Finite Group Databasebeta

← C151×#19282 #50324207

Subgroups — C151×#19282 #50324207

Order 38656.

684 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#3167×C151C211yesmaximal, characteristic, complemented
2#3110×C151C211yesmaximal, characteristic, complemented
3#3109×C151C211yesmaximal, characteristic
4C2×#436×C151C211yesmaximal, characteristic, complemented
5#1703×C151C212yesmaximal, complemented
6#1701×C151C212yesmaximal, complemented
7#1691×C151C212yesmaximal, complemented
8#1685×C151C212yesmaximal, complemented
9#1568×C151C211yesmaximal, characteristic, complemented
10#1552×C151C211yesmaximal, characteristic, complemented
11#1551×C151C211yesmaximal, characteristic, complemented
12C22×M16×C151—21no—
13#533×C151C2211yescharacteristic
14#532×C151C2211yescharacteristic
15C2×C4×D4×C151C2211yescharacteristic
16#498×C151C2211yescharacteristic, complemented
17#492×C151C2211yescharacteristic, complemented
18#487×C151C2211yescharacteristic, complemented
19#486×C151C2211yescharacteristic, complemented
20#484×C151—21no—
21#481×C151—21no—
22#476×C151C2212yes—
23#474×C151C2212yes—
24#465×C151—21no—
25#465×C151—21no—
26#461×C151C2212yes—
27#459×C151C2212yes—
28#450×C151—21no—
29#447×C151—21no—
30#442×C151—22no—
31#440×C151—22no—
32C4×SD16×C151—21no—
33C4×SD16×C151—21no—
34#436×C151—21no—
35#436×C151—21no—
36#436×C151C2212yes—
37#436×C151C2212yes—
38#432×C151C2211yescharacteristic
39#432×C151C2211yescharacteristic
40C2×C4⋊C8×C151C2211yescharacteristic
41C2×C22⋊C8×C151—21no—
42C2×C4×C8×C151C2211yescharacteristic
43#335×C151C2212yescomplemented
44#334×C151C2212yescomplemented
45#333×C151C2212yescomplemented
46#332×C151C2212yescomplemented
47#332×C151C2212yescomplemented
48#331×C151C2212yescomplemented
49C2×#41×C151—21no—
50C22×D4×C151D411yescharacteristic
51C23×C4×C151—21no—
52C2×SD16×C151—22no—
53C2×SD16×C151—21no—
54C2×SD16×C151—21no—
55C2×D8×C151—22no—
56C2×M16×C151—22no—
57C2×M16×C151—22no—
58C2×M16×C151—44no—
59C22×C8×C151—21no—
60C22×C8×C151D411yescharacteristic
61C22×C8×C151D411yescharacteristic
62C4⋊Q8×C151C2311yescharacteristic
63C4⋊Q8×C151C2311yescharacteristic
64C4⋊Q8×C151C2311yescharacteristic
65#127×C151C2311yescharacteristic
66#125×C151—21no—
67#124×C151—21no—
68C22⋊Q8×C151—21no—
69C22⋊Q8×C151—21no—
70#121×C151—21no—
71#121×C151—21no—
72C4×Q8×C151—21no—
73C4×Q8×C151—21no—
74C4×D4×C151—21no—
75C4×D4×C151—21no—
76C4×D4×C151—21no—
77C4×D4×C151—21no—
78C4×D4×C151D412yes—
79C4×D4×C151C2312yes—
80#117×C151—21no—
81C2×C4⋊C4×C151D411yescharacteristic
82C2×C22⋊C4×C151—21no—
83C2×C42×C151C2311yescharacteristic
84#107×C151—22no—
85#106×C151—21no—
86#106×C151—21no—
87#106×C151—22no—
88C4⋊C8×C151—21no—
89C4⋊C8×C151C2312yes—
90C4⋊C8×C151C2312yes—
91C4⋊C8×C151C2312yes—
92#103×C151—21no—
93#103×C151—21no—
94#103×C151—22no—
95#102×C151—22no—
96#102×C151—22no—
97#102×C151—21no—
98#102×C151—21no—
99#102×C151—22no—
100C22⋊C8×C151—21no—
101C22⋊C8×C151—21no—
102C22⋊C8×C151—22no—
103C22⋊C8×C151—22no—
104#97×C151—21no—
105#97×C151—21no—
106C4×C8×C151D411yescharacteristic
107C4×C8×C151D411yescharacteristic
108C4×C8×C151C2311yescharacteristic
109C4×C8×C151C2311yescharacteristic
110C24×C151—21no—
111#41×C151—82no—
112C2×Q8×C151—21no—
113C2×Q8×C151—21no—
114C2×Q8×C151—21no—
115C2×D4×C151—21no—
116C2×D4×C151—21no—
117C2×D4×C151—21no—
118C2×D4×C151—21no—
119C2×D4×C151—42no—
120C2×D4×C151—41no—
121C2×D4×C151C2×D412yes—
122C22×C4×C151—21no—
123C22×C4×C151—22no—
124C22×C4×C151—22no—
125C22×C4×C151—42no—
126C22×C4×C151—42no—
127C22×C4×C151—41no—
128C22×C4×C151C2×D411yescharacteristic
129C22×C4×C151C2×D411yescharacteristic
130C22×C4×C151#4111yescharacteristic
131SD16×C151—42no—
132SD16×C151—44no—
133SD16×C151—42no—
134D8×C151—44no—
135M16×C151—44no—
136M16×C151—44no—
137C2×C8×C151—22no—
138C2×C8×C151—22no—
139C2×C8×C151—22no—
140C2×C8×C151—22no—
141C2×C8×C151—41no—
142C2×C8×C151—42no—
143C2×C8×C151C2×D411yescharacteristic
144C2×C8×C151C2×D411yescharacteristic
145C2×C8×C151C2×D411yescharacteristic
146C2×C8×C151C2×D411yescharacteristic
147C4⋊C4×C151—21no—
148C4⋊C4×C151—21no—
149C4⋊C4×C151—21no—
150C4⋊C4×C151—21no—
151C4⋊C4×C151—21no—
152C4⋊C4×C151—21no—
153C4⋊C4×C151—21no—
154C4⋊C4×C151—41no—
155C4⋊C4×C151—41no—
156C4⋊C4×C151C2×D412yes—
157C22⋊C4×C151—22no—
158C22⋊C4×C151—22no—
159C22⋊C4×C151—41no—
160C22⋊C4×C151—41no—
161C22⋊C4×C151—41no—
162C42×C151—41no—
163C42×C151C2×D411yescharacteristic
164C42×C151C2×D411yescharacteristic
165C42×C151#4111yescharacteristic
166C42×C151C2411yescharacteristic
167C23×C151—22no—
168C23×C151—42no—
169C23×C151—42no—
170C23×C151—42no—
171C23×C151—41no—
172C23×C151#12111yescharacteristic
173Q8×C151—41no—
174Q8×C151—41no—
175Q8×C151—42no—
176Q8×C151—81no—
177D4×C151—22no—
178D4×C151—22no—
179D4×C151—42no—
180D4×C151—41no—
181D4×C151—42no—
182D4×C151—41no—
183D4×C151—81no—
184D4×C151—82no—
185C2×C4×C151—22no—
186C2×C4×C151—21no—
187C2×C4×C151—21no—
188C2×C4×C151—22no—
189C2×C4×C151—22no—
190C2×C4×C151—44no—
191C2×C4×C151—42no—
192C2×C4×C151—42no—
193C2×C4×C151—42no—
194C2×C4×C151—41no—
195C2×C4×C151—41no—
196C2×C4×C151—41no—
197C2×C4×C151—82no—
198C2×C4×C151#12111yescharacteristic
199C2×C4×C151#12111yescharacteristic
200C2×C4×C151#12111yescharacteristic
201C2×C4×C151C22×D411yescharacteristic
202C2×C4×C151C22×D411yescharacteristic
203C2×C4×C151C2×#4111yescharacteristic
204C8×C151—21no—
205C8×C151—21no—
206C8×C151—21no—
207C8×C151—42no—
208C8×C151—42no—
209C8×C151—42no—
210C8×C151AGL(1,ℤ/8)12yes—
211C22×C151—21no—
212C22×C151—21no—
213C22×C151—42no—
214C22×C151—42no—
215C22×C151—42no—
216C22×C151—84no—
217C22×C151—81no—
218C22×C151—81no—
219C22×C151—81no—
220C22×C151#47112yes—
221C22×C151C2×#12111yescharacteristic
222C4×C151—21no—
223C4×C151—21no—
224C4×C151—21no—
225C4×C151—21no—
226C4×C151—42no—
227C4×C151—81no—
228C4×C151—81no—
229C4×C151—81no—
230C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
231C4×C151#57511yescharacteristic
232C4×C151#57512yes—
233C2×C151—22no—
234C2×C151—82no—
235C2×C151—161no—
236C2×C151#303611yescharacteristic
237C2×C151#305411yescharacteristic
238C2×C151C2×#47111yescharacteristic
239#19282C15111yesmaximal, characteristic, direct product factor, Sylow
240C151#1928211yescharacteristic, direct product factor, Sylow
241#3167C2×C15111yescharacteristic, complemented
242#3110C2×C15111yescharacteristic, complemented
243#3109C2×C15111yescharacteristic
244C2×#436C2×C15111yescharacteristic, complemented
245#1703C2×C15112yescomplemented
246#1701C2×C15112yescomplemented
247#1691C2×C15112yescomplemented
248#1685C2×C15112yescomplemented
249#1568C2×C15111yescharacteristic, complemented
250#1552C2×C15111yescharacteristic, complemented
251#1551C2×C15111yescharacteristic, complemented
252C22×M16—21no—
253#533C22×C15111yescharacteristic
254#532C22×C15111yescharacteristic
255C2×C4×D4C22×C15111yescharacteristic
256#498C22×C15111yescharacteristic, complemented
257#492C22×C15111yescharacteristic, complemented
258#487C22×C15111yescharacteristic, complemented
259#486C22×C15111yescharacteristic, complemented
260#484—21no—
261#481—21no—
262#476C22×C15112yes—
263#474C22×C15112yes—
264#465—21no—
265#465—21no—
266#461C22×C15112yes—
267#459C22×C15112yes—
268#450—21no—
269#447—21no—
270#442—22no—
271#440—22no—
272C4×SD16—21no—
273C4×SD16—21no—
274#436—21no—
275#436—21no—
276#436C22×C15112yes—
277#436C22×C15112yes—
278#432C22×C15111yescharacteristic
279#432C22×C15111yescharacteristic
280C2×C4⋊C8C22×C15111yescharacteristic
281C2×C22⋊C8—21no—
282C2×C4×C8C22×C15111yescharacteristic
283#335C22×C15112yescomplemented
284#334C22×C15112yescomplemented
285#333C22×C15112yescomplemented
286#332C22×C15112yescomplemented
287#332C22×C15112yescomplemented
288#331C22×C15112yescomplemented
289C2×#41—21no—
290C22×D4D4×C15111yescharacteristic
291C23×C4—21no—
292C2×SD16—22no—
293C2×SD16—21no—
294C2×SD16—21no—
295C2×D8—22no—
296C2×M16—22no—
297C2×M16—22no—
298C2×M16—44no—
299C22×C8—21no—
300C22×C8D4×C15111yescharacteristic
301C22×C8D4×C15111yescharacteristic
302C4⋊Q8C23×C15111yescharacteristic
303C4⋊Q8C23×C15111yescharacteristic
304C4⋊Q8C23×C15111yescharacteristic
305#127C23×C15111yescharacteristic
306#125—21no—
307#124—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310#121—21no—
311#121—21no—
312C4×Q8—21no—
313C4×Q8—21no—
314C4×D4—21no—
315C4×D4—21no—
316C4×D4—21no—
317C4×D4—21no—
318C4×D4D4×C15112yes—
319C4×D4C23×C15112yes—
320#117—21no—
321C2×C4⋊C4D4×C15111yescharacteristic
322C2×C22⋊C4—21no—
323C2×C42C23×C15111yescharacteristic
324#107—22no—
325#106—21no—
326#106—21no—
327#106—22no—
328C4⋊C8—21no—
329C4⋊C8C23×C15112yes—
330C4⋊C8C23×C15112yes—
331C4⋊C8C23×C15112yes—
332#103—21no—
333#103—21no—
334#103—22no—
335#102—22no—
336#102—22no—
337#102—21no—
338#102—21no—
339#102—22no—
340C22⋊C8—21no—
341C22⋊C8—21no—
342C22⋊C8—22no—
343C22⋊C8—22no—
344#97—21no—
345#97—21no—
346C4×C8D4×C15111yescharacteristic
347C4×C8D4×C15111yescharacteristic
348C4×C8C23×C15111yescharacteristic
349C4×C8C23×C15111yescharacteristic
350C24—21no—
351#41—82no—
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—42no—
360C2×D4—41no—
361C2×D4C2×D4×C15112yes—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—41no—
368C22×C4C2×D4×C15111yescharacteristic
369C22×C4C2×D4×C15111yescharacteristic
370C22×C4#41×C15111yescharacteristic
371SD16—42no—
372SD16—44no—
373SD16—42no—
374D8—44no—
375M16—44no—
376M16—44no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—22no—
381C2×C8—41no—
382C2×C8—42no—
383C2×C8C2×D4×C15111yescharacteristic
384C2×C8C2×D4×C15111yescharacteristic
385C2×C8C2×D4×C15111yescharacteristic
386C2×C8C2×D4×C15111yescharacteristic
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4C2×D4×C15112yes—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C42—41no—
403C42C2×D4×C15111yescharacteristic
404C42C2×D4×C15111yescharacteristic
405C42#41×C15111yescharacteristic
406C42C24×C15111yescharacteristic
407C23—22no—
408C23—42no—
409C23—42no—
410C23—42no—
411C23—41no—
412C23#121×C15111yescharacteristic
413Q8—41no—
414Q8—41no—
415Q8—42no—
416Q8—81no—
417D4—22no—
418D4—22no—
419D4—42no—
420D4—41no—
421D4—42no—
422D4—41no—
423D4—81no—
424D4—82no—
425C2×C4—22no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—44no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—82no—
438C2×C4#121×C15111yescharacteristic
439C2×C4#121×C15111yescharacteristic
440C2×C4#121×C15111yescharacteristic
441C2×C4C22×D4×C15111yescharacteristic
442C2×C4C22×D4×C15111yescharacteristic
443C2×C4C2×#41×C15111yescharacteristic
444C8—21no—
445C8—21no—
446C8—21no—
447C8—42no—
448C8—42no—
449C8—42no—
450C8AGL(1,ℤ/8)×C15112yes—
451C22—21no—
452C22—21no—
453C22—42no—
454C22—42no—
455C22—42no—
456C22—84no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22#471×C15112yes—
461C22C2×#121×C15111yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—42no—
467C4—81no—
468C4—81no—
469C4—81no—
470C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
471C4#575×C15111yescharacteristic
472C4#575×C15112yes—
473C2—22no—
474C2—82no—
475C2—161no—
476C2#3036×C15111yescharacteristic
477C2#3054×C15111yescharacteristic
478C2C2×#471×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radical#3109×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. #3167×C151C2semidirect
2. #3110×C151C2semidirect
4. C2×#436×C151C2semidirect
5. #1703×C151C2semidirect
6. #1701×C151C2semidirect
7. #1691×C151C2semidirect
8. #1685×C151C2semidirect
9. #1568×C151C2semidirect
10. #1552×C151C2semidirect
11. #1551×C151C2semidirect
16. #498×C151C22semidirect
17. #492×C151C22semidirect
18. #487×C151C22semidirect
19. #486×C151C22semidirect
43. #335×C151C22semidirect
44. #334×C151C22semidirect
45. #333×C151C22semidirect
46. #332×C151C22semidirect
47. #332×C151C22semidirect
48. #331×C151C22semidirect
239. #19282C151direct (N × H)
240. C151#19282direct (N × H)
241. #3167C2×C151semidirect
242. #3110C2×C151semidirect
244. C2×#436C2×C151semidirect
245. #1703C2×C151semidirect
246. #1701C2×C151semidirect
247. #1691C2×C151semidirect
248. #1685C2×C151semidirect
249. #1568C2×C151semidirect
250. #1552C2×C151semidirect
251. #1551C2×C151semidirect
256. #498C22×C151semidirect
257. #492C22×C151semidirect
258. #487C22×C151semidirect
259. #486C22×C151semidirect
283. #335C22×C151semidirect
284. #334C22×C151semidirect
285. #333C22×C151semidirect
286. #332C22×C151semidirect
287. #332C22×C151semidirect
288. #331C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3167×C1512
#3110×C1512
#3109×C1512
C2×#436×C1512
#1703×C1512
#1701×C1512
#1691×C1512
#1685×C1512
#1568×C1512
#1552×C1512
#1551×C1512
#19282151