Finite Group Databasebeta

← C151×#24631 #50329556

Subgroups — C151×#24631 #50329556

Order 38656.

974 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#459×C151C211yesmaximal, characteristic
2C2×C4×SD16×C151C211yesmaximal, characteristic, complemented
3#2548×C151C211yesmaximal, characteristic, complemented
4#2354×C151C211yesmaximal, characteristic, complemented
5#2054×C151C212yesmaximal, complemented
6#2012×C151C212yesmaximal, complemented
7#1983×C151C212yesmaximal, complemented
8#1957×C151C211yesmaximal, characteristic, complemented
9#1939×C151C211yesmaximal, characteristic, complemented
10#1926×C151C212yesmaximal, complemented
11#1803×C151C211yesmaximal, characteristic, complemented
12C22×SD16×C151C2211yescharacteristic
13C22×D8×C151C2212yes—
14C2×#127×C151C2211yescharacteristic
15C2×#124×C151C2212yes—
16C2×C4×Q8×C151C2211yescharacteristic
17C2×C4×D4×C151C2211yescharacteristic
18C2×#117×C151—21no—
19#459×C151—24no—
20C4×SD16×C151—24no—
21C2×#106×C151C2211yescharacteristic
22C2×C4⋊C8×C151C2211yescharacteristic
23C2×C4⋊C8×C151C2212yes—
24C2×#103×C151C2211yescharacteristic
25C2×#103×C151C2212yes—
26C2×#102×C151C2211yescharacteristic
27C2×#102×C151C2212yes—
28C2×#102×C151C2212yes—
29C2×#102×C151C2212yes—
30C2×C4×C8×C151C2211yescharacteristic
31#394×C151—22no—
32#390×C151—21no—
33#390×C151—21no—
34#390×C151C2212yes—
35#390×C151C2212yes—
36#388×C151—22no—
37#384×C151C2211yescharacteristic
38#380×C151—21no—
39C4×C4⋊C4×C151C2212yes—
40C4×C4⋊C4×C151C2211yescharacteristic
41#340×C151C2212yes—
42#336×C151C2212yes—
43C22×Q8×C151C2311yescharacteristic
44C22×D4×C151—21no—
45C22×D4×C151—21no—
46C22×D4×C151C2312yes—
47C22×D4×C151C2311yescharacteristic
48C23×C4×C151—21no—
49C2×SD16×C151—22no—
50C2×SD16×C151—22no—
51C2×SD16×C151—22no—
52C2×D8×C151—24no—
53C2×D8×C151—42no—
54C2×D8×C151—42no—
55C22×C8×C151C2312yes—
56C22×C8×C151C2311yescharacteristic
57C22×C8×C151C2311yescharacteristic
58#127×C151—22no—
59#127×C151—22no—
60#124×C151—24no—
61#124×C151—42no—
62C4×Q8×C151—22no—
63C4×Q8×C151—22no—
64C4×D4×C151—22no—
65C4×D4×C151D414yes—
66#117×C151—44no—
67C2×C4⋊C4×C151—21no—
68C2×C4⋊C4×C151—21no—
69C2×C4⋊C4×C151—21no—
70C2×C4⋊C4×C151D411yescharacteristic
71C2×C4⋊C4×C151D411yescharacteristic
72C2×C4⋊C4×C151C2311yescharacteristic
73C2×C4⋊C4×C151C2312yes—
74C2×C4⋊C4×C151C2311yescharacteristic
75C2×C22⋊C4×C151—21no—
76C2×C22⋊C4×C151—22no—
77C2×C22⋊C4×C151—22no—
78C2×C22⋊C4×C151—22no—
79C2×C22⋊C4×C151—22no—
80C2×C22⋊C4×C151—22no—
81C2×C22⋊C4×C151—22no—
82C2×C42×C151—22no—
83C2×C42×C151—21no—
84C2×C42×C151C2312yes—
85C2×C42×C151C2311yescharacteristic
86#106×C151—22no—
87C4⋊C8×C151—22no—
88C4⋊C8×C151—42no—
89#103×C151—22no—
90#103×C151—42no—
91#102×C151—22no—
92#102×C151—24no—
93#102×C151—24no—
94#102×C151—42no—
95C4×C8×C151—22no—
96#95×C151—22no—
97#95×C151D412yes—
98C24×C151—21no—
99C24×C151—22no—
100C2×Q8×C151—21no—
101C2×Q8×C151—21no—
102C2×Q8×C151—21no—
103C2×Q8×C151—21no—
104C2×Q8×C151—21no—
105C2×Q8×C151#4112yes—
106C2×D4×C151—22no—
107C2×D4×C151—21no—
108C2×D4×C151—21no—
109C2×D4×C151—21no—
110C2×D4×C151—22no—
111C2×D4×C151—22no—
112C2×D4×C151—22no—
113C2×D4×C151—21no—
114C2×D4×C151—21no—
115C2×D4×C151—22no—
116C2×D4×C151—22no—
117C2×D4×C151—42no—
118C2×D4×C151—42no—
119C2×D4×C151—42no—
120C2×D4×C151—42no—
121C2×D4×C151—81no—
122C2×D4×C151—81no—
123C2×D4×C151C2×D412yes—
124C22×C4×C151—21no—
125C22×C4×C151—21no—
126C22×C4×C151—24no—
127C22×C4×C151—22no—
128C22×C4×C151—21no—
129C22×C4×C151—42no—
130C22×C4×C151—42no—
131C22×C4×C151C2×D412yes—
132C22×C4×C151C2×D412yes—
133C22×C4×C151C2×D411yescharacteristic
134C22×C4×C151C2×D411yescharacteristic
135C22×C4×C151C2411yescharacteristic
136SD16×C151—28no—
137D8×C151—48no—
138C2×C8×C151—21no—
139C2×C8×C151—21no—
140C2×C8×C151—21no—
141C2×C8×C151—22no—
142C2×C8×C151—21no—
143C2×C8×C151—22no—
144C2×C8×C151—21no—
145C2×C8×C151—22no—
146C2×C8×C151#4112yes—
147C4⋊C4×C151—22no—
148C4⋊C4×C151—22no—
149C4⋊C4×C151—21no—
150C4⋊C4×C151—21no—
151C4⋊C4×C151—22no—
152C4⋊C4×C151—21no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151—42no—
155C4⋊C4×C151—42no—
156C4⋊C4×C151—81no—
157C4⋊C4×C151C2×D412yes—
158C22⋊C4×C151—24no—
159C22⋊C4×C151—44no—
160C22⋊C4×C151—44no—
161C22⋊C4×C151—44no—
162C22⋊C4×C151—82no—
163C22⋊C4×C151—82no—
164C22⋊C4×C151—82no—
165C42×C151—22no—
166C42×C151—22no—
167C42×C151—44no—
168C42×C151—42no—
169C42×C151C2×D412yes—
170C42×C151#4112yes—
171C23×C151—22no—
172C23×C151—41no—
173C23×C151—41no—
174C23×C151—41no—
175C23×C151—41no—
176C23×C151—41no—
177C23×C151—41no—
178C23×C151—42no—
179C23×C151—42no—
180C23×C151—42no—
181C23×C151—42no—
182C23×C151—42no—
183C23×C151—42no—
184C23×C151—42no—
185C23×C151C22×D411yescharacteristic
186Q8×C151—22no—
187Q8×C151—22no—
188Q8×C151—41no—
189Q8×C151—41no—
190D4×C151—22no—
191D4×C151—22no—
192D4×C151—42no—
193D4×C151—42no—
194D4×C151—41no—
195D4×C151—42no—
196D4×C151—41no—
197D4×C151—42no—
198D4×C151—84no—
199D4×C151—84no—
200C2×C4×C151—21no—
201C2×C4×C151—21no—
202C2×C4×C151—22no—
203C2×C4×C151—22no—
204C2×C4×C151—22no—
205C2×C4×C151—22no—
206C2×C4×C151—22no—
207C2×C4×C151—22no—
208C2×C4×C151—22no—
209C2×C4×C151—22no—
210C2×C4×C151—41no—
211C2×C4×C151—41no—
212C2×C4×C151—41no—
213C2×C4×C151—41no—
214C2×C4×C151—48no—
215C2×C4×C151—41no—
216C2×C4×C151—42no—
217C2×C4×C151—42no—
218C2×C4×C151—41no—
219C2×C4×C151—42no—
220C2×C4×C151—41no—
221C2×C4×C151#12112yes—
222C2×C4×C151#12112yes—
223C2×C4×C151#13512yes—
224C2×C4×C151AGL(1,ℤ/8)12yes—
225C2×C4×C151C22×D411yescharacteristic
226C2×C4×C151C2×#4111yescharacteristic
227C2×C4×C151C2×#4111yescharacteristic
228C2×C4×C151C2×#4111yescharacteristic
229C2×C4×C151H(5,𝔽2)11yescharacteristic
230C2×C4×C151H(5,𝔽2)11yescharacteristic
231C8×C151—22no—
232C8×C151—41no—
233C8×C151—42no—
234C22×C151—42no—
235C22×C151—42no—
236C22×C151—42no—
237C22×C151—81no—
238C22×C151—81no—
239C22×C151—81no—
240C22×C151—81no—
241C22×C151—82no—
242C22×C151—82no—
243C22×C151—82no—
244C22×C151—82no—
245C22×C151—82no—
246C22×C151—82no—
247C22×C151—82no—
248C22×C151C2×#12111yescharacteristic
249C22×C151#54611yescharacteristic
250C22×C151#55011yescharacteristic
251C22×C151C2×#13511yescharacteristic
252C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
253C22×C151#57611yescharacteristic
254C22×C151#57711yescharacteristic
255C4×C151—22no—
256C4×C151—42no—
257C4×C151—42no—
258C4×C151—42no—
259C4×C151—42no—
260C4×C151—82no—
261C4×C151—81no—
262C4×C151#46314yes—
263C4×C151#52511yescharacteristic
264C4×C151#53511yescharacteristic
265C4×C151#55311yescharacteristic
266C4×C151#55511yescharacteristic
267C2×C151—82no—
268C2×C151—162no—
269C2×C151#241411yescharacteristic
270C2×C151C2×#46311yescharacteristic
271C2×C151#304511yescharacteristic
272C2×C151#330511yescharacteristic
273C2×C151#333211yescharacteristic
274C2×C151#339411yescharacteristic
275C2×C151#339911yescharacteristic
276#24631C15111yesmaximal, characteristic, direct product factor, Sylow
277C151#2463111yescharacteristic, direct product factor, Sylow
278C2×#459C2×C15111yescharacteristic
279C2×C4×SD16C2×C15111yescharacteristic, complemented
280#2548C2×C15111yescharacteristic, complemented
281#2354C2×C15111yescharacteristic, complemented
282#2054C2×C15112yescomplemented
283#2012C2×C15112yescomplemented
284#1983C2×C15112yescomplemented
285#1957C2×C15111yescharacteristic, complemented
286#1939C2×C15111yescharacteristic, complemented
287#1926C2×C15112yescomplemented
288#1803C2×C15111yescharacteristic, complemented
289C22×SD16C22×C15111yescharacteristic
290C22×D8C22×C15112yes—
291C2×#127C22×C15111yescharacteristic
292C2×#124C22×C15112yes—
293C2×C4×Q8C22×C15111yescharacteristic
294C2×C4×D4C22×C15111yescharacteristic
295C2×#117—21no—
296#459—24no—
297C4×SD16—24no—
298C2×#106C22×C15111yescharacteristic
299C2×C4⋊C8C22×C15111yescharacteristic
300C2×C4⋊C8C22×C15112yes—
301C2×#103C22×C15111yescharacteristic
302C2×#103C22×C15112yes—
303C2×#102C22×C15111yescharacteristic
304C2×#102C22×C15112yes—
305C2×#102C22×C15112yes—
306C2×#102C22×C15112yes—
307C2×C4×C8C22×C15111yescharacteristic
308#394—22no—
309#390—21no—
310#390—21no—
311#390C22×C15112yes—
312#390C22×C15112yes—
313#388—22no—
314#384C22×C15111yescharacteristic
315#380—21no—
316C4×C4⋊C4C22×C15112yes—
317C4×C4⋊C4C22×C15111yescharacteristic
318#340C22×C15112yes—
319#336C22×C15112yes—
320C22×Q8C23×C15111yescharacteristic
321C22×D4—21no—
322C22×D4—21no—
323C22×D4C23×C15112yes—
324C22×D4C23×C15111yescharacteristic
325C23×C4—21no—
326C2×SD16—22no—
327C2×SD16—22no—
328C2×SD16—22no—
329C2×D8—24no—
330C2×D8—42no—
331C2×D8—42no—
332C22×C8C23×C15112yes—
333C22×C8C23×C15111yescharacteristic
334C22×C8C23×C15111yescharacteristic
335#127—22no—
336#127—22no—
337#124—24no—
338#124—42no—
339C4×Q8—22no—
340C4×Q8—22no—
341C4×D4—22no—
342C4×D4D4×C15114yes—
343#117—44no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4D4×C15111yescharacteristic
348C2×C4⋊C4D4×C15111yescharacteristic
349C2×C4⋊C4C23×C15111yescharacteristic
350C2×C4⋊C4C23×C15112yes—
351C2×C4⋊C4C23×C15111yescharacteristic
352C2×C22⋊C4—21no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C42—22no—
360C2×C42—21no—
361C2×C42C23×C15112yes—
362C2×C42C23×C15111yescharacteristic
363#106—22no—
364C4⋊C8—22no—
365C4⋊C8—42no—
366#103—22no—
367#103—42no—
368#102—22no—
369#102—24no—
370#102—24no—
371#102—42no—
372C4×C8—22no—
373#95—22no—
374#95D4×C15112yes—
375C24—21no—
376C24—22no—
377C2×Q8—21no—
378C2×Q8—21no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8#41×C15112yes—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—42no—
395C2×D4—42no—
396C2×D4—42no—
397C2×D4—42no—
398C2×D4—81no—
399C2×D4—81no—
400C2×D4C2×D4×C15112yes—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—24no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—42no—
407C22×C4—42no—
408C22×C4C2×D4×C15112yes—
409C22×C4C2×D4×C15112yes—
410C22×C4C2×D4×C15111yescharacteristic
411C22×C4C2×D4×C15111yescharacteristic
412C22×C4C24×C15111yescharacteristic
413SD16—28no—
414D8—48no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—22no—
419C2×C8—21no—
420C2×C8—22no—
421C2×C8—21no—
422C2×C8—22no—
423C2×C8#41×C15112yes—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—22no—
431C4⋊C4—42no—
432C4⋊C4—42no—
433C4⋊C4—81no—
434C4⋊C4C2×D4×C15112yes—
435C22⋊C4—24no—
436C22⋊C4—44no—
437C22⋊C4—44no—
438C22⋊C4—44no—
439C22⋊C4—82no—
440C22⋊C4—82no—
441C22⋊C4—82no—
442C42—22no—
443C42—22no—
444C42—44no—
445C42—42no—
446C42C2×D4×C15112yes—
447C42#41×C15112yes—
448C23—22no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23—42no—
462C23C22×D4×C15111yescharacteristic
463Q8—22no—
464Q8—22no—
465Q8—41no—
466Q8—41no—
467D4—22no—
468D4—22no—
469D4—42no—
470D4—42no—
471D4—41no—
472D4—42no—
473D4—41no—
474D4—42no—
475D4—84no—
476D4—84no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—48no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—41no—
498C2×C4#121×C15112yes—
499C2×C4#121×C15112yes—
500C2×C4#135×C15112yes—
501C2×C4AGL(1,ℤ/8)×C15112yes—
502C2×C4C22×D4×C15111yescharacteristic
503C2×C4C2×#41×C15111yescharacteristic
504C2×C4C2×#41×C15111yescharacteristic
505C2×C4C2×#41×C15111yescharacteristic
506C2×C4H(5,𝔽2)×C15111yescharacteristic
507C2×C4H(5,𝔽2)×C15111yescharacteristic
508C8—22no—
509C8—42no—
510C8—41no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22—81no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22—82no—
522C22—82no—
523C22—82no—
524C22—82no—
525C22C2×#121×C15111yescharacteristic
526C22#546×C15111yescharacteristic
527C22#550×C15111yescharacteristic
528C22C2×#135×C15111yescharacteristic
529C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
530C22#576×C15111yescharacteristic
531C22#577×C15111yescharacteristic
532C4—22no—
533C4—42no—
534C4—42no—
535C4—42no—
536C4—42no—
537C4—82no—
538C4—81no—
539C4#463×C15114yes—
540C4#525×C15111yescharacteristic
541C4#535×C15111yescharacteristic
542C4#553×C15111yescharacteristic
543C4#555×C15111yescharacteristic
544C2—82no—
545C2—162no—
546C2#2414×C15111yescharacteristic
547C2C2×#463×C15111yescharacteristic
548C2#3045×C15111yescharacteristic
549C2#3305×C15111yescharacteristic
550C2#3332×C15111yescharacteristic
551C2#3394×C15111yescharacteristic
552C2#3399×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#459×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C4⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×SD16×C151C2semidirect
3. #2548×C151C2semidirect
4. #2354×C151C2semidirect
5. #2054×C151C2semidirect
6. #2012×C151C2semidirect
7. #1983×C151C2semidirect
8. #1957×C151C2semidirect
9. #1939×C151C2semidirect
10. #1926×C151C2semidirect
11. #1803×C151C2semidirect
276. #24631C151direct (N × H)
277. C151#24631direct (N × H)
279. C2×C4×SD16C2×C151semidirect
280. #2548C2×C151semidirect
281. #2354C2×C151semidirect
282. #2054C2×C151semidirect
283. #2012C2×C151semidirect
284. #1983C2×C151semidirect
285. #1957C2×C151semidirect
286. #1939C2×C151semidirect
287. #1926C2×C151semidirect
288. #1803C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#459×C1512
C2×C4×SD16×C1512
#2548×C1512
#2354×C1512
#2054×C1512
#2012×C1512
#1983×C1512
#1957×C1512
#1939×C1512
#1926×C1512
#1803×C1512
#24631151