Finite Group Databasebeta

← C151×#19003 #50323928

Subgroups — C151×#19003 #50323928

Order 38656.

808 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#564×C151C211yesmaximal, characteristic, complemented
2#3234×C151C212yesmaximal
3#3142×C151C211yesmaximal, characteristic
4#1663×C151C214yesmaximal, complemented
5#1658×C151C214yesmaximal, complemented
6#1534×C151C211yesmaximal, characteristic, complemented
7#1528×C151C212yesmaximal, complemented
8#564×C151—24no—
9#564×C151—22no—
10#564×C151C2214yes—
11#532×C151C2211yescharacteristic
12C2×#125×C151—22no—
13C2×#125×C151—22no—
14C2×#125×C151—22no—
15C2×#125×C151C2211yescharacteristic
16C2×#125×C151C2212yes—
17#501×C151C2214yes—
18#491×C151C2212yes—
19#490×C151C2212yes—
20#490×C151C2214yes—
21#488×C151—22no—
22#481×C151—22no—
23#480×C151—22no—
24#478×C151—24no—
25#432×C151C2212yes—
26#417×C151—22no—
27C4×M16×C151C2211yescharacteristic
28#330×C151C2218yes—
29#330×C151C2214yes—
30C2×#41×C151—21no—
31C2×M16×C151—21no—
32C4⋊Q8×C151C2311yescharacteristic
33#127×C151C2311yescharacteristic
34#125×C151—28no—
35#125×C151—28no—
36#125×C151—28no—
37#125×C151—28no—
38#125×C151—28no—
39#125×C151—28no—
40#125×C151—22no—
41#125×C151—22no—
42#125×C151—22no—
43#125×C151D414yes—
44#125×C151D412yes—
45#125×C151C2312yes—
46#125×C151C2314yes—
47#124×C151—21no—
48#121×C151—22no—
49C4×D4×C151—22no—
50C2×C4⋊C4×C151—22no—
51C2×C4⋊C4×C151—22no—
52C2×C4⋊C4×C151—22no—
53C2×C4⋊C4×C151—22no—
54C2×C4⋊C4×C151—22no—
55C2×C4⋊C4×C151—22no—
56C2×C4⋊C4×C151D412yes—
57C2×C4⋊C4×C151D412yes—
58C2×C4⋊C4×C151D412yes—
59C2×C42×C151—22no—
60C2×C42×C151C2311yescharacteristic
61#107×C151—24no—
62#106×C151—24no—
63C4⋊C8×C151—22no—
64#103×C151—24no—
65#102×C151—24no—
66#102×C151—24no—
67#102×C151—24no—
68C22⋊C8×C151—22no—
69#97×C151C2312yes—
70#97×C151C2314yes—
71C4×C8×C151—21no—
72#41×C151—44no—
73C2×Q8×C151—21no—
74C2×D4×C151—22no—
75C2×D4×C151—21no—
76C2×D4×C151—41no—
77C22×C4×C151—22no—
78C22×C4×C151—22no—
79C22×C4×C151—22no—
80C22×C4×C151—41no—
81C22×C4×C151C2×D411yescharacteristic
82C22×C4×C151C2×D412yes—
83M16×C151—42no—
84C2×C8×C151—22no—
85C2×C8×C151—24no—
86C4⋊C4×C151—28no—
87C4⋊C4×C151—28no—
88C4⋊C4×C151—28no—
89C4⋊C4×C151—24no—
90C4⋊C4×C151—24no—
91C4⋊C4×C151—24no—
92C4⋊C4×C151—22no—
93C4⋊C4×C151—22no—
94C4⋊C4×C151—22no—
95C4⋊C4×C151—24no—
96C4⋊C4×C151—24no—
97C4⋊C4×C151—24no—
98C4⋊C4×C151—22no—
99C4⋊C4×C151C2×D414yes—
100C4⋊C4×C151C2×D414yes—
101C4⋊C4×C151C2×D414yes—
102C22⋊C4×C151—42no—
103C42×C151—28no—
104C42×C151C2×D411yescharacteristic
105C42×C151C2×D412yes—
106C42×C151C2411yescharacteristic
107C23×C151—41no—
108C23×C151#12011yescharacteristic
109Q8×C151—42no—
110D4×C151—42no—
111D4×C151—44no—
112D4×C151—82no—
113C2×C4×C151—22no—
114C2×C4×C151—24no—
115C2×C4×C151—24no—
116C2×C4×C151—24no—
117C2×C4×C151—42no—
118C2×C4×C151—44no—
119C2×C4×C151—44no—
120C2×C4×C151—44no—
121C2×C4×C151—41no—
122C2×C4×C151—82no—
123C2×C4×C151#12012yes—
124C2×C4×C151#12011yescharacteristic
125C2×C4×C151C22×D411yescharacteristic
126C2×C4×C151C22×D412yes—
127C8×C151—44no—
128C8×C151—42no—
129C22×C151—22no—
130C22×C151—81no—
131C22×C151—82no—
132C22×C151#45412yes—
133C22×C151C2×#12011yescharacteristic
134C4×C151—21no—
135C4×C151—21no—
136C4×C151—22no—
137C4×C151—22no—
138C4×C151—44no—
139C4×C151—44no—
140C4×C151—44no—
141C4×C151—81no—
142C2×C151—22no—
143C2×C151—161no—
144C2×C151C2×#45411yescharacteristic
145C2×C151#302012yes—
146#19003C15111yesmaximal, characteristic, direct product factor, Sylow
147C151#1900311yescharacteristic, direct product factor, Sylow
148C2×#564C2×C15111yescharacteristic, complemented
149#3234C2×C15112yes—
150#3142C2×C15111yescharacteristic
151#1663C2×C15114yescomplemented
152#1658C2×C15114yescomplemented
153#1534C2×C15111yescharacteristic, complemented
154#1528C2×C15112yescomplemented
155#564—24no—
156#564—22no—
157#564C22×C15114yes—
158#532C22×C15111yescharacteristic
159C2×#125—22no—
160C2×#125—22no—
161C2×#125—22no—
162C2×#125C22×C15111yescharacteristic
163C2×#125C22×C15112yes—
164#501C22×C15114yes—
165#491C22×C15112yes—
166#490C22×C15112yes—
167#490C22×C15114yes—
168#488—22no—
169#481—22no—
170#480—22no—
171#478—24no—
172#432C22×C15112yes—
173#417—22no—
174C4×M16C22×C15111yescharacteristic
175#330C22×C15118yes—
176#330C22×C15114yes—
177C2×#41—21no—
178C2×M16—21no—
179C4⋊Q8C23×C15111yescharacteristic
180#127C23×C15111yescharacteristic
181#125—28no—
182#125—28no—
183#125—28no—
184#125—28no—
185#125—28no—
186#125—28no—
187#125—22no—
188#125—22no—
189#125—22no—
190#125D4×C15114yes—
191#125D4×C15112yes—
192#125C23×C15112yes—
193#125C23×C15114yes—
194#124—21no—
195#121—22no—
196C4×D4—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4D4×C15112yes—
204C2×C4⋊C4D4×C15112yes—
205C2×C4⋊C4D4×C15112yes—
206C2×C42—22no—
207C2×C42C23×C15111yescharacteristic
208#107—24no—
209#106—24no—
210C4⋊C8—22no—
211#103—24no—
212#102—24no—
213#102—24no—
214#102—24no—
215C22⋊C8—22no—
216#97C23×C15112yes—
217#97C23×C15114yes—
218C4×C8—21no—
219#41—44no—
220C2×Q8—21no—
221C2×D4—22no—
222C2×D4—21no—
223C2×D4—41no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—41no—
228C22×C4C2×D4×C15111yescharacteristic
229C22×C4C2×D4×C15112yes—
230M16—42no—
231C2×C8—22no—
232C2×C8—24no—
233C4⋊C4—28no—
234C4⋊C4—28no—
235C4⋊C4—28no—
236C4⋊C4—24no—
237C4⋊C4—24no—
238C4⋊C4—24no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—24no—
243C4⋊C4—24no—
244C4⋊C4—24no—
245C4⋊C4—22no—
246C4⋊C4C2×D4×C15114yes—
247C4⋊C4C2×D4×C15114yes—
248C4⋊C4C2×D4×C15114yes—
249C22⋊C4—42no—
250C42—28no—
251C42C2×D4×C15111yescharacteristic
252C42C2×D4×C15112yes—
253C42C24×C15111yescharacteristic
254C23—41no—
255C23#120×C15111yescharacteristic
256Q8—42no—
257D4—42no—
258D4—44no—
259D4—82no—
260C2×C4—22no—
261C2×C4—24no—
262C2×C4—24no—
263C2×C4—24no—
264C2×C4—42no—
265C2×C4—44no—
266C2×C4—44no—
267C2×C4—44no—
268C2×C4—41no—
269C2×C4—82no—
270C2×C4#120×C15112yes—
271C2×C4#120×C15111yescharacteristic
272C2×C4C22×D4×C15112yes—
273C2×C4C22×D4×C15111yescharacteristic
274C8—42no—
275C8—44no—
276C22—22no—
277C22—81no—
278C22—82no—
279C22#454×C15112yes—
280C22C2×#120×C15111yescharacteristic
281C4—21no—
282C4—21no—
283C4—22no—
284C4—22no—
285C4—44no—
286C4—44no—
287C4—44no—
288C4—81no—
289C2—22no—
290C2—161no—
291C2C2×#454×C15111yescharacteristic
292C2#3020×C15112yes—
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#532×C151C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#564×C151C2semidirect
4. #1663×C151C2semidirect
5. #1658×C151C2semidirect
6. #1534×C151C2semidirect
7. #1528×C151C2semidirect
146. #19003C151direct (N × H)
147. C151#19003direct (N × H)
148. C2×#564C2×C151semidirect
151. #1663C2×C151semidirect
152. #1658C2×C151semidirect
153. #1534C2×C151semidirect
154. #1528C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#564×C1512
#3234×C1512
#3142×C1512
#1663×C1512
#1658×C1512
#1534×C1512
#1528×C1512
#19003151