Finite Group Databasebeta

← C151×#20909 #50325834

Subgroups — C151×#20909 #50325834

Order 38656.

2258 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C151C211yesmaximal, characteristic
2C23×C4⋊C4×C151C211yesmaximal, characteristic, complemented
3C2×#417×C151C212yesmaximal, complemented
4C2×#407×C151C211yesmaximal, characteristic, complemented
5#1874×C151C214yesmaximal, complemented
6#1872×C151C214yesmaximal, complemented
7#1736×C151C212yesmaximal, complemented
8C22×#41×C151C2211yescharacteristic
9C24×C4×C151—21no—
10C24×C4×C151C2211yescharacteristic
11C22×M16×C151C2212yes—
12#525×C151—24no—
13#525×C151C418yescomplemented
14C2×#123×C151—21no—
15C2×C22⋊Q8×C151C2212yes—
16C2×#121×C151C2212yes—
17C2×#120×C151—21no—
18C2×C4×D4×C151—22no—
19C2×#117×C151C2211yescharacteristic
20C22×C4⋊C4×C151—22no—
21C22×C4⋊C4×C151—21no—
22C22×C4⋊C4×C151—28no—
23C22×C4⋊C4×C151C2214yes—
24C22×C4⋊C4×C151C2212yes—
25#417×C151—28no—
26C2×#103×C151C2214yescomplemented
27C2×#102×C151C2214yescomplemented
28#407×C151—24no—
29C2×C22⋊C8×C151C2214yes—
30#340×C151C2218yescomplemented
31C25×C151D411yescharacteristic
32C2×#41×C151—24no—
33C2×#41×C151—24no—
34C2×#41×C151—22no—
35C2×#41×C151C2×C414yescomplemented
36C22×Q8×C151C2311yescharacteristic
37C22×D4×C151—22no—
38C22×D4×C151—21no—
39C22×D4×C151C2311yescharacteristic
40C23×C4×C151—24no—
41C23×C4×C151—24no—
42C23×C4×C151—28no—
43C23×C4×C151—21no—
44C23×C4×C151—22no—
45C23×C4×C151—24no—
46C23×C4×C151—48no—
47C23×C4×C151C2×C414yes—
48C23×C4×C151D414yes—
49C23×C4×C151D412yes—
50C23×C4×C151D411yescharacteristic
51C23×C4×C151C2312yes—
52C23×C4×C151C2311yescharacteristic
53C2×M16×C151—24no—
54C2×M16×C151—24no—
55C2×M16×C151—24no—
56C22×C8×C151C2314yes—
57#123×C151—28no—
58C22⋊Q8×C151—24no—
59C22⋊Q8×C151C2×C418yescomplemented
60#121×C151—24no—
61#121×C151C2×C418yescomplemented
62#120×C151—28no—
63C4×D4×C151—216no—
64#117×C151—22no—
65#117×C151C2×C414yescomplemented
66C2×C4⋊C4×C151—28no—
67C2×C4⋊C4×C151—216no—
68C2×C4⋊C4×C151—24no—
69C2×C4⋊C4×C151—22no—
70C2×C4⋊C4×C151—24no—
71C2×C4⋊C4×C151—22no—
72C2×C4⋊C4×C151—216no—
73C2×C4⋊C4×C151D418yescomplemented
74C2×C4⋊C4×C151C2312yes—
75C2×C4⋊C4×C151C2314yes—
76C2×C22⋊C4×C151—22no—
77C2×C22⋊C4×C151—21no—
78C2×C22⋊C4×C151—22no—
79C2×C42×C151—21no—
80#103×C151—28no—
81#102×C151—28no—
82C22⋊C8×C151—28no—
83C24×C151—22no—
84C24×C151—22no—
85C24×C151—24no—
86C24×C151—24no—
87C24×C151—21no—
88C24×C151C22⋊C414yes—
89C24×C151C2×D411yescharacteristic
90C24×C151C2×D412yes—
91#41×C151—216no—
92#41×C151—48no—
93C2×Q8×C151—21no—
94C2×Q8×C151—22no—
95C2×Q8×C151—22no—
96C2×Q8×C151C22×C412yescomplemented
97C2×D4×C151—28no—
98C2×D4×C151—24no—
99C2×D4×C151—22no—
100C2×D4×C151—21no—
101C2×D4×C151—22no—
102C2×D4×C151—42no—
103C2×D4×C151—42no—
104C2×D4×C151—44no—
105C2×D4×C151—44no—
106C2×D4×C151C22×C412yescomplemented
107C22×C4×C151—22no—
108C22×C4×C151—22no—
109C22×C4×C151—216no—
110C22×C4×C151—24no—
111C22×C4×C151—216no—
112C22×C4×C151—24no—
113C22×C4×C151—24no—
114C22×C4×C151—24no—
115C22×C4×C151—216no—
116C22×C4×C151—28no—
117C22×C4×C151—22no—
118C22×C4×C151—21no—
119C22×C4×C151—24no—
120C22×C4×C151—24no—
121C22×C4×C151—432no—
122C22×C4×C151—48no—
123C22×C4×C151—48no—
124C22×C4×C151—48no—
125C22×C4×C151—42no—
126C22×C4×C151—42no—
127C22×C4×C151C22⋊C418yes—
128C22×C4×C151C22⋊C414yes—
129C22×C4×C151C22×C414yes—
130C22×C4×C151C22×C412yes—
131C22×C4×C151C2×D412yes—
132C22×C4×C151C2×D414yes—
133C22×C4×C151C2×D411yescharacteristic
134C22×C4×C151C2×D412yes—
135C22×C4×C151C2×D414yes—
136C22×C4×C151#4114yes—
137C22×C4×C151C2411yescharacteristic
138M16×C151—48no—
139C2×C8×C151—24no—
140C2×C8×C151—24no—
141C2×C8×C151—24no—
142C4⋊C4×C151—216no—
143C4⋊C4×C151—28no—
144C4⋊C4×C151—28no—
145C4⋊C4×C151—24no—
146C4⋊C4×C151—22no—
147C4⋊C4×C151C22×C414yescomplemented
148C4⋊C4×C151C2×D418yes—
149C22⋊C4×C151—24no—
150C22⋊C4×C151—28no—
151C22⋊C4×C151—28no—
152C42×C151—24no—
153C23×C151—216no—
154C23×C151—28no—
155C23×C151—28no—
156C23×C151—22no—
157C23×C151—22no—
158C23×C151—22no—
159C23×C151—22no—
160C23×C151—22no—
161C23×C151—22no—
162C23×C151—28no—
163C23×C151—216no—
164C23×C151—22no—
165C23×C151—41no—
166C23×C151—41no—
167C23×C151—42no—
168C23×C151—42no—
169C23×C151C2×C22⋊C412yes—
170C23×C151C2×C22⋊C414yes—
171C23×C151#12012yes—
172C23×C151#12312yes—
173C23×C151AGL(1,ℤ/8)14yes—
174C23×C151#13714yes—
175C23×C151C22×D411yescharacteristic
176Q8×C151—24no—
177Q8×C151—42no—
178D4×C151—24no—
179D4×C151—48no—
180D4×C151—416no—
181D4×C151—42no—
182C2×C4×C151—22no—
183C2×C4×C151—22no—
184C2×C4×C151—28no—
185C2×C4×C151—28no—
186C2×C4×C151—28no—
187C2×C4×C151—216no—
188C2×C4×C151—22no—
189C2×C4×C151—24no—
190C2×C4×C151—28no—
191C2×C4×C151—416no—
192C2×C4×C151—432no—
193C2×C4×C151—41no—
194C2×C4×C151—41no—
195C2×C4×C151—48no—
196C2×C4×C151—42no—
197C2×C4×C151—42no—
198C2×C4×C151—48no—
199C2×C4×C151C2×C22⋊C414yes—
200C2×C4×C151C2×C22⋊C412yes—
201C2×C4×C151C4×D418yes—
202C2×C4×C151#12012yes—
203C2×C4×C151#12118yes—
204C2×C4×C151#12312yes—
205C2×C4×C151C23×C411yescharacteristic
206C2×C4×C151C22×D412yes—
207C2×C4×C151C22×D411yescharacteristic
208C2×C4×C151C2×#4112yes—
209C8×C151—44no—
210C22×C151—232no—
211C22×C151—24no—
212C22×C151—24no—
213C22×C151—24no—
214C22×C151—24no—
215C22×C151—24no—
216C22×C151—22no—
217C22×C151—24no—
218C22×C151—22no—
219C22×C151—24no—
220C22×C151—24no—
221C22×C151—44no—
222C22×C151—42no—
223C22×C151—82no—
224C22×C151—81no—
225C22×C151—81no—
226C22×C151#38614yes—
227C22×C151#41718yescomplemented
228C22×C151C22×C22⋊C411yescharacteristic
229C22×C151C2×#12011yescharacteristic
230C22×C151C2×#12311yescharacteristic
231C22×C151C2×AGL(1,ℤ/8)12yes—
232C22×C151C2×#13712yes—
233C4×C151—24no—
234C4×C151—44no—
235C4×C151—48no—
236C4×C151—42no—
237C4×C151#38614yes—
238C4×C151C2×C4×D412yes—
239C4×C151C2×#12112yes—
240C2×C151—24no—
241C2×C151—28no—
242C2×C151—82no—
243C2×C151C2×#38611yescharacteristic
244C2×C151C2×#41712yes—
245C2×C151#300311yescharacteristic
246C2×C151#300411yescharacteristic
247C2×C151#309212yes—
248#20909C15111yesmaximal, characteristic, direct product factor, Sylow
249C151#2090911yescharacteristic, direct product factor, Sylow
250C2×#525C2×C15111yescharacteristic
251C23×C4⋊C4C2×C15111yescharacteristic, complemented
252C2×#417C2×C15112yescomplemented
253C2×#407C2×C15111yescharacteristic, complemented
254#1874C2×C15114yescomplemented
255#1872C2×C15114yescomplemented
256#1736C2×C15112yescomplemented
257C22×#41C22×C15111yescharacteristic
258C24×C4—21no—
259C24×C4C22×C15111yescharacteristic
260C22×M16C22×C15112yes—
261#525—24no—
262#525C4×C15118yescomplemented
263C2×#123—21no—
264C2×C22⋊Q8C22×C15112yes—
265C2×#121C22×C15112yes—
266C2×#120—21no—
267C2×C4×D4—22no—
268C2×#117C22×C15111yescharacteristic
269C22×C4⋊C4—22no—
270C22×C4⋊C4—21no—
271C22×C4⋊C4—28no—
272C22×C4⋊C4C22×C15114yes—
273C22×C4⋊C4C22×C15112yes—
274#417—28no—
275C2×#103C22×C15114yescomplemented
276C2×#102C22×C15114yescomplemented
277#407—24no—
278C2×C22⋊C8C22×C15114yes—
279#340C22×C15118yescomplemented
280C25D4×C15111yescharacteristic
281C2×#41—22no—
282C2×#41—24no—
283C2×#41—24no—
284C2×#41C2×C4×C15114yescomplemented
285C22×Q8C23×C15111yescharacteristic
286C22×D4—22no—
287C22×D4—21no—
288C22×D4C23×C15111yescharacteristic
289C23×C4—24no—
290C23×C4—24no—
291C23×C4—28no—
292C23×C4—24no—
293C23×C4—22no—
294C23×C4—21no—
295C23×C4—48no—
296C23×C4C2×C4×C15114yes—
297C23×C4D4×C15112yes—
298C23×C4D4×C15111yescharacteristic
299C23×C4D4×C15114yes—
300C23×C4C23×C15112yes—
301C23×C4C23×C15111yescharacteristic
302C2×M16—24no—
303C2×M16—24no—
304C2×M16—24no—
305C22×C8C23×C15114yes—
306#123—28no—
307C22⋊Q8—24no—
308C22⋊Q8C2×C4×C15118yescomplemented
309#121—24no—
310#121C2×C4×C15118yescomplemented
311#120—28no—
312C4×D4—216no—
313#117—22no—
314#117C2×C4×C15114yescomplemented
315C2×C4⋊C4—28no—
316C2×C4⋊C4—216no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—216no—
322C2×C4⋊C4D4×C15118yescomplemented
323C2×C4⋊C4C23×C15112yes—
324C2×C4⋊C4C23×C15114yes—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C42—21no—
329#103—28no—
330#102—28no—
331C22⋊C8—28no—
332C24—22no—
333C24—22no—
334C24—24no—
335C24—24no—
336C24—21no—
337C24C22⋊C4×C15114yes—
338C24C2×D4×C15111yescharacteristic
339C24C2×D4×C15112yes—
340#41—216no—
341#41—48no—
342C2×Q8—21no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8C22×C4×C15112yescomplemented
346C2×D4—28no—
347C2×D4—24no—
348C2×D4—22no—
349C2×D4—21no—
350C2×D4—22no—
351C2×D4—42no—
352C2×D4—42no—
353C2×D4—44no—
354C2×D4—44no—
355C2×D4C22×C4×C15112yescomplemented
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—216no—
359C22×C4—24no—
360C22×C4—216no—
361C22×C4—24no—
362C22×C4—24no—
363C22×C4—24no—
364C22×C4—216no—
365C22×C4—28no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—432no—
371C22×C4—48no—
372C22×C4—48no—
373C22×C4—48no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4C22⋊C4×C15118yes—
377C22×C4C22⋊C4×C15114yes—
378C22×C4C22×C4×C15114yes—
379C22×C4C22×C4×C15112yes—
380C22×C4C2×D4×C15112yes—
381C22×C4C2×D4×C15114yes—
382C22×C4C2×D4×C15111yescharacteristic
383C22×C4C2×D4×C15112yes—
384C22×C4C2×D4×C15114yes—
385C22×C4#41×C15114yes—
386C22×C4C24×C15111yescharacteristic
387M16—48no—
388C2×C8—24no—
389C2×C8—24no—
390C2×C8—24no—
391C4⋊C4—216no—
392C4⋊C4—28no—
393C4⋊C4—28no—
394C4⋊C4—24no—
395C4⋊C4—22no—
396C4⋊C4C22×C4×C15114yescomplemented
397C4⋊C4C2×D4×C15118yes—
398C22⋊C4—24no—
399C22⋊C4—28no—
400C22⋊C4—28no—
401C42—24no—
402C23—28no—
403C23—28no—
404C23—216no—
405C23—28no—
406C23—216no—
407C23—22no—
408C23—22no—
409C23—22no—
410C23—22no—
411C23—22no—
412C23—22no—
413C23—22no—
414C23—41no—
415C23—41no—
416C23—42no—
417C23—42no—
418C23C2×C22⋊C4×C15112yes—
419C23C2×C22⋊C4×C15114yes—
420C23#120×C15112yes—
421C23#123×C15112yes—
422C23AGL(1,ℤ/8)×C15114yes—
423C23#137×C15114yes—
424C23C22×D4×C15111yescharacteristic
425Q8—24no—
426Q8—42no—
427D4—24no—
428D4—48no—
429D4—416no—
430D4—42no—
431C2×C4—28no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—216no—
435C2×C4—28no—
436C2×C4—28no—
437C2×C4—24no—
438C2×C4—22no—
439C2×C4—28no—
440C2×C4—416no—
441C2×C4—432no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—48no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—48no—
448C2×C4C2×C22⋊C4×C15114yes—
449C2×C4C2×C22⋊C4×C15112yes—
450C2×C4C4×D4×C15118yes—
451C2×C4#120×C15112yes—
452C2×C4#121×C15118yes—
453C2×C4#123×C15112yes—
454C2×C4C23×C4×C15111yescharacteristic
455C2×C4C22×D4×C15112yes—
456C2×C4C22×D4×C15111yescharacteristic
457C2×C4C2×#41×C15112yes—
458C8—44no—
459C22—232no—
460C22—24no—
461C22—24no—
462C22—22no—
463C22—24no—
464C22—22no—
465C22—24no—
466C22—24no—
467C22—24no—
468C22—24no—
469C22—24no—
470C22—44no—
471C22—42no—
472C22—81no—
473C22—81no—
474C22—82no—
475C22#386×C15114yes—
476C22#417×C15118yescomplemented
477C22C22×C22⋊C4×C15111yescharacteristic
478C22C2×#120×C15111yescharacteristic
479C22C2×#123×C15111yescharacteristic
480C22C2×AGL(1,ℤ/8)×C15112yes—
481C22C2×#137×C15112yes—
482C4—24no—
483C4—44no—
484C4—48no—
485C4—42no—
486C4#386×C15114yes—
487C4C2×C4×D4×C15112yes—
488C4C2×#121×C15112yes—
489C2—24no—
490C2—28no—
491C2—82no—
492C2C2×#386×C15111yescharacteristic
493C2C2×#417×C15112yes—
494C2#3003×C15111yescharacteristic
495C2#3004×C15111yescharacteristic
496C2#3092×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC2×#525×C151C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C24×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C4⋊C4×C151C2semidirect
3. C2×#417×C151C2semidirect
4. C2×#407×C151C2semidirect
5. #1874×C151C2semidirect
6. #1872×C151C2semidirect
7. #1736×C151C2semidirect
13. #525×C151C4semidirect
26. C2×#103×C151C22semidirect
27. C2×#102×C151C22semidirect
30. #340×C151C22semidirect
35. C2×#41×C151C2×C4semidirect
59. C22⋊Q8×C151C2×C4semidirect
61. #121×C151C2×C4semidirect
65. #117×C151C2×C4semidirect
73. C2×C4⋊C4×C151D4semidirect
96. C2×Q8×C151C22×C4semidirect
106. C2×D4×C151C22×C4semidirect
147. C4⋊C4×C151C22×C4semidirect
227. C22×C151#417semidirect
248. #20909C151direct (N × H)
249. C151#20909direct (N × H)
251. C23×C4⋊C4C2×C151semidirect
252. C2×#417C2×C151semidirect
253. C2×#407C2×C151semidirect
254. #1874C2×C151semidirect
255. #1872C2×C151semidirect
256. #1736C2×C151semidirect
262. #525C4×C151semidirect
275. C2×#103C22×C151semidirect
276. C2×#102C22×C151semidirect
279. #340C22×C151semidirect
284. C2×#41C2×C4×C151semidirect
308. C22⋊Q8C2×C4×C151semidirect
310. #121C2×C4×C151semidirect
314. #117C2×C4×C151semidirect
322. C2×C4⋊C4D4×C151semidirect
345. C2×Q8C22×C4×C151semidirect
355. C2×D4C22×C4×C151semidirect
396. C4⋊C4C22×C4×C151semidirect
476. C22#417×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1512
C23×C4⋊C4×C1512
C2×#417×C1512
C2×#407×C1512
#1874×C1512
#1872×C1512
#1736×C1512
#20909151