4×C15111yescharacteristic
432C4×C8—21no—
433C4×C8—21no—
434C4×C8—21no—
435C4×C8C23×C15111yescharacteristic
436C4×C8C23×C15111yescharacteristic
437#41—81no—
438#41—81no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C2×D4×C15111yescharacteristic
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4C2×D4×C15111yescharacteristic
449C22×C4—21no—
450C22×C4—41no—
451C22×C4C2×D4×C15111yescharacteristic
452C22×C4C2×D4×C15111yescharacteristic
453C22×C4#41×C15111yescharacteristic
454Q16—81no—
455Q16—81no—
456SD16—42no—
457SD16—42no—
458SD16—81no—
459SD16—81no—
460SD16—81no—
461D8—81no—
462M16—22no—
463M16—41no—
464M16—42no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—42no—
472C2×C8—81no—
473C2×C8C2×D4×C15111yescharacteristic
474C2×C8C2×D4×C15111yescharacteristic
475C2×C8C2×D4×C15111yescharacteristic
476C2×C8C2×D4×C15111yescharacteristic
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4C2×D4×C15111yescharacteristic
490C4⋊C4C2×D4×C15111yescharacteristic
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C42—21no—
500C42—41no—
501C42C2×D4×C15111yescharacteristic
502C42C2×D4×C15111yescharacteristic
503C42#41×C15111yescharacteristic
504C42C24×C15111yescharacteristic
505C23—21no—
506C23—41no—
507C23#121×C15111yescharacteristic
508Q8—21no—
509Q8—21no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516D4—21no—
517D4—21no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—81no—
523D4—81no—
524D4—82no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—82no—
539C2×C4#121×C15111yescharacteristic
540C2×C4#121×C15111yescharacteristic
541C2×C4#121×C15111yescharacteristic
542C2×C4C22×D4×C15111yescharacteristic
543C2×C4C22×D4×C15111yescharacteristic
544C2×C4C2×#41×C15111yescharacteristic
545C8—21no—
546C8—21no—
547C8—21no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8#135×C15112yes—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22C2×#121×C15111yescharacteristic
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4C2×#135×C15111yescharacteristic
576C4#575×C15111yescharacteristic
577C4#576×C15111yescharacteristic
578C4#577×C15111yescharacteristic
579C2—41no—
580C2—81no—
581C2—161no—
582C2#3035×C15111yescharacteristic
583C2#3062×C15111yescharacteristic
584C2#3069×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radical#3212×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
1. #3248×C151C2semidirect
3. #3182×C151C2semidirect
4. #2969×C151C2semidirect
5. #1701×C151C2semidirect
6. #1699×C151C2semidirect
7. #1694×C151C2semidirect
8. #1686×C151C2semidirect
9. #1682×C151C2semidirect
10. #1680×C151C2semidirect
11. #1673×C151C2semidirect
12. #1665×C151C2semidirect
13. #1565×C151C2semidirect
14. #1544×C151C2semidirect
15. #1540×C151C2semidirect
292. #19246C151direct (N × H)
293. C151#19246direct (N × H)
294. #3248C2×C151semidirect
296. #3182C2×C151semidirect
297. #2969C2×C151semidirect
298. #1701C2×C151semidirect
299. #1699C2×C151semidirect
300. #1694C2×C151semidirect
301. #1686C2×C151semidirect
302. #1682C2×C151semidirect
303. #1680C2×C151semidirect
304. #1673C2×C151semidirect
305. #1665C2×C151semidirect
306. #1565C2×C151semidirect
307. #1544C2×C151semidirect
308. #1540C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3248×C1512
#3212×C1512
#3182×C1512
#2969×C1512
#1701×C1512
#1699×C1512
#1694×C1512
#1686×C1512
#1682×C1512
#1680×C1512
#1673×C1512
#1665×C1512
#1565×C1512
#1544×C1512
#1540×C1512
#19246151