Finite Group Databasebeta

← C151×#19412 #50324337

Subgroups — C151×#19412 #50324337

Order 38656.

650 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3207×C151C211yesmaximal, characteristic, complemented
2#3115×C151C211yesmaximal, characteristic, complemented
3#3106×C151C211yesmaximal, characteristic, complemented
4#2988×C151C211yesmaximal, characteristic, complemented
5#1684×C151C211yesmaximal, characteristic, complemented
6#1683×C151C211yesmaximal, characteristic, complemented
7#1678×C151C211yesmaximal, characteristic, complemented
8#1677×C151C211yesmaximal, characteristic, complemented
9#1668×C151C211yesmaximal, characteristic, complemented
10#1667×C151C211yesmaximal, characteristic, complemented
11#1666×C151C211yesmaximal, characteristic, complemented
12#1665×C151C211yesmaximal, characteristic, complemented
13#1572×C151C211yesmaximal, characteristic, complemented
14#1551×C151C211yesmaximal, characteristic, complemented
15#1540×C151C211yesmaximal, characteristic, complemented
16#532×C151C2211yescharacteristic
17#532×C151C2211yescharacteristic
18C4×#41×C151C2211yescharacteristic
19#493×C151C2211yescharacteristic
20#492×C151C2211yescharacteristic
21#487×C151C2211yescharacteristic
22#486×C151C2211yescharacteristic
23#482×C151—21no—
24#482×C151—21no—
25#477×C151C2211yescharacteristic
26#476×C151C2211yescharacteristic
27#475×C151C2211yescharacteristic
28#474×C151C2211yescharacteristic
29#463×C151—21no—
30#463×C151—21no—
31#460×C151C2211yescharacteristic
32#460×C151C2211yescharacteristic
33#459×C151C2211yescharacteristic
34#459×C151C2211yescharacteristic
35#449×C151—21no—
36#449×C151—21no—
37#449×C151—21no—
38#449×C151—21no—
39C8×Q8×C151C2211yescharacteristic
40C8×Q8×C151C2211yescharacteristic
41#442×C151—21no—
42#440×C151—21no—
43C4×SD16×C151—21no—
44C4×D8×C151—21no—
45C8×D4×C151—21no—
46C8×D4×C151—21no—
47C8×D4×C151C2211yescharacteristic
48C8×D4×C151C2211yescharacteristic
49#432×C151C2211yescharacteristic
50#431×C151—21no—
51#431×C151C2211yescharacteristic
52#431×C151C2211yescharacteristic
53C2×C4⋊C8×C151—21no—
54C2×C4⋊C8×C151C2211yescharacteristic
55#335×C151C2211yescharacteristic
56#335×C151C2211yescharacteristic
57#334×C151C2211yescharacteristic
58#334×C151C2211yescharacteristic
59#333×C151C2211yescharacteristic
60#333×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×#41×C151D411yescharacteristic
70C2×SD16×C151—21no—
71C2×SD16×C151—21no—
72C2×SD16×C151—21no—
73C2×SD16×C151—21no—
74C2×D8×C151—21no—
75C2×D8×C151—21no—
76C2×D8×C151—21no—
77C2×D8×C151—21no—
78C22×C8×C151—21no—
79C22×C8×C151—21no—
80C22×C8×C151—21no—
81C4⋊Q8×C151C2311yescharacteristic
82C4⋊Q8×C151C2311yescharacteristic
83#127×C151C2311yescharacteristic
84#127×C151C2311yescharacteristic
85#124×C151—21no—
86#124×C151—21no—
87#121×C151—21no—
88#121×C151—21no—
89#121×C151—21no—
90#121×C151—21no—
91C4×Q8×C151D411yescharacteristic
92C4×Q8×C151C2311yescharacteristic
93C4×D4×C151—21no—
94C4×D4×C151—21no—
95C4×D4×C151—21no—
96C4×D4×C151—21no—
97C4×D4×C151—21no—
98C4×D4×C151—21no—
99C4×D4×C151D411yescharacteristic
100C4×D4×C151C2311yescharacteristic
101#117×C151—21no—
102#117×C151D411yescharacteristic
103C2×C42×C151—21no—
104C2×C42×C151C2311yescharacteristic
105#107×C151—21no—
106#107×C151—21no—
107#106×C151—21no—
108#106×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#102×C151—21no—
125#102×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×C151—21no—
135C22⋊C8×C151—21no—
136C22⋊C8×C151D411yescharacteristic
137C22⋊C8×C151D411yescharacteristic
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—22no—
145#41×C151—22no—
146#41×C151—81no—
147#41×C151—81no—
148#41×C151—82no—
149C2×Q8×C151—21no—
150C2×Q8×C151—21no—
151C2×Q8×C151C2×D411yescharacteristic
152C2×D4×C151—21no—
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—
161C2×D4×C151C2×D411yescharacteristic
162C22×C4×C151—21no—
163C22×C4×C151—21no—
164C22×C4×C151—21no—
165C22×C4×C151—41no—
166C22×C4×C151—41no—
167C22×C4×C151C2×D411yescharacteristic
168C22×C4×C151C2×D411yescharacteristic
169C22×C4×C151#4111yescharacteristic
170SD16×C151—42no—
171SD16×C151—42no—
172SD16×C151—81no—
173SD16×C151—81no—
174D8×C151—42no—
175D8×C151—42no—
176D8×C151—81no—
177D8×C151—81no—
178C2×C8×C151—21no—
179C2×C8×C151—21no—
180C2×C8×C151—21no—
181C2×C8×C151—21no—
182C2×C8×C151—21no—
183C2×C8×C151—21no—
184C2×C8×C151—81no—
185C2×C8×C151—81no—
186C2×C8×C151—81no—
187C2×C8×C151C2×D411yescharacteristic
188C2×C8×C151C2×D411yescharacteristic
189C2×C8×C151C2×D411yescharacteristic
190C2×C8×C151C2×D411yescharacteristic
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×C151C2×D411yescharacteristic
198C4⋊C4×C151C2×D411yescharacteristic
199C22⋊C4×C151—21no—
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×C151—21no—
209C42×C151C2×D411yescharacteristic
210C42×C151C2×D411yescharacteristic
211C42×C151#4111yescharacteristic
212C42×C151C2411yescharacteristic
213C23×C151—21no—
214C23×C151—41no—
215C23×C151—41no—
216C23×C151#12111yescharacteristic
217Q8×C151—21no—
218Q8×C151—41no—
219Q8×C151—41no—
220Q8×C151—81no—
221Q8×C151#13512yes—
222D4×C151—24no—
223D4×C151—21no—
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—
236D4×C151#13512yes—
237C2×C4×C151—24no—
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—21no—
245C2×C4×C151—41no—
246C2×C4×C151—41no—
247C2×C4×C151—41no—
248C2×C4×C151—41no—
249C2×C4×C151—41no—
250C2×C4×C151—81no—
251C2×C4×C151—82no—
252C2×C4×C151—82no—
253C2×C4×C151#12111yescharacteristic
254C2×C4×C151#12111yescharacteristic
255C2×C4×C151#12111yescharacteristic
256C2×C4×C151C22×D411yescharacteristic
257C2×C4×C151C22×D411yescharacteristic
258C2×C4×C151C2×#4111yescharacteristic
259C8×C151—21no—
260C8×C151—21no—
261C8×C151—21no—
262C8×C151—21no—
263C8×C151—41no—
264C8×C151—41no—
265C8×C151—41no—
266C8×C151—41no—
267C8×C151—41no—
268C8×C151—41no—
269C22×C151—21no—
270C22×C151—21no—
271C22×C151—22no—
272C22×C151—21no—
273C22×C151—41no—
274C22×C151—41no—
275C22×C151—81no—
276C22×C151—81no—
277C22×C151—81no—
278C22×C151—81no—
279C22×C151—81no—
280C22×C151—81no—
281C22×C151C2×#12111yescharacteristic
282C4×C151—21no—
283C4×C151—21no—
284C4×C151—22no—
285C4×C151—21no—
286C4×C151—21no—
287C4×C151—41no—
288C4×C151—41no—
289C4×C151—81no—
290C4×C151—81no—
291C4×C151C2×#13511yescharacteristic
292C4×C151C2×#13511yescharacteristic
293C4×C151#57611yescharacteristic
294C4×C151#57711yescharacteristic
295C2×C151—41no—
296C2×C151—42no—
297C2×C151—161no—
298C2×C151—161no—
299C2×C151#304511yescharacteristic
300C2×C151#305011yescharacteristic
301C2×C151#306811yescharacteristic
302#19412C15111yesmaximal, characteristic, direct product factor, Sylow
303C151#1941211yescharacteristic, direct product factor, Sylow
304#3207C2×C15111yescharacteristic, complemented
305#3115C2×C15111yescharacteristic, complemented
306#3106C2×C15111yescharacteristic, complemented
307#2988C2×C15111yescharacteristic, complemented
308#1684C2×C15111yescharacteristic, complemented
309#1683C2×C15111yescharacteristic, complemented
310#1678C2×C15111yescharacteristic, complemented
311#1677C2×C15111yescharacteristic, complemented
312#1668C2×C15111yescharacteristic, complemented
313#1667C2×C15111yescharacteristic, complemented
314#1666C2×C15111yescharacteristic, complemented
315#1665C2×C15111yescharacteristic, complemented
316#1572C2×C15111yescharacteristic, complemented
317#1551C2×C15111yescharacteristic, complemented
318#1540C2×C15111yescharacteristic, complemented
319#532C22×C15111yescharacteristic
320#532C22×C15111yescharacteristic
321C4×#41C22×C15111yescharacteristic
322#493C22×C15111yescharacteristic
323#492C22×C15111yescharacteristic
324#487C22×C15111yescharacteristic
325#486C22×C15111yescharacteristic
326#482—21no—
327#482—21no—
328#477C22×C15111yescharacteristic
329#476C22×C15111yescharacteristic
330#475C22×C15111yescharacteristic
331#474C22×C15111yescharacteristic
332#463—21no—
333#463—21no—
334#460C22×C15111yescharacteristic
335#460C22×C15111yescharacteristic
336#459C22×C15111yescharacteristic
337#459C22×C15111yescharacteristic
338#449—21no—
339#449—21no—
340#449—21no—
341#449—21no—
342C8×Q8C22×C15111yescharacteristic
343C8×Q8C22×C15111yescharacteristic
344#442—21no—
345#440—21no—
346C4×SD16—21no—
347C4×D8—21no—
348C8×D4—21no—
349C8×D4—21no—
350C8×D4C22×C15111yescharacteristic
351C8×D4C22×C15111yescharacteristic
352#432C22×C15111yescharacteristic
353#431—21no—
354#431C22×C15111yescharacteristic
355#431C22×C15111yescharacteristic
356C2×C4⋊C8—21no—
357C2×C4⋊C8C22×C15111yescharacteristic
358#335C22×C15111yescharacteristic
359#335C22×C15111yescharacteristic
360#334C22×C15111yescharacteristic
361#334C22×C15111yescharacteristic
362#333C22×C15111yescharacteristic
363#333C22×C15111yescharacteristic
364#332C22×C15111yescharacteristic
365#332C22×C15111yescharacteristic
366#331C22×C15111yescharacteristic
367#331C22×C15111yescharacteristic
368#331C22×C15111yescharacteristic
369#331C22×C15111yescharacteristic
370C2×#41—21no—
371C2×#41—21no—
372C2×#41D4×C15111yescharacteristic
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×D8—21no—
378C2×D8—21no—
379C2×D8—21no—
380C2×D8—21no—
381C22×C8—21no—
382C22×C8—21no—
383C22×C8—21no—
384C4⋊Q8C23×C15111yescharacteristic
385C4⋊Q8C23×C15111yescharacteristic
386#127C23×C15111yescharacteristic
387#127C23×C15111yescharacteristic
388#124—21no—
389#124—21no—
390#121—21no—
391#121—21no—
392#121—21no—
393#121—21no—
394C4×Q8D4×C15111yescharacteristic
395C4×Q8C23×C15111yescharacteristic
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4D4×C15111yescharacteristic
403C4×D4C23×C15111yescharacteristic
404#117—21no—
405#117D4×C15111yescharacteristic
406C2×C42—21no—
407C2×C42C23×C15111yescharacteristic
408#107—21no—
409#107—21no—
410#106—21no—
411#106—21no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414C4⋊C8—21no—
415C4⋊C8D4×C15111yescharacteristic
416C4⋊C8D4×C15111yescharacteristic
417C4⋊C8C23×C15111yescharacteristic
418C4⋊C8C23×C15111yescharacteristic
419C4⋊C8C23×C15111yescharacteristic
420C4⋊C8C23×C15111yescharacteristic
421C4⋊C8C23×C15111yescharacteristic
422C4⋊C8C23×C15111yescharacteristic
423#103—21no—
424#103—21no—
425#103—21no—
426#103—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435C22⋊C8—21no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8D4×C15111yescharacteristic
440C22⋊C8D4×C15111yescharacteristic
441#97—21no—
442C4×C8—21no—
443C4×C8—21no—
444C4×C8—21no—
445C4×C8C23×C15111yescharacteristic
446C4×C8C23×C15111yescharacteristic
447#41—22no—
448#41—22no—
449#41—81no—
450#41—81no—
451#41—82no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8C2×D4×C15111yescharacteristic
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4C2×D4×C15111yescharacteristic
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4C2×D4×C15111yescharacteristic
471C22×C4C2×D4×C15111yescharacteristic
472C22×C4#41×C15111yescharacteristic
473SD16—42no—
474SD16—42no—
475SD16—81no—
476SD16—81no—
477D8—42no—
478D8—42no—
479D8—81no—
480D8—81no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—81no—
488C2×C8—81no—
489C2×C8—81no—
490C2×C8C2×D4×C15111yescharacteristic
491C2×C8C2×D4×C15111yescharacteristic
492C2×C8C2×D4×C15111yescharacteristic
493C2×C8C2×D4×C15111yescharacteristic
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4C2×D4×C15111yescharacteristic
501C4⋊C4C2×D4×C15111yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42C2×D4×C15111yescharacteristic
513C42C2×D4×C15111yescharacteristic
514C42#41×C15111yescharacteristic
515C42C24×C15111yescharacteristic
516C23—21no—
517C23—41no—
518C23—41no—
519C23#121×C15111yescharacteristic
520Q8—21no—
521Q8—41no—
522Q8—41no—
523Q8—81no—
524Q8#135×C15112yes—
525D4—24no—
526D4—21no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—81no—
536D4—81no—
537D4—82no—
538D4—82no—
539D4#135×C15112yes—
540C2×C4—24no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—81no—
554C2×C4—82no—
555C2×C4—82no—
556C2×C4#121×C15111yescharacteristic
557C2×C4#121×C15111yescharacteristic
558C2×C4#121×C15111yescharacteristic
559C2×C4C22×D4×C15111yescharacteristic
560C2×C4C22×D4×C15111yescharacteristic
561C2×C4C2×#41×C15111yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—41no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—41no—
571C8—41no—
572C22—21no—
573C22—21no—
574C22—22no—
575C22—21no—
576C22—41no—
577C22—41no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22C2×#121×C15111yescharacteristic
585C4—21no—
586C4—21no—
587C4—22no—
588C4—21no—
589C4—21no—
590C4—41no—
591C4—41no—
592C4—81no—
593C4—81no—
594C4C2×#135×C15111yescharacteristic
595C4C2×#135×C15111yescharacteristic
596C4#576×C15111yescharacteristic
597C4#577×C15111yescharacteristic
598C2—41no—
599C2—42no—
600C2—161no—
601C2—161no—
602C2#3045×C15111yescharacteristic
603C2#3050×C15111yescharacteristic
604C2#3068×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
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. #3207×C151C2semidirect
2. #3115×C151C2semidirect
3. #3106×C151C2semidirect
4. #2988×C151C2semidirect
5. #1684×C151C2semidirect
6. #1683×C151C2semidirect
7. #1678×C151C2semidirect
8. #1677×C151C2semidirect
9. #1668×C151C2semidirect
10. #1667×C151C2semidirect
11. #1666×C151C2semidirect
12. #1665×C151C2semidirect
13. #1572×C151C2semidirect
14. #1551×C151C2semidirect
15. #1540×C151C2semidirect
302. #19412C151direct (N × H)
303. C151#19412direct (N × H)
304. #3207C2×C151semidirect
305. #3115C2×C151semidirect
306. #3106C2×C151semidirect
307. #2988C2×C151semidirect
308. #1684C2×C151semidirect
309. #1683C2×C151semidirect
310. #1678C2×C151semidirect
311. #1677C2×C151semidirect
312. #1668C2×C151semidirect
313. #1667C2×C151semidirect
314. #1666C2×C151semidirect
315. #1665C2×C151semidirect
316. #1572C2×C151semidirect
317. #1551C2×C151semidirect
318. #1540C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3207×C1512
#3115×C1512
#3106×C1512
#2988×C1512
#1684×C1512
#1683×C1512
#1678×C1512
#1677×C1512
#1668×C1512
#1667×C1512
#1666×C1512
#1665×C1512
#1572×C1512
#1551×C1512
#1540×C1512
#19412151