Finite Group Databasebeta

← C151×#24483 #50329408

Subgroups — C151×#24483 #50329408

Order 38656.

984 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#481×C151C211yesmaximal, characteristic
2C22×#103×C151C211yesmaximal, characteristic, complemented
3#2436×C151C211yesmaximal, characteristic
4#2345×C151C211yesmaximal, characteristic, complemented
5#2066×C151C212yesmaximal, complemented
6#2042×C151C212yesmaximal, complemented
7#1983×C151C212yesmaximal, complemented
8#1927×C151C212yesmaximal, complemented
9#1893×C151C211yesmaximal, characteristic
10#1850×C151C211yesmaximal, characteristic, complemented
11#1787×C151C211yesmaximal, characteristic, complemented
12C23×Q8×C151C2211yescharacteristic
13C23×C8×C151C2211yescharacteristic
14C2×#124×C151C2212yes—
15C2×#121×C151C2211yescharacteristic
16C22×C4⋊C4×C151C2211yescharacteristic
17#481×C151—24no—
18C2×#106×C151C2211yescharacteristic
19C2×#106×C151C2211yescharacteristic
20C2×C4⋊C8×C151C2212yes—
21C2×#103×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—22no—
31#391×C151C2212yes—
32#389×C151C2212yes—
33#387×C151—22no—
34#386×C151—21no—
35#386×C151—21no—
36#380×C151—21no—
37#380×C151C2211yescharacteristic
38C4×C4⋊C4×C151C2212yes—
39C4×C22⋊C4×C151—21no—
40C4×C22⋊C4×C151C2211yescharacteristic
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×C151—21no—
53C23×C4×C151C2311yescharacteristic
54C22×C8×C151—22no—
55C22×C8×C151—42no—
56C22×C8×C151C2311yescharacteristic
57C22×C8×C151C2312yes—
58C22×C8×C151C2311yescharacteristic
59#124×C151—24no—
60#124×C151—42no—
61#121×C151—22no—
62#121×C151—22no—
63C2×C4⋊C4×C151—21no—
64C2×C4⋊C4×C151—22no—
65C2×C4⋊C4×C151—22no—
66C2×C4⋊C4×C151D414yes—
67C2×C4⋊C4×C151C2311yescharacteristic
68C2×C4⋊C4×C151C2312yes—
69C2×C4⋊C4×C151C2311yescharacteristic
70C2×C4⋊C4×C151C2311yescharacteristic
71C2×C22⋊C4×C151—22no—
72C2×C22⋊C4×C151—22no—
73C2×C22⋊C4×C151—21no—
74C2×C22⋊C4×C151—21no—
75C2×C22⋊C4×C151D411yescharacteristic
76C2×C22⋊C4×C151D411yescharacteristic
77C2×C42×C151—22no—
78C2×C42×C151C2312yes—
79#106×C151—22no—
80#106×C151—22no—
81C4⋊C8×C151—42no—
82#103×C151—24no—
83#103×C151—24no—
84#103×C151—24no—
85#103×C151—42no—
86#102×C151—22no—
87#102×C151—22no—
88#102×C151—42no—
89C22⋊C8×C151—22no—
90#95×C151—22no—
91#95×C151—22no—
92#95×C151—21no—
93#95×C151—22no—
94#95×C151—22no—
95#95×C151D412yes—
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—42no—
114C2×D4×C151—42no—
115C2×D4×C151—42no—
116C22×C4×C151—22no—
117C22×C4×C151—22no—
118C22×C4×C151—21no—
119C22×C4×C151—22no—
120C22×C4×C151—21no—
121C22×C4×C151—24no—
122C22×C4×C151—21no—
123C22×C4×C151—22no—
124C22×C4×C151—44no—
125C22×C4×C151—42no—
126C22×C4×C151—82no—
127C22×C4×C151C2×D412yes—
128C22×C4×C151C2×D412yes—
129C22×C4×C151C2×D411yescharacteristic
130C22×C4×C151C2×D412yes—
131C22×C4×C151#4112yes—
132C22×C4×C151C2411yescharacteristic
133C2×C8×C151—21no—
134C2×C8×C151—21no—
135C2×C8×C151—22no—
136C2×C8×C151—22no—
137C2×C8×C151—22no—
138C2×C8×C151—22no—
139C2×C8×C151—22no—
140C2×C8×C151—44no—
141C4⋊C4×C151—24no—
142C4⋊C4×C151—21no—
143C4⋊C4×C151—21no—
144C4⋊C4×C151—21no—
145C4⋊C4×C151—22no—
146C4⋊C4×C151—21no—
147C4⋊C4×C151—22no—
148C4⋊C4×C151—82no—
149C4⋊C4×C151C2×D412yes—
150C4⋊C4×C151C2×D412yes—
151C22⋊C4×C151—22no—
152C22⋊C4×C151—22no—
153C22⋊C4×C151—44no—
154C22⋊C4×C151—44no—
155C22⋊C4×C151—42no—
156C22⋊C4×C151—42no—
157C42×C151—22no—
158C42×C151—22no—
159C42×C151—82no—
160C23×C151—22no—
161C23×C151—22no—
162C23×C151—41no—
163C23×C151—42no—
164C23×C151—41no—
165C23×C151—41no—
166C23×C151—42no—
167C23×C151#12112yes—
168C23×C151#13512yes—
169C23×C151#13712yes—
170C23×C151C22×D411yescharacteristic
171Q8×C151—24no—
172Q8×C151—24no—
173Q8×C151—48no—
174Q8×C151—42no—
175Q8×C151—42no—
176D4×C151—41no—
177D4×C151—41no—
178D4×C151—42no—
179D4×C151—84no—
180C2×C4×C151—22no—
181C2×C4×C151—22no—
182C2×C4×C151—22no—
183C2×C4×C151—24no—
184C2×C4×C151—22no—
185C2×C4×C151—22no—
186C2×C4×C151—24no—
187C2×C4×C151—22no—
188C2×C4×C151—22no—
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—42no—
196C2×C4×C151—42no—
197C2×C4×C151—42no—
198C2×C4×C151—41no—
199C2×C4×C151—42no—
200C2×C4×C151—42no—
201C2×C4×C151—41no—
202C2×C4×C151—41no—
203C2×C4×C151—42no—
204C2×C4×C151—84no—
205C2×C4×C151#12112yes—
206C2×C4×C151C22×D411yescharacteristic
207C2×C4×C151C2×#4112yes—
208C2×C4×C151C2×#4111yescharacteristic
209C2×C4×C151H(5,𝔽2)12yes—
210C8×C151—41no—
211C8×C151—41no—
212C8×C151—42no—
213C22×C151—22no—
214C22×C151—22no—
215C22×C151—24no—
216C22×C151—24no—
217C22×C151—81no—
218C22×C151—81no—
219C22×C151—81no—
220C22×C151—82no—
221C22×C151—82no—
222C22×C151#46414yes—
223C22×C151C2×#12111yescharacteristic
224C22×C151#54612yes—
225C22×C151C2×#13511yescharacteristic
226C22×C151C2×#13711yescharacteristic
227C22×C151#57712yes—
228C4×C151—22no—
229C4×C151—44no—
230C4×C151—42no—
231C4×C151—42no—
232C4×C151—42no—
233C4×C151—42no—
234C4×C151—81no—
235C4×C151—82no—
236C4×C151#52511yescharacteristic
237C4×C151#53511yescharacteristic
238C4×C151#55112yes—
239C2×C151—24no—
240C2×C151—161no—
241C2×C151#241111yescharacteristic
242C2×C151C2×#46411yescharacteristic
243C2×C151#304211yescharacteristic
244C2×C151#330112yes—
245C2×C151#331612yes—
246#24483C15111yesmaximal, characteristic, direct product factor, Sylow
247C151#2448311yescharacteristic, direct product factor, Sylow
248C2×#481C2×C15111yescharacteristic
249C22×#103C2×C15111yescharacteristic, complemented
250#2436C2×C15111yescharacteristic
251#2345C2×C15111yescharacteristic, complemented
252#2066C2×C15112yescomplemented
253#2042C2×C15112yescomplemented
254#1983C2×C15112yescomplemented
255#1927C2×C15112yescomplemented
256#1893C2×C15111yescharacteristic
257#1850C2×C15111yescharacteristic, complemented
258#1787C2×C15111yescharacteristic, complemented
259C23×Q8C22×C15111yescharacteristic
260C23×C8C22×C15111yescharacteristic
261C2×#124C22×C15112yes—
262C2×#121C22×C15111yescharacteristic
263C22×C4⋊C4C22×C15111yescharacteristic
264#481—24no—
265C2×#106C22×C15111yescharacteristic
266C2×#106C22×C15111yescharacteristic
267C2×C4⋊C8C22×C15112yes—
268C2×#103—24no—
269C2×#103C22×C15112yes—
270C2×#103C22×C15112yes—
271C2×#103C22×C15112yes—
272C2×#103C22×C15112yes—
273C2×#102C22×C15111yescharacteristic
274C2×#102C22×C15111yescharacteristic
275C2×#102C22×C15112yes—
276C2×C22⋊C8C22×C15111yescharacteristic
277#393—22no—
278#391C22×C15112yes—
279#389C22×C15112yes—
280#387—22no—
281#386—21no—
282#386—21no—
283#380—21no—
284#380C22×C15111yescharacteristic
285C4×C4⋊C4C22×C15112yes—
286C4×C22⋊C4—21no—
287C4×C22⋊C4C22×C15111yescharacteristic
288#340C22×C15112yes—
289#336C22×C15112yes—
290C22×Q8—21no—
291C22×Q8—24no—
292C22×Q8—22no—
293C22×Q8—22no—
294C22×Q8—42no—
295C22×Q8C23×C15112yes—
296C22×D4—21no—
297C22×D4C23×C15111yescharacteristic
298C23×C4—21no—
299C23×C4—21no—
300C23×C4C23×C15111yescharacteristic
301C22×C8—22no—
302C22×C8—42no—
303C22×C8C23×C15112yes—
304C22×C8C23×C15111yescharacteristic
305C22×C8C23×C15111yescharacteristic
306#124—24no—
307#124—42no—
308#121—22no—
309#121—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4D4×C15114yes—
314C2×C4⋊C4C23×C15111yescharacteristic
315C2×C4⋊C4C23×C15112yes—
316C2×C4⋊C4C23×C15111yescharacteristic
317C2×C4⋊C4C23×C15111yescharacteristic
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4D4×C15111yescharacteristic
323C2×C22⋊C4D4×C15111yescharacteristic
324C2×C42—22no—
325C2×C42C23×C15112yes—
326#106—22no—
327#106—22no—
328C4⋊C8—42no—
329#103—24no—
330#103—24no—
331#103—24no—
332#103—42no—
333#102—22no—
334#102—22no—
335#102—42no—
336C22⋊C8—22no—
337#95—22no—
338#95—22no—
339#95—21no—
340#95—22no—
341#95—22no—
342#95D4×C15112yes—
343C24—21no—
344C24C2×D4×C15111yescharacteristic
345C2×Q8—22no—
346C2×Q8—28no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—44no—
352C2×Q8—48no—
353C2×Q8—44no—
354C2×Q8—42no—
355C2×Q8#41×C15114yes—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—22no—
359C2×D4—22no—
360C2×D4—42no—
361C2×D4—42no—
362C2×D4—42no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—24no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—44no—
372C22×C4—42no—
373C22×C4—82no—
374C22×C4C2×D4×C15112yes—
375C22×C4C2×D4×C15112yes—
376C22×C4C2×D4×C15111yescharacteristic
377C22×C4C2×D4×C15112yes—
378C22×C4#41×C15112yes—
379C22×C4C24×C15111yescharacteristic
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—44no—
388C4⋊C4—24no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—22no—
395C4⋊C4—82no—
396C4⋊C4C2×D4×C15112yes—
397C4⋊C4C2×D4×C15112yes—
398C22⋊C4—22no—
399C22⋊C4—22no—
400C22⋊C4—44no—
401C22⋊C4—44no—
402C22⋊C4—42no—
403C22⋊C4—42no—
404C42—22no—
405C42—22no—
406C42—82no—
407C23—22no—
408C23—22no—
409C23—41no—
410C23—42no—
411C23—41no—
412C23—41no—
413C23—42no—
414C23#121×C15112yes—
415C23#135×C15112yes—
416C23#137×C15112yes—
417C23C22×D4×C15111yescharacteristic
418Q8—24no—
419Q8—24no—
420Q8—48no—
421Q8—42no—
422Q8—42no—
423D4—41no—
424D4—41no—
425D4—42no—
426D4—84no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—24no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—48no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—84no—
452C2×C4#121×C15112yes—
453C2×C4C22×D4×C15111yescharacteristic
454C2×C4C2×#41×C15112yes—
455C2×C4C2×#41×C15111yescharacteristic
456C2×C4H(5,𝔽2)×C15112yes—
457C8—41no—
458C8—42no—
459C8—41no—
460C22—22no—
461C22—22no—
462C22—24no—
463C22—24no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22—82no—
468C22—82no—
469C22#464×C15114yes—
470C22C2×#121×C15111yescharacteristic
471C22#546×C15112yes—
472C22C2×#135×C15111yescharacteristic
473C22C2×#137×C15111yescharacteristic
474C22#577×C15112yes—
475C4—22no—
476C4—44no—
477C4—42no—
478C4—42no—
479C4—42no—
480C4—42no—
481C4—81no—
482C4—82no—
483C4#525×C15111yescharacteristic
484C4#535×C15111yescharacteristic
485C4#551×C15112yes—
486C2—24no—
487C2—161no—
488C2#2411×C15111yescharacteristic
489C2C2×#464×C15111yescharacteristic
490C2#3042×C15111yescharacteristic
491C2#3301×C15112yes—
492C2#3316×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. C22×#103×C151C2semidirect
4. #2345×C151C2semidirect
5. #2066×C151C2semidirect
6. #2042×C151C2semidirect
7. #1983×C151C2semidirect
8. #1927×C151C2semidirect
10. #1850×C151C2semidirect
11. #1787×C151C2semidirect
246. #24483C151direct (N × H)
247. C151#24483direct (N × H)
249. C22×#103C2×C151semidirect
251. #2345C2×C151semidirect
252. #2066C2×C151semidirect
253. #2042C2×C151semidirect
254. #1983C2×C151semidirect
255. #1927C2×C151semidirect
257. #1850C2×C151semidirect
258. #1787C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#481×C1512
C22×#103×C1512
#2436×C1512
#2345×C1512
#2066×C1512
#2042×C1512
#1983×C1512
#1927×C1512
#1893×C1512
#1850×C1512
#1787×C1512
#24483151