Finite Group Databasebeta

← #46781256

Subgroups — #46781256

Order 33664.

272 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 73 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#30682488C211yesmaximal, characteristic
2#30681784C211yesmaximal, characteristic, complemented
3#30681673C214yesmaximal, complemented
4#432×C263C211yesmaximal, characteristic, complemented
5C2×#16862376—21no—
6#22554470C411yescharacteristic, complemented
7#22554467C411yescharacteristic, complemented
8#22554458—21no—
9#22554444—21no—
10#22554444C2212yes—
11C4×D1052—21no—
12C4×D1052C412yescomplemented
13C2×C4×Dic263—21no—
14C263⋊#95—21no—
15C263⋊#95C2212yes—
16C2×C42×C263C2211yescharacteristic
17C4⋊C8×C263—21no—
18C22⋊C8×C263C2212yes—
19#97×C263—21no—
20#16862376—44no—
21C2×Dic526—21no—
22C2×D1052—21no—
23C2×D1052—21no—
24C2×D1052C2×C412yes—
25C2×C22⋊D263—22no—
26C22×Dic263—22no—
27C2×C4×D263—22no—
28C4⋊Dic263—21no—
29C4⋊Dic263C2×C412yes—
30(C2×D263)⋊C4—22no—
31(C2×D263)⋊C4—22no—
32C4×Dic263—24no—
33C22×C4×C263D411yescharacteristic
34C22×C4×C263D411yescharacteristic
35C22×C4×C263C2311yescharacteristic
36C2×C8×C263—22no—
37C42×C263C2×C411yescharacteristic
38C42×C263C2×C411yescharacteristic
39C42×C263D411yescharacteristic
40C42×C263D411yescharacteristic
41C22×D263—22no—
42Dic526—42no—
43D1052—42no—
44D1052—42no—
45D1052—42no—
46C22⋊D263—44no—
47C2×Dic263—24no—
48C2×Dic263—22no—
49C2×Dic263—42no—
50C2×Dic263—42no—
51C4×D263—44no—
52C23×C263C2×D411yescharacteristic
53C2×C4×C263—22no—
54C2×C4×C263—22no—
55C2×C4×C263—41no—
56C2×C4×C263C22⋊C411yescharacteristic
57C2×C4×C263C22⋊C411yescharacteristic
58C2×C4×C263C22⋊C411yescharacteristic
59C2×C4×C263C22⋊C411yescharacteristic
60C2×C4×C263C22×C411yescharacteristic
61C2×C4×C263C2×D411yescharacteristic
62C8×C263—42no—
63C22×C263—21no—
64C22×C263—21no—
65C22×C263C2×C22⋊C411yescharacteristic
66C22×C263AGL(1,ℤ/8)12yes—
67C2×D263—42no—
68C2×D263—42no—
69C2×D263—42no—
70C4×C263—21no—
71C4×C263—21no—
72C4×C263—21no—
73C4×C263—21no—
74C4×C263—21no—
75C4×C263#10412yes—
76Dic263—44no—
77Dic263—42no—
78C2×C263—22no—
79C2×C263#41011yescharacteristic
80C2×C263#41811yescharacteristic
81C2×C263C2×#10411yescharacteristic
82D263—82no—
83C263#150511yescharacteristic, complemented, Sylow
84#1505—2631nomaximal, Sylow
85#532—2631no—
86#432D26311yescharacteristic, complemented
87#376—2631no—
88#327—2634no—
89C2×#41—5261no—
90C4⋊Q8—2631no—
91#127—2631no—
92#124—5261no—
93#121—2632no—
94#121—5261no—
95C4×D4—2632no—
96C4×D4—5261no—
97C2×C42—5261no—
98C2×C42C2×D26311yescharacteristic
99C4⋊C8—21no—
100C22⋊C8C2×D26312yes—
101#97—21no—
102#95—2632no—
103#95—5261no—
104#41—10524no—
105C2×Q8—5261no—
106C2×D4—2632no—
107C2×D4—5262no—
108C2×D4—5261no—
109C2×D4—5261no—
110C22×C4—5262no—
111C22×C4—5262no—
112C22×C4D105211yescharacteristic
113C22×C4D105211yescharacteristic
114C22×C4C22×D26311yescharacteristic
115C2×C8—22no—
116C4⋊C4—2632no—
117C4⋊C4—5261no—
118C22⋊C4—5262no—
119C22⋊C4—5262no—
120C42—5264no—
121C42C4×D26311yescharacteristic
122C42C4×D26311yescharacteristic
123C42C22⋊D26311yescharacteristic
124C42C22⋊D26311yescharacteristic
125C23—5262no—
126C23C2×D105211yescharacteristic
127Q8—10522no—
128D4—10522no—
129D4—10522no—
130D4—10524no—
131D4—10522no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—41no—
135C2×C4—5264no—
136C2×C4—5262no—
137C2×C4—10524no—
138C2×C4—10522no—
139C2×C4—10522no—
140C2×C4(C2×D263)⋊C411yescharacteristic
141C2×C4(C2×D263)⋊C411yescharacteristic
142C2×C4(C2×D263)⋊C411yescharacteristic
143C2×C4(C2×D263)⋊C411yescharacteristic
144C2×C4C2×C4×D26311yescharacteristic
145C2×C4C2×C22⋊D26311yescharacteristic
146C8—42no—
147C22—21no—
148C22—21no—
149C22—10522no—
150C22—10522no—
151C22—10522no—
152C22C2×(C2×D263)⋊C411yescharacteristic
153C22#2255449812yes—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—21no—
159C4—10524no—
160C4—10522no—
161C4#2255439612yes—
162C2—22no—
163C2—21042no—
164C2#3068191111yescharacteristic
165C2#3068194411yescharacteristic
166C2C2×#2255439611yescharacteristic
subgroupG/H
centerC22C2×(C2×D263)⋊C4
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#432×C263C2
socleC22×C263C2×C22⋊C4
prime radical#30682488C2
cosocleC22×C4×C263C23
hypercenter#432D263
hypocenterC263#1505
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #30681784C2semidirect
3. #30681673C2semidirect
4. #432×C263C2semidirect
6. #22554470C4semidirect
7. #22554467C4semidirect
12. C4×D1052C4semidirect
83. C263#1505semidirect
86. #432D263semidirect

Maximal subgroups

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

subgroupindex
#306824882
#306817842
#306816732
#432×C2632
#1505263