Finite Group Databasebeta

← #46781295

Subgroups — #46781295

Order 33664.

252 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 69 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#30681806C211yesmaximal, 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
13C263⋊#95—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—
32C22×C4×C263D411yescharacteristic
33C22×C4×C263D411yescharacteristic
34C22×C4×C263C2311yescharacteristic
35C2×C8×C263—22no—
36C42×C263C2×C411yescharacteristic
37C42×C263C2×C411yescharacteristic
38C42×C263D411yescharacteristic
39C42×C263D411yescharacteristic
40C22×D263—22no—
41Dic526—42no—
42D1052—42no—
43D1052—42no—
44D1052—42no—
45C22⋊D263—44no—
46C2×Dic263—22no—
47C2×Dic263—42no—
48C2×Dic263—42no—
49C2×Dic263—42no—
50C4×D263—44no—
51C23×C263C2×D411yescharacteristic
52C2×C4×C263—22no—
53C2×C4×C263—41no—
54C2×C4×C263—41no—
55C2×C4×C263C22⋊C411yescharacteristic
56C2×C4×C263C22⋊C411yescharacteristic
57C2×C4×C263C22⋊C411yescharacteristic
58C2×C4×C263C22⋊C411yescharacteristic
59C2×C4×C263C22×C411yescharacteristic
60C2×C4×C263C2×D411yescharacteristic
61C8×C263—42no—
62C22×C263—21no—
63C22×C263—21no—
64C22×C263C2×C22⋊C411yescharacteristic
65C22×C263AGL(1,ℤ/8)12yes—
66C2×D263—42no—
67C2×D263—42no—
68C2×D263—42no—
69C4×C263—21no—
70C4×C263—21no—
71C4×C263—21no—
72C4×C263—21no—
73C4×C263—21no—
74C4×C263—21no—
75Dic263—42no—
76Dic263—82no—
77C2×C263—22no—
78C2×C263#41011yescharacteristic
79C2×C263#41811yescharacteristic
80C2×C263#42111yescharacteristic
81D263—82no—
82C263#151411yescharacteristic, complemented, Sylow
83#1514—2631nomaximal, Sylow
84#532—2631no—
85#432D26311yescharacteristic, complemented
86#383—2631no—
87#327—2634no—
88C2×#41—5261no—
89C4⋊Q8—2631no—
90#127—2631no—
91#124—5261no—
92#121—2632no—
93#121—5261no—
94C4×D4—2632no—
95C4×D4—5261no—
96C2×C42C2×D26311yescharacteristic
97C4⋊C8—21no—
98C22⋊C8C2×D26312yes—
99#97—21no—
100#95—2632no—
101#95—5261no—
102#95—5261no—
103#41—10524no—
104C2×Q8—5261no—
105C2×D4—2632no—
106C2×D4—5262no—
107C2×D4—5261no—
108C2×D4—5261no—
109C22×C4—5262no—
110C22×C4—5262no—
111C22×C4D105211yescharacteristic
112C22×C4D105211yescharacteristic
113C22×C4C22×D26311yescharacteristic
114C2×C8—22no—
115C4⋊C4—2632no—
116C4⋊C4—5261no—
117C22⋊C4—5262no—
118C22⋊C4—5262no—
119C42C4×D26311yescharacteristic
120C42C4×D26311yescharacteristic
121C42C22⋊D26311yescharacteristic
122C42C22⋊D26311yescharacteristic
123C23—5262no—
124C23C2×D105211yescharacteristic
125Q8—10522no—
126D4—10522no—
127D4—10522no—
128D4—10522no—
129D4—10524no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—5262no—
134C2×C4—10524no—
135C2×C4—10522no—
136C2×C4—10522no—
137C2×C4—10522no—
138C2×C4(C2×D263)⋊C411yescharacteristic
139C2×C4(C2×D263)⋊C411yescharacteristic
140C2×C4(C2×D263)⋊C411yescharacteristic
141C2×C4(C2×D263)⋊C411yescharacteristic
142C2×C4C2×C4×D26311yescharacteristic
143C2×C4C2×C22⋊D26311yescharacteristic
144C8—42no—
145C22—21no—
146C22—21no—
147C22—10522no—
148C22—10522no—
149C22—10522no—
150C22C2×(C2×D263)⋊C411yescharacteristic
151C22#2255449812yes—
152C4—21no—
153C4—21no—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—10522no—
159C4—21042no—
160C2—22no—
161C2—21042no—
162C2#3068191111yescharacteristic
163C2#3068194411yescharacteristic
164C2#3068195411yescharacteristic
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#1514
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. #30681806C2semidirect
3. #30681673C2semidirect
4. #432×C263C2semidirect
6. #22554470C4semidirect
7. #22554467C4semidirect
12. C4×D1052C4semidirect
82. C263#1514semidirect
85. #432D263semidirect

Maximal subgroups

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

subgroupindex
#306824882
#306818062
#306816732
#432×C2632
#1514263