Finite Group Databasebeta

← #46809034

Subgroups — #46809034

Order 34432.

112 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 23 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#31770782C211yesmaximal, characteristic
2#31770402C211yesmaximal, characteristic, complemented
3#329×C269C211yesmaximal, characteristic, complemented
4#22575498C411yescharacteristic
5#22575484—21no—
6#22575381—21no—
7#22575372—21no—
8#22575370C411yescharacteristic
9#124×C269C2211yescharacteristic
10#97×C269—21no—
11#16864402—21no—
12#16864401—41no—
13C2×C22⋊D269—41no—
14D4×D269—41no—
15#16864392—41no—
16#16864389—41no—
17#16864386—21no—
18#16864386—41no—
19C2×Q8×C269D411yescharacteristic
20C2×D4×C269C2×C411yescharacteristic
21C2×C8×C269—41no—
22C22⋊C4×C269—41no—
23C42×C269D411yescharacteristic
24C22×D269—41no—
25Dic538—21no—
26D1076—21no—
27C22⋊D269—42no—
28C22⋊D269—41no—
29C2×Dic269—41no—
30C4×D269—41no—
31#14524130—41no—
32#14524130—81no—
33C23×C269—21no—
34Q8×C269—41no—
35D4×C269—41no—
36C2×C4×C269—21no—
37C2×C4×C269—21no—
38C2×C4×C269C22⋊C411yescharacteristic
39C8×C269—42no—
40C22×C269—41no—
41C22×C269—81no—
42C22×C269#9911yescharacteristic
43C2×D269—41no—
44C2×D269—161no—
45C4×C269—21no—
46C4×C269—41no—
47C4×C269—41no—
48Dic269—41no—
49C2×C269—21no—
50C2×C269—81no—
51C2×C269AΣL(1,𝔽16)11yescharacteristic
52D269—81no—
53C269#140311yescharacteristic, complemented, Sylow
54#1403—2691nomaximal, Sylow
55#455—2691no—
56#355—2691no—
57#329D26911yescharacteristic, complemented
58H(5,𝔽2)—2691no—
59#137—5381no—
60#124C2×D26911yescharacteristic
61#104—5381no—
62#101—5381no—
63#100—2691no—
64#97—21no—
65#41—5381no—
66#41—10761no—
67C2×Q8D107611yescharacteristic
68C2×D4—10761no—
69C2×D4—10761no—
70C2×D4C4×D26911yescharacteristic
71Q16—10761no—
72SD16—10761no—
73M16—5381no—
74M16—10761no—
75C2×C8—41no—
76C22⋊C4—41no—
77C42C22⋊D26911yescharacteristic
78C23—21no—
79C23—10761no—
80Q8—41no—
81Q8—5381no—
82D4—41no—
83D4—5381no—
84D4—10762no—
85D4—10761no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4—10761no—
89C2×C4—10761no—
90C2×C4#1686437911yescharacteristic
91C8—42no—
92C8—10761no—
93C8—21521no—
94C22—41no—
95C22—81no—
96C22—10761no—
97C22—43041no—
98C22#2257536711yescharacteristic
99C4—21no—
100C4—41no—
101C4—41no—
102C4—10761no—
103C2—21no—
104C2—81no—
105C2—21521no—
106C2#3177039311yescharacteristic
subgroupG/H
centerC2#31770393
commutatorC2×D4×C269C2×C4
Frattini#124C2×D269
Fitting#329×C269C2
socleC2×C269AΣL(1,𝔽16)
prime radical#22575498C4
cosocle#124×C269C22
hypercenter#329D269
hypocenterC269#1403
LCSG ▷ C2×D4×C269 ▷ C2×C4×C269 ▷ C22×C269 ▷ C2×C269 ▷ C269
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #31770402C2semidirect
3. #329×C269C2semidirect
53. C269#1403semidirect
57. #329D269semidirect

Maximal subgroups

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

subgroupindex
#317707822
#317704022
#329×C2692
#1403269