Finite Group Databasebeta

← C151×#19319 #50324244

Subgroups — C151×#19319 #50324244

Order 38656.

652 conjugacy classes of subgroups.

The subgroup lattice has 480 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#3039×C151C211yesmaximal, characteristic, complemented
4#2970×C151C211yesmaximal, characteristic, complemented
5#1702×C151C212yesmaximal, complemented
6#1700×C151C212yesmaximal, complemented
7#1681×C151C212yesmaximal, complemented
8#1679×C151C212yesmaximal, complemented
9#1569×C151C211yesmaximal, characteristic, complemented
10#1557×C151C211yesmaximal, characteristic, complemented
11#1556×C151C211yesmaximal, characteristic, complemented
12C2×#137×C151—21no—
13#532×C151C2211yescharacteristic
14C2×C4⋊Q8×C151C2211yescharacteristic
15C4×#41×C151C2211yescharacteristic
16#489×C151—21no—
17#489×C151—21no—
18#487×C151C2212yes—
19#486×C151C2212yes—
20#482×C151—21no—
21#475×C151C2211yescharacteristic
22#474×C151C2211yescharacteristic
23#462×C151—21no—
24#462×C151C2212yes—
25#461×C151—21no—
26#461×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#423×C151C2211yescharacteristic
39#419×C151—21no—
40#417×C151—22no—
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—44no—
53C2×Q16×C151—22no—
54C2×SD16×C151—22no—
55C2×SD16×C151—21no—
56C2×D8×C151—21no—
57C2×M16×C151—21no—
58C2×M16×C151D412yes—
59C22×C8×C151—22no—
60C4⋊Q8×C151—21no—
61C4⋊Q8×C151—21no—
62C4⋊Q8×C151—21no—
63C4⋊Q8×C151C2312yes—
64C4⋊Q8×C151C2311yescharacteristic
65#127×C151C2311yescharacteristic
66#124×C151—21no—
67#121×C151—21no—
68#121×C151—21no—
69C4×Q8×C151D411yescharacteristic
70C4×Q8×C151C2311yescharacteristic
71C4×D4×C151—21no—
72C4×D4×C151—21no—
73C4×D4×C151—21no—
74C4×D4×C151—21no—
75C4×D4×C151D411yescharacteristic
76C4×D4×C151C2311yescharacteristic
77#117×C151—21no—
78#117×C151D411yescharacteristic
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151—21no—
81C2×C42×C151—21no—
82C2×C42×C151C2311yescharacteristic
83#107×C151—21no—
84#106×C151—21no—
85C4⋊C8×C151—22no—
86C4⋊C8×C151—21no—
87C4⋊C8×C151C2312yes—
88C4⋊C8×C151C2312yes—
89C4⋊C8×C151C2311yescharacteristic
90C4⋊C8×C151C2311yescharacteristic
91#103×C151—22no—
92#103×C151—22no—
93#103×C151—22no—
94#103×C151—22no—
95#103×C151—21no—
96#102×C151—21no—
97#102×C151—22no—
98#102×C151—22no—
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—42no—
116C2×Q8×C151—42no—
117C2×Q8×C151—41no—
118C2×Q8×C151C2×D411yescharacteristic
119C2×D4×C151—21no—
120C2×D4×C151—21no—
121C2×D4×C151—21no—
122C2×D4×C151—21no—
123C2×D4×C151—41no—
124C2×D4×C151C2×D411yescharacteristic
125C22×C4×C151—21no—
126C22×C4×C151—21no—
127C22×C4×C151—21no—
128C22×C4×C151—41no—
129C22×C4×C151—41no—
130C22×C4×C151C2×D411yescharacteristic
131C22×C4×C151C2×D411yescharacteristic
132C22×C4×C151#4111yescharacteristic
133Q16×C151—44no—
134SD16×C151—42no—
135SD16×C151—44no—
136D8×C151—42no—
137M16×C151—42no—
138M16×C151—42no—
139C2×C8×C151—22no—
140C2×C8×C151—21no—
141C2×C8×C151—21no—
142C2×C8×C151—22no—
143C2×C8×C151—44no—
144C2×C8×C151C2×D412yes—
145C2×C8×C151C2×D412yes—
146C4⋊C4×C151—21no—
147C4⋊C4×C151—21no—
148C4⋊C4×C151—22no—
149C4⋊C4×C151—21no—
150C4⋊C4×C151—22no—
151C4⋊C4×C151—21no—
152C4⋊C4×C151—41no—
153C4⋊C4×C151—41no—
154C4⋊C4×C151C2×D411yescharacteristic
155C4⋊C4×C151C2×D411yescharacteristic
156C22⋊C4×C151—21no—
157C22⋊C4×C151—21no—
158C22⋊C4×C151—21no—
159C22⋊C4×C151—41no—
160C22⋊C4×C151—41no—
161C42×C151—21no—
162C42×C151—21no—
163C42×C151—21no—
164C42×C151C2×D411yescharacteristic
165C42×C151C2×D411yescharacteristic
166C42×C151#4111yescharacteristic
167C42×C151C2411yescharacteristic
168C23×C151—21no—
169C23×C151—41no—
170C23×C151#12111yescharacteristic
171Q8×C151—21no—
172Q8×C151—21no—
173Q8×C151—42no—
174Q8×C151—42no—
175Q8×C151—42no—
176Q8×C151—82no—
177D4×C151—21no—
178D4×C151—42no—
179D4×C151—41no—
180D4×C151—42no—
181D4×C151—41no—
182D4×C151—81no—
183D4×C151—82no—
184D4×C151AGL(1,ℤ/8)12yes—
185C2×C4×C151—21no—
186C2×C4×C151—21no—
187C2×C4×C151—22no—
188C2×C4×C151—21no—
189C2×C4×C151—21no—
190C2×C4×C151—21no—
191C2×C4×C151—41no—
192C2×C4×C151—42no—
193C2×C4×C151—42no—
194C2×C4×C151—42no—
195C2×C4×C151—41no—
196C2×C4×C151—81no—
197C2×C4×C151—82no—
198C2×C4×C151—82no—
199C2×C4×C151#12111yescharacteristic
200C2×C4×C151#12111yescharacteristic
201C2×C4×C151#12111yescharacteristic
202C2×C4×C151C22×D411yescharacteristic
203C2×C4×C151C22×D411yescharacteristic
204C2×C4×C151C2×#4111yescharacteristic
205C8×C151—22no—
206C8×C151—22no—
207C8×C151—42no—
208C8×C151—41no—
209C8×C151—42no—
210C8×C151—41no—
211C22×C151—21no—
212C22×C151—21no—
213C22×C151—22no—
214C22×C151—21no—
215C22×C151—41no—
216C22×C151—41no—
217C22×C151—81no—
218C22×C151—81no—
219C22×C151—81no—
220C22×C151C2×#12111yescharacteristic
221C4×C151—21no—
222C4×C151—21no—
223C4×C151—21no—
224C4×C151—21no—
225C4×C151—41no—
226C4×C151—41no—
227C4×C151—41no—
228C4×C151—81no—
229C4×C151—82no—
230C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
231C4×C151#57512yes—
232C4×C151#57511yescharacteristic
233C2×C151—41no—
234C2×C151—42no—
235C2×C151—161no—
236C2×C151#304011yescharacteristic
237C2×C151#305511yescharacteristic
238C2×C151#306911yescharacteristic
239#19319C15111yesmaximal, characteristic, direct product factor, Sylow
240C151#1931911yescharacteristic, direct product factor, Sylow
241#3141C2×C15111yescharacteristic, complemented
242#3115C2×C15111yescharacteristic
243#3039C2×C15111yescharacteristic, complemented
244#2970C2×C15111yescharacteristic, complemented
245#1702C2×C15112yescomplemented
246#1700C2×C15112yescomplemented
247#1681C2×C15112yescomplemented
248#1679C2×C15112yescomplemented
249#1569C2×C15111yescharacteristic, complemented
250#1557C2×C15111yescharacteristic, complemented
251#1556C2×C15111yescharacteristic, complemented
252C2×#137—21no—
253#532C22×C15111yescharacteristic
254C2×C4⋊Q8C22×C15111yescharacteristic
255C4×#41C22×C15111yescharacteristic
256#489—21no—
257#489—21no—
258#487C22×C15112yes—
259#486C22×C15112yes—
260#482—21no—
261#475C22×C15111yescharacteristic
262#474C22×C15111yescharacteristic
263#462—21no—
264#462C22×C15112yes—
265#461—21no—
266#461C22×C15112yes—
267#460C22×C15111yescharacteristic
268#459C22×C15111yescharacteristic
269#449—21no—
270#446C22×C15112yes—
271#442—21no—
272#440—21no—
273#435—22no—
274C8×D4C22×C15112yes—
275#432—21no—
276#432C22×C15111yescharacteristic
277#432C22×C15111yescharacteristic
278#423C22×C15111yescharacteristic
279#419—21no—
280#417—22no—
281C4×M16C22×C15111yescharacteristic
282C2×#97—21no—
283#335C22×C15112yes—
284#334C22×C15112yes—
285#332C22×C15112yes—
286#332C22×C15112yes—
287#332C22×C15112yes—
288#331C22×C15112yes—
289C2×#41—21no—
290C2×#41D4×C15111yescharacteristic
291C22×Q8—21no—
292#137—44no—
293C2×Q16—22no—
294C2×SD16—21no—
295C2×SD16—22no—
296C2×D8—21no—
297C2×M16—21no—
298C2×M16D4×C15112yes—
299C22×C8—22no—
300C4⋊Q8—21no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8C23×C15112yes—
304C4⋊Q8C23×C15111yescharacteristic
305#127C23×C15111yescharacteristic
306#124—21no—
307#121—21no—
308#121—21no—
309C4×Q8D4×C15111yescharacteristic
310C4×Q8C23×C15111yescharacteristic
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4D4×C15111yescharacteristic
316C4×D4C23×C15111yescharacteristic
317#117—21no—
318#117D4×C15111yescharacteristic
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C42—21no—
322C2×C42C23×C15111yescharacteristic
323#107—21no—
324#106—21no—
325C4⋊C8—22no—
326C4⋊C8—21no—
327C4⋊C8C23×C15112yes—
328C4⋊C8C23×C15112yes—
329C4⋊C8C23×C15111yescharacteristic
330C4⋊C8C23×C15111yescharacteristic
331#103—21no—
332#103—22no—
333#103—22no—
334#103—22no—
335#103—22no—
336#102—21no—
337#102—22no—
338#102—22no—
339#102—21no—
340#102—21no—
341C22⋊C8—21no—
342C22⋊C8—21no—
343C22⋊C8—22no—
344#97—22no—
345#97—21no—
346#97—21no—
347#97D4×C15111yescharacteristic
348#97D4×C15111yescharacteristic
349C4×C8C23×C15112yes—
350#41—22no—
351#41—41no—
352#41—44no—
353C2×Q8—21no—
354C2×Q8—22no—
355C2×Q8—42no—
356C2×Q8—42no—
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—
374SD16—42no—
375SD16—44no—
376D8—42no—
377M16—42no—
378M16—42no—
379C2×C8—22no—
380C2×C8—21no—
381C2×C8—21no—
382C2×C8—22no—
383C2×C8—44no—
384C2×C8C2×D4×C15112yes—
385C2×C8C2×D4×C15112yes—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—21no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4C2×D4×C15111yescharacteristic
395C4⋊C4C2×D4×C15111yescharacteristic
396C22⋊C4—21no—
397C22⋊C4—21no—
398C22⋊C4—21no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C42—21no—
402C42—21no—
403C42—21no—
404C42C2×D4×C15111yescharacteristic
405C42C2×D4×C15111yescharacteristic
406C42#41×C15111yescharacteristic
407C42C24×C15111yescharacteristic
408C23—21no—
409C23—41no—
410C23#121×C15111yescharacteristic
411Q8—21no—
412Q8—21no—
413Q8—42no—
414Q8—42no—
415Q8—42no—
416Q8—82no—
417D4—21no—
418D4—42no—
419D4—41no—
420D4—41no—
421D4—42no—
422D4—81no—
423D4—82no—
424D4AGL(1,ℤ/8)×C15112yes—
425C2×C4—21no—
426C2×C4—22no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—81no—
437C2×C4—82no—
438C2×C4—82no—
439C2×C4#121×C15111yescharacteristic
440C2×C4#121×C15111yescharacteristic
441C2×C4#121×C15111yescharacteristic
442C2×C4C22×D4×C15111yescharacteristic
443C2×C4C22×D4×C15111yescharacteristic
444C2×C4C2×#41×C15111yescharacteristic
445C8—22no—
446C8—22no—
447C8—42no—
448C8—41no—
449C8—42no—
450C8—41no—
451C22—21no—
452C22—21no—
453C22—22no—
454C22—21no—
455C22—41no—
456C22—41no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22C2×#121×C15111yescharacteristic
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—41no—
466C4—41no—
467C4—41no—
468C4—81no—
469C4—82no—
470C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
471C4#575×C15112yes—
472C4#575×C15111yescharacteristic
473C2—41no—
474C2—42no—
475C2—161no—
476C2#3040×C15111yescharacteristic
477C2#3055×C15111yescharacteristic
478C2#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. #3141×C151C2semidirect
3. #3039×C151C2semidirect
4. #2970×C151C2semidirect
5. #1702×C151C2semidirect
6. #1700×C151C2semidirect
7. #1681×C151C2semidirect
8. #1679×C151C2semidirect
9. #1569×C151C2semidirect
10. #1557×C151C2semidirect
11. #1556×C151C2semidirect
239. #19319C151direct (N × H)
240. C151#19319direct (N × H)
241. #3141C2×C151semidirect
243. #3039C2×C151semidirect
244. #2970C2×C151semidirect
245. #1702C2×C151semidirect
246. #1700C2×C151semidirect
247. #1681C2×C151semidirect
248. #1679C2×C151semidirect
249. #1569C2×C151semidirect
250. #1557C2×C151semidirect
251. #1556C2×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
#3039×C1512
#2970×C1512
#1702×C1512
#1700×C1512
#1681×C1512
#1679×C1512
#1569×C1512
#1557×C1512
#1556×C1512
#19319151