Finite Group Databasebeta

← C151×#24628 #50329553

Subgroups — C151×#24628 #50329553

Order 38656.

1034 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#460×C151C211yesmaximal, characteristic, complemented
2C2×C4×SD16×C151C211yesmaximal, characteristic, complemented
3#2541×C151C211yesmaximal, characteristic
4#2355×C151C211yesmaximal, characteristic, complemented
5#2055×C151C212yesmaximal, complemented
6#2014×C151C212yesmaximal, complemented
7#1982×C151C212yesmaximal, complemented
8#1957×C151C211yesmaximal, characteristic, complemented
9#1939×C151C211yesmaximal, characteristic, complemented
10#1926×C151C212yesmaximal, complemented
11#1802×C151C211yesmaximal, characteristic, complemented
12C22×SD16×C151C2211yescharacteristic
13C22×SD16×C151C2212yes—
14C2×#127×C151C2211yescharacteristic
15C2×#127×C151C2212yes—
16C2×#121×C151—21no—
17C2×#121×C151—21no—
18C2×C4×Q8×C151C2211yescharacteristic
19C2×C4×D4×C151C2211yescharacteristic
20#460×C151—24no—
21C4×SD16×C151—24no—
22C2×#106×C151C2211yescharacteristic
23C2×C4⋊C8×C151C2211yescharacteristic
24C2×C4⋊C8×C151C2212yes—
25C2×#103×C151C2211yescharacteristic
26C2×#102×C151C2211yescharacteristic
27C2×#102×C151C2212yes—
28C2×#102×C151C2212yes—
29C2×#102×C151C2212yes—
30C2×#102×C151C2212yes—
31C2×C4×C8×C151C2211yescharacteristic
32#392×C151—22no—
33#391×C151C2212yes—
34#390×C151C2212yes—
35#387×C151—22no—
36#384×C151C2211yescharacteristic
37#382×C151—21no—
38C4×C4⋊C4×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—22no—
46C22×D4×C151—22no—
47C22×D4×C151—21no—
48C22×D4×C151C2312yes—
49C22×D4×C151C2311yescharacteristic
50C23×C4×C151—21no—
51C2×SD16×C151—22no—
52C2×SD16×C151—22no—
53C2×SD16×C151—22no—
54C2×SD16×C151—24no—
55C2×SD16×C151—42no—
56C2×SD16×C151—42no—
57C22×C8×C151C2312yes—
58C22×C8×C151C2311yescharacteristic
59C22×C8×C151C2311yescharacteristic
60#127×C151—24no—
61#127×C151—22no—
62#127×C151—22no—
63#127×C151—42no—
64#121×C151—44no—
65#121×C151—44no—
66C4×Q8×C151—22no—
67C4×Q8×C151D414yescomplemented
68C4×D4×C151—22no—
69C4×D4×C151—22no—
70C2×C4⋊C4×C151—21no—
71C2×C4⋊C4×C151—21no—
72C2×C4⋊C4×C151—21no—
73C2×C4⋊C4×C151D411yescharacteristic
74C2×C4⋊C4×C151D411yescharacteristic
75C2×C4⋊C4×C151C2311yescharacteristic
76C2×C4⋊C4×C151C2312yes—
77C2×C4⋊C4×C151C2311yescharacteristic
78C2×C22⋊C4×C151—22no—
79C2×C22⋊C4×C151—22no—
80C2×C22⋊C4×C151—21no—
81C2×C42×C151—21no—
82C2×C42×C151—22no—
83C2×C42×C151C2312yes—
84C2×C42×C151C2311yescharacteristic
85#106×C151—22no—
86C4⋊C8×C151—22no—
87C4⋊C8×C151—42no—
88#103×C151—22no—
89#102×C151—24no—
90#102×C151—22no—
91#102×C151—24no—
92#102×C151—42no—
93#102×C151—42no—
94C4×C8×C151—22no—
95#95×C151—22no—
96#95×C151—22no—
97#95×C151—22no—
98#95×C151D412yes—
99C24×C151—21no—
100C24×C151—22no—
101C2×Q8×C151—21no—
102C2×Q8×C151—21no—
103C2×Q8×C151—21no—
104C2×Q8×C151—21no—
105C2×Q8×C151—21no—
106C2×Q8×C151C2×D412yes—
107C2×D4×C151—21no—
108C2×D4×C151—22no—
109C2×D4×C151—21no—
110C2×D4×C151—21no—
111C2×D4×C151—22no—
112C2×D4×C151—22no—
113C2×D4×C151—22no—
114C2×D4×C151—21no—
115C2×D4×C151—21no—
116C2×D4×C151—22no—
117C2×D4×C151—22no—
118C2×D4×C151—44no—
119C2×D4×C151—44no—
120C2×D4×C151—44no—
121C2×D4×C151—42no—
122C2×D4×C151—42no—
123C2×D4×C151—44no—
124C2×D4×C151—42no—
125C2×D4×C151—42no—
126C2×D4×C151—82no—
127C2×D4×C151—81no—
128C2×D4×C151—81no—
129C2×D4×C151—82no—
130C2×D4×C151#4112yes—
131C22×C4×C151—21no—
132C22×C4×C151—21no—
133C22×C4×C151—22no—
134C22×C4×C151—21no—
135C22×C4×C151—42no—
136C22×C4×C151—42no—
137C22×C4×C151—42no—
138C22×C4×C151C2×D412yes—
139C22×C4×C151C2×D411yescharacteristic
140C22×C4×C151C2×D412yes—
141C22×C4×C151C2×D411yescharacteristic
142C22×C4×C151C2411yescharacteristic
143SD16×C151—28no—
144SD16×C151—48no—
145C2×C8×C151—21no—
146C2×C8×C151—21no—
147C2×C8×C151—21no—
148C2×C8×C151—22no—
149C2×C8×C151—21no—
150C2×C8×C151—22no—
151C2×C8×C151—21no—
152C2×C8×C151—22no—
153C2×C8×C151#4112yes—
154C4⋊C4×C151—24no—
155C4⋊C4×C151—22no—
156C4⋊C4×C151—21no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—21no—
160C4⋊C4×C151—22no—
161C4⋊C4×C151—42no—
162C4⋊C4×C151—81no—
163C4⋊C4×C151SD1614yescomplemented
164C4⋊C4×C151C2×D412yes—
165C22⋊C4×C151—44no—
166C22⋊C4×C151—42no—
167C22⋊C4×C151—44no—
168C42×C151—24no—
169C42×C151—22no—
170C42×C151—22no—
171C42×C151—82no—
172C42×C151C2×D412yes—
173C42×C151#4112yes—
174C23×C151—22no—
175C23×C151—41no—
176C23×C151—41no—
177C23×C151—41no—
178C23×C151—41no—
179C23×C151—41no—
180C23×C151—41no—
181C23×C151—42no—
182C23×C151—42no—
183C23×C151—42no—
184C23×C151—42no—
185C23×C151—42no—
186C23×C151—42no—
187C23×C151—42no—
188C23×C151C22×D411yescharacteristic
189Q8×C151—22no—
190Q8×C151—22no—
191Q8×C151—41no—
192Q8×C151—41no—
193D4×C151—22no—
194D4×C151—22no—
195D4×C151—42no—
196D4×C151—41no—
197D4×C151—42no—
198D4×C151—42no—
199D4×C151—41no—
200D4×C151—42no—
201D4×C151—88no—
202D4×C151—84no—
203D4×C151—88no—
204D4×C151—84no—
205C2×C4×C151—22no—
206C2×C4×C151—22no—
207C2×C4×C151—21no—
208C2×C4×C151—21no—
209C2×C4×C151—22no—
210C2×C4×C151—22no—
211C2×C4×C151—22no—
212C2×C4×C151—22no—
213C2×C4×C151—22no—
214C2×C4×C151—41no—
215C2×C4×C151—41no—
216C2×C4×C151—41no—
217C2×C4×C151—41no—
218C2×C4×C151—41no—
219C2×C4×C151—42no—
220C2×C4×C151—41no—
221C2×C4×C151—41no—
222C2×C4×C151—42no—
223C2×C4×C151—42no—
224C2×C4×C151—84no—
225C2×C4×C151#12112yes—
226C2×C4×C151#12112yes—
227C2×C4×C151C2×SD1614yes—
228C2×C4×C151C2×SD1612yes—
229C2×C4×C151AGL(1,ℤ/8)12yes—
230C2×C4×C151C22×D411yescharacteristic
231C2×C4×C151C2×#4111yescharacteristic
232C2×C4×C151C2×#4111yescharacteristic
233C2×C4×C151C2×#4111yescharacteristic
234C2×C4×C151H(5,𝔽2)11yescharacteristic
235C2×C4×C151H(5,𝔽2)11yescharacteristic
236C8×C151—22no—
237C8×C151—41no—
238C8×C151—42no—
239C22×C151—42no—
240C22×C151—42no—
241C22×C151—42no—
242C22×C151—81no—
243C22×C151—81no—
244C22×C151—81no—
245C22×C151—81no—
246C22×C151—82no—
247C22×C151—82no—
248C22×C151—82no—
249C22×C151—82no—
250C22×C151—82no—
251C22×C151—82no—
252C22×C151—82no—
253C22×C151C2×#12111yescharacteristic
254C22×C151#54611yescharacteristic
255C22×C151#55011yescharacteristic
256C22×C151C22×SD1611yescharacteristic
257C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
258C22×C151#57611yescharacteristic
259C22×C151#57711yescharacteristic
260C4×C151—24no—
261C4×C151—22no—
262C4×C151—42no—
263C4×C151—42no—
264C4×C151—42no—
265C4×C151—82no—
266C4×C151—81no—
267C4×C151#46014yes—
268C4×C151#52511yescharacteristic
269C4×C151#53511yescharacteristic
270C4×C151#55311yescharacteristic
271C4×C151#55511yescharacteristic
272C2×C151—82no—
273C2×C151—162no—
274C2×C151#241411yescharacteristic
275C2×C151C2×#46011yescharacteristic
276C2×C151#304511yescharacteristic
277C2×C151#329511yescharacteristic
278C2×C151#332411yescharacteristic
279C2×C151#339211yescharacteristic
280C2×C151#339911yescharacteristic
281#24628C15111yesmaximal, characteristic, direct product factor, Sylow
282C151#2462811yescharacteristic, direct product factor, Sylow
283C2×#460C2×C15111yescharacteristic, complemented
284C2×C4×SD16C2×C15111yescharacteristic, complemented
285#2541C2×C15111yescharacteristic
286#2355C2×C15111yescharacteristic, complemented
287#2055C2×C15112yescomplemented
288#2014C2×C15112yescomplemented
289#1982C2×C15112yescomplemented
290#1957C2×C15111yescharacteristic, complemented
291#1939C2×C15111yescharacteristic, complemented
292#1926C2×C15112yescomplemented
293#1802C2×C15111yescharacteristic, complemented
294C22×SD16C22×C15111yescharacteristic
295C22×SD16C22×C15112yes—
296C2×#127C22×C15111yescharacteristic
297C2×#127C22×C15112yes—
298C2×#121—21no—
299C2×#121—21no—
300C2×C4×Q8C22×C15111yescharacteristic
301C2×C4×D4C22×C15111yescharacteristic
302#460—24no—
303C4×SD16—24no—
304C2×#106C22×C15111yescharacteristic
305C2×C4⋊C8C22×C15111yescharacteristic
306C2×C4⋊C8C22×C15112yes—
307C2×#103C22×C15111yescharacteristic
308C2×#102C22×C15111yescharacteristic
309C2×#102C22×C15112yes—
310C2×#102C22×C15112yes—
311C2×#102C22×C15112yes—
312C2×#102C22×C15112yes—
313C2×C4×C8C22×C15111yescharacteristic
314#392—22no—
315#391C22×C15112yes—
316#390C22×C15112yes—
317#387—22no—
318#384C22×C15111yescharacteristic
319#382—21no—
320C4×C4⋊C4—21no—
321C4×C4⋊C4C22×C15112yes—
322C4×C4⋊C4C22×C15111yescharacteristic
323#340C22×C15112yes—
324#336C22×C15112yes—
325C22×Q8C23×C15111yescharacteristic
326C22×D4—21no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—21no—
330C22×D4C23×C15112yes—
331C22×D4C23×C15111yescharacteristic
332C23×C4—21no—
333C2×SD16—22no—
334C2×SD16—22no—
335C2×SD16—24no—
336C2×SD16—22no—
337C2×SD16—42no—
338C2×SD16—42no—
339C22×C8C23×C15112yes—
340C22×C8C23×C15111yescharacteristic
341C22×C8C23×C15111yescharacteristic
342#127—24no—
343#127—22no—
344#127—22no—
345#127—42no—
346#121—44no—
347#121—44no—
348C4×Q8—22no—
349C4×Q8D4×C15114yescomplemented
350C4×D4—22no—
351C4×D4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4D4×C15111yescharacteristic
356C2×C4⋊C4D4×C15111yescharacteristic
357C2×C4⋊C4C23×C15111yescharacteristic
358C2×C4⋊C4C23×C15112yes—
359C2×C4⋊C4C23×C15111yescharacteristic
360C2×C22⋊C4—21no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C42—21no—
364C2×C42—22no—
365C2×C42C23×C15112yes—
366C2×C42C23×C15111yescharacteristic
367#106—22no—
368C4⋊C8—22no—
369C4⋊C8—42no—
370#103—22no—
371#102—24no—
372#102—22no—
373#102—24no—
374#102—42no—
375#102—42no—
376C4×C8—22no—
377#95—22no—
378#95—22no—
379#95—22no—
380#95D4×C15112yes—
381C24—21no—
382C24—22no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8C2×D4×C15112yes—
389C2×D4—21no—
390C2×D4—22no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—44no—
401C2×D4—44no—
402C2×D4—44no—
403C2×D4—42no—
404C2×D4—42no—
405C2×D4—44no—
406C2×D4—42no—
407C2×D4—42no—
408C2×D4—82no—
409C2×D4—81no—
410C2×D4—81no—
411C2×D4—82no—
412C2×D4#41×C15112yes—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4C2×D4×C15112yes—
421C22×C4C2×D4×C15111yescharacteristic
422C22×C4C2×D4×C15112yes—
423C22×C4C2×D4×C15111yescharacteristic
424C22×C4C24×C15111yescharacteristic
425SD16—28no—
426SD16—48no—
427C2×C8—21no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8—22no—
431C2×C8—21no—
432C2×C8—22no—
433C2×C8—21no—
434C2×C8—22no—
435C2×C8#41×C15112yes—
436C4⋊C4—24no—
437C4⋊C4—22no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—42no—
444C4⋊C4—81no—
445C4⋊C4SD16×C15114yescomplemented
446C4⋊C4C2×D4×C15112yes—
447C22⋊C4—44no—
448C22⋊C4—42no—
449C22⋊C4—44no—
450C42—24no—
451C42—22no—
452C42—22no—
453C42—82no—
454C42C2×D4×C15112yes—
455C42#41×C15112yes—
456C23—22no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—41no—
463C23—42no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23C22×D4×C15111yescharacteristic
471Q8—22no—
472Q8—22no—
473Q8—41no—
474Q8—41no—
475D4—22no—
476D4—22no—
477D4—42no—
478D4—41no—
479D4—42no—
480D4—42no—
481D4—41no—
482D4—42no—
483D4—88no—
484D4—84no—
485D4—88no—
486D4—84no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—84no—
507C2×C4#121×C15112yes—
508C2×C4#121×C15112yes—
509C2×C4C2×SD16×C15114yes—
510C2×C4C2×SD16×C15112yes—
511C2×C4AGL(1,ℤ/8)×C15112yes—
512C2×C4C22×D4×C15111yescharacteristic
513C2×C4C2×#41×C15111yescharacteristic
514C2×C4C2×#41×C15111yescharacteristic
515C2×C4C2×#41×C15111yescharacteristic
516C2×C4H(5,𝔽2)×C15111yescharacteristic
517C2×C4H(5,𝔽2)×C15111yescharacteristic
518C8—22no—
519C8—42no—
520C8—41no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22—82no—
529C22—82no—
530C22—82no—
531C22—82no—
532C22—82no—
533C22—82no—
534C22—82no—
535C22C2×#121×C15111yescharacteristic
536C22#546×C15111yescharacteristic
537C22#550×C15111yescharacteristic
538C22C22×SD16×C15111yescharacteristic
539C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
540C22#576×C15111yescharacteristic
541C22#577×C15111yescharacteristic
542C4—24no—
543C4—22no—
544C4—42no—
545C4—42no—
546C4—42no—
547C4—82no—
548C4—81no—
549C4#460×C15114yes—
550C4#525×C15111yescharacteristic
551C4#535×C15111yescharacteristic
552C4#553×C15111yescharacteristic
553C4#555×C15111yescharacteristic
554C2—82no—
555C2—162no—
556C2#2414×C15111yescharacteristic
557C2C2×#460×C15111yescharacteristic
558C2#3045×C15111yescharacteristic
559C2#3295×C15111yescharacteristic
560C2#3324×C15111yescharacteristic
561C2#3392×C15111yescharacteristic
562C2#3399×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#2541×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
1. C2×#460×C151C2semidirect
2. C2×C4×SD16×C151C2semidirect
4. #2355×C151C2semidirect
5. #2055×C151C2semidirect
6. #2014×C151C2semidirect
7. #1982×C151C2semidirect
8. #1957×C151C2semidirect
9. #1939×C151C2semidirect
10. #1926×C151C2semidirect
11. #1802×C151C2semidirect
67. C4×Q8×C151D4semidirect
163. C4⋊C4×C151SD16semidirect
281. #24628C151direct (N × H)
282. C151#24628direct (N × H)
283. C2×#460C2×C151semidirect
284. C2×C4×SD16C2×C151semidirect
286. #2355C2×C151semidirect
287. #2055C2×C151semidirect
288. #2014C2×C151semidirect
289. #1982C2×C151semidirect
290. #1957C2×C151semidirect
291. #1939C2×C151semidirect
292. #1926C2×C151semidirect
293. #1802C2×C151semidirect
349. C4×Q8D4×C151semidirect
445. C4⋊C4SD16×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#460×C1512
C2×C4×SD16×C1512
#2541×C1512
#2355×C1512
#2055×C1512
#2014×C1512
#1982×C1512
#1957×C1512
#1939×C1512
#1926×C1512
#1802×C1512
#24628151