Finite Group Databasebeta

← #34068193

Subgroups — #34068193

Order 19328.

240 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 57 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#23752586C211yesmaximal, characteristic, complemented
2#23752407C212yesmaximal, complemented
3#23751961C211yesmaximal, characteristic, complemented
4D4⋊(C151⋊C8)C212yesmaximal, complemented
5#555×C151C211yesmaximal, characteristic, complemented
6C2×#14558991—22no—
7C2×#14558989—22no—
8#18012736C2211yescharacteristic
9C4⋊(C151⋊C8)C2212yes—
10#18012659—22no—
11C4×C151⋊C8C2211yescharacteristic
12C4⋊Q8×C151C2211yescharacteristic
13#124×C151—22no—
14#121×C151—22no—
15C4×D4×C151C2212yes—
16#117×C151—22no—
17C2×D604—22no—
18C2×D604—21no—
19#14558991—44no—
20#14558989—44no—
21C2×C151⋊C8—21no—
22C2×C151⋊C8—22no—
23C2×Q8×C151D412yes—
24C2×D4×C151—22no—
25C2×D4×C151D412yes—
26C22×C4×C151—22no—
27C4⋊C4×C151—22no—
28C4⋊C4×C151D412yes—
29C22⋊C4×C151—24no—
30C22⋊C4×C151—22no—
31C42×C151—22no—
32C42×C151C2311yescharacteristic
33C22×D151—41no—
34D604—42no—
35D604—42no—
36D604—42no—
37C151⋊C8—22no—
38C151⋊C8—42no—
39C23×C151—22no—
40Q8×C151—42no—
41D4×C151—22no—
42D4×C151—22no—
43D4×C151—82no—
44C2×C4×C151—22no—
45C2×C4×C151—22no—
46C2×C4×C151—42no—
47C2×C4×C151—42no—
48C2×C4×C151C2×D411yescharacteristic
49C2×C4×C151C2×D412yes—
50C22×C151—42no—
51C22×C151—42no—
52C22×C151—42no—
53C22×C151#12011yescharacteristic
54C2×D151—82no—
55C2×D151—81no—
56C4×C151—21no—
57C4×C151—42no—
58C4×C151—42no—
59C4×C151#13512yes—
60C4×C151AGL(1,ℤ/8)12yes—
61C2×C151—82no—
62C2×C151#44912yes—
63C2×C151#45311yescharacteristic
64D151—161no—
65C151#162411yescharacteristic, complemented, Sylow
66#1624—1511nomaximal, Sylow
67#555D15111yescharacteristic, complemented
68#492—1511no—
69#459—1512no—
70#333—1511no—
71D4⋊C8—1512no—
72C2×SD16—3022no—
73C2×D8—3022no—
74C4⋊Q8C2×D15111yescharacteristic
75#127—1511no—
76#124—22no—
77#121—22no—
78C4×D4C2×D15112yes—
79#117—22no—
80C4⋊C8—1512no—
81#102—3022no—
82C4×C8—1511no—
83C2×Q8C22⋊D15112yes—
84C2×D4—22no—
85C2×D4—3022no—
86C2×D4—3021no—
87C2×D4C22⋊D15112yes—
88C22×C4—22no—
89SD16—6044no—
90D8—6044no—
91C2×C8—3021no—
92C2×C8—3022no—
93C4⋊C4—22no—
94C4⋊C4C22⋊D15112yes—
95C22⋊C4—24no—
96C22⋊C4—22no—
97C42—22no—
98C42C22×D15111yescharacteristic
99C23—22no—
100C23—6041no—
101Q8—42no—
102D4—22no—
103D4—22no—
104D4—82no—
105D4—6042no—
106D4—6042no—
107D4—6042no—
108C2×C4—22no—
109C2×C4—22no—
110C2×C4—42no—
111C2×C4—42no—
112C2×C4C2×C22⋊D15111yescharacteristic
113C2×C4C2×C22⋊D15112yes—
114C8—3022no—
115C8—6042no—
116C22—42no—
117C22—42no—
118C22—42no—
119C22—12082no—
120C22—12081no—
121C22#1801270811yescharacteristic
122C4—21no—
123C4—42no—
124C4—42no—
125C4#1801275912yes—
126C4#1801276412yes—
127C2—82no—
128C2—24161no—
129C2#2375235712yes—
130C2#2375238011yescharacteristic
subgroupG/H
centerC22#18012708
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#555×C151C2
socleC22×C151#120
hypercenter#555D151
hypocenterC151#1624
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #555

Complements

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

NH ≅ G/Ntype
1. #23752586C2semidirect
2. #23752407C2semidirect
3. #23751961C2semidirect
4. D4⋊(C151⋊C8)C2semidirect
5. #555×C151C2semidirect
65. C151#1624semidirect
67. #555D151semidirect

Maximal subgroups

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

subgroupindex
#237525862
#237524072
#237519612
D4⋊(C151⋊C8)2
#555×C1512
#1624151