Finite Group Databasebeta

← #34071235

Subgroups — #34071235

Order 19328.

140 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 49 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×Dic1208C211yesmaximal, characteristic, complemented
2#23752487C212yesmaximal
3#23752042C211yesmaximal, characteristic, complemented
4#23752029C212yesmaximal, complemented
5#504×C151C211yesmaximal, characteristic
6#18012769—22no—
7C2×Dic604C2212yes—
8Dic1208—21no—
9Dic1208—21no—
10#18012675C2212yes—
11#18012657—22no—
12#131×C151C2211yescharacteristic
13M32×C151—21no—
14M32×C151C2211yescharacteristic
15C2×C16×C151—21no—
16C2×C16×C151C2211yescharacteristic
17C2×Dic302—22no—
18Dic604—22no—
19Dic604—22no—
20#14558994—42no—
21#14558992—42no—
22#14558988—22no—
23#41×C151D411yescharacteristic
24M16×C151—21no—
25M16×C151D411yescharacteristic
26C2×C8×C151—21no—
27C2×C8×C151C2311yescharacteristic
28C16×C151—21no—
29C16×C151D411yescharacteristic
30C16×C151D411yescharacteristic
31Dic302—42no—
32Dic302—42no—
33C2×Dic151—42no—
34C151⋊C8—42no—
35Q8×C151D811yescharacteristic
36D4×C151—21no—
37D4×C151D811yescharacteristic
38C2×C4×C151—21no—
39C2×C4×C151C2×D411yescharacteristic
40C8×C151—21no—
41C8×C151C2×D411yescharacteristic
42C8×C151#4111yescharacteristic
43C22×C151—21no—
44C22×C151#13511yescharacteristic
45C4×C151—21no—
46C4×C151#12111yescharacteristic
47C4×C151C2×D811yescharacteristic
48Dic151—82no—
49C2×C151—21no—
50C2×C151—41no—
51C2×C151#46611yescharacteristic
52C151#222211yescharacteristic, complemented, Sylow
53#2222—1511nomaximal, Sylow
54C2×Q32—1511no—
55#504D15111yescharacteristic
56#473—1512no—
57#368—1511no—
58#362—1512no—
59#137—3022no—
60C2×Q16—1512no—
61#131C2×D15111yescharacteristic
62Q32—3021no—
63Q32—3021no—
64M32—21no—
65M32C2×D15111yescharacteristic
66C2×C16—21no—
67C2×C16C2×D15111yescharacteristic
68#108—1512no—
69#101—3022no—
70#41D60411yescharacteristic
71C2×Q8—3022no—
72Q16—3022no—
73Q16—3022no—
74Q16—6042no—
75SD16—6042no—
76M16—21no—
77M16—3022no—
78M16D60411yescharacteristic
79C2×C8—21no—
80C2×C8C22×D15111yescharacteristic
81C16—21no—
82C16C22⋊D15111yescharacteristic
83C16C22⋊D15111yescharacteristic
84Q8—6042no—
85Q8—6042no—
86Q8D120811yescharacteristic
87D4—21no—
88D4D120811yescharacteristic
89C2×C4—21no—
90C2×C4—6042no—
91C2×C4C2×D60411yescharacteristic
92C8—21no—
93C8—6042no—
94C8C2×C22⋊D15111yescharacteristic
95C8#1455900411yescharacteristic
96C22—21no—
97C22#1801276111yescharacteristic
98C4—21no—
99C4—12082no—
100C4#1801271311yescharacteristic
101C4C2×D120811yescharacteristic
102C2—21no—
103C2—41no—
104C2#2375244811yescharacteristic
subgroupG/H
centerC2#23752448
commutator, cosocleC2×C8×C151C23
FrattiniC2×C8C22×D151
Fitting#504×C151C2
socleC2×C151#466
prime radical#41×C151D4
hypercenter#504D151
hypocenterC151#2222
LCSG ▷ C2×C8×C151 ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #504

Complements

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

NH ≅ G/Ntype
1. C2×Dic1208C2semidirect
3. #23752042C2semidirect
4. #23752029C2semidirect
52. C151#2222semidirect

Maximal subgroups

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

subgroupindex
C2×Dic12082
#237524872
#237520422
#237520292
#504×C1512
#2222151