Finite Group Databasebeta

← C151×#21581 #50326506

Subgroups — C151×#21581 #50326506

Order 38656.

964 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#484×C151C211yesmaximal, characteristic
2C4×C22⋊Q8×C151C211yesmaximal, characteristic
3C2×C4×C4⋊C4×C151C211yesmaximal, characteristic
4#1927×C151C212yesmaximal, complemented
5#1918×C151C212yesmaximal, complemented
6#1872×C151C211yesmaximal, characteristic
7#1853×C151C211yesmaximal, characteristic
8#1824×C151C211yesmaximal, characteristic
9#1776×C151C212yesmaximal, complemented
10#1763×C151C212yesmaximal, complemented
11#1749×C151C211yesmaximal, characteristic
12C2×C22⋊Q8×C151C2211yescharacteristic
13C2×C4×Q8×C151C2211yescharacteristic
14C22×C4⋊C4×C151C2211yescharacteristic
15C22×C4⋊C4×C151C2211yescharacteristic
16C22×C42×C151—21no—
17C22×C42×C151C2211yescharacteristic
18#484×C151C418yescomplemented
19C2×#107×C151C2212yes—
20C2×#106×C151C2212yes—
21C2×#103×C151C2212yes—
22C2×#103×C151C2212yes—
23C2×C22⋊C8×C151C2211yescharacteristic
24C2×C22⋊C8×C151C2211yescharacteristic
25C2×#97×C151C2212yes—
26#391×C151C2211yescharacteristic
27#389×C151C2211yescharacteristic
28#387×C151—21no—
29#385×C151—21no—
30#380×C151C2211yescharacteristic
31C4×C4⋊C4×C151—21no—
32C4×C4⋊C4×C151—21no—
33C4×C4⋊C4×C151—21no—
34C4×C4⋊C4×C151C2212yes—
35C4×C4⋊C4×C151C2212yes—
36C4×C4⋊C4×C151C2211yescharacteristic
37C4×C22⋊C4×C151—21no—
38C2×#95×C151—21no—
39#340×C151C2212yes—
40#340×C151C2212yes—
41#340×C151C2212yes—
42#340×C151C2212yes—
43#336×C151C2212yes—
44C22×Q8×C151C2311yescharacteristic
45C23×C4×C151—21no—
46C23×C4×C151—21no—
47C23×C4×C151D411yescharacteristic
48C23×C4×C151D411yescharacteristic
49C23×C4×C151C2311yescharacteristic
50C22×C8×C151C2312yes—
51C22×C8×C151C2312yes—
52C22⋊Q8×C151—22no—
53C22⋊Q8×C151C2×C414yes—
54C4×Q8×C151—24no—
55C2×C4⋊C4×C151—21no—
56C2×C4⋊C4×C151—21no—
57C2×C4⋊C4×C151—21no—
58C2×C4⋊C4×C151—22no—
59C2×C4⋊C4×C151—24no—
60C2×C4⋊C4×C151—21no—
61C2×C4⋊C4×C151—21no—
62C2×C4⋊C4×C151C2×C414yes—
63C2×C4⋊C4×C151C2311yescharacteristic
64C2×C4⋊C4×C151C2311yescharacteristic
65C2×C4⋊C4×C151C2312yes—
66C2×C4⋊C4×C151C2311yescharacteristic
67C2×C4⋊C4×C151C2312yes—
68C2×C22⋊C4×C151—21no—
69C2×C22⋊C4×C151—21no—
70C2×C42×C151—24no—
71C2×C42×C151—21no—
72C2×C42×C151—21no—
73C2×C42×C151—22no—
74C2×C42×C151—22no—
75C2×C42×C151—44no—
76C2×C42×C151D411yescharacteristic
77C2×C42×C151D411yescharacteristic
78C2×C42×C151C2311yescharacteristic
79C2×C42×C151C2311yescharacteristic
80#107×C151C2×C418yescomplemented
81#106×C151—24no—
82#103×C151—24no—
83#103×C151C2×C418yescomplemented
84C22⋊C8×C151—22no—
85C22⋊C8×C151C2×C414yes—
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—
94C24×C151C2×D411yescharacteristic
95C2×Q8×C151—21no—
96C2×Q8×C151—22no—
97C2×Q8×C151—22no—
98C2×Q8×C151C22×C412yes—
99C22×C4×C151—22no—
100C22×C4×C151—22no—
101C22×C4×C151—22no—
102C22×C4×C151—22no—
103C22×C4×C151—22no—
104C22×C4×C151—24no—
105C22×C4×C151—24no—
106C22×C4×C151—22no—
107C22×C4×C151—22no—
108C22×C4×C151—22no—
109C22×C4×C151—21no—
110C22×C4×C151—21no—
111C22×C4×C151—22no—
112C22×C4×C151—21no—
113C22×C4×C151—21no—
114C22×C4×C151—41no—
115C22×C4×C151—42no—
116C22×C4×C151—42no—
117C22×C4×C151—42no—
118C22×C4×C151—42no—
119C22×C4×C151C22×C412yes—
120C22×C4×C151C2×D411yescharacteristic
121C22×C4×C151C2×D411yescharacteristic
122C22×C4×C151C2×D411yescharacteristic
123C22×C4×C151C2×D411yescharacteristic
124C22×C4×C151C2×D411yescharacteristic
125C22×C4×C151#4112yes—
126C22×C4×C151C2411yescharacteristic
127C2×C8×C151—22no—
128C2×C8×C151—22no—
129C2×C8×C151—22no—
130C2×C8×C151—22no—
131C2×C8×C151—22no—
132C2×C8×C151C22×C414yes—
133C4⋊C4×C151—24no—
134C4⋊C4×C151—24no—
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—42no—
142C4⋊C4×C151—42no—
143C4⋊C4×C151C22×C414yes—
144C4⋊C4×C151C22×C412yes—
145C4⋊C4×C151#4114yes—
146C22⋊C4×C151—24no—
147C22⋊C4×C151—42no—
148C42×C151—22no—
149C42×C151—22no—
150C42×C151—22no—
151C42×C151—42no—
152C42×C151—44no—
153C42×C151—42no—
154C42×C151—44no—
155C42×C151#4114yes—
156C23×C151—21no—
157C23×C151—21no—
158C23×C151—21no—
159C23×C151—21no—
160C23×C151C4×D412yes—
161C23×C151#13712yes—
162C23×C151#13712yes—
163C23×C151C22×D411yescharacteristic
164Q8×C151—24no—
165Q8×C151—42no—
166C2×C4×C151—28no—
167C2×C4×C151—21no—
168C2×C4×C151—21no—
169C2×C4×C151—21no—
170C2×C4×C151—21no—
171C2×C4×C151—21no—
172C2×C4×C151—21no—
173C2×C4×C151—21no—
174C2×C4×C151—21no—
175C2×C4×C151—24no—
176C2×C4×C151—24no—
177C2×C4×C151—22no—
178C2×C4×C151—22no—
179C2×C4×C151—24no—
180C2×C4×C151—21no—
181C2×C4×C151—24no—
182C2×C4×C151—21no—
183C2×C4×C151—21no—
184C2×C4×C151—44no—
185C2×C4×C151—48no—
186C2×C4×C151—48no—
187C2×C4×C151—41no—
188C2×C4×C151—41no—
189C2×C4×C151—42no—
190C2×C4×C151—42no—
191C2×C4×C151—41no—
192C2×C4×C151—42no—
193C2×C4×C151—41no—
194C2×C4×C151—42no—
195C2×C4×C151—41no—
196C2×C4×C151—41no—
197C2×C4×C151—41no—
198C2×C4×C151—41no—
199C2×C4×C151—41no—
200C2×C4×C151—41no—
201C2×C4×C151C4×D412yes—
202C2×C4×C151#12312yes—
203C2×C4×C151#12312yes—
204C2×C4×C151AGL(1,ℤ/8)12yes—
205C2×C4×C151C23×C411yescharacteristic
206C2×C4×C151C2×#4112yes—
207C2×C4×C151C2×#4112yes—
208C2×C4×C151C2×#4111yescharacteristic
209C8×C151—24no—
210C8×C151—42no—
211C22×C151—22no—
212C22×C151—22no—
213C22×C151—22no—
214C22×C151—22no—
215C22×C151—22no—
216C22×C151—22no—
217C22×C151#44114yes—
218C22×C151C2×C4×D411yescharacteristic
219C22×C151C2×#12311yescharacteristic
220C22×C151#52511yescharacteristic
221C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
222C22×C151C2×#13711yescharacteristic
223C22×C151C2×#13711yescharacteristic
224C22×C151#57511yescharacteristic
225C4×C151—22no—
226C4×C151—22no—
227C4×C151—22no—
228C4×C151—22no—
229C4×C151—41no—
230C4×C151—44no—
231C4×C151—42no—
232C4×C151—44no—
233C4×C151—42no—
234C4×C151—81no—
235C4×C151—81no—
236C4×C151C4×#4112yes—
237C4×C151#52912yes—
238C2×C151—24no—
239C2×C151C4×#12311yescharacteristic
240C2×C151C2×#44111yescharacteristic
241C2×C151C4×AGL(1,ℤ/8)11yescharacteristic
242C2×C151#309211yescharacteristic
243C2×C151#309511yescharacteristic
244C2×C151#311011yescharacteristic
245C2×C151#311711yescharacteristic
246#21581C15111yesmaximal, characteristic, direct product factor, Sylow
247C151#2158111yescharacteristic, direct product factor, Sylow
248C2×#484C2×C15111yescharacteristic
249C4×C22⋊Q8C2×C15111yescharacteristic
250C2×C4×C4⋊C4C2×C15111yescharacteristic
251#1927C2×C15112yescomplemented
252#1918C2×C15112yescomplemented
253#1872C2×C15111yescharacteristic
254#1853C2×C15111yescharacteristic
255#1824C2×C15111yescharacteristic
256#1776C2×C15112yescomplemented
257#1763C2×C15112yescomplemented
258#1749C2×C15111yescharacteristic
259C2×C22⋊Q8C22×C15111yescharacteristic
260C2×C4×Q8C22×C15111yescharacteristic
261C22×C4⋊C4C22×C15111yescharacteristic
262C22×C4⋊C4C22×C15111yescharacteristic
263C22×C42—21no—
264C22×C42C22×C15111yescharacteristic
265#484C4×C15118yescomplemented
266C2×#107C22×C15112yes—
267C2×#106C22×C15112yes—
268C2×#103C22×C15112yes—
269C2×#103C22×C15112yes—
270C2×C22⋊C8C22×C15111yescharacteristic
271C2×C22⋊C8C22×C15111yescharacteristic
272C2×#97C22×C15112yes—
273#391C22×C15111yescharacteristic
274#389C22×C15111yescharacteristic
275#387—21no—
276#385—21no—
277#380C22×C15111yescharacteristic
278C4×C4⋊C4—21no—
279C4×C4⋊C4—21no—
280C4×C4⋊C4—21no—
281C4×C4⋊C4C22×C15112yes—
282C4×C4⋊C4C22×C15112yes—
283C4×C4⋊C4C22×C15111yescharacteristic
284C4×C22⋊C4—21no—
285C2×#95—21no—
286#340C22×C15112yes—
287#340C22×C15112yes—
288#340C22×C15112yes—
289#340C22×C15112yes—
290#336C22×C15112yes—
291C22×Q8C23×C15111yescharacteristic
292C23×C4—21no—
293C23×C4—21no—
294C23×C4D4×C15111yescharacteristic
295C23×C4D4×C15111yescharacteristic
296C23×C4C23×C15111yescharacteristic
297C22×C8C23×C15112yes—
298C22×C8C23×C15112yes—
299C22⋊Q8—22no—
300C22⋊Q8C2×C4×C15114yes—
301C4×Q8—24no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4C2×C4×C15114yes—
310C2×C4⋊C4C23×C15111yescharacteristic
311C2×C4⋊C4C23×C15111yescharacteristic
312C2×C4⋊C4C23×C15112yes—
313C2×C4⋊C4C23×C15112yes—
314C2×C4⋊C4C23×C15111yescharacteristic
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C42—24no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—22no—
321C2×C42—22no—
322C2×C42—44no—
323C2×C42D4×C15111yescharacteristic
324C2×C42D4×C15111yescharacteristic
325C2×C42C23×C15111yescharacteristic
326C2×C42C23×C15111yescharacteristic
327#107C2×C4×C15118yescomplemented
328#106—24no—
329#103—24no—
330#103C2×C4×C15118yescomplemented
331C22⋊C8—22no—
332C22⋊C8C2×C4×C15114yes—
333#97—24no—
334#95—22no—
335#95—22no—
336#95—21no—
337#95—21no—
338#95—21no—
339#95—21no—
340#95—21no—
341C24C2×D4×C15111yescharacteristic
342C2×Q8—21no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8C22×C4×C15112yes—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—41no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4C22×C4×C15112yes—
367C22×C4C2×D4×C15111yescharacteristic
368C22×C4C2×D4×C15111yescharacteristic
369C22×C4C2×D4×C15111yescharacteristic
370C22×C4C2×D4×C15111yescharacteristic
371C22×C4C2×D4×C15111yescharacteristic
372C22×C4#41×C15112yes—
373C22×C4C24×C15111yescharacteristic
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8C22×C4×C15114yes—
380C4⋊C4—24no—
381C4⋊C4—24no—
382C4⋊C4—24no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—42no—
389C4⋊C4—42no—
390C4⋊C4C22×C4×C15114yes—
391C4⋊C4C22×C4×C15112yes—
392C4⋊C4#41×C15114yes—
393C22⋊C4—24no—
394C22⋊C4—42no—
395C42—22no—
396C42—22no—
397C42—22no—
398C42—44no—
399C42—42no—
400C42—42no—
401C42—44no—
402C42#41×C15114yes—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23C4×D4×C15112yes—
408C23#137×C15112yes—
409C23#137×C15112yes—
410C23C22×D4×C15111yescharacteristic
411Q8—24no—
412Q8—42no—
413C2×C4—28no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—24no—
427C2×C4—21no—
428C2×C4—24no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—44no—
432C2×C4—48no—
433C2×C4—48no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4C4×D4×C15112yes—
449C2×C4#123×C15112yes—
450C2×C4#123×C15112yes—
451C2×C4AGL(1,ℤ/8)×C15112yes—
452C2×C4C23×C4×C15111yescharacteristic
453C2×C4C2×#41×C15112yes—
454C2×C4C2×#41×C15112yes—
455C2×C4C2×#41×C15111yescharacteristic
456C8—24no—
457C8—42no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22#441×C15114yes—
465C22C2×C4×D4×C15111yescharacteristic
466C22C2×#123×C15111yescharacteristic
467C22#525×C15111yescharacteristic
468C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
469C22C2×#137×C15111yescharacteristic
470C22C2×#137×C15111yescharacteristic
471C22#575×C15111yescharacteristic
472C4—22no—
473C4—22no—
474C4—22no—
475C4—22no—
476C4—44no—
477C4—44no—
478C4—42no—
479C4—42no—
480C4—41no—
481C4—81no—
482C4—81no—
483C4C4×#41×C15112yes—
484C4#529×C15112yes—
485C2—24no—
486C2C4×#123×C15111yescharacteristic
487C2C2×#441×C15111yescharacteristic
488C2C4×AGL(1,ℤ/8)×C15111yescharacteristic
489C2#3092×C15111yescharacteristic
490C2#3095×C15111yescharacteristic
491C2#3110×C15111yescharacteristic
492C2#3117×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC24×C151C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1927×C151C2semidirect
5. #1918×C151C2semidirect
9. #1776×C151C2semidirect
10. #1763×C151C2semidirect
18. #484×C151C4semidirect
80. #107×C151C2×C4semidirect
83. #103×C151C2×C4semidirect
246. #21581C151direct (N × H)
247. C151#21581direct (N × H)
251. #1927C2×C151semidirect
252. #1918C2×C151semidirect
256. #1776C2×C151semidirect
257. #1763C2×C151semidirect
265. #484C4×C151semidirect
327. #107C2×C4×C151semidirect
330. #103C2×C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#484×C1512
C4×C22⋊Q8×C1512
C2×C4×C4⋊C4×C1512
#1927×C1512
#1918×C1512
#1872×C1512
#1853×C1512
#1824×C1512
#1776×C1512
#1763×C1512
#1749×C1512
#21581151