Finite Group Databasebeta

← C151×#24173 #50329098

Subgroups — C151×#24173 #50329098

Order 38656.

1074 conjugacy classes of subgroups.

The subgroup lattice has 650 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#2567×C151C211yesmaximal, characteristic, complemented
5#2039×C151C212yesmaximal, complemented
6#2007×C151C212yesmaximal, complemented
7#1997×C151C211yesmaximal, characteristic, complemented
8#1980×C151C211yesmaximal, characteristic, complemented
9#1882×C151C212yesmaximal, complemented
10#1859×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#395×C151—22no—
46#391×C151C2212yes—
47#389×C151—22no—
48#384×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—21no—
113C2×C4⋊C4×C151—22no—
114C2×C4⋊C4×C151—21no—
115C2×C4⋊C4×C151—24no—
116C2×C4⋊C4×C151D412yes—
117C2×C4⋊C4×C151C2311yescharacteristic
118C2×C4⋊C4×C151C2312yes—
119C2×C42×C151—21no—
120C2×C42×C151—21no—
121C2×C42×C151C2312yes—
122C2×C42×C151C2311yescharacteristic
123#107×C151—21no—
124#106×C151—21no—
125C4⋊C8×C151—21no—
126C4⋊C8×C151—21no—
127#104×C151—24no—
128#104×C151—42no—
129#104×C151—42no—
130#103×C151—21no—
131#103×C151—21no—
132#103×C151—21no—
133#103×C151—22no—
134#102×C151—21no—
135#102×C151—22no—
136#97×C151—21no—
137C4×C8×C151—21no—
138#95×C151—21no—
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—82no—
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—22no—
169C22×C4×C151—24no—
170C22×C4×C151—21no—
171C22×C4×C151—21no—
172C22×C4×C151—21no—
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—24no—
195C4⋊C4×C151—22no—
196C4⋊C4×C151—22no—
197C4⋊C4×C151—21no—
198C4⋊C4×C151—21no—
199C4⋊C4×C151—21no—
200C4⋊C4×C151—21no—
201C4⋊C4×C151—22no—
202C4⋊C4×C151—22no—
203C4⋊C4×C151—21no—
204C4⋊C4×C151—21no—
205C4⋊C4×C151—41no—
206C4⋊C4×C151—41no—
207C4⋊C4×C151—84no—
208C4⋊C4×C151C2×D411yescharacteristic
209C4⋊C4×C151C2×D411yescharacteristic
210C22⋊C4×C151—24no—
211C22⋊C4×C151—24no—
212C22⋊C4×C151—24no—
213C22⋊C4×C151—21no—
214C22⋊C4×C151—21no—
215C22⋊C4×C151—21no—
216C22⋊C4×C151—22no—
217C22⋊C4×C151—22no—
218C42×C151—24no—
219C42×C151—21no—
220C42×C151—21no—
221C42×C151—21no—
222C42×C151—22no—
223C42×C151—22no—
224C42×C151—41no—
225C42×C151—41no—
226C42×C151C2×D411yescharacteristic
227C42×C151C2×D411yescharacteristic
228C42×C151C2×D411yescharacteristic
229C42×C151C2×D411yescharacteristic
230C23×C151—21no—
231C23×C151—22no—
232C23×C151C22×D411yescharacteristic
233Q8×C151—22no—
234Q8×C151—21no—
235Q8×C151—21no—
236Q8×C151—22no—
237Q8×C151—22no—
238Q8×C151—22no—
239Q8×C151—44no—
240Q8×C151—41no—
241Q8×C151—41no—
242Q8×C151—82no—
243D4×C151—21no—
244D4×C151—21no—
245D4×C151—22no—
246D4×C151—22no—
247D4×C151—42no—
248D4×C151—42no—
249D4×C151—41no—
250D4×C151—42no—
251D4×C151—41no—
252D4×C151—42no—
253D4×C151—84no—
254C2×C4×C151—22no—
255C2×C4×C151—24no—
256C2×C4×C151—24no—
257C2×C4×C151—22no—
258C2×C4×C151—21no—
259C2×C4×C151—21no—
260C2×C4×C151—21no—
261C2×C4×C151—22no—
262C2×C4×C151—41no—
263C2×C4×C151—42no—
264C2×C4×C151—42no—
265C2×C4×C151—41no—
266C2×C4×C151—41no—
267C2×C4×C151—42no—
268C2×C4×C151—42no—
269C2×C4×C151—42no—
270C2×C4×C151—41no—
271C2×C4×C151—41no—
272C2×C4×C151—42no—
273C2×C4×C151—44no—
274C2×C4×C151—42no—
275C2×C4×C151—41no—
276C2×C4×C151—84no—
277C2×C4×C151#12011yescharacteristic
278C2×C4×C151#12011yescharacteristic
279C2×C4×C151#12011yescharacteristic
280C2×C4×C151#12011yescharacteristic
281C2×C4×C151C22×D411yescharacteristic
282C2×C4×C151C22×D411yescharacteristic
283C2×C4×C151C2×#4111yescharacteristic
284C2×C4×C151C2×#4111yescharacteristic
285C2×C4×C151H(5,𝔽2)11yescharacteristic
286C2×C4×C1512−1+411yescharacteristic
287C8×C151—22no—
288C8×C151—41no—
289C8×C151—42no—
290C22×C151—21no—
291C22×C151—21no—
292C22×C151—42no—
293C22×C151—41no—
294C22×C151—41no—
295C22×C151—42no—
296C22×C151—41no—
297C22×C151—42no—
298C22×C151C2×#12011yescharacteristic
299C22×C151#54811yescharacteristic
300C22×C151#55011yescharacteristic
301C4×C151—21no—
302C4×C151—21no—
303C4×C151—21no—
304C4×C151—44no—
305C4×C151—42no—
306C4×C151—41no—
307C4×C151—42no—
308C4×C151—41no—
309C4×C151—41no—
310C4×C151—44no—
311C4×C151—81no—
312C4×C151#45612yes—
313C4×C151#52511yescharacteristic
314C4×C151#53711yescharacteristic
315C4×C151#54611yescharacteristic
316C4×C151#54711yescharacteristic
317C2×C151—21no—
318C2×C151—21no—
319C2×C151—81no—
320C2×C151—82no—
321C2×C151#240711yescharacteristic
322C2×C151C2×#45611yescharacteristic
323C2×C151#301911yescharacteristic
324#24173C15111yesmaximal, characteristic, direct product factor, Sylow
325C151#2417311yescharacteristic, direct product factor, Sylow
326#3511C2×C15111yescharacteristic
327#3037C2×C15111yescharacteristic, complemented
328C4×#137C2×C15111yescharacteristic, complemented
329#2567C2×C15111yescharacteristic, complemented
330#2039C2×C15112yescomplemented
331#2007C2×C15112yescomplemented
332#1997C2×C15111yescharacteristic, complemented
333#1980C2×C15111yescharacteristic, complemented
334#1882C2×C15112yescomplemented
335#1859C2×C15112yescomplemented
336#1806C2×C15111yescharacteristic, complemented
337C2×#137C22×C15111yescharacteristic
338C2×#137C22×C15112yes—
339#556—21no—
340#555—21no—
341#554—21no—
342#553—22no—
343#548—22no—
344#547—21no—
345#542—22no—
346#537C22×C15112yes—
347#533—21no—
348#532—21no—
349#532C22×C15111yescharacteristic
350C2×C4⋊Q8C22×C15111yescharacteristic
351#520C22×C15112yes—
352C4×#41C22×C15111yescharacteristic
353C2×C4×Q8C22×C15111yescharacteristic
354#464—22no—
355#462—21no—
356#460—21no—
357#441—21no—
358#440—21no—
359C4×Q16—21no—
360C4×SD16—21no—
361#428C22×C15111yescharacteristic
362#423C22×C15111yescharacteristic
363C2×#104C22×C15112yes—
364C2×#104C22×C15112yes—
365C2×#104C22×C15112yes—
366#419C22×C15111yescharacteristic
367#417C22×C15112yes—
368#417C22×C15111yescharacteristic
369C4×M16C22×C15111yescharacteristic
370#395—22no—
371#391C22×C15112yes—
372#389—22no—
373#384C22×C15112yes—
374C4×C4⋊C4C22×C15111yescharacteristic
375#343C22×C15112yes—
376#343C22×C15112yes—
377#339C22×C15112yes—
378C2×#41—22no—
379C2×#41C23×C15111yescharacteristic
380C2×#41C23×C15112yes—
381C22×Q8D4×C15112yes—
382C22×Q8C23×C15111yescharacteristic
383#137—22no—
384#137—24no—
385#137—22no—
386#137—42no—
387C2×Q16—21no—
388C2×Q16—22no—
389C2×SD16—21no—
390C2×SD16—22no—
391C2×M16C23×C15112yes—
392C2×M16C23×C15111yescharacteristic
393C2×M16C23×C15111yescharacteristic
394C4⋊Q8—21no—
395C4⋊Q8—21no—
396C4⋊Q8—21no—
397C4⋊Q8—21no—
398C4⋊Q8D4×C15111yescharacteristic
399#127D4×C15111yescharacteristic
400#126—24no—
401#125—22no—
402#124—22no—
403#124—24no—
404#124D4×C15112yes—
405#123—24no—
406C22⋊Q8—22no—
407C22⋊Q8—24no—
408C22⋊Q8—22no—
409C22⋊Q8—22no—
410#121—22no—
411#121—22no—
412#121—22no—
413#121—21no—
414#121—21no—
415#121—24no—
416C4×Q8—22no—
417C4×Q8—22no—
418C4×Q8—21no—
419C4×Q8—21no—
420C4×Q8—21no—
421C4×Q8—21no—
422C4×Q8D4×C15111yescharacteristic
423C4×Q8D4×C15111yescharacteristic
424C4×D4—22no—
425C4×D4—22no—
426C4×D4—21no—
427C4×D4—21no—
428C4×D4—24no—
429C4×D4—21no—
430C4×D4—21no—
431C4×D4D4×C15111yescharacteristic
432C4×D4D4×C15111yescharacteristic
433#117—22no—
434#117—22no—
435#117—21no—
436#117C23×C15111yescharacteristic
437C2×C4⋊C4—21no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4D4×C15112yes—
442C2×C4⋊C4C23×C15111yescharacteristic
443C2×C4⋊C4C23×C15112yes—
444C2×C42—21no—
445C2×C42—21no—
446C2×C42C23×C15112yes—
447C2×C42C23×C15111yescharacteristic
448#107—21no—
449#106—21no—
450C4⋊C8—21no—
451C4⋊C8—21no—
452#104—24no—
453#104—42no—
454#104—42no—
455#103—21no—
456#103—22no—
457#103—21no—
458#103—21no—
459#102—21no—
460#102—22no—
461#97—21no—
462C4×C8—21no—
463#95—21no—
464#95—24no—
465#41—22no—
466#41—22no—
467#41—21no—
468#41—21no—
469#41—21no—
470#41—22no—
471#41—22no—
472#41—21no—
473#41—84no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—82no—
482C2×Q8C2×D4×C15112yes—
483C2×Q8C2×D4×C15111yescharacteristic
484C2×Q8#41×C15112yescomplemented
485C2×D4—21no—
486C2×D4—22no—
487C2×D4—24no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4C2×D4×C15112yes—
491C2×D4C2×D4×C15111yescharacteristic
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4C2×D4×C15111yescharacteristic
501C22×C4C2×D4×C15114yes—
502C22×C4C2×D4×C15111yescharacteristic
503C22×C4C24×C15111yescharacteristic
504Q16—24no—
505Q16—44no—
506SD16—24no—
507SD16—44no—
508M16—21no—
509M16—22no—
510M16—21no—
511M16—22no—
512M16—21no—
513M16#41×C15112yescomplemented
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—22no—
517C4⋊C4—24no—
518C4⋊C4—24no—
519C4⋊C4—24no—
520C4⋊C4—22no—
521C4⋊C4—22no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—84no—
533C4⋊C4C2×D4×C15111yescharacteristic
534C4⋊C4C2×D4×C15111yescharacteristic
535C22⋊C4—24no—
536C22⋊C4—24no—
537C22⋊C4—24no—
538C22⋊C4—21no—
539C22⋊C4—21no—
540C22⋊C4—21no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C42—24no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—22no—
548C42—22no—
549C42—41no—
550C42—41no—
551C42C2×D4×C15111yescharacteristic
552C42C2×D4×C15111yescharacteristic
553C42C2×D4×C15111yescharacteristic
554C42C2×D4×C15111yescharacteristic
555C23—21no—
556C23—22no—
557C23C22×D4×C15111yescharacteristic
558Q8—22no—
559Q8—21no—
560Q8—21no—
561Q8—22no—
562Q8—22no—
563Q8—22no—
564Q8—44no—
565Q8—41no—
566Q8—41no—
567Q8—82no—
568D4—21no—
569D4—21no—
570D4—22no—
571D4—22no—
572D4—42no—
573D4—42no—
574D4—41no—
575D4—42no—
576D4—41no—
577D4—42no—
578D4—84no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—41no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—41no—
591C2×C4—42no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—44no—
599C2×C4—42no—
600C2×C4—41no—
601C2×C4—84no—
602C2×C4#120×C15111yescharacteristic
603C2×C4#120×C15111yescharacteristic
604C2×C4#120×C15111yescharacteristic
605C2×C4#120×C15111yescharacteristic
606C2×C4C22×D4×C15111yescharacteristic
607C2×C4C22×D4×C15111yescharacteristic
608C2×C4C2×#41×C15111yescharacteristic
609C2×C4C2×#41×C15111yescharacteristic
610C2×C4H(5,𝔽2)×C15111yescharacteristic
611C2×C42−1+4×C15111yescharacteristic
612C8—22no—
613C8—41no—
614C8—42no—
615C22—21no—
616C22—21no—
617C22—42no—
618C22—41no—
619C22—41no—
620C22—42no—
621C22—41no—
622C22—42no—
623C22C2×#120×C15111yescharacteristic
624C22#548×C15111yescharacteristic
625C22#550×C15111yescharacteristic
626C4—21no—
627C4—21no—
628C4—21no—
629C4—44no—
630C4—42no—
631C4—41no—
632C4—42no—
633C4—41no—
634C4—41no—
635C4—44no—
636C4—81no—
637C4#456×C15112yes—
638C4#525×C15111yescharacteristic
639C4#537×C15111yescharacteristic
640C4#546×C15111yescharacteristic
641C4#547×C15111yescharacteristic
642C2—21no—
643C2—21no—
644C2—81no—
645C2—82no—
646C2#2407×C15111yescharacteristic
647C2C2×#456×C15111yescharacteristic
648C2#3019×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. #2567×C151C2semidirect
5. #2039×C151C2semidirect
6. #2007×C151C2semidirect
7. #1997×C151C2semidirect
8. #1980×C151C2semidirect
9. #1882×C151C2semidirect
10. #1859×C151C2semidirect
11. #1806×C151C2semidirect
159. C2×Q8×C151#41semidirect
188. M16×C151#41semidirect
324. #24173C151direct (N × H)
325. C151#24173direct (N × H)
327. #3037C2×C151semidirect
328. C4×#137C2×C151semidirect
329. #2567C2×C151semidirect
330. #2039C2×C151semidirect
331. #2007C2×C151semidirect
332. #1997C2×C151semidirect
333. #1980C2×C151semidirect
334. #1882C2×C151semidirect
335. #1859C2×C151semidirect
336. #1806C2×C151semidirect
484. C2×Q8#41×C151semidirect
513. 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
#2567×C1512
#2039×C1512
#2007×C1512
#1997×C1512
#1980×C1512
#1882×C1512
#1859×C1512
#1806×C1512
#24173151