Finite Group Databasebeta

← C151×#24154 #50329079

Subgroups — C151×#24154 #50329079

Order 38656.

1394 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#532×C151C211yesmaximal, characteristic
2C2×#475×C151C211yesmaximal, characteristic, complemented
3C2×#460×C151C211yesmaximal, characteristic, complemented
4C4×C22⋊Q8×C151C211yesmaximal, characteristic, complemented
5#2034×C151C212yesmaximal, complemented
6#2000×C151C212yesmaximal, complemented
7#1988×C151C211yesmaximal, characteristic, complemented
8#1982×C151C211yesmaximal, characteristic, complemented
9#1877×C151C212yesmaximal, complemented
10#1864×C151C212yesmaximal, complemented
11#1797×C151C211yesmaximal, characteristic, complemented
12C22×#41×C151—21no—
13C22×SD16×C151C2212yes—
14#532×C151—24no—
15#532×C151—24no—
16C2×C4⋊Q8×C151C2211yescharacteristic
17C2×#127×C151C2211yescharacteristic
18C2×#124×C151—21no—
19C2×C22⋊Q8×C151C2211yescharacteristic
20C2×#121×C151—21no—
21C2×#121×C151C2212yes—
22C2×C4×Q8×C151C2211yescharacteristic
23C2×C4×D4×C151—21no—
24C2×C4×D4×C151C2212yes—
25C22×C42×C151C2211yescharacteristic
26#475×C151—24no—
27#460×C151—24no—
28C2×#106×C151C2212yes—
29C2×C4⋊C8×C151C2211yescharacteristic
30C2×C4⋊C8×C151C2211yescharacteristic
31C2×#103×C151C2212yes—
32C2×#102×C151C2212yes—
33C2×#102×C151C2212yes—
34C2×#102×C151C2212yes—
35C2×C22⋊C8×C151C2212yes—
36#391×C151C2211yescharacteristic
37#389×C151C2211yescharacteristic
38#387×C151—21no—
39#385×C151—21no—
40#380×C151C2211yescharacteristic
41C4×C4⋊C4×C151—21no—
42C4×C4⋊C4×C151C2211yescharacteristic
43C4×C22⋊C4×C151—21no—
44#340×C151C2212yes—
45#340×C151C2212yes—
46#336×C151C2212yes—
47C2×#41×C151—28no—
48C2×#41×C151—44no—
49C2×#41×C151—44no—
50C22×Q8×C151—21no—
51C22×Q8×C151C2311yescharacteristic
52C22×D4×C151—21no—
53C22×D4×C151—21no—
54C22×D4×C151—22no—
55C22×D4×C151C2312yes—
56C23×C4×C151—22no—
57C23×C4×C151D411yescharacteristic
58C23×C4×C151D411yescharacteristic
59C23×C4×C151C2311yescharacteristic
60C2×SD16×C151—24no—
61C2×SD16×C151—24no—
62C2×SD16×C151—42no—
63C22×C8×C151C2312yes—
64C22×C8×C151C2312yes—
65C4⋊Q8×C151—22no—
66C4⋊Q8×C151D414yes—
67#127×C151—22no—
68#127×C151D414yes—
69#124×C151—28no—
70C22⋊Q8×C151—22no—
71C22⋊Q8×C151—22no—
72#121×C151—28no—
73#121×C151—24no—
74#121×C151—24no—
75C4×Q8×C151—22no—
76C4×Q8×C151—22no—
77C4×D4×C151—28no—
78C4×D4×C151—24no—
79C4×D4×C151—24no—
80C2×C4⋊C4×C151—21no—
81C2×C4⋊C4×C151—21no—
82C2×C4⋊C4×C151—21no—
83C2×C4⋊C4×C151—21no—
84C2×C4⋊C4×C151C2311yescharacteristic
85C2×C4⋊C4×C151C2311yescharacteristic
86C2×C4⋊C4×C151C2312yes—
87C2×C4⋊C4×C151C2311yescharacteristic
88C2×C22⋊C4×C151—22no—
89C2×C22⋊C4×C151—22no—
90C2×C22⋊C4×C151—21no—
91C2×C22⋊C4×C151—21no—
92C2×C42×C151—22no—
93C2×C42×C151—22no—
94C2×C42×C151—21no—
95C2×C42×C151—21no—
96C2×C42×C151D411yescharacteristic
97C2×C42×C151D411yescharacteristic
98C2×C42×C151C2311yescharacteristic
99C2×C42×C151C2311yescharacteristic
100#106×C151—24no—
101C4⋊C8×C151—22no—
102C4⋊C8×C151—22no—
103#103×C151—24no—
104#102×C151—24no—
105#102×C151—24no—
106#102×C151—42no—
107C22⋊C8×C151—42no—
108#95×C151—21no—
109#95×C151—21no—
110#95×C151—21no—
111#95×C151—21no—
112#95×C151—21no—
113C24×C151—22no—
114C24×C151C2×D411yescharacteristic
115#41×C151—432no—
116C2×Q8×C151—24no—
117C2×Q8×C151—21no—
118C2×Q8×C151—21no—
119C2×Q8×C151—21no—
120C2×Q8×C151—21no—
121C2×Q8×C151—21no—
122C2×Q8×C151—42no—
123C2×Q8×C151—42no—
124C2×Q8×C151#4112yescomplemented
125C2×D4×C151—28no—
126C2×D4×C151—24no—
127C2×D4×C151—24no—
128C2×D4×C151—22no—
129C2×D4×C151—22no—
130C2×D4×C151—22no—
131C2×D4×C151—22no—
132C2×D4×C151—22no—
133C2×D4×C151—42no—
134C2×D4×C151—42no—
135C2×D4×C151—44no—
136C2×D4×C151—44no—
137C2×D4×C151—42no—
138C2×D4×C151—42no—
139C2×D4×C151C2×D414yes—
140C22×C4×C151—22no—
141C22×C4×C151—22no—
142C22×C4×C151—28no—
143C22×C4×C151—21no—
144C22×C4×C151—21no—
145C22×C4×C151—22no—
146C22×C4×C151—22no—
147C22×C4×C151—21no—
148C22×C4×C151—21no—
149C22×C4×C151—21no—
150C22×C4×C151—21no—
151C22×C4×C151—21no—
152C22×C4×C151—21no—
153C22×C4×C151—21no—
154C22×C4×C151—21no—
155C22×C4×C151—41no—
156C22×C4×C151—41no—
157C22×C4×C151—44no—
158C22×C4×C151—44no—
159C22×C4×C151SD1614yescomplemented
160C22×C4×C151C2×D411yescharacteristic
161C22×C4×C151C2×D411yescharacteristic
162C22×C4×C151C2×D411yescharacteristic
163C22×C4×C151C2×D411yescharacteristic
164C22×C4×C151C2×D411yescharacteristic
165C22×C4×C151C2411yescharacteristic
166SD16×C151—48no—
167C2×C8×C151—22no—
168C2×C8×C151—22no—
169C2×C8×C151—22no—
170C2×C8×C151—22no—
171C2×C8×C151—22no—
172C2×C8×C151—22no—
173C4⋊C4×C151—24no—
174C4⋊C4×C151—24no—
175C4⋊C4×C151—22no—
176C4⋊C4×C151—21no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151—21no—
180C4⋊C4×C151—21no—
181C4⋊C4×C151—42no—
182C4⋊C4×C151—42no—
183C4⋊C4×C151C2×D414yes—
184C4⋊C4×C151#4112yescomplemented
185C22⋊C4×C151—28no—
186C22⋊C4×C151—28no—
187C22⋊C4×C151—24no—
188C22⋊C4×C151—42no—
189C42×C151—22no—
190C42×C151—22no—
191C42×C151—21no—
192C42×C151—21no—
193C42×C151—42no—
194C42×C151—42no—
195C42×C151C2×D412yes—
196C42×C151C2×D412yes—
197C23×C151—21no—
198C23×C151—21no—
199C23×C151—21no—
200C23×C151—21no—
201C23×C151—21no—
202C23×C151—21no—
203C23×C151—24no—
204C23×C151—42no—
205C23×C151—42no—
206C23×C151—42no—
207C23×C151—42no—
208C23×C151—42no—
209C23×C151—42no—
210C23×C151C2×SD1612yes—
211C23×C151C22×D411yescharacteristic
212Q8×C151—22no—
213Q8×C151—22no—
214Q8×C151—41no—
215Q8×C151—41no—
216Q8×C151—48no—
217D4×C151—24no—
218D4×C151—24no—
219D4×C151—48no—
220D4×C151—416no—
221D4×C151—42no—
222D4×C151—42no—
223D4×C151—48no—
224C2×C4×C151—21no—
225C2×C4×C151—21no—
226C2×C4×C151—21no—
227C2×C4×C151—21no—
228C2×C4×C151—28no—
229C2×C4×C151—24no—
230C2×C4×C151—21no—
231C2×C4×C151—21no—
232C2×C4×C151—22no—
233C2×C4×C151—22no—
234C2×C4×C151—21no—
235C2×C4×C151—21no—
236C2×C4×C151—21no—
237C2×C4×C151—21no—
238C2×C4×C151—416no—
239C2×C4×C151—44no—
240C2×C4×C151—41no—
241C2×C4×C151—41no—
242C2×C4×C151—42no—
243C2×C4×C151—42no—
244C2×C4×C151—41no—
245C2×C4×C151—41no—
246C2×C4×C151—41no—
247C2×C4×C151—41no—
248C2×C4×C151—41no—
249C2×C4×C151—41no—
250C2×C4×C151—41no—
251C2×C4×C151—41no—
252C2×C4×C151—41no—
253C2×C4×C151—41no—
254C2×C4×C151—41no—
255C2×C4×C151—41no—
256C2×C4×C151#12012yes—
257C2×C4×C151#12012yes—
258C2×C4×C151C2×SD1612yes—
259C2×C4×C151C2×SD1612yes—
260C2×C4×C151AGL(1,ℤ/8)12yes—
261C2×C4×C151C22×D411yescharacteristic
262C2×C4×C151C22×D411yescharacteristic
263C2×C4×C151C2×#4111yescharacteristic
264C2×C4×C151C2×#4111yescharacteristic
265C2×C4×C151H(5,𝔽2)11yescharacteristic
266C2×C4×C1512−1+411yescharacteristic
267C8×C151—42no—
268C8×C151—42no—
269C22×C151—22no—
270C22×C151—22no—
271C22×C151—22no—
272C22×C151—41no—
273C22×C151—41no—
274C22×C151—41no—
275C22×C151—41no—
276C22×C151—44no—
277C22×C151—44no—
278C22×C151—44no—
279C22×C151—82no—
280C22×C151—82no—
281C22×C151—82no—
282C22×C151—82no—
283C22×C151C2×#12011yescharacteristic
284C22×C151#52511yescharacteristic
285C22×C151#53711yescharacteristic
286C22×C151C22×SD1611yescharacteristic
287C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
288C22×C151#57511yescharacteristic
289C22×C151#57511yescharacteristic
290C4×C151—22no—
291C4×C151—22no—
292C4×C151—42no—
293C4×C151—41no—
294C4×C151—42no—
295C4×C151—44no—
296C4×C151—41no—
297C4×C151—81no—
298C4×C151—81no—
299C4×C151#45014yes—
300C4×C151#54611yescharacteristic
301C4×C151#54711yescharacteristic
302C4×C151#54811yescharacteristic
303C4×C151#55011yescharacteristic
304C2×C151—42no—
305C2×C151—84no—
306C2×C151#240711yescharacteristic
307C2×C151C2×#45011yescharacteristic
308C2×C151#300511yescharacteristic
309C2×C151#310311yescharacteristic
310C2×C151#311511yescharacteristic
311C2×C151#324611yescharacteristic
312C2×C151#325111yescharacteristic
313#24154C15111yesmaximal, characteristic, direct product factor, Sylow
314C151#2415411yescharacteristic, direct product factor, Sylow
315C2×#532C2×C15111yescharacteristic
316C2×#475C2×C15111yescharacteristic, complemented
317C2×#460C2×C15111yescharacteristic, complemented
318C4×C22⋊Q8C2×C15111yescharacteristic, complemented
319#2034C2×C15112yescomplemented
320#2000C2×C15112yescomplemented
321#1988C2×C15111yescharacteristic, complemented
322#1982C2×C15111yescharacteristic, complemented
323#1877C2×C15112yescomplemented
324#1864C2×C15112yescomplemented
325#1797C2×C15111yescharacteristic, complemented
326C22×#41—21no—
327C22×SD16C22×C15112yes—
328#532—24no—
329#532—24no—
330C2×C4⋊Q8C22×C15111yescharacteristic
331C2×#127C22×C15111yescharacteristic
332C2×#124—21no—
333C2×C22⋊Q8C22×C15111yescharacteristic
334C2×#121—21no—
335C2×#121C22×C15112yes—
336C2×C4×Q8C22×C15111yescharacteristic
337C2×C4×D4—21no—
338C2×C4×D4C22×C15112yes—
339C22×C42C22×C15111yescharacteristic
340#475—24no—
341#460—24no—
342C2×#106C22×C15112yes—
343C2×C4⋊C8C22×C15111yescharacteristic
344C2×C4⋊C8C22×C15111yescharacteristic
345C2×#103C22×C15112yes—
346C2×#102C22×C15112yes—
347C2×#102C22×C15112yes—
348C2×#102C22×C15112yes—
349C2×C22⋊C8C22×C15112yes—
350#391C22×C15111yescharacteristic
351#389C22×C15111yescharacteristic
352#387—21no—
353#385—21no—
354#380C22×C15111yescharacteristic
355C4×C4⋊C4—21no—
356C4×C4⋊C4C22×C15111yescharacteristic
357C4×C22⋊C4—21no—
358#340C22×C15112yes—
359#340C22×C15112yes—
360#336C22×C15112yes—
361C2×#41—28no—
362C2×#41—44no—
363C2×#41—44no—
364C22×Q8—21no—
365C22×Q8C23×C15111yescharacteristic
366C22×D4—22no—
367C22×D4—21no—
368C22×D4—21no—
369C22×D4C23×C15112yes—
370C23×C4—22no—
371C23×C4D4×C15111yescharacteristic
372C23×C4D4×C15111yescharacteristic
373C23×C4C23×C15111yescharacteristic
374C2×SD16—24no—
375C2×SD16—24no—
376C2×SD16—42no—
377C22×C8C23×C15112yes—
378C22×C8C23×C15112yes—
379C4⋊Q8—22no—
380C4⋊Q8D4×C15114yes—
381#127—22no—
382#127D4×C15114yes—
383#124—28no—
384C22⋊Q8—22no—
385C22⋊Q8—22no—
386#121—28no—
387#121—24no—
388#121—24no—
389C4×Q8—22no—
390C4×Q8—22no—
391C4×D4—28no—
392C4×D4—24no—
393C4×D4—24no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4C23×C15111yescharacteristic
399C2×C4⋊C4C23×C15111yescharacteristic
400C2×C4⋊C4C23×C15111yescharacteristic
401C2×C4⋊C4C23×C15112yes—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—21no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42D4×C15111yescharacteristic
411C2×C42D4×C15111yescharacteristic
412C2×C42C23×C15111yescharacteristic
413C2×C42C23×C15111yescharacteristic
414#106—24no—
415C4⋊C8—22no—
416C4⋊C8—22no—
417#103—24no—
418#102—24no—
419#102—24no—
420#102—42no—
421C22⋊C8—42no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—21no—
427C24—22no—
428C24C2×D4×C15111yescharacteristic
429#41—432no—
430C2×Q8—24no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—42no—
437C2×Q8—42no—
438C2×Q8#41×C15112yescomplemented
439C2×D4—28no—
440C2×D4—24no—
441C2×D4—24no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4C2×D4×C15114yes—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—28no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—44no—
472C22×C4—44no—
473C22×C4SD16×C15114yescomplemented
474C22×C4C2×D4×C15111yescharacteristic
475C22×C4C2×D4×C15111yescharacteristic
476C22×C4C2×D4×C15111yescharacteristic
477C22×C4C2×D4×C15111yescharacteristic
478C22×C4C2×D4×C15111yescharacteristic
479C22×C4C24×C15111yescharacteristic
480SD16—48no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—22no—
484C2×C8—22no—
485C2×C8—22no—
486C2×C8—22no—
487C4⋊C4—24no—
488C4⋊C4—24no—
489C4⋊C4—22no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—42no—
496C4⋊C4—42no—
497C4⋊C4C2×D4×C15114yes—
498C4⋊C4#41×C15112yescomplemented
499C22⋊C4—28no—
500C22⋊C4—28no—
501C22⋊C4—24no—
502C22⋊C4—42no—
503C42—22no—
504C42—22no—
505C42—21no—
506C42—21no—
507C42—42no—
508C42—42no—
509C42C2×D4×C15112yes—
510C42C2×D4×C15112yes—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—24no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23C2×SD16×C15112yes—
525C23C22×D4×C15111yescharacteristic
526Q8—22no—
527Q8—22no—
528Q8—48no—
529Q8—41no—
530Q8—41no—
531D4—24no—
532D4—24no—
533D4—48no—
534D4—416no—
535D4—48no—
536D4—42no—
537D4—42no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—28no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—416no—
553C2×C4—44no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4#120×C15112yes—
571C2×C4#120×C15112yes—
572C2×C4C2×SD16×C15112yes—
573C2×C4C2×SD16×C15112yes—
574C2×C4AGL(1,ℤ/8)×C15112yes—
575C2×C4C22×D4×C15111yescharacteristic
576C2×C4C22×D4×C15111yescharacteristic
577C2×C4C2×#41×C15111yescharacteristic
578C2×C4C2×#41×C15111yescharacteristic
579C2×C4H(5,𝔽2)×C15111yescharacteristic
580C2×C42−1+4×C15111yescharacteristic
581C8—42no—
582C8—42no—
583C22—22no—
584C22—22no—
585C22—22no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—44no—
591C22—44no—
592C22—44no—
593C22—82no—
594C22—82no—
595C22—82no—
596C22—82no—
597C22C2×#120×C15111yescharacteristic
598C22#525×C15111yescharacteristic
599C22#537×C15111yescharacteristic
600C22C22×SD16×C15111yescharacteristic
601C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
602C22#575×C15111yescharacteristic
603C22#575×C15111yescharacteristic
604C4—22no—
605C4—22no—
606C4—42no—
607C4—41no—
608C4—42no—
609C4—44no—
610C4—41no—
611C4—81no—
612C4—81no—
613C4#450×C15114yes—
614C4#546×C15111yescharacteristic
615C4#547×C15111yescharacteristic
616C4#548×C15111yescharacteristic
617C4#550×C15111yescharacteristic
618C2—42no—
619C2—84no—
620C2#2407×C15111yescharacteristic
621C2C2×#450×C15111yescharacteristic
622C2#3005×C15111yescharacteristic
623C2#3103×C15111yescharacteristic
624C2#3115×C15111yescharacteristic
625C2#3246×C15111yescharacteristic
626C2#3251×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#532×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#475×C151C2semidirect
3. C2×#460×C151C2semidirect
4. C4×C22⋊Q8×C151C2semidirect
5. #2034×C151C2semidirect
6. #2000×C151C2semidirect
7. #1988×C151C2semidirect
8. #1982×C151C2semidirect
9. #1877×C151C2semidirect
10. #1864×C151C2semidirect
11. #1797×C151C2semidirect
124. C2×Q8×C151#41semidirect
159. C22×C4×C151SD16semidirect
184. C4⋊C4×C151#41semidirect
313. #24154C151direct (N × H)
314. C151#24154direct (N × H)
316. C2×#475C2×C151semidirect
317. C2×#460C2×C151semidirect
318. C4×C22⋊Q8C2×C151semidirect
319. #2034C2×C151semidirect
320. #2000C2×C151semidirect
321. #1988C2×C151semidirect
322. #1982C2×C151semidirect
323. #1877C2×C151semidirect
324. #1864C2×C151semidirect
325. #1797C2×C151semidirect
438. C2×Q8#41×C151semidirect
473. C22×C4SD16×C151semidirect
498. C4⋊C4#41×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#532×C1512
C2×#475×C1512
C2×#460×C1512
C4×C22⋊Q8×C1512
#2034×C1512
#2000×C1512
#1988×C1512
#1982×C1512
#1877×C1512
#1864×C1512
#1797×C1512
#24154151