Finite Group Databasebeta

← C151×#24543 #50329468

Subgroups — C151×#24543 #50329468

Order 38656.

980 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#452×C151C211yesmaximal, characteristic
2C2×#417×C151C211yesmaximal, characteristic
3#2503×C151C211yesmaximal, characteristic, complemented
4#2341×C151C211yesmaximal, characteristic
5#2073×C151C212yesmaximal, complemented
6#2055×C151C212yesmaximal, complemented
7#1894×C151C211yesmaximal, characteristic, complemented
8#1878×C151C212yesmaximal, complemented
9#1851×C151C211yesmaximal, characteristic, complemented
10#1824×C151C211yesmaximal, characteristic, complemented
11#1805×C151C212yesmaximal, complemented
12C22×#41×C151C2211yescharacteristic
13C22×Q16×C151C2211yescharacteristic
14C22×SD16×C151C2211yescharacteristic
15C22×M16×C151C2211yescharacteristic
16C2×C22⋊Q8×C151C2211yescharacteristic
17C2×C4×Q8×C151C2212yes—
18C22×C4⋊C4×C151C2211yescharacteristic
19#452×C151—24no—
20C2×C4⋊C8×C151C2212yes—
21#417×C151—24no—
22C2×#103×C151C2212yes—
23C2×#103×C151C2211yescharacteristic
24C2×#103×C151C2212yes—
25C2×#102×C151C2212yes—
26C2×#102×C151C2211yescharacteristic
27C2×C22⋊C8×C151C2211yescharacteristic
28#400×C151—21no—
29#400×C151—21no—
30#391×C151C2212yes—
31#390×C151—22no—
32#390×C151C2212yes—
33#382×C151C2212yes—
34#381×C151—22no—
35#380×C151—21no—
36#380×C151C2211yescharacteristic
37C4×C22⋊C4×C151—21no—
38C4×C22⋊C4×C151C2211yescharacteristic
39#340×C151C2212yes—
40#340×C151C2212yes—
41#340×C151C2212yes—
42#336×C151C2212yes—
43C2×#41×C151—22no—
44C2×#41×C151—24no—
45C2×#41×C151—42no—
46C2×#41×C151D414yes—
47C22×Q8×C151C2311yescharacteristic
48C22×Q8×C151C2311yescharacteristic
49C22×D4×C151—21no—
50C22×D4×C151C2311yescharacteristic
51C23×C4×C151—21no—
52C23×C4×C151—21no—
53C23×C4×C151C2311yescharacteristic
54C2×Q16×C151—22no—
55C2×Q16×C151—24no—
56C2×SD16×C151—22no—
57C2×SD16×C151—42no—
58C2×M16×C151—22no—
59C2×M16×C151—42no—
60C22×C8×C151C2311yescharacteristic
61C22×C8×C151C2312yes—
62C22×C8×C151C2311yescharacteristic
63C22⋊Q8×C151—22no—
64C22⋊Q8×C151—22no—
65C4×Q8×C151—24no—
66C4×Q8×C151—42no—
67C2×C4⋊C4×C151—22no—
68C2×C4⋊C4×C151—22no—
69C2×C4⋊C4×C151—22no—
70C2×C4⋊C4×C151—21no—
71C2×C4⋊C4×C151—21no—
72C2×C4⋊C4×C151C2312yes—
73C2×C4⋊C4×C151C2311yescharacteristic
74C2×C4⋊C4×C151C2312yes—
75C2×C22⋊C4×C151—22no—
76C2×C22⋊C4×C151—22no—
77C2×C22⋊C4×C151—21no—
78C2×C22⋊C4×C151—21no—
79C2×C22⋊C4×C151D412yes—
80C2×C42×C151—22no—
81C2×C42×C151C2312yes—
82C4⋊C8×C151—42no—
83#103×C151—24no—
84#103×C151—22no—
85#103×C151—42no—
86#102×C151—24no—
87#102×C151—22no—
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
98#41×C151—28no—
99#41×C151—44no—
100#41×C151—48no—
101C2×Q8×C151—21no—
102C2×Q8×C151—22no—
103C2×Q8×C151—21no—
104C2×Q8×C151—21no—
105C2×Q8×C151—22no—
106C2×Q8×C151—22no—
107C2×Q8×C151C2×D412yes—
108C2×Q8×C151#4114yes—
109C2×D4×C151—24no—
110C2×D4×C151—22no—
111C2×D4×C151—21no—
112C2×D4×C151—22no—
113C2×D4×C151—44no—
114C2×D4×C151C2×D412yes—
115C22×C4×C151—21no—
116C22×C4×C151—22no—
117C22×C4×C151—22no—
118C22×C4×C151—24no—
119C22×C4×C151—21no—
120C22×C4×C151—21no—
121C22×C4×C151—22no—
122C22×C4×C151—22no—
123C22×C4×C151—44no—
124C22×C4×C151—44no—
125C22×C4×C151—42no—
126C22×C4×C151C2×D412yes—
127C22×C4×C151C2×D412yes—
128C22×C4×C151C2×D411yescharacteristic
129C22×C4×C151C2×D412yes—
130C22×C4×C151#4112yes—
131C22×C4×C151C2411yescharacteristic
132Q16×C151—44no—
133SD16×C151—44no—
134M16×C151—44no—
135C2×C8×C151—21no—
136C2×C8×C151—21no—
137C2×C8×C151—22no—
138C2×C8×C151—22no—
139C2×C8×C151—22no—
140C2×C8×C151—22no—
141C2×C8×C151—22no—
142C4⋊C4×C151—22no—
143C4⋊C4×C151—21no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—22no—
146C4⋊C4×C151—21no—
147C4⋊C4×C151—22no—
148C4⋊C4×C151—44no—
149C4⋊C4×C151—42no—
150C4⋊C4×C151—42no—
151C22⋊C4×C151—42no—
152C22⋊C4×C151—44no—
153C22⋊C4×C151—42no—
154C22⋊C4×C151—82no—
155C22⋊C4×C151—81no—
156C42×C151—22no—
157C42×C151—22no—
158C42×C151—44no—
159C23×C151—22no—
160C23×C151—22no—
161C23×C151—21no—
162C23×C151—21no—
163C23×C151—22no—
164C23×C151—42no—
165C23×C151—42no—
166C23×C151—41no—
167C23×C151—41no—
168C23×C151#12112yes—
169C23×C151C22×D411yescharacteristic
170Q8×C151—22no—
171Q8×C151—24no—
172Q8×C151—41no—
173Q8×C151—41no—
174Q8×C151—42no—
175Q8×C151#12314yes—
176D4×C151—22no—
177D4×C151—22no—
178D4×C151—48no—
179D4×C151—42no—
180C2×C4×C151—22no—
181C2×C4×C151—24no—
182C2×C4×C151—22no—
183C2×C4×C151—22no—
184C2×C4×C151—22no—
185C2×C4×C151—24no—
186C2×C4×C151—22no—
187C2×C4×C151—22no—
188C2×C4×C151—22no—
189C2×C4×C151—22no—
190C2×C4×C151—22no—
191C2×C4×C151—22no—
192C2×C4×C151—48no—
193C2×C4×C151—41no—
194C2×C4×C151—41no—
195C2×C4×C151—42no—
196C2×C4×C151—42no—
197C2×C4×C151—42no—
198C2×C4×C151—42no—
199C2×C4×C151—44no—
200C2×C4×C151—42no—
201C2×C4×C151—41no—
202C2×C4×C151—41no—
203C2×C4×C151—84no—
204C2×C4×C151#12112yes—
205C2×C4×C151C22×D411yescharacteristic
206C2×C4×C151C2×#4112yes—
207C2×C4×C151C2×#4111yescharacteristic
208C2×C4×C151H(5,𝔽2)12yes—
209C8×C151—41no—
210C8×C151—42no—
211C8×C151—41no—
212C22×C151—22no—
213C22×C151—22no—
214C22×C151—22no—
215C22×C151—42no—
216C22×C151—42no—
217C22×C151—42no—
218C22×C151—42no—
219C22×C151—42no—
220C22×C151—82no—
221C22×C151—82no—
222C22×C151C2×#12111yescharacteristic
223C22×C151#54612yes—
224C22×C151#57512yes—
225C22×C151#57711yescharacteristic
226C22×C151#57811yescharacteristic
227C4×C151—22no—
228C4×C151—24no—
229C4×C151—42no—
230C4×C151—42no—
231C4×C151—81no—
232C4×C151—82no—
233C4×C151—81no—
234C4×C151—82no—
235C4×C151C2×#12311yescharacteristic
236C4×C151#53411yescharacteristic
237C4×C151#55112yes—
238C2×C151—42no—
239C2×C151—82no—
240C2×C151#241211yescharacteristic
241C2×C151#304011yescharacteristic
242C2×C151#304611yescharacteristic
243C2×C151#331712yes—
244C2×C151#332712yes—
245#24543C15111yesmaximal, characteristic, direct product factor, Sylow
246C151#2454311yescharacteristic, direct product factor, Sylow
247C2×#452C2×C15111yescharacteristic
248C2×#417C2×C15111yescharacteristic
249#2503C2×C15111yescharacteristic, complemented
250#2341C2×C15111yescharacteristic
251#2073C2×C15112yescomplemented
252#2055C2×C15112yescomplemented
253#1894C2×C15111yescharacteristic, complemented
254#1878C2×C15112yescomplemented
255#1851C2×C15111yescharacteristic, complemented
256#1824C2×C15111yescharacteristic, complemented
257#1805C2×C15112yescomplemented
258C22×#41C22×C15111yescharacteristic
259C22×Q16C22×C15111yescharacteristic
260C22×SD16C22×C15111yescharacteristic
261C22×M16C22×C15111yescharacteristic
262C2×C22⋊Q8C22×C15111yescharacteristic
263C2×C4×Q8C22×C15112yes—
264C22×C4⋊C4C22×C15111yescharacteristic
265#452—24no—
266C2×C4⋊C8C22×C15112yes—
267#417—24no—
268C2×#103C22×C15111yescharacteristic
269C2×#103C22×C15112yes—
270C2×#103C22×C15112yes—
271C2×#102C22×C15112yes—
272C2×#102C22×C15111yescharacteristic
273C2×C22⋊C8C22×C15111yescharacteristic
274#400—21no—
275#400—21no—
276#391C22×C15112yes—
277#390—22no—
278#390C22×C15112yes—
279#382C22×C15112yes—
280#381—22no—
281#380—21no—
282#380C22×C15111yescharacteristic
283C4×C22⋊C4—21no—
284C4×C22⋊C4C22×C15111yescharacteristic
285#340C22×C15112yes—
286#340C22×C15112yes—
287#340C22×C15112yes—
288#336C22×C15112yes—
289C2×#41—22no—
290C2×#41—24no—
291C2×#41—42no—
292C2×#41D4×C15114yes—
293C22×Q8C23×C15111yescharacteristic
294C22×Q8C23×C15111yescharacteristic
295C22×D4—21no—
296C22×D4C23×C15111yescharacteristic
297C23×C4—21no—
298C23×C4—21no—
299C23×C4C23×C15111yescharacteristic
300C2×Q16—24no—
301C2×Q16—22no—
302C2×SD16—22no—
303C2×SD16—42no—
304C2×M16—22no—
305C2×M16—42no—
306C22×C8C23×C15112yes—
307C22×C8C23×C15111yescharacteristic
308C22×C8C23×C15111yescharacteristic
309C22⋊Q8—22no—
310C22⋊Q8—22no—
311C4×Q8—24no—
312C4×Q8—42no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4C23×C15112yes—
319C2×C4⋊C4C23×C15112yes—
320C2×C4⋊C4C23×C15111yescharacteristic
321C2×C22⋊C4—21no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4D4×C15112yes—
326C2×C42—22no—
327C2×C42C23×C15112yes—
328C4⋊C8—42no—
329#103—24no—
330#103—22no—
331#103—42no—
332#102—24no—
333#102—22no—
334C22⋊C8—22no—
335#95—21no—
336#95—22no—
337#95—22no—
338#95—22no—
339#95—22no—
340#95D4×C15111yescharacteristic
341#95D4×C15111yescharacteristic
342C24—21no—
343C24C2×D4×C15111yescharacteristic
344#41—28no—
345#41—44no—
346#41—48no—
347C2×Q8—21no—
348C2×Q8—22no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8C2×D4×C15112yes—
354C2×Q8#41×C15114yes—
355C2×D4—24no—
356C2×D4—22no—
357C2×D4—21no—
358C2×D4—22no—
359C2×D4—44no—
360C2×D4C2×D4×C15112yes—
361C22×C4—21no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—24no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—44no—
370C22×C4—44no—
371C22×C4—42no—
372C22×C4C2×D4×C15112yes—
373C22×C4C2×D4×C15112yes—
374C22×C4C2×D4×C15111yescharacteristic
375C22×C4C2×D4×C15112yes—
376C22×C4#41×C15112yes—
377C22×C4C24×C15111yescharacteristic
378Q16—44no—
379SD16—44no—
380M16—44no—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—22no—
388C4⋊C4—22no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—44no—
395C4⋊C4—42no—
396C4⋊C4—42no—
397C22⋊C4—42no—
398C22⋊C4—44no—
399C22⋊C4—42no—
400C22⋊C4—82no—
401C22⋊C4—81no—
402C42—22no—
403C42—22no—
404C42—44no—
405C23—22no—
406C23—22no—
407C23—21no—
408C23—21no—
409C23—22no—
410C23—42no—
411C23—42no—
412C23—41no—
413C23—41no—
414C23#121×C15112yes—
415C23C22×D4×C15111yescharacteristic
416Q8—22no—
417Q8—24no—
418Q8—41no—
419Q8—41no—
420Q8—42no—
421Q8#123×C15114yes—
422D4—22no—
423D4—22no—
424D4—48no—
425D4—42no—
426C2×C4—22no—
427C2×C4—24no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—24no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—48no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—44no—
446C2×C4—42no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—84no—
450C2×C4#121×C15112yes—
451C2×C4C22×D4×C15111yescharacteristic
452C2×C4C2×#41×C15112yes—
453C2×C4C2×#41×C15111yescharacteristic
454C2×C4H(5,𝔽2)×C15112yes—
455C8—41no—
456C8—42no—
457C8—41no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—42no—
462C22—42no—
463C22—42no—
464C22—42no—
465C22—42no—
466C22—82no—
467C22—82no—
468C22C2×#121×C15111yescharacteristic
469C22#546×C15112yes—
470C22#575×C15112yes—
471C22#577×C15111yescharacteristic
472C22#578×C15111yescharacteristic
473C4—22no—
474C4—24no—
475C4—42no—
476C4—42no—
477C4—81no—
478C4—82no—
479C4—81no—
480C4—82no—
481C4C2×#123×C15111yescharacteristic
482C4#534×C15111yescharacteristic
483C4#551×C15112yes—
484C2—42no—
485C2—82no—
486C2#2412×C15111yescharacteristic
487C2#3040×C15111yescharacteristic
488C2#3046×C15111yescharacteristic
489C2#3317×C15112yes—
490C2#3327×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×#41×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
3. #2503×C151C2semidirect
5. #2073×C151C2semidirect
6. #2055×C151C2semidirect
7. #1894×C151C2semidirect
8. #1878×C151C2semidirect
9. #1851×C151C2semidirect
10. #1824×C151C2semidirect
11. #1805×C151C2semidirect
245. #24543C151direct (N × H)
246. C151#24543direct (N × H)
249. #2503C2×C151semidirect
251. #2073C2×C151semidirect
252. #2055C2×C151semidirect
253. #1894C2×C151semidirect
254. #1878C2×C151semidirect
255. #1851C2×C151semidirect
256. #1824C2×C151semidirect
257. #1805C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#452×C1512
C2×#417×C1512
#2503×C1512
#2341×C1512
#2073×C1512
#2055×C1512
#1894×C1512
#1878×C1512
#1851×C1512
#1824×C1512
#1805×C1512
#24543151