Finite Group Databasebeta

← C151×#23961 #50328886

Subgroups — C151×#23961 #50328886

Order 38656.

1494 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C151C211yesmaximal, characteristic
2C2×#448×C151C211yesmaximal, characteristic, complemented
3C22×#103×C151C211yesmaximal, characteristic, complemented
4#2409×C151C211yesmaximal, characteristic, complemented
5#2024×C151C212yesmaximal, complemented
6#2000×C151C212yesmaximal, complemented
7#1893×C151C211yesmaximal, characteristic, complemented
8#1877×C151C212yesmaximal, complemented
9#1872×C151C212yesmaximal, complemented
10#1869×C151C211yesmaximal, characteristic, complemented
11#1823×C151C211yesmaximal, characteristic, complemented
12C22×#41×C151—21no—
13C23×Q8×C151C2211yescharacteristic
14C22×SD16×C151C2212yes—
15C23×C8×C151C2211yescharacteristic
16#547×C151—24no—
17#547×C151—24no—
18C2×C4⋊Q8×C151C2211yescharacteristic
19C2×#123×C151—21no—
20C2×#123×C151—21no—
21C2×C22⋊Q8×C151—21no—
22C2×C22⋊Q8×C151C2212yes—
23C2×#121×C151C2211yescharacteristic
24C2×#121×C151C2211yescharacteristic
25C2×C4×D4×C151C2211yescharacteristic
26C2×C4×D4×C151C2211yescharacteristic
27C22×C4⋊C4×C151C2211yescharacteristic
28C22×C4⋊C4×C151C2211yescharacteristic
29#448×C151—24no—
30C2×#103×C151—24no—
31C2×#103×C151C2212yes—
32C2×#103×C151C2212yes—
33C2×#103×C151C2212yes—
34C2×#102×C151C2212yes—
35C2×C22⋊C8×C151C2211yescharacteristic
36C2×C22⋊C8×C151C2212yes—
37#395×C151—21no—
38#393×C151—21no—
39#391×C151C2212yes—
40#386×C151—21no—
41#385×C151—21no—
42#380×C151C2211yescharacteristic
43#340×C151C2212yes—
44#340×C151C2212yes—
45#340×C151C2212yes—
46#336×C151C2212yes—
47C2×#41×C151—28no—
48C2×#41×C151—44no—
49C2×#41×C151—44no—
50C22×Q8×C151—22no—
51C22×Q8×C151—24no—
52C22×Q8×C151—21no—
53C22×Q8×C151—22no—
54C22×Q8×C151—21no—
55C22×Q8×C151—42no—
56C22×Q8×C151C2312yes—
57C22×D4×C151—21no—
58C22×D4×C151—21no—
59C22×D4×C151D411yescharacteristic
60C22×D4×C151C2311yescharacteristic
61C23×C4×C151—21no—
62C23×C4×C151—21no—
63C23×C4×C151—21no—
64C23×C4×C151—21no—
65C23×C4×C151C2311yescharacteristic
66C23×C4×C151C2311yescharacteristic
67C2×SD16×C151—24no—
68C2×SD16×C151—24no—
69C2×SD16×C151—42no—
70C22×C8×C151—22no—
71C22×C8×C151—42no—
72C22×C8×C151C2312yes—
73C22×C8×C151C2312yes—
74C4⋊Q8×C151—22no—
75C4⋊Q8×C151—22no—
76#123×C151—28no—
77#123×C151—28no—
78C22⋊Q8×C151—28no—
79C22⋊Q8×C151—24no—
80C22⋊Q8×C151—42no—
81#121×C151—22no—
82#121×C151—22no—
83#121×C151—22no—
84#121×C151D414yes—
85C4×D4×C151—22no—
86C4×D4×C151—22no—
87C4×D4×C151—22no—
88C4×D4×C151—22no—
89C2×C4⋊C4×C151—21no—
90C2×C4⋊C4×C151—21no—
91C2×C4⋊C4×C151—22no—
92C2×C4⋊C4×C151—21no—
93C2×C4⋊C4×C151—22no—
94C2×C4⋊C4×C151—22no—
95C2×C4⋊C4×C151—22no—
96C2×C4⋊C4×C151D411yescharacteristic
97C2×C4⋊C4×C151D414yes—
98C2×C4⋊C4×C151C2312yes—
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C4⋊C4×C151C2311yescharacteristic
101C2×C4⋊C4×C151C2311yescharacteristic
102C2×C22⋊C4×C151—21no—
103C2×C22⋊C4×C151—21no—
104C2×C22⋊C4×C151—21no—
105C2×C22⋊C4×C151—21no—
106C2×C22⋊C4×C151—22no—
107C2×C22⋊C4×C151D411yescharacteristic
108C2×C22⋊C4×C151D411yescharacteristic
109C2×C42×C151C2311yescharacteristic
110#103×C151—24no—
111#103×C151—24no—
112#103×C151—24no—
113#102×C151—42no—
114C22⋊C8×C151—22no—
115C22⋊C8×C151—42no—
116#95×C151—21no—
117#95×C151—22no—
118#95×C151—22no—
119C24×C151—21no—
120C24×C151C2×D411yescharacteristic
121C24×C151C2×D411yescharacteristic
122#41×C151—432no—
123C2×Q8×C151—24no—
124C2×Q8×C151—22no—
125C2×Q8×C151—28no—
126C2×Q8×C151—22no—
127C2×Q8×C151—22no—
128C2×Q8×C151—22no—
129C2×Q8×C151—22no—
130C2×Q8×C151—44no—
131C2×Q8×C151—48no—
132C2×Q8×C151—44no—
133C2×Q8×C151—42no—
134C2×Q8×C151—42no—
135C2×Q8×C151—42no—
136C2×Q8×C151#4114yescomplemented
137C2×D4×C151—22no—
138C2×D4×C151—22no—
139C2×D4×C151—24no—
140C2×D4×C151—24no—
141C2×D4×C151—21no—
142C2×D4×C151—22no—
143C2×D4×C151—22no—
144C2×D4×C151—42no—
145C2×D4×C151—42no—
146C2×D4×C151—42no—
147C2×D4×C151—42no—
148C2×D4×C151SD1614yescomplemented
149C2×D4×C151C2×D412yes—
150C22×C4×C151—22no—
151C22×C4×C151—22no—
152C22×C4×C151—24no—
153C22×C4×C151—24no—
154C22×C4×C151—24no—
155C22×C4×C151—22no—
156C22×C4×C151—21no—
157C22×C4×C151—21no—
158C22×C4×C151—21no—
159C22×C4×C151—21no—
160C22×C4×C151—21no—
161C22×C4×C151—22no—
162C22×C4×C151—22no—
163C22×C4×C151—22no—
164C22×C4×C151—44no—
165C22×C4×C151—42no—
166C22×C4×C151—42no—
167C22×C4×C151—42no—
168C22×C4×C151—42no—
169C22×C4×C151—42no—
170C22×C4×C151—42no—
171C22×C4×C151—42no—
172C22×C4×C151C2×D411yescharacteristic
173C22×C4×C151C2×D411yescharacteristic
174C22×C4×C151C2×D411yescharacteristic
175C22×C4×C151C2×D412yes—
176C22×C4×C151C2×D412yes—
177C22×C4×C151C2×D411yescharacteristic
178C22×C4×C151C2411yescharacteristic
179SD16×C151—48no—
180C2×C8×C151—22no—
181C2×C8×C151—22no—
182C2×C8×C151—22no—
183C2×C8×C151—22no—
184C2×C8×C151—22no—
185C2×C8×C151—22no—
186C2×C8×C151—44no—
187C4⋊C4×C151—24no—
188C4⋊C4×C151—24no—
189C4⋊C4×C151—24no—
190C4⋊C4×C151—22no—
191C4⋊C4×C151—21no—
192C4⋊C4×C151—21no—
193C4⋊C4×C151—21no—
194C4⋊C4×C151—22no—
195C4⋊C4×C151—22no—
196C4⋊C4×C151—44no—
197C4⋊C4×C151C2×D412yes—
198C4⋊C4×C151C2×D412yes—
199C4⋊C4×C151C2×D412yes—
200C22⋊C4×C151—24no—
201C22⋊C4×C151—24no—
202C22⋊C4×C151—22no—
203C22⋊C4×C151—24no—
204C22⋊C4×C151—22no—
205C22⋊C4×C151—44no—
206C22⋊C4×C151—42no—
207C42×C151—21no—
208C42×C151—21no—
209C23×C151—22no—
210C23×C151—22no—
211C23×C151—21no—
212C23×C151—22no—
213C23×C151—21no—
214C23×C151—22no—
215C23×C151—22no—
216C23×C151—42no—
217C23×C151—41no—
218C23×C151—41no—
219C23×C151—42no—
220C23×C151#12012yes—
221C23×C151C2×SD1612yes—
222C23×C151C2×SD1612yes—
223C23×C151AGL(1,ℤ/8)12yes—
224C23×C151C22×D411yescharacteristic
225Q8×C151—24no—
226Q8×C151—24no—
227Q8×C151—48no—
228Q8×C151—48no—
229Q8×C151—42no—
230Q8×C151—42no—
231D4×C151—28no—
232D4×C151—24no—
233D4×C151—48no—
234D4×C151—48no—
235D4×C151—41no—
236D4×C151—41no—
237C2×C4×C151—21no—
238C2×C4×C151—22no—
239C2×C4×C151—21no—
240C2×C4×C151—22no—
241C2×C4×C151—22no—
242C2×C4×C151—24no—
243C2×C4×C151—22no—
244C2×C4×C151—22no—
245C2×C4×C151—21no—
246C2×C4×C151—21no—
247C2×C4×C151—22no—
248C2×C4×C151—24no—
249C2×C4×C151—22no—
250C2×C4×C151—22no—
251C2×C4×C151—48no—
252C2×C4×C151—48no—
253C2×C4×C151—48no—
254C2×C4×C151—42no—
255C2×C4×C151—42no—
256C2×C4×C151—41no—
257C2×C4×C151—41no—
258C2×C4×C151—41no—
259C2×C4×C151—41no—
260C2×C4×C151—41no—
261C2×C4×C151—41no—
262C2×C4×C151—48no—
263C2×C4×C151—41no—
264C2×C4×C151—41no—
265C2×C4×C151—42no—
266C2×C4×C151—42no—
267C2×C4×C151—42no—
268C2×C4×C151—42no—
269C2×C4×C151#12012yes—
270C2×C4×C151C2×SD1612yes—
271C2×C4×C151C22×D411yescharacteristic
272C2×C4×C151C22×D411yescharacteristic
273C2×C4×C151C2×#4112yes—
274C2×C4×C151H(5,𝔽2)12yes—
275C8×C151—42no—
276C8×C151—42no—
277C22×C151—22no—
278C22×C151—22no—
279C22×C151—24no—
280C22×C151—24no—
281C22×C151—22no—
282C22×C151—24no—
283C22×C151—41no—
284C22×C151—41no—
285C22×C151—42no—
286C22×C151—42no—
287C22×C151—42no—
288C22×C151—42no—
289C22×C151—82no—
290C22×C151—82no—
291C22×C151#45014yes—
292C22×C151C2×#12011yescharacteristic
293C22×C151#54612yes—
294C22×C151C22×SD1611yescharacteristic
295C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
296C22×C151#57812yes—
297C4×C151—22no—
298C4×C151—22no—
299C4×C151—41no—
300C4×C151—44no—
301C4×C151—42no—
302C4×C151—42no—
303C4×C151—42no—
304C4×C151—41no—
305C4×C151—82no—
306C4×C151#52511yescharacteristic
307C4×C151#53511yescharacteristic
308C4×C151#54612yes—
309C2×C151—24no—
310C2×C151—42no—
311C2×C151—82no—
312C2×C151#240411yescharacteristic
313C2×C151C2×#45011yescharacteristic
314C2×C151#301111yescharacteristic
315C2×C151#329812yes—
316C2×C151#330812yes—
317#23961C15111yesmaximal, characteristic, direct product factor, Sylow
318C151#2396111yescharacteristic, direct product factor, Sylow
319C2×#547C2×C15111yescharacteristic
320C2×#448C2×C15111yescharacteristic, complemented
321C22×#103C2×C15111yescharacteristic, complemented
322#2409C2×C15111yescharacteristic, complemented
323#2024C2×C15112yescomplemented
324#2000C2×C15112yescomplemented
325#1893C2×C15111yescharacteristic, complemented
326#1877C2×C15112yescomplemented
327#1872C2×C15112yescomplemented
328#1869C2×C15111yescharacteristic, complemented
329#1823C2×C15111yescharacteristic, complemented
330C22×#41—21no—
331C23×Q8C22×C15111yescharacteristic
332C22×SD16C22×C15112yes—
333C23×C8C22×C15111yescharacteristic
334#547—24no—
335#547—24no—
336C2×C4⋊Q8C22×C15111yescharacteristic
337C2×#123—21no—
338C2×#123—21no—
339C2×C22⋊Q8—21no—
340C2×C22⋊Q8C22×C15112yes—
341C2×#121C22×C15111yescharacteristic
342C2×#121C22×C15111yescharacteristic
343C2×C4×D4C22×C15111yescharacteristic
344C2×C4×D4C22×C15111yescharacteristic
345C22×C4⋊C4C22×C15111yescharacteristic
346C22×C4⋊C4C22×C15111yescharacteristic
347#448—24no—
348C2×#103—24no—
349C2×#103C22×C15112yes—
350C2×#103C22×C15112yes—
351C2×#103C22×C15112yes—
352C2×#102C22×C15112yes—
353C2×C22⋊C8C22×C15111yescharacteristic
354C2×C22⋊C8C22×C15112yes—
355#395—21no—
356#393—21no—
357#391C22×C15112yes—
358#386—21no—
359#385—21no—
360#380C22×C15111yescharacteristic
361#340C22×C15112yes—
362#340C22×C15112yes—
363#340C22×C15112yes—
364#336C22×C15112yes—
365C2×#41—28no—
366C2×#41—44no—
367C2×#41—44no—
368C22×Q8—21no—
369C22×Q8—21no—
370C22×Q8—24no—
371C22×Q8—22no—
372C22×Q8—22no—
373C22×Q8—42no—
374C22×Q8C23×C15112yes—
375C22×D4—21no—
376C22×D4—21no—
377C22×D4D4×C15111yescharacteristic
378C22×D4C23×C15111yescharacteristic
379C23×C4—21no—
380C23×C4—21no—
381C23×C4—21no—
382C23×C4—21no—
383C23×C4C23×C15111yescharacteristic
384C23×C4C23×C15111yescharacteristic
385C2×SD16—24no—
386C2×SD16—24no—
387C2×SD16—42no—
388C22×C8—22no—
389C22×C8—42no—
390C22×C8C23×C15112yes—
391C22×C8C23×C15112yes—
392C4⋊Q8—22no—
393C4⋊Q8—22no—
394#123—28no—
395#123—28no—
396C22⋊Q8—28no—
397C22⋊Q8—24no—
398C22⋊Q8—42no—
399#121—22no—
400#121—22no—
401#121—22no—
402#121D4×C15114yes—
403C4×D4—22no—
404C4×D4—22no—
405C4×D4—22no—
406C4×D4—22no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4D4×C15111yescharacteristic
415C2×C4⋊C4D4×C15114yes—
416C2×C4⋊C4C23×C15112yes—
417C2×C4⋊C4C23×C15111yescharacteristic
418C2×C4⋊C4C23×C15111yescharacteristic
419C2×C4⋊C4C23×C15111yescharacteristic
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—22no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4D4×C15111yescharacteristic
426C2×C22⋊C4D4×C15111yescharacteristic
427C2×C42C23×C15111yescharacteristic
428#103—24no—
429#103—24no—
430#103—24no—
431#102—42no—
432C22⋊C8—22no—
433C22⋊C8—42no—
434#95—21no—
435#95—22no—
436#95—22no—
437C24—21no—
438C24C2×D4×C15111yescharacteristic
439C24C2×D4×C15111yescharacteristic
440#41—432no—
441C2×Q8—24no—
442C2×Q8—22no—
443C2×Q8—28no—
444C2×Q8—22no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—44no—
449C2×Q8—48no—
450C2×Q8—44no—
451C2×Q8—42no—
452C2×Q8—42no—
453C2×Q8—42no—
454C2×Q8#41×C15114yescomplemented
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—24no—
458C2×D4—24no—
459C2×D4—21no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—42no—
465C2×D4—42no—
466C2×D4SD16×C15114yescomplemented
467C2×D4C2×D4×C15112yes—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—44no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4C2×D4×C15111yescharacteristic
491C22×C4C2×D4×C15111yescharacteristic
492C22×C4C2×D4×C15111yescharacteristic
493C22×C4C2×D4×C15112yes—
494C22×C4C2×D4×C15112yes—
495C22×C4C2×D4×C15111yescharacteristic
496C22×C4C24×C15111yescharacteristic
497SD16—48no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—44no—
505C4⋊C4—24no—
506C4⋊C4—24no—
507C4⋊C4—24no—
508C4⋊C4—22no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—44no—
515C4⋊C4C2×D4×C15112yes—
516C4⋊C4C2×D4×C15112yes—
517C4⋊C4C2×D4×C15112yes—
518C22⋊C4—24no—
519C22⋊C4—24no—
520C22⋊C4—22no—
521C22⋊C4—24no—
522C22⋊C4—22no—
523C22⋊C4—44no—
524C22⋊C4—42no—
525C42—21no—
526C42—21no—
527C23—22no—
528C23—22no—
529C23—21no—
530C23—22no—
531C23—21no—
532C23—22no—
533C23—22no—
534C23—42no—
535C23—41no—
536C23—41no—
537C23—42no—
538C23#120×C15112yes—
539C23C2×SD16×C15112yes—
540C23C2×SD16×C15112yes—
541C23AGL(1,ℤ/8)×C15112yes—
542C23C22×D4×C15111yescharacteristic
543Q8—24no—
544Q8—24no—
545Q8—48no—
546Q8—48no—
547Q8—42no—
548Q8—42no—
549D4—28no—
550D4—24no—
551D4—48no—
552D4—48no—
553D4—41no—
554D4—41no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—48no—
570C2×C4—48no—
571C2×C4—48no—
572C2×C4—48no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4#120×C15112yes—
588C2×C4C2×SD16×C15112yes—
589C2×C4C22×D4×C15111yescharacteristic
590C2×C4C22×D4×C15111yescharacteristic
591C2×C4C2×#41×C15112yes—
592C2×C4H(5,𝔽2)×C15112yes—
593C8—42no—
594C8—42no—
595C22—22no—
596C22—22no—
597C22—24no—
598C22—24no—
599C22—22no—
600C22—24no—
601C22—41no—
602C22—41no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—82no—
608C22—82no—
609C22#450×C15114yes—
610C22C2×#120×C15111yescharacteristic
611C22#546×C15112yes—
612C22C22×SD16×C15111yescharacteristic
613C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
614C22#578×C15112yes—
615C4—22no—
616C4—22no—
617C4—41no—
618C4—44no—
619C4—42no—
620C4—42no—
621C4—42no—
622C4—41no—
623C4—82no—
624C4#525×C15111yescharacteristic
625C4#535×C15111yescharacteristic
626C4#546×C15112yes—
627C2—24no—
628C2—42no—
629C2—82no—
630C2#2404×C15111yescharacteristic
631C2C2×#450×C15111yescharacteristic
632C2#3011×C15111yescharacteristic
633C2#3298×C15112yes—
634C2#3308×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#547×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#448×C151C2semidirect
3. C22×#103×C151C2semidirect
4. #2409×C151C2semidirect
5. #2024×C151C2semidirect
6. #2000×C151C2semidirect
7. #1893×C151C2semidirect
8. #1877×C151C2semidirect
9. #1872×C151C2semidirect
10. #1869×C151C2semidirect
11. #1823×C151C2semidirect
136. C2×Q8×C151#41semidirect
148. C2×D4×C151SD16semidirect
317. #23961C151direct (N × H)
318. C151#23961direct (N × H)
320. C2×#448C2×C151semidirect
321. C22×#103C2×C151semidirect
322. #2409C2×C151semidirect
323. #2024C2×C151semidirect
324. #2000C2×C151semidirect
325. #1893C2×C151semidirect
326. #1877C2×C151semidirect
327. #1872C2×C151semidirect
328. #1869C2×C151semidirect
329. #1823C2×C151semidirect
454. C2×Q8#41×C151semidirect
466. C2×D4SD16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C1512
C2×#448×C1512
C22×#103×C1512
#2409×C1512
#2024×C1512
#2000×C1512
#1893×C1512
#1877×C1512
#1872×C1512
#1869×C1512
#1823×C1512
#23961151