Finite Group Databasebeta

← C151×#9231 #50314156

Subgroups — C151×#9231 #50314156

Order 38656.

686 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3101×C151C211yesmaximal, characteristic
2C42×D4×C151C211yesmaximal, characteristic
3#1994×C151C211yesmaximal, characteristic, complemented
4#1503×C151C211yesmaximal, characteristic, complemented
5#1486×C151C211yesmaximal, characteristic
6#1303×C151C211yesmaximal, characteristic, complemented
7#1276×C151C211yesmaximal, characteristic, complemented
8#533×C151C2211yescharacteristic
9C2×C4×D4×C151—21no—
10C2×C4×D4×C151C2211yescharacteristic
11C22×C42×C151—21no—
12#483×C151—21no—
13#476×C151C412yescomplemented
14#461×C151C412yescomplemented
15#450×C151—21no—
16C4×SD16×C151—22no—
17#431×C151C2211yescharacteristic
18#431×C151C2211yescharacteristic
19#423×C151C2211yescharacteristic
20C4×C4⋊C4×C151—21no—
21C4×C4⋊C4×C151C2211yescharacteristic
22C4×C22⋊C4×C151—21no—
23C4×C22⋊C4×C151—22no—
24C43×C151C2211yescharacteristic
25#339×C151—21no—
26#339×C151—21no—
27#328×C151—22no—
28D4⋊C8×C151—22no—
29C22×D4×C151D411yescharacteristic
30C23×C4×C151—22no—
31C23×C4×C151—21no—
32C2×SD16×C151—22no—
33C2×M16×C151—21no—
34C4⋊Q8×C151C2×C411yescharacteristic, complemented
35C4⋊Q8×C151C2×C411yescharacteristic, complemented
36#125×C151—21no—
37C22⋊Q8×C151—21no—
38C22⋊Q8×C151—21no—
39C4×Q8×C151—21no—
40C4×Q8×C151—21no—
41C4×D4×C151—28no—
42C4×D4×C151—21no—
43C4×D4×C151—21no—
44C4×D4×C151C2×C412yes—
45C4×D4×C151D412yes—
46#117×C151—21no—
47C2×C4⋊C4×C151—21no—
48C2×C4⋊C4×C151D411yescharacteristic
49C2×C22⋊C4×C151—22no—
50C2×C22⋊C4×C151—21no—
51C2×C42×C151—21no—
52C2×C42×C151—22no—
53C2×C42×C151—21no—
54C2×C42×C151—21no—
55C2×C42×C151—42no—
56C2×C42×C151—42no—
57C2×C42×C151D411yescharacteristic
58C2×C42×C151D411yescharacteristic
59C2×C42×C151C2311yescharacteristic
60#106×C151—22no—
61C4⋊C8×C151—21no—
62C4⋊C8×C151—21no—
63C4⋊C8×C151—21no—
64C4⋊C8×C151C2×C412yescomplemented
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—
73C24×C151—21no—
74C2×Q8×C151—21no—
75C2×Q8×C151—21no—
76C2×D4×C151—24no—
77C2×D4×C151—21no—
78C2×D4×C151C22⋊C412yes—
79C22×C4×C151—21no—
80C22×C4×C151—28no—
81C22×C4×C151—21no—
82C22×C4×C151—21no—
83C22×C4×C151—22no—
84C22×C4×C151—22no—
85C22×C4×C151—22no—
86C22×C4×C151—44no—
87C22×C4×C151—44no—
88C22×C4×C151—41no—
89C22×C4×C151—41no—
90C22×C4×C151—41no—
91C22×C4×C151—41no—
92C22×C4×C151C2×D411yescharacteristic
93C22×C4×C151C2×D411yescharacteristic
94C22×C4×C151C2×D411yescharacteristic
95SD16×C151—44no—
96M16×C151—41no—
97M16×C151—41no—
98C2×C8×C151—22no—
99C2×C8×C151—41no—
100C2×C8×C151—41no—
101C4⋊C4×C151—24no—
102C4⋊C4×C151—21no—
103C4⋊C4×C151—21no—
104C4⋊C4×C151—21no—
105C4⋊C4×C151—21no—
106C4⋊C4×C151—21no—
107C4⋊C4×C151—41no—
108C4⋊C4×C151—41no—
109C4⋊C4×C151C22⋊C412yes—
110C22⋊C4×C151—28no—
111C22⋊C4×C151—22no—
112C22⋊C4×C151—22no—
113C22⋊C4×C151—41no—
114C42×C151—24no—
115C42×C151—21no—
116C42×C151—21no—
117C42×C151—21no—
118C42×C151—42no—
119C42×C151—44no—
120C42×C151—41no—
121C42×C151—41no—
122C42×C151—41no—
123C42×C151SD1612yescomplemented
124C42×C151C22×C411yescharacteristic
125C42×C151C2×D411yescharacteristic
126C42×C151#4111yescharacteristic
127C42×C151#4111yescharacteristic
128C23×C151—24no—
129C23×C151—22no—
130C23×C151—42no—
131C23×C151—41no—
132C23×C151—41no—
133C23×C151#12011yescharacteristic
134Q8×C151—42no—
135Q8×C151—81no—
136D4×C151—24no—
137D4×C151—22no—
138D4×C151#10414yes—
139C2×C4×C151—22no—
140C2×C4×C151—22no—
141C2×C4×C151—22no—
142C2×C4×C151—22no—
143C2×C4×C151—22no—
144C2×C4×C151—24no—
145C2×C4×C151—22no—
146C2×C4×C151—41no—
147C2×C4×C151—416no—
148C2×C4×C151—41no—
149C2×C4×C151—42no—
150C2×C4×C151—42no—
151C2×C4×C151—41no—
152C2×C4×C151—41no—
153C2×C4×C151—41no—
154C2×C4×C151—42no—
155C2×C4×C151—42no—
156C2×C4×C151—42no—
157C2×C4×C151—42no—
158C2×C4×C151—41no—
159C2×C4×C151—41no—
160C2×C4×C151C2×C22⋊C411yescharacteristic
161C2×C4×C151C4×D411yescharacteristic
162C2×C4×C151C4×D411yescharacteristic
163C2×C4×C151#12111yescharacteristic
164C2×C4×C151#12111yescharacteristic
165C2×C4×C151#12311yescharacteristic
166C2×C4×C151C2×SD1611yescharacteristic
167C2×C4×C151#13511yescharacteristic
168C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C151#13711yescharacteristic
170C8×C151—42no—
171C8×C151—81no—
172C8×C151—81no—
173C22×C151—21no—
174C22×C151—21no—
175C22×C151—24no—
176C22×C151—44no—
177C22×C151—44no—
178C22×C151—42no—
179C22×C151—42no—
180C22×C151#38611yescharacteristic
181C22×C151#45011yescharacteristic
182C22×C151#45211yescharacteristic
183C4×C151—24no—
184C4×C151—21no—
185C4×C151—21no—
186C4×C151—21no—
187C4×C151—42no—
188C4×C151—44no—
189C4×C151—42no—
190C4×C151—81no—
191C4×C151—81no—
192C4×C151C2×#10412yes—
193C4×C151C4×SD1611yescharacteristic
194C4×C151#44011yescharacteristic
195C4×C151#46111yescharacteristic
196C4×C151#46311yescharacteristic
197C2×C151—21no—
198C2×C151—21no—
199C2×C151—44no—
200C2×C151#187711yescharacteristic
201C2×C151#189611yescharacteristic
202C2×C151#190611yescharacteristic
203#9231C15111yesmaximal, characteristic, direct product factor, Sylow
204C151#923111yescharacteristic, direct product factor, Sylow
205#3101C2×C15111yescharacteristic
206C42×D4C2×C15111yescharacteristic
207#1994C2×C15111yescharacteristic, complemented
208#1503C2×C15111yescharacteristic, complemented
209#1486C2×C15111yescharacteristic
210#1303C2×C15111yescharacteristic, complemented
211#1276C2×C15111yescharacteristic, complemented
212#533C22×C15111yescharacteristic
213C2×C4×D4—21no—
214C2×C4×D4C22×C15111yescharacteristic
215C22×C42—21no—
216#483—21no—
217#476C4×C15112yescomplemented
218#461C4×C15112yescomplemented
219#450—21no—
220C4×SD16—22no—
221#431C22×C15111yescharacteristic
222#431C22×C15111yescharacteristic
223#423C22×C15111yescharacteristic
224C4×C4⋊C4—21no—
225C4×C4⋊C4C22×C15111yescharacteristic
226C4×C22⋊C4—21no—
227C4×C22⋊C4—22no—
228C43C22×C15111yescharacteristic
229#339—21no—
230#339—21no—
231#328—22no—
232D4⋊C8—22no—
233C22×D4D4×C15111yescharacteristic
234C23×C4—22no—
235C23×C4—21no—
236C2×SD16—22no—
237C2×M16—21no—
238C4⋊Q8C2×C4×C15111yescharacteristic, complemented
239C4⋊Q8C2×C4×C15111yescharacteristic, complemented
240#125—21no—
241C22⋊Q8—21no—
242C22⋊Q8—21no—
243C4×Q8—21no—
244C4×Q8—21no—
245C4×D4—28no—
246C4×D4—21no—
247C4×D4—21no—
248C4×D4C2×C4×C15112yes—
249C4×D4D4×C15112yes—
250#117—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4D4×C15111yescharacteristic
253C2×C22⋊C4—22no—
254C2×C22⋊C4—21no—
255C2×C42—21no—
256C2×C42—22no—
257C2×C42—21no—
258C2×C42—21no—
259C2×C42—42no—
260C2×C42—42no—
261C2×C42D4×C15111yescharacteristic
262C2×C42D4×C15111yescharacteristic
263C2×C42C23×C15111yescharacteristic
264#106—22no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8C2×C4×C15112yescomplemented
269#103—22no—
270#102—22no—
271C22⋊C8—21no—
272C22⋊C8—21no—
273C4×C8—21no—
274C4×C8—21no—
275#95—22no—
276#95D4×C15112yes—
277C24—21no—
278C2×Q8—21no—
279C2×Q8—21no—
280C2×D4—24no—
281C2×D4—21no—
282C2×D4C22⋊C4×C15112yes—
283C22×C4—21no—
284C22×C4—28no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—44no—
291C22×C4—44no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4C2×D4×C15111yescharacteristic
297C22×C4C2×D4×C15111yescharacteristic
298C22×C4C2×D4×C15111yescharacteristic
299SD16—44no—
300M16—41no—
301M16—41no—
302C2×C8—22no—
303C2×C8—41no—
304C2×C8—41no—
305C4⋊C4—24no—
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4C22⋊C4×C15112yes—
314C22⋊C4—28no—
315C22⋊C4—22no—
316C22⋊C4—22no—
317C22⋊C4—41no—
318C42—24no—
319C42—21no—
320C42—21no—
321C42—21no—
322C42—44no—
323C42—42no—
324C42—41no—
325C42—41no—
326C42—41no—
327C42SD16×C15112yescomplemented
328C42C22×C4×C15111yescharacteristic
329C42C2×D4×C15111yescharacteristic
330C42#41×C15111yescharacteristic
331C42#41×C15111yescharacteristic
332C23—24no—
333C23—22no—
334C23—42no—
335C23—41no—
336C23—41no—
337C23#120×C15111yescharacteristic
338Q8—42no—
339Q8—81no—
340D4—24no—
341D4—22no—
342D4#104×C15114yes—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—24no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—416no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4C2×C22⋊C4×C15111yescharacteristic
365C2×C4C4×D4×C15111yescharacteristic
366C2×C4C4×D4×C15111yescharacteristic
367C2×C4#121×C15111yescharacteristic
368C2×C4#121×C15111yescharacteristic
369C2×C4#123×C15111yescharacteristic
370C2×C4C2×SD16×C15111yescharacteristic
371C2×C4#135×C15111yescharacteristic
372C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
373C2×C4#137×C15111yescharacteristic
374C8—42no—
375C8—81no—
376C8—81no—
377C22—21no—
378C22—21no—
379C22—24no—
380C22—44no—
381C22—44no—
382C22—42no—
383C22—42no—
384C22#386×C15111yescharacteristic
385C22#450×C15111yescharacteristic
386C22#452×C15111yescharacteristic
387C4—24no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—44no—
392C4—42no—
393C4—42no—
394C4—81no—
395C4—81no—
396C4C2×#104×C15112yes—
397C4C4×SD16×C15111yescharacteristic
398C4#440×C15111yescharacteristic
399C4#461×C15111yescharacteristic
400C4#463×C15111yescharacteristic
401C2—21no—
402C2—21no—
403C2—44no—
404C2#1877×C15111yescharacteristic
405C2#1896×C15111yescharacteristic
406C2#1906×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151#121
commutatorC42C22×C4×C151
Frattini, cosocleC2×C42C23×C151
socleC22×C151#386
prime radicalC22×D4×C151D4
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
3. #1994×C151C2semidirect
4. #1503×C151C2semidirect
6. #1303×C151C2semidirect
7. #1276×C151C2semidirect
13. #476×C151C4semidirect
14. #461×C151C4semidirect
34. C4⋊Q8×C151C2×C4semidirect
35. C4⋊Q8×C151C2×C4semidirect
64. C4⋊C8×C151C2×C4semidirect
123. C42×C151SD16semidirect
203. #9231C151direct (N × H)
204. C151#9231direct (N × H)
207. #1994C2×C151semidirect
208. #1503C2×C151semidirect
210. #1303C2×C151semidirect
211. #1276C2×C151semidirect
217. #476C4×C151semidirect
218. #461C4×C151semidirect
238. C4⋊Q8C2×C4×C151semidirect
239. C4⋊Q8C2×C4×C151semidirect
268. C4⋊C8C2×C4×C151semidirect
327. C42SD16×C151semidirect

Maximal subgroups

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

subgroupindex
#3101×C1512
C42×D4×C1512
#1994×C1512
#1503×C1512
#1486×C1512
#1303×C1512
#1276×C1512
#9231151