Finite Group Databasebeta

← #2078×C151 #34065410

Subgroups — #2078×C151 #34065410

Order 19328.

198 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 76 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
2#417×C151C212yesmaximal
3#408×C151C211yesmaximal, characteristic
4#343×C151C212yesmaximal, complemented
5#341×C151C211yesmaximal, characteristic, complemented
6C2×#41×C151C2211yescharacteristic
7C2×M16×C151C2212yes—
8C2×M16×C151C2211yescharacteristic
9C22×C8×C151C2211yescharacteristic
10C2×C4⋊C4×C151C2212yes—
11#107×C151—22no—
12#103×C151—22no—
13#102×C151—22no—
14C22⋊C8×C151—22no—
15#41×C151—22no—
16#41×C151—22no—
17C2×Q8×C151D411yescharacteristic
18C2×D4×C151—21no—
19C2×D4×C151D411yescharacteristic
20C22×C4×C151—21no—
21C22×C4×C151—22no—
22C22×C4×C151C2311yescharacteristic
23M16×C151—22no—
24M16×C151—22no—
25M16×C151—22no—
26C2×C8×C151—22no—
27C2×C8×C151—21no—
28C2×C8×C151—22no—
29C2×C8×C151D412yes—
30C4⋊C4×C151—22no—
31C4⋊C4×C151—22no—
32C23×C151—21no—
33C23×C151#4111yescharacteristic
34Q8×C151—22no—
35D4×C151—22no—
36D4×C151—42no—
37C2×C4×C151—21no—
38C2×C4×C151—41no—
39C2×C4×C151—41no—
40C2×C4×C151—42no—
41C2×C4×C151—82no—
42C2×C4×C151C2×D411yescharacteristic
43C2×C4×C151C2×D411yescharacteristic
44C2×C4×C151#4112yes—
45C2×C4×C151#4112yes—
46C8×C151—22no—
47C8×C151—42no—
48C8×C151—41no—
49C22×C151—21no—
50C22×C151—21no—
51C22×C151—41no—
52C22×C151—41no—
53C22×C151—41no—
54C22×C151#12111yescharacteristic
55C22×C151#12612yes—
56C4×C151—41no—
57C4×C151—82no—
58C4×C151#12311yescharacteristic
59C4×C151#12312yes—
60C4×C151#12411yescharacteristic
61C2×C151—22no—
62C2×C151—81no—
63C2×C151#39711yescharacteristic
64C2×C151#47211yescharacteristic
65C2×C151#47311yescharacteristic
66C151#207811yescharacteristic, direct product factor, Sylow
67#2078C15111yesmaximal, characteristic, direct product factor, Sylow
68C2×#107C2×C15111yescharacteristic, complemented
69#417C2×C15112yes—
70#408C2×C15111yescharacteristic
71#343C2×C15112yescomplemented
72#341C2×C15111yescharacteristic, complemented
73C2×#41C22×C15111yescharacteristic
74C2×M16C22×C15112yes—
75C2×M16C22×C15111yescharacteristic
76C22×C8C22×C15111yescharacteristic
77C2×C4⋊C4C22×C15112yes—
78#107—22no—
79#103—22no—
80#102—22no—
81C22⋊C8—22no—
82#41—22no—
83#41—22no—
84C2×Q8D4×C15111yescharacteristic
85C2×D4—21no—
86C2×D4D4×C15111yescharacteristic
87C22×C4—21no—
88C22×C4—22no—
89C22×C4C23×C15111yescharacteristic
90M16—22no—
91M16—22no—
92M16—22no—
93C2×C8—22no—
94C2×C8—21no—
95C2×C8—22no—
96C2×C8D4×C15112yes—
97C4⋊C4—22no—
98C4⋊C4—22no—
99C23—21no—
100C23#41×C15111yescharacteristic
101Q8—22no—
102D4—22no—
103D4—42no—
104C2×C4—21no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—42no—
108C2×C4—82no—
109C2×C4C2×D4×C15111yescharacteristic
110C2×C4C2×D4×C15111yescharacteristic
111C2×C4#41×C15112yes—
112C2×C4#41×C15112yes—
113C8—22no—
114C8—42no—
115C8—41no—
116C22—21no—
117C22—21no—
118C22—41no—
119C22—41no—
120C22—41no—
121C22#121×C15111yescharacteristic
122C22#126×C15112yes—
123C4—41no—
124C4—82no—
125C4#123×C15111yescharacteristic
126C4#123×C15112yes—
127C4#124×C15111yescharacteristic
128C2—22no—
129C2—81no—
130C2#397×C15111yescharacteristic
131C2#472×C15111yescharacteristic
132C2#473×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#121
commutator, Frattini, cosocleC22×C4C23×C151
prime radicalC2×#41×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#107×C151C2semidirect
4. #343×C151C2semidirect
5. #341×C151C2semidirect
66. C151#2078direct (N × H)
67. #2078C151direct (N × H)
68. C2×#107C2×C151semidirect
71. #343C2×C151semidirect
72. #341C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#107×C1512
#417×C1512
#408×C1512
#343×C1512
#341×C1512
#2078151