Finite Group Databasebeta

← C151×#8709 #50313634

Subgroups — C151×#8709 #50313634

Order 38656.

540 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2285×C151C211yesmaximal, characteristic
2#1797×C151C211yesmaximal, characteristic
3C4×C22⋊C8×C151C211yesmaximal, characteristic
4#1279×C151C214yesmaximal, complemented
5C2×#117×C151—21no—
6C22×C42×C151C2211yescharacteristic
7C2×C4⋊C8×C151C2212yes—
8C2×C22⋊C8×C151—21no—
9C2×C22⋊C8×C151—21no—
10C2×C4×C8×C151C2212yes—
11#384×C151C411yescharacteristic
12#384×C151C411yescharacteristic
13#382×C151—21no—
14#380×C151—21no—
15#380×C151C412yes—
16C4×C4⋊C4×C151—21no—
17C4×C4⋊C4×C151C2212yes—
18#336×C151—21no—
19#336×C151—21no—
20C23×C4×C151C2×C411yescharacteristic
21C23×C4×C151D411yescharacteristic
22C23×C4×C151D411yescharacteristic
23C22×C8×C151—22no—
24C22×C8×C151—22no—
25#117×C151—42no—
26#117×C151—42no—
27C2×C4⋊C4×C151—21no—
28C2×C4⋊C4×C151—21no—
29C2×C4⋊C4×C151—21no—
30C2×C4⋊C4×C151—21no—
31C2×C4⋊C4×C151C2×C412yes—
32C2×C4⋊C4×C151C2×C412yes—
33C2×C22⋊C4×C151—22no—
34C2×C42×C151—24no—
35C2×C42×C151—22no—
36C2×C42×C151C2×C411yescharacteristic
37C2×C42×C151D411yescharacteristic
38C2×C42×C151D411yescharacteristic
39C2×C42×C151C2311yescharacteristic
40C4⋊C8×C151—24no—
41C22⋊C8×C151—24no—
42C22⋊C8×C151—42no—
43C4×C8×C151—24no—
44#95×C151—22no—
45#95×C151—22no—
46C24×C151C22⋊C411yescharacteristic
47C22×C4×C151—22no—
48C22×C4×C151—22no—
49C22×C4×C151—22no—
50C22×C4×C151—22no—
51C22×C4×C151—22no—
52C22×C4×C151—22no—
53C22×C4×C151—22no—
54C22×C4×C151—22no—
55C22×C4×C151—22no—
56C22×C4×C151—41no—
57C22×C4×C151C22⋊C411yescharacteristic
58C22×C4×C151C22⋊C411yescharacteristic
59C22×C4×C151C22⋊C411yescharacteristic
60C22×C4×C151D812yes—
61C22×C4×C151SD1612yes—
62C22×C4×C151C22×C411yescharacteristic
63C22×C4×C151C2×D411yescharacteristic
64C22×C4×C151C2×D411yescharacteristic
65C2×C8×C151—24no—
66C2×C8×C151—42no—
67C2×C8×C151—42no—
68C2×C8×C151—42no—
69C2×C8×C151—42no—
70C2×C8×C151—42no—
71C4⋊C4×C151—24no—
72C4⋊C4×C151—24no—
73C4⋊C4×C151—42no—
74C4⋊C4×C151—42no—
75C4⋊C4×C151—42no—
76C4⋊C4×C151—42no—
77C22⋊C4×C151—44no—
78C42×C151—22no—
79C42×C151—22no—
80C42×C151—22no—
81C42×C151—42no—
82C42×C151—42no—
83C42×C151#4114yes—
84C23×C151—21no—
85C23×C151—21no—
86C23×C151—21no—
87C23×C151—21no—
88C23×C151—21no—
89C23×C151—21no—
90C23×C151#10212yes—
91C23×C151C2×C22⋊C411yescharacteristic
92C2×C4×C151—21no—
93C2×C4×C151—21no—
94C2×C4×C151—21no—
95C2×C4×C151—21no—
96C2×C4×C151—21no—
97C2×C4×C151—21no—
98C2×C4×C151—24no—
99C2×C4×C151—24no—
100C2×C4×C151—21no—
101C2×C4×C151—21no—
102C2×C4×C151—21no—
103C2×C4×C151—44no—
104C2×C4×C151—44no—
105C2×C4×C151—42no—
106C2×C4×C151—42no—
107C2×C4×C151—42no—
108C2×C4×C151—42no—
109C2×C4×C151—42no—
110C2×C4×C151—42no—
111C2×C4×C151#10212yes—
112C2×C4×C151#10412yes—
113C2×C4×C151#11712yes—
114C2×C4×C151#12312yes—
115C2×C4×C151#12312yes—
116C2×C4×C151#13112yes—
117C2×C4×C151#13112yes—
118C2×C4×C151C2×D811yescharacteristic
119C2×C4×C151C2×SD1611yescharacteristic
120C2×C4×C151#13712yes—
121C8×C151—44no—
122C8×C151—82no—
123C22×C151—22no—
124C22×C151—22no—
125C22×C151—22no—
126C22×C151—41no—
127C22×C151—41no—
128C22×C151—41no—
129C22×C151—41no—
130C22×C151#38111yescharacteristic
131C22×C151#40811yescharacteristic
132C22×C151#40811yescharacteristic
133C22×C151C2×#10211yescharacteristic
134C22×C151#41911yescharacteristic
135C22×C151C2×#10411yescharacteristic
136C22×C151#42111yescharacteristic
137C4×C151—22no—
138C4×C151—22no—
139C4×C151—22no—
140C4×C151—41no—
141C4×C151—82no—
142C4×C151—82no—
143C4×C151#43314yes—
144C4×C151#48012yes—
145C4×C151#48312yes—
146C2×C151—42no—
147C2×C151#148011yescharacteristic
148C2×C151#148511yescharacteristic
149C2×C151#149211yescharacteristic
150C2×C151#149711yescharacteristic
151C2×C151#181811yescharacteristic
152C2×C151#182311yescharacteristic
153C2×C151#182611yescharacteristic
154#8709C15111yesmaximal, characteristic, direct product factor, Sylow
155C151#870911yescharacteristic, direct product factor, Sylow
156#2285C2×C15111yescharacteristic
157#1797C2×C15111yescharacteristic
158C4×C22⋊C8C2×C15111yescharacteristic
159#1279C2×C15114yescomplemented
160C2×#117—21no—
161C22×C42C22×C15111yescharacteristic
162C2×C4⋊C8C22×C15112yes—
163C2×C22⋊C8—21no—
164C2×C22⋊C8—21no—
165C2×C4×C8C22×C15112yes—
166#384C4×C15111yescharacteristic
167#384C4×C15111yescharacteristic
168#382—21no—
169#380—21no—
170#380C4×C15112yes—
171C4×C4⋊C4—21no—
172C4×C4⋊C4C22×C15112yes—
173#336—21no—
174#336—21no—
175C23×C4C2×C4×C15111yescharacteristic
176C23×C4D4×C15111yescharacteristic
177C23×C4D4×C15111yescharacteristic
178C22×C8—22no—
179C22×C8—22no—
180#117—42no—
181#117—42no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4C2×C4×C15112yes—
187C2×C4⋊C4C2×C4×C15112yes—
188C2×C22⋊C4—22no—
189C2×C42—24no—
190C2×C42—22no—
191C2×C42C2×C4×C15111yescharacteristic
192C2×C42D4×C15111yescharacteristic
193C2×C42D4×C15111yescharacteristic
194C2×C42C23×C15111yescharacteristic
195C4⋊C8—24no—
196C22⋊C8—24no—
197C22⋊C8—42no—
198C4×C8—24no—
199#95—22no—
200#95—22no—
201C24C22⋊C4×C15111yescharacteristic
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—41no—
212C22×C4C22⋊C4×C15111yescharacteristic
213C22×C4C22⋊C4×C15111yescharacteristic
214C22×C4C22⋊C4×C15111yescharacteristic
215C22×C4D8×C15112yes—
216C22×C4SD16×C15112yes—
217C22×C4C22×C4×C15111yescharacteristic
218C22×C4C2×D4×C15111yescharacteristic
219C22×C4C2×D4×C15111yescharacteristic
220C2×C8—24no—
221C2×C8—42no—
222C2×C8—42no—
223C2×C8—42no—
224C2×C8—42no—
225C2×C8—42no—
226C4⋊C4—24no—
227C4⋊C4—24no—
228C4⋊C4—42no—
229C4⋊C4—42no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C22⋊C4—44no—
233C42—22no—
234C42—22no—
235C42—22no—
236C42—42no—
237C42—42no—
238C42#41×C15114yes—
239C23—21no—
240C23—21no—
241C23—21no—
242C23—21no—
243C23—21no—
244C23—21no—
245C23#102×C15112yes—
246C23C2×C22⋊C4×C15111yescharacteristic
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—24no—
254C2×C4—24no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—44no—
259C2×C4—44no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4#102×C15112yes—
267C2×C4#104×C15112yes—
268C2×C4#117×C15112yes—
269C2×C4#123×C15112yes—
270C2×C4#123×C15112yes—
271C2×C4#131×C15112yes—
272C2×C4#131×C15112yes—
273C2×C4C2×D8×C15111yescharacteristic
274C2×C4C2×SD16×C15111yescharacteristic
275C2×C4#137×C15112yes—
276C8—44no—
277C8—82no—
278C22—22no—
279C22—22no—
280C22—22no—
281C22—41no—
282C22—41no—
283C22—41no—
284C22—41no—
285C22#381×C15111yescharacteristic
286C22#408×C15111yescharacteristic
287C22#408×C15111yescharacteristic
288C22C2×#102×C15111yescharacteristic
289C22#419×C15111yescharacteristic
290C22C2×#104×C15111yescharacteristic
291C22#421×C15111yescharacteristic
292C4—22no—
293C4—22no—
294C4—22no—
295C4—41no—
296C4—82no—
297C4—82no—
298C4#433×C15114yes—
299C4#480×C15112yes—
300C4#483×C15112yes—
301C2—42no—
302C2#1480×C15111yescharacteristic
303C2#1485×C15111yescharacteristic
304C2#1492×C15111yescharacteristic
305C2#1497×C15111yescharacteristic
306C2#1818×C15111yescharacteristic
307C2#1823×C15111yescharacteristic
308C2#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
154. #8709C151direct (N × H)
155. C151#8709direct (N × H)
159. #1279C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2285×C1512
#1797×C1512
C4×C22⋊C8×C1512
#1279×C1512
#8709151