Finite Group Databasebeta

← C151×#19391 #50324316

Subgroups — C151×#19391 #50324316

Order 38656.

696 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3227×C151C211yesmaximal, characteristic, complemented
2C2×#476×C151C211yesmaximal, characteristic, complemented
3#3036×C151C211yesmaximal, characteristic
4#2972×C151C211yesmaximal, characteristic, complemented
5#1677×C151C214yesmaximal, complemented
6#1671×C151C214yesmaximal, complemented
7#1570×C151C211yesmaximal, characteristic, complemented
8#1548×C151C211yesmaximal, characteristic, complemented
9#1540×C151C211yesmaximal, characteristic, complemented
10C2×AGL(1,ℤ/8)×C151—21no—
11#532×C151C2211yescharacteristic
12C2×C4⋊Q8×C151C2211yescharacteristic
13C2×C4×D4×C151C2211yescharacteristic
14#498×C151C2212yescomplemented
15#486×C151C2212yescomplemented
16#481×C151—22no—
17#476×C151—22no—
18#476×C151—22no—
19#476×C151C2214yes—
20#463×C151—22no—
21#461×C151C2212yes—
22#459×C151C2212yes—
23C8×D4×C151—22no—
24C8×D4×C151C2214yes—
25#431×C151C2211yescharacteristic
26#431×C151C2211yescharacteristic
27C2×#106×C151—21no—
28#423×C151C2211yescharacteristic
29C2×C4⋊C8×C151C2211yescharacteristic
30#417×C151—21no—
31C2×#102×C151—21no—
32C2×C22⋊C8×C151—22no—
33#334×C151C2214yescomplemented
34#333×C151C2214yescomplemented
35#332×C151C2212yescomplemented
36#331×C151C2212yescomplemented
37C2×#41×C151—21no—
38C22×Q8×C151—21no—
39C22×D4×C151D411yescharacteristic
40C23×C4×C151—21no—
41AGL(1,ℤ/8)×C151—44no—
42C2×SD16×C151—22no—
43C2×D8×C151—22no—
44C2×M16×C151—21no—
45C22×C8×C151—21no—
46C22×C8×C151—24no—
47C4⋊Q8×C151—21no—
48C4⋊Q8×C151—21no—
49C4⋊Q8×C151—21no—
50C4⋊Q8×C151C2311yescharacteristic
51C4⋊Q8×C151C2312yes—
52#127×C151C2311yescharacteristic
53#124×C151—21no—
54#121×C151—21no—
55#121×C151—21no—
56C4×D4×C151—21no—
57C4×D4×C151—21no—
58C4×D4×C151—21no—
59C4×D4×C151—21no—
60C4×D4×C151D412yes—
61C4×D4×C151C2312yes—
62C2×C4⋊C4×C151—21no—
63C2×C4⋊C4×C151—21no—
64C2×C4⋊C4×C151D411yescharacteristic
65C2×C22⋊C4×C151—21no—
66C2×C42×C151C2311yescharacteristic
67#106×C151—24no—
68#106×C151—24no—
69C4⋊C8×C151—21no—
70C4⋊C8×C151—21no—
71C4⋊C8×C151D412yes—
72C4⋊C8×C151C2312yes—
73C4⋊C8×C151C2312yes—
74C4⋊C8×C151C2312yes—
75#103×C151—22no—
76#102×C151—24no—
77#102×C151—24no—
78#102×C151—22no—
79C22⋊C8×C151—21no—
80C22⋊C8×C151—24no—
81C22⋊C8×C151D412yes—
82C4×C8×C151—21no—
83C4×C8×C151C2312yes—
84C24×C151—21no—
85#41×C151—42no—
86#41×C151—42no—
87C2×Q8×C151—21no—
88C2×Q8×C151—22no—
89C2×Q8×C151—41no—
90C2×Q8×C151—82no—
91C2×D4×C151—21no—
92C2×D4×C151—22no—
93C2×D4×C151—21no—
94C2×D4×C151—21no—
95C2×D4×C151—21no—
96C2×D4×C151—41no—
97C2×D4×C151SD1614yes—
98C2×D4×C151C2×D412yes—
99C22×C4×C151—21no—
100C22×C4×C151—22no—
101C22×C4×C151—22no—
102C22×C4×C151—41no—
103C22×C4×C151—41no—
104C22×C4×C151—82no—
105C22×C4×C151C2×D411yescharacteristic
106C22×C4×C151C2×D411yescharacteristic
107C22×C4×C151#4111yescharacteristic
108SD16×C151—44no—
109D8×C151—44no—
110M16×C151—42no—
111C2×C8×C151—22no—
112C2×C8×C151—22no—
113C2×C8×C151—22no—
114C2×C8×C151—42no—
115C2×C8×C151—84no—
116C2×C8×C151C2×D414yes—
117C4⋊C4×C151—21no—
118C4⋊C4×C151—22no—
119C4⋊C4×C151—22no—
120C4⋊C4×C151—21no—
121C4⋊C4×C151—21no—
122C4⋊C4×C151—41no—
123C4⋊C4×C151—41no—
124C4⋊C4×C151C2×D412yes—
125C22⋊C4×C151—22no—
126C22⋊C4×C151—22no—
127C22⋊C4×C151—41no—
128C22⋊C4×C151—41no—
129C42×C151C2×D411yescharacteristic
130C42×C151C2×D411yescharacteristic
131C42×C151#4111yescharacteristic
132C42×C151C2411yescharacteristic
133C23×C151—22no—
134C23×C151—24no—
135C23×C151—41no—
136C23×C151—81no—
137C23×C151—81no—
138C23×C151#12111yescharacteristic
139Q8×C151—41no—
140Q8×C151—41no—
141Q8×C151—82no—
142Q8×C151—82no—
143D4×C151—22no—
144D4×C151—24no—
145D4×C151—41no—
146D4×C151—41no—
147D4×C151—42no—
148D4×C151—81no—
149D4×C151—82no—
150D4×C151C2×SD1614yes—
151C2×C4×C151—22no—
152C2×C4×C151—22no—
153C2×C4×C151—41no—
154C2×C4×C151—44no—
155C2×C4×C151—42no—
156C2×C4×C151—41no—
157C2×C4×C151—82no—
158C2×C4×C151—81no—
159C2×C4×C151—82no—
160C2×C4×C151—82no—
161C2×C4×C151#12111yescharacteristic
162C2×C4×C151#12111yescharacteristic
163C2×C4×C151#12111yescharacteristic
164C2×C4×C151C2×SD1612yes—
165C2×C4×C151#13512yes—
166C2×C4×C151C22×D411yescharacteristic
167C2×C4×C151C22×D411yescharacteristic
168C2×C4×C151C2×#4111yescharacteristic
169C8×C151—24no—
170C8×C151—42no—
171C8×C151—42no—
172C8×C151—42no—
173C22×C151—21no—
174C22×C151—21no—
175C22×C151—24no—
176C22×C151—42no—
177C22×C151—42no—
178C22×C151—84no—
179C22×C151—81no—
180C22×C151—81no—
181C22×C151—81no—
182C22×C151#46512yes—
183C22×C151C2×#12111yescharacteristic
184C4×C151—21no—
185C4×C151—21no—
186C4×C151—21no—
187C4×C151—42no—
188C4×C151—81no—
189C4×C151—82no—
190C4×C151#46512yes—
191C4×C151C22×SD1611yescharacteristic
192C4×C151C2×#13511yescharacteristic
193C4×C151#57712yes—
194C2×C151—22no—
195C2×C151—44no—
196C2×C151—161no—
197C2×C151#304211yescharacteristic
198C2×C151C2×#46511yescharacteristic
199C2×C151#306811yescharacteristic
200#19391C15111yesmaximal, characteristic, direct product factor, Sylow
201C151#1939111yescharacteristic, direct product factor, Sylow
202#3227C2×C15111yescharacteristic, complemented
203C2×#476C2×C15111yescharacteristic, complemented
204#3036C2×C15111yescharacteristic
205#2972C2×C15111yescharacteristic, complemented
206#1677C2×C15114yescomplemented
207#1671C2×C15114yescomplemented
208#1570C2×C15111yescharacteristic, complemented
209#1548C2×C15111yescharacteristic, complemented
210#1540C2×C15111yescharacteristic, complemented
211C2×AGL(1,ℤ/8)—21no—
212#532C22×C15111yescharacteristic
213C2×C4⋊Q8C22×C15111yescharacteristic
214C2×C4×D4C22×C15111yescharacteristic
215#498C22×C15112yescomplemented
216#486C22×C15112yescomplemented
217#481—22no—
218#476—22no—
219#476—22no—
220#476C22×C15114yes—
221#463—22no—
222#461C22×C15112yes—
223#459C22×C15112yes—
224C8×D4—22no—
225C8×D4C22×C15114yes—
226#431C22×C15111yescharacteristic
227#431C22×C15111yescharacteristic
228C2×#106—21no—
229#423C22×C15111yescharacteristic
230C2×C4⋊C8C22×C15111yescharacteristic
231#417—21no—
232C2×#102—21no—
233C2×C22⋊C8—22no—
234#334C22×C15114yescomplemented
235#333C22×C15114yescomplemented
236#332C22×C15112yescomplemented
237#331C22×C15112yescomplemented
238C2×#41—21no—
239C22×Q8—21no—
240C22×D4D4×C15111yescharacteristic
241C23×C4—21no—
242AGL(1,ℤ/8)—44no—
243C2×SD16—22no—
244C2×D8—22no—
245C2×M16—21no—
246C22×C8—21no—
247C22×C8—24no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8C23×C15112yes—
252C4⋊Q8C23×C15111yescharacteristic
253#127C23×C15111yescharacteristic
254#124—21no—
255#121—21no—
256#121—21no—
257C4×D4—21no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4D4×C15112yes—
262C4×D4C23×C15112yes—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4D4×C15111yescharacteristic
266C2×C22⋊C4—21no—
267C2×C42C23×C15111yescharacteristic
268#106—24no—
269#106—24no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8D4×C15112yes—
273C4⋊C8C23×C15112yes—
274C4⋊C8C23×C15112yes—
275C4⋊C8C23×C15112yes—
276#103—22no—
277#102—24no—
278#102—24no—
279#102—22no—
280C22⋊C8—21no—
281C22⋊C8—24no—
282C22⋊C8D4×C15112yes—
283C4×C8—21no—
284C4×C8C23×C15112yes—
285C24—21no—
286#41—42no—
287#41—42no—
288C2×Q8—21no—
289C2×Q8—22no—
290C2×Q8—41no—
291C2×Q8—82no—
292C2×D4—21no—
293C2×D4—22no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4SD16×C15114yes—
299C2×D4C2×D4×C15112yes—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—82no—
306C22×C4C2×D4×C15111yescharacteristic
307C22×C4C2×D4×C15111yescharacteristic
308C22×C4#41×C15111yescharacteristic
309SD16—44no—
310D8—44no—
311M16—42no—
312C2×C8—22no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—42no—
316C2×C8—84no—
317C2×C8C2×D4×C15114yes—
318C4⋊C4—21no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4C2×D4×C15112yes—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C42C2×D4×C15111yescharacteristic
331C42C2×D4×C15111yescharacteristic
332C42#41×C15111yescharacteristic
333C42C24×C15111yescharacteristic
334C23—22no—
335C23—24no—
336C23—41no—
337C23—81no—
338C23—81no—
339C23#121×C15111yescharacteristic
340Q8—41no—
341Q8—41no—
342Q8—82no—
343Q8—82no—
344D4—24no—
345D4—22no—
346D4—41no—
347D4—41no—
348D4—42no—
349D4—81no—
350D4—82no—
351D4C2×SD16×C15114yes—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—41no—
355C2×C4—44no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—82no—
359C2×C4—81no—
360C2×C4—82no—
361C2×C4—82no—
362C2×C4#121×C15111yescharacteristic
363C2×C4#121×C15111yescharacteristic
364C2×C4#121×C15111yescharacteristic
365C2×C4C2×SD16×C15112yes—
366C2×C4#135×C15112yes—
367C2×C4C22×D4×C15111yescharacteristic
368C2×C4C22×D4×C15111yescharacteristic
369C2×C4C2×#41×C15111yescharacteristic
370C8—24no—
371C8—42no—
372C8—42no—
373C8—42no—
374C22—21no—
375C22—21no—
376C22—24no—
377C22—42no—
378C22—42no—
379C22—84no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22#465×C15112yes—
384C22C2×#121×C15111yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—42no—
389C4—81no—
390C4—82no—
391C4#465×C15112yes—
392C4C22×SD16×C15111yescharacteristic
393C4C2×#135×C15111yescharacteristic
394C4#577×C15112yes—
395C2—22no—
396C2—44no—
397C2—161no—
398C2#3042×C15111yescharacteristic
399C2C2×#465×C15111yescharacteristic
400C2#3068×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radical#3036×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. #3227×C151C2semidirect
2. C2×#476×C151C2semidirect
4. #2972×C151C2semidirect
5. #1677×C151C2semidirect
6. #1671×C151C2semidirect
7. #1570×C151C2semidirect
8. #1548×C151C2semidirect
9. #1540×C151C2semidirect
14. #498×C151C22semidirect
15. #486×C151C22semidirect
33. #334×C151C22semidirect
34. #333×C151C22semidirect
35. #332×C151C22semidirect
36. #331×C151C22semidirect
200. #19391C151direct (N × H)
201. C151#19391direct (N × H)
202. #3227C2×C151semidirect
203. C2×#476C2×C151semidirect
205. #2972C2×C151semidirect
206. #1677C2×C151semidirect
207. #1671C2×C151semidirect
208. #1570C2×C151semidirect
209. #1548C2×C151semidirect
210. #1540C2×C151semidirect
215. #498C22×C151semidirect
216. #486C22×C151semidirect
234. #334C22×C151semidirect
235. #333C22×C151semidirect
236. #332C22×C151semidirect
237. #331C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3227×C1512
C2×#476×C1512
#3036×C1512
#2972×C1512
#1677×C1512
#1671×C1512
#1570×C1512
#1548×C1512
#1540×C1512
#19391151