Finite Group Databasebeta

← C151×#24646 #50329571

Subgroups — C151×#24646 #50329571

Order 38656.

864 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#461×C151C211yesmaximal, characteristic
2C2×#440×C151C211yesmaximal, characteristic
3#2546×C151C211yesmaximal, characteristic, complemented
4#2357×C151C211yesmaximal, characteristic
5#2055×C151C212yesmaximal
6#2013×C151C212yesmaximal
7#1981×C151C212yesmaximal, complemented
8#1960×C151C211yesmaximal, characteristic, complemented
9#1940×C151C211yesmaximal, characteristic, complemented
10#1928×C151C212yesmaximal, complemented
11#1805×C151C211yesmaximal, characteristic, complemented
12C22×SD16×C151C2211yescharacteristic
13C22×SD16×C151C2212yes—
14C2×C4⋊Q8×C151C2211yescharacteristic
15C2×C4⋊Q8×C151C2212yes—
16C2×C4×Q8×C151C2211yescharacteristic
17C2×C4×D4×C151C2211yescharacteristic
18#461×C151—24no—
19#440×C151—24no—
20C2×#107×C151C2211yescharacteristic
21C2×C4⋊C8×C151C2211yescharacteristic
22C2×C4⋊C8×C151C2212yes—
23C2×#103×C151C2211yescharacteristic
24C2×#103×C151C2212yes—
25C2×#103×C151C2212yes—
26C2×#103×C151C2212yes—
27C2×#103×C151C2212yes—
28C2×#102×C151C2211yescharacteristic
29C2×#97×C151C2211yescharacteristic
30#398×C151—21no—
31#398×C151—21no—
32#391×C151C2212yes—
33#390×C151C2212yes—
34#389×C151—22no—
35#388×C151—22no—
36#382×C151C2211yescharacteristic
37#381×C151—21no—
38C4×C4⋊C4×C151C2212yes—
39C4×C4⋊C4×C151C2211yescharacteristic
40C4×C22⋊C4×C151—21no—
41#340×C151C2212yes—
42#336×C151C2212yes—
43C22×Q8×C151C2312yes—
44C22×Q8×C151C2311yescharacteristic
45C22×D4×C151C2311yescharacteristic
46C23×C4×C151—21no—
47C2×SD16×C151—22no—
48C2×SD16×C151—24no—
49C2×SD16×C151—22no—
50C2×SD16×C151—22no—
51C2×SD16×C151—42no—
52C2×SD16×C151—42no—
53C22×C8×C151C2312yes—
54C22×C8×C151C2311yescharacteristic
55C22×C8×C151C2311yescharacteristic
56C4⋊Q8×C151—22no—
57C4⋊Q8×C151—22no—
58C4⋊Q8×C151—24no—
59C4⋊Q8×C151—42no—
60C4×Q8×C151—22no—
61C4×Q8×C151—22no—
62C4×D4×C151—22no—
63C4×D4×C151D414yes—
64C2×C4⋊C4×C151—21no—
65C2×C4⋊C4×C151—22no—
66C2×C4⋊C4×C151—22no—
67C2×C4⋊C4×C151—21no—
68C2×C4⋊C4×C151—21no—
69C2×C4⋊C4×C151D412yes—
70C2×C4⋊C4×C151C2311yescharacteristic
71C2×C4⋊C4×C151C2312yes—
72C2×C4⋊C4×C151C2311yescharacteristic
73C2×C22⋊C4×C151—21no—
74C2×C22⋊C4×C151—22no—
75C2×C22⋊C4×C151—22no—
76C2×C42×C151—21no—
77C2×C42×C151—22no—
78C2×C42×C151C2312yes—
79C2×C42×C151C2311yescharacteristic
80#107×C151—22no—
81C4⋊C8×C151—22no—
82C4⋊C8×C151—42no—
83#103×C151—24no—
84#103×C151—22no—
85#103×C151—24no—
86#103×C151—42no—
87#103×C151—42no—
88#102×C151—22no—
89#97×C151—22no—
90#95×C151—21no—
91#95×C151—22no—
92#95×C151—21no—
93#95×C151—22no—
94#95×C151—22no—
95#95×C151D411yescharacteristic
96#95×C151D411yescharacteristic
97C24×C151—21no—
98C2×Q8×C151—21no—
99C2×Q8×C151—21no—
100C2×Q8×C151—22no—
101C2×Q8×C151—21no—
102C2×Q8×C151—21no—
103C2×Q8×C151—22no—
104C2×Q8×C151—22no—
105C2×Q8×C151—22no—
106C2×Q8×C151—21no—
107C2×Q8×C151—22no—
108C2×Q8×C151—22no—
109C2×Q8×C151#4112yes—
110C2×D4×C151—21no—
111C2×D4×C151—21no—
112C2×D4×C151—21no—
113C2×D4×C151—21no—
114C2×D4×C151—21no—
115C2×D4×C151C2×D412yes—
116C22×C4×C151—21no—
117C22×C4×C151—21no—
118C22×C4×C151—24no—
119C22×C4×C151—21no—
120C22×C4×C151—22no—
121C22×C4×C151—22no—
122C22×C4×C151—82no—
123C22×C4×C151C2×D412yes—
124C22×C4×C151C2×D411yescharacteristic
125C22×C4×C151C2×D411yescharacteristic
126C22×C4×C151C2×D412yes—
127C22×C4×C151C2411yescharacteristic
128SD16×C151—28no—
129SD16×C151—48no—
130C2×C8×C151—21no—
131C2×C8×C151—21no—
132C2×C8×C151—21no—
133C2×C8×C151—22no—
134C2×C8×C151—21no—
135C2×C8×C151—22no—
136C2×C8×C151—21no—
137C2×C8×C151—22no—
138C2×C8×C151#4112yes—
139C4⋊C4×C151—24no—
140C4⋊C4×C151—21no—
141C4⋊C4×C151—21no—
142C4⋊C4×C151—22no—
143C4⋊C4×C151—21no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—44no—
146C4⋊C4×C151—44no—
147C4⋊C4×C151—42no—
148C4⋊C4×C151—42no—
149C4⋊C4×C151—42no—
150C4⋊C4×C151C2×D412yes—
151C22⋊C4×C151—24no—
152C22⋊C4×C151—44no—
153C22⋊C4×C151—82no—
154C42×C151—22no—
155C42×C151—22no—
156C42×C151—42no—
157C42×C151—82no—
158C42×C151C2×D412yes—
159C42×C151#4112yes—
160C23×C151—22no—
161C23×C151—41no—
162C23×C151—41no—
163C23×C151—42no—
164C23×C151—42no—
165C23×C151C22×D411yescharacteristic
166Q8×C151—22no—
167Q8×C151—22no—
168Q8×C151—41no—
169Q8×C151—41no—
170Q8×C151—42no—
171Q8×C151—42no—
172Q8×C151—42no—
173Q8×C151—42no—
174D4×C151—22no—
175D4×C151—22no—
176D4×C151—41no—
177D4×C151—41no—
178C2×C4×C151—22no—
179C2×C4×C151—22no—
180C2×C4×C151—22no—
181C2×C4×C151—22no—
182C2×C4×C151—22no—
183C2×C4×C151—22no—
184C2×C4×C151—22no—
185C2×C4×C151—22no—
186C2×C4×C151—22no—
187C2×C4×C151—41no—
188C2×C4×C151—41no—
189C2×C4×C151—42no—
190C2×C4×C151—42no—
191C2×C4×C151—41no—
192C2×C4×C151—42no—
193C2×C4×C151—42no—
194C2×C4×C151—42no—
195C2×C4×C151—42no—
196C2×C4×C151—42no—
197C2×C4×C151—42no—
198C2×C4×C151—84no—
199C2×C4×C151#12112yes—
200C2×C4×C151#12112yes—
201C2×C4×C151#13714yes—
202C2×C4×C151C22×D411yescharacteristic
203C2×C4×C151C2×#4111yescharacteristic
204C2×C4×C151C2×#4111yescharacteristic
205C2×C4×C151C2×#4111yescharacteristic
206C2×C4×C151H(5,𝔽2)11yescharacteristic
207C2×C4×C151H(5,𝔽2)11yescharacteristic
208C8×C151—22no—
209C8×C151—41no—
210C8×C151—42no—
211C22×C151—42no—
212C22×C151—42no—
213C22×C151—42no—
214C22×C151—82no—
215C22×C151—82no—
216C22×C151C2×#12111yescharacteristic
217C22×C151#54611yescharacteristic
218C22×C151#55011yescharacteristic
219C22×C151C2×#13712yes—
220C22×C151#57712yes—
221C4×C151—22no—
222C4×C151—22no—
223C4×C151—24no—
224C4×C151—42no—
225C4×C151—42no—
226C4×C151—42no—
227C4×C151—82no—
228C4×C151—82no—
229C4×C151—81no—
230C4×C151#52511yescharacteristic
231C4×C151#53511yescharacteristic
232C4×C151#55311yescharacteristic
233C4×C151#55511yescharacteristic
234C2×C151—82no—
235C2×C151#241411yescharacteristic
236C2×C151#303911yescharacteristic
237C2×C151#304211yescharacteristic
238C2×C151#332012yes—
239C2×C151#340012yes—
240#24646C15111yesmaximal, characteristic, direct product factor, Sylow
241C151#2464611yescharacteristic, direct product factor, Sylow
242C2×#461C2×C15111yescharacteristic
243C2×#440C2×C15111yescharacteristic
244#2546C2×C15111yescharacteristic, complemented
245#2357C2×C15111yescharacteristic
246#2055C2×C15112yes—
247#2013C2×C15112yes—
248#1981C2×C15112yescomplemented
249#1960C2×C15111yescharacteristic, complemented
250#1940C2×C15111yescharacteristic, complemented
251#1928C2×C15112yescomplemented
252#1805C2×C15111yescharacteristic, complemented
253C22×SD16C22×C15111yescharacteristic
254C22×SD16C22×C15112yes—
255C2×C4⋊Q8C22×C15111yescharacteristic
256C2×C4⋊Q8C22×C15112yes—
257C2×C4×Q8C22×C15111yescharacteristic
258C2×C4×D4C22×C15111yescharacteristic
259#461—24no—
260#440—24no—
261C2×#107C22×C15111yescharacteristic
262C2×C4⋊C8C22×C15111yescharacteristic
263C2×C4⋊C8C22×C15112yes—
264C2×#103C22×C15111yescharacteristic
265C2×#103C22×C15112yes—
266C2×#103C22×C15112yes—
267C2×#103C22×C15112yes—
268C2×#103C22×C15112yes—
269C2×#102C22×C15111yescharacteristic
270C2×#97C22×C15111yescharacteristic
271#398—21no—
272#398—21no—
273#391C22×C15112yes—
274#390C22×C15112yes—
275#389—22no—
276#388—22no—
277#382C22×C15111yescharacteristic
278#381—21no—
279C4×C4⋊C4C22×C15112yes—
280C4×C4⋊C4C22×C15111yescharacteristic
281C4×C22⋊C4—21no—
282#340C22×C15112yes—
283#336C22×C15112yes—
284C22×Q8C23×C15112yes—
285C22×Q8C23×C15111yescharacteristic
286C22×D4C23×C15111yescharacteristic
287C23×C4—21no—
288C2×SD16—22no—
289C2×SD16—22no—
290C2×SD16—24no—
291C2×SD16—22no—
292C2×SD16—42no—
293C2×SD16—42no—
294C22×C8C23×C15112yes—
295C22×C8C23×C15111yescharacteristic
296C22×C8C23×C15111yescharacteristic
297C4⋊Q8—24no—
298C4⋊Q8—22no—
299C4⋊Q8—22no—
300C4⋊Q8—42no—
301C4×Q8—22no—
302C4×Q8—22no—
303C4×D4—22no—
304C4×D4D4×C15114yes—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4D4×C15112yes—
311C2×C4⋊C4C23×C15111yescharacteristic
312C2×C4⋊C4C23×C15112yes—
313C2×C4⋊C4C23×C15111yescharacteristic
314C2×C22⋊C4—21no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C42—21no—
318C2×C42—22no—
319C2×C42C23×C15112yes—
320C2×C42C23×C15111yescharacteristic
321#107—22no—
322C4⋊C8—22no—
323C4⋊C8—42no—
324#103—24no—
325#103—22no—
326#103—24no—
327#103—42no—
328#103—42no—
329#102—22no—
330#97—22no—
331#95—21no—
332#95—22no—
333#95—21no—
334#95—22no—
335#95—22no—
336#95D4×C15111yescharacteristic
337#95D4×C15111yescharacteristic
338C24—21no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—22no—
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—21no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8#41×C15112yes—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4C2×D4×C15112yes—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—24no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—82no—
364C22×C4C2×D4×C15112yes—
365C22×C4C2×D4×C15111yescharacteristic
366C22×C4C2×D4×C15111yescharacteristic
367C22×C4C2×D4×C15112yes—
368C22×C4C24×C15111yescharacteristic
369SD16—28no—
370SD16—48no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—21no—
374C2×C8—22no—
375C2×C8—21no—
376C2×C8—22no—
377C2×C8—21no—
378C2×C8—22no—
379C2×C8#41×C15112yes—
380C4⋊C4—24no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—44no—
387C4⋊C4—44no—
388C4⋊C4—42no—
389C4⋊C4—42no—
390C4⋊C4—42no—
391C4⋊C4C2×D4×C15112yes—
392C22⋊C4—24no—
393C22⋊C4—44no—
394C22⋊C4—82no—
395C42—22no—
396C42—22no—
397C42—42no—
398C42—82no—
399C42C2×D4×C15112yes—
400C42#41×C15112yes—
401C23—22no—
402C23—41no—
403C23—41no—
404C23—42no—
405C23—42no—
406C23C22×D4×C15111yescharacteristic
407Q8—22no—
408Q8—22no—
409Q8—41no—
410Q8—41no—
411Q8—42no—
412Q8—42no—
413Q8—42no—
414Q8—42no—
415D4—22no—
416D4—22no—
417D4—41no—
418D4—41no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—84no—
440C2×C4#121×C15112yes—
441C2×C4#121×C15112yes—
442C2×C4#137×C15114yes—
443C2×C4C22×D4×C15111yescharacteristic
444C2×C4C2×#41×C15111yescharacteristic
445C2×C4C2×#41×C15111yescharacteristic
446C2×C4C2×#41×C15111yescharacteristic
447C2×C4H(5,𝔽2)×C15111yescharacteristic
448C2×C4H(5,𝔽2)×C15111yescharacteristic
449C8—22no—
450C8—42no—
451C8—41no—
452C22—42no—
453C22—42no—
454C22—42no—
455C22—82no—
456C22—82no—
457C22C2×#121×C15111yescharacteristic
458C22#546×C15111yescharacteristic
459C22#550×C15111yescharacteristic
460C22C2×#137×C15112yes—
461C22#577×C15112yes—
462C4—22no—
463C4—22no—
464C4—24no—
465C4—42no—
466C4—42no—
467C4—42no—
468C4—82no—
469C4—82no—
470C4—81no—
471C4#525×C15111yescharacteristic
472C4#535×C15111yescharacteristic
473C4#553×C15111yescharacteristic
474C4#555×C15111yescharacteristic
475C2—82no—
476C2#2414×C15111yescharacteristic
477C2#3039×C15111yescharacteristic
478C2#3042×C15111yescharacteristic
479C2#3320×C15112yes—
480C2#3400×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C23
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
3. #2546×C151C2semidirect
7. #1981×C151C2semidirect
8. #1960×C151C2semidirect
9. #1940×C151C2semidirect
10. #1928×C151C2semidirect
11. #1805×C151C2semidirect
240. #24646C151direct (N × H)
241. C151#24646direct (N × H)
244. #2546C2×C151semidirect
248. #1981C2×C151semidirect
249. #1960C2×C151semidirect
250. #1940C2×C151semidirect
251. #1928C2×C151semidirect
252. #1805C2×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×#440×C1512
#2546×C1512
#2357×C1512
#2055×C1512
#2013×C1512
#1981×C1512
#1960×C1512
#1940×C1512
#1928×C1512
#1805×C1512
#24646151