Finite Group Databasebeta

← C151×#9488 #50314413

Subgroups — C151×#9488 #50314413

Order 38656.

454 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 134 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
2#2581×C151C211yesmaximal, characteristic
3#1801×C151C211yesmaximal, characteristic
4#1487×C151C212yesmaximal
5#1286×C151C212yesmaximal
6C2×C4×Q8×C151C2211yescharacteristic
7C2×C4×Q8×C151C2211yescharacteristic
8#446×C151—24no—
9#432×C151—22no—
10#431×C151C2212yes—
11#423×C151C2212yes—
12C2×#101×C151—21no—
13#400×C151C412yes—
14#395×C151C412yes—
15#391×C151—21no—
16#389×C151—21no—
17#387×C151—22no—
18#382×C151C2211yescharacteristic
19#343×C151—21no—
20Q8⋊C8×C151—24no—
21C22×Q8×C151C2×C411yescharacteristic
22C22×Q8×C151D411yescharacteristic
23C2×M16×C151—22no—
24C4×Q8×C151—22no—
25C4×Q8×C151—22no—
26C4×Q8×C151—22no—
27C4×Q8×C151—22no—
28C2×C4⋊C4×C151—22no—
29C2×C4⋊C4×C151—21no—
30C2×C4⋊C4×C151—21no—
31C2×C4⋊C4×C151C2×C411yescharacteristic
32C2×C4⋊C4×C151C2×C412yes—
33C2×C4⋊C4×C151D411yescharacteristic
34C2×C42×C151—21no—
35C2×C42×C151D412yes—
36C2×C42×C151C2311yescharacteristic
37C4⋊C8×C151—24no—
38C4⋊C8×C151—22no—
39C4⋊C8×C151—22no—
40C4⋊C8×C151—22no—
41#101×C151—42no—
42C22⋊C8×C151—22no—
43#97×C151—24no—
44C4×C8×C151D414yes—
45#95×C151—22no—
46#95×C151—22no—
47#95×C151—22no—
48#95×C151—21no—
49#95×C151C2×C412yes—
50C2×Q8×C151—22no—
51C2×Q8×C151—21no—
52C2×Q8×C151—21no—
53C2×Q8×C151—22no—
54C2×Q8×C151—22no—
55C2×Q8×C151—42no—
56C22×C4×C151—21no—
57C22×C4×C151—22no—
58C22×C4×C151—21no—
59C22×C4×C151C22⋊C412yes—
60C22×C4×C151C22⋊C412yes—
61C22×C4×C151C22×C411yescharacteristic
62C22×C4×C151C2×D411yescharacteristic
63C22×C4×C151C2×D411yescharacteristic
64M16×C151—42no—
65M16×C151—42no—
66C2×C8×C151—24no—
67C2×C8×C151—42no—
68C4⋊C4×C151—24no—
69C4⋊C4×C151—22no—
70C4⋊C4×C151—22no—
71C4⋊C4×C151—44no—
72C4⋊C4×C151—41no—
73C4⋊C4×C151—41no—
74C4⋊C4×C151—41no—
75C4⋊C4×C151—41no—
76C42×C151—22no—
77C42×C151—22no—
78C42×C151—42no—
79C42×C151C2×D412yes—
80C42×C151#4112yes—
81C23×C151C2×C22⋊C411yescharacteristic
82Q8×C151—24no—
83Q8×C151—42no—
84Q8×C151—42no—
85Q8×C151—42no—
86C2×C4×C151—22no—
87C2×C4×C151—22no—
88C2×C4×C151—22no—
89C2×C4×C151—22no—
90C2×C4×C151—22no—
91C2×C4×C151—41no—
92C2×C4×C151—41no—
93C2×C4×C151—41no—
94C2×C4×C151—41no—
95C2×C4×C151—42no—
96C2×C4×C151—42no—
97C2×C4×C151—42no—
98C2×C4×C151—42no—
99C2×C4×C151—41no—
100C2×C4×C151—42no—
101C2×C4×C151C4×D412yes—
102C2×C4×C151#12011yescharacteristic
103C2×C4×C151#12112yes—
104C2×C4×C151#12311yescharacteristic
105C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
106C2×C4×C151#13712yes—
107C2×C4×C151#13711yescharacteristic
108C8×C151—44no—
109C8×C151—82no—
110C22×C151—21no—
111C22×C151—21no—
112C22×C151#38611yescharacteristic
113C22×C151#41711yescharacteristic
114C22×C151#41911yescharacteristic
115C4×C151—22no—
116C4×C151—21no—
117C4×C151—21no—
118C4×C151—42no—
119C4×C151—42no—
120C4×C151—42no—
121C4×C151—82no—
122C4×C151—81no—
123C4×C151#46812yes—
124C4×C151#47012yes—
125C2×C151—21no—
126C2×C151—21no—
127C2×C151#189111yescharacteristic
128C2×C151#189411yescharacteristic
129C2×C151#191211yescharacteristic
130#9488C15111yesmaximal, characteristic, direct product factor, Sylow
131C151#948811yescharacteristic, direct product factor, Sylow
132#2983C2×C15111yescharacteristic
133#2581C2×C15111yescharacteristic
134#1801C2×C15111yescharacteristic
135#1487C2×C15112yes—
136#1286C2×C15112yes—
137C2×C4×Q8C22×C15111yescharacteristic
138C2×C4×Q8C22×C15111yescharacteristic
139#446—24no—
140#432—22no—
141#431C22×C15112yes—
142#423C22×C15112yes—
143C2×#101—21no—
144#400C4×C15112yes—
145#395C4×C15112yes—
146#391—21no—
147#389—21no—
148#387—22no—
149#382C22×C15111yescharacteristic
150#343—21no—
151Q8⋊C8—24no—
152C22×Q8C2×C4×C15111yescharacteristic
153C22×Q8D4×C15111yescharacteristic
154C2×M16—22no—
155C4×Q8—22no—
156C4×Q8—22no—
157C4×Q8—22no—
158C4×Q8—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4C2×C4×C15111yescharacteristic
163C2×C4⋊C4C2×C4×C15112yes—
164C2×C4⋊C4D4×C15111yescharacteristic
165C2×C42—21no—
166C2×C42D4×C15112yes—
167C2×C42C23×C15111yescharacteristic
168C4⋊C8—24no—
169C4⋊C8—22no—
170C4⋊C8—22no—
171C4⋊C8—22no—
172#101—42no—
173C22⋊C8—22no—
174#97—24no—
175C4×C8D4×C15114yes—
176#95—22no—
177#95—22no—
178#95—22no—
179#95—21no—
180#95C2×C4×C15112yes—
181C2×Q8—22no—
182C2×Q8—21no—
183C2×Q8—21no—
184C2×Q8—22no—
185C2×Q8—22no—
186C2×Q8—42no—
187C22×C4—21no—
188C22×C4—22no—
189C22×C4—21no—
190C22×C4C22⋊C4×C15112yes—
191C22×C4C22⋊C4×C15112yes—
192C22×C4C22×C4×C15111yescharacteristic
193C22×C4C2×D4×C15111yescharacteristic
194C22×C4C2×D4×C15111yescharacteristic
195M16—42no—
196M16—42no—
197C2×C8—24no—
198C2×C8—42no—
199C4⋊C4—24no—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—44no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C42—22no—
208C42—22no—
209C42—42no—
210C42C2×D4×C15112yes—
211C42#41×C15112yes—
212C23C2×C22⋊C4×C15111yescharacteristic
213Q8—24no—
214Q8—42no—
215Q8—42no—
216Q8—42no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4C4×D4×C15112yes—
233C2×C4#120×C15111yescharacteristic
234C2×C4#121×C15112yes—
235C2×C4#123×C15111yescharacteristic
236C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
237C2×C4#137×C15112yes—
238C2×C4#137×C15111yescharacteristic
239C8—44no—
240C8—82no—
241C22—21no—
242C22—21no—
243C22#386×C15111yescharacteristic
244C22#417×C15111yescharacteristic
245C22#419×C15111yescharacteristic
246C4—22no—
247C4—21no—
248C4—21no—
249C4—42no—
250C4—42no—
251C4—42no—
252C4—82no—
253C4—81no—
254C4#468×C15112yes—
255C4#470×C15112yes—
256C2—21no—
257C2—21no—
258C2#1891×C15111yescharacteristic
259C2#1894×C15111yescharacteristic
260C2#1912×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#386
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC23×C151C2×C22⋊C4
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
130. #9488C151direct (N × H)
131. C151#9488direct (N × H)

Maximal subgroups

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

subgroupindex
#2983×C1512
#2581×C1512
#1801×C1512
#1487×C1512
#1286×C1512
#9488151