Finite Group Databasebeta

← C151×#19250 #50324175

Subgroups — C151×#19250 #50324175

Order 38656.

624 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3247×C151C211yesmaximal, characteristic, complemented
2#3212×C151C211yesmaximal, characteristic, complemented
3#3184×C151C211yesmaximal, characteristic, complemented
4#2969×C151C211yesmaximal, characteristic, complemented
5#1702×C151C211yesmaximal, characteristic, complemented
6#1698×C151C211yesmaximal, characteristic, complemented
7#1691×C151C211yesmaximal, characteristic, complemented
8#1687×C151C211yesmaximal, characteristic, complemented
9#1681×C151C211yesmaximal, characteristic, complemented
10#1677×C151C211yesmaximal, characteristic, complemented
11#1672×C151C211yesmaximal, characteristic, complemented
12#1668×C151C211yesmaximal, characteristic, complemented
13#1565×C151C211yesmaximal, characteristic, complemented
14#1543×C151C211yesmaximal, characteristic, complemented
15#1540×C151C211yesmaximal, characteristic, complemented
16#532×C151C2211yescharacteristic
17#532×C151C2211yescharacteristic
18#529×C151C2211yescharacteristic
19#498×C151C2211yescharacteristic
20#495×C151—21no—
21#493×C151C2211yescharacteristic
22#488×C151—21no—
23#486×C151C2211yescharacteristic
24#486×C151C2211yescharacteristic
25#478×C151—21no—
26#477×C151C2211yescharacteristic
27#476×C151C2211yescharacteristic
28#469×C151—21no—
29#469×C151—21no—
30#466×C151—21no—
31#465×C151—21no—
32#463×C151—21no—
33#462×C151C2211yescharacteristic
34#461×C151C2211yescharacteristic
35#460×C151C2211yescharacteristic
36#460×C151C2211yescharacteristic
37#459×C151C2211yescharacteristic
38#459×C151C2211yescharacteristic
39#452×C151—21no—
40#449×C151—21no—
41#446×C151C2211yescharacteristic
42C8×Q8×C151C2211yescharacteristic
43#442×C151—21no—
44#442×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#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×Q16×C151—21no—
70C2×SD16×C151—21no—
71C2×SD16×C151—21no—
72C2×SD16×C151—21no—
73C2×D8×C151—21no—
74C2×D8×C151—21no—
75C2×D8×C151—21no—
76C2×D8×C151—21no—
77C2×M16×C151—21no—
78C2×M16×C151D411yescharacteristic
79C2×M16×C151D411yescharacteristic
80C22×C8×C151—21no—
81C22×C8×C151—21no—
82C4⋊Q8×C151C2311yescharacteristic
83C4⋊Q8×C151C2311yescharacteristic
84#127×C151C2311yescharacteristic
85#127×C151C2311yescharacteristic
86#126×C151—21no—
87#125×C151D411yescharacteristic
88#124×C151—21no—
89#124×C151—21no—
90#124×C151D411yescharacteristic
91#123×C151—21no—
92C22⋊Q8×C151D411yescharacteristic
93#121×C151—21no—
94#121×C151—21no—
95#121×C151—21no—
96#121×C151—21no—
97#121×C151D411yescharacteristic
98C4×Q8×C151C2311yescharacteristic
99C4×D4×C151—21no—
100C4×D4×C151—21no—
101C4×D4×C151—21no—
102C4×D4×C151—21no—
103C4×D4×C151—21no—
104C4×D4×C151C2311yescharacteristic
105#117×C151—21no—
106C2×C42×C151C2311yescharacteristic
107#107×C151—21no—
108#106×C151—21no—
109#106×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#102×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—
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—
146#41×C151—82no—
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—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—41no—
158C2×D4×C151—41no—
159C2×D4×C151C2×D411yescharacteristic
160C22×C4×C151—21no—
161C22×C4×C151—41no—
162C22×C4×C151—41no—
163C22×C4×C151C2×D411yescharacteristic
164C22×C4×C151C2×D411yescharacteristic
165C22×C4×C151#4111yescharacteristic
166Q16×C151—81no—
167SD16×C151—81no—
168SD16×C151—81no—
169SD16×C151—81no—
170D8×C151—42no—
171D8×C151—42no—
172D8×C151—81no—
173D8×C151—81no—
174M16×C151—22no—
175M16×C151—41no—
176M16×C151—42no—
177C2×C8×C151—21no—
178C2×C8×C151—21no—
179C2×C8×C151—21no—
180C2×C8×C151—21no—
181C2×C8×C151—21no—
182C2×C8×C151—21no—
183C2×C8×C151—42no—
184C2×C8×C151—81no—
185C2×C8×C151C2×D411yescharacteristic
186C2×C8×C151C2×D411yescharacteristic
187C2×C8×C151C2×D411yescharacteristic
188C2×C8×C151C2×D411yescharacteristic
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×C151C2×D411yescharacteristic
198C4⋊C4×C151C2×D411yescharacteristic
199C22⋊C4×C151—21no—
200C22⋊C4×C151—21no—
201C22⋊C4×C151—21no—
202C22⋊C4×C151—21no—
203C22⋊C4×C151—21no—
204C22⋊C4×C151—41no—
205C22⋊C4×C151—41no—
206C22⋊C4×C151—41no—
207C22⋊C4×C151—41no—
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—21no—
219Q8×C151—41no—
220Q8×C151—41no—
221Q8×C151—81no—
222D4×C151—21no—
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—81no—
235D4×C151—82no—
236D4×C151—82no—
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—41no—
248C2×C4×C151—41no—
249C2×C4×C151—82no—
250C2×C4×C151—82no—
251C2×C4×C151#12111yescharacteristic
252C2×C4×C151#12111yescharacteristic
253C2×C4×C151#12111yescharacteristic
254C2×C4×C151C22×D411yescharacteristic
255C2×C4×C151C22×D411yescharacteristic
256C2×C4×C151C2×#4111yescharacteristic
257C8×C151—21no—
258C8×C151—21no—
259C8×C151—21no—
260C8×C151—41no—
261C8×C151—41no—
262C8×C151—41no—
263C8×C151—41no—
264C8×C151—41no—
265C8×C151—41no—
266C8×C151#13512yes—
267C22×C151—21no—
268C22×C151—21no—
269C22×C151—21no—
270C22×C151—41no—
271C22×C151—41no—
272C22×C151—41no—
273C22×C151—81no—
274C22×C151—81no—
275C22×C151—81no—
276C22×C151—81no—
277C22×C151—81no—
278C22×C151—81no—
279C22×C151C2×#12111yescharacteristic
280C4×C151—21no—
281C4×C151—21no—
282C4×C151—21no—
283C4×C151—21no—
284C4×C151—41no—
285C4×C151—41no—
286C4×C151—41no—
287C4×C151—81no—
288C4×C151—81no—
289C4×C151C2×#13511yescharacteristic
290C4×C151#57511yescharacteristic
291C4×C151#57611yescharacteristic
292C4×C151#57711yescharacteristic
293C2×C151—41no—
294C2×C151—81no—
295C2×C151—161no—
296C2×C151—161no—
297C2×C151#303511yescharacteristic
298C2×C151#306211yescharacteristic
299C2×C151#306811yescharacteristic
300#19250C15111yesmaximal, characteristic, direct product factor, Sylow
301C151#1925011yescharacteristic, direct product factor, Sylow
302#3247C2×C15111yescharacteristic, complemented
303#3212C2×C15111yescharacteristic, complemented
304#3184C2×C15111yescharacteristic, complemented
305#2969C2×C15111yescharacteristic, complemented
306#1702C2×C15111yescharacteristic, complemented
307#1698C2×C15111yescharacteristic, complemented
308#1691C2×C15111yescharacteristic, complemented
309#1687C2×C15111yescharacteristic, complemented
310#1681C2×C15111yescharacteristic, complemented
311#1677C2×C15111yescharacteristic, complemented
312#1672C2×C15111yescharacteristic, complemented
313#1668C2×C15111yescharacteristic, complemented
314#1565C2×C15111yescharacteristic, complemented
315#1543C2×C15111yescharacteristic, complemented
316#1540C2×C15111yescharacteristic, complemented
317#532C22×C15111yescharacteristic
318#532C22×C15111yescharacteristic
319#529C22×C15111yescharacteristic
320#498C22×C15111yescharacteristic
321#495—21no—
322#493C22×C15111yescharacteristic
323#488—21no—
324#486C22×C15111yescharacteristic
325#486C22×C15111yescharacteristic
326#478—21no—
327#477C22×C15111yescharacteristic
328#476C22×C15111yescharacteristic
329#469—21no—
330#469—21no—
331#466—21no—
332#465—21no—
333#463—21no—
334#462C22×C15111yescharacteristic
335#461C22×C15111yescharacteristic
336#460C22×C15111yescharacteristic
337#460C22×C15111yescharacteristic
338#459C22×C15111yescharacteristic
339#459C22×C15111yescharacteristic
340#452—21no—
341#449—21no—
342#446C22×C15111yescharacteristic
343C8×Q8C22×C15111yescharacteristic
344#442—21no—
345#442—21no—
346#436—21no—
347#436C22×C15111yescharacteristic
348#435—21no—
349C8×D4C22×C15111yescharacteristic
350#433—21no—
351#431C22×C15111yescharacteristic
352#431C22×C15111yescharacteristic
353C2×C4⋊C8C22×C15111yescharacteristic
354#405—21no—
355C4×M16C22×C15111yescharacteristic
356#335C22×C15111yescharacteristic
357#335C22×C15111yescharacteristic
358#334C22×C15111yescharacteristic
359#334C22×C15111yescharacteristic
360#333C22×C15111yescharacteristic
361#333C22×C15111yescharacteristic
362#332C22×C15111yescharacteristic
363#332C22×C15111yescharacteristic
364#331C22×C15111yescharacteristic
365#331C22×C15111yescharacteristic
366#331C22×C15111yescharacteristic
367#331C22×C15111yescharacteristic
368C2×#41—21no—
369C2×#41—21no—
370C2×Q16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×D8—21no—
375C2×D8—21no—
376C2×D8—21no—
377C2×D8—21no—
378C2×M16—21no—
379C2×M16D4×C15111yescharacteristic
380C2×M16D4×C15111yescharacteristic
381C22×C8—21no—
382C22×C8—21no—
383C4⋊Q8C23×C15111yescharacteristic
384C4⋊Q8C23×C15111yescharacteristic
385#127C23×C15111yescharacteristic
386#127C23×C15111yescharacteristic
387#126—21no—
388#125D4×C15111yescharacteristic
389#124—21no—
390#124—21no—
391#124D4×C15111yescharacteristic
392#123—21no—
393C22⋊Q8D4×C15111yescharacteristic
394#121—21no—
395#121—21no—
396#121—21no—
397#121—21no—
398#121D4×C15111yescharacteristic
399C4×Q8C23×C15111yescharacteristic
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4C23×C15111yescharacteristic
406#117—21no—
407C2×C42C23×C15111yescharacteristic
408#107—21no—
409#106—21no—
410#106—21no—
411#106—21no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414C4⋊C8—21no—
415C4⋊C8C23×C15111yescharacteristic
416C4⋊C8C23×C15111yescharacteristic
417C4⋊C8C23×C15111yescharacteristic
418C4⋊C8C23×C15111yescharacteristic
419C4⋊C8C23×C15111yescharacteristic
420C4⋊C8C23×C15111yescharacteristic
421#103—21no—
422#103—21no—
423#103—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433C22⋊C8—21no—
434C22⋊C8—21no—
435C22⋊C8—21no—
436C22⋊C8—21no—
437#97—21no—
438#97D4×C15111yescharacteristic
439#97D4×C15111yescharacteristic
440C4×C8—21no—
441C4×C8—21no—
442C4×C8—21no—
443C4×C8C23×C15111yescharacteristic
444C4×C8C23×C15111yescharacteristic
445#41—81no—
446#41—81no—
447#41—82no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8C2×D4×C15111yescharacteristic
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4C2×D4×C15111yescharacteristic
461C22×C4—21no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4C2×D4×C15111yescharacteristic
465C22×C4C2×D4×C15111yescharacteristic
466C22×C4#41×C15111yescharacteristic
467Q16—81no—
468SD16—81no—
469SD16—81no—
470SD16—81no—
471D8—42no—
472D8—42no—
473D8—81no—
474D8—81no—
475M16—22no—
476M16—41no—
477M16—42no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—42no—
485C2×C8—81no—
486C2×C8C2×D4×C15111yescharacteristic
487C2×C8C2×D4×C15111yescharacteristic
488C2×C8C2×D4×C15111yescharacteristic
489C2×C8C2×D4×C15111yescharacteristic
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4C2×D4×C15111yescharacteristic
499C4⋊C4C2×D4×C15111yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C42—21no—
510C42C2×D4×C15111yescharacteristic
511C42C2×D4×C15111yescharacteristic
512C42#41×C15111yescharacteristic
513C42C24×C15111yescharacteristic
514C23—21no—
515C23—41no—
516C23—41no—
517C23#121×C15111yescharacteristic
518Q8—21no—
519Q8—21no—
520Q8—41no—
521Q8—41no—
522Q8—81no—
523D4—21no—
524D4—21no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—81no—
534D4—81no—
535D4—81no—
536D4—82no—
537D4—82no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—82no—
551C2×C4—82no—
552C2×C4#121×C15111yescharacteristic
553C2×C4#121×C15111yescharacteristic
554C2×C4#121×C15111yescharacteristic
555C2×C4C22×D4×C15111yescharacteristic
556C2×C4C22×D4×C15111yescharacteristic
557C2×C4C2×#41×C15111yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8#135×C15112yes—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22C2×#121×C15111yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—81no—
589C4—81no—
590C4C2×#135×C15111yescharacteristic
591C4#575×C15111yescharacteristic
592C4#576×C15111yescharacteristic
593C4#577×C15111yescharacteristic
594C2—41no—
595C2—81no—
596C2—161no—
597C2—161no—
598C2#3035×C15111yescharacteristic
599C2#3062×C15111yescharacteristic
600C2#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. #3247×C151C2semidirect
2. #3212×C151C2semidirect
3. #3184×C151C2semidirect
4. #2969×C151C2semidirect
5. #1702×C151C2semidirect
6. #1698×C151C2semidirect
7. #1691×C151C2semidirect
8. #1687×C151C2semidirect
9. #1681×C151C2semidirect
10. #1677×C151C2semidirect
11. #1672×C151C2semidirect
12. #1668×C151C2semidirect
13. #1565×C151C2semidirect
14. #1543×C151C2semidirect
15. #1540×C151C2semidirect
300. #19250C151direct (N × H)
301. C151#19250direct (N × H)
302. #3247C2×C151semidirect
303. #3212C2×C151semidirect
304. #3184C2×C151semidirect
305. #2969C2×C151semidirect
306. #1702C2×C151semidirect
307. #1698C2×C151semidirect
308. #1691C2×C151semidirect
309. #1687C2×C151semidirect
310. #1681C2×C151semidirect
311. #1677C2×C151semidirect
312. #1672C2×C151semidirect
313. #1668C2×C151semidirect
314. #1565C2×C151semidirect
315. #1543C2×C151semidirect
316. #1540C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3247×C1512
#3212×C1512
#3184×C1512
#2969×C1512
#1702×C1512
#1698×C1512
#1691×C1512
#1687×C1512
#1681×C1512
#1677×C1512
#1672×C1512
#1668×C1512
#1565×C1512
#1543×C1512
#1540×C1512
#19250151