Finite Group Databasebeta

← C151×#18644 #50323569

Subgroups — C151×#18644 #50323569

Order 38656.

968 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3509×C151C211yesmaximal, characteristic, complemented
2#3208×C151C211yesmaximal, characteristic, complemented
3C2×#486×C151C211yesmaximal, characteristic, complemented
4#3038×C151C211yesmaximal, characteristic
5#1628×C151C214yesmaximal, complemented
6#1626×C151C214yesmaximal, complemented
7#1546×C151C211yesmaximal, characteristic, complemented
8#1493×C151C211yesmaximal, characteristic, complemented
9#1476×C151C211yesmaximal, characteristic, complemented
10C2×AGL(1,ℤ/8)×C151—21no—
11#557×C151—21no—
12#557×C151C2212yescomplemented
13#556×C151—21no—
14#556×C151C2212yescomplemented
15#552×C151—22no—
16#552×C151—22no—
17#541×C151—22no—
18#536×C151—21no—
19#533×C151—21no—
20#533×C151—21no—
21#533×C151C2211yescharacteristic
22C2×C4⋊Q8×C151C2211yescharacteristic
23C2×#127×C151C2211yescharacteristic
24#519×C151—21no—
25C4×#41×C151C2211yescharacteristic
26#492×C151—21no—
27#486×C151—22no—
28#486×C151—21no—
29#486×C151C2214yes—
30#460×C151—21no—
31#460×C151C2212yes—
32#460×C151C2214yes—
33#459×C151—21no—
34#459×C151C2212yes—
35#450×C151—22no—
36#431×C151C2211yescharacteristic
37#423×C151C2211yescharacteristic
38#418×C151—21no—
39C2×#102×C151—22no—
40C2×C4×C8×C151C2211yescharacteristic
41#332×C151C2214yescomplemented
42Q8⋊C8×C151C2212yescomplemented
43Q8⋊C8×C151C2214yescomplemented
44D4⋊C8×C151C2212yescomplemented
45C2×#41×C151D411yescharacteristic
46C22×Q8×C151—21no—
47C22×D4×C151—21no—
48C22×D4×C151—21no—
49C22×D4×C151—21no—
50AGL(1,ℤ/8)×C151—44no—
51C2×SD16×C151—22no—
52C2×SD16×C151—24no—
53C2×D8×C151—22no—
54C2×M16×C151—21no—
55C22×C8×C151—21no—
56C4⋊Q8×C151—21no—
57C4⋊Q8×C151—21no—
58C4⋊Q8×C151—22no—
59C4⋊Q8×C151D412yes—
60C4⋊Q8×C151D411yescharacteristic
61C4⋊Q8×C151D411yescharacteristic
62C4⋊Q8×C151C2312yes—
63#127×C151—21no—
64#127×C151—21no—
65#127×C151—21no—
66#127×C151C2312yes—
67#126×C151—24no—
68#126×C151—24no—
69#125×C151—22no—
70#125×C151—24no—
71#125×C151—22no—
72#125×C151—24no—
73#125×C151—21no—
74#124×C151—22no—
75#123×C151—24no—
76C22⋊Q8×C151—22no—
77C22⋊Q8×C151—22no—
78C22⋊Q8×C151—22no—
79C22⋊Q8×C151—21no—
80C22⋊Q8×C151—22no—
81C22⋊Q8×C151D412yes—
82C4×Q8×C151—22no—
83C4×Q8×C151—22no—
84C4×Q8×C151—22no—
85C4×Q8×C151—22no—
86C4×Q8×C151—22no—
87C4×Q8×C151—21no—
88C4×Q8×C151—22no—
89C4×Q8×C151D411yescharacteristic
90C4×Q8×C151C2311yescharacteristic
91C4×Q8×C151C2312yes—
92C4×D4×C151—21no—
93C4×D4×C151—21no—
94C4×D4×C151D411yescharacteristic
95C4×D4×C151C2311yescharacteristic
96#117×C151—24no—
97#117×C151—22no—
98#117×C151—21no—
99#117×C151—22no—
100#117×C151—21no—
101#117×C151D411yescharacteristic
102C2×C4⋊C4×C151—21no—
103C2×C4⋊C4×C151D412yes—
104C2×C42×C151—21no—
105C2×C42×C151C2311yescharacteristic
106C4⋊C8×C151—21no—
107C4⋊C8×C151C2312yes—
108C4⋊C8×C151C2312yes—
109#102×C151—28no—
110#102×C151—22no—
111#102×C151—22no—
112#102×C151—24no—
113C22⋊C8×C151—21no—
114C4×C8×C151—21no—
115C4×C8×C151—21no—
116C4×C8×C151C2312yes—
117C24×C151—41no—
118#41×C151—22no—
119#41×C151—22no—
120C2×Q8×C151—21no—
121C2×Q8×C151—22no—
122C2×Q8×C151—22no—
123C2×Q8×C151—42no—
124C2×Q8×C151—42no—
125C2×Q8×C151C2×D412yes—
126C2×Q8×C151C2×D411yescharacteristic
127C2×D4×C151—21no—
128C2×D4×C151—22no—
129C2×D4×C151—22no—
130C2×D4×C151—22no—
131C2×D4×C151—44no—
132C2×D4×C151—41no—
133C2×D4×C151—41no—
134C2×D4×C151—41no—
135C2×D4×C151—42no—
136C2×D4×C151—42no—
137C2×D4×C151—82no—
138C2×D4×C151C2×D411yescharacteristic
139C22×C4×C151—22no—
140C22×C4×C151—21no—
141C22×C4×C151—21no—
142C22×C4×C151—21no—
143C22×C4×C151C2×D411yescharacteristic
144C22×C4×C151C2×D411yescharacteristic
145C22×C4×C151C2×D411yescharacteristic
146SD16×C151—44no—
147SD16×C151—84no—
148D8×C151—44no—
149M16×C151—42no—
150C2×C8×C151—22no—
151C2×C8×C151—22no—
152C2×C8×C151—22no—
153C2×C8×C151—42no—
154C4⋊C4×C151—24no—
155C4⋊C4×C151—24no—
156C4⋊C4×C151—24no—
157C4⋊C4×C151—24no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—21no—
161C4⋊C4×C151—21no—
162C4⋊C4×C151—21no—
163C4⋊C4×C151—21no—
164C4⋊C4×C151—22no—
165C4⋊C4×C151—22no—
166C4⋊C4×C151—21no—
167C4⋊C4×C151—22no—
168C4⋊C4×C151C2×D414yes—
169C4⋊C4×C151C2×D412yes—
170C4⋊C4×C151C2×D411yescharacteristic
171C4⋊C4×C151C2×D411yescharacteristic
172C22⋊C4×C151—24no—
173C22⋊C4×C151—24no—
174C22⋊C4×C151—21no—
175C22⋊C4×C151—22no—
176C22⋊C4×C151—21no—
177C22⋊C4×C151—21no—
178C42×C151—24no—
179C42×C151—24no—
180C42×C151—21no—
181C42×C151—21no—
182C42×C151—21no—
183C42×C151—22no—
184C42×C151C2×D411yescharacteristic
185C42×C151C2×D411yescharacteristic
186C42×C151C2×D411yescharacteristic
187C42×C151C2411yescharacteristic
188C23×C151—21no—
189C23×C151—42no—
190C23×C151—82no—
191C23×C151—82no—
192C23×C151—82no—
193C23×C151#12011yescharacteristic
194Q8×C151—21no—
195Q8×C151—21no—
196Q8×C151—24no—
197Q8×C151—42no—
198Q8×C151—42no—
199Q8×C151—44no—
200Q8×C151—42no—
201D4×C151—21no—
202D4×C151—21no—
203D4×C151—44no—
204D4×C151—42no—
205D4×C151—42no—
206D4×C151—42no—
207D4×C151—44no—
208D4×C151—82no—
209D4×C151—82no—
210D4×C151—82no—
211C2×C4×C151—22no—
212C2×C4×C151—22no—
213C2×C4×C151—24no—
214C2×C4×C151—22no—
215C2×C4×C151—22no—
216C2×C4×C151—21no—
217C2×C4×C151—21no—
218C2×C4×C151—21no—
219C2×C4×C151—44no—
220C2×C4×C151—42no—
221C2×C4×C151—42no—
222C2×C4×C151—42no—
223C2×C4×C151#12011yescharacteristic
224C2×C4×C151#12011yescharacteristic
225C2×C4×C151#12011yescharacteristic
226C2×C4×C151#13512yes—
227C2×C4×C151AGL(1,ℤ/8)12yes—
228C2×C4×C151C22×D411yescharacteristic
229C2×C4×C151C22×D411yescharacteristic
230C2×C4×C151C22×D411yescharacteristic
231C8×C151—42no—
232C8×C151—42no—
233C8×C151—42no—
234C22×C151—21no—
235C22×C151—21no—
236C22×C151—41no—
237C22×C151—41no—
238C22×C151—41no—
239C22×C151—82no—
240C22×C151—82no—
241C22×C151—82no—
242C22×C151—164no—
243C22×C151#44912yes—
244C22×C151C2×#12011yescharacteristic
245C4×C151—21no—
246C4×C151—21no—
247C4×C151—41no—
248C4×C151—44no—
249C4×C151—41no—
250C4×C151—42no—
251C4×C151—41no—
252C4×C151—42no—
253C4×C151#44912yes—
254C4×C151#45412yes—
255C4×C151C2×#13511yescharacteristic
256C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
257C4×C151#57712yes—
258C2×C151—22no—
259C2×C151—81no—
260C2×C151—162no—
261C2×C151C2×#44911yescharacteristic
262C2×C151#301011yescharacteristic
263C2×C151C2×#45411yescharacteristic
264#18644C15111yesmaximal, characteristic, direct product factor, Sylow
265C151#1864411yescharacteristic, direct product factor, Sylow
266#3509C2×C15111yescharacteristic, complemented
267#3208C2×C15111yescharacteristic, complemented
268C2×#486C2×C15111yescharacteristic, complemented
269#3038C2×C15111yescharacteristic
270#1628C2×C15114yescomplemented
271#1626C2×C15114yescomplemented
272#1546C2×C15111yescharacteristic, complemented
273#1493C2×C15111yescharacteristic, complemented
274#1476C2×C15111yescharacteristic, complemented
275C2×AGL(1,ℤ/8)—21no—
276#557—21no—
277#557C22×C15112yescomplemented
278#556—21no—
279#556C22×C15112yescomplemented
280#552—22no—
281#552—22no—
282#541—22no—
283#536—21no—
284#533—21no—
285#533—21no—
286#533C22×C15111yescharacteristic
287C2×C4⋊Q8C22×C15111yescharacteristic
288C2×#127C22×C15111yescharacteristic
289#519—21no—
290C4×#41C22×C15111yescharacteristic
291#492—21no—
292#486—22no—
293#486—21no—
294#486C22×C15114yes—
295#460—21no—
296#460C22×C15112yes—
297#460C22×C15114yes—
298#459—21no—
299#459C22×C15112yes—
300#450—22no—
301#431C22×C15111yescharacteristic
302#423C22×C15111yescharacteristic
303#418—21no—
304C2×#102—22no—
305C2×C4×C8C22×C15111yescharacteristic
306#332C22×C15114yescomplemented
307Q8⋊C8C22×C15112yescomplemented
308Q8⋊C8C22×C15114yescomplemented
309D4⋊C8C22×C15112yescomplemented
310C2×#41D4×C15111yescharacteristic
311C22×Q8—21no—
312C22×D4—21no—
313C22×D4—21no—
314C22×D4—21no—
315AGL(1,ℤ/8)—44no—
316C2×SD16—22no—
317C2×SD16—24no—
318C2×D8—22no—
319C2×M16—21no—
320C22×C8—21no—
321C4⋊Q8—22no—
322C4⋊Q8—21no—
323C4⋊Q8—21no—
324C4⋊Q8D4×C15111yescharacteristic
325C4⋊Q8D4×C15112yes—
326C4⋊Q8D4×C15111yescharacteristic
327C4⋊Q8C23×C15112yes—
328#127—21no—
329#127—21no—
330#127—21no—
331#127C23×C15112yes—
332#126—24no—
333#126—24no—
334#125—22no—
335#125—24no—
336#125—22no—
337#125—24no—
338#125—21no—
339#124—22no—
340#123—24no—
341C22⋊Q8—22no—
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344C22⋊Q8—22no—
345C22⋊Q8—21no—
346C22⋊Q8D4×C15112yes—
347C4×Q8—22no—
348C4×Q8—22no—
349C4×Q8—22no—
350C4×Q8—22no—
351C4×Q8—22no—
352C4×Q8—22no—
353C4×Q8—21no—
354C4×Q8D4×C15111yescharacteristic
355C4×Q8C23×C15111yescharacteristic
356C4×Q8C23×C15112yes—
357C4×D4—21no—
358C4×D4—21no—
359C4×D4D4×C15111yescharacteristic
360C4×D4C23×C15111yescharacteristic
361#117—24no—
362#117—22no—
363#117—21no—
364#117—22no—
365#117—21no—
366#117D4×C15111yescharacteristic
367C2×C4⋊C4—21no—
368C2×C4⋊C4D4×C15112yes—
369C2×C42—21no—
370C2×C42C23×C15111yescharacteristic
371C4⋊C8—21no—
372C4⋊C8C23×C15112yes—
373C4⋊C8C23×C15112yes—
374#102—28no—
375#102—22no—
376#102—22no—
377#102—24no—
378C22⋊C8—21no—
379C4×C8—21no—
380C4×C8—21no—
381C4×C8C23×C15112yes—
382C24—41no—
383#41—22no—
384#41—22no—
385C2×Q8—21no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—42no—
389C2×Q8—42no—
390C2×Q8C2×D4×C15112yes—
391C2×Q8C2×D4×C15111yescharacteristic
392C2×D4—21no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—44no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—42no—
401C2×D4—42no—
402C2×D4—82no—
403C2×D4C2×D4×C15111yescharacteristic
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4C2×D4×C15111yescharacteristic
409C22×C4C2×D4×C15111yescharacteristic
410C22×C4C2×D4×C15111yescharacteristic
411SD16—44no—
412SD16—84no—
413D8—44no—
414M16—42no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—42no—
419C4⋊C4—24no—
420C4⋊C4—24no—
421C4⋊C4—24no—
422C4⋊C4—24no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—21no—
432C4⋊C4—22no—
433C4⋊C4C2×D4×C15114yes—
434C4⋊C4C2×D4×C15112yes—
435C4⋊C4C2×D4×C15111yescharacteristic
436C4⋊C4C2×D4×C15111yescharacteristic
437C22⋊C4—24no—
438C22⋊C4—24no—
439C22⋊C4—21no—
440C22⋊C4—22no—
441C22⋊C4—21no—
442C22⋊C4—21no—
443C42—24no—
444C42—24no—
445C42—21no—
446C42—21no—
447C42—21no—
448C42—22no—
449C42C2×D4×C15111yescharacteristic
450C42C2×D4×C15111yescharacteristic
451C42C2×D4×C15111yescharacteristic
452C42C24×C15111yescharacteristic
453C23—21no—
454C23—42no—
455C23—82no—
456C23—82no—
457C23—82no—
458C23#120×C15111yescharacteristic
459Q8—21no—
460Q8—21no—
461Q8—24no—
462Q8—44no—
463Q8—42no—
464Q8—42no—
465Q8—42no—
466D4—21no—
467D4—21no—
468D4—44no—
469D4—42no—
470D4—42no—
471D4—42no—
472D4—44no—
473D4—82no—
474D4—82no—
475D4—82no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—24no—
483C2×C4—21no—
484C2×C4—44no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4#120×C15111yescharacteristic
489C2×C4#120×C15111yescharacteristic
490C2×C4#120×C15111yescharacteristic
491C2×C4#135×C15112yes—
492C2×C4AGL(1,ℤ/8)×C15112yes—
493C2×C4C22×D4×C15111yescharacteristic
494C2×C4C22×D4×C15111yescharacteristic
495C2×C4C22×D4×C15111yescharacteristic
496C8—42no—
497C8—42no—
498C8—42no—
499C22—21no—
500C22—21no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—82no—
505C22—82no—
506C22—82no—
507C22—164no—
508C22#449×C15112yes—
509C22C2×#120×C15111yescharacteristic
510C4—21no—
511C4—21no—
512C4—41no—
513C4—44no—
514C4—41no—
515C4—42no—
516C4—41no—
517C4—42no—
518C4#449×C15112yes—
519C4#454×C15112yes—
520C4C2×#135×C15111yescharacteristic
521C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
522C4#577×C15112yes—
523C2—22no—
524C2—81no—
525C2—162no—
526C2C2×#449×C15111yescharacteristic
527C2#3010×C15111yescharacteristic
528C2C2×#454×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3038×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. #3509×C151C2semidirect
2. #3208×C151C2semidirect
3. C2×#486×C151C2semidirect
5. #1628×C151C2semidirect
6. #1626×C151C2semidirect
7. #1546×C151C2semidirect
8. #1493×C151C2semidirect
9. #1476×C151C2semidirect
12. #557×C151C22semidirect
14. #556×C151C22semidirect
41. #332×C151C22semidirect
42. Q8⋊C8×C151C22semidirect
43. Q8⋊C8×C151C22semidirect
44. D4⋊C8×C151C22semidirect
264. #18644C151direct (N × H)
265. C151#18644direct (N × H)
266. #3509C2×C151semidirect
267. #3208C2×C151semidirect
268. C2×#486C2×C151semidirect
270. #1628C2×C151semidirect
271. #1626C2×C151semidirect
272. #1546C2×C151semidirect
273. #1493C2×C151semidirect
274. #1476C2×C151semidirect
277. #557C22×C151semidirect
279. #556C22×C151semidirect
306. #332C22×C151semidirect
307. Q8⋊C8C22×C151semidirect
308. Q8⋊C8C22×C151semidirect
309. D4⋊C8C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3509×C1512
#3208×C1512
C2×#486×C1512
#3038×C1512
#1628×C1512
#1626×C1512
#1546×C1512
#1493×C1512
#1476×C1512
#18644151