Finite Group Databasebeta

← C151×#8711 #50313636

Subgroups — C151×#8711 #50313636

Order 38656.

496 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2283×C151C211yesmaximal, characteristic
2#1797×C151C211yesmaximal, characteristic
3C4×C22⋊C8×C151C211yesmaximal, characteristic
4#1279×C151C212yesmaximal, complemented
5#1279×C151C212yesmaximal, complemented
6C22×C42×C151C2211yescharacteristic
7C2×C4⋊C8×C151C2212yes—
8C2×C22⋊C8×C151—21no—
9C2×C22⋊C8×C151—21no—
10C2×C4×C8×C151C2212yes—
11#383×C151—21no—
12#382×C151C411yescharacteristic
13#382×C151C411yescharacteristic
14#381×C151—21no—
15#380×C151C411yescharacteristic
16#380×C151C411yescharacteristic
17C4×C4⋊C4×C151C2211yescharacteristic
18C4×C4⋊C4×C151C2211yescharacteristic
19C4×C22⋊C4×C151—21no—
20#376×C151—21no—
21#336×C151—21no—
22#336×C151—21no—
23C23×C4×C151C2×C411yescharacteristic
24C23×C4×C151D411yescharacteristic
25C23×C4×C151D411yescharacteristic
26C22×C8×C151—22no—
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×C151D411yescharacteristic
39C2×C42×C151D411yescharacteristic
40C2×C42×C151C2311yescharacteristic
41C4⋊C8×C151—24no—
42C22⋊C8×C151—24no—
43C22⋊C8×C151—42no—
44C4×C8×C151—24no—
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—21no—
52#95×C151—21no—
53C24×C151C22⋊C411yescharacteristic
54C22×C4×C151—22no—
55C22×C4×C151—22no—
56C22×C4×C151—22no—
57C22×C4×C151—22no—
58C22×C4×C151—22no—
59C22×C4×C151—22no—
60C22×C4×C151—22no—
61C22×C4×C151—21no—
62C22×C4×C151—21no—
63C22×C4×C151—21no—
64C22×C4×C151—21no—
65C22×C4×C151—21no—
66C22×C4×C151—21no—
67C22×C4×C151—41no—
68C22×C4×C151C22⋊C411yescharacteristic
69C22×C4×C151C22⋊C411yescharacteristic
70C22×C4×C151C22⋊C411yescharacteristic
71C22×C4×C151C22×C411yescharacteristic
72C22×C4×C151C2×D411yescharacteristic
73C22×C4×C151C2×D411yescharacteristic
74C2×C8×C151—24no—
75C2×C8×C151—42no—
76C2×C8×C151—42no—
77C2×C8×C151—42no—
78C2×C8×C151—42no—
79C2×C8×C151—42no—
80C4⋊C4×C151—22no—
81C4⋊C4×C151—22no—
82C4⋊C4×C151—22no—
83C4⋊C4×C151—22no—
84C22⋊C4×C151—42no—
85C22⋊C4×C151—42no—
86C42×C151—22no—
87C42×C151—22no—
88C42×C151—22no—
89C42×C151—42no—
90C42×C151—41no—
91C42×C151—41no—
92C42×C151#4114yes—
93C23×C151—21no—
94C23×C151—21no—
95C23×C151—21no—
96C23×C151—21no—
97C23×C151—21no—
98C23×C151—21no—
99C23×C151#10412yes—
100C23×C151C2×C22⋊C411yescharacteristic
101C2×C4×C151—21no—
102C2×C4×C151—21no—
103C2×C4×C151—21no—
104C2×C4×C151—21no—
105C2×C4×C151—21no—
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—44no—
113C2×C4×C151—44no—
114C2×C4×C151—42no—
115C2×C4×C151—42no—
116C2×C4×C151—41no—
117C2×C4×C151—41no—
118C2×C4×C151—41no—
119C2×C4×C151—41no—
120C2×C4×C151—41no—
121C2×C4×C151—41no—
122C2×C4×C151—41no—
123C2×C4×C151—41no—
124C2×C4×C151—41no—
125C2×C4×C151—41no—
126C2×C4×C151—41no—
127C2×C4×C151—41no—
128C2×C4×C151#11712yes—
129C2×C4×C151#12312yes—
130C2×C4×C151#12312yes—
131C2×C4×C151#13112yes—
132C2×C4×C151#13112yes—
133C2×C4×C151#13512yes—
134C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C151#13711yescharacteristic
136C8×C151—44no—
137C8×C151—82no—
138C22×C151—22no—
139C22×C151—22no—
140C22×C151—22no—
141C22×C151—41no—
142C22×C151—41no—
143C22×C151—41no—
144C22×C151—41no—
145C22×C151#38111yescharacteristic
146C22×C151#40811yescharacteristic
147C22×C151#40811yescharacteristic
148C22×C151#41611yescharacteristic
149C22×C151#41711yescharacteristic
150C22×C151C2×#10411yescharacteristic
151C22×C151#42111yescharacteristic
152C4×C151—22no—
153C4×C151—41no—
154C4×C151—41no—
155C4×C151—41no—
156C4×C151—81no—
157C4×C151—81no—
158C4×C151—81no—
159C4×C151—81no—
160C4×C151#43314yes—
161C4×C151#48212yes—
162C4×C151#48512yes—
163C2×C151—42no—
164C2×C151#148211yescharacteristic
165C2×C151#148311yescharacteristic
166C2×C151#149411yescharacteristic
167C2×C151#149511yescharacteristic
168C2×C151#181811yescharacteristic
169C2×C151#182511yescharacteristic
170C2×C151#182611yescharacteristic
171#8711C15111yesmaximal, characteristic, direct product factor, Sylow
172C151#871111yescharacteristic, direct product factor, Sylow
173#2283C2×C15111yescharacteristic
174#1797C2×C15111yescharacteristic
175C4×C22⋊C8C2×C15111yescharacteristic
176#1279C2×C15112yescomplemented
177#1279C2×C15112yescomplemented
178C22×C42C22×C15111yescharacteristic
179C2×C4⋊C8C22×C15112yes—
180C2×C22⋊C8—21no—
181C2×C22⋊C8—21no—
182C2×C4×C8C22×C15112yes—
183#383—21no—
184#382C4×C15111yescharacteristic
185#382C4×C15111yescharacteristic
186#381—21no—
187#380C4×C15111yescharacteristic
188#380C4×C15111yescharacteristic
189C4×C4⋊C4C22×C15111yescharacteristic
190C4×C4⋊C4C22×C15111yescharacteristic
191C4×C22⋊C4—21no—
192#376—21no—
193#336—21no—
194#336—21no—
195C23×C4C2×C4×C15111yescharacteristic
196C23×C4D4×C15111yescharacteristic
197C23×C4D4×C15111yescharacteristic
198C22×C8—22no—
199C22×C8—22no—
200C2×C4⋊C4C2×C4×C15111yescharacteristic
201C2×C4⋊C4C2×C4×C15111yescharacteristic
202C2×C4⋊C4C2×C4×C15111yescharacteristic
203C2×C4⋊C4C2×C4×C15111yescharacteristic
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C42—24no—
207C2×C42—21no—
208C2×C42—21no—
209C2×C42C2×C4×C15111yescharacteristic
210C2×C42D4×C15111yescharacteristic
211C2×C42D4×C15111yescharacteristic
212C2×C42C23×C15111yescharacteristic
213C4⋊C8—24no—
214C22⋊C8—24no—
215C22⋊C8—42no—
216C4×C8—24no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225C24C22⋊C4×C15111yescharacteristic
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—22no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—41no—
240C22×C4C22⋊C4×C15111yescharacteristic
241C22×C4C22⋊C4×C15111yescharacteristic
242C22×C4C22⋊C4×C15111yescharacteristic
243C22×C4C22×C4×C15111yescharacteristic
244C22×C4C2×D4×C15111yescharacteristic
245C22×C4C2×D4×C15111yescharacteristic
246C2×C8—24no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—42no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C22⋊C4—42no—
257C22⋊C4—42no—
258C42—22no—
259C42—22no—
260C42—22no—
261C42—42no—
262C42—41no—
263C42—41no—
264C42#41×C15114yes—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23#104×C15112yes—
272C23C2×C22⋊C4×C15111yescharacteristic
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—44no—
285C2×C4—44no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4#117×C15112yes—
301C2×C4#123×C15112yes—
302C2×C4#123×C15112yes—
303C2×C4#131×C15112yes—
304C2×C4#131×C15112yes—
305C2×C4#135×C15112yes—
306C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
307C2×C4#137×C15111yescharacteristic
308C8—44no—
309C8—82no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22#381×C15111yescharacteristic
318C22#408×C15111yescharacteristic
319C22#408×C15111yescharacteristic
320C22#416×C15111yescharacteristic
321C22#417×C15111yescharacteristic
322C22C2×#104×C15111yescharacteristic
323C22#421×C15111yescharacteristic
324C4—22no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—81no—
329C4—81no—
330C4—81no—
331C4—81no—
332C4#433×C15114yes—
333C4#482×C15112yes—
334C4#485×C15112yes—
335C2—42no—
336C2#1482×C15111yescharacteristic
337C2#1483×C15111yescharacteristic
338C2#1494×C15111yescharacteristic
339C2#1495×C15111yescharacteristic
340C2#1818×C15111yescharacteristic
341C2#1825×C15111yescharacteristic
342C2#1826×C15111yescharacteristic
subgroupG/H
centerC22×C4×C151C2×D4
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
socleC23×C151C2×C22⋊C4
prime radicalC24×C151C22⋊C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1279×C151C2semidirect
5. #1279×C151C2semidirect
171. #8711C151direct (N × H)
172. C151#8711direct (N × H)
176. #1279C2×C151semidirect
177. #1279C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2283×C1512
#1797×C1512
C4×C22⋊C8×C1512
#1279×C1512
#8711151