Finite Group Databasebeta

← C151×#18752 #50323677

Subgroups — C151×#18752 #50323677

Order 38656.

1020 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#554×C151C211yesmaximal, characteristic, complemented
2#3206×C151C211yesmaximal, characteristic, complemented
3#3100×C151C211yesmaximal, characteristic
4#3037×C151C211yesmaximal, characteristic, complemented
5#1644×C151C214yesmaximal, complemented
6#1622×C151C214yesmaximal, complemented
7#1548×C151C211yesmaximal, characteristic, complemented
8#1486×C151C211yesmaximal, characteristic, complemented
9#1479×C151C211yesmaximal, characteristic, complemented
10C2×#137×C151—21no—
11#554×C151—22no—
12#554×C151—22no—
13#554×C151—22no—
14#554×C151C2214yes—
15#532×C151C2211yescharacteristic
16C2×C4⋊Q8×C151C2211yescharacteristic
17C2×#125×C151—21no—
18C2×C22⋊Q8×C151—21no—
19C2×C22⋊Q8×C151—22no—
20C2×C4×Q8×C151C2211yescharacteristic
21C2×C4×D4×C151—21no—
22C2×C4×D4×C151C2211yescharacteristic
23C22×C4⋊C4×C151—21no—
24#492×C151C2212yescomplemented
25#487×C151C2212yescomplemented
26#480×C151—21no—
27#474×C151C2212yes—
28#464×C151—22no—
29#462×C151C2212yescomplemented
30#461×C151—22no—
31#460×C151C2212yescomplemented
32#459×C151C2212yes—
33#448×C151—22no—
34#447×C151—21no—
35C4×D8×C151—22no—
36#431×C151C2211yescharacteristic
37#431×C151C2211yescharacteristic
38#423×C151C2211yescharacteristic
39#417×C151—21no—
40#333×C151C2214yescomplemented
41Q8⋊C8×C151C2214yescomplemented
42D4⋊C8×C151C2214yes—
43C2×#41×C151—21no—
44C22×Q8×C151D411yescharacteristic
45C22×Q8×C151D412yes—
46C22×D4×C151D411yescharacteristic
47C23×C4×C151—22no—
48C23×C4×C151—21no—
49#137×C151—44no—
50C2×Q16×C151—22no—
51C2×SD16×C151—22no—
52C2×SD16×C151—24no—
53C2×D8×C151—22no—
54C2×M16×C151—21no—
55C4⋊Q8×C151—21no—
56C4⋊Q8×C151—21no—
57C4⋊Q8×C151D412yes—
58C4⋊Q8×C151C2311yescharacteristic
59C4⋊Q8×C151C2312yes—
60#127×C151C2311yescharacteristic
61#125×C151—24no—
62#125×C151—24no—
63#124×C151—21no—
64C22⋊Q8×C151—24no—
65C22⋊Q8×C151—28no—
66C22⋊Q8×C151—24no—
67C22⋊Q8×C151—28no—
68#121×C151—21no—
69#121×C151—21no—
70C4×Q8×C151—21no—
71C4×Q8×C151—21no—
72C4×Q8×C151D412yes—
73C4×Q8×C151C2312yes—
74C4×D4×C151—24no—
75C4×D4×C151—24no—
76C4×D4×C151—21no—
77C4×D4×C151—21no—
78C4×D4×C151—21no—
79C4×D4×C151—21no—
80C4×D4×C151D412yes—
81C4×D4×C151C2312yes—
82C2×C4⋊C4×C151—22no—
83C2×C4⋊C4×C151—24no—
84C2×C4⋊C4×C151—22no—
85C2×C4⋊C4×C151—21no—
86C2×C4⋊C4×C151—21no—
87C2×C4⋊C4×C151—21no—
88C2×C4⋊C4×C151—24no—
89C2×C4⋊C4×C151D411yescharacteristic
90C2×C4⋊C4×C151D411yescharacteristic
91C2×C22⋊C4×C151—22no—
92C2×C22⋊C4×C151—21no—
93C2×C42×C151—21no—
94C2×C42×C151C2311yescharacteristic
95#107×C151—22no—
96C4⋊C8×C151—21no—
97C4⋊C8×C151—21no—
98C4⋊C8×C151C2312yes—
99C4⋊C8×C151C2312yes—
100#103×C151—22no—
101#103×C151—24no—
102#102×C151—22no—
103#102×C151—22no—
104#102×C151—22no—
105C22⋊C8×C151—21no—
106C22⋊C8×C151—21no—
107C4×C8×C151—21no—
108C4×C8×C151C2312yes—
109C24×C151—21no—
110#41×C151—42no—
111#41×C151—42no—
112C2×Q8×C151—21no—
113C2×Q8×C151—22no—
114C2×Q8×C151—22no—
115C2×Q8×C151—22no—
116C2×Q8×C151—21no—
117C2×Q8×C151—82no—
118C2×Q8×C151C2×D412yes—
119C2×Q8×C151C2×D414yes—
120C2×D4×C151—24no—
121C2×D4×C151—21no—
122C2×D4×C151—21no—
123C2×D4×C151—21no—
124C2×D4×C151—21no—
125C2×D4×C151—41no—
126C2×D4×C151C2×D412yes—
127C22×C4×C151—21no—
128C22×C4×C151—21no—
129C22×C4×C151—21no—
130C22×C4×C151—22no—
131C22×C4×C151—28no—
132C22×C4×C151—22no—
133C22×C4×C151—22no—
134C22×C4×C151—42no—
135C22×C4×C151—42no—
136C22×C4×C151—41no—
137C22×C4×C151—84no—
138C22×C4×C151C2×D411yescharacteristic
139C22×C4×C151C2×D411yescharacteristic
140C22×C4×C151C2×D411yescharacteristic
141Q16×C151—44no—
142SD16×C151—44no—
143SD16×C151—84no—
144D8×C151—44no—
145M16×C151—42no—
146C2×C8×C151—22no—
147C2×C8×C151—22no—
148C2×C8×C151—22no—
149C4⋊C4×C151—28no—
150C4⋊C4×C151—28no—
151C4⋊C4×C151—21no—
152C4⋊C4×C151—22no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151—22no—
155C4⋊C4×C151—21no—
156C4⋊C4×C151—22no—
157C4⋊C4×C151—22no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—21no—
160C4⋊C4×C151—21no—
161C4⋊C4×C151C2×D412yes—
162C4⋊C4×C151C2×D412yes—
163C22⋊C4×C151—28no—
164C22⋊C4×C151—22no—
165C22⋊C4×C151—22no—
166C22⋊C4×C151—41no—
167C22⋊C4×C151—41no—
168C42×C151—22no—
169C42×C151—22no—
170C42×C151C2×D411yescharacteristic
171C42×C151C2×D411yescharacteristic
172C42×C151C2×D411yescharacteristic
173C42×C151C2411yescharacteristic
174C23×C151—24no—
175C23×C151—22no—
176C23×C151—42no—
177C23×C151—42no—
178C23×C151—41no—
179C23×C151#12011yescharacteristic
180Q8×C151—22no—
181Q8×C151—22no—
182Q8×C151—44no—
183Q8×C151—42no—
184Q8×C151—41no—
185Q8×C151—41no—
186Q8×C151—82no—
187D4×C151—24no—
188D4×C151—22no—
189D4×C151—42no—
190D4×C151—41no—
191D4×C151—41no—
192D4×C151—42no—
193D4×C151—82no—
194D4×C151#13714yescomplemented
195C2×C4×C151—22no—
196C2×C4×C151—22no—
197C2×C4×C151—24no—
198C2×C4×C151—22no—
199C2×C4×C151—22no—
200C2×C4×C151—41no—
201C2×C4×C151—44no—
202C2×C4×C151—42no—
203C2×C4×C151—42no—
204C2×C4×C151—42no—
205C2×C4×C151—42no—
206C2×C4×C151—42no—
207C2×C4×C151—44no—
208C2×C4×C151—41no—
209C2×C4×C151—88no—
210C2×C4×C151—82no—
211C2×C4×C151#12011yescharacteristic
212C2×C4×C151#12011yescharacteristic
213C2×C4×C151#12011yescharacteristic
214C2×C4×C151#13512yes—
215C2×C4×C151AGL(1,ℤ/8)12yes—
216C2×C4×C151C22×D411yescharacteristic
217C2×C4×C151C22×D411yescharacteristic
218C2×C4×C151C22×D411yescharacteristic
219C8×C151—42no—
220C8×C151—42no—
221C8×C151—42no—
222C22×C151—21no—
223C22×C151—21no—
224C22×C151—24no—
225C22×C151—48no—
226C22×C151—42no—
227C22×C151—42no—
228C22×C151—81no—
229C22×C151—81no—
230C22×C151—81no—
231C22×C151#44912yes—
232C22×C151C2×#12011yescharacteristic
233C4×C151—21no—
234C4×C151—21no—
235C4×C151—21no—
236C4×C151—42no—
237C4×C151—42no—
238C4×C151—42no—
239C4×C151—44no—
240C4×C151—81no—
241C4×C151#44912yes—
242C4×C151C2×#13511yescharacteristic
243C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
244C4×C151C2×#13712yes—
245C2×C151—22no—
246C2×C151—44no—
247C2×C151—161no—
248C2×C151C2×#44911yescharacteristic
249C2×C151#300411yescharacteristic
250C2×C151#301911yescharacteristic
251#18752C15111yesmaximal, characteristic, direct product factor, Sylow
252C151#1875211yescharacteristic, direct product factor, Sylow
253C2×#554C2×C15111yescharacteristic, complemented
254#3206C2×C15111yescharacteristic, complemented
255#3100C2×C15111yescharacteristic
256#3037C2×C15111yescharacteristic, complemented
257#1644C2×C15114yescomplemented
258#1622C2×C15114yescomplemented
259#1548C2×C15111yescharacteristic, complemented
260#1486C2×C15111yescharacteristic, complemented
261#1479C2×C15111yescharacteristic, complemented
262C2×#137—21no—
263#554—22no—
264#554—22no—
265#554—22no—
266#554C22×C15114yes—
267#532C22×C15111yescharacteristic
268C2×C4⋊Q8C22×C15111yescharacteristic
269C2×#125—21no—
270C2×C22⋊Q8—21no—
271C2×C22⋊Q8—22no—
272C2×C4×Q8C22×C15111yescharacteristic
273C2×C4×D4—21no—
274C2×C4×D4C22×C15111yescharacteristic
275C22×C4⋊C4—21no—
276#492C22×C15112yescomplemented
277#487C22×C15112yescomplemented
278#480—21no—
279#474C22×C15112yes—
280#464—22no—
281#462C22×C15112yescomplemented
282#461—22no—
283#460C22×C15112yescomplemented
284#459C22×C15112yes—
285#448—22no—
286#447—21no—
287C4×D8—22no—
288#431C22×C15111yescharacteristic
289#431C22×C15111yescharacteristic
290#423C22×C15111yescharacteristic
291#417—21no—
292#333C22×C15114yescomplemented
293Q8⋊C8C22×C15114yescomplemented
294D4⋊C8C22×C15114yes—
295C2×#41—21no—
296C22×Q8D4×C15111yescharacteristic
297C22×Q8D4×C15112yes—
298C22×D4D4×C15111yescharacteristic
299C23×C4—22no—
300C23×C4—21no—
301#137—44no—
302C2×Q16—22no—
303C2×SD16—22no—
304C2×SD16—24no—
305C2×D8—22no—
306C2×M16—21no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8D4×C15112yes—
310C4⋊Q8C23×C15111yescharacteristic
311C4⋊Q8C23×C15112yes—
312#127C23×C15111yescharacteristic
313#125—24no—
314#125—24no—
315#124—21no—
316C22⋊Q8—24no—
317C22⋊Q8—28no—
318C22⋊Q8—24no—
319C22⋊Q8—28no—
320#121—21no—
321#121—21no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×Q8D4×C15112yes—
325C4×Q8C23×C15112yes—
326C4×D4—24no—
327C4×D4—24no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—21no—
331C4×D4—21no—
332C4×D4D4×C15112yes—
333C4×D4C23×C15112yes—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4D4×C15111yescharacteristic
342C2×C4⋊C4D4×C15111yescharacteristic
343C2×C22⋊C4—22no—
344C2×C22⋊C4—21no—
345C2×C42—21no—
346C2×C42C23×C15111yescharacteristic
347#107—22no—
348C4⋊C8—21no—
349C4⋊C8—21no—
350C4⋊C8C23×C15112yes—
351C4⋊C8C23×C15112yes—
352#103—24no—
353#103—22no—
354#102—22no—
355#102—22no—
356#102—22no—
357C22⋊C8—21no—
358C22⋊C8—21no—
359C4×C8—21no—
360C4×C8C23×C15112yes—
361C24—21no—
362#41—42no—
363#41—42no—
364C2×Q8—21no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—21no—
369C2×Q8—82no—
370C2×Q8C2×D4×C15112yes—
371C2×Q8C2×D4×C15114yes—
372C2×D4—24no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—41no—
378C2×D4C2×D4×C15112yes—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—28no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—41no—
389C22×C4—84no—
390C22×C4C2×D4×C15111yescharacteristic
391C22×C4C2×D4×C15111yescharacteristic
392C22×C4C2×D4×C15111yescharacteristic
393Q16—44no—
394SD16—44no—
395SD16—84no—
396D8—44no—
397M16—42no—
398C2×C8—22no—
399C2×C8—22no—
400C2×C8—22no—
401C4⋊C4—28no—
402C4⋊C4—28no—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4C2×D4×C15112yes—
414C4⋊C4C2×D4×C15112yes—
415C22⋊C4—28no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C42—22no—
421C42—22no—
422C42C2×D4×C15111yescharacteristic
423C42C2×D4×C15111yescharacteristic
424C42C2×D4×C15111yescharacteristic
425C42C24×C15111yescharacteristic
426C23—24no—
427C23—22no—
428C23—42no—
429C23—42no—
430C23—41no—
431C23#120×C15111yescharacteristic
432Q8—22no—
433Q8—22no—
434Q8—44no—
435Q8—42no—
436Q8—41no—
437Q8—41no—
438Q8—82no—
439D4—24no—
440D4—22no—
441D4—42no—
442D4—41no—
443D4—41no—
444D4—42no—
445D4—82no—
446D4#137×C15114yescomplemented
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—24no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—44no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—44no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—41no—
461C2×C4—88no—
462C2×C4—82no—
463C2×C4#120×C15111yescharacteristic
464C2×C4#120×C15111yescharacteristic
465C2×C4#120×C15111yescharacteristic
466C2×C4#135×C15112yes—
467C2×C4AGL(1,ℤ/8)×C15112yes—
468C2×C4C22×D4×C15111yescharacteristic
469C2×C4C22×D4×C15111yescharacteristic
470C2×C4C22×D4×C15111yescharacteristic
471C8—42no—
472C8—42no—
473C8—42no—
474C22—21no—
475C22—21no—
476C22—24no—
477C22—48no—
478C22—42no—
479C22—42no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22#449×C15112yes—
484C22C2×#120×C15111yescharacteristic
485C4—21no—
486C4—21no—
487C4—21no—
488C4—42no—
489C4—42no—
490C4—42no—
491C4—44no—
492C4—81no—
493C4#449×C15112yes—
494C4C2×#135×C15111yescharacteristic
495C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
496C4C2×#137×C15112yes—
497C2—22no—
498C2—44no—
499C2—161no—
500C2C2×#449×C15111yescharacteristic
501C2#3004×C15111yescharacteristic
502C2#3019×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3100×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#554×C151C2semidirect
2. #3206×C151C2semidirect
4. #3037×C151C2semidirect
5. #1644×C151C2semidirect
6. #1622×C151C2semidirect
7. #1548×C151C2semidirect
8. #1486×C151C2semidirect
9. #1479×C151C2semidirect
24. #492×C151C22semidirect
25. #487×C151C22semidirect
29. #462×C151C22semidirect
31. #460×C151C22semidirect
40. #333×C151C22semidirect
41. Q8⋊C8×C151C22semidirect
194. D4×C151#137semidirect
251. #18752C151direct (N × H)
252. C151#18752direct (N × H)
253. C2×#554C2×C151semidirect
254. #3206C2×C151semidirect
256. #3037C2×C151semidirect
257. #1644C2×C151semidirect
258. #1622C2×C151semidirect
259. #1548C2×C151semidirect
260. #1486C2×C151semidirect
261. #1479C2×C151semidirect
276. #492C22×C151semidirect
277. #487C22×C151semidirect
281. #462C22×C151semidirect
283. #460C22×C151semidirect
292. #333C22×C151semidirect
293. Q8⋊C8C22×C151semidirect
446. D4#137×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#554×C1512
#3206×C1512
#3100×C1512
#3037×C1512
#1644×C1512
#1622×C1512
#1548×C1512
#1486×C1512
#1479×C1512
#18752151