Finite Group Databasebeta

← C151×#24548 #50329473

Subgroups — C151×#24548 #50329473

Order 38656.

1024 conjugacy classes of subgroups.

The subgroup lattice has 502 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#2502×C151C211yesmaximal, characteristic, complemented
4#2339×C151C211yesmaximal, characteristic
5#2072×C151C212yesmaximal, complemented
6#2056×C151C212yesmaximal, complemented
7#1894×C151C211yesmaximal, characteristic, complemented
8#1877×C151C212yesmaximal, complemented
9#1851×C151C211yesmaximal, characteristic, complemented
10#1823×C151C211yesmaximal, characteristic, complemented
11#1802×C151C212yesmaximal, complemented
12C22×#41×C151C2211yescharacteristic
13C22×Q16×C151C2211yescharacteristic
14C22×SD16×C151C2211yescharacteristic
15C22×M16×C151C2211yescharacteristic
16C2×C22⋊Q8×C151C2211yescharacteristic
17C2×C4×D4×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#398×C151—21no—
29#398×C151—21no—
30#391×C151C2212yes—
31#391×C151C2212yes—
32#386×C151—22no—
33#385×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×Q8×C151C2311yescharacteristic
49C22×D4×C151—21no—
50C22×D4×C151C2311yescharacteristic
51C23×C4×C151—21no—
52C23×C4×C151—22no—
53C23×C4×C151—21no—
54C23×C4×C151C2311yescharacteristic
55C2×Q16×C151—22no—
56C2×Q16×C151—42no—
57C2×SD16×C151—22no—
58C2×SD16×C151—24no—
59C2×M16×C151—22no—
60C2×M16×C151—42no—
61C22×C8×C151C2311yescharacteristic
62C22×C8×C151C2312yes—
63C22×C8×C151C2311yescharacteristic
64C22⋊Q8×C151—22no—
65C22⋊Q8×C151—22no—
66C4×D4×C151—24no—
67C4×D4×C151—42no—
68C2×C4⋊C4×C151—22no—
69C2×C4⋊C4×C151—22no—
70C2×C4⋊C4×C151—21no—
71C2×C4⋊C4×C151—21no—
72C2×C4⋊C4×C151—22no—
73C2×C4⋊C4×C151—22no—
74C2×C4⋊C4×C151C2312yes—
75C2×C4⋊C4×C151C2311yescharacteristic
76C2×C4⋊C4×C151C2312yes—
77C2×C22⋊C4×C151—22no—
78C2×C22⋊C4×C151—21no—
79C2×C22⋊C4×C151—21no—
80C2×C22⋊C4×C151D412yes—
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—21no—
103C2×Q8×C151—22no—
104C2×Q8×C151—21no—
105C2×Q8×C151—22no—
106C2×Q8×C151—22no—
107C2×Q8×C151—22no—
108C2×Q8×C151C2×D412yes—
109C2×D4×C151—24no—
110C2×D4×C151—21no—
111C2×D4×C151—22no—
112C2×D4×C151—44no—
113C2×D4×C151C2×D412yes—
114C2×D4×C151#4114yes—
115C22×C4×C151—22no—
116C22×C4×C151—22no—
117C22×C4×C151—21no—
118C22×C4×C151—24no—
119C22×C4×C151—21no—
120C22×C4×C151—22no—
121C22×C4×C151—22no—
122C22×C4×C151—21no—
123C22×C4×C151—44no—
124C22×C4×C151—44no—
125C22×C4×C151—42no—
126C22×C4×C151—44no—
127C22×C4×C151—82no—
128C22×C4×C151—81no—
129C22×C4×C151—81no—
130C22×C4×C151C2×D412yes—
131C22×C4×C151C2×D411yescharacteristic
132C22×C4×C151C2×D412yes—
133C22×C4×C151C2×D412yes—
134C22×C4×C151#4112yes—
135C22×C4×C151C2411yescharacteristic
136Q16×C151—44no—
137SD16×C151—44no—
138M16×C151—44no—
139C2×C8×C151—21no—
140C2×C8×C151—21no—
141C2×C8×C151—22no—
142C2×C8×C151—22no—
143C2×C8×C151—22no—
144C2×C8×C151—22no—
145C2×C8×C151—22no—
146C4⋊C4×C151—22no—
147C4⋊C4×C151—21no—
148C4⋊C4×C151—22no—
149C4⋊C4×C151—22no—
150C4⋊C4×C151—21no—
151C4⋊C4×C151—22no—
152C4⋊C4×C151—42no—
153C4⋊C4×C151—42no—
154C4⋊C4×C151—82no—
155C4⋊C4×C151—82no—
156C22⋊C4×C151—24no—
157C22⋊C4×C151—44no—
158C22⋊C4×C151—42no—
159C22⋊C4×C151—81no—
160C42×C151—22no—
161C42×C151—22no—
162C23×C151—22no—
163C23×C151—24no—
164C23×C151—22no—
165C23×C151—22no—
166C23×C151—21no—
167C23×C151—21no—
168C23×C151—42no—
169C23×C151—41no—
170C23×C151—41no—
171C23×C151#12112yes—
172C23×C151C22×D411yescharacteristic
173Q8×C151—22no—
174Q8×C151—22no—
175Q8×C151—42no—
176Q8×C151—41no—
177Q8×C151—41no—
178Q8×C151—42no—
179D4×C151—22no—
180D4×C151—24no—
181D4×C151—48no—
182D4×C151#12314yes—
183C2×C4×C151—22no—
184C2×C4×C151—22no—
185C2×C4×C151—22no—
186C2×C4×C151—22no—
187C2×C4×C151—22no—
188C2×C4×C151—24no—
189C2×C4×C151—22no—
190C2×C4×C151—22no—
191C2×C4×C151—22no—
192C2×C4×C151—22no—
193C2×C4×C151—48no—
194C2×C4×C151—42no—
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—42no—
202C2×C4×C151—41no—
203C2×C4×C151—42no—
204C2×C4×C151—41no—
205C2×C4×C151—42no—
206C2×C4×C151—88no—
207C2×C4×C151—84no—
208C2×C4×C151#12112yes—
209C2×C4×C151#13714yes—
210C2×C4×C151C22×D411yescharacteristic
211C2×C4×C151C2×#4112yes—
212C2×C4×C151C2×#4111yescharacteristic
213C2×C4×C151H(5,𝔽2)12yes—
214C8×C151—41no—
215C8×C151—42no—
216C8×C151—41no—
217C22×C151—22no—
218C22×C151—24no—
219C22×C151—22no—
220C22×C151—22no—
221C22×C151—42no—
222C22×C151—44no—
223C22×C151—42no—
224C22×C151—42no—
225C22×C151—44no—
226C22×C151—42no—
227C22×C151C2×#12111yescharacteristic
228C22×C151#54612yes—
229C22×C151C2×#13712yes—
230C22×C151#57611yescharacteristic
231C22×C151#57711yescharacteristic
232C4×C151—22no—
233C4×C151—24no—
234C4×C151—42no—
235C4×C151—42no—
236C4×C151—81no—
237C4×C151—81no—
238C4×C151—82no—
239C4×C151—82no—
240C4×C151C2×#12311yescharacteristic
241C4×C151#53411yescharacteristic
242C4×C151#55112yes—
243C2×C151—42no—
244C2×C151—44no—
245C2×C151#241211yescharacteristic
246C2×C151#303911yescharacteristic
247C2×C151#304511yescharacteristic
248C2×C151#331412yes—
249C2×C151#333112yes—
250#24548C15111yesmaximal, characteristic, direct product factor, Sylow
251C151#2454811yescharacteristic, direct product factor, Sylow
252C2×#452C2×C15111yescharacteristic
253C2×#417C2×C15111yescharacteristic
254#2502C2×C15111yescharacteristic, complemented
255#2339C2×C15111yescharacteristic
256#2072C2×C15112yescomplemented
257#2056C2×C15112yescomplemented
258#1894C2×C15111yescharacteristic, complemented
259#1877C2×C15112yescomplemented
260#1851C2×C15111yescharacteristic, complemented
261#1823C2×C15111yescharacteristic, complemented
262#1802C2×C15112yescomplemented
263C22×#41C22×C15111yescharacteristic
264C22×Q16C22×C15111yescharacteristic
265C22×SD16C22×C15111yescharacteristic
266C22×M16C22×C15111yescharacteristic
267C2×C22⋊Q8C22×C15111yescharacteristic
268C2×C4×D4C22×C15112yes—
269C22×C4⋊C4C22×C15111yescharacteristic
270#452—24no—
271C2×C4⋊C8C22×C15112yes—
272#417—24no—
273C2×#103C22×C15112yes—
274C2×#103C22×C15111yescharacteristic
275C2×#103C22×C15112yes—
276C2×#102C22×C15111yescharacteristic
277C2×#102C22×C15112yes—
278C2×C22⋊C8C22×C15111yescharacteristic
279#398—21no—
280#398—21no—
281#391C22×C15112yes—
282#391C22×C15112yes—
283#386—22no—
284#385—22no—
285#384C22×C15112yes—
286#381—21no—
287#380C22×C15111yescharacteristic
288C4×C22⋊C4C22×C15111yescharacteristic
289C2×#95—21no—
290#340C22×C15112yes—
291#340C22×C15112yes—
292#340C22×C15112yes—
293#336C22×C15112yes—
294C2×#41—22no—
295C2×#41—24no—
296C2×#41—42no—
297C2×#41D4×C15114yes—
298C22×Q8C23×C15111yescharacteristic
299C22×Q8C23×C15111yescharacteristic
300C22×D4—21no—
301C22×D4C23×C15111yescharacteristic
302C23×C4—21no—
303C23×C4—21no—
304C23×C4—22no—
305C23×C4C23×C15111yescharacteristic
306C2×Q16—22no—
307C2×Q16—42no—
308C2×SD16—24no—
309C2×SD16—22no—
310C2×M16—22no—
311C2×M16—42no—
312C22×C8C23×C15112yes—
313C22×C8C23×C15111yescharacteristic
314C22×C8C23×C15111yescharacteristic
315C22⋊Q8—22no—
316C22⋊Q8—22no—
317C4×D4—24no—
318C4×D4—42no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4C23×C15112yes—
326C2×C4⋊C4C23×C15112yes—
327C2×C4⋊C4C23×C15111yescharacteristic
328C2×C22⋊C4—21no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4D4×C15112yes—
332C2×C42C23×C15112yes—
333C4⋊C8—42no—
334#103—24no—
335#103—22no—
336#103—42no—
337#102—24no—
338#102—22no—
339C22⋊C8—22no—
340#95—21no—
341#95—22no—
342#95—22no—
343#95—22no—
344#95—22no—
345#95D4×C15111yescharacteristic
346#95D4×C15111yescharacteristic
347C24—21no—
348C24C2×D4×C15111yescharacteristic
349#41—28no—
350#41—44no—
351#41—48no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—22no—
355C2×Q8—21no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8C2×D4×C15112yes—
360C2×D4—24no—
361C2×D4—21no—
362C2×D4—22no—
363C2×D4—44no—
364C2×D4C2×D4×C15112yes—
365C2×D4#41×C15114yes—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—24no—
370C22×C4—21no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—44no—
375C22×C4—44no—
376C22×C4—42no—
377C22×C4—44no—
378C22×C4—82no—
379C22×C4—81no—
380C22×C4—81no—
381C22×C4C2×D4×C15112yes—
382C22×C4C2×D4×C15111yescharacteristic
383C22×C4C2×D4×C15112yes—
384C22×C4C2×D4×C15112yes—
385C22×C4#41×C15112yes—
386C22×C4C24×C15111yescharacteristic
387Q16—44no—
388SD16—44no—
389M16—44no—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—22no—
397C4⋊C4—22no—
398C4⋊C4—21no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—42no—
404C4⋊C4—42no—
405C4⋊C4—82no—
406C4⋊C4—82no—
407C22⋊C4—24no—
408C22⋊C4—44no—
409C22⋊C4—42no—
410C22⋊C4—81no—
411C42—22no—
412C42—22no—
413C23—22no—
414C23—24no—
415C23—22no—
416C23—22no—
417C23—21no—
418C23—21no—
419C23—42no—
420C23—41no—
421C23—41no—
422C23#121×C15112yes—
423C23C22×D4×C15111yescharacteristic
424Q8—22no—
425Q8—22no—
426Q8—42no—
427Q8—41no—
428Q8—41no—
429Q8—42no—
430D4—22no—
431D4—24no—
432D4—48no—
433D4#123×C15114yes—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—24no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—48no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—42no—
457C2×C4—88no—
458C2×C4—84no—
459C2×C4#121×C15112yes—
460C2×C4#137×C15114yes—
461C2×C4C22×D4×C15111yescharacteristic
462C2×C4C2×#41×C15112yes—
463C2×C4C2×#41×C15111yescharacteristic
464C2×C4H(5,𝔽2)×C15112yes—
465C8—41no—
466C8—42no—
467C8—41no—
468C22—22no—
469C22—24no—
470C22—22no—
471C22—22no—
472C22—42no—
473C22—42no—
474C22—44no—
475C22—42no—
476C22—42no—
477C22—44no—
478C22C2×#121×C15111yescharacteristic
479C22#546×C15112yes—
480C22C2×#137×C15112yes—
481C22#576×C15111yescharacteristic
482C22#577×C15111yescharacteristic
483C4—22no—
484C4—24no—
485C4—42no—
486C4—42no—
487C4—81no—
488C4—82no—
489C4—81no—
490C4—82no—
491C4C2×#123×C15111yescharacteristic
492C4#534×C15111yescharacteristic
493C4#551×C15112yes—
494C2—42no—
495C2—44no—
496C2#2412×C15111yescharacteristic
497C2#3039×C15111yescharacteristic
498C2#3045×C15111yescharacteristic
499C2#3314×C15112yes—
500C2#3331×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. #2502×C151C2semidirect
5. #2072×C151C2semidirect
6. #2056×C151C2semidirect
7. #1894×C151C2semidirect
8. #1877×C151C2semidirect
9. #1851×C151C2semidirect
10. #1823×C151C2semidirect
11. #1802×C151C2semidirect
250. #24548C151direct (N × H)
251. C151#24548direct (N × H)
254. #2502C2×C151semidirect
256. #2072C2×C151semidirect
257. #2056C2×C151semidirect
258. #1894C2×C151semidirect
259. #1877C2×C151semidirect
260. #1851C2×C151semidirect
261. #1823C2×C151semidirect
262. #1802C2×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
#2502×C1512
#2339×C1512
#2072×C1512
#2056×C1512
#1894×C1512
#1877×C1512
#1851×C1512
#1823×C1512
#1802×C1512
#24548151