Finite Group Databasebeta

← #2075×C151 #34065407

Subgroups — #2075×C151 #34065407

Order 19328.

256 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 96 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×#107×C151C211yesmaximal, characteristic, complemented
2C2×C22⋊C8×C151C211yesmaximal, characteristic
3#380×C151C212yesmaximal
4#340×C151C211yesmaximal, characteristic, complemented
5#340×C151C212yesmaximal, complemented
6C23×C4×C151C2211yescharacteristic
7C22×C8×C151C2211yescharacteristic
8C22×C8×C151C2211yescharacteristic
9C2×C4⋊C4×C151C2212yes—
10C2×C4⋊C4×C151C2212yes—
11C2×C22⋊C4×C151—22no—
12#107×C151—22no—
13C22⋊C8×C151—22no—
14#95×C151—22no—
15C24×C151D411yescharacteristic
16C22×C4×C151—21no—
17C22×C4×C151—21no—
18C22×C4×C151—22no—
19C22×C4×C151—22no—
20C22×C4×C151—22no—
21C22×C4×C151—22no—
22C22×C4×C151D411yescharacteristic
23C22×C4×C151C2311yescharacteristic
24C2×C8×C151—22no—
25C2×C8×C151—21no—
26C2×C8×C151—22no—
27C2×C8×C151D412yes—
28C4⋊C4×C151—22no—
29C4⋊C4×C151—22no—
30C4⋊C4×C151—22no—
31C4⋊C4×C151—22no—
32C22⋊C4×C151—44no—
33C23×C151—21no—
34C23×C151—22no—
35C23×C151—21no—
36C23×C151—22no—
37C23×C151D812yes—
38C23×C151C2×D411yescharacteristic
39C2×C4×C151—21no—
40C2×C4×C151—22no—
41C2×C4×C151—41no—
42C2×C4×C151—41no—
43C2×C4×C151—42no—
44C2×C4×C151—42no—
45C2×C4×C151—42no—
46C2×C4×C151—42no—
47C2×C4×C151—42no—
48C2×C4×C151—42no—
49C2×C4×C151—42no—
50C2×C4×C151C2×D411yescharacteristic
51C2×C4×C151#4112yes—
52C2×C4×C151#4112yes—
53C2×C4×C151#4111yescharacteristic
54C8×C151—22no—
55C8×C151—41no—
56C22×C151—22no—
57C22×C151—24no—
58C22×C151—41no—
59C22×C151—41no—
60C22×C151—42no—
61C22×C151#12111yescharacteristic
62C22×C151#12312yes—
63C22×C151C2×D811yescharacteristic
64C22×C151#13511yescharacteristic
65C22×C151#13712yes—
66C4×C151—41no—
67C4×C151—82no—
68C4×C151—82no—
69C4×C151#12311yescharacteristic
70C4×C151#12411yescharacteristic
71C4×C151#12612yes—
72C2×C151—42no—
73C2×C151#39711yescharacteristic
74C2×C151#46611yescharacteristic
75C2×C151#47011yescharacteristic
76C2×C151#48012yes—
77C2×C151#48512yes—
78C151#207511yescharacteristic, direct product factor, Sylow
79#2075C15111yesmaximal, characteristic, direct product factor, Sylow
80C2×#107C2×C15111yescharacteristic, complemented
81C2×C22⋊C8C2×C15111yescharacteristic
82#380C2×C15112yes—
83#340C2×C15111yescharacteristic, complemented
84#340C2×C15112yescomplemented
85C23×C4C22×C15111yescharacteristic
86C22×C8C22×C15111yescharacteristic
87C22×C8C22×C15111yescharacteristic
88C2×C4⋊C4C22×C15112yes—
89C2×C4⋊C4C22×C15112yes—
90C2×C22⋊C4—22no—
91#107—22no—
92C22⋊C8—22no—
93#95—22no—
94C24D4×C15111yescharacteristic
95C22×C4—21no—
96C22×C4—22no—
97C22×C4—22no—
98C22×C4—21no—
99C22×C4—22no—
100C22×C4—22no—
101C22×C4D4×C15111yescharacteristic
102C22×C4C23×C15111yescharacteristic
103C2×C8—22no—
104C2×C8—22no—
105C2×C8—21no—
106C2×C8D4×C15112yes—
107C4⋊C4—22no—
108C4⋊C4—22no—
109C4⋊C4—22no—
110C4⋊C4—22no—
111C22⋊C4—44no—
112C23—21no—
113C23—22no—
114C23—21no—
115C23—22no—
116C23D8×C15112yes—
117C23C2×D4×C15111yescharacteristic
118C2×C4—21no—
119C2×C4—22no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—42no—
123C2×C4—42no—
124C2×C4—42no—
125C2×C4—42no—
126C2×C4—42no—
127C2×C4—42no—
128C2×C4—42no—
129C2×C4C2×D4×C15111yescharacteristic
130C2×C4#41×C15112yes—
131C2×C4#41×C15112yes—
132C2×C4#41×C15111yescharacteristic
133C8—22no—
134C8—41no—
135C22—22no—
136C22—24no—
137C22—41no—
138C22—41no—
139C22—42no—
140C22#121×C15111yescharacteristic
141C22#123×C15112yes—
142C22C2×D8×C15111yescharacteristic
143C22#135×C15111yescharacteristic
144C22#137×C15112yes—
145C4—41no—
146C4—82no—
147C4—82no—
148C4#123×C15111yescharacteristic
149C4#124×C15111yescharacteristic
150C4#126×C15112yes—
151C2—42no—
152C2#397×C15111yescharacteristic
153C2#466×C15111yescharacteristic
154C2#470×C15111yescharacteristic
155C2#480×C15112yes—
156C2#485×C15112yes—
subgroupG/H
center, socleC23×C151C2×D4
commutator, Frattini, cosocleC22×C4C23×C151
prime radicalC24×C151D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#107×C151C2semidirect
4. #340×C151C2semidirect
5. #340×C151C2semidirect
78. C151#2075direct (N × H)
79. #2075C151direct (N × H)
80. C2×#107C2×C151semidirect
83. #340C2×C151semidirect
84. #340C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#107×C1512
C2×C22⋊C8×C1512
#380×C1512
#340×C1512
#2075151