Finite Group Databasebeta

← C151×#24529 #50329454

Subgroups — C151×#24529 #50329454

Order 38656.

966 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#451×C151C211yesmaximal, characteristic
2C22×#103×C151C211yesmaximal, characteristic
3#2503×C151C211yesmaximal, characteristic
4Q8×C22⋊C4×C151C211yesmaximal, characteristic
5#2074×C151C212yesmaximal, complemented
6#2056×C151C212yesmaximal, complemented
7#1892×C151C211yesmaximal, characteristic
8#1878×C151C212yesmaximal, complemented
9#1850×C151C211yesmaximal, characteristic
10#1823×C151C211yesmaximal, characteristic
11#1805×C151C212yesmaximal, complemented
12C23×Q8×C151C2211yescharacteristic
13C22×Q16×C151C2211yescharacteristic
14C22×Q16×C151C2211yescharacteristic
15C23×C8×C151C2211yescharacteristic
16C2×C22⋊Q8×C151C2211yescharacteristic
17C2×C4×Q8×C151C2212yes—
18C22×C4⋊C4×C151C2211yescharacteristic
19#451×C151—24no—
20C2×C4⋊C8×C151C2212yes—
21C2×#103×C151—24no—
22C2×#103×C151C2212yes—
23C2×#103×C151C2212yes—
24C2×#103×C151C2211yescharacteristic
25C2×#103×C151C2211yescharacteristic
26C2×#103×C151C2212yes—
27C2×C22⋊C8×C151C2211yescharacteristic
28#400×C151—22no—
29#391×C151—22no—
30#391×C151C2212yes—
31#391×C151C2212yes—
32#382×C151C2212yes—
33#381×C151—21no—
34#381×C151—21no—
35#380×C151—21no—
36#380×C151C2211yescharacteristic
37C4×C22⋊C4×C151—21no—
38C4×C22⋊C4×C151C2211yescharacteristic
39#340×C151C2212yes—
40#340×C151C2212yes—
41#340×C151C2212yes—
42#336×C151C2212yes—
43C22×Q8×C151—24no—
44C22×Q8×C151—21no—
45C22×Q8×C151—22no—
46C22×Q8×C151—42no—
47C22×Q8×C151D414yes—
48C22×Q8×C151C2311yescharacteristic
49C22×Q8×C151C2311yescharacteristic
50C22×Q8×C151C2311yescharacteristic
51C23×C4×C151—21no—
52C23×C4×C151—21no—
53C23×C4×C151C2311yescharacteristic
54C2×Q16×C151—22no—
55C2×Q16×C151—22no—
56C2×Q16×C151—24no—
57C2×Q16×C151—42no—
58C22×C8×C151—22no—
59C22×C8×C151—42no—
60C22×C8×C151C2311yescharacteristic
61C22×C8×C151C2312yes—
62C22×C8×C151C2311yescharacteristic
63C22⋊Q8×C151—22no—
64C22⋊Q8×C151—22no—
65C4×Q8×C151—24no—
66C4×Q8×C151—42no—
67C2×C4⋊C4×C151—22no—
68C2×C4⋊C4×C151—22no—
69C2×C4⋊C4×C151—22no—
70C2×C4⋊C4×C151—21no—
71C2×C4⋊C4×C151—21no—
72C2×C4⋊C4×C151C2312yes—
73C2×C4⋊C4×C151C2311yescharacteristic
74C2×C4⋊C4×C151C2312yes—
75C2×C22⋊C4×C151—21no—
76C2×C22⋊C4×C151—21no—
77C2×C22⋊C4×C151D411yescharacteristic
78C2×C22⋊C4×C151D411yescharacteristic
79C2×C42×C151—22no—
80C2×C42×C151C2312yes—
81C4⋊C8×C151—42no—
82#103×C151—24no—
83#103×C151—24no—
84#103×C151—22no—
85#103×C151—22no—
86#103×C151—42no—
87C22⋊C8×C151—22no—
88#95×C151—22no—
89#95×C151—22no—
90#95×C151—21no—
91#95×C151—22no—
92#95×C151—22no—
93#95×C151—22no—
94#95×C151—22no—
95#95×C151D412yes—
96C24×C151C2×D411yescharacteristic
97C2×Q8×C151—24no—
98C2×Q8×C151—21no—
99C2×Q8×C151—21no—
100C2×Q8×C151—22no—
101C2×Q8×C151—28no—
102C2×Q8×C151—21no—
103C2×Q8×C151—22no—
104C2×Q8×C151—21no—
105C2×Q8×C151—22no—
106C2×Q8×C151—22no—
107C2×Q8×C151—22no—
108C2×Q8×C151—44no—
109C2×Q8×C151—44no—
110C2×Q8×C151—48no—
111C2×Q8×C151C2×D412yes—
112C2×Q8×C151C2×D412yes—
113C2×Q8×C151#4114yes—
114C22×C4×C151—21no—
115C22×C4×C151—22no—
116C22×C4×C151—22no—
117C22×C4×C151—24no—
118C22×C4×C151—21no—
119C22×C4×C151—21no—
120C22×C4×C151—21no—
121C22×C4×C151—22no—
122C22×C4×C151—22no—
123C22×C4×C151—44no—
124C22×C4×C151—42no—
125C22×C4×C151—42no—
126C22×C4×C151—42no—
127C22×C4×C151C2×D412yes—
128C22×C4×C151C2×D412yes—
129C22×C4×C151C2×D411yescharacteristic
130C22×C4×C151C2×D412yes—
131C22×C4×C151#4112yes—
132C22×C4×C151C2411yescharacteristic
133Q16×C151—44no—
134Q16×C151—44no—
135C2×C8×C151—21no—
136C2×C8×C151—21no—
137C2×C8×C151—22no—
138C2×C8×C151—22no—
139C2×C8×C151—22no—
140C2×C8×C151—22no—
141C2×C8×C151—22no—
142C2×C8×C151—44no—
143C4⋊C4×C151—22no—
144C4⋊C4×C151—21no—
145C4⋊C4×C151—22no—
146C4⋊C4×C151—22no—
147C4⋊C4×C151—21no—
148C4⋊C4×C151—22no—
149C4⋊C4×C151—44no—
150C4⋊C4×C151—42no—
151C4⋊C4×C151—42no—
152C22⋊C4×C151—22no—
153C22⋊C4×C151—22no—
154C22⋊C4×C151—42no—
155C22⋊C4×C151—42no—
156C42×C151—22no—
157C42×C151—22no—
158C42×C151—44no—
159C23×C151—22no—
160C23×C151—22no—
161C23×C151#12112yes—
162C23×C151#13512yes—
163C23×C151#13712yes—
164C23×C151C22×D411yescharacteristic
165Q8×C151—22no—
166Q8×C151—24no—
167Q8×C151—22no—
168Q8×C151—22no—
169Q8×C151—48no—
170Q8×C151—42no—
171Q8×C151—41no—
172Q8×C151—41no—
173Q8×C151—42no—
174Q8×C151#12314yes—
175C2×C4×C151—22no—
176C2×C4×C151—24no—
177C2×C4×C151—22no—
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—22no—
185C2×C4×C151—22no—
186C2×C4×C151—22no—
187C2×C4×C151—22no—
188C2×C4×C151—48no—
189C2×C4×C151—42no—
190C2×C4×C151—41no—
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—42no—
199C2×C4×C151—42no—
200C2×C4×C151—84no—
201C2×C4×C151#12112yes—
202C2×C4×C151C22×D411yescharacteristic
203C2×C4×C151C2×#4112yes—
204C2×C4×C151C2×#4111yescharacteristic
205C2×C4×C151H(5,𝔽2)12yes—
206C8×C151—41no—
207C8×C151—42no—
208C8×C151—41no—
209C22×C151—22no—
210C22×C151—22no—
211C22×C151—24no—
212C22×C151—24no—
213C22×C151#46414yes—
214C22×C151C2×#12111yescharacteristic
215C22×C151#54612yes—
216C22×C151C2×#13511yescharacteristic
217C22×C151C2×#13711yescharacteristic
218C22×C151#57812yes—
219C4×C151—22no—
220C4×C151—24no—
221C4×C151—42no—
222C4×C151—42no—
223C4×C151—42no—
224C4×C151—81no—
225C4×C151—82no—
226C4×C151—81no—
227C4×C151—82no—
228C4×C151C2×#12311yescharacteristic
229C4×C151#53411yescharacteristic
230C4×C151#55112yes—
231C2×C151—24no—
232C2×C151#241211yescharacteristic
233C2×C151C2×#46411yescharacteristic
234C2×C151#304411yescharacteristic
235C2×C151#330012yes—
236C2×C151#331212yes—
237#24529C15111yesmaximal, characteristic, direct product factor, Sylow
238C151#2452911yescharacteristic, direct product factor, Sylow
239C2×#451C2×C15111yescharacteristic
240C22×#103C2×C15111yescharacteristic
241#2503C2×C15111yescharacteristic
242Q8×C22⋊C4C2×C15111yescharacteristic
243#2074C2×C15112yescomplemented
244#2056C2×C15112yescomplemented
245#1892C2×C15111yescharacteristic
246#1878C2×C15112yescomplemented
247#1850C2×C15111yescharacteristic
248#1823C2×C15111yescharacteristic
249#1805C2×C15112yescomplemented
250C23×Q8C22×C15111yescharacteristic
251C22×Q16C22×C15111yescharacteristic
252C22×Q16C22×C15111yescharacteristic
253C23×C8C22×C15111yescharacteristic
254C2×C22⋊Q8C22×C15111yescharacteristic
255C2×C4×Q8C22×C15112yes—
256C22×C4⋊C4C22×C15111yescharacteristic
257#451—24no—
258C2×C4⋊C8C22×C15112yes—
259C2×#103—24no—
260C2×#103C22×C15112yes—
261C2×#103C22×C15111yescharacteristic
262C2×#103C22×C15112yes—
263C2×#103C22×C15111yescharacteristic
264C2×#103C22×C15112yes—
265C2×C22⋊C8C22×C15111yescharacteristic
266#400—22no—
267#391—22no—
268#391C22×C15112yes—
269#391C22×C15112yes—
270#382C22×C15112yes—
271#381—21no—
272#381—21no—
273#380—21no—
274#380C22×C15111yescharacteristic
275C4×C22⋊C4—21no—
276C4×C22⋊C4C22×C15111yescharacteristic
277#340C22×C15112yes—
278#340C22×C15112yes—
279#340C22×C15112yes—
280#336C22×C15112yes—
281C22×Q8—22no—
282C22×Q8—21no—
283C22×Q8—24no—
284C22×Q8—42no—
285C22×Q8D4×C15114yes—
286C22×Q8C23×C15111yescharacteristic
287C22×Q8C23×C15111yescharacteristic
288C22×Q8C23×C15111yescharacteristic
289C23×C4—21no—
290C23×C4—21no—
291C23×C4C23×C15111yescharacteristic
292C2×Q16—24no—
293C2×Q16—22no—
294C2×Q16—22no—
295C2×Q16—42no—
296C22×C8—22no—
297C22×C8—42no—
298C22×C8C23×C15112yes—
299C22×C8C23×C15111yescharacteristic
300C22×C8C23×C15111yescharacteristic
301C22⋊Q8—22no—
302C22⋊Q8—22no—
303C4×Q8—24no—
304C4×Q8—42no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4C23×C15112yes—
311C2×C4⋊C4C23×C15112yes—
312C2×C4⋊C4C23×C15111yescharacteristic
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4D4×C15111yescharacteristic
316C2×C22⋊C4D4×C15111yescharacteristic
317C2×C42—22no—
318C2×C42C23×C15112yes—
319C4⋊C8—42no—
320#103—24no—
321#103—24no—
322#103—22no—
323#103—22no—
324#103—42no—
325C22⋊C8—22no—
326#95—22no—
327#95—22no—
328#95—21no—
329#95—22no—
330#95—22no—
331#95—22no—
332#95—22no—
333#95D4×C15112yes—
334C24C2×D4×C15111yescharacteristic
335C2×Q8—24no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—22no—
339C2×Q8—28no—
340C2×Q8—21no—
341C2×Q8—22no—
342C2×Q8—21no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—44no—
347C2×Q8—44no—
348C2×Q8—48no—
349C2×Q8C2×D4×C15112yes—
350C2×Q8C2×D4×C15112yes—
351C2×Q8#41×C15114yes—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—24no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—44no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4C2×D4×C15112yes—
366C22×C4C2×D4×C15112yes—
367C22×C4C2×D4×C15111yescharacteristic
368C22×C4C2×D4×C15112yes—
369C22×C4#41×C15112yes—
370C22×C4C24×C15111yescharacteristic
371Q16—44no—
372Q16—44no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—44no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—44no—
388C4⋊C4—42no—
389C4⋊C4—42no—
390C22⋊C4—22no—
391C22⋊C4—22no—
392C22⋊C4—42no—
393C22⋊C4—42no—
394C42—22no—
395C42—22no—
396C42—44no—
397C23—22no—
398C23—22no—
399C23#121×C15112yes—
400C23#135×C15112yes—
401C23#137×C15112yes—
402C23C22×D4×C15111yescharacteristic
403Q8—22no—
404Q8—24no—
405Q8—22no—
406Q8—22no—
407Q8—48no—
408Q8—42no—
409Q8—41no—
410Q8—41no—
411Q8—42no—
412Q8#123×C15114yes—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—24no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—48no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—84no—
439C2×C4#121×C15112yes—
440C2×C4C22×D4×C15111yescharacteristic
441C2×C4C2×#41×C15112yes—
442C2×C4C2×#41×C15111yescharacteristic
443C2×C4H(5,𝔽2)×C15112yes—
444C8—41no—
445C8—42no—
446C8—41no—
447C22—22no—
448C22—22no—
449C22—24no—
450C22—24no—
451C22#464×C15114yes—
452C22C2×#121×C15111yescharacteristic
453C22#546×C15112yes—
454C22C2×#135×C15111yescharacteristic
455C22C2×#137×C15111yescharacteristic
456C22#578×C15112yes—
457C4—22no—
458C4—24no—
459C4—42no—
460C4—42no—
461C4—42no—
462C4—81no—
463C4—82no—
464C4—81no—
465C4—82no—
466C4C2×#123×C15111yescharacteristic
467C4#534×C15111yescharacteristic
468C4#551×C15112yes—
469C2—24no—
470C2#2412×C15111yescharacteristic
471C2C2×#464×C15111yescharacteristic
472C2#3044×C15111yescharacteristic
473C2#3300×C15112yes—
474C2#3312×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. #2074×C151C2semidirect
6. #2056×C151C2semidirect
8. #1878×C151C2semidirect
11. #1805×C151C2semidirect
237. #24529C151direct (N × H)
238. C151#24529direct (N × H)
243. #2074C2×C151semidirect
244. #2056C2×C151semidirect
246. #1878C2×C151semidirect
249. #1805C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#451×C1512
C22×#103×C1512
#2503×C1512
Q8×C22⋊C4×C1512
#2074×C1512
#2056×C1512
#1892×C1512
#1878×C1512
#1850×C1512
#1823×C1512
#1805×C1512
#24529151