Finite Group Databasebeta

← C151×#24544 #50329469

Subgroups — C151×#24544 #50329469

Order 38656.

1106 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#449×C151C211yesmaximal, characteristic
2C2×#417×C151C211yesmaximal, characteristic, complemented
3#2501×C151C211yesmaximal, characteristic, complemented
4#2339×C151C211yesmaximal, characteristic, complemented
5#2072×C151C212yesmaximal, complemented
6#2055×C151C212yesmaximal, complemented
7#1895×C151C211yesmaximal, characteristic, complemented
8#1879×C151C212yesmaximal, complemented
9#1851×C151C211yesmaximal, characteristic, complemented
10#1824×C151C211yesmaximal, characteristic, complemented
11#1802×C151C212yesmaximal, complemented
12C22×#41×C151C2211yescharacteristic
13C22×SD16×C151C2211yescharacteristic
14C22×D8×C151C2211yescharacteristic
15C22×M16×C151C2211yescharacteristic
16C2×#123×C151—22no—
17C2×#121×C151C2211yescharacteristic
18C2×C4×D4×C151C2212yes—
19C22×C4⋊C4×C151C2211yescharacteristic
20#449×C151—24no—
21C2×C4⋊C8×C151C2212yes—
22#417×C151—24no—
23C2×#103×C151C2212yes—
24C2×#103×C151C2211yescharacteristic
25C2×#102×C151C2212yes—
26C2×#102×C151C2211yescharacteristic
27C2×#102×C151C2212yes—
28C2×C22⋊C8×C151C2211yescharacteristic
29#399×C151—21no—
30#399×C151—21no—
31#391×C151C2212yes—
32#390×C151C2212yes—
33#386×C151—22no—
34#384×C151C2212yes—
35#381×C151—21no—
36#380×C151C2211yescharacteristic
37C4×C22⋊C4×C151C2211yescharacteristic
38C2×#95×C151—21no—
39#340×C151C2212yes—
40#340×C151C2212yes—
41#340×C151C2212yes—
42#336×C151C2212yes—
43C2×#41×C151—24no—
44C2×#41×C151—22no—
45C2×#41×C151—42no—
46C2×#41×C151D414yes—
47C22×Q8×C151C2311yescharacteristic
48C22×D4×C151—21no—
49C22×D4×C151—21no—
50C22×D4×C151C2311yescharacteristic
51C22×D4×C151C2311yescharacteristic
52C23×C4×C151—21no—
53C23×C4×C151—22no—
54C23×C4×C151—21no—
55C23×C4×C151C2311yescharacteristic
56C2×SD16×C151—22no—
57C2×SD16×C151—42no—
58C2×D8×C151—22no—
59C2×D8×C151—24no—
60C2×M16×C151—22no—
61C2×M16×C151—42no—
62C22×C8×C151C2311yescharacteristic
63C22×C8×C151C2312yes—
64C22×C8×C151C2311yescharacteristic
65#123×C151—48no—
66#121×C151—22no—
67#121×C151—22no—
68C4×D4×C151—24no—
69C4×D4×C151—42no—
70C2×C4⋊C4×C151—22no—
71C2×C4⋊C4×C151—22no—
72C2×C4⋊C4×C151—22no—
73C2×C4⋊C4×C151—22no—
74C2×C4⋊C4×C151—21no—
75C2×C4⋊C4×C151C2312yes—
76C2×C4⋊C4×C151C2311yescharacteristic
77C2×C4⋊C4×C151C2312yes—
78C2×C22⋊C4×C151—22no—
79C2×C22⋊C4×C151—22no—
80C2×C22⋊C4×C151—22no—
81C2×C22⋊C4×C151—21no—
82C2×C22⋊C4×C151—21no—
83C2×C22⋊C4×C151D412yes—
84C2×C42×C151C2312yes—
85C4⋊C8×C151—42no—
86#103×C151—24no—
87#103×C151—22no—
88#102×C151—24no—
89#102×C151—22no—
90#102×C151—42no—
91C22⋊C8×C151—22no—
92#95×C151—21no—
93#95×C151—22no—
94#95×C151—22no—
95#95×C151D411yescharacteristic
96#95×C151D411yescharacteristic
97C24×C151—21no—
98C24×C151—21no—
99C24×C151C2×D411yescharacteristic
100#41×C151—28no—
101#41×C151—44no—
102#41×C151—48no—
103C2×Q8×C151—21no—
104C2×Q8×C151—22no—
105C2×Q8×C151—22no—
106C2×Q8×C151C2×D412yes—
107C2×D4×C151—24no—
108C2×D4×C151—21no—
109C2×D4×C151—21no—
110C2×D4×C151—21no—
111C2×D4×C151—22no—
112C2×D4×C151—22no—
113C2×D4×C151—22no—
114C2×D4×C151—44no—
115C2×D4×C151—44no—
116C2×D4×C151—42no—
117C2×D4×C151C2×D412yes—
118C2×D4×C151#4114yes—
119C22×C4×C151—22no—
120C22×C4×C151—22no—
121C22×C4×C151—21no—
122C22×C4×C151—24no—
123C22×C4×C151—22no—
124C22×C4×C151—22no—
125C22×C4×C151—21no—
126C22×C4×C151—44no—
127C22×C4×C151—44no—
128C22×C4×C151—44no—
129C22×C4×C151—42no—
130C22×C4×C151—44no—
131C22×C4×C151—82no—
132C22×C4×C151C2×D412yes—
133C22×C4×C151C2×D411yescharacteristic
134C22×C4×C151C2×D412yes—
135C22×C4×C151C2×D412yes—
136C22×C4×C151#4112yes—
137C22×C4×C151C2411yescharacteristic
138SD16×C151—44no—
139D8×C151—44no—
140M16×C151—44no—
141C2×C8×C151—21no—
142C2×C8×C151—21no—
143C2×C8×C151—22no—
144C2×C8×C151—22no—
145C2×C8×C151—22no—
146C2×C8×C151—22no—
147C2×C8×C151—22no—
148C4⋊C4×C151—22no—
149C4⋊C4×C151—21no—
150C4⋊C4×C151—22no—
151C4⋊C4×C151—22no—
152C4⋊C4×C151—21no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151—44no—
155C4⋊C4×C151—42no—
156C4⋊C4×C151—44no—
157C22⋊C4×C151—24no—
158C22⋊C4×C151—44no—
159C22⋊C4×C151—44no—
160C22⋊C4×C151—42no—
161C22⋊C4×C151—44no—
162C22⋊C4×C151—81no—
163C42×C151—22no—
164C42×C151—22no—
165C23×C151—22no—
166C23×C151—24no—
167C23×C151—22no—
168C23×C151—22no—
169C23×C151—21no—
170C23×C151—21no—
171C23×C151—42no—
172C23×C151—41no—
173C23×C151—41no—
174C23×C151—41no—
175C23×C151—42no—
176C23×C151—42no—
177C23×C151—41no—
178C23×C151—41no—
179C23×C151#12112yes—
180C23×C151C22×D411yescharacteristic
181Q8×C151—22no—
182Q8×C151—22no—
183Q8×C151—42no—
184D4×C151—22no—
185D4×C151—24no—
186D4×C151—48no—
187D4×C151—41no—
188D4×C151—41no—
189D4×C151—42no—
190D4×C151—84no—
191D4×C151#12314yescomplemented
192C2×C4×C151—22no—
193C2×C4×C151—22no—
194C2×C4×C151—22no—
195C2×C4×C151—22no—
196C2×C4×C151—22no—
197C2×C4×C151—24no—
198C2×C4×C151—22no—
199C2×C4×C151—22no—
200C2×C4×C151—22no—
201C2×C4×C151—22no—
202C2×C4×C151—48no—
203C2×C4×C151—42no—
204C2×C4×C151—41no—
205C2×C4×C151—42no—
206C2×C4×C151—42no—
207C2×C4×C151—42no—
208C2×C4×C151—42no—
209C2×C4×C151—42no—
210C2×C4×C151—42no—
211C2×C4×C151—42no—
212C2×C4×C151—88no—
213C2×C4×C151—84no—
214C2×C4×C151#12112yes—
215C2×C4×C151AGL(1,ℤ/8)14yes—
216C2×C4×C151C22×D411yescharacteristic
217C2×C4×C151C2×#4112yes—
218C2×C4×C151C2×#4111yescharacteristic
219C2×C4×C151H(5,𝔽2)12yes—
220C8×C151—41no—
221C8×C151—42no—
222C8×C151—41no—
223C22×C151—22no—
224C22×C151—24no—
225C22×C151—22no—
226C22×C151—22no—
227C22×C151—42no—
228C22×C151—44no—
229C22×C151—42no—
230C22×C151—42no—
231C22×C151—44no—
232C22×C151—42no—
233C22×C151—82no—
234C22×C151—81no—
235C22×C151—81no—
236C22×C151—81no—
237C22×C151—82no—
238C22×C151C2×#12111yescharacteristic
239C22×C151#54612yes—
240C22×C151C2×AGL(1,ℤ/8)12yes—
241C22×C151#57711yescharacteristic
242C22×C151#57811yescharacteristic
243C4×C151—22no—
244C4×C151—24no—
245C4×C151—42no—
246C4×C151—42no—
247C4×C151—82no—
248C4×C151—81no—
249C4×C151—82no—
250C4×C151C2×#12311yescharacteristic
251C4×C151#53411yescharacteristic
252C4×C151#55112yes—
253C2×C151—42no—
254C2×C151—44no—
255C2×C151—161no—
256C2×C151#241211yescharacteristic
257C2×C151#303811yescharacteristic
258C2×C151#304611yescharacteristic
259C2×C151#330612yes—
260C2×C151#333012yes—
261#24544C15111yesmaximal, characteristic, direct product factor, Sylow
262C151#2454411yescharacteristic, direct product factor, Sylow
263C2×#449C2×C15111yescharacteristic
264C2×#417C2×C15111yescharacteristic, complemented
265#2501C2×C15111yescharacteristic, complemented
266#2339C2×C15111yescharacteristic, complemented
267#2072C2×C15112yescomplemented
268#2055C2×C15112yescomplemented
269#1895C2×C15111yescharacteristic, complemented
270#1879C2×C15112yescomplemented
271#1851C2×C15111yescharacteristic, complemented
272#1824C2×C15111yescharacteristic, complemented
273#1802C2×C15112yescomplemented
274C22×#41C22×C15111yescharacteristic
275C22×SD16C22×C15111yescharacteristic
276C22×D8C22×C15111yescharacteristic
277C22×M16C22×C15111yescharacteristic
278C2×#123—22no—
279C2×#121C22×C15111yescharacteristic
280C2×C4×D4C22×C15112yes—
281C22×C4⋊C4C22×C15111yescharacteristic
282#449—24no—
283C2×C4⋊C8C22×C15112yes—
284#417—24no—
285C2×#103C22×C15112yes—
286C2×#103C22×C15111yescharacteristic
287C2×#102C22×C15111yescharacteristic
288C2×#102C22×C15112yes—
289C2×#102C22×C15112yes—
290C2×C22⋊C8C22×C15111yescharacteristic
291#399—21no—
292#399—21no—
293#391C22×C15112yes—
294#390C22×C15112yes—
295#386—22no—
296#384C22×C15112yes—
297#381—21no—
298#380C22×C15111yescharacteristic
299C4×C22⋊C4C22×C15111yescharacteristic
300C2×#95—21no—
301#340C22×C15112yes—
302#340C22×C15112yes—
303#340C22×C15112yes—
304#336C22×C15112yes—
305C2×#41—22no—
306C2×#41—24no—
307C2×#41—42no—
308C2×#41D4×C15114yes—
309C22×Q8C23×C15111yescharacteristic
310C22×D4—21no—
311C22×D4—21no—
312C22×D4C23×C15111yescharacteristic
313C22×D4C23×C15111yescharacteristic
314C23×C4—21no—
315C23×C4—21no—
316C23×C4—22no—
317C23×C4C23×C15111yescharacteristic
318C2×SD16—22no—
319C2×SD16—42no—
320C2×D8—24no—
321C2×D8—22no—
322C2×M16—22no—
323C2×M16—42no—
324C22×C8C23×C15112yes—
325C22×C8C23×C15111yescharacteristic
326C22×C8C23×C15111yescharacteristic
327#123—48no—
328#121—22no—
329#121—22no—
330C4×D4—24no—
331C4×D4—42no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4C23×C15112yes—
338C2×C4⋊C4C23×C15112yes—
339C2×C4⋊C4C23×C15111yescharacteristic
340C2×C22⋊C4—22no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4D4×C15112yes—
346C2×C42C23×C15112yes—
347C4⋊C8—42no—
348#103—24no—
349#103—22no—
350#102—24no—
351#102—22no—
352#102—42no—
353C22⋊C8—22no—
354#95—21no—
355#95—22no—
356#95—22no—
357#95D4×C15111yescharacteristic
358#95D4×C15111yescharacteristic
359C24—21no—
360C24—21no—
361C24C2×D4×C15111yescharacteristic
362#41—28no—
363#41—44no—
364#41—48no—
365C2×Q8—21no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8C2×D4×C15112yes—
369C2×D4—24no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—44no—
377C2×D4—44no—
378C2×D4—42no—
379C2×D4C2×D4×C15112yes—
380C2×D4#41×C15114yes—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—21no—
384C22×C4—24no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—21no—
388C22×C4—44no—
389C22×C4—44no—
390C22×C4—44no—
391C22×C4—42no—
392C22×C4—44no—
393C22×C4—82no—
394C22×C4C2×D4×C15112yes—
395C22×C4C2×D4×C15111yescharacteristic
396C22×C4C2×D4×C15112yes—
397C22×C4C2×D4×C15112yes—
398C22×C4#41×C15112yes—
399C22×C4C24×C15111yescharacteristic
400SD16—44no—
401D8—44no—
402M16—44no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8—22no—
406C2×C8—22no—
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—22no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—44no—
417C4⋊C4—42no—
418C4⋊C4—44no—
419C22⋊C4—24no—
420C22⋊C4—44no—
421C22⋊C4—44no—
422C22⋊C4—42no—
423C22⋊C4—44no—
424C22⋊C4—81no—
425C42—22no—
426C42—22no—
427C23—22no—
428C23—24no—
429C23—22no—
430C23—22no—
431C23—21no—
432C23—21no—
433C23—42no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—42no—
438C23—42no—
439C23—41no—
440C23—41no—
441C23#121×C15112yes—
442C23C22×D4×C15111yescharacteristic
443Q8—22no—
444Q8—22no—
445Q8—42no—
446D4—22no—
447D4—24no—
448D4—48no—
449D4—41no—
450D4—41no—
451D4—42no—
452D4—84no—
453D4#123×C15114yescomplemented
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—48no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—88no—
475C2×C4—84no—
476C2×C4#121×C15112yes—
477C2×C4AGL(1,ℤ/8)×C15114yes—
478C2×C4C22×D4×C15111yescharacteristic
479C2×C4C2×#41×C15112yes—
480C2×C4C2×#41×C15111yescharacteristic
481C2×C4H(5,𝔽2)×C15112yes—
482C8—41no—
483C8—42no—
484C8—41no—
485C22—22no—
486C22—24no—
487C22—22no—
488C22—22no—
489C22—42no—
490C22—42no—
491C22—44no—
492C22—42no—
493C22—42no—
494C22—44no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—82no—
499C22—82no—
500C22C2×#121×C15111yescharacteristic
501C22#546×C15112yes—
502C22C2×AGL(1,ℤ/8)×C15112yes—
503C22#577×C15111yescharacteristic
504C22#578×C15111yescharacteristic
505C4—22no—
506C4—24no—
507C4—42no—
508C4—42no—
509C4—82no—
510C4—81no—
511C4—82no—
512C4C2×#123×C15111yescharacteristic
513C4#534×C15111yescharacteristic
514C4#551×C15112yes—
515C2—42no—
516C2—44no—
517C2—161no—
518C2#2412×C15111yescharacteristic
519C2#3038×C15111yescharacteristic
520C2#3046×C15111yescharacteristic
521C2#3306×C15112yes—
522C2#3330×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#449×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C22⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#417×C151C2semidirect
3. #2501×C151C2semidirect
4. #2339×C151C2semidirect
5. #2072×C151C2semidirect
6. #2055×C151C2semidirect
7. #1895×C151C2semidirect
8. #1879×C151C2semidirect
9. #1851×C151C2semidirect
10. #1824×C151C2semidirect
11. #1802×C151C2semidirect
191. D4×C151#123semidirect
261. #24544C151direct (N × H)
262. C151#24544direct (N × H)
264. C2×#417C2×C151semidirect
265. #2501C2×C151semidirect
266. #2339C2×C151semidirect
267. #2072C2×C151semidirect
268. #2055C2×C151semidirect
269. #1895C2×C151semidirect
270. #1879C2×C151semidirect
271. #1851C2×C151semidirect
272. #1824C2×C151semidirect
273. #1802C2×C151semidirect
453. D4#123×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#449×C1512
C2×#417×C1512
#2501×C1512
#2339×C1512
#2072×C1512
#2055×C1512
#1895×C1512
#1879×C1512
#1851×C1512
#1824×C1512
#1802×C1512
#24544151