Finite Group Databasebeta

← C151×#24609 #50329534

Subgroups — C151×#24609 #50329534

Order 38656.

860 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#483×C151C211yesmaximal, characteristic
2C2×#432×C151C211yesmaximal, characteristic
3#2855×C151C211yesmaximal, characteristic
4C2×#389×C151C211yesmaximal, characteristic
5#2088×C151C212yesmaximal, complemented
6#2068×C151C212yesmaximal, complemented
7#1943×C151C212yesmaximal, complemented
8#1935×C151C212yesmaximal, complemented
9#1872×C151C211yesmaximal, characteristic
10#1852×C151C211yesmaximal, characteristic
11#1823×C151C211yesmaximal, characteristic
12C2×C22⋊Q8×C151C2211yescharacteristic
13C22×C4⋊C4×C151—21no—
14C22×C4⋊C4×C151C2211yescharacteristic
15C22×C4⋊C4×C151C2211yescharacteristic
16C22×C42×C151C2211yescharacteristic
17#483×C151—24no—
18#432×C151—24no—
19C2×#107×C151C2212yes—
20C2×#106×C151C2212yes—
21C2×C4⋊C8×C151C2212yes—
22C2×#103×C151C2212yes—
23C2×#103×C151C2212yes—
24C2×C22⋊C8×C151C2211yescharacteristic
25C2×C22⋊C8×C151C2211yescharacteristic
26C2×#97×C151C2212yes—
27#391×C151C2211yescharacteristic
28#391×C151C2211yescharacteristic
29#389×C151—21no—
30#389×C151—21no—
31#389×C151C2211yescharacteristic
32#389×C151C2211yescharacteristic
33#389×C151C2212yes—
34#389×C151C2212yes—
35#387×C151—21no—
36#387×C151—21no—
37#385×C151—21no—
38#381×C151—21no—
39#380×C151C2211yescharacteristic
40C2×#95×C151—21no—
41#340×C151C2212yes—
42#340×C151C2212yes—
43#340×C151C2212yes—
44#340×C151C2212yes—
45C22×Q8×C151C2311yescharacteristic
46C23×C4×C151—21no—
47C23×C4×C151—21no—
48C23×C4×C151D411yescharacteristic
49C23×C4×C151D411yescharacteristic
50C23×C4×C151C2311yescharacteristic
51C22×C8×C151C2312yes—
52C22×C8×C151C2312yes—
53C22⋊Q8×C151—22no—
54C22⋊Q8×C151—22no—
55C2×C4⋊C4×C151—21no—
56C2×C4⋊C4×C151—24no—
57C2×C4⋊C4×C151—22no—
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—21no—
60C2×C4⋊C4×C151—21no—
61C2×C4⋊C4×C151—21no—
62C2×C4⋊C4×C151—21no—
63C2×C4⋊C4×C151—22no—
64C2×C4⋊C4×C151—22no—
65C2×C4⋊C4×C151—44no—
66C2×C4⋊C4×C151C2311yescharacteristic
67C2×C4⋊C4×C151C2311yescharacteristic
68C2×C4⋊C4×C151C2312yes—
69C2×C4⋊C4×C151C2311yescharacteristic
70C2×C4⋊C4×C151C2312yes—
71C2×C22⋊C4×C151—21no—
72C2×C22⋊C4×C151—21no—
73C2×C42×C151—22no—
74C2×C42×C151—22no—
75C2×C42×C151D411yescharacteristic
76C2×C42×C151D411yescharacteristic
77C2×C42×C151C2311yescharacteristic
78C2×C42×C151C2311yescharacteristic
79#107×C151—24no—
80#106×C151—24no—
81C4⋊C8×C151—24no—
82#103×C151—24no—
83#103×C151—24no—
84C22⋊C8×C151—22no—
85C22⋊C8×C151D414yes—
86#97×C151—24no—
87#95×C151—22no—
88#95×C151—22no—
89#95×C151—21no—
90#95×C151—21no—
91#95×C151—21no—
92#95×C151—21no—
93#95×C151—21no—
94#95×C151—21no—
95#95×C151—21no—
96C24×C151C2×D411yescharacteristic
97C2×Q8×C151—21no—
98C2×Q8×C151—22no—
99C2×Q8×C151—21no—
100C2×Q8×C151—22no—
101C22×C4×C151—22no—
102C22×C4×C151—22no—
103C22×C4×C151—24no—
104C22×C4×C151—22no—
105C22×C4×C151—22no—
106C22×C4×C151—22no—
107C22×C4×C151—22no—
108C22×C4×C151—22no—
109C22×C4×C151—22no—
110C22×C4×C151—21no—
111C22×C4×C151—21no—
112C22×C4×C151—21no—
113C22×C4×C151—21no—
114C22×C4×C151—22no—
115C22×C4×C151—41no—
116C22×C4×C151—42no—
117C22×C4×C151—42no—
118C22×C4×C151—42no—
119C22×C4×C151—42no—
120C22×C4×C151—42no—
121C22×C4×C151C2×D411yescharacteristic
122C22×C4×C151C2×D411yescharacteristic
123C22×C4×C151C2×D411yescharacteristic
124C22×C4×C151C2×D411yescharacteristic
125C22×C4×C151C2×D412yes—
126C22×C4×C151C2×D411yescharacteristic
127C22×C4×C151#4112yes—
128C22×C4×C151C2411yescharacteristic
129C2×C8×C151—22no—
130C2×C8×C151—22no—
131C2×C8×C151—22no—
132C2×C8×C151—22no—
133C2×C8×C151—22no—
134C2×C8×C151C2×D414yes—
135C4⋊C4×C151—24no—
136C4⋊C4×C151—22no—
137C4⋊C4×C151—22no—
138C4⋊C4×C151—21no—
139C4⋊C4×C151—22no—
140C4⋊C4×C151—22no—
141C4⋊C4×C151—21no—
142C4⋊C4×C151—22no—
143C4⋊C4×C151—42no—
144C4⋊C4×C151—44no—
145C4⋊C4×C151—44no—
146C4⋊C4×C151—42no—
147C4⋊C4×C151—42no—
148C4⋊C4×C151—42no—
149C4⋊C4×C151#4114yes—
150C22⋊C4×C151—42no—
151C22⋊C4×C151—42no—
152C42×C151—22no—
153C42×C151—22no—
154C42×C151—21no—
155C42×C151—21no—
156C42×C151—21no—
157C42×C151—21no—
158C23×C151—21no—
159C23×C151—21no—
160C23×C151—21no—
161C23×C151—21no—
162C23×C151#12112yes—
163C23×C151AGL(1,ℤ/8)12yes—
164C23×C151#13712yes—
165C23×C151C22×D411yescharacteristic
166Q8×C151—42no—
167Q8×C151—42no—
168C2×C4×C151—21no—
169C2×C4×C151—21no—
170C2×C4×C151—21no—
171C2×C4×C151—21no—
172C2×C4×C151—24no—
173C2×C4×C151—24no—
174C2×C4×C151—21no—
175C2×C4×C151—21no—
176C2×C4×C151—21no—
177C2×C4×C151—24no—
178C2×C4×C151—21no—
179C2×C4×C151—21no—
180C2×C4×C151—21no—
181C2×C4×C151—21no—
182C2×C4×C151—21no—
183C2×C4×C151—21no—
184C2×C4×C151—44no—
185C2×C4×C151—48no—
186C2×C4×C151—42no—
187C2×C4×C151—42no—
188C2×C4×C151—44no—
189C2×C4×C151—41no—
190C2×C4×C151—41no—
191C2×C4×C151—42no—
192C2×C4×C151—41no—
193C2×C4×C151—41no—
194C2×C4×C151—41no—
195C2×C4×C151—41no—
196C2×C4×C151—41no—
197C2×C4×C151—41no—
198C2×C4×C151—42no—
199C2×C4×C151—41no—
200C2×C4×C151—41no—
201C2×C4×C151—42no—
202C2×C4×C151—41no—
203C2×C4×C151—41no—
204C2×C4×C151—84no—
205C2×C4×C151#12112yes—
206C2×C4×C151#13712yes—
207C2×C4×C151C22×D411yescharacteristic
208C2×C4×C151C2×#4112yes—
209C2×C4×C151C2×#4111yescharacteristic
210C2×C4×C1512−1+412yes—
211C8×C151—24no—
212C8×C151—42no—
213C22×C151—22no—
214C22×C151—22no—
215C22×C151—22no—
216C22×C151—22no—
217C22×C151—22no—
218C22×C151—22no—
219C22×C151#46814yes—
220C22×C151C2×#12111yescharacteristic
221C22×C151#52511yescharacteristic
222C22×C151#53611yescharacteristic
223C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
224C22×C151C2×#13711yescharacteristic
225C22×C151C2×#13711yescharacteristic
226C22×C151#57511yescharacteristic
227C4×C151—22no—
228C4×C151—22no—
229C4×C151—44no—
230C4×C151—41no—
231C4×C151—41no—
232C4×C151—41no—
233C4×C151—81no—
234C4×C151—81no—
235C4×C151—81no—
236C4×C151—82no—
237C4×C151—81no—
238C4×C151#54712yes—
239C4×C151#55212yes—
240C2×C151—24no—
241C2×C151#241311yescharacteristic
242C2×C151C2×#46811yescharacteristic
243C2×C151#305611yescharacteristic
244C2×C151#311311yescharacteristic
245C2×C151#311411yescharacteristic
246C2×C151#323611yescharacteristic
247C2×C151#323811yescharacteristic
248#24609C15111yesmaximal, characteristic, direct product factor, Sylow
249C151#2460911yescharacteristic, direct product factor, Sylow
250C2×#483C2×C15111yescharacteristic
251C2×#432C2×C15111yescharacteristic
252#2855C2×C15111yescharacteristic
253C2×#389C2×C15111yescharacteristic
254#2088C2×C15112yescomplemented
255#2068C2×C15112yescomplemented
256#1943C2×C15112yescomplemented
257#1935C2×C15112yescomplemented
258#1872C2×C15111yescharacteristic
259#1852C2×C15111yescharacteristic
260#1823C2×C15111yescharacteristic
261C2×C22⋊Q8C22×C15111yescharacteristic
262C22×C4⋊C4—21no—
263C22×C4⋊C4C22×C15111yescharacteristic
264C22×C4⋊C4C22×C15111yescharacteristic
265C22×C42C22×C15111yescharacteristic
266#483—24no—
267#432—24no—
268C2×#107C22×C15112yes—
269C2×#106C22×C15112yes—
270C2×C4⋊C8C22×C15112yes—
271C2×#103C22×C15112yes—
272C2×#103C22×C15112yes—
273C2×C22⋊C8C22×C15111yescharacteristic
274C2×C22⋊C8C22×C15111yescharacteristic
275C2×#97C22×C15112yes—
276#391C22×C15111yescharacteristic
277#391C22×C15111yescharacteristic
278#389—21no—
279#389—21no—
280#389C22×C15112yes—
281#389C22×C15111yescharacteristic
282#389C22×C15111yescharacteristic
283#389C22×C15112yes—
284#387—21no—
285#387—21no—
286#385—21no—
287#381—21no—
288#380C22×C15111yescharacteristic
289C2×#95—21no—
290#340C22×C15112yes—
291#340C22×C15112yes—
292#340C22×C15112yes—
293#340C22×C15112yes—
294C22×Q8C23×C15111yescharacteristic
295C23×C4—21no—
296C23×C4—21no—
297C23×C4D4×C15111yescharacteristic
298C23×C4D4×C15111yescharacteristic
299C23×C4C23×C15111yescharacteristic
300C22×C8C23×C15112yes—
301C22×C8C23×C15112yes—
302C22⋊Q8—22no—
303C22⋊Q8—22no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4C23×C15112yes—
316C2×C4⋊C4C23×C15111yescharacteristic
317C2×C4⋊C4C23×C15111yescharacteristic
318C2×C4⋊C4C23×C15111yescharacteristic
319C2×C4⋊C4C23×C15112yes—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C42—22no—
323C2×C42—22no—
324C2×C42D4×C15111yescharacteristic
325C2×C42D4×C15111yescharacteristic
326C2×C42C23×C15111yescharacteristic
327C2×C42C23×C15111yescharacteristic
328#107—24no—
329#106—24no—
330C4⋊C8—24no—
331#103—24no—
332#103—24no—
333C22⋊C8—22no—
334C22⋊C8D4×C15114yes—
335#97—24no—
336#95—22no—
337#95—22no—
338#95—21no—
339#95—21no—
340#95—21no—
341#95—21no—
342#95—21no—
343#95—21no—
344#95—21no—
345C24C2×D4×C15111yescharacteristic
346C2×Q8—21no—
347C2×Q8—22no—
348C2×Q8—21no—
349C2×Q8—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—24no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—41no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4C2×D4×C15111yescharacteristic
371C22×C4C2×D4×C15111yescharacteristic
372C22×C4C2×D4×C15111yescharacteristic
373C22×C4C2×D4×C15111yescharacteristic
374C22×C4C2×D4×C15112yes—
375C22×C4C2×D4×C15111yescharacteristic
376C22×C4#41×C15112yes—
377C22×C4C24×C15111yescharacteristic
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8—22no—
383C2×C8C2×D4×C15114yes—
384C4⋊C4—24no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—21no—
391C4⋊C4—22no—
392C4⋊C4—44no—
393C4⋊C4—44no—
394C4⋊C4—42no—
395C4⋊C4—42no—
396C4⋊C4—42no—
397C4⋊C4—42no—
398C4⋊C4#41×C15114yes—
399C22⋊C4—42no—
400C22⋊C4—42no—
401C42—22no—
402C42—22no—
403C42—21no—
404C42—21no—
405C42—21no—
406C42—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23#121×C15112yes—
412C23AGL(1,ℤ/8)×C15112yes—
413C23#137×C15112yes—
414C23C22×D4×C15111yescharacteristic
415Q8—42no—
416Q8—42no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—24no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—44no—
434C2×C4—48no—
435C2×C4—44no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—84no—
454C2×C4#121×C15112yes—
455C2×C4#137×C15112yes—
456C2×C4C22×D4×C15111yescharacteristic
457C2×C4C2×#41×C15112yes—
458C2×C4C2×#41×C15111yescharacteristic
459C2×C42−1+4×C15112yes—
460C8—24no—
461C8—42no—
462C22—22no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—22no—
467C22—22no—
468C22#468×C15114yes—
469C22C2×#121×C15111yescharacteristic
470C22#525×C15111yescharacteristic
471C22#536×C15111yescharacteristic
472C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
473C22C2×#137×C15111yescharacteristic
474C22C2×#137×C15111yescharacteristic
475C22#575×C15111yescharacteristic
476C4—22no—
477C4—22no—
478C4—44no—
479C4—41no—
480C4—41no—
481C4—41no—
482C4—81no—
483C4—81no—
484C4—81no—
485C4—82no—
486C4—81no—
487C4#547×C15112yes—
488C4#552×C15112yes—
489C2—24no—
490C2#2413×C15111yescharacteristic
491C2C2×#468×C15111yescharacteristic
492C2#3056×C15111yescharacteristic
493C2#3113×C15111yescharacteristic
494C2#3114×C15111yescharacteristic
495C2#3236×C15111yescharacteristic
496C2#3238×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC24×C151C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
5. #2088×C151C2semidirect
6. #2068×C151C2semidirect
7. #1943×C151C2semidirect
8. #1935×C151C2semidirect
248. #24609C151direct (N × H)
249. C151#24609direct (N × H)
254. #2088C2×C151semidirect
255. #2068C2×C151semidirect
256. #1943C2×C151semidirect
257. #1935C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#483×C1512
C2×#432×C1512
#2855×C1512
C2×#389×C1512
#2088×C1512
#2068×C1512
#1943×C1512
#1935×C1512
#1872×C1512
#1852×C1512
#1823×C1512
#24609151