Finite Group Databasebeta

← C151×#24145 #50329070

Subgroups — C151×#24145 #50329070

Order 38656.

1038 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#3509×C151C211yesmaximal, characteristic, complemented
2#3077×C151C211yesmaximal, characteristic, complemented
3C4×AGL(1,ℤ/8)×C151C211yesmaximal, characteristic
4#2547×C151C211yesmaximal, characteristic, complemented
5#2038×C151C212yesmaximal, complemented
6#2003×C151C212yesmaximal
7#1986×C151C211yesmaximal, characteristic, complemented
8#1966×C151C211yesmaximal, characteristic, complemented
9#1888×C151C212yesmaximal, complemented
10#1857×C151C212yesmaximal, complemented
11#1806×C151C211yesmaximal, characteristic, complemented
12C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
13#557×C151—21no—
14#557×C151—21no—
15#556×C151—21no—
16#556×C151—21no—
17#552×C151—22no—
18#552×C151—22no—
19#541×C151—22no—
20#536×C151C2212yes—
21#533×C151—21no—
22#533×C151—21no—
23#533×C151C2211yescharacteristic
24C2×C4⋊Q8×C151C2211yescharacteristic
25C2×#124×C151C2212yes—
26#519×C151C2212yes—
27C4×#41×C151C2211yescharacteristic
28C2×C4×D4×C151C2211yescharacteristic
29#478×C151—22no—
30#476×C151—21no—
31#474×C151—21no—
32#442×C151—21no—
33#440×C151—21no—
34C4×SD16×C151—21no—
35C4×D8×C151—21no—
36#428×C151C2211yescharacteristic
37#428×C151C2212yes—
38#423×C151C2211yescharacteristic
39C2×#104×C151C2212yes—
40#418×C151C2211yescharacteristic
41#418×C151C2212yes—
42#417×C151C2211yescharacteristic
43C2×#101×C151C2212yes—
44C2×#101×C151C2212yes—
45C4×M16×C151C2211yescharacteristic
46#397×C151—22no—
47#391×C151C2212yes—
48#380×C151—22no—
49C4×C4⋊C4×C151C2211yescharacteristic
50#339×C151C2212yes—
51#339×C151C2212yes—
52#339×C151C2212yes—
53C2×#41×C151C2311yescharacteristic
54C22×Q8×C151C2312yes—
55C22×D4×C151C2311yescharacteristic
56C23×C4×C151—21no—
57AGL(1,ℤ/8)×C151—22no—
58AGL(1,ℤ/8)×C151—22no—
59C2×SD16×C151—21no—
60C2×D8×C151—21no—
61C2×M16×C151C2311yescharacteristic
62C2×M16×C151C2312yes—
63C2×M16×C151C2311yescharacteristic
64C4⋊Q8×C151—21no—
65C4⋊Q8×C151—21no—
66C4⋊Q8×C151—21no—
67C4⋊Q8×C151—21no—
68C4⋊Q8×C151—22no—
69C4⋊Q8×C151D411yescharacteristic
70C4⋊Q8×C151D411yescharacteristic
71#126×C151—24no—
72#126×C151—24no—
73#125×C151—22no—
74#125×C151—22no—
75#125×C151—24no—
76#125×C151—24no—
77#125×C151D412yes—
78#124×C151—22no—
79#124×C151—24no—
80#124×C151—42no—
81#123×C151—24no—
82C22⋊Q8×C151—22no—
83C22⋊Q8×C151—22no—
84C22⋊Q8×C151—21no—
85C22⋊Q8×C151—21no—
86C22⋊Q8×C151—22no—
87C22⋊Q8×C151—22no—
88C4×Q8×C151—22no—
89C4×Q8×C151—22no—
90C4×Q8×C151—22no—
91C4×Q8×C151—22no—
92C4×Q8×C151—22no—
93C4×Q8×C151—22no—
94C4×Q8×C151—21no—
95C4×Q8×C151—21no—
96C4×Q8×C151D411yescharacteristic
97C4×Q8×C151D411yescharacteristic
98C4×D4×C151—21no—
99C4×D4×C151—21no—
100C4×D4×C151—21no—
101C4×D4×C151—21no—
102C4×D4×C151—21no—
103C4×D4×C151—21no—
104C4×D4×C151D411yescharacteristic
105C4×D4×C151D411yescharacteristic
106#117×C151—22no—
107#117×C151—22no—
108#117×C151—24no—
109#117×C151—21no—
110#117×C151C2311yescharacteristic
111#117×C151C2312yes—
112C2×C4⋊C4×C151—21no—
113C2×C4⋊C4×C151D412yes—
114C2×C4⋊C4×C151D412yes—
115C2×C4⋊C4×C151C2311yescharacteristic
116C2×C22⋊C4×C151—24no—
117C2×C22⋊C4×C151—21no—
118C2×C42×C151—21no—
119C2×C42×C151C2312yes—
120C2×C42×C151C2311yescharacteristic
121#107×C151—21no—
122#107×C151—22no—
123#106×C151—21no—
124#106×C151—22no—
125C4⋊C8×C151—21no—
126C4⋊C8×C151—21no—
127#104×C151—42no—
128#103×C151—21no—
129#102×C151—21no—
130#102×C151—21no—
131#102×C151—21no—
132#102×C151—22no—
133#102×C151—22no—
134#101×C151—24no—
135#101×C151—42no—
136#97×C151—21no—
137C4×C8×C151—21no—
138#95×C151—21no—
139#95×C151—24no—
140C24×C151—21no—
141#41×C151—21no—
142#41×C151—21no—
143#41×C151—21no—
144#41×C151—21no—
145C2×Q8×C151—21no—
146C2×Q8×C151—21no—
147C2×Q8×C151—22no—
148C2×Q8×C151—22no—
149C2×Q8×C151—22no—
150C2×Q8×C151—22no—
151C2×Q8×C151—22no—
152C2×Q8×C151—22no—
153C2×Q8×C151C2×D411yescharacteristic
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151—21no—
160C2×D4×C151C2×D411yescharacteristic
161C2×D4×C151#4112yes—
162C22×C4×C151—21no—
163C22×C4×C151—21no—
164C22×C4×C151—21no—
165C22×C4×C151—21no—
166C22×C4×C151—22no—
167C22×C4×C151—44no—
168C22×C4×C151—41no—
169C22×C4×C151—41no—
170C22×C4×C151C2×D414yes—
171C22×C4×C151C2×D411yescharacteristic
172C22×C4×C151C2×D411yescharacteristic
173C22×C4×C151C2411yescharacteristic
174SD16×C151—24no—
175D8×C151—24no—
176M16×C151—21no—
177M16×C151—22no—
178M16×C151—21no—
179M16×C151—22no—
180M16×C151—21no—
181M16×C151#4112yes—
182C2×C8×C151—21no—
183C2×C8×C151—21no—
184C2×C8×C151—22no—
185C4⋊C4×C151—24no—
186C4⋊C4×C151—24no—
187C4⋊C4×C151—24no—
188C4⋊C4×C151—24no—
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—22no—
198C4⋊C4×C151—22no—
199C4⋊C4×C151—21no—
200C4⋊C4×C151—21no—
201C4⋊C4×C151—42no—
202C4⋊C4×C151C2×D411yescharacteristic
203C4⋊C4×C151C2×D412yes—
204C4⋊C4×C151C2×D411yescharacteristic
205C4⋊C4×C151C2×D412yes—
206C22⋊C4×C151—24no—
207C22⋊C4×C151—24no—
208C22⋊C4×C151—21no—
209C22⋊C4×C151—22no—
210C22⋊C4×C151—21no—
211C22⋊C4×C151—21no—
212C22⋊C4×C151—48no—
213C22⋊C4×C151—41no—
214C22⋊C4×C151—41no—
215C42×C151—24no—
216C42×C151—24no—
217C42×C151—21no—
218C42×C151—21no—
219C42×C151—21no—
220C42×C151—22no—
221C42×C151—22no—
222C42×C151—22no—
223C42×C151C2×D411yescharacteristic
224C42×C151C2×D411yescharacteristic
225C42×C151C2×D411yescharacteristic
226C42×C151C2×D411yescharacteristic
227C23×C151—21no—
228C23×C151—22no—
229C23×C151—42no—
230C23×C151—42no—
231C23×C151—41no—
232C23×C151—41no—
233C23×C151C22×D411yescharacteristic
234Q8×C151—21no—
235Q8×C151—21no—
236Q8×C151—42no—
237Q8×C151—42no—
238Q8×C151—42no—
239Q8×C151—42no—
240Q8×C151—42no—
241Q8×C151—42no—
242D4×C151—21no—
243D4×C151—22no—
244D4×C151—21no—
245D4×C151—22no—
246D4×C151—41no—
247D4×C151—41no—
248D4×C151—41no—
249D4×C151—41no—
250C2×C4×C151—22no—
251C2×C4×C151—24no—
252C2×C4×C151—22no—
253C2×C4×C151—22no—
254C2×C4×C151—21no—
255C2×C4×C151—21no—
256C2×C4×C151—21no—
257C2×C4×C151—24no—
258C2×C4×C151—24no—
259C2×C4×C151—41no—
260C2×C4×C151—42no—
261C2×C4×C151—41no—
262C2×C4×C151—41no—
263C2×C4×C151—42no—
264C2×C4×C151—42no—
265C2×C4×C151—42no—
266C2×C4×C151—42no—
267C2×C4×C151—41no—
268C2×C4×C151—42no—
269C2×C4×C151—82no—
270C2×C4×C151—82no—
271C2×C4×C151#12011yescharacteristic
272C2×C4×C151#12011yescharacteristic
273C2×C4×C151#12011yescharacteristic
274C2×C4×C151#12011yescharacteristic
275C2×C4×C151C22×D411yescharacteristic
276C2×C4×C151C22×D411yescharacteristic
277C2×C4×C151C2×#4111yescharacteristic
278C2×C4×C151C2×#4111yescharacteristic
279C2×C4×C151H(5,𝔽2)11yescharacteristic
280C2×C4×C1512−1+411yescharacteristic
281C8×C151—22no—
282C8×C151—41no—
283C8×C151—42no—
284C22×C151—21no—
285C22×C151—21no—
286C22×C151—44no—
287C22×C151—41no—
288C22×C151—42no—
289C22×C151—41no—
290C22×C151—41no—
291C22×C151—82no—
292C22×C151—81no—
293C22×C151—81no—
294C22×C151C2×#12011yescharacteristic
295C22×C151#54611yescharacteristic
296C22×C151#54711yescharacteristic
297C4×C151—21no—
298C4×C151—21no—
299C4×C151—21no—
300C4×C151—44no—
301C4×C151—41no—
302C4×C151—41no—
303C4×C151—42no—
304C4×C151—41no—
305C4×C151—42no—
306C4×C151—82no—
307C4×C151—81no—
308C4×C151#45412yes—
309C4×C151#52511yescharacteristic
310C4×C151#53711yescharacteristic
311C4×C151#54811yescharacteristic
312C4×C151#55011yescharacteristic
313C2×C151—21no—
314C2×C151—21no—
315C2×C151—81no—
316C2×C151—82no—
317C2×C151#240711yescharacteristic
318C2×C151C2×#45411yescharacteristic
319C2×C151#302011yescharacteristic
320#24145C15111yesmaximal, characteristic, direct product factor, Sylow
321C151#2414511yescharacteristic, direct product factor, Sylow
322#3509C2×C15111yescharacteristic, complemented
323#3077C2×C15111yescharacteristic, complemented
324C4×AGL(1,ℤ/8)C2×C15111yescharacteristic
325#2547C2×C15111yescharacteristic, complemented
326#2038C2×C15112yescomplemented
327#2003C2×C15112yes—
328#1986C2×C15111yescharacteristic, complemented
329#1966C2×C15111yescharacteristic, complemented
330#1888C2×C15112yescomplemented
331#1857C2×C15112yescomplemented
332#1806C2×C15111yescharacteristic, complemented
333C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
334#557—21no—
335#557—21no—
336#556—21no—
337#556—21no—
338#552—22no—
339#552—22no—
340#541—22no—
341#536C22×C15112yes—
342#533—21no—
343#533—21no—
344#533C22×C15111yescharacteristic
345C2×C4⋊Q8C22×C15111yescharacteristic
346C2×#124C22×C15112yes—
347#519C22×C15112yes—
348C4×#41C22×C15111yescharacteristic
349C2×C4×D4C22×C15111yescharacteristic
350#478—22no—
351#476—21no—
352#474—21no—
353#442—21no—
354#440—21no—
355C4×SD16—21no—
356C4×D8—21no—
357#428C22×C15112yes—
358#428C22×C15111yescharacteristic
359#423C22×C15111yescharacteristic
360C2×#104C22×C15112yes—
361#418C22×C15112yes—
362#418C22×C15111yescharacteristic
363#417C22×C15111yescharacteristic
364C2×#101C22×C15112yes—
365C2×#101C22×C15112yes—
366C4×M16C22×C15111yescharacteristic
367#397—22no—
368#391C22×C15112yes—
369#380—22no—
370C4×C4⋊C4C22×C15111yescharacteristic
371#339C22×C15112yes—
372#339C22×C15112yes—
373#339C22×C15112yes—
374C2×#41C23×C15111yescharacteristic
375C22×Q8C23×C15112yes—
376C22×D4C23×C15111yescharacteristic
377C23×C4—21no—
378AGL(1,ℤ/8)—22no—
379AGL(1,ℤ/8)—22no—
380C2×SD16—21no—
381C2×D8—21no—
382C2×M16C23×C15111yescharacteristic
383C2×M16C23×C15112yes—
384C2×M16C23×C15111yescharacteristic
385C4⋊Q8—22no—
386C4⋊Q8—21no—
387C4⋊Q8—21no—
388C4⋊Q8—21no—
389C4⋊Q8—21no—
390C4⋊Q8D4×C15111yescharacteristic
391C4⋊Q8D4×C15111yescharacteristic
392#126—24no—
393#126—24no—
394#125—22no—
395#125—22no—
396#125—24no—
397#125—24no—
398#125D4×C15112yes—
399#124—22no—
400#124—24no—
401#124—42no—
402#123—24no—
403C22⋊Q8—22no—
404C22⋊Q8—22no—
405C22⋊Q8—21no—
406C22⋊Q8—21no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409C4×Q8—22no—
410C4×Q8—22no—
411C4×Q8—22no—
412C4×Q8—22no—
413C4×Q8—22no—
414C4×Q8—22no—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×Q8D4×C15111yescharacteristic
418C4×Q8D4×C15111yescharacteristic
419C4×D4—21no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4—21no—
425C4×D4D4×C15111yescharacteristic
426C4×D4D4×C15111yescharacteristic
427#117—22no—
428#117—22no—
429#117—24no—
430#117—21no—
431#117C23×C15111yescharacteristic
432#117C23×C15112yes—
433C2×C4⋊C4—21no—
434C2×C4⋊C4D4×C15112yes—
435C2×C4⋊C4D4×C15112yes—
436C2×C4⋊C4C23×C15111yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—24no—
439C2×C42—21no—
440C2×C42C23×C15112yes—
441C2×C42C23×C15111yescharacteristic
442#107—21no—
443#107—22no—
444#106—21no—
445#106—22no—
446C4⋊C8—21no—
447C4⋊C8—21no—
448#104—42no—
449#103—21no—
450#102—21no—
451#102—21no—
452#102—21no—
453#102—22no—
454#102—22no—
455#101—24no—
456#101—42no—
457#97—21no—
458C4×C8—21no—
459#95—21no—
460#95—24no—
461C24—21no—
462#41—21no—
463#41—21no—
464#41—21no—
465#41—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—22no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8C2×D4×C15111yescharacteristic
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4C2×D4×C15111yescharacteristic
482C2×D4#41×C15112yes—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—44no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4C2×D4×C15114yes—
492C22×C4C2×D4×C15111yescharacteristic
493C22×C4C2×D4×C15111yescharacteristic
494C22×C4C24×C15111yescharacteristic
495SD16—24no—
496D8—24no—
497M16—21no—
498M16—22no—
499M16—21no—
500M16—22no—
501M16—21no—
502M16#41×C15112yes—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—22no—
506C4⋊C4—24no—
507C4⋊C4—24no—
508C4⋊C4—24no—
509C4⋊C4—24no—
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—22no—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—42no—
523C4⋊C4C2×D4×C15111yescharacteristic
524C4⋊C4C2×D4×C15112yes—
525C4⋊C4C2×D4×C15111yescharacteristic
526C4⋊C4C2×D4×C15112yes—
527C22⋊C4—24no—
528C22⋊C4—24no—
529C22⋊C4—21no—
530C22⋊C4—22no—
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—48no—
534C22⋊C4—41no—
535C22⋊C4—41no—
536C42—24no—
537C42—24no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—22no—
542C42—22no—
543C42—22no—
544C42C2×D4×C15111yescharacteristic
545C42C2×D4×C15111yescharacteristic
546C42C2×D4×C15111yescharacteristic
547C42C2×D4×C15111yescharacteristic
548C23—21no—
549C23—22no—
550C23—42no—
551C23—42no—
552C23—41no—
553C23—41no—
554C23C22×D4×C15111yescharacteristic
555Q8—21no—
556Q8—21no—
557Q8—42no—
558Q8—42no—
559Q8—42no—
560Q8—42no—
561Q8—42no—
562Q8—42no—
563D4—21no—
564D4—22no—
565D4—21no—
566D4—22no—
567D4—41no—
568D4—41no—
569D4—41no—
570D4—41no—
571C2×C4—22no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—21no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—41no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—82no—
591C2×C4—82no—
592C2×C4#120×C15111yescharacteristic
593C2×C4#120×C15111yescharacteristic
594C2×C4#120×C15111yescharacteristic
595C2×C4#120×C15111yescharacteristic
596C2×C4C22×D4×C15111yescharacteristic
597C2×C4C22×D4×C15111yescharacteristic
598C2×C4C2×#41×C15111yescharacteristic
599C2×C4C2×#41×C15111yescharacteristic
600C2×C4H(5,𝔽2)×C15111yescharacteristic
601C2×C42−1+4×C15111yescharacteristic
602C8—22no—
603C8—41no—
604C8—42no—
605C22—21no—
606C22—21no—
607C22—44no—
608C22—41no—
609C22—42no—
610C22—41no—
611C22—41no—
612C22—82no—
613C22—81no—
614C22—81no—
615C22C2×#120×C15111yescharacteristic
616C22#546×C15111yescharacteristic
617C22#547×C15111yescharacteristic
618C4—21no—
619C4—21no—
620C4—21no—
621C4—44no—
622C4—41no—
623C4—41no—
624C4—42no—
625C4—41no—
626C4—42no—
627C4—82no—
628C4—81no—
629C4#454×C15112yes—
630C4#525×C15111yescharacteristic
631C4#537×C15111yescharacteristic
632C4#548×C15111yescharacteristic
633C4#550×C15111yescharacteristic
634C2—21no—
635C2—21no—
636C2—82no—
637C2—81no—
638C2#2407×C15111yescharacteristic
639C2C2×#454×C15111yescharacteristic
640C2#3020×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×AGL(1,ℤ/8)×C151C22
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
1. #3509×C151C2semidirect
2. #3077×C151C2semidirect
4. #2547×C151C2semidirect
5. #2038×C151C2semidirect
7. #1986×C151C2semidirect
8. #1966×C151C2semidirect
9. #1888×C151C2semidirect
10. #1857×C151C2semidirect
11. #1806×C151C2semidirect
320. #24145C151direct (N × H)
321. C151#24145direct (N × H)
322. #3509C2×C151semidirect
323. #3077C2×C151semidirect
325. #2547C2×C151semidirect
326. #2038C2×C151semidirect
328. #1986C2×C151semidirect
329. #1966C2×C151semidirect
330. #1888C2×C151semidirect
331. #1857C2×C151semidirect
332. #1806C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3509×C1512
#3077×C1512
C4×AGL(1,ℤ/8)×C1512
#2547×C1512
#2038×C1512
#2003×C1512
#1986×C1512
#1966×C1512
#1888×C1512
#1857×C1512
#1806×C1512
#24145151