Finite Group Databasebeta

← C151×#24581 #50329506

Subgroups — C151×#24581 #50329506

Order 38656.

868 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#480×C151C211yesmaximal, characteristic
2C22×#106×C151C211yesmaximal, characteristic, complemented
3#2504×C151C211yesmaximal, characteristic
4#2344×C151C211yesmaximal, characteristic, complemented
5#2085×C151C212yesmaximal, complemented
6#2065×C151C212yesmaximal, complemented
7#1949×C151C212yesmaximal, complemented
8#1926×C151C212yesmaximal, complemented
9#1893×C151C211yesmaximal, characteristic
10#1850×C151C211yesmaximal, characteristic, complemented
11#1824×C151C211yesmaximal, characteristic, complemented
12C23×C8×C151C2211yescharacteristic
13C2×#121×C151C2211yescharacteristic
14C2×#117×C151—21no—
15C22×C4⋊C4×C151C2211yescharacteristic
16C22×C4⋊C4×C151C2211yescharacteristic
17#480×C151—24no—
18C2×#107×C151C2211yescharacteristic
19C2×#107×C151C2211yescharacteristic
20C2×#106×C151—24no—
21C2×#106×C151C2212yes—
22C2×#106×C151C2212yes—
23C2×C4⋊C8×C151C2212yes—
24C2×#102×C151C2212yes—
25C2×#102×C151C2211yescharacteristic
26C2×#102×C151C2211yescharacteristic
27C2×C22⋊C8×C151C2211yescharacteristic
28#397×C151—22no—
29#390×C151C2212yes—
30#389×C151C2212yes—
31#387×C151—22no—
32#386×C151—21no—
33#386×C151—21no—
34#382×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#121×C151—22no—
54#121×C151—22no—
55#117×C151—44no—
56C2×C4⋊C4×C151—21no—
57C2×C4⋊C4×C151—22no—
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—22no—
60C2×C4⋊C4×C151—22no—
61C2×C4⋊C4×C151—21no—
62C2×C4⋊C4×C151D414yes—
63C2×C4⋊C4×C151C2312yes—
64C2×C4⋊C4×C151C2311yescharacteristic
65C2×C4⋊C4×C151C2312yes—
66C2×C4⋊C4×C151C2311yescharacteristic
67C2×C4⋊C4×C151C2311yescharacteristic
68C2×C22⋊C4×C151—21no—
69C2×C22⋊C4×C151—22no—
70C2×C22⋊C4×C151—22no—
71C2×C22⋊C4×C151—21no—
72C2×C22⋊C4×C151D411yescharacteristic
73C2×C22⋊C4×C151D411yescharacteristic
74C2×C42×C151—22no—
75C2×C42×C151C2312yes—
76#107×C151—22no—
77#107×C151—22no—
78#106×C151—24no—
79#106×C151—24no—
80C4⋊C8×C151—24no—
81#102×C151—24no—
82#102×C151—22no—
83#102×C151—22no—
84C22⋊C8×C151—22no—
85#95×C151—22no—
86#95×C151—21no—
87#95×C151—22no—
88#95×C151—22no—
89#95×C151—22no—
90#95×C151D412yes—
91C24×C151—21no—
92C24×C151C2×D411yescharacteristic
93C2×D4×C151—21no—
94C2×D4×C151—22no—
95C2×D4×C151—21no—
96C2×D4×C151—22no—
97C2×D4×C151—42no—
98C2×D4×C151—42no—
99C2×D4×C151—42no—
100C22×C4×C151—22no—
101C22×C4×C151—22no—
102C22×C4×C151—24no—
103C22×C4×C151—21no—
104C22×C4×C151—21no—
105C22×C4×C151—21no—
106C22×C4×C151—22no—
107C22×C4×C151—22no—
108C22×C4×C151—42no—
109C22×C4×C151—42no—
110C22×C4×C151—42no—
111C22×C4×C151—82no—
112C22×C4×C151C2×D412yes—
113C22×C4×C151C2×D412yes—
114C22×C4×C151C2×D411yescharacteristic
115C22×C4×C151C2×D412yes—
116C22×C4×C151#4112yes—
117C22×C4×C151C2411yescharacteristic
118C2×C8×C151—28no—
119C2×C8×C151—22no—
120C2×C8×C151—22no—
121C2×C8×C151—21no—
122C2×C8×C151—21no—
123C2×C8×C151—22no—
124C2×C8×C151—22no—
125C2×C8×C151#4114yes—
126C4⋊C4×C151—24no—
127C4⋊C4×C151—21no—
128C4⋊C4×C151—21no—
129C4⋊C4×C151—22no—
130C4⋊C4×C151—21no—
131C4⋊C4×C151—22no—
132C4⋊C4×C151—22no—
133C4⋊C4×C151—21no—
134C4⋊C4×C151—22no—
135C4⋊C4×C151—44no—
136C4⋊C4×C151—42no—
137C4⋊C4×C151C2×D412yes—
138C4⋊C4×C151C2×D412yes—
139C22⋊C4×C151—22no—
140C22⋊C4×C151—22no—
141C22⋊C4×C151—42no—
142C22⋊C4×C151—42no—
143C22⋊C4×C151—82no—
144C22⋊C4×C151—82no—
145C42×C151—22no—
146C42×C151—22no—
147C42×C151—44no—
148C23×C151—22no—
149C23×C151—22no—
150C23×C151—41no—
151C23×C151—42no—
152C23×C151—41no—
153C23×C151—41no—
154C23×C151—42no—
155C23×C151#12112yes—
156C23×C151#13512yes—
157C23×C151AGL(1,ℤ/8)12yes—
158C23×C151C22×D411yescharacteristic
159D4×C151—41no—
160D4×C151—41no—
161D4×C151—42no—
162D4×C151—84no—
163C2×C4×C151—22no—
164C2×C4×C151—22no—
165C2×C4×C151—22no—
166C2×C4×C151—24no—
167C2×C4×C151—22no—
168C2×C4×C151—22no—
169C2×C4×C151—22no—
170C2×C4×C151—22no—
171C2×C4×C151—22no—
172C2×C4×C151—22no—
173C2×C4×C151—22no—
174C2×C4×C151—22no—
175C2×C4×C151—41no—
176C2×C4×C151—41no—
177C2×C4×C151—41no—
178C2×C4×C151—41no—
179C2×C4×C151—48no—
180C2×C4×C151—41no—
181C2×C4×C151—42no—
182C2×C4×C151—42no—
183C2×C4×C151—41no—
184C2×C4×C151—42no—
185C2×C4×C151—41no—
186C2×C4×C151—42no—
187C2×C4×C151—42no—
188C2×C4×C151—42no—
189C2×C4×C151—84no—
190C2×C4×C151#12112yes—
191C2×C4×C151C22×D411yescharacteristic
192C2×C4×C151C2×#4112yes—
193C2×C4×C151C2×#4111yescharacteristic
194C2×C4×C1512−1+412yes—
195C8×C151—24no—
196C8×C151—41no—
197C8×C151—41no—
198C22×C151—24no—
199C22×C151—24no—
200C22×C151—22no—
201C22×C151—22no—
202C22×C151—82no—
203C22×C151—82no—
204C22×C151—81no—
205C22×C151—81no—
206C22×C151—81no—
207C22×C151#46314yes—
208C22×C151C2×#12111yescharacteristic
209C22×C151#54712yes—
210C22×C151C2×#13511yescharacteristic
211C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
212C22×C151#57712yes—
213C4×C151—22no—
214C4×C151—42no—
215C4×C151—42no—
216C4×C151—42no—
217C4×C151—42no—
218C4×C151—82no—
219C4×C151—81no—
220C4×C151—82no—
221C4×C151#52511yescharacteristic
222C4×C151#53611yescharacteristic
223C4×C151#55212yes—
224C2×C151—24no—
225C2×C151—161no—
226C2×C151#241311yescharacteristic
227C2×C151C2×#46311yescharacteristic
228C2×C151#304311yescharacteristic
229C2×C151#333712yes—
230C2×C151#334512yes—
231#24581C15111yesmaximal, characteristic, direct product factor, Sylow
232C151#2458111yescharacteristic, direct product factor, Sylow
233C2×#480C2×C15111yescharacteristic
234C22×#106C2×C15111yescharacteristic, complemented
235#2504C2×C15111yescharacteristic
236#2344C2×C15111yescharacteristic, complemented
237#2085C2×C15112yescomplemented
238#2065C2×C15112yescomplemented
239#1949C2×C15112yescomplemented
240#1926C2×C15112yescomplemented
241#1893C2×C15111yescharacteristic
242#1850C2×C15111yescharacteristic, complemented
243#1824C2×C15111yescharacteristic, complemented
244C23×C8C22×C15111yescharacteristic
245C2×#121C22×C15111yescharacteristic
246C2×#117—21no—
247C22×C4⋊C4C22×C15111yescharacteristic
248C22×C4⋊C4C22×C15111yescharacteristic
249#480—24no—
250C2×#107C22×C15111yescharacteristic
251C2×#107C22×C15111yescharacteristic
252C2×#106—24no—
253C2×#106C22×C15112yes—
254C2×#106C22×C15112yes—
255C2×C4⋊C8C22×C15112yes—
256C2×#102C22×C15111yescharacteristic
257C2×#102C22×C15111yescharacteristic
258C2×#102C22×C15112yes—
259C2×C22⋊C8C22×C15111yescharacteristic
260#397—22no—
261#390C22×C15112yes—
262#389C22×C15112yes—
263#387—22no—
264#386—21no—
265#386—21no—
266#382C22×C15112yes—
267#381—21no—
268#380C22×C15111yescharacteristic
269C4×C4⋊C4C22×C15112yes—
270C4×C22⋊C4C22×C15111yescharacteristic
271#340C22×C15112yes—
272#340C22×C15112yes—
273#340C22×C15112yes—
274#336C22×C15112yes—
275C22×D4—21no—
276C22×D4C23×C15111yescharacteristic
277C23×C4—21no—
278C23×C4—21no—
279C23×C4C23×C15111yescharacteristic
280C22×C8—22no—
281C22×C8—24no—
282C22×C8C23×C15111yescharacteristic
283C22×C8C23×C15111yescharacteristic
284C22×C8C23×C15112yes—
285#121—22no—
286#121—22no—
287#117—44no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4D4×C15114yes—
295C2×C4⋊C4C23×C15112yes—
296C2×C4⋊C4C23×C15111yescharacteristic
297C2×C4⋊C4C23×C15112yes—
298C2×C4⋊C4C23×C15111yescharacteristic
299C2×C4⋊C4C23×C15111yescharacteristic
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—22no—
304C2×C22⋊C4D4×C15111yescharacteristic
305C2×C22⋊C4D4×C15111yescharacteristic
306C2×C42—22no—
307C2×C42C23×C15112yes—
308#107—22no—
309#107—22no—
310#106—24no—
311#106—24no—
312C4⋊C8—24no—
313#102—24no—
314#102—22no—
315#102—22no—
316C22⋊C8—22no—
317#95—22no—
318#95—21no—
319#95—22no—
320#95—22no—
321#95—22no—
322#95D4×C15112yes—
323C24—21no—
324C24C2×D4×C15111yescharacteristic
325C2×D4—21no—
326C2×D4—22no—
327C2×D4—21no—
328C2×D4—22no—
329C2×D4—42no—
330C2×D4—42no—
331C2×D4—42no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—24no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—82no—
344C22×C4C2×D4×C15112yes—
345C22×C4C2×D4×C15112yes—
346C22×C4C2×D4×C15111yescharacteristic
347C22×C4C2×D4×C15112yes—
348C22×C4#41×C15112yes—
349C22×C4C24×C15111yescharacteristic
350C2×C8—28no—
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—21no—
354C2×C8—21no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8#41×C15114yes—
358C4⋊C4—24no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—22no—
362C4⋊C4—21no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—21no—
366C4⋊C4—22no—
367C4⋊C4—44no—
368C4⋊C4—42no—
369C4⋊C4C2×D4×C15112yes—
370C4⋊C4C2×D4×C15112yes—
371C22⋊C4—22no—
372C22⋊C4—22no—
373C22⋊C4—42no—
374C22⋊C4—42no—
375C22⋊C4—82no—
376C22⋊C4—82no—
377C42—22no—
378C42—22no—
379C42—44no—
380C23—22no—
381C23—22no—
382C23—41no—
383C23—42no—
384C23—41no—
385C23—41no—
386C23—42no—
387C23#121×C15112yes—
388C23#135×C15112yes—
389C23AGL(1,ℤ/8)×C15112yes—
390C23C22×D4×C15111yescharacteristic
391D4—41no—
392D4—41no—
393D4—42no—
394D4—84no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—24no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—48no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—84no—
422C2×C4#121×C15112yes—
423C2×C4C22×D4×C15111yescharacteristic
424C2×C4C2×#41×C15112yes—
425C2×C4C2×#41×C15111yescharacteristic
426C2×C42−1+4×C15112yes—
427C8—24no—
428C8—41no—
429C8—41no—
430C22—22no—
431C22—22no—
432C22—24no—
433C22—24no—
434C22—81no—
435C22—81no—
436C22—81no—
437C22—82no—
438C22—82no—
439C22#463×C15114yes—
440C22C2×#121×C15111yescharacteristic
441C22#547×C15112yes—
442C22C2×#135×C15111yescharacteristic
443C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
444C22#577×C15112yes—
445C4—22no—
446C4—42no—
447C4—42no—
448C4—42no—
449C4—42no—
450C4—81no—
451C4—82no—
452C4—82no—
453C4#525×C15111yescharacteristic
454C4#536×C15111yescharacteristic
455C4#552×C15112yes—
456C2—24no—
457C2—161no—
458C2#2413×C15111yescharacteristic
459C2C2×#463×C15111yescharacteristic
460C2#3043×C15111yescharacteristic
461C2#3337×C15112yes—
462C2#3345×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×#106×C151C2semidirect
4. #2344×C151C2semidirect
5. #2085×C151C2semidirect
6. #2065×C151C2semidirect
7. #1949×C151C2semidirect
8. #1926×C151C2semidirect
10. #1850×C151C2semidirect
11. #1824×C151C2semidirect
231. #24581C151direct (N × H)
232. C151#24581direct (N × H)
234. C22×#106C2×C151semidirect
236. #2344C2×C151semidirect
237. #2085C2×C151semidirect
238. #2065C2×C151semidirect
239. #1949C2×C151semidirect
240. #1926C2×C151semidirect
242. #1850C2×C151semidirect
243. #1824C2×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×#106×C1512
#2504×C1512
#2344×C1512
#2085×C1512
#2065×C1512
#1949×C1512
#1926×C1512
#1893×C1512
#1850×C1512
#1824×C1512
#24581151