Finite Group Databasebeta

← C151×#19318 #50324243

Subgroups — C151×#19318 #50324243

Order 38656.

620 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3141×C151C211yesmaximal, characteristic, complemented
2#3115×C151C211yesmaximal, characteristic
3#3079×C151C211yesmaximal, characteristic, complemented
4#2970×C151C211yesmaximal, characteristic, complemented
5#1704×C151C212yesmaximal, complemented
6#1698×C151C212yesmaximal, complemented
7#1683×C151C212yesmaximal, complemented
8#1677×C151C212yesmaximal, complemented
9#1569×C151C211yesmaximal, characteristic, complemented
10#1558×C151C211yesmaximal, characteristic, complemented
11#1557×C151C211yesmaximal, characteristic, complemented
12#532×C151C2211yescharacteristic
13C2×C4⋊Q8×C151C2211yescharacteristic
14C4×#41×C151C2211yescharacteristic
15#489×C151—21no—
16#489×C151—21no—
17#487×C151C2212yes—
18#486×C151C2212yes—
19#482×C151—21no—
20#477×C151C2212yes—
21#476×C151C2212yes—
22#475×C151—21no—
23#475×C151C2211yescharacteristic
24#474×C151—21no—
25#474×C151C2211yescharacteristic
26#460×C151C2211yescharacteristic
27#459×C151C2211yescharacteristic
28#449×C151—21no—
29#446×C151C2212yes—
30#442×C151—21no—
31#440×C151—21no—
32#435×C151—22no—
33C8×D4×C151C2212yes—
34#432×C151—21no—
35#432×C151C2211yescharacteristic
36#432×C151C2211yescharacteristic
37#428×C151—21no—
38#423×C151C2211yescharacteristic
39#417×C151—21no—
40#417×C151—22no—
41C4×M16×C151C2211yescharacteristic
42C2×#97×C151—21no—
43#335×C151C2212yes—
44#334×C151C2212yes—
45#333×C151C2212yes—
46#333×C151C2212yes—
47#332×C151C2212yes—
48#331×C151C2212yes—
49C2×#41×C151—21no—
50C2×#41×C151D411yescharacteristic
51C22×Q8×C151—21no—
52C2×SD16×C151—21no—
53C2×D8×C151—21no—
54C2×M16×C151—21no—
55C2×M16×C151D412yes—
56C22×C8×C151—22no—
57C4⋊Q8×C151—21no—
58C4⋊Q8×C151—21no—
59C4⋊Q8×C151—21no—
60C4⋊Q8×C151C2311yescharacteristic
61C4⋊Q8×C151C2312yes—
62#127×C151C2311yescharacteristic
63#124×C151—21no—
64#121×C151—21no—
65#121×C151—21no—
66C4×Q8×C151D411yescharacteristic
67C4×Q8×C151C2311yescharacteristic
68C4×D4×C151—21no—
69C4×D4×C151—21no—
70C4×D4×C151—21no—
71C4×D4×C151—21no—
72C4×D4×C151D411yescharacteristic
73C4×D4×C151C2311yescharacteristic
74#117×C151—21no—
75#117×C151D411yescharacteristic
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—21no—
78C2×C42×C151—21no—
79C2×C42×C151C2311yescharacteristic
80#107×C151—22no—
81#107×C151—21no—
82#106×C151—22no—
83#106×C151—21no—
84C4⋊C8×C151—22no—
85C4⋊C8×C151—21no—
86C4⋊C8×C151C2312yes—
87C4⋊C8×C151C2312yes—
88C4⋊C8×C151C2311yescharacteristic
89C4⋊C8×C151C2311yescharacteristic
90#103×C151—22no—
91#103×C151—22no—
92#103×C151—22no—
93#103×C151—21no—
94#102×C151—22no—
95#102×C151—21no—
96#102×C151—22no—
97#102×C151—22no—
98#102×C151—21no—
99#102×C151—21no—
100C22⋊C8×C151—21no—
101C22⋊C8×C151—21no—
102C22⋊C8×C151—22no—
103#97×C151—22no—
104#97×C151—21no—
105#97×C151—21no—
106#97×C151D411yescharacteristic
107#97×C151D411yescharacteristic
108C4×C8×C151C2312yes—
109#41×C151—22no—
110#41×C151—41no—
111#41×C151—44no—
112C2×Q8×C151—21no—
113C2×Q8×C151—22no—
114C2×Q8×C151—41no—
115C2×Q8×C151—82no—
116C2×Q8×C151C2×D411yescharacteristic
117C2×D4×C151—21no—
118C2×D4×C151—21no—
119C2×D4×C151—21no—
120C2×D4×C151—21no—
121C2×D4×C151—41no—
122C2×D4×C151C2×D411yescharacteristic
123C22×C4×C151—21no—
124C22×C4×C151—21no—
125C22×C4×C151—21no—
126C22×C4×C151—41no—
127C22×C4×C151—41no—
128C22×C4×C151C2×D411yescharacteristic
129C22×C4×C151C2×D411yescharacteristic
130C22×C4×C151#4111yescharacteristic
131SD16×C151—42no—
132D8×C151—42no—
133M16×C151—42no—
134M16×C151—42no—
135C2×C8×C151—22no—
136C2×C8×C151—21no—
137C2×C8×C151—21no—
138C2×C8×C151—22no—
139C2×C8×C151—44no—
140C2×C8×C151C2×D412yes—
141C2×C8×C151C2×D412yes—
142C4⋊C4×C151—21no—
143C4⋊C4×C151—21no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—22no—
146C4⋊C4×C151—21no—
147C4⋊C4×C151—21no—
148C4⋊C4×C151—41no—
149C4⋊C4×C151—41no—
150C4⋊C4×C151C2×D411yescharacteristic
151C4⋊C4×C151C2×D411yescharacteristic
152C22⋊C4×C151—21no—
153C22⋊C4×C151—21no—
154C22⋊C4×C151—21no—
155C22⋊C4×C151—41no—
156C22⋊C4×C151—41no—
157C42×C151—21no—
158C42×C151—21no—
159C42×C151—21no—
160C42×C151C2×D411yescharacteristic
161C42×C151C2×D411yescharacteristic
162C42×C151#4111yescharacteristic
163C42×C151C2411yescharacteristic
164C23×C151—21no—
165C23×C151—41no—
166C23×C151#12111yescharacteristic
167Q8×C151—21no—
168Q8×C151—21no—
169Q8×C151—42no—
170Q8×C151—82no—
171Q8×C151—82no—
172D4×C151—21no—
173D4×C151—42no—
174D4×C151—41no—
175D4×C151—42no—
176D4×C151—41no—
177D4×C151—81no—
178D4×C151—82no—
179D4×C151#13712yes—
180C2×C4×C151—21no—
181C2×C4×C151—22no—
182C2×C4×C151—21no—
183C2×C4×C151—21no—
184C2×C4×C151—21no—
185C2×C4×C151—21no—
186C2×C4×C151—41no—
187C2×C4×C151—42no—
188C2×C4×C151—42no—
189C2×C4×C151—42no—
190C2×C4×C151—41no—
191C2×C4×C151—81no—
192C2×C4×C151—82no—
193C2×C4×C151—82no—
194C2×C4×C151#12111yescharacteristic
195C2×C4×C151#12111yescharacteristic
196C2×C4×C151#12111yescharacteristic
197C2×C4×C151C22×D411yescharacteristic
198C2×C4×C151C22×D411yescharacteristic
199C2×C4×C151C2×#4111yescharacteristic
200C8×C151—22no—
201C8×C151—22no—
202C8×C151—41no—
203C8×C151—42no—
204C8×C151—42no—
205C8×C151—41no—
206C22×C151—21no—
207C22×C151—21no—
208C22×C151—22no—
209C22×C151—21no—
210C22×C151—41no—
211C22×C151—41no—
212C22×C151—81no—
213C22×C151—81no—
214C22×C151—81no—
215C22×C151C2×#12111yescharacteristic
216C4×C151—21no—
217C4×C151—21no—
218C4×C151—21no—
219C4×C151—21no—
220C4×C151—41no—
221C4×C151—41no—
222C4×C151—41no—
223C4×C151—81no—
224C4×C151—82no—
225C4×C151C2×#13711yescharacteristic
226C4×C151#57512yes—
227C4×C151#57511yescharacteristic
228C2×C151—41no—
229C2×C151—42no—
230C2×C151—161no—
231C2×C151#304011yescharacteristic
232C2×C151#305611yescharacteristic
233C2×C151#306811yescharacteristic
234#19318C15111yesmaximal, characteristic, direct product factor, Sylow
235C151#1931811yescharacteristic, direct product factor, Sylow
236#3141C2×C15111yescharacteristic, complemented
237#3115C2×C15111yescharacteristic
238#3079C2×C15111yescharacteristic, complemented
239#2970C2×C15111yescharacteristic, complemented
240#1704C2×C15112yescomplemented
241#1698C2×C15112yescomplemented
242#1683C2×C15112yescomplemented
243#1677C2×C15112yescomplemented
244#1569C2×C15111yescharacteristic, complemented
245#1558C2×C15111yescharacteristic, complemented
246#1557C2×C15111yescharacteristic, complemented
247#532C22×C15111yescharacteristic
248C2×C4⋊Q8C22×C15111yescharacteristic
249C4×#41C22×C15111yescharacteristic
250#489—21no—
251#489—21no—
252#487C22×C15112yes—
253#486C22×C15112yes—
254#482—21no—
255#477C22×C15112yes—
256#476C22×C15112yes—
257#475—21no—
258#475C22×C15111yescharacteristic
259#474—21no—
260#474C22×C15111yescharacteristic
261#460C22×C15111yescharacteristic
262#459C22×C15111yescharacteristic
263#449—21no—
264#446C22×C15112yes—
265#442—21no—
266#440—21no—
267#435—22no—
268C8×D4C22×C15112yes—
269#432—21no—
270#432C22×C15111yescharacteristic
271#432C22×C15111yescharacteristic
272#428—21no—
273#423C22×C15111yescharacteristic
274#417—21no—
275#417—22no—
276C4×M16C22×C15111yescharacteristic
277C2×#97—21no—
278#335C22×C15112yes—
279#334C22×C15112yes—
280#333C22×C15112yes—
281#333C22×C15112yes—
282#332C22×C15112yes—
283#331C22×C15112yes—
284C2×#41—21no—
285C2×#41D4×C15111yescharacteristic
286C22×Q8—21no—
287C2×SD16—21no—
288C2×D8—21no—
289C2×M16—21no—
290C2×M16D4×C15112yes—
291C22×C8—22no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8—21no—
295C4⋊Q8C23×C15112yes—
296C4⋊Q8C23×C15111yescharacteristic
297#127C23×C15111yescharacteristic
298#124—21no—
299#121—21no—
300#121—21no—
301C4×Q8D4×C15111yescharacteristic
302C4×Q8C23×C15111yescharacteristic
303C4×D4—21no—
304C4×D4—21no—
305C4×D4—21no—
306C4×D4—21no—
307C4×D4D4×C15111yescharacteristic
308C4×D4C23×C15111yescharacteristic
309#117—21no—
310#117D4×C15111yescharacteristic
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C42—21no—
314C2×C42C23×C15111yescharacteristic
315#107—22no—
316#107—21no—
317#106—22no—
318#106—21no—
319C4⋊C8—22no—
320C4⋊C8—21no—
321C4⋊C8C23×C15112yes—
322C4⋊C8C23×C15112yes—
323C4⋊C8C23×C15111yescharacteristic
324C4⋊C8C23×C15111yescharacteristic
325#103—22no—
326#103—21no—
327#103—22no—
328#103—22no—
329#102—22no—
330#102—21no—
331#102—22no—
332#102—22no—
333#102—21no—
334#102—21no—
335C22⋊C8—21no—
336C22⋊C8—21no—
337C22⋊C8—22no—
338#97—22no—
339#97—21no—
340#97—21no—
341#97D4×C15111yescharacteristic
342#97D4×C15111yescharacteristic
343C4×C8C23×C15112yes—
344#41—22no—
345#41—41no—
346#41—44no—
347C2×Q8—21no—
348C2×Q8—22no—
349C2×Q8—41no—
350C2×Q8—82no—
351C2×Q8C2×D4×C15111yescharacteristic
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—41no—
357C2×D4C2×D4×C15111yescharacteristic
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4C2×D4×C15111yescharacteristic
364C22×C4C2×D4×C15111yescharacteristic
365C22×C4#41×C15111yescharacteristic
366SD16—42no—
367D8—42no—
368M16—42no—
369M16—42no—
370C2×C8—22no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—22no—
374C2×C8—44no—
375C2×C8C2×D4×C15112yes—
376C2×C8C2×D4×C15112yes—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4C2×D4×C15111yescharacteristic
386C4⋊C4C2×D4×C15111yescharacteristic
387C22⋊C4—21no—
388C22⋊C4—21no—
389C22⋊C4—21no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C42—21no—
393C42—21no—
394C42—21no—
395C42C2×D4×C15111yescharacteristic
396C42C2×D4×C15111yescharacteristic
397C42#41×C15111yescharacteristic
398C42C24×C15111yescharacteristic
399C23—21no—
400C23—41no—
401C23#121×C15111yescharacteristic
402Q8—21no—
403Q8—21no—
404Q8—42no—
405Q8—82no—
406Q8—82no—
407D4—21no—
408D4—42no—
409D4—41no—
410D4—41no—
411D4—42no—
412D4—81no—
413D4—82no—
414D4#137×C15112yes—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—81no—
427C2×C4—82no—
428C2×C4—82no—
429C2×C4#121×C15111yescharacteristic
430C2×C4#121×C15111yescharacteristic
431C2×C4#121×C15111yescharacteristic
432C2×C4C22×D4×C15111yescharacteristic
433C2×C4C22×D4×C15111yescharacteristic
434C2×C4C2×#41×C15111yescharacteristic
435C8—22no—
436C8—22no—
437C8—41no—
438C8—42no—
439C8—42no—
440C8—41no—
441C22—21no—
442C22—21no—
443C22—22no—
444C22—21no—
445C22—41no—
446C22—41no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22C2×#121×C15111yescharacteristic
451C4—21no—
452C4—21no—
453C4—21no—
454C4—21no—
455C4—41no—
456C4—41no—
457C4—41no—
458C4—81no—
459C4—82no—
460C4C2×#137×C15111yescharacteristic
461C4#575×C15112yes—
462C4#575×C15111yescharacteristic
463C2—41no—
464C2—42no—
465C2—161no—
466C2#3040×C15111yescharacteristic
467C2#3056×C15111yescharacteristic
468C2#3068×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radical#3115×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. #3141×C151C2semidirect
3. #3079×C151C2semidirect
4. #2970×C151C2semidirect
5. #1704×C151C2semidirect
6. #1698×C151C2semidirect
7. #1683×C151C2semidirect
8. #1677×C151C2semidirect
9. #1569×C151C2semidirect
10. #1558×C151C2semidirect
11. #1557×C151C2semidirect
234. #19318C151direct (N × H)
235. C151#19318direct (N × H)
236. #3141C2×C151semidirect
238. #3079C2×C151semidirect
239. #2970C2×C151semidirect
240. #1704C2×C151semidirect
241. #1698C2×C151semidirect
242. #1683C2×C151semidirect
243. #1677C2×C151semidirect
244. #1569C2×C151semidirect
245. #1558C2×C151semidirect
246. #1557C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3141×C1512
#3115×C1512
#3079×C1512
#2970×C1512
#1704×C1512
#1698×C1512
#1683×C1512
#1677×C1512
#1569×C1512
#1558×C1512
#1557×C1512
#19318151