Finite Group Databasebeta

← #2129×C151 #34065461

Subgroups — #2129×C151 #34065461

Order 19328.

238 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 84 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#536×C151C211yesmaximal, characteristic
2#410×C151C212yesmaximal
3#354×C151C214yesmaximal, complemented
4C2×#41×C151C2211yescharacteristic
5C22×Q8×C151C411yescharacteristic, complemented
6C4⋊Q8×C151C412yescomplemented
7#124×C151C2212yes—
8#123×C151—22no—
9C22⋊Q8×C151—22no—
10#117×C151—22no—
11#117×C151C411yescharacteristic, complemented
12#99×C151—22no—
13#99×C151C2214yes—
14#41×C151—42no—
15C2×Q8×C151—21no—
16C2×Q8×C151—42no—
17C2×Q8×C151C2×C412yes—
18C2×Q8×C151C2×C411yescharacteristic
19C2×D4×C151D412yes—
20C2×D4×C151C2311yescharacteristic
21C22×C4×C151—21no—
22C22×C4×C151C2×C411yescharacteristic
23C22×C4×C151D412yes—
24C4⋊C4×C151—24no—
25C4⋊C4×C151—21no—
26C4⋊C4×C151—42no—
27C22⋊C4×C151—21no—
28C22⋊C4×C151—24no—
29C22⋊C4×C151—24no—
30C42×C151—42no—
31C42×C151C2×C412yes—
32C23×C151C22⋊C411yescharacteristic
33C23×C151C2×D412yes—
34Q8×C151—41no—
35Q8×C151—42no—
36Q8×C151—42no—
37D4×C151—42no—
38D4×C151—41no—
39C2×C4×C151—22no—
40C2×C4×C151—22no—
41C2×C4×C151—22no—
42C2×C4×C151—22no—
43C2×C4×C151—22no—
44C2×C4×C151—42no—
45C2×C4×C151—44no—
46C2×C4×C151C22⋊C412yes—
47C2×C4×C151C22⋊C411yescharacteristic
48C2×C4×C151C22×C411yescharacteristic
49C22×C151—21no—
50C22×C151—22no—
51C22×C151—41no—
52C22×C151—42no—
53C22×C151C2×C22⋊C411yescharacteristic
54C4×C151—22no—
55C4×C151—21no—
56C4×C151—42no—
57C4×C151—42no—
58C4×C151—84no—
59C4×C151#9912yes—
60C2×C151—21no—
61C2×C151—42no—
62C2×C151—41no—
63C2×C151C2×#9911yescharacteristic
64C151#212911yescharacteristic, direct product factor, Sylow
65#2129C15111yesmaximal, characteristic, direct product factor, Sylow
66#536C2×C15111yescharacteristic
67#410C2×C15112yes—
68#354C2×C15114yescomplemented
69C2×#41C22×C15111yescharacteristic
70C22×Q8C4×C15111yescharacteristic, complemented
71C4⋊Q8C4×C15112yescomplemented
72#124C22×C15112yes—
73#123—22no—
74C22⋊Q8—22no—
75#117—22no—
76#117C4×C15111yescharacteristic, complemented
77#99—22no—
78#99C22×C15114yes—
79#41—42no—
80C2×Q8—21no—
81C2×Q8—42no—
82C2×Q8C2×C4×C15112yes—
83C2×Q8C2×C4×C15111yescharacteristic
84C2×D4D4×C15112yes—
85C2×D4C23×C15111yescharacteristic
86C22×C4—21no—
87C22×C4C2×C4×C15111yescharacteristic
88C22×C4D4×C15112yes—
89C4⋊C4—21no—
90C4⋊C4—24no—
91C4⋊C4—42no—
92C22⋊C4—21no—
93C22⋊C4—24no—
94C22⋊C4—24no—
95C42—42no—
96C42C2×C4×C15112yes—
97C23C22⋊C4×C15111yescharacteristic
98C23C2×D4×C15112yes—
99Q8—41no—
100Q8—42no—
101Q8—42no—
102D4—42no—
103D4—41no—
104C2×C4—22no—
105C2×C4—22no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—22no—
109C2×C4—42no—
110C2×C4—44no—
111C2×C4C22⋊C4×C15112yes—
112C2×C4C22⋊C4×C15111yescharacteristic
113C2×C4C22×C4×C15111yescharacteristic
114C22—21no—
115C22—22no—
116C22—41no—
117C22—42no—
118C22C2×C22⋊C4×C15111yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—42no—
123C4—84no—
124C4#99×C15112yes—
125C2—21no—
126C2—42no—
127C2—41no—
128C2C2×#99×C15111yescharacteristic
subgroupG/H
center, socleC2×C151C2×#99
commutatorC2×C4C22×C4×C151
Frattini, cosocleC2×D4C23×C151
prime radicalC2×#41×C151C22
LCSG ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C151 ◁ C2×C4×C151 ◁ C2×#41×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #354×C151C2semidirect
5. C22×Q8×C151C4semidirect
6. C4⋊Q8×C151C4semidirect
11. #117×C151C4semidirect
64. C151#2129direct (N × H)
65. #2129C151direct (N × H)
68. #354C2×C151semidirect
70. C22×Q8C4×C151semidirect
71. C4⋊Q8C4×C151semidirect
76. #117C4×C151semidirect

Maximal subgroups

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

subgroupindex
#536×C1512
#410×C1512
#354×C1512
#2129151