Finite Group Databasebeta

← C151×#24482 #50329407

Subgroups — C151×#24482 #50329407

Order 38656.

958 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#484×C151C211yesmaximal, characteristic
2C22×#103×C151C211yesmaximal, characteristic
3#2434×C151C211yesmaximal, characteristic
4#2345×C151C211yesmaximal, characteristic
5#2068×C151C212yesmaximal, complemented
6#2043×C151C212yesmaximal, complemented
7#1981×C151C212yesmaximal, complemented
8#1928×C151C212yesmaximal, complemented
9#1892×C151C211yesmaximal, characteristic
10#1850×C151C211yesmaximal, characteristic
11#1787×C151C211yesmaximal, characteristic
12C23×Q8×C151C2211yescharacteristic
13C23×C8×C151C2211yescharacteristic
14C2×C4⋊Q8×C151C2212yes—
15C2×C22⋊Q8×C151C2211yescharacteristic
16C22×C4⋊C4×C151C2211yescharacteristic
17#484×C151—24no—
18C2×#107×C151C2211yescharacteristic
19C2×#107×C151C2211yescharacteristic
20C2×C4⋊C8×C151C2212yes—
21C2×#103×C151—24no—
22C2×#103×C151C2212yes—
23C2×#103×C151C2212yes—
24C2×#103×C151C2212yes—
25C2×#103×C151C2211yescharacteristic
26C2×#103×C151C2211yescharacteristic
27C2×#103×C151C2212yes—
28C2×#103×C151C2212yes—
29C2×C22⋊C8×C151C2211yescharacteristic
30#395×C151—22no—
31#391×C151C2212yes—
32#389×C151C2212yes—
33#387×C151—22no—
34#385×C151—21no—
35#385×C151—21no—
36#380×C151—21no—
37#380×C151C2211yescharacteristic
38C4×C4⋊C4×C151C2212yes—
39C4×C22⋊C4×C151—21no—
40C4×C22⋊C4×C151C2211yescharacteristic
41#340×C151C2212yes—
42#336×C151C2212yes—
43C22×Q8×C151—22no—
44C22×Q8×C151—24no—
45C22×Q8×C151—22no—
46C22×Q8×C151—21no—
47C22×Q8×C151—42no—
48C22×Q8×C151C2311yescharacteristic
49C22×Q8×C151C2312yes—
50C23×C4×C151—21no—
51C23×C4×C151—21no—
52C23×C4×C151C2311yescharacteristic
53C22×C8×C151—22no—
54C22×C8×C151—42no—
55C22×C8×C151C2311yescharacteristic
56C22×C8×C151C2312yes—
57C22×C8×C151C2311yescharacteristic
58C4⋊Q8×C151—24no—
59C4⋊Q8×C151—42no—
60C22⋊Q8×C151—22no—
61C22⋊Q8×C151—22no—
62C2×C4⋊C4×C151—21no—
63C2×C4⋊C4×C151—22no—
64C2×C4⋊C4×C151—22no—
65C2×C4⋊C4×C151—22no—
66C2×C4⋊C4×C151—21no—
67C2×C4⋊C4×C151—22no—
68C2×C4⋊C4×C151D414yes—
69C2×C4⋊C4×C151C2311yescharacteristic
70C2×C4⋊C4×C151C2312yes—
71C2×C4⋊C4×C151C2311yescharacteristic
72C2×C4⋊C4×C151C2311yescharacteristic
73C2×C22⋊C4×C151—21no—
74C2×C22⋊C4×C151—21no—
75C2×C22⋊C4×C151D411yescharacteristic
76C2×C22⋊C4×C151D411yescharacteristic
77C2×C42×C151—22no—
78C2×C42×C151C2312yes—
79#107×C151—22no—
80#107×C151—22no—
81C4⋊C8×C151—42no—
82#103×C151—24no—
83#103×C151—24no—
84#103×C151—22no—
85#103×C151—22no—
86#103×C151—24no—
87#103×C151—42no—
88#103×C151—42no—
89C22⋊C8×C151—22no—
90#95×C151—22no—
91#95×C151—22no—
92#95×C151—21no—
93#95×C151—22no—
94#95×C151—22no—
95#95×C151D412yes—
96C24×C151C2×D411yescharacteristic
97C2×Q8×C151—22no—
98C2×Q8×C151—28no—
99C2×Q8×C151—22no—
100C2×Q8×C151—21no—
101C2×Q8×C151—22no—
102C2×Q8×C151—22no—
103C2×Q8×C151—21no—
104C2×Q8×C151—22no—
105C2×Q8×C151—22no—
106C2×Q8×C151—22no—
107C2×Q8×C151—44no—
108C2×Q8×C151—48no—
109C2×Q8×C151—44no—
110C2×Q8×C151—42no—
111C2×Q8×C151#4114yes—
112C22×C4×C151—22no—
113C22×C4×C151—22no—
114C22×C4×C151—21no—
115C22×C4×C151—21no—
116C22×C4×C151—22no—
117C22×C4×C151—24no—
118C22×C4×C151—21no—
119C22×C4×C151—22no—
120C22×C4×C151—21no—
121C22×C4×C151—44no—
122C22×C4×C151—42no—
123C22×C4×C151—82no—
124C22×C4×C151C2×D412yes—
125C22×C4×C151C2×D411yescharacteristic
126C22×C4×C151C2×D412yes—
127C22×C4×C151C2×D412yes—
128C22×C4×C151#4112yes—
129C22×C4×C151C2411yescharacteristic
130C2×C8×C151—21no—
131C2×C8×C151—21no—
132C2×C8×C151—22no—
133C2×C8×C151—22no—
134C2×C8×C151—22no—
135C2×C8×C151—22no—
136C2×C8×C151—22no—
137C2×C8×C151—44no—
138C4⋊C4×C151—24no—
139C4⋊C4×C151—21no—
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—82no—
149C4⋊C4×C151C2×D412yes—
150C4⋊C4×C151C2×D412yes—
151C22⋊C4×C151—22no—
152C22⋊C4×C151—42no—
153C22⋊C4×C151—42no—
154C22⋊C4×C151Q1614yes—
155C42×C151—22no—
156C42×C151—22no—
157C42×C151—82no—
158C23×C151—22no—
159C23×C151—22no—
160C23×C151#12112yes—
161C23×C151C2×Q1612yes—
162C23×C151#13712yes—
163C23×C151C22×D411yescharacteristic
164Q8×C151—24no—
165Q8×C151—24no—
166Q8×C151—48no—
167Q8×C151—42no—
168Q8×C151—42no—
169Q8×C151—41no—
170Q8×C151—41no—
171Q8×C151—42no—
172C2×C4×C151—22no—
173C2×C4×C151—22no—
174C2×C4×C151—22no—
175C2×C4×C151—22no—
176C2×C4×C151—22no—
177C2×C4×C151—24no—
178C2×C4×C151—22no—
179C2×C4×C151—22no—
180C2×C4×C151—24no—
181C2×C4×C151—22no—
182C2×C4×C151—22no—
183C2×C4×C151—22no—
184C2×C4×C151—48no—
185C2×C4×C151—42no—
186C2×C4×C151—42no—
187C2×C4×C151—42no—
188C2×C4×C151—42no—
189C2×C4×C151—41no—
190C2×C4×C151—41no—
191C2×C4×C151—42no—
192C2×C4×C151—42no—
193C2×C4×C151—42no—
194C2×C4×C151—42no—
195C2×C4×C151—42no—
196C2×C4×C151—84no—
197C2×C4×C151#12112yes—
198C2×C4×C151C2×Q1614yes—
199C2×C4×C151C22×D411yescharacteristic
200C2×C4×C151C2×#4112yes—
201C2×C4×C151C2×#4111yescharacteristic
202C2×C4×C151H(5,𝔽2)12yes—
203C8×C151—41no—
204C8×C151—41no—
205C8×C151—42no—
206C22×C151—22no—
207C22×C151—22no—
208C22×C151—24no—
209C22×C151—24no—
210C22×C151#46214yes—
211C22×C151C2×#12111yescharacteristic
212C22×C151#54612yes—
213C22×C151C22×Q1611yescharacteristic
214C22×C151C2×#13711yescharacteristic
215C22×C151#57712yes—
216C4×C151—22no—
217C4×C151—24no—
218C4×C151—44no—
219C4×C151—42no—
220C4×C151—42no—
221C4×C151—42no—
222C4×C151—81no—
223C4×C151—81no—
224C4×C151—82no—
225C4×C151#52511yescharacteristic
226C4×C151#53511yescharacteristic
227C4×C151#55112yes—
228C2×C151—24no—
229C2×C151#241111yescharacteristic
230C2×C151C2×#46211yescharacteristic
231C2×C151#304211yescharacteristic
232C2×C151#329912yes—
233C2×C151#332012yes—
234#24482C15111yesmaximal, characteristic, direct product factor, Sylow
235C151#2448211yescharacteristic, direct product factor, Sylow
236C2×#484C2×C15111yescharacteristic
237C22×#103C2×C15111yescharacteristic
238#2434C2×C15111yescharacteristic
239#2345C2×C15111yescharacteristic
240#2068C2×C15112yescomplemented
241#2043C2×C15112yescomplemented
242#1981C2×C15112yescomplemented
243#1928C2×C15112yescomplemented
244#1892C2×C15111yescharacteristic
245#1850C2×C15111yescharacteristic
246#1787C2×C15111yescharacteristic
247C23×Q8C22×C15111yescharacteristic
248C23×C8C22×C15111yescharacteristic
249C2×C4⋊Q8C22×C15112yes—
250C2×C22⋊Q8C22×C15111yescharacteristic
251C22×C4⋊C4C22×C15111yescharacteristic
252#484—24no—
253C2×#107C22×C15111yescharacteristic
254C2×#107C22×C15111yescharacteristic
255C2×C4⋊C8C22×C15112yes—
256C2×#103—24no—
257C2×#103C22×C15111yescharacteristic
258C2×#103C22×C15111yescharacteristic
259C2×#103C22×C15112yes—
260C2×#103C22×C15112yes—
261C2×#103C22×C15112yes—
262C2×#103C22×C15112yes—
263C2×#103C22×C15112yes—
264C2×C22⋊C8C22×C15111yescharacteristic
265#395—22no—
266#391C22×C15112yes—
267#389C22×C15112yes—
268#387—22no—
269#385—21no—
270#385—21no—
271#380—21no—
272#380C22×C15111yescharacteristic
273C4×C4⋊C4C22×C15112yes—
274C4×C22⋊C4—21no—
275C4×C22⋊C4C22×C15111yescharacteristic
276#340C22×C15112yes—
277#336C22×C15112yes—
278C22×Q8—21no—
279C22×Q8—24no—
280C22×Q8—22no—
281C22×Q8—22no—
282C22×Q8—42no—
283C22×Q8C23×C15111yescharacteristic
284C22×Q8C23×C15112yes—
285C23×C4—21no—
286C23×C4—21no—
287C23×C4C23×C15111yescharacteristic
288C22×C8—22no—
289C22×C8—42no—
290C22×C8C23×C15112yes—
291C22×C8C23×C15111yescharacteristic
292C22×C8C23×C15111yescharacteristic
293C4⋊Q8—24no—
294C4⋊Q8—42no—
295C22⋊Q8—22no—
296C22⋊Q8—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4D4×C15114yes—
304C2×C4⋊C4C23×C15111yescharacteristic
305C2×C4⋊C4C23×C15112yes—
306C2×C4⋊C4C23×C15111yescharacteristic
307C2×C4⋊C4C23×C15111yescharacteristic
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4D4×C15111yescharacteristic
311C2×C22⋊C4D4×C15111yescharacteristic
312C2×C42—22no—
313C2×C42C23×C15112yes—
314#107—22no—
315#107—22no—
316C4⋊C8—42no—
317#103—24no—
318#103—24no—
319#103—24no—
320#103—22no—
321#103—22no—
322#103—42no—
323#103—42no—
324C22⋊C8—22no—
325#95—22no—
326#95—22no—
327#95—21no—
328#95—22no—
329#95—22no—
330#95D4×C15112yes—
331C24C2×D4×C15111yescharacteristic
332C2×Q8—22no—
333C2×Q8—28no—
334C2×Q8—22no—
335C2×Q8—21no—
336C2×Q8—22no—
337C2×Q8—22no—
338C2×Q8—21no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—44no—
343C2×Q8—48no—
344C2×Q8—44no—
345C2×Q8—42no—
346C2×Q8#41×C15114yes—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—24no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—21no—
356C22×C4—44no—
357C22×C4—42no—
358C22×C4—82no—
359C22×C4C2×D4×C15112yes—
360C22×C4C2×D4×C15111yescharacteristic
361C22×C4C2×D4×C15112yes—
362C22×C4C2×D4×C15112yes—
363C22×C4#41×C15112yes—
364C22×C4C24×C15111yescharacteristic
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—22no—
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—44no—
373C4⋊C4—24no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—22no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—44no—
381C4⋊C4—44no—
382C4⋊C4—42no—
383C4⋊C4—82no—
384C4⋊C4C2×D4×C15112yes—
385C4⋊C4C2×D4×C15112yes—
386C22⋊C4—22no—
387C22⋊C4—42no—
388C22⋊C4—42no—
389C22⋊C4Q16×C15114yes—
390C42—22no—
391C42—22no—
392C42—82no—
393C23—22no—
394C23—22no—
395C23#121×C15112yes—
396C23C2×Q16×C15112yes—
397C23#137×C15112yes—
398C23C22×D4×C15111yescharacteristic
399Q8—24no—
400Q8—24no—
401Q8—48no—
402Q8—42no—
403Q8—42no—
404Q8—41no—
405Q8—41no—
406Q8—42no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—24no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—24no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—48no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—84no—
432C2×C4#121×C15112yes—
433C2×C4C2×Q16×C15114yes—
434C2×C4C22×D4×C15111yescharacteristic
435C2×C4C2×#41×C15112yes—
436C2×C4C2×#41×C15111yescharacteristic
437C2×C4H(5,𝔽2)×C15112yes—
438C8—41no—
439C8—42no—
440C8—41no—
441C22—22no—
442C22—22no—
443C22—24no—
444C22—24no—
445C22#462×C15114yes—
446C22C2×#121×C15111yescharacteristic
447C22#546×C15112yes—
448C22C22×Q16×C15111yescharacteristic
449C22C2×#137×C15111yescharacteristic
450C22#577×C15112yes—
451C4—22no—
452C4—24no—
453C4—44no—
454C4—42no—
455C4—42no—
456C4—42no—
457C4—81no—
458C4—81no—
459C4—82no—
460C4#525×C15111yescharacteristic
461C4#535×C15111yescharacteristic
462C4#551×C15112yes—
463C2—24no—
464C2#2411×C15111yescharacteristic
465C2C2×#462×C15111yescharacteristic
466C2#3042×C15111yescharacteristic
467C2#3299×C15112yes—
468C2#3320×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC24×C151C2×D4
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
5. #2068×C151C2semidirect
6. #2043×C151C2semidirect
7. #1981×C151C2semidirect
8. #1928×C151C2semidirect
234. #24482C151direct (N × H)
235. C151#24482direct (N × H)
240. #2068C2×C151semidirect
241. #2043C2×C151semidirect
242. #1981C2×C151semidirect
243. #1928C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#484×C1512
C22×#103×C1512
#2434×C1512
#2345×C1512
#2068×C1512
#2043×C1512
#1981×C1512
#1928×C1512
#1892×C1512
#1850×C1512
#1787×C1512
#24482151