Finite Group Databasebeta

← C151×#8703 #50313628

Subgroups — C151×#8703 #50313628

Order 38656.

530 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 150 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
1C2×#382×C151C211yesmaximal, characteristic
2#1817×C151C212yesmaximal
3#1280×C151C214yesmaximal
4C22×C4⋊C4×C151C412yes—
5C22×C42×C151C2211yescharacteristic
6C2×C22⋊C8×C151C2214yes—
7#382×C151—22no—
8#382×C151—22no—
9C2×#95×C151C412yes—
10C2×#95×C151C2212yes—
11#336×C151—22no—
12#336×C151—22no—
13C23×C4×C151C2×C411yescharacteristic
14C23×C4×C151C2×C411yescharacteristic
15C23×C4×C151C2×C414yes—
16C23×C4×C151C2311yescharacteristic
17C22×C8×C151—24no—
18C2×C4⋊C4×C151—22no—
19C2×C4⋊C4×C151—22no—
20C2×C4⋊C4×C151—44no—
21C2×C42×C151—24no—
22C2×C42×C151D412yes—
23C2×C42×C151D412yes—
24C22⋊C8×C151—28no—
25#95×C151—24no—
26#95×C151—24no—
27C24×C151C22×C411yescharacteristic
28C22×C4×C151—22no—
29C22×C4×C151—22no—
30C22×C4×C151—22no—
31C22×C4×C151—22no—
32C22×C4×C151—24no—
33C22×C4×C151—24no—
34C22×C4×C151—28no—
35C22×C4×C151—42no—
36C22×C4×C151—44no—
37C22×C4×C151—44no—
38C22×C4×C151C22⋊C412yes—
39C22×C4×C151C22⋊C411yescharacteristic
40C22×C4×C151C22⋊C411yescharacteristic
41C22×C4×C151C2×D412yes—
42C22×C4×C151#4114yes—
43C2×C8×C151—48no—
44C2×C8×C151—44no—
45C4⋊C4×C151—44no—
46C4⋊C4×C151—44no—
47C42×C151—24no—
48C42×C151—24no—
49C23×C151—22no—
50C23×C151—21no—
51C23×C151—21no—
52C23×C151C2×C22⋊C411yescharacteristic
53C23×C151#11712yes—
54C23×C151#13114yes—
55C2×C4×C151—28no—
56C2×C4×C151—21no—
57C2×C4×C151—21no—
58C2×C4×C151—24no—
59C2×C4×C151—21no—
60C2×C4×C151—21no—
61C2×C4×C151—22no—
62C2×C4×C151—24no—
63C2×C4×C151—44no—
64C2×C4×C151—44no—
65C2×C4×C151—44no—
66C2×C4×C151—44no—
67C2×C4×C151—44no—
68C2×C4×C151—88no—
69C2×C4×C151#10012yes—
70C2×C4×C151#10112yes—
71C2×C4×C151#12314yes—
72C8×C151—84no—
73C22×C151—22no—
74C22×C151—22no—
75C22×C151—24no—
76C22×C151—24no—
77C22×C151#38111yescharacteristic
78C22×C151#40812yes—
79C22×C151#41012yes—
80C22×C151C2×#10011yescharacteristic
81C22×C151C2×#10111yescharacteristic
82C22×C151#43314yes—
83C4×C151—24no—
84C4×C151—22no—
85C4×C151—22no—
86C4×C151—42no—
87C4×C151—84no—
88C2×C151—24no—
89C2×C151#146912yes—
90C2×C151#147012yes—
91C2×C151#181811yescharacteristic
92C2×C151#182011yescharacteristic
93C2×C151#182111yescharacteristic
94#8703C15111yesmaximal, characteristic, direct product factor, Sylow
95C151#870311yescharacteristic, direct product factor, Sylow
96C2×#382C2×C15111yescharacteristic
97#1817C2×C15112yes—
98#1280C2×C15114yes—
99C22×C4⋊C4C4×C15112yes—
100C22×C42C22×C15111yescharacteristic
101C2×C22⋊C8C22×C15114yes—
102#382—22no—
103#382—22no—
104C2×#95C4×C15112yes—
105C2×#95C22×C15112yes—
106#336—22no—
107#336—22no—
108C23×C4C2×C4×C15111yescharacteristic
109C23×C4C2×C4×C15111yescharacteristic
110C23×C4C2×C4×C15114yes—
111C23×C4C23×C15111yescharacteristic
112C22×C8—24no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—44no—
116C2×C42—24no—
117C2×C42D4×C15112yes—
118C2×C42D4×C15112yes—
119C22⋊C8—28no—
120#95—24no—
121#95—24no—
122C24C22×C4×C15111yescharacteristic
123C22×C4—22no—
124C22×C4—22no—
125C22×C4—22no—
126C22×C4—22no—
127C22×C4—24no—
128C22×C4—24no—
129C22×C4—28no—
130C22×C4—42no—
131C22×C4—44no—
132C22×C4—44no—
133C22×C4C22⋊C4×C15112yes—
134C22×C4C22⋊C4×C15111yescharacteristic
135C22×C4C22⋊C4×C15111yescharacteristic
136C22×C4C2×D4×C15112yes—
137C22×C4#41×C15114yes—
138C2×C8—48no—
139C2×C8—44no—
140C4⋊C4—44no—
141C4⋊C4—44no—
142C42—24no—
143C42—24no—
144C23—22no—
145C23—21no—
146C23—21no—
147C23C2×C22⋊C4×C15111yescharacteristic
148C23#117×C15112yes—
149C23#131×C15114yes—
150C2×C4—28no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—24no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—44no—
159C2×C4—44no—
160C2×C4—44no—
161C2×C4—44no—
162C2×C4—44no—
163C2×C4—88no—
164C2×C4#100×C15112yes—
165C2×C4#101×C15112yes—
166C2×C4#123×C15114yes—
167C8—84no—
168C22—22no—
169C22—22no—
170C22—24no—
171C22—24no—
172C22#381×C15111yescharacteristic
173C22#408×C15112yes—
174C22#410×C15112yes—
175C22C2×#100×C15111yescharacteristic
176C22C2×#101×C15111yescharacteristic
177C22#433×C15114yes—
178C4—24no—
179C4—22no—
180C4—22no—
181C4—42no—
182C4—84no—
183C2—24no—
184C2#1469×C15112yes—
185C2#1470×C15112yes—
186C2#1818×C15111yescharacteristic
187C2#1820×C15111yescharacteristic
188C2#1821×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C2×C22⋊C4
commutatorC24C22×C4×C151
Frattini, cosocleC23×C4C23×C151
prime radicalC24×C151C22×C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
94. #8703C151direct (N × H)
95. C151#8703direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#382×C1512
#1817×C1512
#1280×C1512
#8703151