Finite Group Databasebeta

← C151×#10017 #50314942

Subgroups — C151×#10017 #50314942

Order 38656.

528 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 122 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#3104×C151C212yesmaximal
2#2399×C151C211yesmaximal, characteristic
3#1995×C151C211yesmaximal, characteristic
4#1487×C151C212yesmaximal
5#1274×C151C211yesmaximal, characteristic
6#533×C151C2211yescharacteristic
7C2×C4×Q8×C151C2212yes—
8#484×C151—22no—
9#477×C151—22no—
10#462×C151—22no—
11#451×C151—22no—
12C4×Q16×C151—24no—
13#431×C151C2212yes—
14#423×C151C2211yescharacteristic
15#398×C151—22no—
16#395×C151—22no—
17C4×C4⋊C4×C151—22no—
18#376×C151C2211yescharacteristic
19#339×C151—22no—
20Q8⋊C8×C151—24no—
21C22×Q8×C151D412yes—
22C2×Q16×C151—24no—
23C2×M16×C151—21no—
24C4⋊Q8×C151D412yes—
25#125×C151—21no—
26C22⋊Q8×C151—22no—
27C4×Q8×C151—22no—
28C4×Q8×C151—22no—
29C4×Q8×C151—22no—
30C4×Q8×C151—22no—
31C4×Q8×C151—22no—
32#117×C151—21no—
33C2×C4⋊C4×C151—24no—
34C2×C4⋊C4×C151—22no—
35C2×C4⋊C4×C151D412yes—
36C2×C42×C151—22no—
37C2×C42×C151D412yes—
38C2×C42×C151C2311yescharacteristic
39#107×C151—24no—
40C4⋊C8×C151—22no—
41C4⋊C8×C151—22no—
42#103×C151—24no—
43#103×C151—24no—
44C22⋊C8×C151—22no—
45C4×C8×C151D414yes—
46#95×C151—22no—
47#95×C151—22no—
48#95×C151—22no—
49C2×Q8×C151—22no—
50C2×Q8×C151—22no—
51C2×Q8×C151—22no—
52C2×Q8×C151—44no—
53C22×C4×C151—22no—
54C22×C4×C151—22no—
55C22×C4×C151—22no—
56C22×C4×C151C2×D412yes—
57C22×C4×C151C2×D411yescharacteristic
58Q16×C151—48no—
59M16×C151—42no—
60C2×C8×C151—24no—
61C2×C8×C151—41no—
62C4⋊C4×C151—22no—
63C4⋊C4×C151—22no—
64C4⋊C4×C151—22no—
65C4⋊C4×C151—22no—
66C4⋊C4×C151—48no—
67C4⋊C4×C151—42no—
68C4⋊C4×C151—42no—
69C4⋊C4×C151—42no—
70C22⋊C4×C151—41no—
71C42×C151—22no—
72C42×C151—42no—
73C42×C151—42no—
74C42×C151—41no—
75C42×C151Q1614yescomplemented
76C42×C151C2×D411yescharacteristic
77C42×C151C2×D412yes—
78C42×C151#4111yescharacteristic
79C23×C151#12011yescharacteristic
80Q8×C151—24no—
81Q8×C151—24no—
82Q8×C151—42no—
83Q8×C151—42no—
84Q8×C151—44no—
85C2×C4×C151—24no—
86C2×C4×C151—24no—
87C2×C4×C151—42no—
88C2×C4×C151—42no—
89C2×C4×C151—44no—
90C2×C4×C151—42no—
91C2×C4×C151—44no—
92C2×C4×C151—42no—
93C2×C4×C151—42no—
94C2×C4×C151#12012yes—
95C2×C4×C151#12112yes—
96C2×C4×C151#12111yescharacteristic
97C2×C4×C151#12711yescharacteristic
98C2×C4×C151C2×Q1612yes—
99C2×C4×C151#13712yes—
100C8×C151—44no—
101C8×C151—81no—
102C22×C151—22no—
103C22×C151#39211yescharacteristic
104C22×C151#45112yes—
105C4×C151—22no—
106C4×C151—22no—
107C4×C151—44no—
108C4×C151—44no—
109C4×C151—82no—
110C4×C151—82no—
111C4×C151#46212yes—
112C4×C151#49411yescharacteristic
113C4×C151#49711yescharacteristic
114C2×C151—22no—
115C2×C151#201012yes—
116C2×C151#201611yescharacteristic
117#10017C15111yesmaximal, characteristic, direct product factor, Sylow
118C151#1001711yescharacteristic, direct product factor, Sylow
119#3104C2×C15112yes—
120#2399C2×C15111yescharacteristic
121#1995C2×C15111yescharacteristic
122#1487C2×C15112yes—
123#1274C2×C15111yescharacteristic
124#533C22×C15111yescharacteristic
125C2×C4×Q8C22×C15112yes—
126#484—22no—
127#477—22no—
128#462—22no—
129#451—22no—
130C4×Q16—24no—
131#431C22×C15112yes—
132#423C22×C15111yescharacteristic
133#398—22no—
134#395—22no—
135C4×C4⋊C4—22no—
136#376C22×C15111yescharacteristic
137#339—22no—
138Q8⋊C8—24no—
139C22×Q8D4×C15112yes—
140C2×Q16—24no—
141C2×M16—21no—
142C4⋊Q8D4×C15112yes—
143#125—21no—
144C22⋊Q8—22no—
145C4×Q8—22no—
146C4×Q8—22no—
147C4×Q8—22no—
148C4×Q8—22no—
149C4×Q8—22no—
150#117—21no—
151C2×C4⋊C4—24no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4D4×C15112yes—
154C2×C42—22no—
155C2×C42D4×C15112yes—
156C2×C42C23×C15111yescharacteristic
157#107—24no—
158C4⋊C8—22no—
159C4⋊C8—22no—
160#103—24no—
161#103—24no—
162C22⋊C8—22no—
163C4×C8D4×C15114yes—
164#95—22no—
165#95—22no—
166#95—22no—
167C2×Q8—22no—
168C2×Q8—22no—
169C2×Q8—22no—
170C2×Q8—44no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4C2×D4×C15112yes—
175C22×C4C2×D4×C15111yescharacteristic
176Q16—48no—
177M16—42no—
178C2×C8—24no—
179C2×C8—41no—
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—48no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C22⋊C4—41no—
189C42—22no—
190C42—42no—
191C42—42no—
192C42—41no—
193C42Q16×C15114yescomplemented
194C42C2×D4×C15111yescharacteristic
195C42C2×D4×C15112yes—
196C42#41×C15111yescharacteristic
197C23#120×C15111yescharacteristic
198Q8—24no—
199Q8—24no—
200Q8—42no—
201Q8—42no—
202Q8—44no—
203C2×C4—24no—
204C2×C4—24no—
205C2×C4—42no—
206C2×C4—44no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—44no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4#120×C15112yes—
213C2×C4#121×C15112yes—
214C2×C4#121×C15111yescharacteristic
215C2×C4#127×C15111yescharacteristic
216C2×C4C2×Q16×C15112yes—
217C2×C4#137×C15112yes—
218C8—44no—
219C8—81no—
220C22—22no—
221C22#392×C15111yescharacteristic
222C22#451×C15112yes—
223C4—22no—
224C4—22no—
225C4—44no—
226C4—44no—
227C4—82no—
228C4—82no—
229C4#462×C15112yes—
230C4#494×C15111yescharacteristic
231C4#497×C15111yescharacteristic
232C2—22no—
233C2#2010×C15112yes—
234C2#2016×C15111yescharacteristic
subgroupG/H
centerC2×C4×C151#127
commutator, Frattini, cosocleC2×C42C23×C151
socleC22×C151#392
prime radicalC23×C151#120
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
75. C42×C151Q16semidirect
117. #10017C151direct (N × H)
118. C151#10017direct (N × H)
193. C42Q16×C151semidirect

Maximal subgroups

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

subgroupindex
#3104×C1512
#2399×C1512
#1995×C1512
#1487×C1512
#1274×C1512
#10017151