Finite Group Databasebeta

← C151×#24172 #50329097

Subgroups — C151×#24172 #50329097

Order 38656.

1058 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3511×C151C211yesmaximal, characteristic
2#3037×C151C211yesmaximal, characteristic, complemented
3C4×#137×C151C211yesmaximal, characteristic, complemented
4#2568×C151C211yesmaximal, characteristic, complemented
5#2040×C151C212yesmaximal, complemented
6#2007×C151C212yesmaximal, complemented
7#1997×C151C211yesmaximal, characteristic, complemented
8#1980×C151C211yesmaximal, characteristic, complemented
9#1882×C151C212yesmaximal, complemented
10#1860×C151C212yesmaximal, complemented
11#1806×C151C211yesmaximal, characteristic, complemented
12C2×#137×C151C2211yescharacteristic
13C2×#137×C151C2212yes—
14#556×C151—21no—
15#555×C151—21no—
16#554×C151—21no—
17#553×C151—22no—
18#548×C151—22no—
19#547×C151—21no—
20#542×C151—22no—
21#537×C151C2212yes—
22#533×C151—21no—
23#532×C151—21no—
24#532×C151C2211yescharacteristic
25C2×C4⋊Q8×C151C2211yescharacteristic
26#520×C151C2212yes—
27C4×#41×C151C2211yescharacteristic
28C2×C4×Q8×C151C2211yescharacteristic
29#464×C151—22no—
30#462×C151—21no—
31#460×C151—21no—
32#441×C151—21no—
33#440×C151—21no—
34C4×Q16×C151—21no—
35C4×SD16×C151—21no—
36#428×C151C2211yescharacteristic
37#423×C151C2211yescharacteristic
38C2×#104×C151C2212yes—
39C2×#104×C151C2212yes—
40C2×#104×C151C2212yes—
41#419×C151C2211yescharacteristic
42#417×C151C2212yes—
43#417×C151C2211yescharacteristic
44C4×M16×C151C2211yescharacteristic
45#400×C151—22no—
46#391×C151—22no—
47#391×C151C2212yes—
48#382×C151C2212yes—
49C4×C4⋊C4×C151C2211yescharacteristic
50#343×C151C2212yes—
51#343×C151C2212yes—
52#339×C151C2212yes—
53C2×#41×C151—22no—
54C2×#41×C151C2311yescharacteristic
55C2×#41×C151C2312yes—
56C22×Q8×C151D412yes—
57C22×Q8×C151C2311yescharacteristic
58#137×C151—22no—
59#137×C151—22no—
60#137×C151—24no—
61#137×C151—42no—
62C2×Q16×C151—21no—
63C2×Q16×C151—22no—
64C2×SD16×C151—21no—
65C2×SD16×C151—22no—
66C2×M16×C151C2312yes—
67C2×M16×C151C2311yescharacteristic
68C2×M16×C151C2311yescharacteristic
69C4⋊Q8×C151—21no—
70C4⋊Q8×C151—21no—
71C4⋊Q8×C151—21no—
72C4⋊Q8×C151—21no—
73C4⋊Q8×C151D411yescharacteristic
74#127×C151D411yescharacteristic
75#126×C151—24no—
76#125×C151—22no—
77#124×C151—22no—
78#124×C151—24no—
79#124×C151D412yes—
80#123×C151—24no—
81C22⋊Q8×C151—22no—
82C22⋊Q8×C151—24no—
83C22⋊Q8×C151—22no—
84C22⋊Q8×C151—22no—
85#121×C151—22no—
86#121×C151—22no—
87#121×C151—22no—
88#121×C151—21no—
89#121×C151—21no—
90#121×C151—24no—
91C4×Q8×C151—22no—
92C4×Q8×C151—21no—
93C4×Q8×C151—21no—
94C4×Q8×C151—21no—
95C4×Q8×C151—21no—
96C4×Q8×C151—22no—
97C4×Q8×C151D411yescharacteristic
98C4×Q8×C151D411yescharacteristic
99C4×D4×C151—22no—
100C4×D4×C151—22no—
101C4×D4×C151—21no—
102C4×D4×C151—21no—
103C4×D4×C151—24no—
104C4×D4×C151—21no—
105C4×D4×C151—21no—
106C4×D4×C151D411yescharacteristic
107C4×D4×C151D411yescharacteristic
108#117×C151—22no—
109#117×C151—22no—
110#117×C151—21no—
111#117×C151C2311yescharacteristic
112C2×C4⋊C4×C151—22no—
113C2×C4⋊C4×C151—21no—
114C2×C4⋊C4×C151—21no—
115C2×C4⋊C4×C151D412yes—
116C2×C4⋊C4×C151C2311yescharacteristic
117C2×C4⋊C4×C151C2312yes—
118C2×C42×C151—21no—
119C2×C42×C151—21no—
120C2×C42×C151C2312yes—
121C2×C42×C151C2311yescharacteristic
122#107×C151—21no—
123#106×C151—21no—
124C4⋊C8×C151—21no—
125C4⋊C8×C151—21no—
126#104×C151—24no—
127#104×C151—42no—
128#104×C151—42no—
129#103×C151—21no—
130#103×C151—21no—
131#103×C151—21no—
132#103×C151—22no—
133#102×C151—21no—
134#102×C151—22no—
135#97×C151—21no—
136C4×C8×C151—21no—
137#95×C151—21no—
138#95×C151—24no—
139#95×C151—24no—
140#41×C151—22no—
141#41×C151—22no—
142#41×C151—21no—
143#41×C151—21no—
144#41×C151—21no—
145#41×C151—22no—
146#41×C151—22no—
147#41×C151—21no—
148#41×C151—84no—
149C2×Q8×C151—22no—
150C2×Q8×C151—22no—
151C2×Q8×C151—21no—
152C2×Q8×C151—21no—
153C2×Q8×C151—21no—
154C2×Q8×C151—21no—
155C2×Q8×C151—21no—
156C2×Q8×C151—44no—
157C2×Q8×C151C2×D412yes—
158C2×Q8×C151C2×D411yescharacteristic
159C2×Q8×C151#4112yescomplemented
160C2×D4×C151—21no—
161C2×D4×C151—22no—
162C2×D4×C151—24no—
163C2×D4×C151—21no—
164C2×D4×C151—21no—
165C2×D4×C151C2×D412yes—
166C2×D4×C151C2×D411yescharacteristic
167C22×C4×C151—21no—
168C22×C4×C151—24no—
169C22×C4×C151—21no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—22no—
173C22×C4×C151—22no—
174C22×C4×C151—21no—
175C22×C4×C151C2×D411yescharacteristic
176C22×C4×C151C2×D414yes—
177C22×C4×C151C2×D411yescharacteristic
178C22×C4×C151C2411yescharacteristic
179Q16×C151—24no—
180Q16×C151—44no—
181SD16×C151—24no—
182SD16×C151—44no—
183M16×C151—21no—
184M16×C151—22no—
185M16×C151—21no—
186M16×C151—22no—
187M16×C151—21no—
188M16×C151#4112yescomplemented
189C2×C8×C151—21no—
190C2×C8×C151—21no—
191C2×C8×C151—22no—
192C4⋊C4×C151—24no—
193C4⋊C4×C151—24no—
194C4⋊C4×C151—22no—
195C4⋊C4×C151—22no—
196C4⋊C4×C151—21no—
197C4⋊C4×C151—21no—
198C4⋊C4×C151—21no—
199C4⋊C4×C151—21no—
200C4⋊C4×C151—22no—
201C4⋊C4×C151—22no—
202C4⋊C4×C151—21no—
203C4⋊C4×C151—21no—
204C4⋊C4×C151—42no—
205C4⋊C4×C151—41no—
206C4⋊C4×C151—41no—
207C4⋊C4×C151C2×D411yescharacteristic
208C4⋊C4×C151C2×D411yescharacteristic
209C22⋊C4×C151—24no—
210C22⋊C4×C151—24no—
211C22⋊C4×C151—24no—
212C22⋊C4×C151—21no—
213C22⋊C4×C151—21no—
214C22⋊C4×C151—21no—
215C22⋊C4×C151—22no—
216C22⋊C4×C151—22no—
217C42×C151—24no—
218C42×C151—21no—
219C42×C151—21no—
220C42×C151—21no—
221C42×C151—22no—
222C42×C151—22no—
223C42×C151—41no—
224C42×C151—41no—
225C42×C151C2×D411yescharacteristic
226C42×C151C2×D411yescharacteristic
227C42×C151C2×D411yescharacteristic
228C42×C151C2×D411yescharacteristic
229C23×C151—21no—
230C23×C151—22no—
231C23×C151C22×D411yescharacteristic
232Q8×C151—22no—
233Q8×C151—21no—
234Q8×C151—21no—
235Q8×C151—22no—
236Q8×C151—22no—
237Q8×C151—22no—
238Q8×C151—41no—
239Q8×C151—41no—
240Q8×C151—44no—
241Q8×C151—82no—
242D4×C151—21no—
243D4×C151—21no—
244D4×C151—22no—
245D4×C151—22no—
246D4×C151—42no—
247D4×C151—42no—
248D4×C151—41no—
249D4×C151—42no—
250D4×C151—41no—
251D4×C151—42no—
252D4×C151—84no—
253C2×C4×C151—22no—
254C2×C4×C151—24no—
255C2×C4×C151—22no—
256C2×C4×C151—21no—
257C2×C4×C151—21no—
258C2×C4×C151—21no—
259C2×C4×C151—22no—
260C2×C4×C151—41no—
261C2×C4×C151—42no—
262C2×C4×C151—41no—
263C2×C4×C151—41no—
264C2×C4×C151—42no—
265C2×C4×C151—42no—
266C2×C4×C151—41no—
267C2×C4×C151—41no—
268C2×C4×C151—42no—
269C2×C4×C151—44no—
270C2×C4×C151—42no—
271C2×C4×C151—42no—
272C2×C4×C151—42no—
273C2×C4×C151—41no—
274C2×C4×C151—42no—
275C2×C4×C151—84no—
276C2×C4×C151#12011yescharacteristic
277C2×C4×C151#12011yescharacteristic
278C2×C4×C151#12011yescharacteristic
279C2×C4×C151#12011yescharacteristic
280C2×C4×C151C22×D411yescharacteristic
281C2×C4×C151C22×D411yescharacteristic
282C2×C4×C151C2×#4111yescharacteristic
283C2×C4×C151C2×#4111yescharacteristic
284C2×C4×C151H(5,𝔽2)11yescharacteristic
285C2×C4×C1512−1+411yescharacteristic
286C8×C151—22no—
287C8×C151—41no—
288C8×C151—42no—
289C22×C151—21no—
290C22×C151—21no—
291C22×C151—42no—
292C22×C151—41no—
293C22×C151—41no—
294C22×C151—42no—
295C22×C151—41no—
296C22×C151—42no—
297C22×C151C2×#12011yescharacteristic
298C22×C151#54811yescharacteristic
299C22×C151#55011yescharacteristic
300C4×C151—21no—
301C4×C151—21no—
302C4×C151—21no—
303C4×C151—42no—
304C4×C151—41no—
305C4×C151—42no—
306C4×C151—41no—
307C4×C151—44no—
308C4×C151—41no—
309C4×C151—82no—
310C4×C151—81no—
311C4×C151#45512yes—
312C4×C151#52511yescharacteristic
313C4×C151#53711yescharacteristic
314C4×C151#54611yescharacteristic
315C4×C151#54711yescharacteristic
316C2×C151—21no—
317C2×C151—21no—
318C2×C151—81no—
319C2×C151—82no—
320C2×C151#240711yescharacteristic
321C2×C151C2×#45511yescharacteristic
322C2×C151#302011yescharacteristic
323#24172C15111yesmaximal, characteristic, direct product factor, Sylow
324C151#2417211yescharacteristic, direct product factor, Sylow
325#3511C2×C15111yescharacteristic
326#3037C2×C15111yescharacteristic, complemented
327C4×#137C2×C15111yescharacteristic, complemented
328#2568C2×C15111yescharacteristic, complemented
329#2040C2×C15112yescomplemented
330#2007C2×C15112yescomplemented
331#1997C2×C15111yescharacteristic, complemented
332#1980C2×C15111yescharacteristic, complemented
333#1882C2×C15112yescomplemented
334#1860C2×C15112yescomplemented
335#1806C2×C15111yescharacteristic, complemented
336C2×#137C22×C15111yescharacteristic
337C2×#137C22×C15112yes—
338#556—21no—
339#555—21no—
340#554—21no—
341#553—22no—
342#548—22no—
343#547—21no—
344#542—22no—
345#537C22×C15112yes—
346#533—21no—
347#532—21no—
348#532C22×C15111yescharacteristic
349C2×C4⋊Q8C22×C15111yescharacteristic
350#520C22×C15112yes—
351C4×#41C22×C15111yescharacteristic
352C2×C4×Q8C22×C15111yescharacteristic
353#464—22no—
354#462—21no—
355#460—21no—
356#441—21no—
357#440—21no—
358C4×Q16—21no—
359C4×SD16—21no—
360#428C22×C15111yescharacteristic
361#423C22×C15111yescharacteristic
362C2×#104C22×C15112yes—
363C2×#104C22×C15112yes—
364C2×#104C22×C15112yes—
365#419C22×C15111yescharacteristic
366#417C22×C15112yes—
367#417C22×C15111yescharacteristic
368C4×M16C22×C15111yescharacteristic
369#400—22no—
370#391—22no—
371#391C22×C15112yes—
372#382C22×C15112yes—
373C4×C4⋊C4C22×C15111yescharacteristic
374#343C22×C15112yes—
375#343C22×C15112yes—
376#339C22×C15112yes—
377C2×#41—22no—
378C2×#41C23×C15111yescharacteristic
379C2×#41C23×C15112yes—
380C22×Q8D4×C15112yes—
381C22×Q8C23×C15111yescharacteristic
382#137—22no—
383#137—24no—
384#137—22no—
385#137—42no—
386C2×Q16—21no—
387C2×Q16—22no—
388C2×SD16—21no—
389C2×SD16—22no—
390C2×M16C23×C15112yes—
391C2×M16C23×C15111yescharacteristic
392C2×M16C23×C15111yescharacteristic
393C4⋊Q8—21no—
394C4⋊Q8—21no—
395C4⋊Q8—21no—
396C4⋊Q8—21no—
397C4⋊Q8D4×C15111yescharacteristic
398#127D4×C15111yescharacteristic
399#126—24no—
400#125—22no—
401#124—22no—
402#124—24no—
403#124D4×C15112yes—
404#123—24no—
405C22⋊Q8—22no—
406C22⋊Q8—24no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409#121—22no—
410#121—22no—
411#121—22no—
412#121—21no—
413#121—21no—
414#121—24no—
415C4×Q8—22no—
416C4×Q8—22no—
417C4×Q8—21no—
418C4×Q8—21no—
419C4×Q8—21no—
420C4×Q8—21no—
421C4×Q8D4×C15111yescharacteristic
422C4×Q8D4×C15111yescharacteristic
423C4×D4—22no—
424C4×D4—22no—
425C4×D4—21no—
426C4×D4—21no—
427C4×D4—24no—
428C4×D4—21no—
429C4×D4—21no—
430C4×D4D4×C15111yescharacteristic
431C4×D4D4×C15111yescharacteristic
432#117—22no—
433#117—22no—
434#117—21no—
435#117C23×C15111yescharacteristic
436C2×C4⋊C4—22no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4D4×C15112yes—
440C2×C4⋊C4C23×C15111yescharacteristic
441C2×C4⋊C4C23×C15112yes—
442C2×C42—21no—
443C2×C42—21no—
444C2×C42C23×C15112yes—
445C2×C42C23×C15111yescharacteristic
446#107—21no—
447#106—21no—
448C4⋊C8—21no—
449C4⋊C8—21no—
450#104—24no—
451#104—42no—
452#104—42no—
453#103—21no—
454#103—22no—
455#103—21no—
456#103—21no—
457#102—21no—
458#102—22no—
459#97—21no—
460C4×C8—21no—
461#95—21no—
462#95—24no—
463#95—24no—
464#41—22no—
465#41—22no—
466#41—21no—
467#41—21no—
468#41—21no—
469#41—22no—
470#41—22no—
471#41—21no—
472#41—84no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—44no—
481C2×Q8C2×D4×C15112yes—
482C2×Q8C2×D4×C15111yescharacteristic
483C2×Q8#41×C15112yescomplemented
484C2×D4—21no—
485C2×D4—22no—
486C2×D4—24no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4C2×D4×C15112yes—
490C2×D4C2×D4×C15111yescharacteristic
491C22×C4—21no—
492C22×C4—24no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4C2×D4×C15111yescharacteristic
500C22×C4C2×D4×C15114yes—
501C22×C4C2×D4×C15111yescharacteristic
502C22×C4C24×C15111yescharacteristic
503Q16—24no—
504Q16—44no—
505SD16—24no—
506SD16—44no—
507M16—21no—
508M16—22no—
509M16—21no—
510M16—22no—
511M16—21no—
512M16#41×C15112yescomplemented
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—22no—
516C4⋊C4—24no—
517C4⋊C4—24no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—42no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4C2×D4×C15111yescharacteristic
532C4⋊C4C2×D4×C15111yescharacteristic
533C22⋊C4—24no—
534C22⋊C4—24no—
535C22⋊C4—24no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C42—24no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—22no—
546C42—22no—
547C42—41no—
548C42—41no—
549C42C2×D4×C15111yescharacteristic
550C42C2×D4×C15111yescharacteristic
551C42C2×D4×C15111yescharacteristic
552C42C2×D4×C15111yescharacteristic
553C23—21no—
554C23—22no—
555C23C22×D4×C15111yescharacteristic
556Q8—22no—
557Q8—21no—
558Q8—21no—
559Q8—22no—
560Q8—22no—
561Q8—22no—
562Q8—44no—
563Q8—41no—
564Q8—41no—
565Q8—82no—
566D4—21no—
567D4—21no—
568D4—22no—
569D4—22no—
570D4—42no—
571D4—42no—
572D4—41no—
573D4—42no—
574D4—41no—
575D4—42no—
576D4—84no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—44no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—84no—
600C2×C4#120×C15111yescharacteristic
601C2×C4#120×C15111yescharacteristic
602C2×C4#120×C15111yescharacteristic
603C2×C4#120×C15111yescharacteristic
604C2×C4C22×D4×C15111yescharacteristic
605C2×C4C22×D4×C15111yescharacteristic
606C2×C4C2×#41×C15111yescharacteristic
607C2×C4C2×#41×C15111yescharacteristic
608C2×C4H(5,𝔽2)×C15111yescharacteristic
609C2×C42−1+4×C15111yescharacteristic
610C8—22no—
611C8—41no—
612C8—42no—
613C22—21no—
614C22—21no—
615C22—42no—
616C22—41no—
617C22—41no—
618C22—42no—
619C22—41no—
620C22—42no—
621C22C2×#120×C15111yescharacteristic
622C22#548×C15111yescharacteristic
623C22#550×C15111yescharacteristic
624C4—21no—
625C4—21no—
626C4—21no—
627C4—42no—
628C4—41no—
629C4—42no—
630C4—41no—
631C4—44no—
632C4—41no—
633C4—82no—
634C4—81no—
635C4#455×C15112yes—
636C4#525×C15111yescharacteristic
637C4#537×C15111yescharacteristic
638C4#546×C15111yescharacteristic
639C4#547×C15111yescharacteristic
640C2—21no—
641C2—21no—
642C2—81no—
643C2—82no—
644C2#2407×C15111yescharacteristic
645C2C2×#455×C15111yescharacteristic
646C2#3020×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3511×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #3037×C151C2semidirect
3. C4×#137×C151C2semidirect
4. #2568×C151C2semidirect
5. #2040×C151C2semidirect
6. #2007×C151C2semidirect
7. #1997×C151C2semidirect
8. #1980×C151C2semidirect
9. #1882×C151C2semidirect
10. #1860×C151C2semidirect
11. #1806×C151C2semidirect
159. C2×Q8×C151#41semidirect
188. M16×C151#41semidirect
323. #24172C151direct (N × H)
324. C151#24172direct (N × H)
326. #3037C2×C151semidirect
327. C4×#137C2×C151semidirect
328. #2568C2×C151semidirect
329. #2040C2×C151semidirect
330. #2007C2×C151semidirect
331. #1997C2×C151semidirect
332. #1980C2×C151semidirect
333. #1882C2×C151semidirect
334. #1860C2×C151semidirect
335. #1806C2×C151semidirect
483. C2×Q8#41×C151semidirect
512. M16#41×C151semidirect

Maximal subgroups

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

subgroupindex
#3511×C1512
#3037×C1512
C4×#137×C1512
#2568×C1512
#2040×C1512
#2007×C1512
#1997×C1512
#1980×C1512
#1882×C1512
#1860×C1512
#1806×C1512
#24172151