Finite Group Databasebeta

← C151×#9403 #50314328

Subgroups — C151×#9403 #50314328

Order 38656.

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

normal subgroups only

This group has 570 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#2975×C151C211yesmaximal, characteristic
2#2542×C151C211yesmaximal, characteristic
3#1800×C151C211yesmaximal, characteristic
4#1549×C151C212yesmaximal, complemented
5#1303×C151C212yesmaximal, complemented
6C2×C4⋊Q8×C151C2211yescharacteristic
7C2×C22⋊Q8×C151—22no—
8C2×C4×D4×C151C2211yescharacteristic
9#436×C151—24no—
10#431×C151C2212yes—
11#423×C151C2212yes—
12C2×#100×C151—21no—
13#407×C151—22no—
14#399×C151C414yes—
15#390×C151—21no—
16#384×C151—21no—
17C4×C4⋊C4×C151C2211yescharacteristic
18#343×C151—21no—
19#332×C151—24no—
20C22×Q8×C151—21no—
21C22×D4×C151D411yescharacteristic
22C23×C4×C151D412yes—
23C2×M16×C151—24no—
24C2×M16×C151—22no—
25C4⋊Q8×C151—22no—
26C4⋊Q8×C151—22no—
27C22⋊Q8×C151—48no—
28C4×D4×C151—22no—
29C4×D4×C151—22no—
30C2×C4⋊C4×C151—21no—
31C2×C4⋊C4×C151—24no—
32C2×C4⋊C4×C151—21no—
33C2×C4⋊C4×C151C2×C412yes—
34C2×C4⋊C4×C151D411yescharacteristic
35C2×C22⋊C4×C151—24no—
36C2×C22⋊C4×C151C2×C412yes—
37C2×C42×C151—21no—
38C2×C42×C151C2311yescharacteristic
39C4⋊C8×C151—22no—
40C4⋊C8×C151—22no—
41C4⋊C8×C151D414yes—
42#100×C151—42no—
43C22⋊C8×C151—24no—
44C22⋊C8×C151—22no—
45C4×C8×C151—22no—
46#95×C151C2×C412yes—
47C24×C151C22⋊C412yes—
48C2×Q8×C151—44no—
49C2×Q8×C151—41no—
50C2×Q8×C151—41no—
51C2×D4×C151—22no—
52C2×D4×C151—21no—
53C2×D4×C151—22no—
54C2×D4×C151—21no—
55C22×C4×C151—22no—
56C22×C4×C151—22no—
57C22×C4×C151—22no—
58C22×C4×C151—22no—
59C22×C4×C151—44no—
60C22×C4×C151C22⋊C412yes—
61C22×C4×C151C22×C411yescharacteristic
62C22×C4×C151C2×D411yescharacteristic
63C22×C4×C151C2×D411yescharacteristic
64M16×C151—42no—
65M16×C151—42no—
66M16×C151—84no—
67C2×C8×C151—24no—
68C2×C8×C151—42no—
69C4⋊C4×C151—24no—
70C4⋊C4×C151—22no—
71C4⋊C4×C151—24no—
72C4⋊C4×C151—48no—
73C4⋊C4×C151—42no—
74C22⋊C4×C151—24no—
75C22⋊C4×C151—48no—
76C42×C151—41no—
77C42×C151—41no—
78C42×C151C2×D412yes—
79C42×C151#4112yes—
80C23×C151—22no—
81C23×C151—22no—
82C23×C151—22no—
83C23×C151—42no—
84C23×C151—42no—
85C23×C151C2×C22⋊C411yescharacteristic
86Q8×C151—82no—
87Q8×C151—82no—
88D4×C151—42no—
89D4×C151—42no—
90C2×C4×C151—22no—
91C2×C4×C151—24no—
92C2×C4×C151—22no—
93C2×C4×C151—41no—
94C2×C4×C151—42no—
95C2×C4×C151—42no—
96C2×C4×C151—44no—
97C2×C4×C151—42no—
98C2×C4×C151—44no—
99C2×C4×C151—42no—
100C2×C4×C151—82no—
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—44no—
113C22×C151—42no—
114C22×C151—42no—
115C22×C151—42no—
116C22×C151—82no—
117C22×C151#38611yescharacteristic
118C22×C151#41711yescharacteristic
119C22×C151#41911yescharacteristic
120C4×C151—21no—
121C4×C151—22no—
122C4×C151—44no—
123C4×C151—42no—
124C4×C151—82no—
125C4×C151#45312yes—
126C4×C151#46812yes—
127C4×C151#47012yes—
128C2×C151—21no—
129C2×C151—21no—
130C2×C151—82no—
131C2×C151#188711yescharacteristic
132C2×C151#189411yescharacteristic
133C2×C151#191511yescharacteristic
134#9403C15111yesmaximal, characteristic, direct product factor, Sylow
135C151#940311yescharacteristic, direct product factor, Sylow
136#2975C2×C15111yescharacteristic
137#2542C2×C15111yescharacteristic
138#1800C2×C15111yescharacteristic
139#1549C2×C15112yescomplemented
140#1303C2×C15112yescomplemented
141C2×C4⋊Q8C22×C15111yescharacteristic
142C2×C22⋊Q8—22no—
143C2×C4×D4C22×C15111yescharacteristic
144#436—24no—
145#431C22×C15112yes—
146#423C22×C15112yes—
147C2×#100—21no—
148#407—22no—
149#399C4×C15114yes—
150#390—21no—
151#384—21no—
152C4×C4⋊C4C22×C15111yescharacteristic
153#343—21no—
154#332—24no—
155C22×Q8—21no—
156C22×D4D4×C15111yescharacteristic
157C23×C4D4×C15112yes—
158C2×M16—24no—
159C2×M16—22no—
160C4⋊Q8—22no—
161C4⋊Q8—22no—
162C22⋊Q8—48no—
163C4×D4—22no—
164C4×D4—22no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—24no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4C2×C4×C15112yes—
169C2×C4⋊C4D4×C15111yescharacteristic
170C2×C22⋊C4—24no—
171C2×C22⋊C4C2×C4×C15112yes—
172C2×C42—21no—
173C2×C42C23×C15111yescharacteristic
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8D4×C15114yes—
177#100—42no—
178C22⋊C8—24no—
179C22⋊C8—22no—
180C4×C8—22no—
181#95C2×C4×C15112yes—
182C24C22⋊C4×C15112yes—
183C2×Q8—44no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×D4—22no—
187C2×D4—21no—
188C2×D4—22no—
189C2×D4—21no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—44no—
195C22×C4C22⋊C4×C15112yes—
196C22×C4C22×C4×C15111yescharacteristic
197C22×C4C2×D4×C15111yescharacteristic
198C22×C4C2×D4×C15111yescharacteristic
199M16—42no—
200M16—42no—
201M16—84no—
202C2×C8—24no—
203C2×C8—42no—
204C4⋊C4—24no—
205C4⋊C4—22no—
206C4⋊C4—24no—
207C4⋊C4—48no—
208C4⋊C4—42no—
209C22⋊C4—24no—
210C22⋊C4—48no—
211C42—41no—
212C42—41no—
213C42C2×D4×C15112yes—
214C42#41×C15112yes—
215C23—22no—
216C23—22no—
217C23—22no—
218C23—42no—
219C23—42no—
220C23C2×C22⋊C4×C15111yescharacteristic
221Q8—82no—
222Q8—82no—
223D4—42no—
224D4—42no—
225C2×C4—22no—
226C2×C4—24no—
227C2×C4—22no—
228C2×C4—41no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—44no—
232C2×C4—42no—
233C2×C4—44no—
234C2×C4—42no—
235C2×C4—82no—
236C2×C4C4×D4×C15112yes—
237C2×C4#120×C15111yescharacteristic
238C2×C4#121×C15112yes—
239C2×C4#123×C15111yescharacteristic
240C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
241C2×C4#137×C15112yes—
242C2×C4#137×C15111yescharacteristic
243C8—44no—
244C8—82no—
245C22—21no—
246C22—21no—
247C22—44no—
248C22—42no—
249C22—42no—
250C22—42no—
251C22—82no—
252C22#386×C15111yescharacteristic
253C22#417×C15111yescharacteristic
254C22#419×C15111yescharacteristic
255C4—21no—
256C4—22no—
257C4—44no—
258C4—42no—
259C4—82no—
260C4#453×C15112yes—
261C4#468×C15112yes—
262C4#470×C15112yes—
263C2—21no—
264C2—21no—
265C2—82no—
266C2#1887×C15111yescharacteristic
267C2#1894×C15111yescharacteristic
268C2#1915×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#386
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC22×D4×C151D4
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
4. #1549×C151C2semidirect
5. #1303×C151C2semidirect
134. #9403C151direct (N × H)
135. C151#9403direct (N × H)
139. #1549C2×C151semidirect
140. #1303C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2975×C1512
#2542×C1512
#1800×C1512
#1549×C1512
#1303×C1512
#9403151