Finite Group Databasebeta

← #46809393

Subgroups — #46809393

Order 34432.

272 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 81 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#31770662C211yesmaximal, characteristic, complemented
2#31770451C211yesmaximal, characteristic, complemented
3#31770339C214yesmaximal, complemented
4#532×C269C211yesmaximal, characteristic
5C2×C4×Dic269—21no—
6C4⋊#14524130—21no—
7C22⋊#14524130C2212yes—
8#22575364—21no—
9#22575360—21no—
10#22575360C2212yes—
11C2×#41×C269—21no—
12C4⋊Q8×C269C411yescharacteristic, complemented
13#127×C269C411yescharacteristic, complemented
14#124×C269—21no—
15#121×C269—21no—
16#121×C269C2212yes—
17C4×D4×C269—21no—
18C4×D4×C269C412yescomplemented
19C2×C42×C269C2211yescharacteristic
20C22×Dic269—22no—
21C2×#14524130—22no—
22C4×Dic269—24no—
23#41×C269—44no—
24C2×Q8×C269—21no—
25C2×D4×C269—22no—
26C2×D4×C269—21no—
27C2×D4×C269—21no—
28C2×D4×C269C2×C412yes—
29C22×C4×C269—22no—
30C22×C4×C269D411yescharacteristic
31C22×C4×C269D411yescharacteristic
32C22×C4×C269C2311yescharacteristic
33C4⋊C4×C269—21no—
34C4⋊C4×C269C2×C412yes—
35C22⋊C4×C269—22no—
36C22⋊C4×C269—22no—
37C42×C269C2×C411yescharacteristic
38C42×C269C2×C411yescharacteristic
39C42×C269D411yescharacteristic
40C42×C269D411yescharacteristic
41C2×Dic269—24no—
42C2×Dic269—42no—
43C2×Dic269—42no—
44#14524130—42no—
45C23×C269—22no—
46C23×C269C2×D411yescharacteristic
47Q8×C269—42no—
48D4×C269—42no—
49D4×C269—42no—
50D4×C269—44no—
51D4×C269—42no—
52C2×C4×C269—22no—
53C2×C4×C269—22no—
54C2×C4×C269—22no—
55C2×C4×C269—41no—
56C2×C4×C269—44no—
57C2×C4×C269C22⋊C411yescharacteristic
58C2×C4×C269C22⋊C411yescharacteristic
59C2×C4×C269C22⋊C411yescharacteristic
60C2×C4×C269C22⋊C411yescharacteristic
61C2×C4×C269C22×C411yescharacteristic
62C2×C4×C269C2×D411yescharacteristic
63C22×C269—21no—
64C22×C269—21no—
65C22×C269—42no—
66C22×C269—42no—
67C22×C269—42no—
68C22×C269C2×C22⋊C411yescharacteristic
69C22×C269AGL(1,ℤ/8)12yes—
70C4×C269—21no—
71C4×C269—21no—
72C4×C269—21no—
73C4×C269—21no—
74C4×C269—21no—
75C4×C269—42no—
76C4×C269#10412yes—
77Dic269—44no—
78C2×C269—22no—
79C2×C269—82no—
80C2×C269#41011yescharacteristic
81C2×C269#41811yescharacteristic
82C2×C269C2×#10411yescharacteristic
83C269#150511yescharacteristic, complemented, Sylow
84#1505—2691nomaximal, Sylow
85#532D26911yescharacteristic
86#432—2691no—
87#376—2691no—
88#327—2694no—
89C2×#41—21no—
90C4⋊Q8Dic26911yescharacteristic, complemented
91#127Dic26911yescharacteristic, complemented
92#124—21no—
93#121—21no—
94#121C2×D26912yes—
95C4×D4—21no—
96C4×D4Dic26912yescomplemented
97C2×C42—5381no—
98C2×C42C2×D26911yescharacteristic
99C4⋊C8—5381no—
100C22⋊C8—2692no—
101#97—5381no—
102#95—2692no—
103#95—5381no—
104#41—44no—
105C2×Q8—21no—
106C2×D4—22no—
107C2×D4—21no—
108C2×D4—21no—
109C2×D4C2×Dic26912yes—
110C22×C4—22no—
111C22×C4—5382no—
112C22×C4C22⋊D26911yescharacteristic
113C22×C4C22⋊D26911yescharacteristic
114C22×C4C22×D26911yescharacteristic
115C2×C8—5382no—
116C4⋊C4—21no—
117C4⋊C4C2×Dic26912yes—
118C22⋊C4—22no—
119C22⋊C4—22no—
120C42—5384no—
121C42C2×Dic26911yescharacteristic
122C42C2×Dic26911yescharacteristic
123C42C22⋊D26911yescharacteristic
124C42C22⋊D26911yescharacteristic
125C23—22no—
126C23C2×C22⋊D26911yescharacteristic
127Q8—42no—
128D4—42no—
129D4—42no—
130D4—44no—
131D4—42no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—41no—
136C2×C4—44no—
137C2×C4—5384no—
138C2×C4—10762no—
139C2×C4—10762no—
140C2×C4C22⋊Dic26911yescharacteristic
141C2×C4C22⋊Dic26911yescharacteristic
142C2×C4C22⋊Dic26911yescharacteristic
143C2×C4C22⋊Dic26911yescharacteristic
144C2×C4C22×Dic26911yescharacteristic
145C2×C4C2×C22⋊D26911yescharacteristic
146C8—10762no—
147C22—21no—
148C22—21no—
149C22—42no—
150C22—42no—
151C22—42no—
152C22C2×C22⋊Dic26911yescharacteristic
153C22#2257547912yes—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—21no—
159C4—42no—
160C4—10764no—
161C4#2257538012yes—
162C2—22no—
163C2—82no—
164C2#3177057911yescharacteristic
165C2#3177061011yescharacteristic
166C2C2×#2257538011yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic269
commutatorC2×C4×C269C22×C4
FrattiniC22×C4C22×D269
Fitting, prime radical#532×C269C2
socleC22×C269C2×C22⋊C4
cosocleC22×C4×C269C23
hypercenter#532D269
hypocenterC269#1505
LCSG ▷ C2×C4×C269 ▷ C22×C269 ▷ C269
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #31770662C2semidirect
2. #31770451C2semidirect
3. #31770339C2semidirect
12. C4⋊Q8×C269C4semidirect
13. #127×C269C4semidirect
18. C4×D4×C269C4semidirect
83. C269#1505semidirect
90. C4⋊Q8Dic269semidirect
91. #127Dic269semidirect
96. C4×D4Dic269semidirect

Maximal subgroups

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

subgroupindex
#317706622
#317704512
#317703392
#532×C2692
#1505269