Finite Group Databasebeta

← #34067844

Subgroups — #34067844

Order 19328.

254 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 67 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#23752763C211yesmaximal, characteristic
2#23752234C212yesmaximal, complemented
3#23751961C211yesmaximal, characteristic, complemented
4#23751955C212yesmaximal, complemented
5#333×C151C211yesmaximal, characteristic, complemented
6C2×#14559005C412yes—
7C2×#14558987—22no—
8#18012736C2211yescharacteristic
9#18012728C412yes—
10#18012714—22no—
11#18012701—22no—
12C42×D151C2211yescharacteristic
13C4⋊(C151⋊C8)C2212yes—
14Dic151⋊C8—22no—
15C4⋊Q8×C151C2211yescharacteristic
16C4⋊C8×C151C2212yes—
17#14559005—44no—
18C2×D604—22no—
19C2×D604—22no—
20C2×D604C2×C412yes—
21C2×C4×D151—22no—
22C2×C4×D151C2×C411yescharacteristic
23C2×C4×D151D412yes—
24#14558987—44no—
25C2×C151⋊C8—22no—
26(C2×D151)⋊C4—24no—
27C4×Dic151C2×C411yescharacteristic
28C4×Dic151D412yes—
29C2×Q8×C151C2×C412yes—
30C2×C8×C151—22no—
31C4⋊C4×C151—22no—
32C42×C151C2311yescharacteristic
33C22×D151—22no—
34C22×D151C22⋊C411yescharacteristic
35D604—42no—
36D604—44no—
37D604—42no—
38D604—42no—
39C2×Dic151C22⋊C412yes—
40C2×Dic151C22⋊C411yescharacteristic
41C4×D151—22no—
42C4×D151—22no—
43C4×D151—22no—
44C4×D151—44no—
45C151⋊C8—42no—
46Q8×C151—42no—
47C2×C4×C151—22no—
48C2×C4×C151C22×C411yescharacteristic
49C2×C4×C151C2×D412yes—
50C8×C151—42no—
51C22×C151C2×C22⋊C411yescharacteristic
52C2×D151—21no—
53C2×D151—22no—
54C2×D151—42no—
55C2×D151—44no—
56C4×C151—21no—
57C4×C151—42no—
58C4×C151AGL(1,ℤ/8)12yes—
59C4×C151#13712yes—
60Dic151—22no—
61Dic151#10012yes—
62C2×C151C2×#10011yescharacteristic
63C2×C151#41712yes—
64D151—41no—
65D151—82no—
66C151#156011yescharacteristic, complemented, Sylow
67#1560—1511nomaximal, Sylow
68#532—1511no—
69#423—1512no—
70#333—1511no—
71#333D15111yescharacteristic, complemented
72#331—1512no—
73C2×#41—1512no—
74C2×M16—3022no—
75C4⋊Q8C2×D15111yescharacteristic
76#127—1511no—
77#124—1512no—
78#121—3022no—
79C4×D4—3022no—
80C2×C42—1511no—
81C4⋊C8—3022no—
82C4⋊C8—1512no—
83C4⋊C8C2×D15112yes—
84#41—6044no—
85C2×Q8C4×D15112yes—
86C2×D4—3022no—
87C2×D4—3022no—
88C2×D4—1512no—
89C22×C4—3022no—
90C22×C4—1511no—
91C22×C4—1512no—
92M16—6044no—
93C2×C8—22no—
94C2×C8—3022no—
95C4⋊C4—22no—
96C22⋊C4—3024no—
97C42—1511no—
98C42—1512no—
99C42C22×D15111yescharacteristic
100C23—3022no—
101C23—1511no—
102Q8—42no—
103D4—6042no—
104D4—6044no—
105D4—6042no—
106D4—6042no—
107C2×C4—22no—
108C2×C4—3022no—
109C2×C4—3022no—
110C2×C4—3022no—
111C2×C4—6044no—
112C2×C4—1512no—
113C2×C4—1511no—
114C2×C4C2×C4×D15111yescharacteristic
115C2×C4D4×D15112yes—
116C8—42no—
117C8—6042no—
118C22—3022no—
119C22—3021no—
120C22—6044no—
121C22—6042no—
122C22C22⋊C4×D15111yescharacteristic
123C4—21no—
124C4—42no—
125C4—3022no—
126C4—1512no—
127C4#1801276612yes—
128C4#1801277112yes—
129C2—6041no—
130C2—12082no—
131C2#100×D15111yescharacteristic
132C2#2375221212yes—
subgroupG/H
centerC22C22⋊C4×D151
commutatorC2×C4×C151C22×C4
FrattiniC42C22×D151
Fitting#333×C151C2
socleC22×C151C2×C22⋊C4
prime radical#23752763C2
cosocleC42×C151C23
hypercenter#333D151
hypocenterC151#1560
LCSG ▷ C2×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #23752234C2semidirect
3. #23751961C2semidirect
4. #23751955C2semidirect
5. #333×C151C2semidirect
66. C151#1560semidirect
71. #333D151semidirect

Maximal subgroups

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

subgroupindex
#237527632
#237522342
#237519612
#237519552
#333×C1512
#1560151