Finite Group Databasebeta

← C151×#24643 #50329568

Subgroups — C151×#24643 #50329568

Order 38656.

896 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#461×C151C211yesmaximal, characteristic, complemented
2C2×#442×C151C211yesmaximal, characteristic
3#2547×C151C211yesmaximal, characteristic, complemented
4#2357×C151C211yesmaximal, characteristic, complemented
5#2055×C151C212yesmaximal, complemented
6#2012×C151C212yesmaximal
7#1983×C151C212yesmaximal, complemented
8#1960×C151C211yesmaximal, characteristic, complemented
9#1940×C151C211yesmaximal, characteristic, complemented
10#1927×C151C212yesmaximal, complemented
11#1804×C151C211yesmaximal, characteristic, complemented
12C22×SD16×C151C2212yes—
13C22×D8×C151C2211yescharacteristic
14C2×C4⋊Q8×C151C2211yescharacteristic
15C2×#124×C151C2212yes—
16C2×C4×D4×C151C2211yescharacteristic
17C2×C4×D4×C151C2211yescharacteristic
18#461×C151—24no—
19#442×C151—24no—
20C2×#106×C151C2211yescharacteristic
21C2×C4⋊C8×C151C2211yescharacteristic
22C2×C4⋊C8×C151C2212yes—
23C2×#103×C151C2212yes—
24C2×#103×C151C2212yes—
25C2×#103×C151C2212yes—
26C2×#102×C151C2211yescharacteristic
27C2×#102×C151C2211yescharacteristic
28C2×#102×C151C2212yes—
29C2×#97×C151C2211yescharacteristic
30#397×C151—21no—
31#397×C151—21no—
32#391×C151C2212yes—
33#390×C151C2212yes—
34#388×C151—22no—
35#382×C151C2211yescharacteristic
36#381×C151—21no—
37#380×C151—22no—
38C4×C4⋊C4×C151C2212yes—
39C4×C4⋊C4×C151C2211yescharacteristic
40C4×C22⋊C4×C151—21no—
41#340×C151C2212yes—
42#336×C151C2212yes—
43C22×Q8×C151C2312yes—
44C22×D4×C151C2311yescharacteristic
45C22×D4×C151C2311yescharacteristic
46C23×C4×C151—21no—
47C23×C4×C151—21no—
48C2×SD16×C151—24no—
49C2×SD16×C151—42no—
50C2×SD16×C151—42no—
51C2×D8×C151—22no—
52C2×D8×C151—22no—
53C2×D8×C151—22no—
54C22×C8×C151C2312yes—
55C22×C8×C151C2311yescharacteristic
56C22×C8×C151C2311yescharacteristic
57C4⋊Q8×C151—22no—
58C4⋊Q8×C151—22no—
59#124×C151—24no—
60#124×C151—42no—
61C4×D4×C151—22no—
62C4×D4×C151—22no—
63C4×D4×C151—22no—
64C4×D4×C151D414yes—
65C2×C4⋊C4×C151—21no—
66C2×C4⋊C4×C151—21no—
67C2×C4⋊C4×C151D412yes—
68C2×C4⋊C4×C151C2311yescharacteristic
69C2×C4⋊C4×C151C2312yes—
70C2×C4⋊C4×C151C2311yescharacteristic
71C2×C22⋊C4×C151—21no—
72C2×C22⋊C4×C151—22no—
73C2×C22⋊C4×C151—22no—
74C2×C22⋊C4×C151—22no—
75C2×C22⋊C4×C151—21no—
76C2×C22⋊C4×C151—22no—
77C2×C42×C151—22no—
78C2×C42×C151C2312yes—
79C2×C42×C151C2311yescharacteristic
80#106×C151—22no—
81C4⋊C8×C151—22no—
82C4⋊C8×C151—42no—
83#103×C151—24no—
84#103×C151—24no—
85#103×C151—42no—
86#102×C151—22no—
87#102×C151—22no—
88#102×C151—42no—
89#97×C151—22no—
90#95×C151—21no—
91#95×C151—22no—
92#95×C151—22no—
93#95×C151—22no—
94#95×C151—21no—
95#95×C151D411yescharacteristic
96#95×C151D411yescharacteristic
97C24×C151—21no—
98C24×C151—21no—
99C2×Q8×C151—22no—
100C2×Q8×C151—22no—
101C2×Q8×C151—22no—
102C2×Q8×C151—22no—
103C2×Q8×C151—22no—
104C2×Q8×C151—22no—
105C2×D4×C151—21no—
106C2×D4×C151—21no—
107C2×D4×C151—21no—
108C2×D4×C151—21no—
109C2×D4×C151—21no—
110C2×D4×C151—21no—
111C2×D4×C151—21no—
112C2×D4×C151—21no—
113C2×D4×C151—21no—
114C2×D4×C151—21no—
115C2×D4×C151C2×D412yes—
116C2×D4×C151#4112yes—
117C22×C4×C151—21no—
118C22×C4×C151—24no—
119C22×C4×C151—21no—
120C22×C4×C151—22no—
121C22×C4×C151—22no—
122C22×C4×C151—44no—
123C22×C4×C151—42no—
124C22×C4×C151—82no—
125C22×C4×C151C2×D412yes—
126C22×C4×C151C2×D412yes—
127C22×C4×C151C2×D411yescharacteristic
128C22×C4×C151C2×D411yescharacteristic
129C22×C4×C151C2411yescharacteristic
130SD16×C151—48no—
131D8×C151—28no—
132C2×C8×C151—21no—
133C2×C8×C151—21no—
134C2×C8×C151—21no—
135C2×C8×C151—22no—
136C2×C8×C151—22no—
137C2×C8×C151—21no—
138C2×C8×C151—21no—
139C2×C8×C151—22no—
140C2×C8×C151#4112yes—
141C4⋊C4×C151—21no—
142C4⋊C4×C151—21no—
143C4⋊C4×C151—22no—
144C4⋊C4×C151—21no—
145C4⋊C4×C151—22no—
146C4⋊C4×C151—42no—
147C4⋊C4×C151—42no—
148C4⋊C4×C151—42no—
149C4⋊C4×C151C2×D412yes—
150C22⋊C4×C151—24no—
151C22⋊C4×C151—44no—
152C22⋊C4×C151—44no—
153C22⋊C4×C151—44no—
154C22⋊C4×C151—42no—
155C22⋊C4×C151—82no—
156C42×C151—22no—
157C42×C151—22no—
158C42×C151—82no—
159C42×C151C2×D412yes—
160C42×C151#4112yes—
161C23×C151—22no—
162C23×C151—22no—
163C23×C151—41no—
164C23×C151—41no—
165C23×C151—41no—
166C23×C151—41no—
167C23×C151—42no—
168C23×C151—42no—
169C23×C151—42no—
170C23×C151—42no—
171C23×C151C22×D411yescharacteristic
172Q8×C151—42no—
173Q8×C151—42no—
174Q8×C151—42no—
175Q8×C151—42no—
176D4×C151—22no—
177D4×C151—22no—
178D4×C151—22no—
179D4×C151—22no—
180D4×C151—41no—
181D4×C151—41no—
182D4×C151—41no—
183D4×C151—41no—
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—22no—
191C2×C4×C151—22no—
192C2×C4×C151—22no—
193C2×C4×C151—42no—
194C2×C4×C151—42no—
195C2×C4×C151—41no—
196C2×C4×C151—42no—
197C2×C4×C151—42no—
198C2×C4×C151—42no—
199C2×C4×C151—42no—
200C2×C4×C151—42no—
201C2×C4×C151—42no—
202C2×C4×C151—84no—
203C2×C4×C151—84no—
204C2×C4×C151#12112yes—
205C2×C4×C151#12112yes—
206C2×C4×C151C22×D411yescharacteristic
207C2×C4×C151C2×#4111yescharacteristic
208C2×C4×C151C2×#4111yescharacteristic
209C2×C4×C151C2×#4111yescharacteristic
210C2×C4×C151H(5,𝔽2)11yescharacteristic
211C2×C4×C151H(5,𝔽2)11yescharacteristic
212C8×C151—22no—
213C8×C151—41no—
214C8×C151—42no—
215C22×C151—42no—
216C22×C151—42no—
217C22×C151—42no—
218C22×C151—42no—
219C22×C151—44no—
220C22×C151—82no—
221C22×C151—82no—
222C22×C151—81no—
223C22×C151—81no—
224C22×C151—82no—
225C22×C151C2×#12111yescharacteristic
226C22×C151#54611yescharacteristic
227C22×C151#55011yescharacteristic
228C22×C151#57512yes—
229C22×C151#57712yes—
230C4×C151—22no—
231C4×C151—22no—
232C4×C151—42no—
233C4×C151—42no—
234C4×C151—42no—
235C4×C151—82no—
236C4×C151—82no—
237C4×C151—81no—
238C4×C151#52511yescharacteristic
239C4×C151#53511yescharacteristic
240C4×C151#55311yescharacteristic
241C4×C151#55511yescharacteristic
242C2×C151—82no—
243C2×C151—82no—
244C2×C151#241411yescharacteristic
245C2×C151#304011yescharacteristic
246C2×C151#304211yescharacteristic
247C2×C151#330712yes—
248C2×C151#340112yes—
249#24643C15111yesmaximal, characteristic, direct product factor, Sylow
250C151#2464311yescharacteristic, direct product factor, Sylow
251C2×#461C2×C15111yescharacteristic, complemented
252C2×#442C2×C15111yescharacteristic
253#2547C2×C15111yescharacteristic, complemented
254#2357C2×C15111yescharacteristic, complemented
255#2055C2×C15112yescomplemented
256#2012C2×C15112yes—
257#1983C2×C15112yescomplemented
258#1960C2×C15111yescharacteristic, complemented
259#1940C2×C15111yescharacteristic, complemented
260#1927C2×C15112yescomplemented
261#1804C2×C15111yescharacteristic, complemented
262C22×SD16C22×C15112yes—
263C22×D8C22×C15111yescharacteristic
264C2×C4⋊Q8C22×C15111yescharacteristic
265C2×#124C22×C15112yes—
266C2×C4×D4C22×C15111yescharacteristic
267C2×C4×D4C22×C15111yescharacteristic
268#461—24no—
269#442—24no—
270C2×#106C22×C15111yescharacteristic
271C2×C4⋊C8C22×C15111yescharacteristic
272C2×C4⋊C8C22×C15112yes—
273C2×#103C22×C15112yes—
274C2×#103C22×C15112yes—
275C2×#103C22×C15112yes—
276C2×#102C22×C15111yescharacteristic
277C2×#102C22×C15111yescharacteristic
278C2×#102C22×C15112yes—
279C2×#97C22×C15111yescharacteristic
280#397—21no—
281#397—21no—
282#391C22×C15112yes—
283#390C22×C15112yes—
284#388—22no—
285#382C22×C15111yescharacteristic
286#381—21no—
287#380—22no—
288C4×C4⋊C4C22×C15112yes—
289C4×C4⋊C4C22×C15111yescharacteristic
290C4×C22⋊C4—21no—
291#340C22×C15112yes—
292#336C22×C15112yes—
293C22×Q8C23×C15112yes—
294C22×D4C23×C15111yescharacteristic
295C22×D4C23×C15111yescharacteristic
296C23×C4—21no—
297C23×C4—21no—
298C2×SD16—24no—
299C2×SD16—42no—
300C2×SD16—42no—
301C2×D8—22no—
302C2×D8—22no—
303C2×D8—22no—
304C22×C8C23×C15112yes—
305C22×C8C23×C15111yescharacteristic
306C22×C8C23×C15111yescharacteristic
307C4⋊Q8—22no—
308C4⋊Q8—22no—
309#124—24no—
310#124—42no—
311C4×D4—22no—
312C4×D4—22no—
313C4×D4—22no—
314C4×D4D4×C15114yes—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4D4×C15112yes—
318C2×C4⋊C4C23×C15111yescharacteristic
319C2×C4⋊C4C23×C15112yes—
320C2×C4⋊C4C23×C15111yescharacteristic
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C42—22no—
328C2×C42C23×C15112yes—
329C2×C42C23×C15111yescharacteristic
330#106—22no—
331C4⋊C8—22no—
332C4⋊C8—42no—
333#103—24no—
334#103—24no—
335#103—42no—
336#102—22no—
337#102—22no—
338#102—42no—
339#97—22no—
340#95—21no—
341#95—22no—
342#95—22no—
343#95—22no—
344#95—21no—
345#95D4×C15111yescharacteristic
346#95D4×C15111yescharacteristic
347C24—21no—
348C24—21no—
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—22no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4C2×D4×C15112yes—
366C2×D4#41×C15112yes—
367C22×C4—21no—
368C22×C4—24no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—44no—
373C22×C4—42no—
374C22×C4—82no—
375C22×C4C2×D4×C15112yes—
376C22×C4C2×D4×C15112yes—
377C22×C4C2×D4×C15111yescharacteristic
378C22×C4C2×D4×C15111yescharacteristic
379C22×C4C24×C15111yescharacteristic
380SD16—48no—
381D8—28no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8—22no—
390C2×C8#41×C15112yes—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—21no—
395C4⋊C4—22no—
396C4⋊C4—42no—
397C4⋊C4—42no—
398C4⋊C4—42no—
399C4⋊C4C2×D4×C15112yes—
400C22⋊C4—24no—
401C22⋊C4—44no—
402C22⋊C4—44no—
403C22⋊C4—44no—
404C22⋊C4—42no—
405C22⋊C4—82no—
406C42—22no—
407C42—22no—
408C42—82no—
409C42C2×D4×C15112yes—
410C42#41×C15112yes—
411C23—22no—
412C23—22no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—42no—
418C23—42no—
419C23—42no—
420C23—42no—
421C23C22×D4×C15111yescharacteristic
422Q8—42no—
423Q8—42no—
424Q8—42no—
425Q8—42no—
426D4—22no—
427D4—22no—
428D4—22no—
429D4—22no—
430D4—41no—
431D4—41no—
432D4—41no—
433D4—41no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—84no—
453C2×C4—84no—
454C2×C4#121×C15112yes—
455C2×C4#121×C15112yes—
456C2×C4C22×D4×C15111yescharacteristic
457C2×C4C2×#41×C15111yescharacteristic
458C2×C4C2×#41×C15111yescharacteristic
459C2×C4C2×#41×C15111yescharacteristic
460C2×C4H(5,𝔽2)×C15111yescharacteristic
461C2×C4H(5,𝔽2)×C15111yescharacteristic
462C8—22no—
463C8—42no—
464C8—41no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—42no—
469C22—44no—
470C22—82no—
471C22—82no—
472C22—81no—
473C22—81no—
474C22—82no—
475C22C2×#121×C15111yescharacteristic
476C22#546×C15111yescharacteristic
477C22#550×C15111yescharacteristic
478C22#575×C15112yes—
479C22#577×C15112yes—
480C4—22no—
481C4—22no—
482C4—42no—
483C4—42no—
484C4—42no—
485C4—82no—
486C4—82no—
487C4—81no—
488C4#525×C15111yescharacteristic
489C4#535×C15111yescharacteristic
490C4#553×C15111yescharacteristic
491C4#555×C15111yescharacteristic
492C2—82no—
493C2—82no—
494C2#2414×C15111yescharacteristic
495C2#3040×C15111yescharacteristic
496C2#3042×C15111yescharacteristic
497C2#3307×C15112yes—
498C2#3401×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D8×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C4⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#461×C151C2semidirect
3. #2547×C151C2semidirect
4. #2357×C151C2semidirect
5. #2055×C151C2semidirect
7. #1983×C151C2semidirect
8. #1960×C151C2semidirect
9. #1940×C151C2semidirect
10. #1927×C151C2semidirect
11. #1804×C151C2semidirect
249. #24643C151direct (N × H)
250. C151#24643direct (N × H)
251. C2×#461C2×C151semidirect
253. #2547C2×C151semidirect
254. #2357C2×C151semidirect
255. #2055C2×C151semidirect
257. #1983C2×C151semidirect
258. #1960C2×C151semidirect
259. #1940C2×C151semidirect
260. #1927C2×C151semidirect
261. #1804C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#461×C1512
C2×#442×C1512
#2547×C1512
#2357×C1512
#2055×C1512
#2012×C1512
#1983×C1512
#1960×C1512
#1940×C1512
#1927×C1512
#1804×C1512
#24643151