Finite Group Databasebeta

← C151×#13024 #50317949

Subgroups — C151×#13024 #50317949

Order 38656.

466 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3414×C151C211yesmaximal, characteristic
2C2×#444×C151C211yesmaximal, characteristic, complemented
3#2148×C151C211yesmaximal, characteristic, complemented
4#2143×C151C211yesmaximal, characteristic, complemented
5#1975×C151C211yesmaximal, characteristic, complemented
6#1388×C151C211yesmaximal, characteristic, complemented
7#1377×C151C211yesmaximal, characteristic, complemented
8C2×#135×C151C2211yescharacteristic
9C2×#135×C151C2211yescharacteristic
10C2×#131×C151—21no—
11#510×C151—21no—
12#510×C151C412yescomplemented
13#509×C151—21no—
14#509×C151C412yescomplemented
15#508×C151—22no—
16C2×M32×C151C2211yescharacteristic
17C2×M32×C151C2211yescharacteristic
18#444×C151—22no—
19#444×C151—22no—
20C2×#108×C151C2211yescharacteristic
21C2×#108×C151C2211yescharacteristic
22C2×#104×C151—21no—
23C2×#104×C151—21no—
24#408×C151—21no—
25C2×#97×C151C2211yescharacteristic
26#362×C151—21no—
27#361×C151—21no—
28#359×C151—22no—
29C2×#41×C151—21no—
30C2×#41×C151—21no—
31#135×C151—21no—
32#135×C151—21no—
33#135×C151—21no—
34#135×C151—21no—
35#135×C151—21no—
36#135×C151—21no—
37#135×C151C2×C412yes—
38#135×C151D412yes—
39C2×Q16×C151C2×C411yescharacteristic
40C2×Q16×C151D411yescharacteristic
41C2×SD16×C151—21no—
42C2×SD16×C151—21no—
43C2×D8×C151C2×C411yescharacteristic
44C2×D8×C151D411yescharacteristic
45#131×C151—24no—
46#131×C151—42no—
47C2×M16×C151—21no—
48C2×M16×C151—21no—
49C2×M16×C151—41no—
50C22×C8×C151—41no—
51C22×C8×C151D411yescharacteristic
52C22×C8×C151C2311yescharacteristic
53C2×C42×C151D411yescharacteristic
54Q32×C151—22no—
55SD32×C151—22no—
56SD32×C151—22no—
57D16×C151—22no—
58M32×C151—21no—
59M32×C151—21no—
60M32×C151—21no—
61M32×C151C2×C412yes—
62C2×C16×C151—21no—
63C2×C16×C151—21no—
64#108×C151—21no—
65#108×C151—21no—
66#108×C151—21no—
67#108×C151D412yes—
68#104×C151—24no—
69#104×C151—42no—
70C22⋊C8×C151—42no—
71#97×C151—21no—
72#97×C151—21no—
73#41×C151—22no—
74#41×C151—22no—
75#41×C151—41no—
76#41×C151—41no—
77#41×C151—41no—
78#41×C151—41no—
79#41×C151—41no—
80#41×C151—41no—
81C2×Q8×C151—21no—
82C2×Q8×C151—21no—
83C2×D4×C151—21no—
84C2×D4×C151—21no—
85C2×D4×C151—41no—
86C2×D4×C151—41no—
87C22×C4×C151—21no—
88C22×C4×C151—41no—
89C22×C4×C151—41no—
90C22×C4×C151C2×D411yescharacteristic
91Q16×C151—21no—
92Q16×C151—21no—
93Q16×C151—21no—
94Q16×C151C22⋊C412yes—
95SD16×C151—22no—
96SD16×C151—22no—
97SD16×C151—41no—
98SD16×C151—41no—
99D8×C151—21no—
100D8×C151—21no—
101D8×C151—21no—
102D8×C151C22⋊C412yes—
103M16×C151—22no—
104M16×C151—44no—
105M16×C151—41no—
106M16×C151—41no—
107M16×C151—41no—
108C2×C8×C151—21no—
109C2×C8×C151—21no—
110C2×C8×C151—44no—
111C2×C8×C151—41no—
112C2×C8×C151—41no—
113C2×C8×C151D812yes—
114C2×C8×C151C22×C411yescharacteristic
115C2×C8×C151C2×D411yescharacteristic
116C2×C8×C151C2×D411yescharacteristic
117C2×C8×C151C2×D411yescharacteristic
118C2×C8×C151#4111yescharacteristic
119C2×C8×C151#4111yescharacteristic
120C42×C151—21no—
121C42×C151—21no—
122C16×C151—22no—
123C16×C151—41no—
124C23×C151—41no—
125C23×C151—41no—
126C23×C151#13511yescharacteristic
127Q8×C151—22no—
128Q8×C151—41no—
129Q8×C151—41no—
130Q8×C151—41no—
131D4×C151—22no—
132D4×C151—42no—
133D4×C151—42no—
134D4×C151—41no—
135D4×C151—41no—
136D4×C151—41no—
137D4×C151—81no—
138D4×C151—81no—
139C2×C4×C151—41no—
140C2×C4×C151—42no—
141C2×C4×C151—42no—
142C2×C4×C151—41no—
143C2×C4×C151—41no—
144C2×C4×C151—81no—
145C2×C4×C151—81no—
146C2×C4×C151—81no—
147C2×C4×C151C4×D411yescharacteristic
148C2×C4×C151#12011yescharacteristic
149C2×C4×C151#12111yescharacteristic
150C2×C4×C151C2×D811yescharacteristic
151C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
153C8×C151—22no—
154C8×C151—42no—
155C8×C151—81no—
156C8×C151C2×C22⋊C411yescharacteristic
157C8×C151C4×D411yescharacteristic
158C8×C151#12111yescharacteristic
159C8×C151#12311yescharacteristic
160C22×C151—41no—
161C22×C151—42no—
162C22×C151—82no—
163C22×C151—82no—
164C22×C151—81no—
165C22×C151C4×D811yescharacteristic
166C22×C151#44911yescharacteristic
167C22×C151#46311yescharacteristic
168C4×C151—42no—
169C4×C151—81no—
170C4×C151—81no—
171C4×C151#38611yescharacteristic
172C4×C151#44211yescharacteristic
173C4×C151#44711yescharacteristic
174C4×C151#45911yescharacteristic
175C2×C151—21no—
176C2×C151—21no—
177C2×C151—21no—
178C2×C151—82no—
179C2×C151—161no—
180C2×C151#187911yescharacteristic
181#13024C15111yesmaximal, characteristic, direct product factor, Sylow
182C151#1302411yescharacteristic, direct product factor, Sylow
183#3414C2×C15111yescharacteristic
184C2×#444C2×C15111yescharacteristic, complemented
185#2148C2×C15111yescharacteristic, complemented
186#2143C2×C15111yescharacteristic, complemented
187#1975C2×C15111yescharacteristic, complemented
188#1388C2×C15111yescharacteristic, complemented
189#1377C2×C15111yescharacteristic, complemented
190C2×#135C22×C15111yescharacteristic
191C2×#135C22×C15111yescharacteristic
192C2×#131—21no—
193#510—21no—
194#510C4×C15112yescomplemented
195#509—21no—
196#509C4×C15112yescomplemented
197#508—22no—
198C2×M32C22×C15111yescharacteristic
199C2×M32C22×C15111yescharacteristic
200#444—22no—
201#444—22no—
202C2×#108C22×C15111yescharacteristic
203C2×#108C22×C15111yescharacteristic
204C2×#104—21no—
205C2×#104—21no—
206#408—21no—
207C2×#97C22×C15111yescharacteristic
208#362—21no—
209#361—21no—
210#359—22no—
211C2×#41—21no—
212C2×#41—21no—
213#135—21no—
214#135—21no—
215#135—21no—
216#135—21no—
217#135—21no—
218#135—21no—
219#135C2×C4×C15112yes—
220#135D4×C15112yes—
221C2×Q16C2×C4×C15111yescharacteristic
222C2×Q16D4×C15111yescharacteristic
223C2×SD16—21no—
224C2×SD16—21no—
225C2×D8C2×C4×C15111yescharacteristic
226C2×D8D4×C15111yescharacteristic
227#131—24no—
228#131—42no—
229C2×M16—21no—
230C2×M16—21no—
231C2×M16—41no—
232C22×C8—41no—
233C22×C8D4×C15111yescharacteristic
234C22×C8C23×C15111yescharacteristic
235C2×C42D4×C15111yescharacteristic
236Q32—22no—
237SD32—22no—
238SD32—22no—
239D16—22no—
240M32—21no—
241M32—21no—
242M32—21no—
243M32C2×C4×C15112yes—
244C2×C16—21no—
245C2×C16—21no—
246#108—21no—
247#108—21no—
248#108—21no—
249#108D4×C15112yes—
250#104—24no—
251#104—42no—
252C22⋊C8—42no—
253#97—21no—
254#97—21no—
255#41—22no—
256#41—22no—
257#41—41no—
258#41—41no—
259#41—41no—
260#41—41no—
261#41—41no—
262#41—41no—
263C2×Q8—21no—
264C2×Q8—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—41no—
268C2×D4—41no—
269C22×C4—21no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4C2×D4×C15111yescharacteristic
273Q16—21no—
274Q16—21no—
275Q16—21no—
276Q16C22⋊C4×C15112yes—
277SD16—22no—
278SD16—22no—
279SD16—41no—
280SD16—41no—
281D8—21no—
282D8—21no—
283D8—21no—
284D8C22⋊C4×C15112yes—
285M16—22no—
286M16—44no—
287M16—41no—
288M16—41no—
289M16—41no—
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—44no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8D8×C15112yes—
296C2×C8C22×C4×C15111yescharacteristic
297C2×C8C2×D4×C15111yescharacteristic
298C2×C8C2×D4×C15111yescharacteristic
299C2×C8C2×D4×C15111yescharacteristic
300C2×C8#41×C15111yescharacteristic
301C2×C8#41×C15111yescharacteristic
302C42—21no—
303C42—21no—
304C16—22no—
305C16—41no—
306C23—41no—
307C23—41no—
308C23#135×C15111yescharacteristic
309Q8—22no—
310Q8—41no—
311Q8—41no—
312Q8—41no—
313D4—22no—
314D4—42no—
315D4—42no—
316D4—41no—
317D4—41no—
318D4—41no—
319D4—81no—
320D4—81no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4C4×D4×C15111yescharacteristic
330C2×C4#120×C15111yescharacteristic
331C2×C4#121×C15111yescharacteristic
332C2×C4C2×D8×C15111yescharacteristic
333C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
334C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
335C8—22no—
336C8—42no—
337C8—81no—
338C8C2×C22⋊C4×C15111yescharacteristic
339C8C4×D4×C15111yescharacteristic
340C8#121×C15111yescharacteristic
341C8#123×C15111yescharacteristic
342C22—41no—
343C22—42no—
344C22—82no—
345C22—82no—
346C22—81no—
347C22C4×D8×C15111yescharacteristic
348C22#449×C15111yescharacteristic
349C22#463×C15111yescharacteristic
350C4—42no—
351C4—81no—
352C4—81no—
353C4#386×C15111yescharacteristic
354C4#442×C15111yescharacteristic
355C4#447×C15111yescharacteristic
356C4#459×C15111yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—82no—
361C2—161no—
362C2#1879×C15111yescharacteristic
subgroupG/H
centerC4×C151#447
commutatorC2×C8C22×C4×C151
Frattini, cosocleC22×C8C23×C151
socleC2×C151#1879
prime radical#3414×C151C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C151 ◁ C22×C4×C151 ◁ C2×#97×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#444×C151C2semidirect
3. #2148×C151C2semidirect
4. #2143×C151C2semidirect
5. #1975×C151C2semidirect
6. #1388×C151C2semidirect
7. #1377×C151C2semidirect
12. #510×C151C4semidirect
14. #509×C151C4semidirect
181. #13024C151direct (N × H)
182. C151#13024direct (N × H)
184. C2×#444C2×C151semidirect
185. #2148C2×C151semidirect
186. #2143C2×C151semidirect
187. #1975C2×C151semidirect
188. #1388C2×C151semidirect
189. #1377C2×C151semidirect
194. #510C4×C151semidirect
196. #509C4×C151semidirect

Maximal subgroups

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

subgroupindex
#3414×C1512
C2×#444×C1512
#2148×C1512
#2143×C1512
#1975×C1512
#1388×C1512
#1377×C1512
#13024151