Finite Group Databasebeta

← C151×#24146 #50329071

Subgroups — C151×#24146 #50329071

Order 38656.

1142 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3508×C151C211yesmaximal, characteristic
2#3078×C151C211yesmaximal, characteristic, complemented
3C4×#137×C151C211yesmaximal, characteristic, complemented
4#2548×C151C211yesmaximal, characteristic, complemented
5#2037×C151C212yesmaximal, complemented
6#2004×C151C212yesmaximal, complemented
7#1986×C151C211yesmaximal, characteristic, complemented
8#1965×C151C211yesmaximal, characteristic, complemented
9#1885×C151C212yesmaximal, complemented
10#1856×C151C212yesmaximal, complemented
11#1806×C151C211yesmaximal, characteristic, complemented
12C2×#137×C151C2211yescharacteristic
13#559×C151—21no—
14#559×C151—21no—
15#550×C151—21no—
16#550×C151—21no—
17#546×C151—22no—
18#546×C151—22no—
19#540×C151—22no—
20#535×C151C2212yes—
21#533×C151C2211yescharacteristic
22#532×C151—21no—
23#532×C151—21no—
24C2×#127×C151C2211yescharacteristic
25C2×#124×C151C2212yes—
26#518×C151C2212yes—
27C4×#41×C151C2211yescharacteristic
28C2×C4×Q8×C151C2211yescharacteristic
29#479×C151—22no—
30#477×C151—21no—
31#475×C151—21no—
32#441×C151—21no—
33#440×C151—21no—
34C4×Q16×C151—21no—
35C4×SD16×C151—21no—
36#428×C151C2211yescharacteristic
37#428×C151C2212yes—
38#423×C151C2211yescharacteristic
39C2×#104×C151C2212yes—
40#419×C151C2211yescharacteristic
41#419×C151C2212yes—
42#417×C151C2211yescharacteristic
43C2×#100×C151C2212yes—
44C2×#100×C151C2212yes—
45C4×M16×C151C2211yescharacteristic
46#394×C151—22no—
47#390×C151—22no—
48#390×C151C2212yes—
49C4×C4⋊C4×C151C2211yescharacteristic
50#339×C151C2212yes—
51#339×C151C2212yes—
52#339×C151C2212yes—
53C2×#41×C151—22no—
54C2×#41×C151—22no—
55C2×#41×C151C2311yescharacteristic
56C22×Q8×C151C2311yescharacteristic
57C22×D4×C151D412yes—
58C22×D4×C151D412yes—
59C22×D4×C151C2312yes—
60#137×C151—22no—
61#137×C151—22no—
62C2×Q16×C151—21no—
63C2×SD16×C151—21no—
64C2×M16×C151C2311yescharacteristic
65C2×M16×C151C2312yes—
66C2×M16×C151C2311yescharacteristic
67C4⋊Q8×C151D411yescharacteristic
68C4⋊Q8×C151D411yescharacteristic
69#127×C151—22no—
70#127×C151—21no—
71#127×C151—21no—
72#127×C151—21no—
73#127×C151—21no—
74#125×C151D412yes—
75#124×C151—22no—
76#124×C151—22no—
77#124×C151—22no—
78#124×C151—24no—
79#124×C151—42no—
80#123×C151—24no—
81#123×C151—24no—
82C22⋊Q8×C151—21no—
83C22⋊Q8×C151—21no—
84#121×C151—22no—
85#121×C151—22no—
86#121×C151—24no—
87#121×C151—24no—
88#121×C151—22no—
89#121×C151—22no—
90#120×C151—24no—
91C4×Q8×C151—21no—
92C4×Q8×C151—21no—
93C4×Q8×C151—21no—
94C4×Q8×C151—21no—
95C4×Q8×C151—21no—
96C4×Q8×C151—21no—
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—22no—
104C4×D4×C151—22no—
105C4×D4×C151—22no—
106C4×D4×C151—22no—
107C4×D4×C151D411yescharacteristic
108C4×D4×C151D411yescharacteristic
109#117×C151—21no—
110#117×C151C2311yescharacteristic
111#117×C151C2312yes—
112C2×C4⋊C4×C151—21no—
113C2×C4⋊C4×C151—21no—
114C2×C4⋊C4×C151C2311yescharacteristic
115C2×C22⋊C4×C151—24no—
116C2×C22⋊C4×C151—24no—
117C2×C22⋊C4×C151—24no—
118C2×C42×C151—21no—
119C2×C42×C151—21no—
120C2×C42×C151C2312yes—
121C2×C42×C151C2311yescharacteristic
122#107×C151—21no—
123#107×C151—22no—
124#106×C151—21no—
125#106×C151—22no—
126C4⋊C8×C151—21no—
127C4⋊C8×C151—21no—
128#104×C151—42no—
129#103×C151—21no—
130#103×C151—21no—
131#103×C151—22no—
132#103×C151—22no—
133#103×C151—21no—
134#102×C151—21no—
135#100×C151—24no—
136#100×C151—42no—
137#97×C151—21no—
138C4×C8×C151—21no—
139#95×C151—21no—
140C24×C151C2×D414yes—
141#41×C151—21no—
142#41×C151—21no—
143#41×C151—21no—
144#41×C151—21no—
145#41×C151—84no—
146#41×C151—84no—
147C2×Q8×C151—21no—
148C2×Q8×C151—21no—
149C2×Q8×C151—21no—
150C2×Q8×C151—21no—
151C2×Q8×C151—21no—
152C2×Q8×C151—21no—
153C2×Q8×C151—21no—
154C2×Q8×C151C2×D411yescharacteristic
155C2×Q8×C151#4112yescomplemented
156C2×D4×C151—21no—
157C2×D4×C151—24no—
158C2×D4×C151—24no—
159C2×D4×C151—22no—
160C2×D4×C151—22no—
161C2×D4×C151—22no—
162C2×D4×C151—22no—
163C2×D4×C151—22no—
164C2×D4×C151—22no—
165C2×D4×C151—22no—
166C2×D4×C151—22no—
167C2×D4×C151—22no—
168C2×D4×C151—22no—
169C2×D4×C151—44no—
170C2×D4×C151—82no—
171C2×D4×C151C2×D411yescharacteristic
172C22×C4×C151—21no—
173C22×C4×C151—24no—
174C22×C4×C151—24no—
175C22×C4×C151—21no—
176C22×C4×C151—21no—
177C22×C4×C151—21no—
178C22×C4×C151—22no—
179C22×C4×C151—21no—
180C22×C4×C151C2×D411yescharacteristic
181C22×C4×C151C2×D411yescharacteristic
182C22×C4×C151C2411yescharacteristic
183Q16×C151—24no—
184SD16×C151—24no—
185M16×C151—21no—
186M16×C151—22no—
187M16×C151—21no—
188M16×C151—22no—
189M16×C151—21no—
190M16×C151#4112yescomplemented
191C2×C8×C151—21no—
192C2×C8×C151—21no—
193C2×C8×C151—22no—
194C4⋊C4×C151—21no—
195C4⋊C4×C151—21no—
196C4⋊C4×C151—21no—
197C4⋊C4×C151—21no—
198C4⋊C4×C151—22no—
199C4⋊C4×C151—22no—
200C4⋊C4×C151—21no—
201C4⋊C4×C151—21no—
202C4⋊C4×C151—42no—
203C4⋊C4×C151—41no—
204C4⋊C4×C151—41no—
205C4⋊C4×C151C2×D411yescharacteristic
206C4⋊C4×C151C2×D412yes—
207C4⋊C4×C151C2×D411yescharacteristic
208C4⋊C4×C151C2×D412yes—
209C22⋊C4×C151—24no—
210C22⋊C4×C151—24no—
211C22⋊C4×C151—24no—
212C22⋊C4×C151—24no—
213C22⋊C4×C151—21no—
214C22⋊C4×C151—22no—
215C22⋊C4×C151—21no—
216C22⋊C4×C151—21no—
217C22⋊C4×C151—48no—
218C22⋊C4×C151—84no—
219C42×C151—21no—
220C42×C151—21no—
221C42×C151—21no—
222C42×C151—22no—
223C42×C151—22no—
224C42×C151—22no—
225C42×C151—41no—
226C42×C151—41no—
227C42×C151C2×D411yescharacteristic
228C42×C151C2×D411yescharacteristic
229C42×C151C2×D411yescharacteristic
230C42×C151C2×D411yescharacteristic
231C23×C151—24no—
232C23×C151—21no—
233C23×C151—24no—
234C23×C151—24no—
235C23×C151—44no—
236C23×C151—44no—
237C23×C151C22×D411yescharacteristic
238Q8×C151—22no—
239Q8×C151—21no—
240Q8×C151—21no—
241Q8×C151—22no—
242Q8×C151—42no—
243Q8×C151—41no—
244Q8×C151—41no—
245Q8×C151—42no—
246D4×C151—21no—
247D4×C151—21no—
248D4×C151—44no—
249D4×C151—41no—
250D4×C151—41no—
251D4×C151—42no—
252D4×C151—42no—
253D4×C151—42no—
254D4×C151—42no—
255D4×C151—44no—
256D4×C151—82no—
257D4×C151—82no—
258D4×C151—84no—
259D4×C151—84no—
260C2×C4×C151—22no—
261C2×C4×C151—22no—
262C2×C4×C151—22no—
263C2×C4×C151—21no—
264C2×C4×C151—21no—
265C2×C4×C151—21no—
266C2×C4×C151—22no—
267C2×C4×C151—41no—
268C2×C4×C151—42no—
269C2×C4×C151—41no—
270C2×C4×C151—41no—
271C2×C4×C151—41no—
272C2×C4×C151—41no—
273C2×C4×C151—42no—
274C2×C4×C151—42no—
275C2×C4×C151—42no—
276C2×C4×C151—42no—
277C2×C4×C151—41no—
278C2×C4×C151—42no—
279C2×C4×C151—84no—
280C2×C4×C151—84no—
281C2×C4×C151#12011yescharacteristic
282C2×C4×C151#12011yescharacteristic
283C2×C4×C151#12011yescharacteristic
284C2×C4×C151#12011yescharacteristic
285C2×C4×C151C22×D411yescharacteristic
286C2×C4×C151C22×D411yescharacteristic
287C2×C4×C151C2×#4111yescharacteristic
288C2×C4×C151C2×#4111yescharacteristic
289C2×C4×C151H(5,𝔽2)11yescharacteristic
290C2×C4×C1512−1+411yescharacteristic
291C8×C151—22no—
292C8×C151—41no—
293C8×C151—42no—
294C22×C151—21no—
295C22×C151—21no—
296C22×C151—41no—
297C22×C151—44no—
298C22×C151—41no—
299C22×C151—44no—
300C22×C151—41no—
301C22×C151—44no—
302C22×C151—84no—
303C22×C151—84no—
304C22×C151C2×#12011yescharacteristic
305C22×C151#54611yescharacteristic
306C22×C151#54711yescharacteristic
307C4×C151—21no—
308C4×C151—21no—
309C4×C151—21no—
310C4×C151—41no—
311C4×C151—42no—
312C4×C151—41no—
313C4×C151—42no—
314C4×C151—41no—
315C4×C151—42no—
316C4×C151—82no—
317C4×C151—81no—
318C4×C151#45512yes—
319C4×C151#52511yescharacteristic
320C4×C151#53711yescharacteristic
321C4×C151#54811yescharacteristic
322C4×C151#55011yescharacteristic
323C2×C151—21no—
324C2×C151—21no—
325C2×C151—81no—
326C2×C151—84no—
327C2×C151#240711yescharacteristic
328C2×C151C2×#45511yescharacteristic
329C2×C151#301911yescharacteristic
330#24146C15111yesmaximal, characteristic, direct product factor, Sylow
331C151#2414611yescharacteristic, direct product factor, Sylow
332#3508C2×C15111yescharacteristic
333#3078C2×C15111yescharacteristic, complemented
334C4×#137C2×C15111yescharacteristic, complemented
335#2548C2×C15111yescharacteristic, complemented
336#2037C2×C15112yescomplemented
337#2004C2×C15112yescomplemented
338#1986C2×C15111yescharacteristic, complemented
339#1965C2×C15111yescharacteristic, complemented
340#1885C2×C15112yescomplemented
341#1856C2×C15112yescomplemented
342#1806C2×C15111yescharacteristic, complemented
343C2×#137C22×C15111yescharacteristic
344#559—21no—
345#559—21no—
346#550—21no—
347#550—21no—
348#546—22no—
349#546—22no—
350#540—22no—
351#535C22×C15112yes—
352#533C22×C15111yescharacteristic
353#532—21no—
354#532—21no—
355C2×#127C22×C15111yescharacteristic
356C2×#124C22×C15112yes—
357#518C22×C15112yes—
358C4×#41C22×C15111yescharacteristic
359C2×C4×Q8C22×C15111yescharacteristic
360#479—22no—
361#477—21no—
362#475—21no—
363#441—21no—
364#440—21no—
365C4×Q16—21no—
366C4×SD16—21no—
367#428C22×C15112yes—
368#428C22×C15111yescharacteristic
369#423C22×C15111yescharacteristic
370C2×#104C22×C15112yes—
371#419C22×C15112yes—
372#419C22×C15111yescharacteristic
373#417C22×C15111yescharacteristic
374C2×#100C22×C15112yes—
375C2×#100C22×C15112yes—
376C4×M16C22×C15111yescharacteristic
377#394—22no—
378#390—22no—
379#390C22×C15112yes—
380C4×C4⋊C4C22×C15111yescharacteristic
381#339C22×C15112yes—
382#339C22×C15112yes—
383#339C22×C15112yes—
384C2×#41—22no—
385C2×#41—22no—
386C2×#41C23×C15111yescharacteristic
387C22×Q8C23×C15111yescharacteristic
388C22×D4D4×C15112yes—
389C22×D4D4×C15112yes—
390C22×D4C23×C15112yes—
391#137—22no—
392#137—22no—
393C2×Q16—21no—
394C2×SD16—21no—
395C2×M16C23×C15111yescharacteristic
396C2×M16C23×C15112yes—
397C2×M16C23×C15111yescharacteristic
398C4⋊Q8D4×C15111yescharacteristic
399C4⋊Q8D4×C15111yescharacteristic
400#127—22no—
401#127—21no—
402#127—21no—
403#127—21no—
404#127—21no—
405#125D4×C15112yes—
406#124—22no—
407#124—22no—
408#124—22no—
409#124—24no—
410#124—42no—
411#123—24no—
412#123—24no—
413C22⋊Q8—21no—
414C22⋊Q8—21no—
415#121—22no—
416#121—22no—
417#121—24no—
418#121—24no—
419#121—22no—
420#121—22no—
421#120—24no—
422C4×Q8—21no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8—21no—
426C4×Q8—21no—
427C4×Q8—21no—
428C4×Q8D4×C15111yescharacteristic
429C4×Q8D4×C15111yescharacteristic
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4—22no—
435C4×D4—22no—
436C4×D4—22no—
437C4×D4—22no—
438C4×D4D4×C15111yescharacteristic
439C4×D4D4×C15111yescharacteristic
440#117—21no—
441#117C23×C15111yescharacteristic
442#117C23×C15112yes—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4C23×C15111yescharacteristic
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C42—21no—
450C2×C42—21no—
451C2×C42C23×C15112yes—
452C2×C42C23×C15111yescharacteristic
453#107—21no—
454#107—22no—
455#106—21no—
456#106—22no—
457C4⋊C8—21no—
458C4⋊C8—21no—
459#104—42no—
460#103—21no—
461#103—21no—
462#103—21no—
463#103—22no—
464#103—22no—
465#102—21no—
466#100—24no—
467#100—42no—
468#97—21no—
469C4×C8—21no—
470#95—21no—
471C24C2×D4×C15114yes—
472#41—21no—
473#41—21no—
474#41—21no—
475#41—21no—
476#41—84no—
477#41—84no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8C2×D4×C15111yescharacteristic
486C2×Q8#41×C15112yescomplemented
487C2×D4—21no—
488C2×D4—24no—
489C2×D4—24no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—22no—
499C2×D4—22no—
500C2×D4—44no—
501C2×D4—82no—
502C2×D4C2×D4×C15111yescharacteristic
503C22×C4—21no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4C2×D4×C15111yescharacteristic
512C22×C4C2×D4×C15111yescharacteristic
513C22×C4C24×C15111yescharacteristic
514Q16—24no—
515SD16—24no—
516M16—21no—
517M16—22no—
518M16—21no—
519M16—22no—
520M16—21no—
521M16#41×C15112yescomplemented
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—22no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—42no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4C2×D4×C15111yescharacteristic
537C4⋊C4C2×D4×C15112yes—
538C4⋊C4C2×D4×C15111yescharacteristic
539C4⋊C4C2×D4×C15112yes—
540C22⋊C4—24no—
541C22⋊C4—24no—
542C22⋊C4—24no—
543C22⋊C4—24no—
544C22⋊C4—21no—
545C22⋊C4—22no—
546C22⋊C4—21no—
547C22⋊C4—21no—
548C22⋊C4—48no—
549C22⋊C4—84no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—22no—
554C42—22no—
555C42—22no—
556C42—41no—
557C42—41no—
558C42C2×D4×C15111yescharacteristic
559C42C2×D4×C15111yescharacteristic
560C42C2×D4×C15111yescharacteristic
561C42C2×D4×C15111yescharacteristic
562C23—24no—
563C23—21no—
564C23—24no—
565C23—24no—
566C23—44no—
567C23—44no—
568C23C22×D4×C15111yescharacteristic
569Q8—22no—
570Q8—21no—
571Q8—21no—
572Q8—22no—
573Q8—42no—
574Q8—42no—
575Q8—41no—
576Q8—41no—
577D4—21no—
578D4—21no—
579D4—44no—
580D4—41no—
581D4—41no—
582D4—44no—
583D4—42no—
584D4—42no—
585D4—42no—
586D4—42no—
587D4—82no—
588D4—82no—
589D4—84no—
590D4—84no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—41no—
599C2×C4—42no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—42no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—84no—
611C2×C4—84no—
612C2×C4#120×C15111yescharacteristic
613C2×C4#120×C15111yescharacteristic
614C2×C4#120×C15111yescharacteristic
615C2×C4#120×C15111yescharacteristic
616C2×C4C22×D4×C15111yescharacteristic
617C2×C4C22×D4×C15111yescharacteristic
618C2×C4C2×#41×C15111yescharacteristic
619C2×C4C2×#41×C15111yescharacteristic
620C2×C4H(5,𝔽2)×C15111yescharacteristic
621C2×C42−1+4×C15111yescharacteristic
622C8—22no—
623C8—41no—
624C8—42no—
625C22—21no—
626C22—21no—
627C22—41no—
628C22—44no—
629C22—41no—
630C22—44no—
631C22—41no—
632C22—44no—
633C22—84no—
634C22—84no—
635C22C2×#120×C15111yescharacteristic
636C22#546×C15111yescharacteristic
637C22#547×C15111yescharacteristic
638C4—21no—
639C4—21no—
640C4—21no—
641C4—41no—
642C4—42no—
643C4—41no—
644C4—42no—
645C4—41no—
646C4—42no—
647C4—82no—
648C4—81no—
649C4#455×C15112yes—
650C4#525×C15111yescharacteristic
651C4#537×C15111yescharacteristic
652C4#548×C15111yescharacteristic
653C4#550×C15111yescharacteristic
654C2—21no—
655C2—21no—
656C2—84no—
657C2—81no—
658C2#2407×C15111yescharacteristic
659C2C2×#455×C15111yescharacteristic
660C2#3019×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3508×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. #3078×C151C2semidirect
3. C4×#137×C151C2semidirect
4. #2548×C151C2semidirect
5. #2037×C151C2semidirect
6. #2004×C151C2semidirect
7. #1986×C151C2semidirect
8. #1965×C151C2semidirect
9. #1885×C151C2semidirect
10. #1856×C151C2semidirect
11. #1806×C151C2semidirect
155. C2×Q8×C151#41semidirect
190. M16×C151#41semidirect
330. #24146C151direct (N × H)
331. C151#24146direct (N × H)
333. #3078C2×C151semidirect
334. C4×#137C2×C151semidirect
335. #2548C2×C151semidirect
336. #2037C2×C151semidirect
337. #2004C2×C151semidirect
338. #1986C2×C151semidirect
339. #1965C2×C151semidirect
340. #1885C2×C151semidirect
341. #1856C2×C151semidirect
342. #1806C2×C151semidirect
486. C2×Q8#41×C151semidirect
521. M16#41×C151semidirect

Maximal subgroups

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

subgroupindex
#3508×C1512
#3078×C1512
C4×#137×C1512
#2548×C1512
#2037×C1512
#2004×C1512
#1986×C1512
#1965×C1512
#1885×C1512
#1856×C1512
#1806×C1512
#24146151