Finite Group Databasebeta

← C151×#8710 #50313635

Subgroups — C151×#8710 #50313635

Order 38656.

540 conjugacy classes of subgroups.

The subgroup lattice has 306 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—44no—
26C2×C4⋊C4×C151—21no—
27C2×C4⋊C4×C151—21no—
28C2×C4⋊C4×C151—21no—
29C2×C4⋊C4×C151—21no—
30C2×C4⋊C4×C151C2×C412yes—
31C2×C4⋊C4×C151C2×C412yes—
32C2×C22⋊C4×C151—22no—
33C2×C42×C151—24no—
34C2×C42×C151—22no—
35C2×C42×C151C2×C411yescharacteristic
36C2×C42×C151D411yescharacteristic
37C2×C42×C151D411yescharacteristic
38C2×C42×C151C2311yescharacteristic
39C4⋊C8×C151—24no—
40C22⋊C8×C151—24no—
41C22⋊C8×C151—42no—
42C4×C8×C151—24no—
43#95×C151—22no—
44#95×C151—22no—
45C24×C151C22⋊C411yescharacteristic
46C22×C4×C151—22no—
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—41no—
56C22×C4×C151C22⋊C411yescharacteristic
57C22×C4×C151C22⋊C411yescharacteristic
58C22×C4×C151C22⋊C411yescharacteristic
59C22×C4×C151SD1612yes—
60C22×C4×C151Q1612yes—
61C22×C4×C151C22×C411yescharacteristic
62C22×C4×C151C2×D411yescharacteristic
63C22×C4×C151C2×D411yescharacteristic
64C2×C8×C151—24no—
65C2×C8×C151—42no—
66C2×C8×C151—42no—
67C2×C8×C151—42no—
68C2×C8×C151—42no—
69C2×C8×C151—42no—
70C4⋊C4×C151—24no—
71C4⋊C4×C151—24no—
72C4⋊C4×C151—42no—
73C4⋊C4×C151—42no—
74C4⋊C4×C151—42no—
75C4⋊C4×C151—42no—
76C22⋊C4×C151—44no—
77C42×C151—22no—
78C42×C151—22no—
79C42×C151—22no—
80C42×C151—44no—
81C42×C151#4114yes—
82C23×C151—21no—
83C23×C151—21no—
84C23×C151—21no—
85C23×C151—21no—
86C23×C151—21no—
87C23×C151—21no—
88C23×C151#10312yes—
89C23×C151C2×C22⋊C411yescharacteristic
90C2×C4×C151—21no—
91C2×C4×C151—21no—
92C2×C4×C151—21no—
93C2×C4×C151—21no—
94C2×C4×C151—21no—
95C2×C4×C151—21no—
96C2×C4×C151—24no—
97C2×C4×C151—24no—
98C2×C4×C151—21no—
99C2×C4×C151—21no—
100C2×C4×C151—21no—
101C2×C4×C151—44no—
102C2×C4×C151—44no—
103C2×C4×C151—42no—
104C2×C4×C151—42no—
105C2×C4×C151—42no—
106C2×C4×C151—42no—
107C2×C4×C151—42no—
108C2×C4×C151—42no—
109C2×C4×C151#10312yes—
110C2×C4×C151#10412yes—
111C2×C4×C151#11712yes—
112C2×C4×C151#12312yes—
113C2×C4×C151#12312yes—
114C2×C4×C151#13112yes—
115C2×C4×C151#13112yes—
116C2×C4×C151C2×SD1611yescharacteristic
117C2×C4×C151C2×Q1611yescharacteristic
118C2×C4×C151AGL(1,ℤ/8)12yes—
119C8×C151—44no—
120C8×C151—82no—
121C22×C151—22no—
122C22×C151—22no—
123C22×C151—22no—
124C22×C151—41no—
125C22×C151—41no—
126C22×C151—41no—
127C22×C151—41no—
128C22×C151#38111yescharacteristic
129C22×C151#40811yescharacteristic
130C22×C151#40811yescharacteristic
131C22×C151C2×#10311yescharacteristic
132C22×C151#41811yescharacteristic
133C22×C151C2×#10411yescharacteristic
134C22×C151#42111yescharacteristic
135C4×C151—22no—
136C4×C151—22no—
137C4×C151—22no—
138C4×C151—41no—
139C4×C151—82no—
140C4×C151—82no—
141C4×C151#43314yes—
142C4×C151#48112yes—
143C4×C151#48412yes—
144C2×C151—42no—
145C2×C151#148111yescharacteristic
146C2×C151#148411yescharacteristic
147C2×C151#149311yescharacteristic
148C2×C151#149611yescharacteristic
149C2×C151#181811yescharacteristic
150C2×C151#182411yescharacteristic
151C2×C151#182611yescharacteristic
152#8710C15111yesmaximal, characteristic, direct product factor, Sylow
153C151#871011yescharacteristic, direct product factor, Sylow
154#2285C2×C15111yescharacteristic
155#1797C2×C15111yescharacteristic
156C4×C22⋊C8C2×C15111yescharacteristic
157#1279C2×C15114yescomplemented
158C2×#117—21no—
159C22×C42C22×C15111yescharacteristic
160C2×C4⋊C8C22×C15112yes—
161C2×C22⋊C8—21no—
162C2×C22⋊C8—21no—
163C2×C4×C8C22×C15112yes—
164#384C4×C15111yescharacteristic
165#384C4×C15111yescharacteristic
166#382—21no—
167#380—21no—
168#380C4×C15112yes—
169C4×C4⋊C4—21no—
170C4×C4⋊C4C22×C15112yes—
171#336—21no—
172#336—21no—
173C23×C4C2×C4×C15111yescharacteristic
174C23×C4D4×C15111yescharacteristic
175C23×C4D4×C15111yescharacteristic
176C22×C8—22no—
177C22×C8—22no—
178#117—44no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4C2×C4×C15112yes—
184C2×C4⋊C4C2×C4×C15112yes—
185C2×C22⋊C4—22no—
186C2×C42—24no—
187C2×C42—22no—
188C2×C42C2×C4×C15111yescharacteristic
189C2×C42D4×C15111yescharacteristic
190C2×C42D4×C15111yescharacteristic
191C2×C42C23×C15111yescharacteristic
192C4⋊C8—24no—
193C22⋊C8—24no—
194C22⋊C8—42no—
195C4×C8—24no—
196#95—22no—
197#95—22no—
198C24C22⋊C4×C15111yescharacteristic
199C22×C4—22no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—41no—
209C22×C4C22⋊C4×C15111yescharacteristic
210C22×C4C22⋊C4×C15111yescharacteristic
211C22×C4C22⋊C4×C15111yescharacteristic
212C22×C4SD16×C15112yes—
213C22×C4Q16×C15112yes—
214C22×C4C22×C4×C15111yescharacteristic
215C22×C4C2×D4×C15111yescharacteristic
216C22×C4C2×D4×C15111yescharacteristic
217C2×C8—24no—
218C2×C8—42no—
219C2×C8—42no—
220C2×C8—42no—
221C2×C8—42no—
222C2×C8—42no—
223C4⋊C4—24no—
224C4⋊C4—24no—
225C4⋊C4—42no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C4⋊C4—42no—
229C22⋊C4—44no—
230C42—22no—
231C42—22no—
232C42—22no—
233C42—44no—
234C42#41×C15114yes—
235C23—21no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23#103×C15112yes—
242C23C2×C22⋊C4×C15111yescharacteristic
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—24no—
250C2×C4—24no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—44no—
255C2×C4—44no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4#103×C15112yes—
263C2×C4#104×C15112yes—
264C2×C4#117×C15112yes—
265C2×C4#123×C15112yes—
266C2×C4#123×C15112yes—
267C2×C4#131×C15112yes—
268C2×C4#131×C15112yes—
269C2×C4C2×SD16×C15111yescharacteristic
270C2×C4C2×Q16×C15111yescharacteristic
271C2×C4AGL(1,ℤ/8)×C15112yes—
272C8—44no—
273C8—82no—
274C22—22no—
275C22—22no—
276C22—22no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—41no—
281C22#381×C15111yescharacteristic
282C22#408×C15111yescharacteristic
283C22#408×C15111yescharacteristic
284C22C2×#103×C15111yescharacteristic
285C22#418×C15111yescharacteristic
286C22C2×#104×C15111yescharacteristic
287C22#421×C15111yescharacteristic
288C4—22no—
289C4—22no—
290C4—22no—
291C4—41no—
292C4—82no—
293C4—82no—
294C4#433×C15114yes—
295C4#481×C15112yes—
296C4#484×C15112yes—
297C2—42no—
298C2#1481×C15111yescharacteristic
299C2#1484×C15111yescharacteristic
300C2#1493×C15111yescharacteristic
301C2#1496×C15111yescharacteristic
302C2#1818×C15111yescharacteristic
303C2#1824×C15111yescharacteristic
304C2#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
152. #8710C151direct (N × H)
153. C151#8710direct (N × H)
157. #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
#8710151