Finite Group Databasebeta

← C151×#24499 #50329424

Subgroups — C151×#24499 #50329424

Order 38656.

950 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#482×C151C211yesmaximal, characteristic
2C2×#419×C151C211yesmaximal, characteristic, complemented
3#2436×C151C211yesmaximal, characteristic
4#2346×C151C211yesmaximal, characteristic, complemented
5#2066×C151C212yesmaximal, complemented
6#2042×C151C212yesmaximal, complemented
7#1983×C151C212yesmaximal, complemented
8#1928×C151C212yesmaximal, complemented
9#1895×C151C211yesmaximal, characteristic
10#1851×C151C211yesmaximal, characteristic, complemented
11#1787×C151C211yesmaximal, characteristic, complemented
12C23×Q8×C151C2211yescharacteristic
13C22×M16×C151C2211yescharacteristic
14C2×#124×C151C2212yes—
15C2×#121×C151C2211yescharacteristic
16C2×#117×C151C2211yescharacteristic
17#482×C151—24no—
18C2×#107×C151C2211yescharacteristic
19C2×#106×C151C2211yescharacteristic
20C2×C4⋊C8×C151C2212yes—
21#419×C151—24no—
22C2×#103×C151C2212yes—
23C2×#103×C151C2212yes—
24C2×#103×C151C2212yes—
25C2×#103×C151C2212yes—
26C2×#102×C151C2211yescharacteristic
27C2×#102×C151C2211yescharacteristic
28C2×#102×C151C2212yes—
29C2×C22⋊C8×C151C2211yescharacteristic
30#393×C151—21no—
31#393×C151—21no—
32#391×C151C2212yes—
33#389×C151C2212yes—
34#388×C151—22no—
35#386×C151—22no—
36#382×C151—21no—
37#380×C151C2211yescharacteristic
38C4×C4⋊C4×C151C2212yes—
39C4×C22⋊C4×C151C2211yescharacteristic
40#376×C151—21no—
41#340×C151C2212yes—
42#336×C151C2212yes—
43C22×Q8×C151—22no—
44C22×Q8×C151—24no—
45C22×Q8×C151—22no—
46C22×Q8×C151—21no—
47C22×Q8×C151—42no—
48C22×Q8×C151C2312yes—
49C22×D4×C151—21no—
50C22×D4×C151C2311yescharacteristic
51C23×C4×C151—21no—
52C23×C4×C151C2311yescharacteristic
53C2×M16×C151—22no—
54C2×M16×C151—42no—
55C22×C8×C151C2311yescharacteristic
56C22×C8×C151C2312yes—
57C22×C8×C151C2311yescharacteristic
58#124×C151—24no—
59#124×C151—42no—
60#121×C151—22no—
61#121×C151—22no—
62#117×C151—22no—
63#117×C151D414yes—
64C2×C4⋊C4×C151—22no—
65C2×C4⋊C4×C151C2311yescharacteristic
66C2×C4⋊C4×C151C2312yes—
67C2×C4⋊C4×C151C2311yescharacteristic
68C2×C4⋊C4×C151C2311yescharacteristic
69C2×C22⋊C4×C151—22no—
70C2×C22⋊C4×C151—22no—
71C2×C22⋊C4×C151—21no—
72C2×C22⋊C4×C151—21no—
73C2×C22⋊C4×C151—21no—
74C2×C22⋊C4×C151D412yes—
75C2×C42×C151—21no—
76C2×C42×C151—22no—
77C2×C42×C151C2312yes—
78#107×C151—22no—
79#106×C151—22no—
80C4⋊C8×C151—42no—
81#103×C151—24no—
82#103×C151—24no—
83#103×C151—24no—
84#103×C151—42no—
85#102×C151—22no—
86#102×C151—22no—
87#102×C151—42no—
88C22⋊C8×C151—22no—
89#95×C151—21no—
90#95×C151—22no—
91#95×C151—22no—
92#95×C151—22no—
93#95×C151—22no—
94#95×C151D411yescharacteristic
95#95×C151D411yescharacteristic
96C24×C151—21no—
97C24×C151C2×D411yescharacteristic
98C2×Q8×C151—22no—
99C2×Q8×C151—28no—
100C2×Q8×C151—22no—
101C2×Q8×C151—22no—
102C2×Q8×C151—22no—
103C2×Q8×C151—22no—
104C2×Q8×C151—44no—
105C2×Q8×C151—48no—
106C2×Q8×C151—44no—
107C2×Q8×C151—42no—
108C2×Q8×C151#4114yes—
109C2×D4×C151—21no—
110C2×D4×C151—21no—
111C2×D4×C151—22no—
112C2×D4×C151—22no—
113C2×D4×C151—44no—
114C2×D4×C151—42no—
115C22×C4×C151—22no—
116C22×C4×C151—22no—
117C22×C4×C151—21no—
118C22×C4×C151—21no—
119C22×C4×C151—22no—
120C22×C4×C151—21no—
121C22×C4×C151—22no—
122C22×C4×C151—44no—
123C22×C4×C151—42no—
124C22×C4×C151C2×D412yes—
125C22×C4×C151C2×D412yes—
126C22×C4×C151C2×D411yescharacteristic
127C22×C4×C151C2×D412yes—
128C22×C4×C151#4112yes—
129C22×C4×C151C2411yescharacteristic
130M16×C151—44no—
131C2×C8×C151—21no—
132C2×C8×C151—21no—
133C2×C8×C151—22no—
134C2×C8×C151—22no—
135C2×C8×C151—22no—
136C2×C8×C151—22no—
137C2×C8×C151—22no—
138C4⋊C4×C151—21no—
139C4⋊C4×C151—21no—
140C4⋊C4×C151—21no—
141C4⋊C4×C151—22no—
142C4⋊C4×C151—21no—
143C4⋊C4×C151—22no—
144C4⋊C4×C151—82no—
145C4⋊C4×C151C2×D412yes—
146C4⋊C4×C151C2×D412yes—
147C22⋊C4×C151—24no—
148C22⋊C4×C151—42no—
149C22⋊C4×C151—44no—
150C22⋊C4×C151—44no—
151C22⋊C4×C151—42no—
152C22⋊C4×C151—81no—
153C42×C151—24no—
154C42×C151—22no—
155C42×C151—22no—
156C42×C151—44no—
157C23×C151—22no—
158C23×C151—22no—
159C23×C151—21no—
160C23×C151—21no—
161C23×C151—41no—
162C23×C151—42no—
163C23×C151—42no—
164C23×C151—41no—
165C23×C151—41no—
166C23×C151#12112yes—
167C23×C151C22×D411yescharacteristic
168Q8×C151—24no—
169Q8×C151—24no—
170Q8×C151—48no—
171Q8×C151—42no—
172Q8×C151—42no—
173D4×C151—41no—
174D4×C151—41no—
175D4×C151—42no—
176D4×C151—84no—
177C2×C4×C151—22no—
178C2×C4×C151—22no—
179C2×C4×C151—22no—
180C2×C4×C151—24no—
181C2×C4×C151—22no—
182C2×C4×C151—22no—
183C2×C4×C151—24no—
184C2×C4×C151—22no—
185C2×C4×C151—22no—
186C2×C4×C151—22no—
187C2×C4×C151—22no—
188C2×C4×C151—22no—
189C2×C4×C151—22no—
190C2×C4×C151—48no—
191C2×C4×C151—42no—
192C2×C4×C151—42no—
193C2×C4×C151—42no—
194C2×C4×C151—41no—
195C2×C4×C151—41no—
196C2×C4×C151—41no—
197C2×C4×C151—42no—
198C2×C4×C151—42no—
199C2×C4×C151—42no—
200C2×C4×C151—42no—
201C2×C4×C151#12112yes—
202C2×C4×C151C22×D411yescharacteristic
203C2×C4×C151C2×#4112yes—
204C2×C4×C151C2×#4111yescharacteristic
205C2×C4×C151H(5,𝔽2)12yes—
206C8×C151—41no—
207C8×C151—41no—
208C8×C151—42no—
209C22×C151—22no—
210C22×C151—22no—
211C22×C151—22no—
212C22×C151—42no—
213C22×C151—42no—
214C22×C151—81no—
215C22×C151—81no—
216C22×C151—81no—
217C22×C151—82no—
218C22×C151—82no—
219C22×C151C2×#12111yescharacteristic
220C22×C151#54612yes—
221C22×C151#57512yes—
222C22×C151#57711yescharacteristic
223C22×C151#57811yescharacteristic
224C4×C151—22no—
225C4×C151—44no—
226C4×C151—42no—
227C4×C151—42no—
228C4×C151—42no—
229C4×C151—42no—
230C4×C151—81no—
231C4×C151—82no—
232C4×C151#52511yescharacteristic
233C4×C151#53511yescharacteristic
234C4×C151#55112yes—
235C2×C151—42no—
236C2×C151—161no—
237C2×C151#241111yescharacteristic
238C2×C151#304011yescharacteristic
239C2×C151#304611yescharacteristic
240C2×C151#332112yes—
241C2×C151#332712yes—
242#24499C15111yesmaximal, characteristic, direct product factor, Sylow
243C151#2449911yescharacteristic, direct product factor, Sylow
244C2×#482C2×C15111yescharacteristic
245C2×#419C2×C15111yescharacteristic, complemented
246#2436C2×C15111yescharacteristic
247#2346C2×C15111yescharacteristic, complemented
248#2066C2×C15112yescomplemented
249#2042C2×C15112yescomplemented
250#1983C2×C15112yescomplemented
251#1928C2×C15112yescomplemented
252#1895C2×C15111yescharacteristic
253#1851C2×C15111yescharacteristic, complemented
254#1787C2×C15111yescharacteristic, complemented
255C23×Q8C22×C15111yescharacteristic
256C22×M16C22×C15111yescharacteristic
257C2×#124C22×C15112yes—
258C2×#121C22×C15111yescharacteristic
259C2×#117C22×C15111yescharacteristic
260#482—24no—
261C2×#107C22×C15111yescharacteristic
262C2×#106C22×C15111yescharacteristic
263C2×C4⋊C8C22×C15112yes—
264#419—24no—
265C2×#103C22×C15112yes—
266C2×#103C22×C15112yes—
267C2×#103C22×C15112yes—
268C2×#103C22×C15112yes—
269C2×#102C22×C15111yescharacteristic
270C2×#102C22×C15111yescharacteristic
271C2×#102C22×C15112yes—
272C2×C22⋊C8C22×C15111yescharacteristic
273#393—21no—
274#393—21no—
275#391C22×C15112yes—
276#389C22×C15112yes—
277#388—22no—
278#386—22no—
279#382—21no—
280#380C22×C15111yescharacteristic
281C4×C4⋊C4C22×C15112yes—
282C4×C22⋊C4C22×C15111yescharacteristic
283#376—21no—
284#340C22×C15112yes—
285#336C22×C15112yes—
286C22×Q8—21no—
287C22×Q8—24no—
288C22×Q8—22no—
289C22×Q8—22no—
290C22×Q8—42no—
291C22×Q8C23×C15112yes—
292C22×D4—21no—
293C22×D4C23×C15111yescharacteristic
294C23×C4—21no—
295C23×C4C23×C15111yescharacteristic
296C2×M16—22no—
297C2×M16—42no—
298C22×C8C23×C15112yes—
299C22×C8C23×C15111yescharacteristic
300C22×C8C23×C15111yescharacteristic
301#124—24no—
302#124—42no—
303#121—22no—
304#121—22no—
305#117—22no—
306#117D4×C15114yes—
307C2×C4⋊C4—22no—
308C2×C4⋊C4C23×C15111yescharacteristic
309C2×C4⋊C4C23×C15112yes—
310C2×C4⋊C4C23×C15111yescharacteristic
311C2×C4⋊C4C23×C15111yescharacteristic
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4D4×C15112yes—
318C2×C42—21no—
319C2×C42—22no—
320C2×C42C23×C15112yes—
321#107—22no—
322#106—22no—
323C4⋊C8—42no—
324#103—24no—
325#103—24no—
326#103—24no—
327#103—42no—
328#102—22no—
329#102—22no—
330#102—42no—
331C22⋊C8—22no—
332#95—21no—
333#95—22no—
334#95—22no—
335#95—22no—
336#95—22no—
337#95D4×C15111yescharacteristic
338#95D4×C15111yescharacteristic
339C24—21no—
340C24C2×D4×C15111yescharacteristic
341C2×Q8—22no—
342C2×Q8—28no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—44no—
348C2×Q8—48no—
349C2×Q8—44no—
350C2×Q8—42no—
351C2×Q8#41×C15114yes—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—22no—
355C2×D4—22no—
356C2×D4—44no—
357C2×D4—42no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—22no—
365C22×C4—44no—
366C22×C4—42no—
367C22×C4C2×D4×C15112yes—
368C22×C4C2×D4×C15112yes—
369C22×C4C2×D4×C15111yescharacteristic
370C22×C4C2×D4×C15112yes—
371C22×C4#41×C15112yes—
372C22×C4C24×C15111yescharacteristic
373M16—44no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—22no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—82no—
388C4⋊C4C2×D4×C15112yes—
389C4⋊C4C2×D4×C15112yes—
390C22⋊C4—24no—
391C22⋊C4—42no—
392C22⋊C4—44no—
393C22⋊C4—44no—
394C22⋊C4—42no—
395C22⋊C4—81no—
396C42—24no—
397C42—22no—
398C42—22no—
399C42—44no—
400C23—22no—
401C23—22no—
402C23—21no—
403C23—21no—
404C23—41no—
405C23—42no—
406C23—42no—
407C23—41no—
408C23—41no—
409C23#121×C15112yes—
410C23C22×D4×C15111yescharacteristic
411Q8—24no—
412Q8—24no—
413Q8—48no—
414Q8—42no—
415Q8—42no—
416D4—41no—
417D4—41no—
418D4—42no—
419D4—84no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—24no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—24no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—48no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4#121×C15112yes—
445C2×C4C22×D4×C15111yescharacteristic
446C2×C4C2×#41×C15112yes—
447C2×C4C2×#41×C15111yescharacteristic
448C2×C4H(5,𝔽2)×C15112yes—
449C8—41no—
450C8—42no—
451C8—41no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—42no—
456C22—42no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—82no—
461C22—82no—
462C22C2×#121×C15111yescharacteristic
463C22#546×C15112yes—
464C22#575×C15112yes—
465C22#577×C15111yescharacteristic
466C22#578×C15111yescharacteristic
467C4—22no—
468C4—44no—
469C4—42no—
470C4—42no—
471C4—42no—
472C4—42no—
473C4—81no—
474C4—82no—
475C4#525×C15111yescharacteristic
476C4#535×C15111yescharacteristic
477C4#551×C15112yes—
478C2—42no—
479C2—161no—
480C2#2411×C15111yescharacteristic
481C2#3040×C15111yescharacteristic
482C2#3046×C15111yescharacteristic
483C2#3321×C15112yes—
484C2#3327×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#121×C151C22
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×#419×C151C2semidirect
4. #2346×C151C2semidirect
5. #2066×C151C2semidirect
6. #2042×C151C2semidirect
7. #1983×C151C2semidirect
8. #1928×C151C2semidirect
10. #1851×C151C2semidirect
11. #1787×C151C2semidirect
242. #24499C151direct (N × H)
243. C151#24499direct (N × H)
245. C2×#419C2×C151semidirect
247. #2346C2×C151semidirect
248. #2066C2×C151semidirect
249. #2042C2×C151semidirect
250. #1983C2×C151semidirect
251. #1928C2×C151semidirect
253. #1851C2×C151semidirect
254. #1787C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#482×C1512
C2×#419×C1512
#2436×C1512
#2346×C1512
#2066×C1512
#2042×C1512
#1983×C1512
#1928×C1512
#1895×C1512
#1851×C1512
#1787×C1512
#24499151