Finite Group Databasebeta

← C151×#8725 #50313650

Subgroups — C151×#8725 #50313650

Order 38656.

630 conjugacy classes of subgroups; only the 206 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 206 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×#384×C151C211yesmaximal, characteristic
2#1797×C151C212yesmaximal
3#1296×C151C214yesmaximal, complemented
4C22×C4⋊C4×C151—22no—
5C22×C4⋊C4×C151C412yes—
6C22×C42×C151C2211yescharacteristic
7C2×C4⋊C8×C151C2214yes—
8C2×C22⋊C8×C151—22no—
9#384×C151—22no—
10#384×C151C412yes—
11#384×C151C2212yes—
12#336×C151—22no—
13C23×C4×C151—22no—
14C23×C4×C151C2×C411yescharacteristic
15C23×C4×C151D412yes—
16C22×C8×C151—24no—
17C2×C4⋊C4×C151—22no—
18C2×C4⋊C4×C151—24no—
19C2×C4⋊C4×C151—24no—
20C2×C4⋊C4×C151—44no—
21C2×C4⋊C4×C151—48no—
22C2×C4⋊C4×C151C2×C414yes—
23C2×C42×C151—24no—
24C2×C42×C151C2×C411yescharacteristic
25C2×C42×C151D412yes—
26C2×C42×C151C2311yescharacteristic
27C4⋊C8×C151—28no—
28C22⋊C8×C151—44no—
29C24×C151C22⋊C411yescharacteristic
30C22×C4×C151—22no—
31C22×C4×C151—22no—
32C22×C4×C151—22no—
33C22×C4×C151—24no—
34C22×C4×C151—24no—
35C22×C4×C151—24no—
36C22×C4×C151—48no—
37C22×C4×C151—44no—
38C22×C4×C151C22⋊C411yescharacteristic
39C22×C4×C151C22⋊C412yes—
40C22×C4×C151SD1614yes—
41C22×C4×C151Q1614yes—
42C22×C4×C151C22×C411yescharacteristic
43C22×C4×C151C2×D412yes—
44C2×C8×C151—44no—
45C2×C8×C151—44no—
46C2×C8×C151—44no—
47C4⋊C4×C151—44no—
48C4⋊C4×C151—44no—
49C4⋊C4×C151—48no—
50C4⋊C4×C151—48no—
51C42×C151—22no—
52C42×C151—24no—
53C42×C151#4114yes—
54C23×C151—21no—
55C23×C151—21no—
56C23×C151—22no—
57C23×C151#10012yes—
58C23×C151#10314yes—
59C23×C151C2×C22⋊C411yescharacteristic
60C2×C4×C151—28no—
61C2×C4×C151—21no—
62C2×C4×C151—22no—
63C2×C4×C151—21no—
64C2×C4×C151—21no—
65C2×C4×C151—21no—
66C2×C4×C151—22no—
67C2×C4×C151—28no—
68C2×C4×C151—28no—
69C2×C4×C151—44no—
70C2×C4×C151—48no—
71C2×C4×C151—88no—
72C2×C4×C151#10112yes—
73C2×C4×C151#10314yes—
74C2×C4×C151#11712yes—
75C2×C4×C151#12314yes—
76C2×C4×C151C2×SD1612yes—
77C2×C4×C151C2×Q1612yes—
78C2×C4×C151AGL(1,ℤ/8)14yes—
79C8×C151—84no—
80C22×C151—24no—
81C22×C151—22no—
82C22×C151—22no—
83C22×C151—24no—
84C22×C151#33314yes—
85C22×C151#38111yescharacteristic
86C22×C151C2×#10011yescharacteristic
87C22×C151C2×#10111yescharacteristic
88C22×C151C2×#10312yes—
89C22×C151#41812yes—
90C4×C151—22no—
91C4×C151—22no—
92C4×C151—24no—
93C4×C151—84no—
94C4×C151#48114yes—
95C4×C151#48414yes—
96C2×C151—24no—
97C2×C151C2×#33311yescharacteristic
98C2×C151#154912yes—
99C2×C151#155511yescharacteristic
100C2×C151#182111yescharacteristic
101C2×C151#182412yes—
102#8725C15111yesmaximal, characteristic, direct product factor, Sylow
103C151#872511yescharacteristic, direct product factor, Sylow
104C2×#384C2×C15111yescharacteristic
105#1797C2×C15112yes—
106#1296C2×C15114yescomplemented
107C22×C4⋊C4—22no—
108C22×C4⋊C4C4×C15112yes—
109C22×C42C22×C15111yescharacteristic
110C2×C4⋊C8C22×C15114yes—
111C2×C22⋊C8—22no—
112#384—22no—
113#384C4×C15112yes—
114#384C22×C15112yes—
115#336—22no—
116C23×C4—22no—
117C23×C4C2×C4×C15111yescharacteristic
118C23×C4D4×C15112yes—
119C22×C8—24no—
120C2×C4⋊C4—24no—
121C2×C4⋊C4—22no—
122C2×C4⋊C4—24no—
123C2×C4⋊C4—44no—
124C2×C4⋊C4—48no—
125C2×C4⋊C4C2×C4×C15114yes—
126C2×C42—24no—
127C2×C42C2×C4×C15111yescharacteristic
128C2×C42D4×C15112yes—
129C2×C42C23×C15111yescharacteristic
130C4⋊C8—28no—
131C22⋊C8—44no—
132C24C22⋊C4×C15111yescharacteristic
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—22no—
136C22×C4—24no—
137C22×C4—24no—
138C22×C4—24no—
139C22×C4—48no—
140C22×C4—44no—
141C22×C4C22⋊C4×C15111yescharacteristic
142C22×C4C22⋊C4×C15112yes—
143C22×C4SD16×C15114yes—
144C22×C4Q16×C15114yes—
145C22×C4C22×C4×C15111yescharacteristic
146C22×C4C2×D4×C15112yes—
147C2×C8—44no—
148C2×C8—44no—
149C2×C8—44no—
150C4⋊C4—44no—
151C4⋊C4—44no—
152C4⋊C4—48no—
153C4⋊C4—48no—
154C42—22no—
155C42—24no—
156C42#41×C15114yes—
157C23—21no—
158C23—21no—
159C23—22no—
160C23#100×C15112yes—
161C23#103×C15114yes—
162C23C2×C22⋊C4×C15111yescharacteristic
163C2×C4—28no—
164C2×C4—21no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—28no—
171C2×C4—28no—
172C2×C4—44no—
173C2×C4—48no—
174C2×C4—88no—
175C2×C4#101×C15112yes—
176C2×C4#103×C15114yes—
177C2×C4#117×C15112yes—
178C2×C4#123×C15114yes—
179C2×C4C2×SD16×C15112yes—
180C2×C4C2×Q16×C15112yes—
181C2×C4AGL(1,ℤ/8)×C15114yes—
182C8—84no—
183C22—22no—
184C22—24no—
185C22—24no—
186C22—22no—
187C22#333×C15114yes—
188C22#381×C15111yescharacteristic
189C22C2×#100×C15111yescharacteristic
190C22C2×#101×C15111yescharacteristic
191C22C2×#103×C15112yes—
192C22#418×C15112yes—
193C4—22no—
194C4—22no—
195C4—24no—
196C4—84no—
197C4#481×C15114yes—
198C4#484×C15114yes—
199C2—24no—
200C2C2×#333×C15111yescharacteristic
201C2#1549×C15112yes—
202C2#1555×C15111yescharacteristic
203C2#1821×C15111yescharacteristic
204C2#1824×C15112yes—
subgroupG/H
center, socleC23×C151C2×C22⋊C4
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC24×C151C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1296×C151C2semidirect
102. #8725C151direct (N × H)
103. C151#8725direct (N × H)
106. #1296C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#384×C1512
#1797×C1512
#1296×C1512
#8725151