Finite Group Databasebeta

← C151×#9393 #50314318

Subgroups — C151×#9393 #50314318

Order 38656.

558 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 154 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#2972×C151C211yesmaximal, characteristic
2#2547×C151C211yesmaximal, characteristic
3#1800×C151C211yesmaximal, characteristic
4#1546×C151C212yesmaximal, complemented
5#1303×C151C212yesmaximal, complemented
6C2×C4⋊Q8×C151C2211yescharacteristic
7C2×#124×C151—21no—
8C2×C4×D4×C151C2211yescharacteristic
9C8×D4×C151—24no—
10#431×C151C2212yes—
11#423×C151C2212yes—
12C2×#100×C151—21no—
13C2×C22⋊C8×C151—22no—
14#397×C151C414yes—
15#391×C151—21no—
16#380×C151—22no—
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—22no—
24C22×C8×C151—24no—
25C4⋊Q8×C151—22no—
26C4⋊Q8×C151—22no—
27#124×C151—42no—
28#124×C151—42no—
29C4×D4×C151—22no—
30C4×D4×C151—22no—
31C2×C4⋊C4×C151—21no—
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×C151—24no—
47#95×C151C2×C412yes—
48C24×C151C22⋊C412yes—
49C2×Q8×C151—42no—
50C2×Q8×C151—41no—
51C2×Q8×C151—41no—
52C2×Q8×C151—42no—
53C2×D4×C151—22no—
54C2×D4×C151—22no—
55C2×D4×C151D812yes—
56C2×D4×C151SD1612yes—
57C22×C4×C151—22no—
58C22×C4×C151—22no—
59C22×C4×C151—22no—
60C22×C4×C151—22no—
61C22×C4×C151—44no—
62C22×C4×C151C22⋊C412yes—
63C22×C4×C151C22×C411yescharacteristic
64C22×C4×C151C2×D411yescharacteristic
65C22×C4×C151C2×D411yescharacteristic
66M16×C151—42no—
67M16×C151—42no—
68C2×C8×C151—24no—
69C2×C8×C151—42no—
70C2×C8×C151—84no—
71C4⋊C4×C151—22no—
72C4⋊C4×C151—24no—
73C4⋊C4×C151—42no—
74C4⋊C4×C151—41no—
75C4⋊C4×C151—41no—
76C22⋊C4×C151—24no—
77C22⋊C4×C151—48no—
78C42×C151—41no—
79C42×C151—41no—
80C42×C151C2×D412yes—
81C42×C151#4112yes—
82C23×C151—22no—
83C23×C151—22no—
84C23×C151—42no—
85C23×C151—42no—
86C23×C151#10214yes—
87C23×C151C2×C22⋊C411yescharacteristic
88Q8×C151—82no—
89Q8×C151—82no—
90D4×C151—24no—
91D4×C151—24no—
92C2×C4×C151—22no—
93C2×C4×C151—22no—
94C2×C4×C151—41no—
95C2×C4×C151—44no—
96C2×C4×C151—42no—
97C2×C4×C151—42no—
98C2×C4×C151—42no—
99C2×C4×C151—42no—
100C2×C4×C151—42no—
101C2×C4×C151—42no—
102C2×C4×C151—42no—
103C2×C4×C151—82no—
104C2×C4×C151C4×D412yes—
105C2×C4×C151#12011yescharacteristic
106C2×C4×C151#12112yes—
107C2×C4×C151#12311yescharacteristic
108C2×C4×C151C2×D811yescharacteristic
109C2×C4×C151C2×SD1611yescharacteristic
110C2×C4×C151#13512yes—
111C8×C151—44no—
112C8×C151—82no—
113C22×C151—21no—
114C22×C151—21no—
115C22×C151—24no—
116C22×C151—44no—
117C22×C151—42no—
118C22×C151—42no—
119C22×C151—82no—
120C22×C151#38611yescharacteristic
121C22×C151C2×#10211yescharacteristic
122C22×C151#41611yescharacteristic
123C4×C151—21no—
124C4×C151—22no—
125C4×C151—42no—
126C4×C151—82no—
127C4×C151—82no—
128C4×C151#45512yes—
129C4×C151#46512yes—
130C4×C151#46612yes—
131C2×C151—21no—
132C2×C151—21no—
133C2×C151—44no—
134C2×C151#188511yescharacteristic
135C2×C151#189311yescharacteristic
136C2×C151#191511yescharacteristic
137#9393C15111yesmaximal, characteristic, direct product factor, Sylow
138C151#939311yescharacteristic, direct product factor, Sylow
139#2972C2×C15111yescharacteristic
140#2547C2×C15111yescharacteristic
141#1800C2×C15111yescharacteristic
142#1546C2×C15112yescomplemented
143#1303C2×C15112yescomplemented
144C2×C4⋊Q8C22×C15111yescharacteristic
145C2×#124—21no—
146C2×C4×D4C22×C15111yescharacteristic
147C8×D4—24no—
148#431C22×C15112yes—
149#423C22×C15112yes—
150C2×#100—21no—
151C2×C22⋊C8—22no—
152#397C4×C15114yes—
153#391—21no—
154#380—22no—
155C4×C4⋊C4C22×C15111yescharacteristic
156#343—21no—
157#332—24no—
158C22×Q8—21no—
159C22×D4D4×C15111yescharacteristic
160C23×C4D4×C15112yes—
161C2×M16—22no—
162C22×C8—24no—
163C4⋊Q8—22no—
164C4⋊Q8—22no—
165#124—42no—
166#124—42no—
167C4×D4—22no—
168C4×D4—22no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4C2×C4×C15112yes—
172C2×C4⋊C4D4×C15111yescharacteristic
173C2×C22⋊C4—24no—
174C2×C22⋊C4C2×C4×C15112yes—
175C2×C42—21no—
176C2×C42C23×C15111yescharacteristic
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8D4×C15114yes—
180#100—42no—
181C22⋊C8—24no—
182C22⋊C8—22no—
183C4×C8—22no—
184#95—24no—
185#95C2×C4×C15112yes—
186C24C22⋊C4×C15112yes—
187C2×Q8—42no—
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8—42no—
191C2×D4—22no—
192C2×D4—22no—
193C2×D4D8×C15112yes—
194C2×D4SD16×C15112yes—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4—44no—
200C22×C4C22⋊C4×C15112yes—
201C22×C4C22×C4×C15111yescharacteristic
202C22×C4C2×D4×C15111yescharacteristic
203C22×C4C2×D4×C15111yescharacteristic
204M16—42no—
205M16—42no—
206C2×C8—24no—
207C2×C8—42no—
208C2×C8—84no—
209C4⋊C4—22no—
210C4⋊C4—24no—
211C4⋊C4—42no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C22⋊C4—24no—
215C22⋊C4—48no—
216C42—41no—
217C42—41no—
218C42C2×D4×C15112yes—
219C42#41×C15112yes—
220C23—22no—
221C23—22no—
222C23—42no—
223C23—42no—
224C23#102×C15114yes—
225C23C2×C22⋊C4×C15111yescharacteristic
226Q8—82no—
227Q8—82no—
228D4—24no—
229D4—24no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—41no—
233C2×C4—44no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—82no—
242C2×C4C4×D4×C15112yes—
243C2×C4#120×C15111yescharacteristic
244C2×C4#121×C15112yes—
245C2×C4#123×C15111yescharacteristic
246C2×C4C2×D8×C15111yescharacteristic
247C2×C4C2×SD16×C15111yescharacteristic
248C2×C4#135×C15112yes—
249C8—44no—
250C8—82no—
251C22—21no—
252C22—21no—
253C22—24no—
254C22—44no—
255C22—42no—
256C22—42no—
257C22—82no—
258C22#386×C15111yescharacteristic
259C22C2×#102×C15111yescharacteristic
260C22#416×C15111yescharacteristic
261C4—21no—
262C4—22no—
263C4—42no—
264C4—82no—
265C4—82no—
266C4#455×C15112yes—
267C4#465×C15112yes—
268C4#466×C15112yes—
269C2—21no—
270C2—21no—
271C2—44no—
272C2#1885×C15111yescharacteristic
273C2#1893×C15111yescharacteristic
274C2#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. #1546×C151C2semidirect
5. #1303×C151C2semidirect
137. #9393C151direct (N × H)
138. C151#9393direct (N × H)
142. #1546C2×C151semidirect
143. #1303C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2972×C1512
#2547×C1512
#1800×C1512
#1546×C1512
#1303×C1512
#9393151