Finite Group Databasebeta

← C151×#8714 #50313639

Subgroups — C151×#8714 #50313639

Order 38656.

544 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2283×C151C211yesmaximal, characteristic
2#1817×C151C211yesmaximal, characteristic
3#1434×C151C211yesmaximal, characteristic
4#1294×C151C212yesmaximal
5#1294×C151C212yesmaximal
6C22×C42×C151C2211yescharacteristic
7C2×C22⋊C8×C151C2212yes—
8#383×C151—21no—
9#382×C151C411yescharacteristic, complemented
10#382×C151C411yescharacteristic, complemented
11#381×C151—21no—
12#380×C151C2211yescharacteristic
13#380×C151C2211yescharacteristic
14C4×C4⋊C4×C151C411yescharacteristic, complemented
15C4×C4⋊C4×C151C411yescharacteristic, complemented
16C4×C22⋊C4×C151—21no—
17#376×C151—21no—
18C2×#95×C151—21no—
19C2×#95×C151—21no—
20C2×#95×C151C2212yes—
21#336×C151—21no—
22#336×C151—21no—
23C23×C4×C151—22no—
24C23×C4×C151D411yescharacteristic
25C23×C4×C151D411yescharacteristic
26C23×C4×C151C2311yescharacteristic
27C22×C8×C151—22no—
28C2×C4⋊C4×C151C2×C411yescharacteristic
29C2×C4⋊C4×C151C2×C411yescharacteristic
30C2×C4⋊C4×C151C2×C411yescharacteristic
31C2×C4⋊C4×C151C2×C411yescharacteristic
32C2×C22⋊C4×C151—21no—
33C2×C22⋊C4×C151—21no—
34C2×C42×C151—24no—
35C2×C42×C151—21no—
36C2×C42×C151—21no—
37C2×C42×C151C2×C411yescharacteristic
38C2×C42×C151C2×C411yescharacteristic
39C2×C42×C151D411yescharacteristic
40C2×C42×C151D411yescharacteristic
41C22⋊C8×C151—24no—
42#95×C151—24no—
43#95×C151—21no—
44#95×C151—21no—
45#95×C151—21no—
46#95×C151—21no—
47#95×C151—21no—
48#95×C151—21no—
49#95×C151—21no—
50#95×C151—21no—
51#95×C151—24no—
52#95×C151—42no—
53C24×C151C2×D411yescharacteristic
54C22×C4×C151—22no—
55C22×C4×C151—22no—
56C22×C4×C151—22no—
57C22×C4×C151—21no—
58C22×C4×C151—21no—
59C22×C4×C151—22no—
60C22×C4×C151—24no—
61C22×C4×C151—21no—
62C22×C4×C151—21no—
63C22×C4×C151—21no—
64C22×C4×C151—21no—
65C22×C4×C151—41no—
66C22×C4×C151—41no—
67C22×C4×C151—41no—
68C22×C4×C151—42no—
69C22×C4×C151—42no—
70C22×C4×C151—42no—
71C22×C4×C151—42no—
72C22×C4×C151—42no—
73C22×C4×C151—42no—
74C22×C4×C151C22⋊C411yescharacteristic
75C22×C4×C151C22⋊C411yescharacteristic
76C22×C4×C151C22⋊C411yescharacteristic
77C22×C4×C151C22⋊C411yescharacteristic
78C22×C4×C151C22×C411yescharacteristic
79C22×C4×C151C2×D411yescharacteristic
80C22×C4×C151#4114yes—
81C2×C8×C151—42no—
82C2×C8×C151—42no—
83C2×C8×C151—42no—
84C4⋊C4×C151—41no—
85C4⋊C4×C151—41no—
86C4⋊C4×C151—41no—
87C4⋊C4×C151—41no—
88C22⋊C4×C151—42no—
89C22⋊C4×C151—41no—
90C22⋊C4×C151—41no—
91C42×C151—22no—
92C42×C151—22no—
93C42×C151—22no—
94C42×C151—22no—
95C42×C151—42no—
96C42×C151—42no—
97C23×C151—21no—
98C23×C151—21no—
99C23×C151—21no—
100C23×C151—21no—
101C23×C151C2×C22⋊C411yescharacteristic
102C23×C151#12312yes—
103C23×C151#13512yes—
104C23×C151AGL(1,ℤ/8)11yescharacteristic
105C23×C151#13711yescharacteristic
106C2×C4×C151—21no—
107C2×C4×C151—21no—
108C2×C4×C151—21no—
109C2×C4×C151—21no—
110C2×C4×C151—21no—
111C2×C4×C151—21no—
112C2×C4×C151—21no—
113C2×C4×C151—21no—
114C2×C4×C151—21no—
115C2×C4×C151—21no—
116C2×C4×C151—21no—
117C2×C4×C151—21no—
118C2×C4×C151—21no—
119C2×C4×C151—21no—
120C2×C4×C151—21no—
121C2×C4×C151—44no—
122C2×C4×C151—44no—
123C2×C4×C151—42no—
124C2×C4×C151—42no—
125C2×C4×C151—44no—
126C2×C4×C151—44no—
127C2×C4×C151—44no—
128C2×C4×C151—41no—
129C2×C4×C151—41no—
130C2×C4×C151—41no—
131C2×C4×C151—41no—
132C2×C4×C151—41no—
133C2×C4×C151—41no—
134C2×C4×C151—41no—
135C2×C4×C151—41no—
136C2×C4×C151—41no—
137C2×C4×C151—41no—
138C2×C4×C151—41no—
139C2×C4×C151—41no—
140C2×C4×C151—82no—
141C2×C4×C151—82no—
142C2×C4×C151—82no—
143C2×C4×C151—82no—
144C2×C4×C151#10412yes—
145C2×C4×C151#11712yes—
146C2×C4×C151#12312yes—
147C8×C151—82no—
148C22×C151—22no—
149C22×C151—22no—
150C22×C151—22no—
151C22×C151—21no—
152C22×C151—21no—
153C22×C151—21no—
154C22×C151—21no—
155C22×C151—22no—
156C22×C151#38111yescharacteristic
157C22×C151#41011yescharacteristic
158C22×C151#41011yescharacteristic
159C22×C151#41611yescharacteristic
160C22×C151#41711yescharacteristic
161C22×C151C2×#10411yescharacteristic
162C22×C151#42111yescharacteristic
163C22×C151#48212yes—
164C22×C151#48512yes—
165C4×C151—22no—
166C4×C151—22no—
167C4×C151—22no—
168C4×C151—41no—
169C4×C151—41no—
170C4×C151—41no—
171C4×C151—84no—
172C4×C151—81no—
173C4×C151—81no—
174C4×C151—81no—
175C4×C151—81no—
176C2×C151—22no—
177C2×C151—22no—
178C2×C151#150011yescharacteristic
179C2×C151#150911yescharacteristic
180C2×C151#151211yescharacteristic
181C2×C151#152111yescharacteristic
182C2×C151#182011yescharacteristic
183C2×C151#182511yescharacteristic
184C2×C151#182611yescharacteristic
185#8714C15111yesmaximal, characteristic, direct product factor, Sylow
186C151#871411yescharacteristic, direct product factor, Sylow
187#2283C2×C15111yescharacteristic
188#1817C2×C15111yescharacteristic
189#1434C2×C15111yescharacteristic
190#1294C2×C15112yes—
191#1294C2×C15112yes—
192C22×C42C22×C15111yescharacteristic
193C2×C22⋊C8C22×C15112yes—
194#383—21no—
195#382C4×C15111yescharacteristic, complemented
196#382C4×C15111yescharacteristic, complemented
197#381—21no—
198#380C22×C15111yescharacteristic
199#380C22×C15111yescharacteristic
200C4×C4⋊C4C4×C15111yescharacteristic, complemented
201C4×C4⋊C4C4×C15111yescharacteristic, complemented
202C4×C22⋊C4—21no—
203#376—21no—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95C22×C15112yes—
207#336—21no—
208#336—21no—
209C23×C4—22no—
210C23×C4D4×C15111yescharacteristic
211C23×C4D4×C15111yescharacteristic
212C23×C4C23×C15111yescharacteristic
213C22×C8—22no—
214C2×C4⋊C4C2×C4×C15111yescharacteristic
215C2×C4⋊C4C2×C4×C15111yescharacteristic
216C2×C4⋊C4C2×C4×C15111yescharacteristic
217C2×C4⋊C4C2×C4×C15111yescharacteristic
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C42—24no—
221C2×C42—21no—
222C2×C42—21no—
223C2×C42C2×C4×C15111yescharacteristic
224C2×C42C2×C4×C15111yescharacteristic
225C2×C42D4×C15111yescharacteristic
226C2×C42D4×C15111yescharacteristic
227C22⋊C8—24no—
228#95—24no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—24no—
238#95—42no—
239C24C2×D4×C15111yescharacteristic
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—24no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4C22⋊C4×C15111yescharacteristic
261C22×C4C22⋊C4×C15111yescharacteristic
262C22×C4C22⋊C4×C15111yescharacteristic
263C22×C4C22⋊C4×C15111yescharacteristic
264C22×C4C22×C4×C15111yescharacteristic
265C22×C4C2×D4×C15111yescharacteristic
266C22×C4#41×C15114yes—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—42no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C22⋊C4—42no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C42—22no—
278C42—22no—
279C42—22no—
280C42—22no—
281C42—42no—
282C42—42no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23C2×C22⋊C4×C15111yescharacteristic
288C23#123×C15112yes—
289C23#135×C15112yes—
290C23AGL(1,ℤ/8)×C15111yescharacteristic
291C23#137×C15111yescharacteristic
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—44no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4#104×C15112yes—
331C2×C4#117×C15112yes—
332C2×C4#123×C15112yes—
333C8—82no—
334C22—22no—
335C22—22no—
336C22—22no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22#381×C15111yescharacteristic
343C22#410×C15111yescharacteristic
344C22#410×C15111yescharacteristic
345C22#416×C15111yescharacteristic
346C22#417×C15111yescharacteristic
347C22C2×#104×C15111yescharacteristic
348C22#421×C15111yescharacteristic
349C22#482×C15112yes—
350C22#485×C15112yes—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—84no—
358C4—81no—
359C4—81no—
360C4—81no—
361C4—81no—
362C2—22no—
363C2—22no—
364C2#1500×C15111yescharacteristic
365C2#1509×C15111yescharacteristic
366C2#1512×C15111yescharacteristic
367C2#1521×C15111yescharacteristic
368C2#1820×C15111yescharacteristic
369C2#1825×C15111yescharacteristic
370C2#1826×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C2×C22⋊C4
commutatorC22×C4C22×C4×C151
Frattini, cosocleC23×C4C23×C151
prime radicalC24×C151C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
9. #382×C151C4semidirect
10. #382×C151C4semidirect
14. C4×C4⋊C4×C151C4semidirect
15. C4×C4⋊C4×C151C4semidirect
185. #8714C151direct (N × H)
186. C151#8714direct (N × H)
195. #382C4×C151semidirect
196. #382C4×C151semidirect
200. C4×C4⋊C4C4×C151semidirect
201. C4×C4⋊C4C4×C151semidirect

Maximal subgroups

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

subgroupindex
#2283×C1512
#1817×C1512
#1434×C1512
#1294×C1512
#8714151