Finite Group Databasebeta

← C151×#24331 #50329256

Subgroups — C151×#24331 #50329256

Order 38656.

1078 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×#554×C151C211yesmaximal, characteristic
2C2×#477×C151C211yesmaximal, characteristic, complemented
3C2×C4×SD16×C151C211yesmaximal, characteristic
4#2582×C151C211yesmaximal, characteristic, complemented
5#2059×C151C212yesmaximal, complemented
6#2026×C151C212yesmaximal, complemented
7#1990×C151C211yesmaximal, characteristic, complemented
8#1984×C151C211yesmaximal, characteristic, complemented
9#1877×C151C212yesmaximal
10#1862×C151C212yesmaximal
11#1802×C151C211yesmaximal, characteristic
12C22×SD16×C151C2211yescharacteristic
13#554×C151—24no—
14#554×C151—24no—
15C2×C4⋊Q8×C151C2211yescharacteristic
16C2×#125×C151C2212yes—
17C2×C22⋊Q8×C151—21no—
18C2×C22⋊Q8×C151—22no—
19C2×C4×Q8×C151C2211yescharacteristic
20C2×C4×Q8×C151C2211yescharacteristic
21C2×C4×D4×C151C2212yes—
22C2×C4×D4×C151C2211yescharacteristic
23C22×C4⋊C4×C151—21no—
24#477×C151—24no—
25C4×SD16×C151—24no—
26C2×#107×C151C2212yes—
27C2×#106×C151C2211yescharacteristic
28C2×C4⋊C8×C151C2211yescharacteristic
29C2×#103×C151C2212yes—
30C2×#103×C151C2211yescharacteristic
31C2×#102×C151C2211yescharacteristic
32C2×#102×C151C2212yes—
33C2×C4×C8×C151C2211yescharacteristic
34#398×C151—22no—
35#391×C151—21no—
36#391×C151C2212yes—
37#389×C151—21no—
38#389×C151C2212yes—
39#384×C151C2211yescharacteristic
40#340×C151C2212yes—
41#340×C151C2212yes—
42#340×C151C2212yes—
43#336×C151C2212yes—
44#336×C151C2212yes—
45C22×Q8×C151—21no—
46C22×Q8×C151D411yescharacteristic
47C22×Q8×C151C2311yescharacteristic
48C22×D4×C151C2311yescharacteristic
49C23×C4×C151—21no—
50C23×C4×C151—22no—
51C2×SD16×C151—22no—
52C2×SD16×C151—22no—
53C2×SD16×C151Q814yescomplemented
54C22×C8×C151C2311yescharacteristic
55C22×C8×C151C2312yes—
56C22×C8×C151C2311yescharacteristic
57C4⋊Q8×C151—22no—
58C4⋊Q8×C151D414yes—
59#125×C151—24no—
60#125×C151—24no—
61C22⋊Q8×C151—28no—
62C22⋊Q8×C151—216no—
63C4×Q8×C151—22no—
64C4×Q8×C151—22no—
65C4×Q8×C151—22no—
66C4×Q8×C151—22no—
67C4×D4×C151—24no—
68C4×D4×C151—24no—
69C4×D4×C151—22no—
70C4×D4×C151D414yes—
71C2×C4⋊C4×C151—28no—
72C2×C4⋊C4×C151—22no—
73C2×C4⋊C4×C151—21no—
74C2×C4⋊C4×C151—22no—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151—22no—
79C2×C4⋊C4×C151D411yescharacteristic
80C2×C4⋊C4×C151D412yes—
81C2×C4⋊C4×C151C2312yes—
82C2×C4⋊C4×C151C2311yescharacteristic
83C2×C4⋊C4×C151C2311yescharacteristic
84C2×C4⋊C4×C151C2312yes—
85C2×C22⋊C4×C151—22no—
86C2×C22⋊C4×C151—21no—
87C2×C42×C151—21no—
88C2×C42×C151C2312yes—
89C2×C42×C151C2311yescharacteristic
90#107×C151—24no—
91#106×C151—22no—
92C4⋊C8×C151—22no—
93#103×C151—22no—
94#103×C151—24no—
95#102×C151—22no—
96#102×C151—24no—
97C4×C8×C151—22no—
98#95×C151—22no—
99#95×C151—22no—
100#95×C151—22no—
101C24×C151—21no—
102C2×Q8×C151—22no—
103C2×Q8×C151—24no—
104C2×Q8×C151—22no—
105C2×Q8×C151—22no—
106C2×Q8×C151—21no—
107C2×Q8×C151—21no—
108C2×Q8×C151—21no—
109C2×Q8×C151—21no—
110C2×Q8×C151—21no—
111C2×Q8×C151—81no—
112C2×Q8×C151—81no—
113C2×Q8×C151C2×Q812yes—
114C2×D4×C151—21no—
115C2×D4×C151—21no—
116C2×D4×C151—21no—
117C2×D4×C151C2×D412yes—
118C2×D4×C151C2×Q812yes—
119C2×D4×C151#4112yes—
120C22×C4×C151—21no—
121C22×C4×C151—21no—
122C22×C4×C151—22no—
123C22×C4×C151—28no—
124C22×C4×C151—24no—
125C22×C4×C151—22no—
126C22×C4×C151—21no—
127C22×C4×C151—42no—
128C22×C4×C151—42no—
129C22×C4×C151—82no—
130C22×C4×C151—82no—
131C22×C4×C151C2×D412yes—
132C22×C4×C151C2×D412yes—
133C22×C4×C151C2×D411yescharacteristic
134C22×C4×C151C2×D411yescharacteristic
135C22×C4×C151C2411yescharacteristic
136SD16×C151—28no—
137C2×C8×C151—21no—
138C2×C8×C151—21no—
139C2×C8×C151—21no—
140C2×C8×C151—22no—
141C2×C8×C151—22no—
142C2×C8×C151—21no—
143C2×C8×C151—21no—
144C2×C8×C151—22no—
145C2×C8×C151C2×Q812yes—
146C4⋊C4×C151—28no—
147C4⋊C4×C151—28no—
148C4⋊C4×C151—22no—
149C4⋊C4×C151—24no—
150C4⋊C4×C151—24no—
151C4⋊C4×C151—21no—
152C4⋊C4×C151—22no—
153C4⋊C4×C151—21no—
154C4⋊C4×C151—21no—
155C4⋊C4×C151—22no—
156C4⋊C4×C151—22no—
157C4⋊C4×C151—42no—
158C4⋊C4×C151—42no—
159C4⋊C4×C151—81no—
160C4⋊C4×C151—82no—
161C4⋊C4×C151C2×D412yes—
162C4⋊C4×C151C2×D414yes—
163C22⋊C4×C151—28no—
164C22⋊C4×C151—24no—
165C42×C151—22no—
166C42×C151—22no—
167C42×C151—42no—
168C42×C151C2×D412yes—
169C42×C151C2×D412yes—
170C23×C151—22no—
171C23×C151—22no—
172C23×C151—22no—
173C23×C151—41no—
174C23×C151—41no—
175C23×C151—41no—
176C23×C151—41no—
177C23×C151C22×D411yescharacteristic
178Q8×C151—22no—
179Q8×C151—22no—
180Q8×C151—41no—
181Q8×C151—41no—
182Q8×C151—44no—
183Q8×C151—84no—
184D4×C151—22no—
185D4×C151—22no—
186D4×C151—22no—
187D4×C151C22⋊Q814yes—
188C2×C4×C151—21no—
189C2×C4×C151—21no—
190C2×C4×C151—22no—
191C2×C4×C151—24no—
192C2×C4×C151—22no—
193C2×C4×C151—22no—
194C2×C4×C151—22no—
195C2×C4×C151—22no—
196C2×C4×C151—22no—
197C2×C4×C151—22no—
198C2×C4×C151—22no—
199C2×C4×C151—41no—
200C2×C4×C151—41no—
201C2×C4×C151—41no—
202C2×C4×C151—41no—
203C2×C4×C151—42no—
204C2×C4×C151—42no—
205C2×C4×C151—48no—
206C2×C4×C151—41no—
207C2×C4×C151—42no—
208C2×C4×C151—42no—
209C2×C4×C151—42no—
210C2×C4×C151—41no—
211C2×C4×C151—41no—
212C2×C4×C151—88no—
213C2×C4×C151#12012yes—
214C2×C4×C151#12012yes—
215C2×C4×C151#13512yes—
216C2×C4×C151#13712yes—
217C2×C4×C151C22×D411yescharacteristic
218C2×C4×C151C22×D411yescharacteristic
219C2×C4×C151C22×Q811yescharacteristic
220C2×C4×C151C2×#4111yescharacteristic
221C2×C4×C1512−1+411yescharacteristic
222C2×C4×C1512−1+411yescharacteristic
223C8×C151—22no—
224C8×C151—41no—
225C8×C151—42no—
226C22×C151—24no—
227C22×C151—42no—
228C22×C151—42no—
229C22×C151—42no—
230C22×C151—42no—
231C22×C151—42no—
232C22×C151—42no—
233C22×C151C2×#12011yescharacteristic
234C22×C151#54811yescharacteristic
235C22×C151D4×Q811yescharacteristic
236C22×C151C2×#13511yescharacteristic
237C22×C151C2×#13711yescharacteristic
238C22×C151#57611yescharacteristic
239C22×C151#57711yescharacteristic
240C4×C151—22no—
241C4×C151—42no—
242C4×C151—42no—
243C4×C151—42no—
244C4×C151—42no—
245C4×C151—44no—
246C4×C151—82no—
247C4×C151—81no—
248C4×C151#45214yes—
249C4×C151C2×C22⋊Q811yescharacteristic
250C4×C151#53611yescharacteristic
251C4×C151#54811yescharacteristic
252C4×C151D4×Q811yescharacteristic
253C2×C151—44no—
254C2×C151#240911yescharacteristic
255C2×C151C2×#45211yescharacteristic
256C2×C151#301211yescharacteristic
257C2×C151#336111yescharacteristic
258C2×C151#337211yescharacteristic
259C2×C151#338111yescharacteristic
260C2×C151#338511yescharacteristic
261#24331C15111yesmaximal, characteristic, direct product factor, Sylow
262C151#2433111yescharacteristic, direct product factor, Sylow
263C2×#554C2×C15111yescharacteristic
264C2×#477C2×C15111yescharacteristic, complemented
265C2×C4×SD16C2×C15111yescharacteristic
266#2582C2×C15111yescharacteristic, complemented
267#2059C2×C15112yescomplemented
268#2026C2×C15112yescomplemented
269#1990C2×C15111yescharacteristic, complemented
270#1984C2×C15111yescharacteristic, complemented
271#1877C2×C15112yes—
272#1862C2×C15112yes—
273#1802C2×C15111yescharacteristic
274C22×SD16C22×C15111yescharacteristic
275#554—24no—
276#554—24no—
277C2×C4⋊Q8C22×C15111yescharacteristic
278C2×#125C22×C15112yes—
279C2×C22⋊Q8—21no—
280C2×C22⋊Q8—22no—
281C2×C4×Q8C22×C15111yescharacteristic
282C2×C4×Q8C22×C15111yescharacteristic
283C2×C4×D4C22×C15112yes—
284C2×C4×D4C22×C15111yescharacteristic
285C22×C4⋊C4—21no—
286#477—24no—
287C4×SD16—24no—
288C2×#107C22×C15112yes—
289C2×#106C22×C15111yescharacteristic
290C2×C4⋊C8C22×C15111yescharacteristic
291C2×#103C22×C15112yes—
292C2×#103C22×C15111yescharacteristic
293C2×#102C22×C15112yes—
294C2×#102C22×C15111yescharacteristic
295C2×C4×C8C22×C15111yescharacteristic
296#398—22no—
297#391—21no—
298#391C22×C15112yes—
299#389—21no—
300#389C22×C15112yes—
301#384C22×C15111yescharacteristic
302#340C22×C15112yes—
303#340C22×C15112yes—
304#340C22×C15112yes—
305#336C22×C15112yes—
306#336C22×C15112yes—
307C22×Q8—21no—
308C22×Q8D4×C15111yescharacteristic
309C22×Q8C23×C15111yescharacteristic
310C22×D4C23×C15111yescharacteristic
311C23×C4—21no—
312C23×C4—22no—
313C2×SD16—22no—
314C2×SD16—22no—
315C2×SD16Q8×C15114yescomplemented
316C22×C8C23×C15111yescharacteristic
317C22×C8C23×C15112yes—
318C22×C8C23×C15111yescharacteristic
319C4⋊Q8—22no—
320C4⋊Q8D4×C15114yes—
321#125—24no—
322#125—24no—
323C22⋊Q8—28no—
324C22⋊Q8—216no—
325C4×Q8—22no—
326C4×Q8—22no—
327C4×Q8—22no—
328C4×Q8—22no—
329C4×D4—24no—
330C4×D4—24no—
331C4×D4—22no—
332C4×D4D4×C15114yes—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4D4×C15111yescharacteristic
342C2×C4⋊C4D4×C15112yes—
343C2×C4⋊C4C23×C15111yescharacteristic
344C2×C4⋊C4C23×C15112yes—
345C2×C4⋊C4C23×C15111yescharacteristic
346C2×C4⋊C4C23×C15112yes—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—21no—
349C2×C42—21no—
350C2×C42C23×C15112yes—
351C2×C42C23×C15111yescharacteristic
352#107—24no—
353#106—22no—
354C4⋊C8—22no—
355#103—22no—
356#103—24no—
357#102—24no—
358#102—22no—
359C4×C8—22no—
360#95—22no—
361#95—22no—
362#95—22no—
363C24—21no—
364C2×Q8—22no—
365C2×Q8—24no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—21no—
369C2×Q8—21no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—21no—
373C2×Q8—81no—
374C2×Q8—81no—
375C2×Q8C2×Q8×C15112yes—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4C2×D4×C15112yes—
380C2×D4C2×Q8×C15112yes—
381C2×D4#41×C15112yes—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—28no—
386C22×C4—24no—
387C22×C4—22no—
388C22×C4—21no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4—82no—
392C22×C4—82no—
393C22×C4C2×D4×C15112yes—
394C22×C4C2×D4×C15112yes—
395C22×C4C2×D4×C15111yescharacteristic
396C22×C4C2×D4×C15111yescharacteristic
397C22×C4C24×C15111yescharacteristic
398SD16—28no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—22no—
403C2×C8—22no—
404C2×C8—21no—
405C2×C8—21no—
406C2×C8—22no—
407C2×C8C2×Q8×C15112yes—
408C4⋊C4—28no—
409C4⋊C4—28no—
410C4⋊C4—22no—
411C4⋊C4—24no—
412C4⋊C4—24no—
413C4⋊C4—21no—
414C4⋊C4—22no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—42no—
420C4⋊C4—42no—
421C4⋊C4—81no—
422C4⋊C4—82no—
423C4⋊C4C2×D4×C15112yes—
424C4⋊C4C2×D4×C15114yes—
425C22⋊C4—28no—
426C22⋊C4—24no—
427C42—22no—
428C42—22no—
429C42—42no—
430C42C2×D4×C15112yes—
431C42C2×D4×C15112yes—
432C23—22no—
433C23—22no—
434C23—22no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23C22×D4×C15111yescharacteristic
440Q8—22no—
441Q8—22no—
442Q8—44no—
443Q8—41no—
444Q8—41no—
445Q8—84no—
446D4—22no—
447D4—22no—
448D4—22no—
449D4C22⋊Q8×C15114yes—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—48no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—88no—
475C2×C4#120×C15112yes—
476C2×C4#120×C15112yes—
477C2×C4#135×C15112yes—
478C2×C4#137×C15112yes—
479C2×C4C22×D4×C15111yescharacteristic
480C2×C4C22×D4×C15111yescharacteristic
481C2×C4C22×Q8×C15111yescharacteristic
482C2×C4C2×#41×C15111yescharacteristic
483C2×C42−1+4×C15111yescharacteristic
484C2×C42−1+4×C15111yescharacteristic
485C8—22no—
486C8—41no—
487C8—42no—
488C22—24no—
489C22—42no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22C2×#120×C15111yescharacteristic
496C22#548×C15111yescharacteristic
497C22D4×Q8×C15111yescharacteristic
498C22C2×#135×C15111yescharacteristic
499C22C2×#137×C15111yescharacteristic
500C22#576×C15111yescharacteristic
501C22#577×C15111yescharacteristic
502C4—22no—
503C4—42no—
504C4—42no—
505C4—42no—
506C4—42no—
507C4—44no—
508C4—82no—
509C4—81no—
510C4#452×C15114yes—
511C4C2×C22⋊Q8×C15111yescharacteristic
512C4#536×C15111yescharacteristic
513C4#548×C15111yescharacteristic
514C4D4×Q8×C15111yescharacteristic
515C2—44no—
516C2#2409×C15111yescharacteristic
517C2C2×#452×C15111yescharacteristic
518C2#3012×C15111yescharacteristic
519C2#3361×C15111yescharacteristic
520C2#3372×C15111yescharacteristic
521C2#3381×C15111yescharacteristic
522C2#3385×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×Q8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#477×C151C2semidirect
4. #2582×C151C2semidirect
5. #2059×C151C2semidirect
6. #2026×C151C2semidirect
7. #1990×C151C2semidirect
8. #1984×C151C2semidirect
53. C2×SD16×C151Q8semidirect
261. #24331C151direct (N × H)
262. C151#24331direct (N × H)
264. C2×#477C2×C151semidirect
266. #2582C2×C151semidirect
267. #2059C2×C151semidirect
268. #2026C2×C151semidirect
269. #1990C2×C151semidirect
270. #1984C2×C151semidirect
315. C2×SD16Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#554×C1512
C2×#477×C1512
C2×C4×SD16×C1512
#2582×C1512
#2059×C1512
#2026×C1512
#1990×C1512
#1984×C1512
#1877×C1512
#1862×C1512
#1802×C1512
#24331151