Finite Group Databasebeta

← C151×#19569 #50324494

Subgroups — C151×#19569 #50324494

Order 38656.

602 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3246×C151C211yesmaximal, characteristic, complemented
2#3216×C151C211yesmaximal, characteristic, complemented
3#3207×C151C211yesmaximal, characteristic
4#2986×C151C211yesmaximal, characteristic, complemented
5#1702×C151C211yesmaximal, characteristic, complemented
6#1700×C151C211yesmaximal, characteristic, complemented
7#1688×C151C211yesmaximal, characteristic, complemented
8#1686×C151C211yesmaximal, characteristic, complemented
9#1682×C151C211yesmaximal, characteristic, complemented
10#1680×C151C211yesmaximal, characteristic, complemented
11#1668×C151C211yesmaximal, characteristic, complemented
12#1666×C151C211yesmaximal, characteristic, complemented
13#1573×C151C211yesmaximal, characteristic, complemented
14#1553×C151C211yesmaximal, characteristic, complemented
15#1540×C151C211yesmaximal, characteristic, complemented
16#533×C151C2211yescharacteristic
17#532×C151C2211yescharacteristic
18#532×C151C2211yescharacteristic
19#497×C151—21no—
20#493×C151C2211yescharacteristic
21#492×C151C2211yescharacteristic
22#489×C151—21no—
23#487×C151C2211yescharacteristic
24#486×C151C2211yescharacteristic
25#476×C151—21no—
26#475×C151C2211yescharacteristic
27#475×C151C2211yescharacteristic
28#465×C151—21no—
29#465×C151—21no—
30#463×C151—21no—
31#463×C151—21no—
32#462×C151C2211yescharacteristic
33#462×C151C2211yescharacteristic
34#461×C151—21no—
35#460×C151C2211yescharacteristic
36#460×C151C2211yescharacteristic
37#460×C151C2211yescharacteristic
38#460×C151C2211yescharacteristic
39#452×C151—21no—
40#452×C151—21no—
41#449×C151—21no—
42#449×C151—21no—
43#446×C151—21no—
44#446×C151C2211yescharacteristic
45#446×C151C2211yescharacteristic
46C8×Q8×C151—21no—
47C8×Q8×C151C2211yescharacteristic
48C8×Q8×C151C2211yescharacteristic
49#433×C151—21no—
50#433×C151—21no—
51#432×C151C2211yescharacteristic
52#431×C151C2211yescharacteristic
53#431×C151C2211yescharacteristic
54C2×C4⋊C8×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#331×C151C2211yescharacteristic
64#331×C151C2211yescharacteristic
65#331×C151C2211yescharacteristic
66#331×C151C2211yescharacteristic
67C2×#41×C151—21no—
68C2×#41×C151—21no—
69C2×Q16×C151—21no—
70C2×Q16×C151—21no—
71C2×SD16×C151—21no—
72C2×SD16×C151—21no—
73C2×SD16×C151—21no—
74C2×SD16×C151—21no—
75C2×SD16×C151—21no—
76C2×SD16×C151—21no—
77C2×D8×C151—21no—
78C2×D8×C151—21no—
79C22×C8×C151—21no—
80C4⋊Q8×C151D411yescharacteristic
81C4⋊Q8×C151D411yescharacteristic
82C4⋊Q8×C151C2311yescharacteristic
83C4⋊Q8×C151C2311yescharacteristic
84#127×C151C2311yescharacteristic
85#127×C151C2311yescharacteristic
86#125×C151—21no—
87#124×C151—21no—
88#124×C151—21no—
89C22⋊Q8×C151—21no—
90C22⋊Q8×C151D411yescharacteristic
91C22⋊Q8×C151D411yescharacteristic
92#121×C151—21no—
93#121×C151—21no—
94#121×C151—21no—
95#121×C151—21no—
96C4×Q8×C151—21no—
97C4×Q8×C151C2311yescharacteristic
98C4×Q8×C151C2311yescharacteristic
99C4×D4×C151—21no—
100C4×D4×C151—21no—
101C4×D4×C151—21no—
102C4×D4×C151—21no—
103#117×C151—21no—
104C2×C42×C151C2311yescharacteristic
105#106×C151—21no—
106#106×C151—21no—
107C4⋊C8×C151—21no—
108C4⋊C8×C151—21no—
109C4⋊C8×C151—21no—
110C4⋊C8×C151—21no—
111C4⋊C8×C151—21no—
112C4⋊C8×C151D411yescharacteristic
113C4⋊C8×C151D411yescharacteristic
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#102×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×C151D411yescharacteristic
135C22⋊C8×C151D411yescharacteristic
136#97×C151—21no—
137#97×C151—21no—
138#97×C151—21no—
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—
146#41×C151—81no—
147#41×C151—81no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151—21no—
151C2×Q8×C151C2×D411yescharacteristic
152C2×Q8×C151C2×D411yescharacteristic
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151—41no—
160C2×D4×C151—41no—
161C22×C4×C151—41no—
162C22×C4×C151—41no—
163C22×C4×C151C2×D411yescharacteristic
164C22×C4×C151C2×D411yescharacteristic
165C22×C4×C151#4111yescharacteristic
166Q16×C151—81no—
167Q16×C151—81no—
168SD16×C151—81no—
169SD16×C151—81no—
170SD16×C151—81no—
171SD16×C151—81no—
172SD16×C151—81no—
173SD16×C151—81no—
174D8×C151—81no—
175D8×C151—81no—
176C2×C8×C151—21no—
177C2×C8×C151—21no—
178C2×C8×C151—21no—
179C2×C8×C151—21no—
180C2×C8×C151—21no—
181C2×C8×C151—21no—
182C2×C8×C151—81no—
183C2×C8×C151C2×D411yescharacteristic
184C2×C8×C151C2×D411yescharacteristic
185C2×C8×C151C2×D411yescharacteristic
186C2×C8×C151C2×D411yescharacteristic
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—21no—
195C4⋊C4×C151—21no—
196C4⋊C4×C151—21no—
197C4⋊C4×C151—21no—
198C4⋊C4×C151C2×D411yescharacteristic
199C4⋊C4×C151C2×D411yescharacteristic
200C22⋊C4×C151—21no—
201C22⋊C4×C151—21no—
202C22⋊C4×C151—41no—
203C22⋊C4×C151—41no—
204C22⋊C4×C151—41no—
205C22⋊C4×C151—41no—
206C42×C151—21no—
207C42×C151—21no—
208C42×C151C2×D411yescharacteristic
209C42×C151C2×D411yescharacteristic
210C42×C151#4111yescharacteristic
211C42×C151C2411yescharacteristic
212C23×C151—41no—
213C23×C151—41no—
214C23×C151#12111yescharacteristic
215Q8×C151—21no—
216Q8×C151—21no—
217Q8×C151—21no—
218Q8×C151—21no—
219Q8×C151—42no—
220Q8×C151—41no—
221Q8×C151—41no—
222Q8×C151—41no—
223Q8×C151—41no—
224D4×C151—41no—
225D4×C151—41no—
226D4×C151—41no—
227D4×C151—41no—
228D4×C151—41no—
229D4×C151—41no—
230D4×C151—41no—
231D4×C151—41no—
232D4×C151—81no—
233D4×C151—81no—
234D4×C151—82no—
235D4×C151—82no—
236C2×C4×C151—21no—
237C2×C4×C151—21no—
238C2×C4×C151—21no—
239C2×C4×C151—21no—
240C2×C4×C151—21no—
241C2×C4×C151—21no—
242C2×C4×C151—21no—
243C2×C4×C151—21no—
244C2×C4×C151—41no—
245C2×C4×C151—41no—
246C2×C4×C151—41no—
247C2×C4×C151—82no—
248C2×C4×C151—82no—
249C2×C4×C151#12111yescharacteristic
250C2×C4×C151#12111yescharacteristic
251C2×C4×C151#12111yescharacteristic
252C2×C4×C151C22×D411yescharacteristic
253C2×C4×C151C22×D411yescharacteristic
254C2×C4×C151C2×#4111yescharacteristic
255C8×C151—21no—
256C8×C151—21no—
257C8×C151—21no—
258C8×C151—21no—
259C8×C151—41no—
260C8×C151—41no—
261C8×C151—41no—
262C8×C151—41no—
263C8×C151—41no—
264C8×C151—41no—
265C22×C151—21no—
266C22×C151—21no—
267C22×C151—21no—
268C22×C151—81no—
269C22×C151—81no—
270C22×C151—81no—
271C22×C151—81no—
272C22×C151—81no—
273C22×C151—81no—
274C22×C151C2×#12111yescharacteristic
275C4×C151—21no—
276C4×C151—21no—
277C4×C151—21no—
278C4×C151—21no—
279C4×C151—41no—
280C4×C151—41no—
281C4×C151—41no—
282C4×C151—41no—
283C4×C151—81no—
284C4×C151—81no—
285C4×C151#57611yescharacteristic
286C4×C151#57711yescharacteristic
287C4×C151#57711yescharacteristic
288C4×C151#57711yescharacteristic
289C2×C151—41no—
290C2×C151—161no—
291C2×C151—161no—
292C2×C151#304311yescharacteristic
293C2×C151#306211yescharacteristic
294C2×C151#306711yescharacteristic
295#19569C15111yesmaximal, characteristic, direct product factor, Sylow
296C151#1956911yescharacteristic, direct product factor, Sylow
297#3246C2×C15111yescharacteristic, complemented
298#3216C2×C15111yescharacteristic, complemented
299#3207C2×C15111yescharacteristic
300#2986C2×C15111yescharacteristic, complemented
301#1702C2×C15111yescharacteristic, complemented
302#1700C2×C15111yescharacteristic, complemented
303#1688C2×C15111yescharacteristic, complemented
304#1686C2×C15111yescharacteristic, complemented
305#1682C2×C15111yescharacteristic, complemented
306#1680C2×C15111yescharacteristic, complemented
307#1668C2×C15111yescharacteristic, complemented
308#1666C2×C15111yescharacteristic, complemented
309#1573C2×C15111yescharacteristic, complemented
310#1553C2×C15111yescharacteristic, complemented
311#1540C2×C15111yescharacteristic, complemented
312#533C22×C15111yescharacteristic
313#532C22×C15111yescharacteristic
314#532C22×C15111yescharacteristic
315#497—21no—
316#493C22×C15111yescharacteristic
317#492C22×C15111yescharacteristic
318#489—21no—
319#487C22×C15111yescharacteristic
320#486C22×C15111yescharacteristic
321#476—21no—
322#475C22×C15111yescharacteristic
323#475C22×C15111yescharacteristic
324#465—21no—
325#465—21no—
326#463—21no—
327#463—21no—
328#462C22×C15111yescharacteristic
329#462C22×C15111yescharacteristic
330#461—21no—
331#460C22×C15111yescharacteristic
332#460C22×C15111yescharacteristic
333#460C22×C15111yescharacteristic
334#460C22×C15111yescharacteristic
335#452—21no—
336#452—21no—
337#449—21no—
338#449—21no—
339#446—21no—
340#446C22×C15111yescharacteristic
341#446C22×C15111yescharacteristic
342C8×Q8—21no—
343C8×Q8C22×C15111yescharacteristic
344C8×Q8C22×C15111yescharacteristic
345#433—21no—
346#433—21no—
347#432C22×C15111yescharacteristic
348#431C22×C15111yescharacteristic
349#431C22×C15111yescharacteristic
350C2×C4⋊C8C22×C15111yescharacteristic
351#335C22×C15111yescharacteristic
352#335C22×C15111yescharacteristic
353#334C22×C15111yescharacteristic
354#334C22×C15111yescharacteristic
355#332C22×C15111yescharacteristic
356#332C22×C15111yescharacteristic
357#332C22×C15111yescharacteristic
358#332C22×C15111yescharacteristic
359#331C22×C15111yescharacteristic
360#331C22×C15111yescharacteristic
361#331C22×C15111yescharacteristic
362#331C22×C15111yescharacteristic
363C2×#41—21no—
364C2×#41—21no—
365C2×Q16—21no—
366C2×Q16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×D8—21no—
374C2×D8—21no—
375C22×C8—21no—
376C4⋊Q8D4×C15111yescharacteristic
377C4⋊Q8D4×C15111yescharacteristic
378C4⋊Q8C23×C15111yescharacteristic
379C4⋊Q8C23×C15111yescharacteristic
380#127C23×C15111yescharacteristic
381#127C23×C15111yescharacteristic
382#125—21no—
383#124—21no—
384#124—21no—
385C22⋊Q8—21no—
386C22⋊Q8D4×C15111yescharacteristic
387C22⋊Q8D4×C15111yescharacteristic
388#121—21no—
389#121—21no—
390#121—21no—
391#121—21no—
392C4×Q8—21no—
393C4×Q8C23×C15111yescharacteristic
394C4×Q8C23×C15111yescharacteristic
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399#117—21no—
400C2×C42C23×C15111yescharacteristic
401#106—21no—
402#106—21no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8D4×C15111yescharacteristic
409C4⋊C8D4×C15111yescharacteristic
410C4⋊C8C23×C15111yescharacteristic
411C4⋊C8C23×C15111yescharacteristic
412C4⋊C8C23×C15111yescharacteristic
413C4⋊C8C23×C15111yescharacteristic
414C4⋊C8C23×C15111yescharacteristic
415C4⋊C8C23×C15111yescharacteristic
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8D4×C15111yescharacteristic
431C22⋊C8D4×C15111yescharacteristic
432#97—21no—
433#97—21no—
434#97—21no—
435C4×C8—21no—
436C4×C8—21no—
437C4×C8—21no—
438C4×C8C23×C15111yescharacteristic
439C4×C8C23×C15111yescharacteristic
440#41—81no—
441#41—81no—
442#41—81no—
443#41—81no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8C2×D4×C15111yescharacteristic
448C2×Q8C2×D4×C15111yescharacteristic
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—41no—
456C2×D4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4C2×D4×C15111yescharacteristic
460C22×C4C2×D4×C15111yescharacteristic
461C22×C4#41×C15111yescharacteristic
462Q16—81no—
463Q16—81no—
464SD16—81no—
465SD16—81no—
466SD16—81no—
467SD16—81no—
468SD16—81no—
469SD16—81no—
470D8—81no—
471D8—81no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—81no—
479C2×C8C2×D4×C15111yescharacteristic
480C2×C8C2×D4×C15111yescharacteristic
481C2×C8C2×D4×C15111yescharacteristic
482C2×C8C2×D4×C15111yescharacteristic
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4C2×D4×C15111yescharacteristic
495C4⋊C4C2×D4×C15111yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C42—21no—
503C42—21no—
504C42C2×D4×C15111yescharacteristic
505C42C2×D4×C15111yescharacteristic
506C42#41×C15111yescharacteristic
507C42C24×C15111yescharacteristic
508C23—41no—
509C23—41no—
510C23#121×C15111yescharacteristic
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—21no—
515Q8—42no—
516Q8—41no—
517Q8—41no—
518Q8—41no—
519Q8—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—81no—
529D4—81no—
530D4—82no—
531D4—82no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—82no—
544C2×C4—82no—
545C2×C4#121×C15111yescharacteristic
546C2×C4#121×C15111yescharacteristic
547C2×C4#121×C15111yescharacteristic
548C2×C4C22×D4×C15111yescharacteristic
549C2×C4C22×D4×C15111yescharacteristic
550C2×C4C2×#41×C15111yescharacteristic
551C8—21no—
552C8—21no—
553C8—21no—
554C8—21no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—41no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22C2×#121×C15111yescharacteristic
571C4—21no—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—81no—
580C4—81no—
581C4#576×C15111yescharacteristic
582C4#577×C15111yescharacteristic
583C4#577×C15111yescharacteristic
584C4#577×C15111yescharacteristic
585C2—41no—
586C2—161no—
587C2—161no—
588C2#3043×C15111yescharacteristic
589C2#3062×C15111yescharacteristic
590C2#3067×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radical#3207×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. #3246×C151C2semidirect
2. #3216×C151C2semidirect
4. #2986×C151C2semidirect
5. #1702×C151C2semidirect
6. #1700×C151C2semidirect
7. #1688×C151C2semidirect
8. #1686×C151C2semidirect
9. #1682×C151C2semidirect
10. #1680×C151C2semidirect
11. #1668×C151C2semidirect
12. #1666×C151C2semidirect
13. #1573×C151C2semidirect
14. #1553×C151C2semidirect
15. #1540×C151C2semidirect
295. #19569C151direct (N × H)
296. C151#19569direct (N × H)
297. #3246C2×C151semidirect
298. #3216C2×C151semidirect
300. #2986C2×C151semidirect
301. #1702C2×C151semidirect
302. #1700C2×C151semidirect
303. #1688C2×C151semidirect
304. #1686C2×C151semidirect
305. #1682C2×C151semidirect
306. #1680C2×C151semidirect
307. #1668C2×C151semidirect
308. #1666C2×C151semidirect
309. #1573C2×C151semidirect
310. #1553C2×C151semidirect
311. #1540C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3246×C1512
#3216×C1512
#3207×C1512
#2986×C1512
#1702×C1512
#1700×C1512
#1688×C1512
#1686×C1512
#1682×C1512
#1680×C1512
#1668×C1512
#1666×C1512
#1573×C1512
#1553×C1512
#1540×C1512
#19569151