Finite Group Databasebeta

← C151×#9406 #50314331

Subgroups — C151×#9406 #50314331

Order 38656.

554 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2983×C151C211yesmaximal, characteristic, complemented
2#2548×C151C211yesmaximal, characteristic
3#1801×C151C211yesmaximal, characteristic, complemented
4#1545×C151C212yesmaximal
5#1303×C151C212yesmaximal, complemented
6C2×#127×C151C2211yescharacteristic
7C2×#124×C151—21no—
8C2×C4×Q8×C151C2211yescharacteristic
9#446×C151—24no—
10#432×C151—22no—
11#431×C151C2212yes—
12#423×C151C2212yes—
13C2×#101×C151—21no—
14#394×C151C414yes—
15#390×C151—21no—
16#390×C151—22no—
17C4×C4⋊C4×C151C2211yescharacteristic
18#343×C151—21no—
19#331×C151—24no—
20C22×Q8×C151D411yescharacteristic
21C22×D4×C151—21no—
22C22×D4×C151—21no—
23C22×D4×C151C2×C412yes—
24C2×M16×C151—22no—
25#127×C151—22no—
26#127×C151—22no—
27#124×C151—44no—
28C4×Q8×C151—22no—
29C4×Q8×C151—22no—
30C2×C4⋊C4×C151—21no—
31C2×C4⋊C4×C151C2×C412yes—
32C2×C4⋊C4×C151D411yescharacteristic
33C2×C22⋊C4×C151—24no—
34C2×C22⋊C4×C151—24no—
35C2×C42×C151—21no—
36C2×C42×C151D412yes—
37C2×C42×C151C2311yescharacteristic
38C4⋊C8×C151—24no—
39C4⋊C8×C151—22no—
40C4⋊C8×C151—22no—
41C4⋊C8×C151D414yes—
42#101×C151—42no—
43C22⋊C8×C151—22no—
44#97×C151—24no—
45C4×C8×C151—22no—
46#95×C151C2×C412yes—
47C24×C151—22no—
48C2×Q8×C151—22no—
49C2×Q8×C151—21no—
50C2×Q8×C151—22no—
51C2×Q8×C151—21no—
52C2×D4×C151—24no—
53C2×D4×C151—44no—
54C2×D4×C151—41no—
55C2×D4×C151—42no—
56C2×D4×C151—41no—
57C2×D4×C151—42no—
58C2×D4×C151—41no—
59C2×D4×C151—41no—
60C2×D4×C151—82no—
61C22×C4×C151—22no—
62C22×C4×C151C22⋊C412yes—
63C22×C4×C151C22⋊C412yes—
64C22×C4×C151C22×C411yescharacteristic
65C22×C4×C151C2×D411yescharacteristic
66C22×C4×C151C2×D411yescharacteristic
67M16×C151—42no—
68M16×C151—42no—
69C2×C8×C151—24no—
70C2×C8×C151—42no—
71C4⋊C4×C151—24no—
72C4⋊C4×C151—22no—
73C4⋊C4×C151—42no—
74C22⋊C4×C151—48no—
75C22⋊C4×C151—84no—
76C42×C151—22no—
77C42×C151—22no—
78C42×C151—42no—
79C42×C151C2×D412yes—
80C42×C151#4112yes—
81C23×C151—44no—
82C23×C151—44no—
83C23×C151—42no—
84C23×C151—42no—
85C23×C151—42no—
86C23×C151C2×C22⋊C411yescharacteristic
87Q8×C151—42no—
88Q8×C151—42no—
89D4×C151—84no—
90D4×C151—82no—
91D4×C151—82no—
92D4×C151—82no—
93D4×C151—82no—
94C2×C4×C151—22no—
95C2×C4×C151—22no—
96C2×C4×C151—22no—
97C2×C4×C151—22no—
98C2×C4×C151—22no—
99C2×C4×C151—41no—
100C2×C4×C151—42no—
101C2×C4×C151—42no—
102C2×C4×C151—42no—
103C2×C4×C151—42no—
104C2×C4×C151C4×D412yes—
105C2×C4×C151#12011yescharacteristic
106C2×C4×C151#12112yes—
107C2×C4×C151#12311yescharacteristic
108C2×C4×C151AGL(1,ℤ/8)12yes—
109C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
110C2×C4×C151#13711yescharacteristic
111C8×C151—44no—
112C8×C151—82no—
113C22×C151—21no—
114C22×C151—21no—
115C22×C151—84no—
116C22×C151—84no—
117C22×C151—82no—
118C22×C151—82no—
119C22×C151—82no—
120C22×C151#38611yescharacteristic
121C22×C151#41711yescharacteristic
122C22×C151#41811yescharacteristic
123C4×C151—21no—
124C4×C151—22no—
125C4×C151—42no—
126C4×C151—42no—
127C4×C151—82no—
128C4×C151#45412yes—
129C4×C151#46812yes—
130C4×C151#46912yes—
131C2×C151—21no—
132C2×C151—21no—
133C2×C151—162no—
134C2×C151#188811yescharacteristic
135C2×C151#189511yescharacteristic
136C2×C151#191411yescharacteristic
137#9406C15111yesmaximal, characteristic, direct product factor, Sylow
138C151#940611yescharacteristic, direct product factor, Sylow
139#2983C2×C15111yescharacteristic, complemented
140#2548C2×C15111yescharacteristic
141#1801C2×C15111yescharacteristic, complemented
142#1545C2×C15112yes—
143#1303C2×C15112yescomplemented
144C2×#127C22×C15111yescharacteristic
145C2×#124—21no—
146C2×C4×Q8C22×C15111yescharacteristic
147#446—24no—
148#432—22no—
149#431C22×C15112yes—
150#423C22×C15112yes—
151C2×#101—21no—
152#394C4×C15114yes—
153#390—21no—
154#390—22no—
155C4×C4⋊C4C22×C15111yescharacteristic
156#343—21no—
157#331—24no—
158C22×Q8D4×C15111yescharacteristic
159C22×D4—21no—
160C22×D4—21no—
161C22×D4C2×C4×C15112yes—
162C2×M16—22no—
163#127—22no—
164#127—22no—
165#124—44no—
166C4×Q8—22no—
167C4×Q8—22no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4C2×C4×C15112yes—
170C2×C4⋊C4D4×C15111yescharacteristic
171C2×C22⋊C4—24no—
172C2×C22⋊C4—24no—
173C2×C42—21no—
174C2×C42D4×C15112yes—
175C2×C42C23×C15111yescharacteristic
176C4⋊C8—24no—
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8D4×C15114yes—
180#101—42no—
181C22⋊C8—22no—
182#97—24no—
183C4×C8—22no—
184#95C2×C4×C15112yes—
185C24—22no—
186C2×Q8—22no—
187C2×Q8—21no—
188C2×Q8—22no—
189C2×Q8—21no—
190C2×D4—24no—
191C2×D4—44no—
192C2×D4—41no—
193C2×D4—42no—
194C2×D4—41no—
195C2×D4—42no—
196C2×D4—41no—
197C2×D4—41no—
198C2×D4—82no—
199C22×C4—22no—
200C22×C4C22⋊C4×C15112yes—
201C22×C4C22⋊C4×C15112yes—
202C22×C4C22×C4×C15111yescharacteristic
203C22×C4C2×D4×C15111yescharacteristic
204C22×C4C2×D4×C15111yescharacteristic
205M16—42no—
206M16—42no—
207C2×C8—24no—
208C2×C8—42no—
209C4⋊C4—24no—
210C4⋊C4—22no—
211C4⋊C4—42no—
212C22⋊C4—48no—
213C22⋊C4—84no—
214C42—22no—
215C42—22no—
216C42—42no—
217C42C2×D4×C15112yes—
218C42#41×C15112yes—
219C23—44no—
220C23—44no—
221C23—42no—
222C23—42no—
223C23—42no—
224C23C2×C22⋊C4×C15111yescharacteristic
225Q8—42no—
226Q8—42no—
227D4—84no—
228D4—82no—
229D4—82no—
230D4—82no—
231D4—82no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4C4×D4×C15112yes—
243C2×C4#120×C15111yescharacteristic
244C2×C4#121×C15112yes—
245C2×C4#123×C15111yescharacteristic
246C2×C4AGL(1,ℤ/8)×C15112yes—
247C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
248C2×C4#137×C15111yescharacteristic
249C8—44no—
250C8—82no—
251C22—21no—
252C22—21no—
253C22—84no—
254C22—84no—
255C22—82no—
256C22—82no—
257C22—82no—
258C22#386×C15111yescharacteristic
259C22#417×C15111yescharacteristic
260C22#418×C15111yescharacteristic
261C4—21no—
262C4—22no—
263C4—42no—
264C4—42no—
265C4—82no—
266C4#454×C15112yes—
267C4#468×C15112yes—
268C4#469×C15112yes—
269C2—21no—
270C2—21no—
271C2—162no—
272C2#1888×C15111yescharacteristic
273C2#1895×C15111yescharacteristic
274C2#1914×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#386
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC2×#127×C151C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2983×C151C2semidirect
3. #1801×C151C2semidirect
5. #1303×C151C2semidirect
137. #9406C151direct (N × H)
138. C151#9406direct (N × H)
139. #2983C2×C151semidirect
141. #1801C2×C151semidirect
143. #1303C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2983×C1512
#2548×C1512
#1801×C1512
#1545×C1512
#1303×C1512
#9406151