Finite Group Databasebeta

← C151×#18572 #50323497

Subgroups — C151×#18572 #50323497

Order 38656.

954 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3522×C151C211yesmaximal, characteristic
2#3239×C151C211yesmaximal, characteristic, complemented
3#3141×C151C211yesmaximal, characteristic, complemented
4C2×#462×C151C211yesmaximal, characteristic, complemented
5#1645×C151C212yesmaximal, complemented
6#1644×C151C212yesmaximal, complemented
7#1641×C151C212yesmaximal, complemented
8#1640×C151C212yesmaximal, complemented
9#1551×C151C211yesmaximal, characteristic, complemented
10#1491×C151C211yesmaximal, characteristic, complemented
11#1483×C151C211yesmaximal, characteristic, complemented
12C22×Q16×C151—21no—
13#559×C151—21no—
14#559×C151C2211yescharacteristic
15Q82×C151C2211yescharacteristic
16#554×C151—21no—
17#554×C151C2211yescharacteristic
18#550×C151C2211yescharacteristic
19#548×C151—21no—
20#547×C151—22no—
21#547×C151—21no—
22#542×C151—22no—
23#542×C151—21no—
24#532×C151—21no—
25#532×C151C2211yescharacteristic
26C2×C4⋊Q8×C151C2211yescharacteristic
27#529×C151—21no—
28#529×C151C2211yescharacteristic
29#520×C151—21no—
30C2×C4×Q8×C151C2211yescharacteristic
31#501×C151—21no—
32#489×C151—22no—
33#489×C151—21no—
34#487×C151C2212yes—
35#486×C151C2212yes—
36#484×C151—21no—
37#481×C151—21no—
38#475×C151C2212yes—
39#474×C151C2212yes—
40#462×C151—21no—
41#462×C151—21no—
42#462×C151C2212yes—
43#462×C151C2212yes—
44#432×C151C2211yescharacteristic
45C2×C4⋊C8×C151C2211yescharacteristic
46#417×C151—22no—
47C2×#103×C151—21no—
48C4×M16×C151C2211yescharacteristic
49#333×C151C2212yes—
50#331×C151C2212yes—
51Q8⋊C8×C151C2212yes—
52Q8⋊C8×C151C2212yes—
53Q8⋊C8×C151C2212yes—
54D4⋊C8×C151C2212yes—
55C2×#41×C151—22no—
56C2×#41×C151—21no—
57C2×#41×C151D412yes—
58C22×Q8×C151—21no—
59C22×Q8×C151D411yescharacteristic
60C2×Q16×C151—22no—
61C2×Q16×C151—22no—
62C2×Q16×C151—44no—
63C2×M16×C151—21no—
64C22×C8×C151—21no—
65C4⋊Q8×C151—21no—
66C4⋊Q8×C151—21no—
67C4⋊Q8×C151—21no—
68C4⋊Q8×C151—22no—
69C4⋊Q8×C151—21no—
70C4⋊Q8×C151—21no—
71C4⋊Q8×C151C2312yes—
72C4⋊Q8×C151C2311yescharacteristic
73#127×C151—21no—
74#127×C151C2311yescharacteristic
75#126×C151—22no—
76#126×C151—21no—
77#125×C151—21no—
78#125×C151D411yescharacteristic
79#124×C151—22no—
80#124×C151—22no—
81#124×C151—21no—
82#124×C151—21no—
83#124×C151D411yescharacteristic
84#124×C151D412yes—
85#123×C151—22no—
86#123×C151—22no—
87#123×C151—22no—
88#123×C151—22no—
89#123×C151—21no—
90C22⋊Q8×C151—22no—
91C22⋊Q8×C151—22no—
92C22⋊Q8×C151—22no—
93C22⋊Q8×C151—22no—
94C22⋊Q8×C151—21no—
95C22⋊Q8×C151D411yescharacteristic
96#121×C151—22no—
97#121×C151—22no—
98#121×C151—21no—
99#121×C151—21no—
100#121×C151—21no—
101#121×C151D411yescharacteristic
102C4×Q8×C151—21no—
103C4×Q8×C151—21no—
104C4×Q8×C151—21no—
105C4×Q8×C151—21no—
106C4×Q8×C151D411yescharacteristic
107C4×Q8×C151D411yescharacteristic
108C4×Q8×C151C2311yescharacteristic
109C4×Q8×C151C2311yescharacteristic
110C4×Q8×C151C2311yescharacteristic
111C4×D4×C151—22no—
112C4×D4×C151—22no—
113C4×D4×C151—22no—
114C4×D4×C151—21no—
115C4×D4×C151—21no—
116C4×D4×C151—21no—
117C4×D4×C151—21no—
118C4×D4×C151—21no—
119C4×D4×C151—21no—
120C4×D4×C151—21no—
121C4×D4×C151C2311yescharacteristic
122#117×C151—22no—
123#117×C151—21no—
124C2×C4⋊C4×C151—22no—
125C2×C4⋊C4×C151—21no—
126C2×C4⋊C4×C151—21no—
127C2×C4⋊C4×C151—21no—
128C2×C4⋊C4×C151—21no—
129C2×C4⋊C4×C151D411yescharacteristic
130C2×C42×C151—21no—
131C2×C42×C151C2311yescharacteristic
132#107×C151—22no—
133#106×C151—22no—
134C4⋊C8×C151—21no—
135C4⋊C8×C151C2312yes—
136C4⋊C8×C151C2312yes—
137#103×C151—22no—
138#103×C151—22no—
139#103×C151—24no—
140#103×C151—22no—
141#102×C151—24no—
142#102×C151—22no—
143C22⋊C8×C151—21no—
144#97×C151—21no—
145#97×C151—21no—
146C4×C8×C151C2312yes—
147#41×C151—44no—
148#41×C151—42no—
149#41×C151—42no—
150#41×C151—84no—
151C2×Q8×C151—22no—
152C2×Q8×C151—21no—
153C2×Q8×C151—22no—
154C2×Q8×C151—22no—
155C2×Q8×C151—41no—
156C2×Q8×C151—42no—
157C2×Q8×C151—42no—
158C2×Q8×C151—41no—
159C2×Q8×C151C2×D411yescharacteristic
160C2×Q8×C151C2×D411yescharacteristic
161C2×Q8×C151C2×D411yescharacteristic
162C2×Q8×C151C2×D412yes—
163C2×D4×C151—22no—
164C2×D4×C151—22no—
165C2×D4×C151—21no—
166C2×D4×C151—22no—
167C2×D4×C151—21no—
168C2×D4×C151—21no—
169C2×D4×C151C2×D411yescharacteristic
170C2×D4×C151C2×D412yes—
171C22×C4×C151—22no—
172C22×C4×C151—21no—
173C22×C4×C151—21no—
174C22×C4×C151—22no—
175C22×C4×C151—22no—
176C22×C4×C151—21no—
177C22×C4×C151—22no—
178C22×C4×C151—41no—
179C22×C4×C151C2×D411yescharacteristic
180C22×C4×C151C2×D411yescharacteristic
181C22×C4×C151C2×D411yescharacteristic
182Q16×C151—44no—
183Q16×C151—44no—
184M16×C151—42no—
185C2×C8×C151—22no—
186C2×C8×C151—22no—
187C2×C8×C151—22no—
188C2×C8×C151—42no—
189C4⋊C4×C151—22no—
190C4⋊C4×C151—22no—
191C4⋊C4×C151—22no—
192C4⋊C4×C151—22no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—21no—
196C4⋊C4×C151—21no—
197C4⋊C4×C151—21no—
198C4⋊C4×C151—21no—
199C4⋊C4×C151—21no—
200C4⋊C4×C151—21no—
201C4⋊C4×C151—21no—
202C4⋊C4×C151—21no—
203C4⋊C4×C151—21no—
204C4⋊C4×C151—22no—
205C4⋊C4×C151—22no—
206C4⋊C4×C151—41no—
207C4⋊C4×C151—41no—
208C4⋊C4×C151C2×D411yescharacteristic
209C4⋊C4×C151C2×D411yescharacteristic
210C4⋊C4×C151C2×D411yescharacteristic
211C4⋊C4×C151C2×D411yescharacteristic
212C22⋊C4×C151—22no—
213C22⋊C4×C151—22no—
214C22⋊C4×C151—22no—
215C22⋊C4×C151—22no—
216C22⋊C4×C151—22no—
217C22⋊C4×C151—21no—
218C22⋊C4×C151—22no—
219C22⋊C4×C151—21no—
220C22⋊C4×C151—21no—
221C22⋊C4×C151—22no—
222C22⋊C4×C151—21no—
223C22⋊C4×C151—21no—
224C42×C151—22no—
225C42×C151—21no—
226C42×C151—21no—
227C42×C151—21no—
228C42×C151—21no—
229C42×C151—21no—
230C42×C151C2×D411yescharacteristic
231C42×C151C2×D411yescharacteristic
232C42×C151C2×D411yescharacteristic
233C42×C151C2411yescharacteristic
234C23×C151—21no—
235C23×C151—22no—
236C23×C151#12011yescharacteristic
237Q8×C151—21no—
238Q8×C151—21no—
239Q8×C151—21no—
240Q8×C151—22no—
241Q8×C151—42no—
242Q8×C151—42no—
243Q8×C151—42no—
244Q8×C151—42no—
245Q8×C151—82no—
246Q8×C151—82no—
247Q8×C151AGL(1,ℤ/8)12yes—
248D4×C151—22no—
249D4×C151—42no—
250D4×C151—44no—
251D4×C151—44no—
252D4×C151—42no—
253D4×C151—41no—
254D4×C151—41no—
255D4×C151—42no—
256D4×C151—82no—
257C2×C4×C151—21no—
258C2×C4×C151—22no—
259C2×C4×C151—21no—
260C2×C4×C151—21no—
261C2×C4×C151—22no—
262C2×C4×C151—21no—
263C2×C4×C151—21no—
264C2×C4×C151—21no—
265C2×C4×C151—22no—
266C2×C4×C151—21no—
267C2×C4×C151—21no—
268C2×C4×C151—21no—
269C2×C4×C151—42no—
270C2×C4×C151—44no—
271C2×C4×C151—42no—
272C2×C4×C151—41no—
273C2×C4×C151—41no—
274C2×C4×C151—42no—
275C2×C4×C151—82no—
276C2×C4×C151—82no—
277C2×C4×C151—82no—
278C2×C4×C151—82no—
279C2×C4×C151#12011yescharacteristic
280C2×C4×C151#12011yescharacteristic
281C2×C4×C151#12011yescharacteristic
282C2×C4×C151C22×D411yescharacteristic
283C2×C4×C151C22×D411yescharacteristic
284C2×C4×C151C22×D411yescharacteristic
285C8×C151—42no—
286C8×C151—42no—
287C8×C151—42no—
288C22×C151—21no—
289C22×C151—21no—
290C22×C151—42no—
291C22×C151—41no—
292C22×C151—41no—
293C22×C151—42no—
294C22×C151—42no—
295C22×C151—41no—
296C22×C151#45512yes—
297C22×C151C2×#12011yescharacteristic
298C4×C151—21no—
299C4×C151—22no—
300C4×C151—21no—
301C4×C151—21no—
302C4×C151—21no—
303C4×C151—41no—
304C4×C151—41no—
305C4×C151—41no—
306C4×C151—41no—
307C4×C151—41no—
308C4×C151—42no—
309C4×C151—41no—
310C4×C151—82no—
311C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
312C4×C151#57511yescharacteristic
313C4×C151#57812yes—
314C2×C151—22no—
315C2×C151—81no—
316C2×C151—82no—
317C2×C151#300611yescharacteristic
318C2×C151#301111yescharacteristic
319C2×C151C2×#45511yescharacteristic
320#18572C15111yesmaximal, characteristic, direct product factor, Sylow
321C151#1857211yescharacteristic, direct product factor, Sylow
322#3522C2×C15111yescharacteristic
323#3239C2×C15111yescharacteristic, complemented
324#3141C2×C15111yescharacteristic, complemented
325C2×#462C2×C15111yescharacteristic, complemented
326#1645C2×C15112yescomplemented
327#1644C2×C15112yescomplemented
328#1641C2×C15112yescomplemented
329#1640C2×C15112yescomplemented
330#1551C2×C15111yescharacteristic, complemented
331#1491C2×C15111yescharacteristic, complemented
332#1483C2×C15111yescharacteristic, complemented
333C22×Q16—21no—
334#559—21no—
335#559C22×C15111yescharacteristic
336Q82C22×C15111yescharacteristic
337#554—21no—
338#554C22×C15111yescharacteristic
339#550C22×C15111yescharacteristic
340#548—21no—
341#547—22no—
342#547—21no—
343#542—22no—
344#542—21no—
345#532—21no—
346#532C22×C15111yescharacteristic
347C2×C4⋊Q8C22×C15111yescharacteristic
348#529—21no—
349#529C22×C15111yescharacteristic
350#520—21no—
351C2×C4×Q8C22×C15111yescharacteristic
352#501—21no—
353#489—22no—
354#489—21no—
355#487C22×C15112yes—
356#486C22×C15112yes—
357#484—21no—
358#481—21no—
359#475C22×C15112yes—
360#474C22×C15112yes—
361#462—21no—
362#462—21no—
363#462C22×C15112yes—
364#462C22×C15112yes—
365#432C22×C15111yescharacteristic
366C2×C4⋊C8C22×C15111yescharacteristic
367#417—22no—
368C2×#103—21no—
369C4×M16C22×C15111yescharacteristic
370#333C22×C15112yes—
371#331C22×C15112yes—
372Q8⋊C8C22×C15112yes—
373Q8⋊C8C22×C15112yes—
374Q8⋊C8C22×C15112yes—
375D4⋊C8C22×C15112yes—
376C2×#41—22no—
377C2×#41—21no—
378C2×#41D4×C15112yes—
379C22×Q8—21no—
380C22×Q8D4×C15111yescharacteristic
381C2×Q16—22no—
382C2×Q16—22no—
383C2×Q16—44no—
384C2×M16—21no—
385C22×C8—21no—
386C4⋊Q8—22no—
387C4⋊Q8—21no—
388C4⋊Q8—21no—
389C4⋊Q8—21no—
390C4⋊Q8—21no—
391C4⋊Q8—21no—
392C4⋊Q8C23×C15112yes—
393C4⋊Q8C23×C15111yescharacteristic
394#127—21no—
395#127C23×C15111yescharacteristic
396#126—22no—
397#126—21no—
398#125—21no—
399#125D4×C15111yescharacteristic
400#124—22no—
401#124—22no—
402#124—21no—
403#124—21no—
404#124D4×C15111yescharacteristic
405#124D4×C15112yes—
406#123—22no—
407#123—22no—
408#123—22no—
409#123—22no—
410#123—21no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415C22⋊Q8—21no—
416C22⋊Q8D4×C15111yescharacteristic
417#121—22no—
418#121—22no—
419#121—21no—
420#121—21no—
421#121—21no—
422#121D4×C15111yescharacteristic
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8—21no—
426C4×Q8—21no—
427C4×Q8D4×C15111yescharacteristic
428C4×Q8D4×C15111yescharacteristic
429C4×Q8C23×C15111yescharacteristic
430C4×Q8C23×C15111yescharacteristic
431C4×Q8C23×C15111yescharacteristic
432C4×D4—22no—
433C4×D4—22no—
434C4×D4—22no—
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—21no—
440C4×D4—21no—
441C4×D4—21no—
442C4×D4C23×C15111yescharacteristic
443#117—22no—
444#117—21no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4D4×C15111yescharacteristic
451C2×C42—21no—
452C2×C42C23×C15111yescharacteristic
453#107—22no—
454#106—22no—
455C4⋊C8—21no—
456C4⋊C8C23×C15112yes—
457C4⋊C8C23×C15112yes—
458#103—24no—
459#103—22no—
460#103—22no—
461#103—22no—
462#102—24no—
463#102—22no—
464C22⋊C8—21no—
465#97—21no—
466#97—21no—
467C4×C8C23×C15112yes—
468#41—44no—
469#41—42no—
470#41—42no—
471#41—84no—
472C2×Q8—22no—
473C2×Q8—21no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—41no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8—41no—
480C2×Q8C2×D4×C15111yescharacteristic
481C2×Q8C2×D4×C15111yescharacteristic
482C2×Q8C2×D4×C15111yescharacteristic
483C2×Q8C2×D4×C15112yes—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—21no—
487C2×D4—22no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4C2×D4×C15111yescharacteristic
491C2×D4C2×D4×C15112yes—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—41no—
500C22×C4C2×D4×C15111yescharacteristic
501C22×C4C2×D4×C15111yescharacteristic
502C22×C4C2×D4×C15111yescharacteristic
503Q16—44no—
504Q16—44no—
505M16—42no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—42no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4C2×D4×C15111yescharacteristic
530C4⋊C4C2×D4×C15111yescharacteristic
531C4⋊C4C2×D4×C15111yescharacteristic
532C4⋊C4C2×D4×C15111yescharacteristic
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—21no—
539C22⋊C4—22no—
540C22⋊C4—21no—
541C22⋊C4—21no—
542C22⋊C4—22no—
543C22⋊C4—21no—
544C22⋊C4—21no—
545C42—22no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42C2×D4×C15111yescharacteristic
552C42C2×D4×C15111yescharacteristic
553C42C2×D4×C15111yescharacteristic
554C42C24×C15111yescharacteristic
555C23—21no—
556C23—22no—
557C23#120×C15111yescharacteristic
558Q8—21no—
559Q8—21no—
560Q8—21no—
561Q8—22no—
562Q8—42no—
563Q8—42no—
564Q8—42no—
565Q8—42no—
566Q8—82no—
567Q8—82no—
568Q8AGL(1,ℤ/8)×C15112yes—
569D4—22no—
570D4—42no—
571D4—44no—
572D4—44no—
573D4—42no—
574D4—41no—
575D4—41no—
576D4—42no—
577D4—82no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—42no—
591C2×C4—44no—
592C2×C4—42no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—82no—
597C2×C4—82no—
598C2×C4—82no—
599C2×C4—82no—
600C2×C4#120×C15111yescharacteristic
601C2×C4#120×C15111yescharacteristic
602C2×C4#120×C15111yescharacteristic
603C2×C4C22×D4×C15111yescharacteristic
604C2×C4C22×D4×C15111yescharacteristic
605C2×C4C22×D4×C15111yescharacteristic
606C8—42no—
607C8—42no—
608C8—42no—
609C22—21no—
610C22—21no—
611C22—42no—
612C22—41no—
613C22—41no—
614C22—42no—
615C22—42no—
616C22—41no—
617C22#455×C15112yes—
618C22C2×#120×C15111yescharacteristic
619C4—21no—
620C4—22no—
621C4—21no—
622C4—21no—
623C4—21no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—42no—
630C4—41no—
631C4—82no—
632C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
633C4#575×C15111yescharacteristic
634C4#578×C15112yes—
635C2—22no—
636C2—81no—
637C2—82no—
638C2#3006×C15111yescharacteristic
639C2#3011×C15111yescharacteristic
640C2C2×#455×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3522×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
2. #3239×C151C2semidirect
3. #3141×C151C2semidirect
4. C2×#462×C151C2semidirect
5. #1645×C151C2semidirect
6. #1644×C151C2semidirect
7. #1641×C151C2semidirect
8. #1640×C151C2semidirect
9. #1551×C151C2semidirect
10. #1491×C151C2semidirect
11. #1483×C151C2semidirect
320. #18572C151direct (N × H)
321. C151#18572direct (N × H)
323. #3239C2×C151semidirect
324. #3141C2×C151semidirect
325. C2×#462C2×C151semidirect
326. #1645C2×C151semidirect
327. #1644C2×C151semidirect
328. #1641C2×C151semidirect
329. #1640C2×C151semidirect
330. #1551C2×C151semidirect
331. #1491C2×C151semidirect
332. #1483C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3522×C1512
#3239×C1512
#3141×C1512
C2×#462×C1512
#1645×C1512
#1644×C1512
#1641×C1512
#1640×C1512
#1551×C1512
#1491×C1512
#1483×C1512
#18572151