Finite Group Databasebeta

← #46809619

Subgroups — #46809619

Order 34432.

254 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 67 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#31771156C211yesmaximal, characteristic
2#31770627C212yesmaximal, complemented
3#31770354C211yesmaximal, characteristic, complemented
4#31770348C212yesmaximal, complemented
5#333×C269C211yesmaximal, characteristic, complemented
6C2×#16864403C412yes—
7C2×#16864385—22no—
8#22575450C2211yescharacteristic
9#22575442C412yes—
10#22575428—22no—
11#22575415—22no—
12C42×D269C2211yescharacteristic
13C4⋊#14524130C2212yes—
14#22575382—22no—
15C4⋊Q8×C269C2211yescharacteristic
16C4⋊C8×C269C2212yes—
17#16864403—44no—
18C2×D1076—22no—
19C2×D1076—22no—
20C2×D1076C2×C412yes—
21C2×C4×D269—22no—
22C2×C4×D269C2×C411yescharacteristic
23C2×C4×D269D412yes—
24#16864385—44no—
25C2×#14524130—22no—
26#16864379—24no—
27C4×Dic269C2×C411yescharacteristic
28C4×Dic269D412yes—
29C2×Q8×C269C2×C412yes—
30C2×C8×C269—22no—
31C4⋊C4×C269—22no—
32C42×C269C2311yescharacteristic
33C22×D269—22no—
34C22×D269C22⋊C411yescharacteristic
35D1076—42no—
36D1076—44no—
37D1076—42no—
38D1076—42no—
39C2×Dic269C22⋊C412yes—
40C2×Dic269C22⋊C411yescharacteristic
41C4×D269—22no—
42C4×D269—22no—
43C4×D269—22no—
44C4×D269—44no—
45#14524130—42no—
46Q8×C269—42no—
47C2×C4×C269—22no—
48C2×C4×C269C22×C411yescharacteristic
49C2×C4×C269C2×D412yes—
50C8×C269—42no—
51C22×C269C2×C22⋊C411yescharacteristic
52C2×D269—21no—
53C2×D269—22no—
54C2×D269—42no—
55C2×D269—44no—
56C4×C269—21no—
57C4×C269—42no—
58C4×C269AGL(1,ℤ/8)12yes—
59C4×C269#13712yes—
60Dic269—22no—
61Dic269#10012yes—
62C2×C269C2×#10011yescharacteristic
63C2×C269#41712yes—
64D269—41no—
65D269—82no—
66C269#156011yescharacteristic, complemented, Sylow
67#1560—2691nomaximal, Sylow
68#532—2691no—
69#423—2692no—
70#333—2691no—
71#333D26911yescharacteristic, complemented
72#331—2692no—
73C2×#41—2692no—
74C2×M16—5382no—
75C4⋊Q8C2×D26911yescharacteristic
76#127—2691no—
77#124—2692no—
78#121—5382no—
79C4×D4—5382no—
80C2×C42—2691no—
81C4⋊C8—2692no—
82C4⋊C8—5382no—
83C4⋊C8C2×D26912yes—
84#41—10764no—
85C2×Q8C4×D26912yes—
86C2×D4—2692no—
87C2×D4—5382no—
88C2×D4—5382no—
89C22×C4—2691no—
90C22×C4—2692no—
91C22×C4—5382no—
92M16—10764no—
93C2×C8—22no—
94C2×C8—5382no—
95C4⋊C4—22no—
96C22⋊C4—5384no—
97C42—2691no—
98C42—2692no—
99C42C22×D26911yescharacteristic
100C23—2691no—
101C23—5382no—
102Q8—42no—
103D4—10762no—
104D4—10764no—
105D4—10762no—
106D4—10762no—
107C2×C4—22no—
108C2×C4—2691no—
109C2×C4—2692no—
110C2×C4—5382no—
111C2×C4—5382no—
112C2×C4—5382no—
113C2×C4—10764no—
114C2×C4C2×C4×D26911yescharacteristic
115C2×C4D4×D26912yes—
116C8—42no—
117C8—10762no—
118C22—5381no—
119C22—5382no—
120C22—10762no—
121C22—10764no—
122C22C22⋊C4×D26911yescharacteristic
123C4—21no—
124C4—42no—
125C4—2692no—
126C4—5382no—
127C4#2257548012yes—
128C4#2257548512yes—
129C2—10761no—
130C2—21522no—
131C2#100×D26911yescharacteristic
132C2#3177060512yes—
subgroupG/H
centerC22C22⋊C4×D269
commutatorC2×C4×C269C22×C4
FrattiniC42C22×D269
Fitting#333×C269C2
socleC22×C269C2×C22⋊C4
prime radical#31771156C2
cosocleC42×C269C23
hypercenter#333D269
hypocenterC269#1560
LCSG ▷ C2×C4×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #31770627C2semidirect
3. #31770354C2semidirect
4. #31770348C2semidirect
5. #333×C269C2semidirect
66. C269#1560semidirect
71. #333D269semidirect

Maximal subgroups

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

subgroupindex
#317711562
#317706272
#317703542
#317703482
#333×C2692
#1560269