Finite Group Databasebeta

← C151×#18625 #50323550

Subgroups — C151×#18625 #50323550

Order 38656.

1056 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3508×C151C211yesmaximal, characteristic
2#3230×C151C211yesmaximal, characteristic, complemented
3C2×#492×C151C211yesmaximal, characteristic, complemented
4#3079×C151C211yesmaximal, characteristic, complemented
5#1631×C151C214yesmaximal, complemented
6#1630×C151C214yesmaximal, complemented
7#1545×C151C211yesmaximal, characteristic, complemented
8#1493×C151C211yesmaximal, characteristic, complemented
9#1476×C151C211yesmaximal, characteristic, complemented
10C22×SD16×C151—22no—
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#500×C151—21no—
27#492×C151—22no—
28#492×C151C2214yes—
29#487×C151—21no—
30#484×C151—22no—
31#477×C151C2212yescomplemented
32#477×C151C2214yescomplemented
33#476×C151C2212yescomplemented
34#475×C151—21no—
35#474×C151—21no—
36#431×C151C2211yescharacteristic
37#428×C151—21no—
38#423×C151C2211yescharacteristic
39#417×C151—21no—
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—
52C2×SD16×C151—28no—
53C2×SD16×C151—48no—
54C2×M16×C151—21no—
55C22×C8×C151—21no—
56C4⋊Q8×C151—21no—
57C4⋊Q8×C151—21no—
58C4⋊Q8×C151—21no—
59C4⋊Q8×C151D411yescharacteristic
60C4⋊Q8×C151D411yescharacteristic
61C4⋊Q8×C151C2312yes—
62#127×C151—22no—
63#127×C151—21no—
64#127×C151—21no—
65#127×C151D412yes—
66#127×C151C2312yes—
67#125×C151—21no—
68#124×C151—22no—
69#124×C151—22no—
70#124×C151—22no—
71#123×C151—24no—
72#123×C151—24no—
73C22⋊Q8×C151—21no—
74C22⋊Q8×C151D412yes—
75#121×C151—22no—
76#121×C151—22no—
77#121×C151—22no—
78#121×C151—24no—
79#121×C151—24no—
80#121×C151—22no—
81#120×C151—24no—
82C4×Q8×C151—21no—
83C4×Q8×C151D411yescharacteristic
84C4×Q8×C151C2311yescharacteristic
85C4×Q8×C151C2312yes—
86C4×D4×C151—22no—
87C4×D4×C151—22no—
88C4×D4×C151—22no—
89C4×D4×C151—21no—
90C4×D4×C151—21no—
91C4×D4×C151—22no—
92C4×D4×C151—22no—
93C4×D4×C151—22no—
94C4×D4×C151D411yescharacteristic
95C4×D4×C151C2311yescharacteristic
96#117×C151—21no—
97#117×C151—21no—
98#117×C151D411yescharacteristic
99C2×C4⋊C4×C151—21no—
100C2×C4⋊C4×C151—21no—
101C2×C22⋊C4×C151—24no—
102C2×C42×C151—21no—
103C2×C42×C151C2311yescharacteristic
104#107×C151—22no—
105#107×C151—24no—
106#106×C151—22no—
107C4⋊C8×C151—21no—
108C4⋊C8×C151C2312yes—
109C4⋊C8×C151C2312yes—
110#103×C151—22no—
111#103×C151—24no—
112#102×C151—22no—
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—44no—
125C2×Q8×C151—41no—
126C2×Q8×C151C2×D411yescharacteristic
127C2×Q8×C151C2×D412yes—
128C2×D4×C151—21no—
129C2×D4×C151—24no—
130C2×D4×C151—24no—
131C2×D4×C151—22no—
132C2×D4×C151—22no—
133C2×D4×C151—22no—
134C2×D4×C151—22no—
135C2×D4×C151—22no—
136C2×D4×C151—44no—
137C2×D4×C151—42no—
138C2×D4×C151—42no—
139C2×D4×C151—82no—
140C2×D4×C151C2×D411yescharacteristic
141C2×D4×C151C2×D414yes—
142C22×C4×C151—24no—
143C22×C4×C151—24no—
144C22×C4×C151—21no—
145C22×C4×C151—21no—
146C22×C4×C151—21no—
147C22×C4×C151—41no—
148C22×C4×C151C2×D411yescharacteristic
149C22×C4×C151C2×D411yescharacteristic
150C22×C4×C151C2×D411yescharacteristic
151SD16×C151—416no—
152M16×C151—42no—
153C2×C8×C151—24no—
154C2×C8×C151—22no—
155C2×C8×C151—22no—
156C2×C8×C151—22no—
157C4⋊C4×C151—21no—
158C4⋊C4×C151—21no—
159C4⋊C4×C151—21no—
160C4⋊C4×C151—21no—
161C4⋊C4×C151—22no—
162C4⋊C4×C151—21no—
163C4⋊C4×C151—22no—
164C4⋊C4×C151—22no—
165C4⋊C4×C151—22no—
166C4⋊C4×C151—41no—
167C4⋊C4×C151—41no—
168C4⋊C4×C151C2×D411yescharacteristic
169C4⋊C4×C151C2×D411yescharacteristic
170C4⋊C4×C151C2×D412yes—
171C22⋊C4×C151—24no—
172C22⋊C4×C151—24no—
173C22⋊C4×C151—24no—
174C22⋊C4×C151—24no—
175C22⋊C4×C151—21no—
176C22⋊C4×C151—22no—
177C22⋊C4×C151—21no—
178C22⋊C4×C151—21no—
179C42×C151—21no—
180C42×C151—21no—
181C42×C151—21no—
182C42×C151—22no—
183C42×C151C2×D411yescharacteristic
184C42×C151C2×D411yescharacteristic
185C42×C151C2×D411yescharacteristic
186C42×C151C2411yescharacteristic
187C23×C151—24no—
188C23×C151—21no—
189C23×C151—44no—
190C23×C151—82no—
191C23×C151—82no—
192C23×C151#12011yescharacteristic
193Q8×C151—21no—
194Q8×C151—21no—
195Q8×C151—24no—
196Q8×C151—44no—
197Q8×C151—42no—
198Q8×C151—82no—
199D4×C151—21no—
200D4×C151—21no—
201D4×C151—44no—
202D4×C151—42no—
203D4×C151—42no—
204D4×C151—42no—
205D4×C151—44no—
206D4×C151—44no—
207D4×C151—44no—
208D4×C151—82no—
209D4×C151—84no—
210D4×C151—84no—
211C2×C4×C151—22no—
212C2×C4×C151—22no—
213C2×C4×C151—22no—
214C2×C4×C151—21no—
215C2×C4×C151—22no—
216C2×C4×C151—21no—
217C2×C4×C151—21no—
218C2×C4×C151—42no—
219C2×C4×C151—42no—
220C2×C4×C151—42no—
221C2×C4×C151—42no—
222C2×C4×C151—84no—
223C2×C4×C151—84no—
224C2×C4×C151—82no—
225C2×C4×C151#12011yescharacteristic
226C2×C4×C151#12011yescharacteristic
227C2×C4×C151#12011yescharacteristic
228C2×C4×C151#13512yes—
229C2×C4×C151#13712yes—
230C2×C4×C151C22×D411yescharacteristic
231C2×C4×C151C22×D411yescharacteristic
232C2×C4×C151C22×D411yescharacteristic
233C8×C151—24no—
234C8×C151—42no—
235C8×C151—42no—
236C22×C151—21no—
237C22×C151—21no—
238C22×C151—41no—
239C22×C151—44no—
240C22×C151—41no—
241C22×C151—44no—
242C22×C151—41no—
243C22×C151—44no—
244C22×C151—164no—
245C22×C151#45212yes—
246C22×C151C2×#12011yescharacteristic
247C4×C151—21no—
248C4×C151—21no—
249C4×C151—41no—
250C4×C151—41no—
251C4×C151—42no—
252C4×C151—41no—
253C4×C151—42no—
254C4×C151—82no—
255C4×C151#45212yes—
256C4×C151#45312yes—
257C4×C151C2×#13511yescharacteristic
258C4×C151C2×#13711yescharacteristic
259C4×C151#57712yes—
260C2×C151—22no—
261C2×C151—81no—
262C2×C151—84no—
263C2×C151C2×#45211yescharacteristic
264C2×C151#300911yescharacteristic
265C2×C151C2×#45311yescharacteristic
266#18625C15111yesmaximal, characteristic, direct product factor, Sylow
267C151#1862511yescharacteristic, direct product factor, Sylow
268#3508C2×C15111yescharacteristic
269#3230C2×C15111yescharacteristic, complemented
270C2×#492C2×C15111yescharacteristic, complemented
271#3079C2×C15111yescharacteristic, complemented
272#1631C2×C15114yescomplemented
273#1630C2×C15114yescomplemented
274#1545C2×C15111yescharacteristic, complemented
275#1493C2×C15111yescharacteristic, complemented
276#1476C2×C15111yescharacteristic, complemented
277C22×SD16—22no—
278#559—21no—
279#559C22×C15112yes—
280#550—21no—
281#550C22×C15112yes—
282#546—22no—
283#546—22no—
284#540—22no—
285#535—21no—
286#533C22×C15111yescharacteristic
287#532—21no—
288#532—21no—
289C2×C4⋊Q8C22×C15111yescharacteristic
290C2×#127C22×C15111yescharacteristic
291#518—21no—
292C4×#41C22×C15111yescharacteristic
293#500—21no—
294#492—22no—
295#492C22×C15114yes—
296#487—21no—
297#484—22no—
298#477C22×C15112yescomplemented
299#477C22×C15114yescomplemented
300#476C22×C15112yescomplemented
301#475—21no—
302#474—21no—
303#431C22×C15111yescharacteristic
304#428—21no—
305#423C22×C15111yescharacteristic
306#417—21no—
307C2×C4×C8C22×C15111yescharacteristic
308#331C22×C15114yes—
309Q8⋊C8C22×C15112yescomplemented
310Q8⋊C8C22×C15114yescomplemented
311D4⋊C8C22×C15112yescomplemented
312C2×#41—22no—
313C2×#41—22no—
314C2×#41D4×C15111yescharacteristic
315C22×Q8—21no—
316C22×D4—21no—
317C22×D4—21no—
318C22×D4D4×C15112yes—
319C2×SD16—28no—
320C2×SD16—48no—
321C2×M16—21no—
322C22×C8—21no—
323C4⋊Q8—21no—
324C4⋊Q8—21no—
325C4⋊Q8—21no—
326C4⋊Q8D4×C15111yescharacteristic
327C4⋊Q8D4×C15111yescharacteristic
328C4⋊Q8C23×C15112yes—
329#127—22no—
330#127—21no—
331#127—21no—
332#127D4×C15112yes—
333#127C23×C15112yes—
334#125—21no—
335#124—22no—
336#124—22no—
337#124—22no—
338#123—24no—
339#123—24no—
340C22⋊Q8—21no—
341C22⋊Q8D4×C15112yes—
342#121—22no—
343#121—22no—
344#121—22no—
345#121—24no—
346#121—24no—
347#121—22no—
348#120—24no—
349C4×Q8—21no—
350C4×Q8D4×C15111yescharacteristic
351C4×Q8C23×C15111yescharacteristic
352C4×Q8C23×C15112yes—
353C4×D4—22no—
354C4×D4—22no—
355C4×D4—22no—
356C4×D4—21no—
357C4×D4—21no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4D4×C15111yescharacteristic
362C4×D4C23×C15111yescharacteristic
363#117—21no—
364#117—21no—
365#117D4×C15111yescharacteristic
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C22⋊C4—24no—
369C2×C42—21no—
370C2×C42C23×C15111yescharacteristic
371#107—22no—
372#107—24no—
373#106—22no—
374C4⋊C8—21no—
375C4⋊C8C23×C15112yes—
376C4⋊C8C23×C15112yes—
377#103—22no—
378#103—24no—
379#102—22no—
380C22⋊C8—21no—
381C4×C8—21no—
382C4×C8—21no—
383C4×C8C23×C15112yes—
384C24—22no—
385#41—22no—
386#41—22no—
387#41—84no—
388#41—84no—
389C2×Q8—21no—
390C2×Q8—22no—
391C2×Q8—44no—
392C2×Q8—41no—
393C2×Q8C2×D4×C15111yescharacteristic
394C2×Q8C2×D4×C15112yes—
395C2×D4—21no—
396C2×D4—24no—
397C2×D4—24no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—44no—
404C2×D4—42no—
405C2×D4—42no—
406C2×D4—82no—
407C2×D4C2×D4×C15111yescharacteristic
408C2×D4C2×D4×C15114yes—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—41no—
415C22×C4C2×D4×C15111yescharacteristic
416C22×C4C2×D4×C15111yescharacteristic
417C22×C4C2×D4×C15111yescharacteristic
418SD16—416no—
419M16—42no—
420C2×C8—24no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—22no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—22no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—41no—
434C4⋊C4—41no—
435C4⋊C4C2×D4×C15111yescharacteristic
436C4⋊C4C2×D4×C15111yescharacteristic
437C4⋊C4C2×D4×C15112yes—
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—24no—
441C22⋊C4—24no—
442C22⋊C4—21no—
443C22⋊C4—22no—
444C22⋊C4—21no—
445C22⋊C4—21no—
446C42—21no—
447C42—21no—
448C42—21no—
449C42—22no—
450C42C2×D4×C15111yescharacteristic
451C42C2×D4×C15111yescharacteristic
452C42C2×D4×C15111yescharacteristic
453C42C24×C15111yescharacteristic
454C23—24no—
455C23—21no—
456C23—44no—
457C23—82no—
458C23—82no—
459C23#120×C15111yescharacteristic
460Q8—21no—
461Q8—21no—
462Q8—24no—
463Q8—44no—
464Q8—42no—
465Q8—82no—
466D4—21no—
467D4—21no—
468D4—44no—
469D4—42no—
470D4—44no—
471D4—44no—
472D4—42no—
473D4—42no—
474D4—44no—
475D4—82no—
476D4—84no—
477D4—84no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—84no—
490C2×C4—84no—
491C2×C4—82no—
492C2×C4#120×C15111yescharacteristic
493C2×C4#120×C15111yescharacteristic
494C2×C4#120×C15111yescharacteristic
495C2×C4#135×C15112yes—
496C2×C4#137×C15112yes—
497C2×C4C22×D4×C15111yescharacteristic
498C2×C4C22×D4×C15111yescharacteristic
499C2×C4C22×D4×C15111yescharacteristic
500C8—24no—
501C8—42no—
502C8—42no—
503C22—21no—
504C22—21no—
505C22—41no—
506C22—44no—
507C22—41no—
508C22—44no—
509C22—41no—
510C22—44no—
511C22—164no—
512C22#452×C15112yes—
513C22C2×#120×C15111yescharacteristic
514C4—21no—
515C4—21no—
516C4—41no—
517C4—41no—
518C4—42no—
519C4—41no—
520C4—42no—
521C4—82no—
522C4#452×C15112yes—
523C4#453×C15112yes—
524C4C2×#135×C15111yescharacteristic
525C4C2×#137×C15111yescharacteristic
526C4#577×C15112yes—
527C2—22no—
528C2—84no—
529C2—81no—
530C2C2×#452×C15111yescharacteristic
531C2#3009×C15111yescharacteristic
532C2C2×#453×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. #3230×C151C2semidirect
3. C2×#492×C151C2semidirect
4. #3079×C151C2semidirect
5. #1631×C151C2semidirect
6. #1630×C151C2semidirect
7. #1545×C151C2semidirect
8. #1493×C151C2semidirect
9. #1476×C151C2semidirect
31. #477×C151C22semidirect
32. #477×C151C22semidirect
33. #476×C151C22semidirect
42. Q8⋊C8×C151C22semidirect
43. Q8⋊C8×C151C22semidirect
44. D4⋊C8×C151C22semidirect
266. #18625C151direct (N × H)
267. C151#18625direct (N × H)
269. #3230C2×C151semidirect
270. C2×#492C2×C151semidirect
271. #3079C2×C151semidirect
272. #1631C2×C151semidirect
273. #1630C2×C151semidirect
274. #1545C2×C151semidirect
275. #1493C2×C151semidirect
276. #1476C2×C151semidirect
298. #477C22×C151semidirect
299. #477C22×C151semidirect
300. #476C22×C151semidirect
309. Q8⋊C8C22×C151semidirect
310. Q8⋊C8C22×C151semidirect
311. 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
#3230×C1512
C2×#492×C1512
#3079×C1512
#1631×C1512
#1630×C1512
#1545×C1512
#1493×C1512
#1476×C1512
#18625151