Finite Group Databasebeta

← #22612056

Subgroups — #22612056

Order 9344.

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×Dic584C211yesmaximal, characteristic, complemented
2#17988862C212yesmaximal
3#17988417C211yesmaximal, characteristic, complemented
4#17988404C212yesmaximal, complemented
5#504×C73C211yesmaximal, characteristic
6#14556621—22no—
7C2×Dic292C2212yes—
8Dic584—21no—
9Dic584—21no—
10#14556527C2212yes—
11#14556509—22no—
12#131×C73C2211yescharacteristic
13M32×C73—21no—
14M32×C73C2211yescharacteristic
15C2×C16×C73—21no—
16C2×C16×C73C2211yescharacteristic
17C2×Dic146—22no—
18Dic292—22no—
19Dic292—22no—
20#11924018—42no—
21#11924016—42no—
22#11924012—22no—
23#41×C73D411yescharacteristic
24M16×C73—21no—
25M16×C73D411yescharacteristic
26C2×C8×C73—21no—
27C2×C8×C73C2311yescharacteristic
28C16×C73—21no—
29C16×C73D411yescharacteristic
30C16×C73D411yescharacteristic
31Q8×C73D811yescharacteristic
32D4×C73—21no—
33D4×C73D811yescharacteristic
34C2×C4×C73—21no—
35C2×C4×C73C2×D411yescharacteristic
36C2×Dic73—42no—
37Dic146—42no—
38Dic146—42no—
39C8×C73—21no—
40C8×C73C2×D411yescharacteristic
41C8×C73#4111yescharacteristic
42#10596831—42no—
43C22×C73—21no—
44C22×C73#13511yescharacteristic
45C4×C73—21no—
46C4×C73#12111yescharacteristic
47C4×C73C2×D811yescharacteristic
48Dic73—82no—
49C2×C73—21no—
50C2×C73—41no—
51C2×C73#46611yescharacteristic
52#2222—731nomaximal, Sylow
53C73#222211yescharacteristic, complemented, Sylow
54C2×Q32—731no—
55#504D7311yescharacteristic
56#473—732no—
57#368—731no—
58#362—732no—
59#137—1462no—
60C2×Q16—732no—
61#131C2×D7311yescharacteristic
62Q32—1461no—
63Q32—1461no—
64M32—21no—
65M32C2×D7311yescharacteristic
66C2×C16—21no—
67C2×C16C2×D7311yescharacteristic
68#108—732no—
69#101—1462no—
70#41D29211yescharacteristic
71C2×Q8—1462no—
72Q16—2922no—
73Q16—1462no—
74Q16—1462no—
75SD16—2922no—
76M16—21no—
77M16—1462no—
78M16D29211yescharacteristic
79C2×C8—21no—
80C2×C8C22×D7311yescharacteristic
81C16—21no—
82C16C22⋊D7311yescharacteristic
83C16C22⋊D7311yescharacteristic
84Q8—2922no—
85Q8—2922no—
86Q8D58411yescharacteristic
87D4—21no—
88D4D58411yescharacteristic
89C2×C4—21no—
90C2×C4—2922no—
91C2×C4C2×D29211yescharacteristic
92C8—21no—
93C8—2922no—
94C8C2×C22⋊D7311yescharacteristic
95C8#1192402811yescharacteristic
96C22—21no—
97C22#1455661311yescharacteristic
98C4—21no—
99C4—5842no—
100C4#1455656511yescharacteristic
101C4C2×D58411yescharacteristic
102C2—21no—
103C2—41no—
104C2#1798882311yescharacteristic
subgroupG/H
centerC2#17988823
commutatorC2×C8×C73C23
FrattiniC2×C8C22×D73
Fitting#504×C73C2
socleC2×C73#466
hypercenter#504D73
hypocenterC73#2222
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #504

Complements

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

NH ≅ G/Ntype
1. C2×Dic584C2semidirect
3. #17988417C2semidirect
4. #17988404C2semidirect
53. C73#2222semidirect