Finite Group Databasebeta

← #22625052

Subgroups — #22625052

Order 9344.

112 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 20 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#17989495C211yesmaximal, characteristic, complemented
2#17989442C211yesmaximal, characteristic, complemented
3#17988765C211yesmaximal, characteristic
4#14556652—21no—
5#14556646—21no—
6#14556621—21no—
7#14556578C2211yescharacteristic
8#14556518—21no—
9#14556508C411yescharacteristic
10H(5,𝔽2)×C73C411yescharacteristic
11#11924037—41no—
12C2×#10596833—41no—
13C2×Dic146D411yescharacteristic
14#11924018—41no—
15#11924016—41no—
16#11924012—21no—
17C22⋊Dic73—41no—
18C4×Dic73D411yescharacteristic
19#41×C73—21no—
20#41×C73—41no—
21C2×D4×C73—41no—
22C2×D4×C73—41no—
23C2×D4×C73C2×C411yescharacteristic
24C23×C73—21no—
25C23×C73—41no—
26Q8×C73—21no—
27D4×C73—21no—
28D4×C73—41no—
29D4×C73—42no—
30D4×C73—41no—
31C2×C4×C73—41no—
32C2×C4×C73—41no—
33C2×C4×C73C22⋊C411yescharacteristic
34C2×Dic73—21no—
35C2×Dic73—21no—
36Dic146—41no—
37#10596833—42no—
38#10596833—81no—
39#10596831—41no—
40C22×C73—41no—
41C22×C73—41no—
42C22×C73—81no—
43C22×C73—161no—
44C22×C73#9911yescharacteristic
45C4×C73—21no—
46C4×C73—41no—
47Dic73—41no—
48Dic73—41no—
49C2×C73—21no—
50C2×C73—81no—
51C2×C73—81no—
52C2×C73AΣL(1,𝔽16)11yescharacteristic
53#1403—731nomaximal, Sylow
54C73#140311yescharacteristic, complemented, Sylow
55#455—731no—
56#355—731no—
57#329—731no—
58H(5,𝔽2)#6440811yescharacteristic
59#137—1461no—
60#124—731no—
61#104—1461no—
62#101—1461no—
63#100—731no—
64#97—1461no—
65#41—21no—
66#41—41no—
67C2×Q8—731no—
68C2×D4—41no—
69C2×D4—41no—
70C2×D4C2×#6440811yescharacteristic
71Q16—2921no—
72SD16—2921no—
73M16—2921no—
74M16—1461no—
75C2×C8—2921no—
76C22⋊C4—2921no—
77C42—731no—
78C23—21no—
79C23—41no—
80Q8—21no—
81Q8—2921no—
82D4—21no—
83D4—41no—
84D4—42no—
85D4—41no—
86C2×C4—41no—
87C2×C4—41no—
88C2×C4—1461no—
89C2×C4—1461no—
90C2×C4C22⋊#6440811yescharacteristic
91C8—2921no—
92C8—2922no—
93C8—5841no—
94C22—41no—
95C22—41no—
96C22—81no—
97C22—161no—
98C22#1455664911yescharacteristic
99C4—21no—
100C4—41no—
101C4—2921no—
102C4—2921no—
103C2—21no—
104C2—81no—
105C2—81no—
106C2#1798948711yescharacteristic
subgroupG/H
centerC2#17989487
commutatorC2×D4×C73C2×C4
FrattiniC2×D4C2×#64408
FittingH(5,𝔽2)×C73C4
socleC2×C73AΣL(1,𝔽16)
hypercenterH(5,𝔽2)#64408
hypocenterC73#1403
LCSG ▷ C2×D4×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #17989495C2semidirect
2. #17989442C2semidirect
54. C73#1403semidirect