Finite Group Databasebeta

← C151×#18634 #50323559

Subgroups — C151×#18634 #50323559

Order 38656.

1024 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3508×C151C211yesmaximal, characteristic
2#3229×C151C211yesmaximal, characteristic, complemented
3C2×#486×C151C211yesmaximal, characteristic, complemented
4#3039×C151C211yesmaximal, characteristic, complemented
5#1642×C151C214yesmaximal, complemented
6#1640×C151C214yesmaximal, complemented
7#1545×C151C211yesmaximal, characteristic, complemented
8#1493×C151C211yesmaximal, characteristic, complemented
9#1476×C151C211yesmaximal, characteristic, complemented
10C2×#137×C151—21no—
11#559×C151—21no—
12#559×C151C2212yes—
13#550×C151—21no—
14#550×C151C2212yes—
15#546×C151—22no—
16#546×C151—22no—
17#540×C151—22no—
18#535×C151—21no—
19#533×C151C2211yescharacteristic
20#532×C151—21no—
21#532×C151—21no—
22C2×C4⋊Q8×C151C2211yescharacteristic
23C2×#127×C151C2211yescharacteristic
24#518×C151—21no—
25C4×#41×C151C2211yescharacteristic
26#498×C151—21no—
27#487×C151—21no—
28#486×C151—22no—
29#486×C151C2214yes—
30#483×C151—22no—
31#475×C151C2214yescomplemented
32#462×C151—21no—
33#462×C151C2212yescomplemented
34#461×C151—21no—
35#461×C151C2212yescomplemented
36#431×C151C2211yescharacteristic
37#423×C151C2211yescharacteristic
38#419×C151—21no—
39C2×#102×C151—22no—
40C2×C4×C8×C151C2211yescharacteristic
41#331×C151C2214yes—
42Q8⋊C8×C151C2212yescomplemented
43Q8⋊C8×C151C2214yescomplemented
44D4⋊C8×C151C2212yescomplemented
45C2×#41×C151—22no—
46C2×#41×C151—22no—
47C2×#41×C151D411yescharacteristic
48C22×Q8×C151—21no—
49C22×D4×C151—21no—
50C22×D4×C151—21no—
51C22×D4×C151D412yes—
52#137×C151—44no—
53C2×Q16×C151—22no—
54C2×SD16×C151—22no—
55C2×M16×C151—21no—
56C22×C8×C151—21no—
57C4⋊Q8×C151—21no—
58C4⋊Q8×C151—21no—
59C4⋊Q8×C151—21no—
60C4⋊Q8×C151D411yescharacteristic
61C4⋊Q8×C151D411yescharacteristic
62C4⋊Q8×C151C2312yes—
63#127×C151—22no—
64#127×C151—21no—
65#127×C151—21no—
66#127×C151D412yes—
67#127×C151C2312yes—
68#125×C151—21no—
69#124×C151—22no—
70#124×C151—22no—
71#124×C151—22no—
72#123×C151—24no—
73#123×C151—24no—
74C22⋊Q8×C151—21no—
75C22⋊Q8×C151D412yes—
76#121×C151—22no—
77#121×C151—22no—
78#121×C151—22no—
79#121×C151—24no—
80#121×C151—24no—
81#121×C151—22no—
82#120×C151—24no—
83C4×Q8×C151—21no—
84C4×Q8×C151D411yescharacteristic
85C4×Q8×C151C2311yescharacteristic
86C4×Q8×C151C2312yes—
87C4×D4×C151—22no—
88C4×D4×C151—22no—
89C4×D4×C151—22no—
90C4×D4×C151—21no—
91C4×D4×C151—21no—
92C4×D4×C151—22no—
93C4×D4×C151—22no—
94C4×D4×C151—22no—
95C4×D4×C151D411yescharacteristic
96C4×D4×C151C2311yescharacteristic
97#117×C151—21no—
98#117×C151—21no—
99#117×C151D411yescharacteristic
100C2×C4⋊C4×C151—21no—
101C2×C4⋊C4×C151—21no—
102C2×C22⋊C4×C151—24no—
103C2×C42×C151—21no—
104C2×C42×C151C2311yescharacteristic
105#106×C151—24no—
106C4⋊C8×C151—21no—
107C4⋊C8×C151C2312yes—
108C4⋊C8×C151C2312yes—
109#103×C151—22no—
110#103×C151—22no—
111#103×C151—24no—
112#102×C151—28no—
113C22⋊C8×C151—21no—
114C4×C8×C151—21no—
115C4×C8×C151—21no—
116C4×C8×C151C2312yes—
117C24×C151—22no—
118#41×C151—22no—
119#41×C151—22no—
120#41×C151—84no—
121#41×C151—84no—
122C2×Q8×C151—21no—
123C2×Q8×C151—22no—
124C2×Q8×C151—41no—
125C2×Q8×C151—42no—
126C2×Q8×C151—42no—
127C2×Q8×C151C2×D412yes—
128C2×Q8×C151C2×D411yescharacteristic
129C2×D4×C151—21no—
130C2×D4×C151—24no—
131C2×D4×C151—24no—
132C2×D4×C151—22no—
133C2×D4×C151—22no—
134C2×D4×C151—22no—
135C2×D4×C151—22no—
136C2×D4×C151—22no—
137C2×D4×C151—44no—
138C2×D4×C151—42no—
139C2×D4×C151—42no—
140C2×D4×C151—82no—
141C2×D4×C151C2×D411yescharacteristic
142C2×D4×C151C2×D414yes—
143C22×C4×C151—24no—
144C22×C4×C151—24no—
145C22×C4×C151—21no—
146C22×C4×C151—21no—
147C22×C4×C151—21no—
148C22×C4×C151—41no—
149C22×C4×C151C2×D411yescharacteristic
150C22×C4×C151C2×D411yescharacteristic
151C22×C4×C151C2×D411yescharacteristic
152Q16×C151—44no—
153SD16×C151—44no—
154M16×C151—42no—
155C2×C8×C151—22no—
156C2×C8×C151—22no—
157C2×C8×C151—22no—
158C2×C8×C151—42no—
159C4⋊C4×C151—21no—
160C4⋊C4×C151—21no—
161C4⋊C4×C151—21no—
162C4⋊C4×C151—21no—
163C4⋊C4×C151—22no—
164C4⋊C4×C151—21no—
165C4⋊C4×C151—22no—
166C4⋊C4×C151—22no—
167C4⋊C4×C151—22no—
168C4⋊C4×C151—41no—
169C4⋊C4×C151—41no—
170C4⋊C4×C151C2×D411yescharacteristic
171C4⋊C4×C151C2×D411yescharacteristic
172C4⋊C4×C151C2×D412yes—
173C22⋊C4×C151—24no—
174C22⋊C4×C151—24no—
175C22⋊C4×C151—24no—
176C22⋊C4×C151—24no—
177C22⋊C4×C151—21no—
178C22⋊C4×C151—22no—
179C22⋊C4×C151—21no—
180C22⋊C4×C151—21no—
181C42×C151—21no—
182C42×C151—21no—
183C42×C151—21no—
184C42×C151—22no—
185C42×C151C2×D411yescharacteristic
186C42×C151C2×D411yescharacteristic
187C42×C151C2×D411yescharacteristic
188C42×C151C2411yescharacteristic
189C23×C151—24no—
190C23×C151—21no—
191C23×C151—44no—
192C23×C151—82no—
193C23×C151—82no—
194C23×C151#12011yescharacteristic
195Q8×C151—21no—
196Q8×C151—21no—
197Q8×C151—24no—
198Q8×C151—42no—
199Q8×C151—42no—
200Q8×C151—42no—
201Q8×C151—82no—
202D4×C151—21no—
203D4×C151—21no—
204D4×C151—44no—
205D4×C151—42no—
206D4×C151—42no—
207D4×C151—42no—
208D4×C151—44no—
209D4×C151—44no—
210D4×C151—44no—
211D4×C151—82no—
212D4×C151—84no—
213D4×C151—84no—
214C2×C4×C151—22no—
215C2×C4×C151—22no—
216C2×C4×C151—22no—
217C2×C4×C151—21no—
218C2×C4×C151—22no—
219C2×C4×C151—21no—
220C2×C4×C151—21no—
221C2×C4×C151—42no—
222C2×C4×C151—42no—
223C2×C4×C151—42no—
224C2×C4×C151—42no—
225C2×C4×C151—84no—
226C2×C4×C151—84no—
227C2×C4×C151—82no—
228C2×C4×C151#12011yescharacteristic
229C2×C4×C151#12011yescharacteristic
230C2×C4×C151#12011yescharacteristic
231C2×C4×C151#13512yes—
232C2×C4×C151AGL(1,ℤ/8)12yes—
233C2×C4×C151C22×D411yescharacteristic
234C2×C4×C151C22×D411yescharacteristic
235C2×C4×C151C22×D411yescharacteristic
236C8×C151—42no—
237C8×C151—42no—
238C8×C151—42no—
239C22×C151—21no—
240C22×C151—21no—
241C22×C151—41no—
242C22×C151—44no—
243C22×C151—41no—
244C22×C151—44no—
245C22×C151—41no—
246C22×C151—44no—
247C22×C151—164no—
248C22×C151#44912yes—
249C22×C151C2×#12011yescharacteristic
250C4×C151—21no—
251C4×C151—21no—
252C4×C151—41no—
253C4×C151—41no—
254C4×C151—42no—
255C4×C151—41no—
256C4×C151—42no—
257C4×C151—82no—
258C4×C151#44912yes—
259C4×C151#45512yes—
260C4×C151C2×#13511yescharacteristic
261C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
262C4×C151#57712yes—
263C2×C151—22no—
264C2×C151—81no—
265C2×C151—84no—
266C2×C151C2×#44911yescharacteristic
267C2×C151#300911yescharacteristic
268C2×C151C2×#45511yescharacteristic
269#18634C15111yesmaximal, characteristic, direct product factor, Sylow
270C151#1863411yescharacteristic, direct product factor, Sylow
271#3508C2×C15111yescharacteristic
272#3229C2×C15111yescharacteristic, complemented
273C2×#486C2×C15111yescharacteristic, complemented
274#3039C2×C15111yescharacteristic, complemented
275#1642C2×C15114yescomplemented
276#1640C2×C15114yescomplemented
277#1545C2×C15111yescharacteristic, complemented
278#1493C2×C15111yescharacteristic, complemented
279#1476C2×C15111yescharacteristic, complemented
280C2×#137—21no—
281#559—21no—
282#559C22×C15112yes—
283#550—21no—
284#550C22×C15112yes—
285#546—22no—
286#546—22no—
287#540—22no—
288#535—21no—
289#533C22×C15111yescharacteristic
290#532—21no—
291#532—21no—
292C2×C4⋊Q8C22×C15111yescharacteristic
293C2×#127C22×C15111yescharacteristic
294#518—21no—
295C4×#41C22×C15111yescharacteristic
296#498—21no—
297#487—21no—
298#486—22no—
299#486C22×C15114yes—
300#483—22no—
301#475C22×C15114yescomplemented
302#462—21no—
303#462C22×C15112yescomplemented
304#461—21no—
305#461C22×C15112yescomplemented
306#431C22×C15111yescharacteristic
307#423C22×C15111yescharacteristic
308#419—21no—
309C2×#102—22no—
310C2×C4×C8C22×C15111yescharacteristic
311#331C22×C15114yes—
312Q8⋊C8C22×C15112yescomplemented
313Q8⋊C8C22×C15114yescomplemented
314D4⋊C8C22×C15112yescomplemented
315C2×#41—22no—
316C2×#41—22no—
317C2×#41D4×C15111yescharacteristic
318C22×Q8—21no—
319C22×D4—21no—
320C22×D4—21no—
321C22×D4D4×C15112yes—
322#137—44no—
323C2×Q16—22no—
324C2×SD16—22no—
325C2×M16—21no—
326C22×C8—21no—
327C4⋊Q8—21no—
328C4⋊Q8—21no—
329C4⋊Q8—21no—
330C4⋊Q8D4×C15111yescharacteristic
331C4⋊Q8D4×C15111yescharacteristic
332C4⋊Q8C23×C15112yes—
333#127—22no—
334#127—21no—
335#127—21no—
336#127D4×C15112yes—
337#127C23×C15112yes—
338#125—21no—
339#124—22no—
340#124—22no—
341#124—22no—
342#123—24no—
343#123—24no—
344C22⋊Q8—21no—
345C22⋊Q8D4×C15112yes—
346#121—22no—
347#121—22no—
348#121—22no—
349#121—24no—
350#121—24no—
351#121—22no—
352#120—24no—
353C4×Q8—21no—
354C4×Q8D4×C15111yescharacteristic
355C4×Q8C23×C15111yescharacteristic
356C4×Q8C23×C15112yes—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—21no—
361C4×D4—21no—
362C4×D4—22no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4D4×C15111yescharacteristic
366C4×D4C23×C15111yescharacteristic
367#117—21no—
368#117—21no—
369#117D4×C15111yescharacteristic
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C22⋊C4—24no—
373C2×C42—21no—
374C2×C42C23×C15111yescharacteristic
375#106—24no—
376C4⋊C8—21no—
377C4⋊C8C23×C15112yes—
378C4⋊C8C23×C15112yes—
379#103—24no—
380#103—22no—
381#103—22no—
382#102—28no—
383C22⋊C8—21no—
384C4×C8—21no—
385C4×C8—21no—
386C4×C8C23×C15112yes—
387C24—22no—
388#41—22no—
389#41—22no—
390#41—84no—
391#41—84no—
392C2×Q8—21no—
393C2×Q8—22no—
394C2×Q8—41no—
395C2×Q8—42no—
396C2×Q8—42no—
397C2×Q8C2×D4×C15112yes—
398C2×Q8C2×D4×C15111yescharacteristic
399C2×D4—21no—
400C2×D4—24no—
401C2×D4—24no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—44no—
408C2×D4—42no—
409C2×D4—42no—
410C2×D4—82no—
411C2×D4C2×D4×C15111yescharacteristic
412C2×D4C2×D4×C15114yes—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—41no—
419C22×C4C2×D4×C15111yescharacteristic
420C22×C4C2×D4×C15111yescharacteristic
421C22×C4C2×D4×C15111yescharacteristic
422Q16—44no—
423SD16—44no—
424M16—42no—
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—22no—
428C2×C8—42no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—22no—
434C4⋊C4—21no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—41no—
439C4⋊C4—41no—
440C4⋊C4C2×D4×C15111yescharacteristic
441C4⋊C4C2×D4×C15111yescharacteristic
442C4⋊C4C2×D4×C15112yes—
443C22⋊C4—24no—
444C22⋊C4—24no—
445C22⋊C4—24no—
446C22⋊C4—24no—
447C22⋊C4—21no—
448C22⋊C4—22no—
449C22⋊C4—21no—
450C22⋊C4—21no—
451C42—21no—
452C42—21no—
453C42—21no—
454C42—22no—
455C42C2×D4×C15111yescharacteristic
456C42C2×D4×C15111yescharacteristic
457C42C2×D4×C15111yescharacteristic
458C42C24×C15111yescharacteristic
459C23—24no—
460C23—21no—
461C23—44no—
462C23—82no—
463C23—82no—
464C23#120×C15111yescharacteristic
465Q8—21no—
466Q8—21no—
467Q8—24no—
468Q8—42no—
469Q8—42no—
470Q8—42no—
471Q8—82no—
472D4—21no—
473D4—21no—
474D4—44no—
475D4—42no—
476D4—44no—
477D4—44no—
478D4—42no—
479D4—42no—
480D4—44no—
481D4—82no—
482D4—84no—
483D4—84no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—84no—
496C2×C4—84no—
497C2×C4—82no—
498C2×C4#120×C15111yescharacteristic
499C2×C4#120×C15111yescharacteristic
500C2×C4#120×C15111yescharacteristic
501C2×C4#135×C15112yes—
502C2×C4AGL(1,ℤ/8)×C15112yes—
503C2×C4C22×D4×C15111yescharacteristic
504C2×C4C22×D4×C15111yescharacteristic
505C2×C4C22×D4×C15111yescharacteristic
506C8—42no—
507C8—42no—
508C8—42no—
509C22—21no—
510C22—21no—
511C22—41no—
512C22—44no—
513C22—41no—
514C22—44no—
515C22—41no—
516C22—44no—
517C22—164no—
518C22#449×C15112yes—
519C22C2×#120×C15111yescharacteristic
520C4—21no—
521C4—21no—
522C4—41no—
523C4—41no—
524C4—42no—
525C4—41no—
526C4—42no—
527C4—82no—
528C4#449×C15112yes—
529C4#455×C15112yes—
530C4C2×#135×C15111yescharacteristic
531C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
532C4#577×C15112yes—
533C2—22no—
534C2—84no—
535C2—81no—
536C2C2×#449×C15111yescharacteristic
537C2#3009×C15111yescharacteristic
538C2C2×#455×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3508×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
2. #3229×C151C2semidirect
3. C2×#486×C151C2semidirect
4. #3039×C151C2semidirect
5. #1642×C151C2semidirect
6. #1640×C151C2semidirect
7. #1545×C151C2semidirect
8. #1493×C151C2semidirect
9. #1476×C151C2semidirect
31. #475×C151C22semidirect
33. #462×C151C22semidirect
35. #461×C151C22semidirect
42. Q8⋊C8×C151C22semidirect
43. Q8⋊C8×C151C22semidirect
44. D4⋊C8×C151C22semidirect
269. #18634C151direct (N × H)
270. C151#18634direct (N × H)
272. #3229C2×C151semidirect
273. C2×#486C2×C151semidirect
274. #3039C2×C151semidirect
275. #1642C2×C151semidirect
276. #1640C2×C151semidirect
277. #1545C2×C151semidirect
278. #1493C2×C151semidirect
279. #1476C2×C151semidirect
301. #475C22×C151semidirect
303. #462C22×C151semidirect
305. #461C22×C151semidirect
312. Q8⋊C8C22×C151semidirect
313. Q8⋊C8C22×C151semidirect
314. D4⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3508×C1512
#3229×C1512
C2×#486×C1512
#3039×C1512
#1642×C1512
#1640×C1512
#1545×C1512
#1493×C1512
#1476×C1512
#18634151