Finite Group Databasebeta

← #22625056

Subgroups — #22625056

Order 9344.

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

normal subgroups only

This group has 106 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#17989497C211yesmaximal, characteristic, complemented
2#17989447C211yesmaximal, characteristic, complemented
3#17988770C211yesmaximal, characteristic
4#14556658—21no—
5#14556652—21no—
6#14556621—21no—
7#14556589C2211yescharacteristic
8#14556518—21no—
9#14556510C411yescharacteristic
102−1+4×C73C411yescharacteristic
11#11924037—41no—
12C2×#10596833—41no—
13C2×Dic146D411yescharacteristic
14#11924018—41no—
15#11924016—41no—
16#11924012—21no—
17#11924007—41no—
18C4×Dic73D411yescharacteristic
19#41×C73—21no—
20#41×C73—41no—
21#41×C73—41no—
22C2×Q8×C73—41no—
23C2×Q8×C73C2×C411yescharacteristic
24Q8×C73—21no—
25Q8×C73—41no—
26Q8×C73—41no—
27D4×C73—21no—
28D4×C73—41no—
29D4×C73—41no—
30C2×C4×C73—21no—
31C2×C4×C73—41no—
32C2×C4×C73—42no—
33C2×C4×C73C22⋊C411yescharacteristic
34C2×Dic73—21no—
35C2×Dic73—21no—
36Dic146—41no—
37#10596833—81no—
38#10596833—81no—
39#10596831—41no—
40C22×C73—41no—
41C22×C73#9911yescharacteristic
42C4×C73—21no—
43C4×C73—41no—
44C4×C73—41no—
45Dic73—21no—
46Dic73—21no—
47Dic73—41no—
48C2×C73—21no—
49C2×C73—81no—
50C2×C73AΣL(1,𝔽16)11yescharacteristic
51#1405—731nomaximal, Sylow
52C73#140511yescharacteristic, complemented, Sylow
53#456—731no—
54#356—731no—
55#333—731no—
562−1+4#6440811yescharacteristic
57#137—1461no—
58C4⋊Q8—731no—
59C4⋊C8—1461no—
60#104—1461no—
61#101—731no—
62#101—1461no—
63#41—21no—
64#41—41no—
65#41—41no—
66C2×Q8—41no—
67C2×Q8—731no—
68C2×Q8C2×#6440811yescharacteristic
69Q16—2921no—
70SD16—2921no—
71M16—2921no—
72M16—1461no—
73C2×C8—2921no—
74C4⋊C4—2921no—
75C42—731no—
76Q8—21no—
77Q8—41no—
78Q8—41no—
79Q8—2921no—
80D4—21no—
81D4—41no—
82D4—41no—
83C2×C4—21no—
84C2×C4—41no—
85C2×C4—42no—
86C2×C4—1461no—
87C2×C4—1461no—
88C2×C4C22⋊#6440811yescharacteristic
89C8—2921no—
90C8—5841no—
91C8—5841no—
92C22—41no—
93C22#1455664911yescharacteristic
94C4—21no—
95C4—41no—
96C4—41no—
97C4—2921no—
98C4—1461no—
99C4—1461no—
100C2—21no—
101C2—81no—
102C2#1798948711yescharacteristic
subgroupG/H
centerC2#17989487
commutatorC2×Q8×C73C2×C4
FrattiniC2×Q8C2×#64408
Fitting2−1+4×C73C4
socleC2×C73AΣL(1,𝔽16)
hypercenter2−1+4#64408
hypocenterC73#1405
LCSG ▷ C2×Q8×C73 ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
1. #17989497C2semidirect
2. #17989447C2semidirect
52. C73#1405semidirect