Finite Group Databasebeta

← #3186×C151 #34066518

Subgroups — #3186×C151 #34066518

Order 19328.

520 conjugacy classes of subgroups; only the 188 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 188 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×#121×C151C212yesmaximal, complemented
2#480×C151C214yesmaximal, complemented
3#466×C151C214yesmaximal, complemented
4#447×C151C214yesmaximal, complemented
5C2×C22⋊C8×C151C211yesmaximal, characteristic, complemented
6C22×D4×C151—22no—
7C22×D4×C151C2212yescomplemented
8C23×C4×C151C2211yescharacteristic
9C2×D8×C151C2214yescomplemented
10C22×C8×C151C2212yescomplemented
11#121×C151—22no—
12#121×C151—22no—
13#121×C151C2214yes—
14#121×C151C2214yescomplemented
15C2×C4⋊C4×C151C2212yescomplemented
16C2×C22⋊C4×C151—22no—
17#107×C151C2214yescomplemented
18#102×C151C2218yescomplemented
19C22⋊C8×C151C2214yescomplemented
20C24×C151—22no—
21C24×C151D411yescharacteristic
22C2×D4×C151—24no—
23C2×D4×C151—24no—
24C2×D4×C151—22no—
25C2×D4×C151—44no—
26C2×D4×C151—48no—
27C2×D4×C151C2314yes—
28C22×C4×C151—22no—
29C22×C4×C151—42no—
30C22×C4×C151D412yes—
31C22×C4×C151D411yescharacteristic
32C22×C4×C151C2312yes—
33C22×C4×C151C2311yescharacteristic
34D8×C151—44no—
35C2×C8×C151—42no—
36C2×C8×C151C2314yes—
37C4⋊C4×C151—22no—
38C4⋊C4×C151C2314yes—
39C22⋊C4×C151—24no—
40C22⋊C4×C151—24no—
41C23×C151—24no—
42C23×C151—41no—
43C23×C151—41no—
44C23×C151—44no—
45C23×C151—44no—
46C23×C151—44no—
47C23×C151D814yescomplemented
48C23×C151C2×D412yes—
49C23×C151C2×D411yescharacteristic
50D4×C151—28no—
51D4×C151—44no—
52D4×C151—48no—
53D4×C151—48no—
54C2×C4×C151—22no—
55C2×C4×C151—24no—
56C2×C4×C151—24no—
57C2×C4×C151—42no—
58C2×C4×C151—41no—
59C2×C4×C151—44no—
60C2×C4×C151C2×D411yescharacteristic
61C2×C4×C151C2×D412yes—
62C2×C4×C151C2411yescharacteristic
63C8×C151—24no—
64C22×C151—22no—
65C22×C151—21no—
66C22×C151—22no—
67C22×C151—21no—
68C22×C151—44no—
69C22×C151—44no—
70C22×C151—44no—
71C22×C151—44no—
72C22×C151—88no—
73C22×C151C2×D814yes—
74C22×C151C2×D812yes—
75C22×C151C22×D411yescharacteristic
76C4×C151—21no—
77C4×C151—22no—
78C4×C151—44no—
79C4×C151H(5,𝔽2)12yes—
80C2×C151—24no—
81C2×C151—22no—
82C2×C151—84no—
83C2×C151#53411yescharacteristic
84C2×C151C22×D811yescharacteristic
85C2×C151#57511yescharacteristic
86C151#318611yescharacteristic, direct product factor, Sylow
87#3186C15111yesmaximal, characteristic, direct product factor, Sylow
88C2×#121C2×C15112yescomplemented
89#480C2×C15114yescomplemented
90#466C2×C15114yescomplemented
91#447C2×C15114yescomplemented
92C2×C22⋊C8C2×C15111yescharacteristic, complemented
93C22×D4—22no—
94C22×D4C22×C15112yescomplemented
95C23×C4C22×C15111yescharacteristic
96C2×D8C22×C15114yescomplemented
97C22×C8C22×C15112yescomplemented
98#121—22no—
99#121—22no—
100#121C22×C15114yes—
101#121C22×C15114yescomplemented
102C2×C4⋊C4C22×C15112yescomplemented
103C2×C22⋊C4—22no—
104#107C22×C15114yescomplemented
105#102C22×C15118yescomplemented
106C22⋊C8C22×C15114yescomplemented
107C24—22no—
108C24D4×C15111yescharacteristic
109C2×D4—24no—
110C2×D4—24no—
111C2×D4—22no—
112C2×D4—44no—
113C2×D4—48no—
114C2×D4C23×C15114yes—
115C22×C4—22no—
116C22×C4—42no—
117C22×C4D4×C15112yes—
118C22×C4D4×C15111yescharacteristic
119C22×C4C23×C15112yes—
120C22×C4C23×C15111yescharacteristic
121D8—44no—
122C2×C8—42no—
123C2×C8C23×C15114yes—
124C4⋊C4—22no—
125C4⋊C4C23×C15114yes—
126C22⋊C4—24no—
127C22⋊C4—24no—
128C23—24no—
129C23—41no—
130C23—41no—
131C23—44no—
132C23—44no—
133C23—44no—
134C23D8×C15114yescomplemented
135C23C2×D4×C15112yes—
136C23C2×D4×C15111yescharacteristic
137D4—28no—
138D4—44no—
139D4—48no—
140D4—48no—
141C2×C4—22no—
142C2×C4—24no—
143C2×C4—24no—
144C2×C4—41no—
145C2×C4—42no—
146C2×C4—44no—
147C2×C4C2×D4×C15111yescharacteristic
148C2×C4C2×D4×C15112yes—
149C2×C4C24×C15111yescharacteristic
150C8—24no—
151C22—22no—
152C22—21no—
153C22—22no—
154C22—21no—
155C22—44no—
156C22—44no—
157C22—44no—
158C22—44no—
159C22—88no—
160C22C2×D8×C15114yes—
161C22C2×D8×C15112yes—
162C22C22×D4×C15111yescharacteristic
163C4—22no—
164C4—21no—
165C4—44no—
166C4H(5,𝔽2)×C15112yes—
167C2—24no—
168C2—22no—
169C2—84no—
170C2#534×C15111yescharacteristic
171C2C22×D8×C15111yescharacteristic
172C2#575×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C22×D4
commutator, Frattini, cosocleC2×C4C24×C151
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#121×C151C2semidirect
2. #480×C151C2semidirect
3. #466×C151C2semidirect
4. #447×C151C2semidirect
5. C2×C22⋊C8×C151C2semidirect
7. C22×D4×C151C22semidirect
9. C2×D8×C151C22semidirect
10. C22×C8×C151C22semidirect
14. #121×C151C22semidirect
15. C2×C4⋊C4×C151C22semidirect
17. #107×C151C22semidirect
18. #102×C151C22semidirect
19. C22⋊C8×C151C22semidirect
47. C23×C151D8semidirect
86. C151#3186direct (N × H)
87. #3186C151direct (N × H)
88. C2×#121C2×C151semidirect
89. #480C2×C151semidirect
90. #466C2×C151semidirect
91. #447C2×C151semidirect
92. C2×C22⋊C8C2×C151semidirect
94. C22×D4C22×C151semidirect
96. C2×D8C22×C151semidirect
97. C22×C8C22×C151semidirect
101. #121C22×C151semidirect
102. C2×C4⋊C4C22×C151semidirect
104. #107C22×C151semidirect
105. #102C22×C151semidirect
106. C22⋊C8C22×C151semidirect
134. C23D8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#121×C1512
#480×C1512
#466×C1512
#447×C1512
C2×C22⋊C8×C1512
#3186151