Finite Group Databasebeta

← C151×#9234 #50314159

Subgroups — C151×#9234 #50314159

Order 38656.

604 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3103×C151C211yesmaximal, characteristic
2C42×Q8×C151C211yesmaximal, characteristic, complemented
3#1962×C151C211yesmaximal, characteristic
4#1502×C151C211yesmaximal, characteristic
5#1487×C151C211yesmaximal, characteristic, complemented
6#1303×C151C211yesmaximal, characteristic, complemented
7#1276×C151C211yesmaximal, characteristic, complemented
8#532×C151C2211yescharacteristic
9C2×C4×Q8×C151—21no—
10C2×C4×Q8×C151C2211yescharacteristic
11#481×C151—21no—
12#475×C151C412yescomplemented
13#460×C151C412yescomplemented
14#448×C151—21no—
15C4×SD16×C151—22no—
16#431×C151C2211yescharacteristic
17#431×C151C2211yescharacteristic
18#423×C151C2211yescharacteristic
19C2×#104×C151—21no—
20C2×#104×C151—21no—
21C4×C4⋊C4×C151—21no—
22C4×C4⋊C4×C151—21no—
23C4×C4⋊C4×C151—22no—
24C4×C4⋊C4×C151C2211yescharacteristic
25C43×C151—21no—
26C43×C151C2211yescharacteristic
27#327×C151—22no—
28Q8⋊C8×C151—22no—
29C2×#41×C151—21no—
30C22×Q8×C151D411yescharacteristic
31C2×SD16×C151—22no—
32C2×M16×C151—21no—
33C4⋊Q8×C151C2×C411yescharacteristic
34#127×C151C2×C411yescharacteristic
35#124×C151—21no—
36#121×C151—21no—
37#121×C151—21no—
38C4×Q8×C151—28no—
39C4×Q8×C151—21no—
40C4×Q8×C151—21no—
41C4×Q8×C151C2×C412yes—
42C4×Q8×C151D412yes—
43C4×D4×C151—21no—
44C4×D4×C151—21no—
45C2×C4⋊C4×C151—22no—
46C2×C4⋊C4×C151—21no—
47C2×C4⋊C4×C151—21no—
48C2×C4⋊C4×C151D411yescharacteristic
49C2×C42×C151—22no—
50C2×C42×C151—21no—
51C2×C42×C151—21no—
52C2×C42×C151—22no—
53C2×C42×C151—21no—
54C2×C42×C151—21no—
55C2×C42×C151D411yescharacteristic
56C2×C42×C151D411yescharacteristic
57C2×C42×C151C2311yescharacteristic
58#106×C151—22no—
59C4⋊C8×C151—21no—
60C4⋊C8×C151—21no—
61C4⋊C8×C151—21no—
62C4⋊C8×C151C2×C412yes—
63#104×C151—42no—
64#104×C151—42no—
65#103×C151—22no—
66#102×C151—22no—
67C22⋊C8×C151—21no—
68C22⋊C8×C151—21no—
69C4×C8×C151—21no—
70C4×C8×C151—21no—
71#95×C151—22no—
72#95×C151D412yes—
73#41×C151—41no—
74#41×C151—41no—
75#41×C151—41no—
76#41×C151—41no—
77C2×Q8×C151—24no—
78C2×Q8×C151—21no—
79C2×Q8×C151—21no—
80C2×Q8×C151C22⋊C412yes—
81C2×D4×C151—21no—
82C2×D4×C151—21no—
83C2×D4×C151—21no—
84C2×D4×C151—41no—
85C22×C4×C151—21no—
86C22×C4×C151—21no—
87C22×C4×C151—21no—
88C22×C4×C151—21no—
89C22×C4×C151—22no—
90C22×C4×C151—41no—
91C22×C4×C151C2×D411yescharacteristic
92C22×C4×C151C2×D411yescharacteristic
93C22×C4×C151C2×D411yescharacteristic
94SD16×C151—44no—
95M16×C151—41no—
96M16×C151—41no—
97C2×C8×C151—22no—
98C2×C8×C151—41no—
99C2×C8×C151—41no—
100C4⋊C4×C151—28no—
101C4⋊C4×C151—24no—
102C4⋊C4×C151—22no—
103C4⋊C4×C151—22no—
104C4⋊C4×C151—21no—
105C4⋊C4×C151—21no—
106C4⋊C4×C151—21no—
107C4⋊C4×C151C22⋊C412yes—
108C22⋊C4×C151—41no—
109C22⋊C4×C151—41no—
110C42×C151—28no—
111C42×C151—24no—
112C42×C151—22no—
113C42×C151—22no—
114C42×C151—21no—
115C42×C151—21no—
116C42×C151—21no—
117C42×C151—42no—
118C42×C151—44no—
119C42×C151—41no—
120C42×C151—41no—
121C42×C151SD1612yescomplemented
122C42×C151C22×C411yescharacteristic
123C42×C151C2×D411yescharacteristic
124C42×C151#4111yescharacteristic
125C42×C151#4111yescharacteristic
126C23×C151—41no—
127C23×C151#12011yescharacteristic
128Q8×C151—24no—
129Q8×C151—22no—
130Q8×C151—41no—
131Q8×C151—41no—
132Q8×C151#10414yescomplemented
133D4×C151—42no—
134D4×C151—41no—
135D4×C151—41no—
136D4×C151—81no—
137D4×C151—81no—
138D4×C151—81no—
139C2×C4×C151—24no—
140C2×C4×C151—22no—
141C2×C4×C151—22no—
142C2×C4×C151—22no—
143C2×C4×C151—22no—
144C2×C4×C151—22no—
145C2×C4×C151—22no—
146C2×C4×C151—24no—
147C2×C4×C151—22no—
148C2×C4×C151—41no—
149C2×C4×C151—41no—
150C2×C4×C151—42no—
151C2×C4×C151—42no—
152C2×C4×C151—41no—
153C2×C4×C151—42no—
154C2×C4×C151—41no—
155C2×C4×C151—81no—
156C2×C4×C151—81no—
157C2×C4×C151C2×C22⋊C411yescharacteristic
158C2×C4×C151C4×D411yescharacteristic
159C2×C4×C151C4×D411yescharacteristic
160C2×C4×C151#12111yescharacteristic
161C2×C4×C151#12111yescharacteristic
162C2×C4×C151#12311yescharacteristic
163C2×C4×C151C2×SD1611yescharacteristic
164C2×C4×C151#13511yescharacteristic
165C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C151#13711yescharacteristic
167C8×C151—42no—
168C8×C151—81no—
169C8×C151—81no—
170C22×C151—21no—
171C22×C151—21no—
172C22×C151—81no—
173C22×C151—81no—
174C22×C151—81no—
175C22×C151#38611yescharacteristic
176C22×C151#44811yescharacteristic
177C22×C151#44911yescharacteristic
178C4×C151—24no—
179C4×C151—24no—
180C4×C151—21no—
181C4×C151—21no—
182C4×C151—21no—
183C4×C151—42no—
184C4×C151—44no—
185C4×C151—42no—
186C4×C151—81no—
187C4×C151C2×#10412yes—
188C4×C151C4×SD1611yescharacteristic
189C4×C151#44011yescharacteristic
190C4×C151#46011yescharacteristic
191C4×C151#46411yescharacteristic
192C2×C151—21no—
193C2×C151—21no—
194C2×C151—161no—
195C2×C151#188011yescharacteristic
196C2×C151#189611yescharacteristic
197C2×C151#190611yescharacteristic
198#9234C15111yesmaximal, characteristic, direct product factor, Sylow
199C151#923411yescharacteristic, direct product factor, Sylow
200#3103C2×C15111yescharacteristic
201C42×Q8C2×C15111yescharacteristic, complemented
202#1962C2×C15111yescharacteristic
203#1502C2×C15111yescharacteristic
204#1487C2×C15111yescharacteristic, complemented
205#1303C2×C15111yescharacteristic, complemented
206#1276C2×C15111yescharacteristic, complemented
207#532C22×C15111yescharacteristic
208C2×C4×Q8—21no—
209C2×C4×Q8C22×C15111yescharacteristic
210#481—21no—
211#475C4×C15112yescomplemented
212#460C4×C15112yescomplemented
213#448—21no—
214C4×SD16—22no—
215#431C22×C15111yescharacteristic
216#431C22×C15111yescharacteristic
217#423C22×C15111yescharacteristic
218C2×#104—21no—
219C2×#104—21no—
220C4×C4⋊C4—21no—
221C4×C4⋊C4—21no—
222C4×C4⋊C4—22no—
223C4×C4⋊C4C22×C15111yescharacteristic
224C43—21no—
225C43C22×C15111yescharacteristic
226#327—22no—
227Q8⋊C8—22no—
228C2×#41—21no—
229C22×Q8D4×C15111yescharacteristic
230C2×SD16—22no—
231C2×M16—21no—
232C4⋊Q8C2×C4×C15111yescharacteristic
233#127C2×C4×C15111yescharacteristic
234#124—21no—
235#121—21no—
236#121—21no—
237C4×Q8—28no—
238C4×Q8—21no—
239C4×Q8—21no—
240C4×Q8C2×C4×C15112yes—
241C4×Q8D4×C15112yes—
242C4×D4—21no—
243C4×D4—21no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4D4×C15111yescharacteristic
248C2×C42—22no—
249C2×C42—21no—
250C2×C42—21no—
251C2×C42—22no—
252C2×C42—21no—
253C2×C42—21no—
254C2×C42D4×C15111yescharacteristic
255C2×C42D4×C15111yescharacteristic
256C2×C42C23×C15111yescharacteristic
257#106—22no—
258C4⋊C8—21no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8C2×C4×C15112yes—
262#104—42no—
263#104—42no—
264#103—22no—
265#102—22no—
266C22⋊C8—21no—
267C22⋊C8—21no—
268C4×C8—21no—
269C4×C8—21no—
270#95—22no—
271#95D4×C15112yes—
272#41—41no—
273#41—41no—
274#41—41no—
275#41—41no—
276C2×Q8—24no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8C22⋊C4×C15112yes—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—41no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—22no—
289C22×C4—41no—
290C22×C4C2×D4×C15111yescharacteristic
291C22×C4C2×D4×C15111yescharacteristic
292C22×C4C2×D4×C15111yescharacteristic
293SD16—44no—
294M16—41no—
295M16—41no—
296C2×C8—22no—
297C2×C8—41no—
298C2×C8—41no—
299C4⋊C4—28no—
300C4⋊C4—24no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—21no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4C22⋊C4×C15112yes—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C42—28no—
310C42—24no—
311C42—22no—
312C42—22no—
313C42—21no—
314C42—21no—
315C42—21no—
316C42—42no—
317C42—44no—
318C42—41no—
319C42—41no—
320C42SD16×C15112yescomplemented
321C42C22×C4×C15111yescharacteristic
322C42C2×D4×C15111yescharacteristic
323C42#41×C15111yescharacteristic
324C42#41×C15111yescharacteristic
325C23—41no—
326C23#120×C15111yescharacteristic
327Q8—24no—
328Q8—22no—
329Q8—41no—
330Q8—41no—
331Q8#104×C15114yescomplemented
332D4—42no—
333D4—41no—
334D4—41no—
335D4—81no—
336D4—81no—
337D4—81no—
338C2×C4—22no—
339C2×C4—24no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—24no—
346C2×C4—22no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—41no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4C2×C22⋊C4×C15111yescharacteristic
357C2×C4C4×D4×C15111yescharacteristic
358C2×C4C4×D4×C15111yescharacteristic
359C2×C4#121×C15111yescharacteristic
360C2×C4#121×C15111yescharacteristic
361C2×C4#123×C15111yescharacteristic
362C2×C4C2×SD16×C15111yescharacteristic
363C2×C4#135×C15111yescharacteristic
364C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
365C2×C4#137×C15111yescharacteristic
366C8—42no—
367C8—81no—
368C8—81no—
369C22—21no—
370C22—21no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22#386×C15111yescharacteristic
375C22#448×C15111yescharacteristic
376C22#449×C15111yescharacteristic
377C4—24no—
378C4—24no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—42no—
383C4—44no—
384C4—42no—
385C4—81no—
386C4C2×#104×C15112yes—
387C4C4×SD16×C15111yescharacteristic
388C4#440×C15111yescharacteristic
389C4#460×C15111yescharacteristic
390C4#464×C15111yescharacteristic
391C2—21no—
392C2—21no—
393C2—161no—
394C2#1880×C15111yescharacteristic
395C2#1896×C15111yescharacteristic
396C2#1906×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151#121
commutatorC42C22×C4×C151
Frattini, cosocleC2×C42C23×C151
socleC22×C151#386
prime radical#532×C151C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C2×C42×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C42×Q8×C151C2semidirect
5. #1487×C151C2semidirect
6. #1303×C151C2semidirect
7. #1276×C151C2semidirect
12. #475×C151C4semidirect
13. #460×C151C4semidirect
121. C42×C151SD16semidirect
132. Q8×C151#104semidirect
198. #9234C151direct (N × H)
199. C151#9234direct (N × H)
201. C42×Q8C2×C151semidirect
204. #1487C2×C151semidirect
205. #1303C2×C151semidirect
206. #1276C2×C151semidirect
211. #475C4×C151semidirect
212. #460C4×C151semidirect
320. C42SD16×C151semidirect
331. Q8#104×C151semidirect

Maximal subgroups

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

subgroupindex
#3103×C1512
C42×Q8×C1512
#1962×C1512
#1502×C1512
#1487×C1512
#1303×C1512
#1276×C1512
#9234151