Finite Group Databasebeta

← C151×#8727 #50313652

Subgroups — C151×#8727 #50313652

Order 38656.

514 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2285×C151C211yesmaximal, characteristic
2#1797×C151C211yesmaximal, characteristic
3#1797×C151C211yesmaximal, characteristic
4#1296×C151C212yesmaximal, complemented
5#1296×C151C212yesmaximal, complemented
6C2×#117×C151—21no—
7C22×C42×C151C2211yescharacteristic
8C2×C4⋊C8×C151C2212yes—
9C2×C4⋊C8×C151C2212yes—
10C2×C22⋊C8×C151—21no—
11C2×C22⋊C8×C151—21no—
12#384×C151C2211yescharacteristic
13#384×C151C2211yescharacteristic
14#382×C151—21no—
15#380×C151—21no—
16#380×C151C412yes—
17C4×C4⋊C4×C151—21no—
18C4×C4⋊C4×C151C412yes—
19#336×C151—21no—
20#336×C151—21no—
21C23×C4×C151C2×C411yescharacteristic
22C23×C4×C151D411yescharacteristic
23C23×C4×C151D411yescharacteristic
24C22×C8×C151—22no—
25C22×C8×C151—22no—
26#117×C151—44no—
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—
41C4⋊C8×C151—24no—
42C22⋊C8×C151—42no—
43C22⋊C8×C151—42no—
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—21no—
53C22×C4×C151—21no—
54C22×C4×C151—22no—
55C22×C4×C151—22no—
56C22×C4×C151—41no—
57C22×C4×C151—41no—
58C22×C4×C151C22⋊C411yescharacteristic
59C22×C4×C151C22⋊C411yescharacteristic
60C22×C4×C151C22⋊C411yescharacteristic
61C22×C4×C151SD1612yes—
62C22×C4×C151Q1612yes—
63C22×C4×C151C22×C411yescharacteristic
64C22×C4×C151C2×D411yescharacteristic
65C22×C4×C151C2×D411yescharacteristic
66C2×C8×C151—42no—
67C2×C8×C151—42no—
68C2×C8×C151—42no—
69C2×C8×C151—42no—
70C2×C8×C151—42no—
71C2×C8×C151—42no—
72C4⋊C4×C151—42no—
73C4⋊C4×C151—42no—
74C4⋊C4×C151—42no—
75C4⋊C4×C151—41no—
76C4⋊C4×C151—42no—
77C4⋊C4×C151—42no—
78C4⋊C4×C151—41no—
79C22⋊C4×C151—44no—
80C42×C151—22no—
81C42×C151—22no—
82C42×C151—22no—
83C42×C151—44no—
84C42×C151#4114yes—
85C23×C151—21no—
86C23×C151—21no—
87C23×C151—21no—
88C23×C151—21no—
89C23×C151—21no—
90C23×C151—21no—
91C23×C151#10312yes—
92C23×C151C2×C22⋊C411yescharacteristic
93C2×C4×C151—21no—
94C2×C4×C151—21no—
95C2×C4×C151—21no—
96C2×C4×C151—21no—
97C2×C4×C151—24no—
98C2×C4×C151—24no—
99C2×C4×C151—21no—
100C2×C4×C151—21no—
101C2×C4×C151—21no—
102C2×C4×C151—21no—
103C2×C4×C151—21no—
104C2×C4×C151—21no—
105C2×C4×C151—44no—
106C2×C4×C151—42no—
107C2×C4×C151—42no—
108C2×C4×C151—42no—
109C2×C4×C151—42no—
110C2×C4×C151—42no—
111C2×C4×C151—42no—
112C2×C4×C151—42no—
113C2×C4×C151—42no—
114C2×C4×C151#10312yes—
115C2×C4×C151#11712yes—
116C2×C4×C151#12312yes—
117C2×C4×C151#12312yes—
118C2×C4×C151C2×SD1611yescharacteristic
119C2×C4×C151C2×Q1611yescharacteristic
120C2×C4×C151#13512yes—
121C2×C4×C151AGL(1,ℤ/8)12yes—
122C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C151#13711yescharacteristic
124C8×C151—82no—
125C8×C151—82no—
126C22×C151—22no—
127C22×C151—22no—
128C22×C151—22no—
129C22×C151—41no—
130C22×C151—41no—
131C22×C151—41no—
132C22×C151—41no—
133C22×C151#38111yescharacteristic
134C22×C151#41311yescharacteristic
135C22×C151#41311yescharacteristic
136C22×C151C2×#10311yescharacteristic
137C22×C151#41611yescharacteristic
138C22×C151#41711yescharacteristic
139C22×C151#41811yescharacteristic
140C4×C151—22no—
141C4×C151—22no—
142C4×C151—41no—
143C4×C151—41no—
144C4×C151—82no—
145C4×C151—82no—
146C4×C151#48112yes—
147C4×C151#48212yes—
148C4×C151#48412yes—
149C4×C151#48512yes—
150C2×C151—42no—
151C2×C151#154211yescharacteristic
152C2×C151#155011yescharacteristic
153C2×C151#155311yescharacteristic
154C2×C151#155711yescharacteristic
155C2×C151#182211yescharacteristic
156C2×C151#182411yescharacteristic
157C2×C151#182511yescharacteristic
158#8727C15111yesmaximal, characteristic, direct product factor, Sylow
159C151#872711yescharacteristic, direct product factor, Sylow
160#2285C2×C15111yescharacteristic
161#1797C2×C15111yescharacteristic
162#1797C2×C15111yescharacteristic
163#1296C2×C15112yescomplemented
164#1296C2×C15112yescomplemented
165C2×#117—21no—
166C22×C42C22×C15111yescharacteristic
167C2×C4⋊C8C22×C15112yes—
168C2×C4⋊C8C22×C15112yes—
169C2×C22⋊C8—21no—
170C2×C22⋊C8—21no—
171#384C22×C15111yescharacteristic
172#384C22×C15111yescharacteristic
173#382—21no—
174#380—21no—
175#380C4×C15112yes—
176C4×C4⋊C4—21no—
177C4×C4⋊C4C4×C15112yes—
178#336—21no—
179#336—21no—
180C23×C4C2×C4×C15111yescharacteristic
181C23×C4D4×C15111yescharacteristic
182C23×C4D4×C15111yescharacteristic
183C22×C8—22no—
184C22×C8—22no—
185#117—44no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4C2×C4×C15112yes—
191C2×C4⋊C4C2×C4×C15112yes—
192C2×C22⋊C4—22no—
193C2×C42—24no—
194C2×C42—22no—
195C2×C42C2×C4×C15111yescharacteristic
196C2×C42D4×C15111yescharacteristic
197C2×C42D4×C15111yescharacteristic
198C2×C42C23×C15111yescharacteristic
199C4⋊C8—24no—
200C4⋊C8—24no—
201C22⋊C8—42no—
202C22⋊C8—42no—
203#95—22no—
204#95—22no—
205C24C22⋊C4×C15111yescharacteristic
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4C22⋊C4×C15111yescharacteristic
218C22×C4C22⋊C4×C15111yescharacteristic
219C22×C4C22⋊C4×C15111yescharacteristic
220C22×C4SD16×C15112yes—
221C22×C4Q16×C15112yes—
222C22×C4C22×C4×C15111yescharacteristic
223C22×C4C2×D4×C15111yescharacteristic
224C22×C4C2×D4×C15111yescharacteristic
225C2×C8—42no—
226C2×C8—42no—
227C2×C8—42no—
228C2×C8—42no—
229C2×C8—42no—
230C2×C8—42no—
231C4⋊C4—42no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C22⋊C4—44no—
239C42—22no—
240C42—22no—
241C42—22no—
242C42—44no—
243C42#41×C15114yes—
244C23—21no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23#103×C15112yes—
251C23C2×C22⋊C4×C15111yescharacteristic
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—24no—
257C2×C4—24no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—44no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4#103×C15112yes—
274C2×C4#117×C15112yes—
275C2×C4#123×C15112yes—
276C2×C4#123×C15112yes—
277C2×C4C2×SD16×C15111yescharacteristic
278C2×C4C2×Q16×C15111yescharacteristic
279C2×C4#135×C15112yes—
280C2×C4AGL(1,ℤ/8)×C15112yes—
281C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
282C2×C4#137×C15111yescharacteristic
283C8—82no—
284C8—82no—
285C22—22no—
286C22—22no—
287C22—22no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22#381×C15111yescharacteristic
293C22#413×C15111yescharacteristic
294C22#413×C15111yescharacteristic
295C22C2×#103×C15111yescharacteristic
296C22#416×C15111yescharacteristic
297C22#417×C15111yescharacteristic
298C22#418×C15111yescharacteristic
299C4—22no—
300C4—22no—
301C4—41no—
302C4—41no—
303C4—82no—
304C4—82no—
305C4#481×C15112yes—
306C4#482×C15112yes—
307C4#484×C15112yes—
308C4#485×C15112yes—
309C2—42no—
310C2#1542×C15111yescharacteristic
311C2#1550×C15111yescharacteristic
312C2#1553×C15111yescharacteristic
313C2#1557×C15111yescharacteristic
314C2#1822×C15111yescharacteristic
315C2#1824×C15111yescharacteristic
316C2#1825×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C2×C22⋊C4
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC24×C151C22⋊C4
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
4. #1296×C151C2semidirect
5. #1296×C151C2semidirect
158. #8727C151direct (N × H)
159. C151#8727direct (N × H)
163. #1296C2×C151semidirect
164. #1296C2×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
#1296×C1512
#8727151