Finite Group Databasebeta

← #22611813

Subgroups — #22611813

Order 9344.

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

normal subgroups only

This group has 146 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#17989019C211yesmaximal, characteristic
2#17988705C212yesmaximal, complemented
3#17988417C211yesmaximal, characteristic, complemented
4#17988395C212yesmaximal, complemented
5C4×C16×C73C211yesmaximal, characteristic, complemented
6#14556613C2212yes—
7#14556597—22no—
8Dic584C411yescharacteristic, complemented
9#14556536C412yescomplemented
10D1168C411yescharacteristic, complemented
11#14556527C2212yes—
12#14556519—22no—
13C2×C16×C73C2211yescharacteristic
14C2×C16×C73C2211yescharacteristic
15C4×C8×C73C2211yescharacteristic
16#11924028—22no—
17Dic292C2×C412yes—
18#11924017—22no—
19D584C2×C412yes—
20#11924012—22no—
21#11924011—42no—
22C8×D73—42no—
23C2×C8×C73D411yescharacteristic
24C2×C8×C73C2311yescharacteristic
25C42×C73D411yescharacteristic
26C16×C73—21no—
27C16×C73C2×C411yescharacteristic
28C16×C73C2×C411yescharacteristic
29C2×C4×C73—21no—
30C2×C4×C73C2×D411yescharacteristic
31C22⋊D73—42no—
32D292—22no—
33C4×D73—42no—
34Dic146—22no—
35C8×C73D811yescharacteristic
36C8×C73D811yescharacteristic
37C8×C73C22×C411yescharacteristic
38C8×C73#4111yescharacteristic
39#10596831—42no—
40C22×C73#13511yescharacteristic
41C2×D73—42no—
42C4×C73—22no—
43C4×C73C4×D411yescharacteristic
44C4×C73C2×D811yescharacteristic
45Dic73—42no—
46C2×C73—21no—
47C2×C73C4×D811yescharacteristic
48D73—82no—
49#2178—731nomaximal, Sylow
50C73#217811yescharacteristic, complemented, Sylow
51#508—731no—
52#443—732no—
53#368—731no—
54#359—732no—
55C4×C16D7311yescharacteristic, complemented
56#135—732no—
57#131—1462no—
58Q32—731no—
59SD32—732no—
60D16—731no—
61C2×C16C2×D7311yescharacteristic
62C2×C16C2×D7311yescharacteristic
63#108—732no—
64#104—1462no—
65C4×C8C2×D7311yescharacteristic
66#41—1462no—
67Q16—732no—
68SD16—1462no—
69D8—732no—
70M16—2922no—
71M16—1462no—
72C2×C8—2922no—
73C2×C8D29211yescharacteristic
74C2×C8C22×D7311yescharacteristic
75C42D29211yescharacteristic
76C16—21no—
77C16C4×D7311yescharacteristic
78C16C4×D7311yescharacteristic
79Q8—1462no—
80D4—2922no—
81D4—1462no—
82C2×C4—21no—
83C2×C4—2922no—
84C2×C4C2×D29211yescharacteristic
85C8—2922no—
86C8D58411yescharacteristic
87C8D58411yescharacteristic
88C8C2×C4×D7311yescharacteristic
89C8#1192402811yescharacteristic
90C22—2922no—
91C22#1455661311yescharacteristic
92C4—22no—
93C4—2922no—
94C4C4×D29211yescharacteristic
95C4C2×D58411yescharacteristic
96C2—21no—
97C2—5842no—
98C2C4×D58411yescharacteristic
subgroupG/H
centerC8D584
commutatorC8×C73C22×C4
FrattiniC2×C8C22×D73
FittingC4×C16×C73C2
socleC2×C73C4×D8
hypercenterC4×C16D73
hypocenterC73#2178
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C8 ◁ C2×C8 ◁ C4×C8 ◁ C4×C16

Complements

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

NH ≅ G/Ntype
2. #17988705C2semidirect
3. #17988417C2semidirect
4. #17988395C2semidirect
5. C4×C16×C73C2semidirect
8. Dic584C4semidirect
9. #14556536C4semidirect
10. D1168C4semidirect
50. C73#2178semidirect
55. C4×C16D73semidirect