Finite Group Databasebeta

← C151×#9760 #50314685

Subgroups — C151×#9760 #50314685

Order 38656.

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

normal subgroups only

This group has 478 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#3147×C151C211yesmaximal, characteristic
2#1835×C151C211yesmaximal, characteristic, complemented
3#1517×C151C214yesmaximal, complemented
4#1452×C151C211yesmaximal, characteristic, complemented
5C2×#135×C151—22no—
6#532×C151C2212yes—
7#495×C151—22no—
8#494×C151C411yescharacteristic, complemented
9#493×C151C411yescharacteristic, complemented
10#492×C151C412yescomplemented
11#431×C151C2212yes—
12C2×C4×C8×C151C2211yescharacteristic
13#382×C151C2212yes—
14#340×C151—22no—
15#327×C151—28no—
16#322×C151—22no—
17C2×#41×C151—22no—
18#135×C151—48no—
19C2×Q16×C151—22no—
20C2×SD16×C151—24no—
21C2×D8×C151—22no—
22C22×C8×C151D412yes—
23C4⋊Q8×C151C2×C412yes—
24#127×C151C2×C412yes—
25#124×C151—22no—
26#121×C151—24no—
27C4×D4×C151—24no—
28C2×C4⋊C4×C151—22no—
29C2×C42×C151C2311yescharacteristic
30C4⋊C8×C151—22no—
31C22⋊C8×C151D414yes—
32C4×C8×C151—22no—
33C4×C8×C151C2×C411yescharacteristic
34C4×C8×C151C2×C411yescharacteristic
35C4×C8×C151D412yes—
36#95×C151—24no—
37#41×C151—48no—
38C2×Q8×C151—22no—
39C2×D4×C151—22no—
40C2×D4×C151—24no—
41C2×D4×C151—42no—
42C22×C4×C151—42no—
43C22×C4×C151—42no—
44C22×C4×C151C2×D412yes—
45C22×C4×C151C2×D411yescharacteristic
46Q16×C151—44no—
47SD16×C151—48no—
48D8×C151—44no—
49C2×C8×C151—24no—
50C2×C8×C151—24no—
51C2×C8×C151C22⋊C412yes—
52C2×C8×C151C22⋊C412yes—
53C4⋊C4×C151—24no—
54C4⋊C4×C151—44no—
55C22⋊C4×C151—44no—
56C42×C151C22×C411yescharacteristic
57C42×C151C2×D411yescharacteristic
58C42×C151#4112yes—
59C23×C151—42no—
60C23×C151#12711yescharacteristic
61Q8×C151—44no—
62D4×C151—44no—
63D4×C151—84no—
64D4×C151—84no—
65C2×C4×C151—42no—
66C2×C4×C151—42no—
67C2×C4×C151—84no—
68C2×C4×C151—84no—
69C2×C4×C151—82no—
70C2×C4×C151C2×C22⋊C411yescharacteristic
71C2×C4×C151C4×D412yes—
72C2×C4×C151#12112yes—
73C2×C4×C151#12411yescharacteristic
74C2×C4×C151AGL(1,ℤ/8)14yes—
75C8×C151—22no—
76C8×C151—22no—
77C8×C151—44no—
78C22×C151—22no—
79C22×C151—82no—
80C22×C151—84no—
81C22×C151#39011yescharacteristic
82C22×C151#49612yes—
83C4×C151—22no—
84C4×C151—22no—
85C4×C151—82no—
86C4×C151—162no—
87C4×C151#41812yes—
88C4×C151#49012yes—
89C2×C151—22no—
90C2×C151—162no—
91C2×C151#196111yescharacteristic
92C2×C151#197612yes—
93#9760C15111yesmaximal, characteristic, direct product factor, Sylow
94C151#976011yescharacteristic, direct product factor, Sylow
95#3147C2×C15111yescharacteristic
96#1835C2×C15111yescharacteristic, complemented
97#1517C2×C15114yescomplemented
98#1452C2×C15111yescharacteristic, complemented
99C2×#135—22no—
100#532C22×C15112yes—
101#495—22no—
102#494C4×C15111yescharacteristic, complemented
103#493C4×C15111yescharacteristic, complemented
104#492C4×C15112yescomplemented
105#431C22×C15112yes—
106C2×C4×C8C22×C15111yescharacteristic
107#382C22×C15112yes—
108#340—22no—
109#327—28no—
110#322—22no—
111C2×#41—22no—
112#135—48no—
113C2×Q16—22no—
114C2×SD16—24no—
115C2×D8—22no—
116C22×C8D4×C15112yes—
117C4⋊Q8C2×C4×C15112yes—
118#127C2×C4×C15112yes—
119#124—22no—
120#121—24no—
121C4×D4—24no—
122C2×C4⋊C4—22no—
123C2×C42C23×C15111yescharacteristic
124C4⋊C8—22no—
125C22⋊C8D4×C15114yes—
126C4×C8—22no—
127C4×C8C2×C4×C15111yescharacteristic
128C4×C8C2×C4×C15111yescharacteristic
129C4×C8D4×C15112yes—
130#95—24no—
131#41—48no—
132C2×Q8—22no—
133C2×D4—22no—
134C2×D4—24no—
135C2×D4—42no—
136C22×C4—42no—
137C22×C4—42no—
138C22×C4C2×D4×C15112yes—
139C22×C4C2×D4×C15111yescharacteristic
140Q16—44no—
141SD16—48no—
142D8—44no—
143C2×C8—24no—
144C2×C8—24no—
145C2×C8C22⋊C4×C15112yes—
146C2×C8C22⋊C4×C15112yes—
147C4⋊C4—24no—
148C4⋊C4—44no—
149C22⋊C4—44no—
150C42C22×C4×C15111yescharacteristic
151C42C2×D4×C15111yescharacteristic
152C42#41×C15112yes—
153C23—42no—
154C23#127×C15111yescharacteristic
155Q8—44no—
156D4—44no—
157D4—84no—
158D4—84no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—84no—
162C2×C4—84no—
163C2×C4—82no—
164C2×C4C2×C22⋊C4×C15111yescharacteristic
165C2×C4C4×D4×C15112yes—
166C2×C4#121×C15112yes—
167C2×C4#124×C15111yescharacteristic
168C2×C4AGL(1,ℤ/8)×C15114yes—
169C8—22no—
170C8—22no—
171C8—44no—
172C22—22no—
173C22—82no—
174C22—84no—
175C22#390×C15111yescharacteristic
176C22#496×C15112yes—
177C4—22no—
178C4—22no—
179C4—82no—
180C4—162no—
181C4#418×C15112yes—
182C4#490×C15112yes—
183C2—22no—
184C2—162no—
185C2#1961×C15111yescharacteristic
186C2#1976×C15112yes—
subgroupG/H
center, socleC22×C151#390
commutatorC42C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radical#3147×C151C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1835×C151C2semidirect
3. #1517×C151C2semidirect
4. #1452×C151C2semidirect
8. #494×C151C4semidirect
9. #493×C151C4semidirect
10. #492×C151C4semidirect
93. #9760C151direct (N × H)
94. C151#9760direct (N × H)
96. #1835C2×C151semidirect
97. #1517C2×C151semidirect
98. #1452C2×C151semidirect
102. #494C4×C151semidirect
103. #493C4×C151semidirect
104. #492C4×C151semidirect

Maximal subgroups

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

subgroupindex
#3147×C1512
#1835×C1512
#1517×C1512
#1452×C1512
#9760151