Finite Group Databasebeta

← C151×#24576 #50329501

Subgroups — C151×#24576 #50329501

Order 38656.

924 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#480×C151C211yesmaximal, characteristic
2C22×#107×C151C211yesmaximal, characteristic, complemented
3#2501×C151C211yesmaximal, characteristic
4#2344×C151C211yesmaximal, characteristic, complemented
5#2083×C151C212yesmaximal, complemented
6#2067×C151C212yesmaximal, complemented
7#1947×C151C212yesmaximal, complemented
8#1925×C151C212yesmaximal, complemented
9#1893×C151C211yesmaximal, characteristic
10#1850×C151C211yesmaximal, characteristic, complemented
11#1823×C151C211yesmaximal, characteristic, complemented
12C23×C8×C151C2211yescharacteristic
13C2×#123×C151—21no—
14C2×#123×C151—21no—
15C2×#121×C151C2211yescharacteristic
16C2×#117×C151—21no—
17C22×C4⋊C4×C151C2211yescharacteristic
18C22×C4⋊C4×C151C2211yescharacteristic
19#480×C151—24no—
20C2×#107×C151—24no—
21C2×#107×C151C2211yescharacteristic
22C2×#107×C151C2212yes—
23C2×#107×C151C2212yes—
24C2×#107×C151C2211yescharacteristic
25C2×C4⋊C8×C151C2212yes—
26C2×#102×C151C2212yes—
27C2×#102×C151C2211yescharacteristic
28C2×#102×C151C2211yescharacteristic
29C2×C22⋊C8×C151C2211yescharacteristic
30#399×C151—22no—
31#390×C151C2212yes—
32#389×C151C2212yes—
33#387×C151—22no—
34#384×C151C2212yes—
35#381×C151—21no—
36#380×C151C2211yescharacteristic
37C4×C4⋊C4×C151C2212yes—
38C4×C22⋊C4×C151C2211yescharacteristic
39#340×C151C2212yes—
40#340×C151C2212yes—
41#340×C151C2212yes—
42#336×C151C2212yes—
43C22×D4×C151—21no—
44C22×D4×C151C2311yescharacteristic
45C23×C4×C151—21no—
46C23×C4×C151—21no—
47C23×C4×C151C2311yescharacteristic
48C22×C8×C151—22no—
49C22×C8×C151—24no—
50C22×C8×C151C2311yescharacteristic
51C22×C8×C151C2311yescharacteristic
52C22×C8×C151C2312yes—
53#123×C151—44no—
54#123×C151—44no—
55#121×C151—22no—
56#121×C151—22no—
57#117×C151—44no—
58C2×C4⋊C4×C151—21no—
59C2×C4⋊C4×C151—22no—
60C2×C4⋊C4×C151—22no—
61C2×C4⋊C4×C151—22no—
62C2×C4⋊C4×C151—22no—
63C2×C4⋊C4×C151—22no—
64C2×C4⋊C4×C151—22no—
65C2×C4⋊C4×C151—21no—
66C2×C4⋊C4×C151D414yes—
67C2×C4⋊C4×C151C2312yes—
68C2×C4⋊C4×C151C2311yescharacteristic
69C2×C4⋊C4×C151C2312yes—
70C2×C4⋊C4×C151C2311yescharacteristic
71C2×C4⋊C4×C151C2311yescharacteristic
72C2×C22⋊C4×C151—22no—
73C2×C22⋊C4×C151—22no—
74C2×C22⋊C4×C151—21no—
75C2×C22⋊C4×C151—21no—
76C2×C22⋊C4×C151D411yescharacteristic
77C2×C22⋊C4×C151D411yescharacteristic
78C2×C42×C151—22no—
79C2×C42×C151C2312yes—
80#107×C151—24no—
81#107×C151—24no—
82#107×C151—22no—
83#107×C151—22no—
84C4⋊C8×C151—24no—
85#102×C151—24no—
86#102×C151—22no—
87#102×C151—22no—
88C22⋊C8×C151—22no—
89#95×C151—22no—
90#95×C151—21no—
91#95×C151—22no—
92#95×C151D412yes—
93C24×C151—21no—
94C24×C151C2×D411yescharacteristic
95C2×D4×C151—21no—
96C2×D4×C151—22no—
97C2×D4×C151—21no—
98C2×D4×C151—22no—
99C2×D4×C151—42no—
100C2×D4×C151—42no—
101C2×D4×C151—42no—
102C22×C4×C151—22no—
103C22×C4×C151—22no—
104C22×C4×C151—24no—
105C22×C4×C151—21no—
106C22×C4×C151—21no—
107C22×C4×C151—22no—
108C22×C4×C151—22no—
109C22×C4×C151—21no—
110C22×C4×C151—42no—
111C22×C4×C151—42no—
112C22×C4×C151—42no—
113C22×C4×C151—42no—
114C22×C4×C151—42no—
115C22×C4×C151C2×D412yes—
116C22×C4×C151C2×D411yescharacteristic
117C22×C4×C151C2×D412yes—
118C22×C4×C151C2×D412yes—
119C22×C4×C151#4112yes—
120C22×C4×C151C2411yescharacteristic
121C2×C8×C151—28no—
122C2×C8×C151—22no—
123C2×C8×C151—22no—
124C2×C8×C151—21no—
125C2×C8×C151—21no—
126C2×C8×C151—22no—
127C2×C8×C151—22no—
128C2×C8×C151#4114yes—
129C4⋊C4×C151—24no—
130C4⋊C4×C151—21no—
131C4⋊C4×C151—21no—
132C4⋊C4×C151—22no—
133C4⋊C4×C151—21no—
134C4⋊C4×C151—22no—
135C4⋊C4×C151—22no—
136C4⋊C4×C151—21no—
137C4⋊C4×C151—22no—
138C4⋊C4×C151—44no—
139C4⋊C4×C151—42no—
140C4⋊C4×C151—44no—
141C4⋊C4×C151—44no—
142C4⋊C4×C151C2×D412yes—
143C4⋊C4×C151C2×D412yes—
144C22⋊C4×C151—22no—
145C22⋊C4×C151—44no—
146C22⋊C4×C151—42no—
147C22⋊C4×C151—42no—
148C22⋊C4×C151—44no—
149C22⋊C4×C151D814yes—
150C42×C151—22no—
151C42×C151—22no—
152C42×C151—44no—
153C23×C151—22no—
154C23×C151—22no—
155C23×C151—41no—
156C23×C151—42no—
157C23×C151—41no—
158C23×C151—41no—
159C23×C151—42no—
160C23×C151#12112yes—
161C23×C151C2×D812yes—
162C23×C151AGL(1,ℤ/8)12yes—
163C23×C151C22×D411yescharacteristic
164D4×C151—41no—
165D4×C151—41no—
166D4×C151—42no—
167D4×C151—84no—
168C2×C4×C151—22no—
169C2×C4×C151—22no—
170C2×C4×C151—22no—
171C2×C4×C151—22no—
172C2×C4×C151—22no—
173C2×C4×C151—24no—
174C2×C4×C151—22no—
175C2×C4×C151—22no—
176C2×C4×C151—22no—
177C2×C4×C151—22no—
178C2×C4×C151—22no—
179C2×C4×C151—41no—
180C2×C4×C151—41no—
181C2×C4×C151—41no—
182C2×C4×C151—41no—
183C2×C4×C151—48no—
184C2×C4×C151—41no—
185C2×C4×C151—42no—
186C2×C4×C151—42no—
187C2×C4×C151—42no—
188C2×C4×C151—42no—
189C2×C4×C151—41no—
190C2×C4×C151—42no—
191C2×C4×C151—41no—
192C2×C4×C151—42no—
193C2×C4×C151—84no—
194C2×C4×C151#12112yes—
195C2×C4×C151C2×D814yes—
196C2×C4×C151C22×D411yescharacteristic
197C2×C4×C151C2×#4112yes—
198C2×C4×C151C2×#4111yescharacteristic
199C2×C4×C1512−1+412yes—
200C8×C151—24no—
201C8×C151—41no—
202C8×C151—41no—
203C22×C151—24no—
204C22×C151—24no—
205C22×C151—22no—
206C22×C151—22no—
207C22×C151—82no—
208C22×C151—82no—
209C22×C151—81no—
210C22×C151—81no—
211C22×C151—81no—
212C22×C151#45914yes—
213C22×C151C2×#12111yescharacteristic
214C22×C151#54712yes—
215C22×C151C22×D811yescharacteristic
216C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
217C22×C151#57812yes—
218C4×C151—24no—
219C4×C151—22no—
220C4×C151—42no—
221C4×C151—42no—
222C4×C151—42no—
223C4×C151—82no—
224C4×C151—82no—
225C4×C151—81no—
226C4×C151#52511yescharacteristic
227C4×C151#53611yescharacteristic
228C4×C151#55212yes—
229C2×C151—24no—
230C2×C151—161no—
231C2×C151#241311yescharacteristic
232C2×C151C2×#45911yescharacteristic
233C2×C151#304411yescharacteristic
234C2×C151#333412yes—
235C2×C151#334312yes—
236#24576C15111yesmaximal, characteristic, direct product factor, Sylow
237C151#2457611yescharacteristic, direct product factor, Sylow
238C2×#480C2×C15111yescharacteristic
239C22×#107C2×C15111yescharacteristic, complemented
240#2501C2×C15111yescharacteristic
241#2344C2×C15111yescharacteristic, complemented
242#2083C2×C15112yescomplemented
243#2067C2×C15112yescomplemented
244#1947C2×C15112yescomplemented
245#1925C2×C15112yescomplemented
246#1893C2×C15111yescharacteristic
247#1850C2×C15111yescharacteristic, complemented
248#1823C2×C15111yescharacteristic, complemented
249C23×C8C22×C15111yescharacteristic
250C2×#123—21no—
251C2×#123—21no—
252C2×#121C22×C15111yescharacteristic
253C2×#117—21no—
254C22×C4⋊C4C22×C15111yescharacteristic
255C22×C4⋊C4C22×C15111yescharacteristic
256#480—24no—
257C2×#107—24no—
258C2×#107C22×C15111yescharacteristic
259C2×#107C22×C15111yescharacteristic
260C2×#107C22×C15112yes—
261C2×#107C22×C15112yes—
262C2×C4⋊C8C22×C15112yes—
263C2×#102C22×C15111yescharacteristic
264C2×#102C22×C15111yescharacteristic
265C2×#102C22×C15112yes—
266C2×C22⋊C8C22×C15111yescharacteristic
267#399—22no—
268#390C22×C15112yes—
269#389C22×C15112yes—
270#387—22no—
271#384C22×C15112yes—
272#381—21no—
273#380C22×C15111yescharacteristic
274C4×C4⋊C4C22×C15112yes—
275C4×C22⋊C4C22×C15111yescharacteristic
276#340C22×C15112yes—
277#340C22×C15112yes—
278#340C22×C15112yes—
279#336C22×C15112yes—
280C22×D4—21no—
281C22×D4C23×C15111yescharacteristic
282C23×C4—21no—
283C23×C4—21no—
284C23×C4C23×C15111yescharacteristic
285C22×C8—22no—
286C22×C8—24no—
287C22×C8C23×C15111yescharacteristic
288C22×C8C23×C15111yescharacteristic
289C22×C8C23×C15112yes—
290#123—44no—
291#123—44no—
292#121—22no—
293#121—22no—
294#117—44no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4D4×C15114yes—
304C2×C4⋊C4C23×C15112yes—
305C2×C4⋊C4C23×C15111yescharacteristic
306C2×C4⋊C4C23×C15112yes—
307C2×C4⋊C4C23×C15111yescharacteristic
308C2×C4⋊C4C23×C15111yescharacteristic
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4D4×C15111yescharacteristic
314C2×C22⋊C4D4×C15111yescharacteristic
315C2×C42—22no—
316C2×C42C23×C15112yes—
317#107—24no—
318#107—24no—
319#107—22no—
320#107—22no—
321C4⋊C8—24no—
322#102—24no—
323#102—22no—
324#102—22no—
325C22⋊C8—22no—
326#95—22no—
327#95—21no—
328#95—22no—
329#95D4×C15112yes—
330C24—21no—
331C24C2×D4×C15111yescharacteristic
332C2×D4—21no—
333C2×D4—22no—
334C2×D4—21no—
335C2×D4—22no—
336C2×D4—42no—
337C2×D4—42no—
338C2×D4—42no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—24no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4C2×D4×C15112yes—
353C22×C4C2×D4×C15111yescharacteristic
354C22×C4C2×D4×C15112yes—
355C22×C4C2×D4×C15112yes—
356C22×C4#41×C15112yes—
357C22×C4C24×C15111yescharacteristic
358C2×C8—28no—
359C2×C8—22no—
360C2×C8—22no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8—22no—
364C2×C8—22no—
365C2×C8#41×C15114yes—
366C4⋊C4—24no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—22no—
370C4⋊C4—21no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—21no—
374C4⋊C4—22no—
375C4⋊C4—44no—
376C4⋊C4—42no—
377C4⋊C4—44no—
378C4⋊C4—44no—
379C4⋊C4C2×D4×C15112yes—
380C4⋊C4C2×D4×C15112yes—
381C22⋊C4—22no—
382C22⋊C4—44no—
383C22⋊C4—42no—
384C22⋊C4—42no—
385C22⋊C4—44no—
386C22⋊C4D8×C15114yes—
387C42—22no—
388C42—22no—
389C42—44no—
390C23—22no—
391C23—22no—
392C23—41no—
393C23—42no—
394C23—41no—
395C23—41no—
396C23—42no—
397C23#121×C15112yes—
398C23C2×D8×C15112yes—
399C23AGL(1,ℤ/8)×C15112yes—
400C23C22×D4×C15111yescharacteristic
401D4—41no—
402D4—41no—
403D4—42no—
404D4—84no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—24no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—48no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—84no—
431C2×C4#121×C15112yes—
432C2×C4C2×D8×C15114yes—
433C2×C4C22×D4×C15111yescharacteristic
434C2×C4C2×#41×C15112yes—
435C2×C4C2×#41×C15111yescharacteristic
436C2×C42−1+4×C15112yes—
437C8—24no—
438C8—41no—
439C8—41no—
440C22—22no—
441C22—22no—
442C22—24no—
443C22—24no—
444C22—81no—
445C22—81no—
446C22—81no—
447C22—82no—
448C22—82no—
449C22#459×C15114yes—
450C22C2×#121×C15111yescharacteristic
451C22#547×C15112yes—
452C22C22×D8×C15111yescharacteristic
453C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
454C22#578×C15112yes—
455C4—22no—
456C4—24no—
457C4—42no—
458C4—42no—
459C4—42no—
460C4—82no—
461C4—81no—
462C4—82no—
463C4#525×C15111yescharacteristic
464C4#536×C15111yescharacteristic
465C4#552×C15112yes—
466C2—24no—
467C2—161no—
468C2#2413×C15111yescharacteristic
469C2C2×#459×C15111yescharacteristic
470C2#3044×C15111yescharacteristic
471C2#3334×C15112yes—
472C2#3343×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×#107×C151C2semidirect
4. #2344×C151C2semidirect
5. #2083×C151C2semidirect
6. #2067×C151C2semidirect
7. #1947×C151C2semidirect
8. #1925×C151C2semidirect
10. #1850×C151C2semidirect
11. #1823×C151C2semidirect
236. #24576C151direct (N × H)
237. C151#24576direct (N × H)
239. C22×#107C2×C151semidirect
241. #2344C2×C151semidirect
242. #2083C2×C151semidirect
243. #2067C2×C151semidirect
244. #1947C2×C151semidirect
245. #1925C2×C151semidirect
247. #1850C2×C151semidirect
248. #1823C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#480×C1512
C22×#107×C1512
#2501×C1512
#2344×C1512
#2083×C1512
#2067×C1512
#1947×C1512
#1925×C1512
#1893×C1512
#1850×C1512
#1823×C1512
#24576151