Finite Group Databasebeta

← C151×#19313 #50324238

Subgroups — C151×#19313 #50324238

Order 38656.

684 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3152×C151C211yesmaximal, characteristic, complemented
2#3115×C151C211yesmaximal, characteristic
3#3079×C151C211yesmaximal, characteristic, complemented
4#2970×C151C211yesmaximal, characteristic, complemented
5#1690×C151C212yesmaximal, complemented
6#1686×C151C212yesmaximal, complemented
7#1669×C151C212yesmaximal, complemented
8#1665×C151C212yesmaximal, complemented
9#1569×C151C211yesmaximal, characteristic, complemented
10#1557×C151C211yesmaximal, characteristic, complemented
11#1556×C151C211yesmaximal, characteristic, complemented
12C2×#137×C151—22no—
13#532×C151C2211yescharacteristic
14C2×C4⋊Q8×C151C2211yescharacteristic
15C4×#41×C151C2211yescharacteristic
16#497×C151—21no—
17#497×C151—21no—
18#494×C151C2212yes—
19#492×C151C2212yes—
20#482×C151—21no—
21#477×C151—21no—
22#476×C151—21no—
23#475×C151C2211yescharacteristic
24#475×C151C2212yes—
25#474×C151C2211yescharacteristic
26#474×C151C2212yes—
27#460×C151C2211yescharacteristic
28#459×C151C2211yescharacteristic
29#449×C151—21no—
30#446×C151C2212yes—
31#442×C151—21no—
32#440×C151—21no—
33#435×C151—22no—
34C8×D4×C151C2212yes—
35#432×C151—21no—
36#432×C151C2211yescharacteristic
37#432×C151C2211yescharacteristic
38#428×C151—21no—
39#423×C151C2211yescharacteristic
40#417×C151—21no—
41C4×M16×C151C2211yescharacteristic
42C2×#97×C151—21no—
43#335×C151C2212yes—
44#334×C151C2212yes—
45#332×C151C2212yes—
46#332×C151C2212yes—
47#332×C151C2212yes—
48#331×C151C2212yes—
49C2×#41×C151—21no—
50C2×#41×C151D411yescharacteristic
51C22×Q8×C151—21no—
52#137×C151—48no—
53C2×Q16×C151—22no—
54C2×Q16×C151—22no—
55C2×SD16×C151—22no—
56C2×SD16×C151—22no—
57C2×SD16×C151—21no—
58C2×D8×C151—21no—
59C2×M16×C151—21no—
60C2×M16×C151D412yes—
61C22×C8×C151—22no—
62C4⋊Q8×C151—21no—
63C4⋊Q8×C151—21no—
64C4⋊Q8×C151—21no—
65C4⋊Q8×C151C2312yes—
66C4⋊Q8×C151C2311yescharacteristic
67#127×C151C2311yescharacteristic
68#124×C151—21no—
69#121×C151—21no—
70#121×C151—21no—
71C4×Q8×C151D411yescharacteristic
72C4×Q8×C151C2311yescharacteristic
73C4×D4×C151—21no—
74C4×D4×C151—21no—
75C4×D4×C151—21no—
76C4×D4×C151—21no—
77C4×D4×C151D411yescharacteristic
78C4×D4×C151C2311yescharacteristic
79#117×C151—21no—
80#117×C151D411yescharacteristic
81C2×C4⋊C4×C151—21no—
82C2×C4⋊C4×C151—21no—
83C2×C42×C151—21no—
84C2×C42×C151C2311yescharacteristic
85#107×C151—22no—
86#107×C151—21no—
87#106×C151—22no—
88#106×C151—21no—
89C4⋊C8×C151—22no—
90C4⋊C8×C151—21no—
91C4⋊C8×C151C2312yes—
92C4⋊C8×C151C2312yes—
93C4⋊C8×C151C2311yescharacteristic
94C4⋊C8×C151C2311yescharacteristic
95#103×C151—22no—
96#103×C151—21no—
97#102×C151—22no—
98#102×C151—21no—
99#102×C151—21no—
100#102×C151—21no—
101C22⋊C8×C151—21no—
102C22⋊C8×C151—21no—
103C22⋊C8×C151—22no—
104#97×C151—22no—
105#97×C151—21no—
106#97×C151—21no—
107#97×C151D411yescharacteristic
108#97×C151D411yescharacteristic
109C4×C8×C151C2312yes—
110#41×C151—22no—
111#41×C151—41no—
112#41×C151—44no—
113C2×Q8×C151—21no—
114C2×Q8×C151—22no—
115C2×Q8×C151—44no—
116C2×Q8×C151—41no—
117C2×Q8×C151C2×D411yescharacteristic
118C2×D4×C151—21no—
119C2×D4×C151—21no—
120C2×D4×C151—21no—
121C2×D4×C151—21no—
122C2×D4×C151—41no—
123C2×D4×C151C2×D411yescharacteristic
124C22×C4×C151—21no—
125C22×C4×C151—21no—
126C22×C4×C151—21no—
127C22×C4×C151—41no—
128C22×C4×C151—41no—
129C22×C4×C151C2×D411yescharacteristic
130C22×C4×C151C2×D411yescharacteristic
131C22×C4×C151#4111yescharacteristic
132Q16×C151—44no—
133Q16×C151—44no—
134SD16×C151—44no—
135SD16×C151—42no—
136SD16×C151—44no—
137D8×C151—42no—
138M16×C151—24no—
139M16×C151—42no—
140C2×C8×C151—22no—
141C2×C8×C151—21no—
142C2×C8×C151—21no—
143C2×C8×C151—22no—
144C2×C8×C151—44no—
145C2×C8×C151C2×D412yes—
146C2×C8×C151C2×D412yes—
147C4⋊C4×C151—21no—
148C4⋊C4×C151—21no—
149C4⋊C4×C151—22no—
150C4⋊C4×C151—21no—
151C4⋊C4×C151—22no—
152C4⋊C4×C151—21no—
153C4⋊C4×C151—41no—
154C4⋊C4×C151—41no—
155C4⋊C4×C151C2×D411yescharacteristic
156C4⋊C4×C151C2×D411yescharacteristic
157C22⋊C4×C151—21no—
158C22⋊C4×C151—21no—
159C22⋊C4×C151—21no—
160C22⋊C4×C151—41no—
161C22⋊C4×C151—41no—
162C42×C151—21no—
163C42×C151—21no—
164C42×C151—21no—
165C42×C151C2×D411yescharacteristic
166C42×C151C2×D411yescharacteristic
167C42×C151#4111yescharacteristic
168C42×C151C2411yescharacteristic
169C23×C151—21no—
170C23×C151—41no—
171C23×C151#12111yescharacteristic
172Q8×C151—21no—
173Q8×C151—21no—
174Q8×C151—42no—
175Q8×C151—42no—
176Q8×C151—42no—
177Q8×C151—82no—
178D4×C151—21no—
179D4×C151—42no—
180D4×C151—42no—
181D4×C151—41no—
182D4×C151—41no—
183D4×C151—81no—
184D4×C151—82no—
185D4×C151#13712yescomplemented
186C2×C4×C151—22no—
187C2×C4×C151—21no—
188C2×C4×C151—21no—
189C2×C4×C151—21no—
190C2×C4×C151—21no—
191C2×C4×C151—21no—
192C2×C4×C151—41no—
193C2×C4×C151—42no—
194C2×C4×C151—42no—
195C2×C4×C151—42no—
196C2×C4×C151—41no—
197C2×C4×C151—81no—
198C2×C4×C151—82no—
199C2×C4×C151—82no—
200C2×C4×C151#12111yescharacteristic
201C2×C4×C151#12111yescharacteristic
202C2×C4×C151#12111yescharacteristic
203C2×C4×C151C22×D411yescharacteristic
204C2×C4×C151C22×D411yescharacteristic
205C2×C4×C151C2×#4111yescharacteristic
206C8×C151—22no—
207C8×C151—42no—
208C8×C151—41no—
209C8×C151—42no—
210C8×C151—41no—
211C8×C151AGL(1,ℤ/8)14yes—
212C22×C151—21no—
213C22×C151—21no—
214C22×C151—22no—
215C22×C151—21no—
216C22×C151—41no—
217C22×C151—41no—
218C22×C151—81no—
219C22×C151—81no—
220C22×C151—81no—
221C22×C151C2×#12111yescharacteristic
222C4×C151—21no—
223C4×C151—21no—
224C4×C151—21no—
225C4×C151—21no—
226C4×C151—41no—
227C4×C151—41no—
228C4×C151—41no—
229C4×C151—81no—
230C4×C151—82no—
231C4×C151C2×AGL(1,ℤ/8)12yes—
232C4×C151C2×#13711yescharacteristic
233C4×C151#57511yescharacteristic
234C2×C151—41no—
235C2×C151—42no—
236C2×C151—161no—
237C2×C151#303811yescharacteristic
238C2×C151#305611yescharacteristic
239C2×C151#306911yescharacteristic
240#19313C15111yesmaximal, characteristic, direct product factor, Sylow
241C151#1931311yescharacteristic, direct product factor, Sylow
242#3152C2×C15111yescharacteristic, complemented
243#3115C2×C15111yescharacteristic
244#3079C2×C15111yescharacteristic, complemented
245#2970C2×C15111yescharacteristic, complemented
246#1690C2×C15112yescomplemented
247#1686C2×C15112yescomplemented
248#1669C2×C15112yescomplemented
249#1665C2×C15112yescomplemented
250#1569C2×C15111yescharacteristic, complemented
251#1557C2×C15111yescharacteristic, complemented
252#1556C2×C15111yescharacteristic, complemented
253C2×#137—22no—
254#532C22×C15111yescharacteristic
255C2×C4⋊Q8C22×C15111yescharacteristic
256C4×#41C22×C15111yescharacteristic
257#497—21no—
258#497—21no—
259#494C22×C15112yes—
260#492C22×C15112yes—
261#482—21no—
262#477—21no—
263#476—21no—
264#475C22×C15112yes—
265#475C22×C15111yescharacteristic
266#474C22×C15112yes—
267#474C22×C15111yescharacteristic
268#460C22×C15111yescharacteristic
269#459C22×C15111yescharacteristic
270#449—21no—
271#446C22×C15112yes—
272#442—21no—
273#440—21no—
274#435—22no—
275C8×D4C22×C15112yes—
276#432—21no—
277#432C22×C15111yescharacteristic
278#432C22×C15111yescharacteristic
279#428—21no—
280#423C22×C15111yescharacteristic
281#417—21no—
282C4×M16C22×C15111yescharacteristic
283C2×#97—21no—
284#335C22×C15112yes—
285#334C22×C15112yes—
286#332C22×C15112yes—
287#332C22×C15112yes—
288#332C22×C15112yes—
289#331C22×C15112yes—
290C2×#41—21no—
291C2×#41D4×C15111yescharacteristic
292C22×Q8—21no—
293#137—48no—
294C2×Q16—22no—
295C2×Q16—22no—
296C2×SD16—21no—
297C2×SD16—22no—
298C2×SD16—22no—
299C2×D8—21no—
300C2×M16—21no—
301C2×M16D4×C15112yes—
302C22×C8—22no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8C23×C15112yes—
307C4⋊Q8C23×C15111yescharacteristic
308#127C23×C15111yescharacteristic
309#124—21no—
310#121—21no—
311#121—21no—
312C4×Q8D4×C15111yescharacteristic
313C4×Q8C23×C15111yescharacteristic
314C4×D4—21no—
315C4×D4—21no—
316C4×D4—21no—
317C4×D4—21no—
318C4×D4D4×C15111yescharacteristic
319C4×D4C23×C15111yescharacteristic
320#117—21no—
321#117D4×C15111yescharacteristic
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C42—21no—
325C2×C42C23×C15111yescharacteristic
326#107—22no—
327#107—21no—
328#106—22no—
329#106—21no—
330C4⋊C8—22no—
331C4⋊C8—21no—
332C4⋊C8C23×C15112yes—
333C4⋊C8C23×C15112yes—
334C4⋊C8C23×C15111yescharacteristic
335C4⋊C8C23×C15111yescharacteristic
336#103—22no—
337#103—21no—
338#102—22no—
339#102—21no—
340#102—21no—
341#102—21no—
342C22⋊C8—21no—
343C22⋊C8—21no—
344C22⋊C8—22no—
345#97—22no—
346#97—21no—
347#97—21no—
348#97D4×C15111yescharacteristic
349#97D4×C15111yescharacteristic
350C4×C8C23×C15112yes—
351#41—22no—
352#41—41no—
353#41—44no—
354C2×Q8—21no—
355C2×Q8—22no—
356C2×Q8—44no—
357C2×Q8—41no—
358C2×Q8C2×D4×C15111yescharacteristic
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—41no—
364C2×D4C2×D4×C15111yescharacteristic
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4C2×D4×C15111yescharacteristic
371C22×C4C2×D4×C15111yescharacteristic
372C22×C4#41×C15111yescharacteristic
373Q16—44no—
374Q16—44no—
375SD16—44no—
376SD16—42no—
377SD16—44no—
378D8—42no—
379M16—24no—
380M16—42no—
381C2×C8—22no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—22no—
385C2×C8—44no—
386C2×C8C2×D4×C15112yes—
387C2×C8C2×D4×C15112yes—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4C2×D4×C15111yescharacteristic
397C4⋊C4C2×D4×C15111yescharacteristic
398C22⋊C4—21no—
399C22⋊C4—21no—
400C22⋊C4—21no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C42—21no—
404C42—21no—
405C42—21no—
406C42C2×D4×C15111yescharacteristic
407C42C2×D4×C15111yescharacteristic
408C42#41×C15111yescharacteristic
409C42C24×C15111yescharacteristic
410C23—21no—
411C23—41no—
412C23#121×C15111yescharacteristic
413Q8—21no—
414Q8—21no—
415Q8—42no—
416Q8—42no—
417Q8—42no—
418Q8—82no—
419D4—21no—
420D4—42no—
421D4—42no—
422D4—41no—
423D4—41no—
424D4—81no—
425D4—82no—
426D4#137×C15112yescomplemented
427C2×C4—22no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—81no—
439C2×C4—82no—
440C2×C4—82no—
441C2×C4#121×C15111yescharacteristic
442C2×C4#121×C15111yescharacteristic
443C2×C4#121×C15111yescharacteristic
444C2×C4C22×D4×C15111yescharacteristic
445C2×C4C22×D4×C15111yescharacteristic
446C2×C4C2×#41×C15111yescharacteristic
447C8—22no—
448C8—42no—
449C8—41no—
450C8—42no—
451C8—41no—
452C8AGL(1,ℤ/8)×C15114yes—
453C22—21no—
454C22—21no—
455C22—22no—
456C22—21no—
457C22—41no—
458C22—41no—
459C22—81no—
460C22—81no—
461C22—81no—
462C22C2×#121×C15111yescharacteristic
463C4—21no—
464C4—21no—
465C4—21no—
466C4—21no—
467C4—41no—
468C4—41no—
469C4—41no—
470C4—81no—
471C4—82no—
472C4C2×AGL(1,ℤ/8)×C15112yes—
473C4C2×#137×C15111yescharacteristic
474C4#575×C15111yescharacteristic
475C2—41no—
476C2—42no—
477C2—161no—
478C2#3038×C15111yescharacteristic
479C2#3056×C15111yescharacteristic
480C2#3069×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. #3152×C151C2semidirect
3. #3079×C151C2semidirect
4. #2970×C151C2semidirect
5. #1690×C151C2semidirect
6. #1686×C151C2semidirect
7. #1669×C151C2semidirect
8. #1665×C151C2semidirect
9. #1569×C151C2semidirect
10. #1557×C151C2semidirect
11. #1556×C151C2semidirect
185. D4×C151#137semidirect
240. #19313C151direct (N × H)
241. C151#19313direct (N × H)
242. #3152C2×C151semidirect
244. #3079C2×C151semidirect
245. #2970C2×C151semidirect
246. #1690C2×C151semidirect
247. #1686C2×C151semidirect
248. #1669C2×C151semidirect
249. #1665C2×C151semidirect
250. #1569C2×C151semidirect
251. #1557C2×C151semidirect
252. #1556C2×C151semidirect
426. D4#137×C151semidirect

Maximal subgroups

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

subgroupindex
#3152×C1512
#3115×C1512
#3079×C1512
#2970×C1512
#1690×C1512
#1686×C1512
#1669×C1512
#1665×C1512
#1569×C1512
#1557×C1512
#1556×C1512
#19313151