Finite Group Databasebeta

← C151×#24015 #50328940

Subgroups — C151×#24015 #50328940

Order 38656.

1468 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C151C211yesmaximal, characteristic
2C2×#482×C151C212yesmaximal, complemented
3#2311×C151C211yesmaximal, characteristic, complemented
4#2034×C151C212yesmaximal, complemented
5#2033×C151C212yesmaximal, complemented
6#1874×C151C212yesmaximal, complemented
7#1854×C151C212yesmaximal, complemented
8#1786×C151C212yesmaximal, complemented
9#1780×C151C211yesmaximal, characteristic, complemented
10C22×#41×C151C2211yescharacteristic
11C23×D4×C151C2211yescharacteristic
12#535×C151—28no—
13C2×#127×C151—21no—
14C2×#124×C151—21no—
15C2×#121×C151C2212yes—
16C2×#121×C151C2212yes—
17C2×#120×C151—21no—
18C2×#120×C151—21no—
19C2×#117×C151C2211yescharacteristic
20C2×#117×C151C2211yescharacteristic, complemented
21C22×C4⋊C4×C151C2211yescharacteristic, complemented
22#482×C151—28no—
23C2×#107×C151C2212yescomplemented
24C2×#106×C151C2212yescomplemented
25C2×#102×C151C2212yes—
26C2×#102×C151C2212yes—
27C2×#102×C151C2212yes—
28C2×#102×C151C2212yes—
29C2×C22⋊C8×C151C2212yes—
30C2×C22⋊C8×C151C2212yescomplemented
31C2×C22⋊C8×C151C2211yescharacteristic, complemented
32C2×C22⋊C8×C151C2211yescharacteristic, complemented
33#391×C151—21no—
34#390×C151—21no—
35#386×C151—21no—
36#386×C151—21no—
37#380×C151C2212yes—
38#380×C151C2212yescomplemented
39#340×C151C2212yescomplemented
40#340×C151C2212yescomplemented
41C25×C151—21no—
42C2×#41×C151—24no—
43C2×#41×C151—24no—
44C2×#41×C151—41no—
45C2×#41×C151—41no—
46C22×Q8×C151D411yescharacteristic
47C22×D4×C151—24no—
48C22×D4×C151—21no—
49C22×D4×C151—22no—
50C22×D4×C151—22no—
51C22×D4×C151—24no—
52C22×D4×C151—41no—
53C22×D4×C151—41no—
54C22×D4×C151D411yescharacteristic
55C22×D4×C151D411yescharacteristic
56C22×D4×C151D411yescharacteristic
57C22×D4×C151C2312yes—
58C23×C4×C151—21no—
59C23×C4×C151C2311yescharacteristic
60C23×C4×C151C2311yescharacteristic
61C23×C4×C151C2311yescharacteristic
62C22×C8×C151C2312yes—
63C22×C8×C151C2312yes—
64#127×C151—28no—
65#124×C151—28no—
66#121×C151—24no—
67#121×C151—24no—
68#121×C151—24no—
69#121×C151D418yes—
70#120×C151—28no—
71#120×C151—28no—
72#117×C151—24no—
73#117×C151—24no—
74C2×C4⋊C4×C151—21no—
75C2×C4⋊C4×C151—41no—
76C2×C4⋊C4×C151—41no—
77C2×C4⋊C4×C151C2312yes—
78C2×C4⋊C4×C151C2312yes—
79C2×C4⋊C4×C151C2312yes—
80C2×C22⋊C4×C151—22no—
81C2×C22⋊C4×C151—22no—
82C2×C22⋊C4×C151—21no—
83C2×C22⋊C4×C151—21no—
84C2×C22⋊C4×C151—22no—
85C2×C22⋊C4×C151—22no—
86C2×C42×C151—21no—
87C2×C42×C151—21no—
88#107×C151—24no—
89#106×C151—24no—
90#102×C151—24no—
91#102×C151—24no—
92#102×C151—42no—
93#102×C151—42no—
94C22⋊C8×C151—24no—
95C22⋊C8×C151—24no—
96C22⋊C8×C151—41no—
97C22⋊C8×C151—41no—
98#95×C151—22no—
99#95×C151—22no—
100C24×C151—24no—
101C24×C151—22no—
102C24×C151—42no—
103C24×C151—42no—
104C24×C151—82no—
105C24×C151—82no—
106C24×C151C2×D411yescharacteristic
107C24×C151C2×D411yescharacteristic
108C24×C151C2×D411yescharacteristic
109#41×C151—48no—
110#41×C151—48no—
111C2×Q8×C151—22no—
112C2×Q8×C151—22no—
113C2×Q8×C151—41no—
114C2×D4×C151—24no—
115C2×D4×C151—22no—
116C2×D4×C151—22no—
117C2×D4×C151—22no—
118C2×D4×C151—22no—
119C2×D4×C151—28no—
120C2×D4×C151—28no—
121C2×D4×C151—22no—
122C2×D4×C151—22no—
123C2×D4×C151—22no—
124C2×D4×C151—22no—
125C2×D4×C151—22no—
126C2×D4×C151—22no—
127C2×D4×C151—22no—
128C2×D4×C151—48no—
129C2×D4×C151—48no—
130C2×D4×C151—41no—
131C2×D4×C151—41no—
132C2×D4×C151—41no—
133C2×D4×C151—42no—
134C2×D4×C151—42no—
135C2×D4×C151—82no—
136C2×D4×C151—82no—
137C2×D4×C151—82no—
138C2×D4×C151—82no—
139C2×D4×C151C2×D414yes—
140C22×C4×C151—22no—
141C22×C4×C151—22no—
142C22×C4×C151—21no—
143C22×C4×C151—21no—
144C22×C4×C151—21no—
145C22×C4×C151—21no—
146C22×C4×C151—22no—
147C22×C4×C151—22no—
148C22×C4×C151—22no—
149C22×C4×C151—21no—
150C22×C4×C151—21no—
151C22×C4×C151—22no—
152C22×C4×C151—22no—
153C22×C4×C151—42no—
154C22×C4×C151—82no—
155C22×C4×C151C2×D411yescharacteristic
156C22×C4×C151C2×D411yescharacteristic
157C22×C4×C151C2×D414yes—
158C22×C4×C151C2×D411yescharacteristic
159C22×C4×C151#4114yes—
160C22×C4×C151C2411yescharacteristic
161C2×C8×C151—22no—
162C2×C8×C151—22no—
163C2×C8×C151—22no—
164C2×C8×C151—22no—
165C2×C8×C151—22no—
166C2×C8×C151—22no—
167C4⋊C4×C151—22no—
168C4⋊C4×C151—22no—
169C4⋊C4×C151—22no—
170C4⋊C4×C151—22no—
171C4⋊C4×C151—22no—
172C4⋊C4×C151—42no—
173C4⋊C4×C151C2×D414yes—
174C22⋊C4×C151—24no—
175C22⋊C4×C151—28no—
176C22⋊C4×C151—28no—
177C22⋊C4×C151—42no—
178C22⋊C4×C151—82no—
179C22⋊C4×C151—82no—
180C42×C151—24no—
181C42×C151—42no—
182C23×C151—21no—
183C23×C151—21no—
184C23×C151—21no—
185C23×C151—21no—
186C23×C151—22no—
187C23×C151—22no—
188C23×C151—22no—
189C23×C151—22no—
190C23×C151—24no—
191C23×C151—21no—
192C23×C151—21no—
193C23×C151—21no—
194C23×C151—22no—
195C23×C151—22no—
196C23×C151—48no—
197C23×C151—42no—
198C23×C151—42no—
199C23×C151—42no—
200C23×C151—42no—
201C23×C151—42no—
202C23×C151—42no—
203C23×C151—88no—
204C23×C151—88no—
205C23×C151—84no—
206C23×C151—84no—
207C23×C151#12012yes—
208C23×C151#12312yes—
209C23×C151C22×D411yescharacteristic
210Q8×C151—44no—
211D4×C151—24no—
212D4×C151—24no—
213D4×C151—44no—
214D4×C151—44no—
215D4×C151—48no—
216D4×C151—44no—
217D4×C151—42no—
218D4×C151—42no—
219D4×C151—88no—
220D4×C151—88no—
221C2×C4×C151—21no—
222C2×C4×C151—21no—
223C2×C4×C151—21no—
224C2×C4×C151—21no—
225C2×C4×C151—24no—
226C2×C4×C151—24no—
227C2×C4×C151—24no—
228C2×C4×C151—24no—
229C2×C4×C151—21no—
230C2×C4×C151—24no—
231C2×C4×C151—21no—
232C2×C4×C151—21no—
233C2×C4×C151—42no—
234C2×C4×C151—42no—
235C2×C4×C151—42no—
236C2×C4×C151—42no—
237C2×C4×C151—42no—
238C2×C4×C151—42no—
239C2×C4×C151—42no—
240C2×C4×C151—42no—
241C2×C4×C151—42no—
242C2×C4×C151—42no—
243C2×C4×C151—84no—
244C2×C4×C151#12012yes—
245C2×C4×C151#12312yes—
246C2×C4×C151C22×D412yes—
247C2×C4×C151C2×#4112yes—
248C2×C4×C151H(5,𝔽2)11yescharacteristic
249C2×C4×C151H(5,𝔽2)11yescharacteristic
250C8×C151—42no—
251C8×C151—42no—
252C22×C151—24no—
253C22×C151—22no—
254C22×C151—22no—
255C22×C151—24no—
256C22×C151—42no—
257C22×C151—41no—
258C22×C151—41no—
259C22×C151—41no—
260C22×C151—41no—
261C22×C151—42no—
262C22×C151—42no—
263C22×C151—41no—
264C22×C151—44no—
265C22×C151—41no—
266C22×C151—41no—
267C22×C151—42no—
268C22×C151—44no—
269C22×C151—44no—
270C22×C151—816no—
271C22×C151—82no—
272C22×C151—82no—
273C22×C151—82no—
274C22×C151—82no—
275C22×C151C2×#12011yescharacteristic
276C22×C151C2×#12311yescharacteristic
277C22×C151#53411yescharacteristic
278C22×C151#57612yes—
279C22×C151#57712yes—
280C4×C151—22no—
281C4×C151—22no—
282C4×C151—41no—
283C4×C151—44no—
284C4×C151—82no—
285C4×C151—82no—
286C4×C151#54612yes—
287C4×C151#54612yes—
288C2×C151—42no—
289C2×C151—42no—
290C2×C151—81no—
291C2×C151—84no—
292C2×C151#240511yescharacteristic
293C2×C151#301212yes—
294C2×C151#309612yes—
295C2×C151#319911yescharacteristic
296C2×C151#320011yescharacteristic
297#24015C15111yesmaximal, characteristic, direct product factor, Sylow
298C151#2401511yescharacteristic, direct product factor, Sylow
299C2×#535C2×C15111yescharacteristic
300C2×#482C2×C15112yescomplemented
301#2311C2×C15111yescharacteristic, complemented
302#2034C2×C15112yescomplemented
303#2033C2×C15112yescomplemented
304#1874C2×C15112yescomplemented
305#1854C2×C15112yescomplemented
306#1786C2×C15112yescomplemented
307#1780C2×C15111yescharacteristic, complemented
308C22×#41C22×C15111yescharacteristic
309C23×D4C22×C15111yescharacteristic
310#535—28no—
311C2×#127—21no—
312C2×#124—21no—
313C2×#121C22×C15112yes—
314C2×#121C22×C15112yes—
315C2×#120—21no—
316C2×#120—21no—
317C2×#117C22×C15111yescharacteristic
318C2×#117C22×C15111yescharacteristic, complemented
319C22×C4⋊C4C22×C15111yescharacteristic, complemented
320#482—28no—
321C2×#107C22×C15112yescomplemented
322C2×#106C22×C15112yescomplemented
323C2×#102C22×C15112yes—
324C2×#102C22×C15112yes—
325C2×#102C22×C15112yes—
326C2×#102C22×C15112yes—
327C2×C22⋊C8C22×C15112yes—
328C2×C22⋊C8C22×C15112yescomplemented
329C2×C22⋊C8C22×C15111yescharacteristic, complemented
330C2×C22⋊C8C22×C15111yescharacteristic, complemented
331#391—21no—
332#390—21no—
333#386—21no—
334#386—21no—
335#380C22×C15112yes—
336#380C22×C15112yescomplemented
337#340C22×C15112yescomplemented
338#340C22×C15112yescomplemented
339C25—21no—
340C2×#41—24no—
341C2×#41—24no—
342C2×#41—41no—
343C2×#41—41no—
344C22×Q8D4×C15111yescharacteristic
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—21no—
350C22×D4—41no—
351C22×D4—41no—
352C22×D4D4×C15111yescharacteristic
353C22×D4D4×C15111yescharacteristic
354C22×D4D4×C15111yescharacteristic
355C22×D4C23×C15112yes—
356C23×C4—21no—
357C23×C4C23×C15111yescharacteristic
358C23×C4C23×C15111yescharacteristic
359C23×C4C23×C15111yescharacteristic
360C22×C8C23×C15112yes—
361C22×C8C23×C15112yes—
362#127—28no—
363#124—28no—
364#121—24no—
365#121—24no—
366#121—24no—
367#121D4×C15118yes—
368#120—28no—
369#120—28no—
370#117—24no—
371#117—24no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—41no—
374C2×C4⋊C4—41no—
375C2×C4⋊C4C23×C15112yes—
376C2×C4⋊C4C23×C15112yes—
377C2×C4⋊C4C23×C15112yes—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C42—21no—
385C2×C42—21no—
386#107—24no—
387#106—24no—
388#102—24no—
389#102—24no—
390#102—42no—
391#102—42no—
392C22⋊C8—24no—
393C22⋊C8—24no—
394C22⋊C8—41no—
395C22⋊C8—41no—
396#95—22no—
397#95—22no—
398C24—24no—
399C24—22no—
400C24—42no—
401C24—42no—
402C24—82no—
403C24—82no—
404C24C2×D4×C15111yescharacteristic
405C24C2×D4×C15111yescharacteristic
406C24C2×D4×C15111yescharacteristic
407#41—48no—
408#41—48no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—41no—
412C2×D4—24no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—28no—
418C2×D4—28no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—48no—
427C2×D4—48no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—41no—
431C2×D4—42no—
432C2×D4—42no—
433C2×D4—82no—
434C2×D4—82no—
435C2×D4—82no—
436C2×D4—82no—
437C2×D4C2×D4×C15114yes—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—42no—
452C22×C4—82no—
453C22×C4C2×D4×C15111yescharacteristic
454C22×C4C2×D4×C15111yescharacteristic
455C22×C4C2×D4×C15114yes—
456C22×C4C2×D4×C15111yescharacteristic
457C22×C4#41×C15114yes—
458C22×C4C24×C15111yescharacteristic
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—42no—
471C4⋊C4C2×D4×C15114yes—
472C22⋊C4—24no—
473C22⋊C4—28no—
474C22⋊C4—28no—
475C22⋊C4—42no—
476C22⋊C4—82no—
477C22⋊C4—82no—
478C42—24no—
479C42—42no—
480C23—21no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—22no—
485C23—22no—
486C23—22no—
487C23—22no—
488C23—24no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—22no—
493C23—22no—
494C23—48no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—88no—
502C23—88no—
503C23—84no—
504C23—84no—
505C23#120×C15112yes—
506C23#123×C15112yes—
507C23C22×D4×C15111yescharacteristic
508Q8—44no—
509D4—24no—
510D4—24no—
511D4—44no—
512D4—44no—
513D4—48no—
514D4—44no—
515D4—42no—
516D4—42no—
517D4—88no—
518D4—88no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—84no—
542C2×C4#120×C15112yes—
543C2×C4#123×C15112yes—
544C2×C4C22×D4×C15112yes—
545C2×C4C2×#41×C15112yes—
546C2×C4H(5,𝔽2)×C15111yescharacteristic
547C2×C4H(5,𝔽2)×C15111yescharacteristic
548C8—42no—
549C8—42no—
550C22—22no—
551C22—22no—
552C22—24no—
553C22—24no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—42no—
559C22—42no—
560C22—41no—
561C22—44no—
562C22—41no—
563C22—41no—
564C22—42no—
565C22—44no—
566C22—44no—
567C22—42no—
568C22—816no—
569C22—82no—
570C22—82no—
571C22—82no—
572C22—82no—
573C22C2×#120×C15111yescharacteristic
574C22C2×#123×C15111yescharacteristic
575C22#534×C15111yescharacteristic
576C22#576×C15112yes—
577C22#577×C15112yes—
578C4—22no—
579C4—22no—
580C4—41no—
581C4—44no—
582C4—82no—
583C4—82no—
584C4#546×C15112yes—
585C4#546×C15112yes—
586C2—42no—
587C2—42no—
588C2—81no—
589C2—84no—
590C2#2405×C15111yescharacteristic
591C2#3012×C15112yes—
592C2#3096×C15112yes—
593C2#3199×C15111yescharacteristic
594C2#3200×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#535×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×#41×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#482×C151C2semidirect
3. #2311×C151C2semidirect
4. #2034×C151C2semidirect
5. #2033×C151C2semidirect
6. #1874×C151C2semidirect
7. #1854×C151C2semidirect
8. #1786×C151C2semidirect
9. #1780×C151C2semidirect
20. C2×#117×C151C22semidirect
21. C22×C4⋊C4×C151C22semidirect
23. C2×#107×C151C22semidirect
24. C2×#106×C151C22semidirect
30. C2×C22⋊C8×C151C22semidirect
31. C2×C22⋊C8×C151C22semidirect
32. C2×C22⋊C8×C151C22semidirect
38. #380×C151C22semidirect
39. #340×C151C22semidirect
40. #340×C151C22semidirect
297. #24015C151direct (N × H)
298. C151#24015direct (N × H)
300. C2×#482C2×C151semidirect
301. #2311C2×C151semidirect
302. #2034C2×C151semidirect
303. #2033C2×C151semidirect
304. #1874C2×C151semidirect
305. #1854C2×C151semidirect
306. #1786C2×C151semidirect
307. #1780C2×C151semidirect
318. C2×#117C22×C151semidirect
319. C22×C4⋊C4C22×C151semidirect
321. C2×#107C22×C151semidirect
322. C2×#106C22×C151semidirect
328. C2×C22⋊C8C22×C151semidirect
329. C2×C22⋊C8C22×C151semidirect
330. C2×C22⋊C8C22×C151semidirect
336. #380C22×C151semidirect
337. #340C22×C151semidirect
338. #340C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#535×C1512
C2×#482×C1512
#2311×C1512
#2034×C1512
#2033×C1512
#1874×C1512
#1854×C1512
#1786×C1512
#1780×C1512
#24015151