Finite Group Databasebeta

← #46781452

Subgroups — #46781452

Order 33664.

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

normal subgroups only

This group has 242 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#30681995C211yesmaximal, characteristic, complemented
2#30681991C211yesmaximal, characteristic, complemented
3#30681684C212yesmaximal, complemented
4#30681682C212yesmaximal, complemented
5#532×C263C211yesmaximal, characteristic
6C4⋊(C263⋊C8)C2212yes—
7C4⋊(C263⋊C8)C2212yes—
8C22⋊(C263⋊C8)—21no—
9C22⋊(C263⋊C8)—21no—
10#22554381—21no—
11C4×C263⋊C8—21no—
12C2×#41×C263—21no—
13C4⋊Q8×C263C2211yescharacteristic
14#127×C263C2211yescharacteristic
15#124×C263—21no—
16#121×C263—21no—
17#121×C263C412yes—
18C4×D4×C263—21no—
19C4×D4×C263C412yes—
20C2×C42×C263C2211yescharacteristic
21C2×C263⋊C8—22no—
22C2×C263⋊C8—22no—
23#41×C263—44no—
24C2×Q8×C263—21no—
25C2×D4×C263—22no—
26C2×D4×C263—21no—
27C2×D4×C263—21no—
28C2×D4×C263C2×C412yes—
29C22×C4×C263—22no—
30C22×C4×C263C2×C411yescharacteristic
31C22×C4×C263D411yescharacteristic
32C22×C4×C263D411yescharacteristic
33C4⋊C4×C263—21no—
34C4⋊C4×C263C2×C412yes—
35C22⋊C4×C263—22no—
36C22⋊C4×C263—22no—
37C42×C263C2×C411yescharacteristic
38C42×C263D411yescharacteristic
39C42×C263D411yescharacteristic
40C42×C263C2311yescharacteristic
41C263⋊C8—42no—
42C263⋊C8—42no—
43C23×C263—22no—
44C23×C263C22⋊C411yescharacteristic
45Q8×C263—42no—
46D4×C263—42no—
47D4×C263—44no—
48D4×C263—42no—
49D4×C263—42no—
50C2×C4×C263—22no—
51C2×C4×C263—22no—
52C2×C4×C263—22no—
53C2×C4×C263—41no—
54C2×C4×C263—44no—
55C2×C4×C263C22⋊C411yescharacteristic
56C2×C4×C263C22⋊C411yescharacteristic
57C2×C4×C263C22⋊C411yescharacteristic
58C2×C4×C263C22×C411yescharacteristic
59C2×C4×C263C2×D411yescharacteristic
60C2×C4×C263C2×D411yescharacteristic
61C22×C263—21no—
62C22×C263—21no—
63C22×C263—21no—
64C22×C263—42no—
65C22×C263—42no—
66C22×C263—42no—
67C22×C263C2×C22⋊C411yescharacteristic
68C4×C263—21no—
69C4×C263—21no—
70C4×C263—21no—
71C4×C263—21no—
72C4×C263—42no—
73C4×C263#13512yes—
74C4×C263AGL(1,ℤ/8)12yes—
75C2×C263—41no—
76C2×C263—82no—
77C2×C263#41311yescharacteristic
78C2×C263#41611yescharacteristic
79C2×C263#41811yescharacteristic
80C263#155311yescharacteristic, complemented, Sylow
81#1553—2631nomaximal, Sylow
82#532D26311yescharacteristic
83#432—2631no—
84#431—2631no—
85#332—2632no—
86#331—2632no—
87C2×#41—21no—
88C4⋊Q8C2×D26311yescharacteristic
89#127C2×D26311yescharacteristic
90#124—21no—
91#121—21no—
92#121Dic26312yes—
93C4×D4—21no—
94C4×D4Dic26312yes—
95C2×C42C2×D26311yescharacteristic
96C4⋊C8—2632no—
97C4⋊C8—2632no—
98C22⋊C8—5261no—
99C22⋊C8—5261no—
100#97—5261no—
101C4×C8—5261no—
102#41—44no—
103C2×Q8—21no—
104C2×D4—22no—
105C2×D4—21no—
106C2×D4—21no—
107C2×D4C2×Dic26312yes—
108C22×C4—22no—
109C22×C4C2×Dic26311yescharacteristic
110C22×C4C22⋊D26311yescharacteristic
111C22×C4C22⋊D26311yescharacteristic
112C2×C8—5262no—
113C2×C8—5262no—
114C4⋊C4—21no—
115C4⋊C4C2×Dic26312yes—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C42C2×Dic26311yescharacteristic
119C42C22⋊D26311yescharacteristic
120C42C22⋊D26311yescharacteristic
121C42C22×D26311yescharacteristic
122C23—22no—
123C23C22⋊Dic26311yescharacteristic
124Q8—42no—
125D4—42no—
126D4—44no—
127D4—42no—
128D4—42no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—41no—
133C2×C4—44no—
134C2×C4C22⋊Dic26311yescharacteristic
135C2×C4C22⋊Dic26311yescharacteristic
136C2×C4C22⋊Dic26311yescharacteristic
137C2×C4C22×Dic26311yescharacteristic
138C2×C4C2×C22⋊D26311yescharacteristic
139C2×C4C2×C22⋊D26311yescharacteristic
140C8—10522no—
141C8—10522no—
142C22—21no—
143C22—21no—
144C22—21no—
145C22—42no—
146C22—42no—
147C22—42no—
148C22C2×C22⋊Dic26311yescharacteristic
149C4—21no—
150C4—21no—
151C4—21no—
152C4—21no—
153C4—42no—
154C4#2255449012yes—
155C4#2255449612yes—
156C2—41no—
157C2—82no—
158C2#3068192211yescharacteristic
159C2#3068193411yescharacteristic
160C2#3068194311yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic263
commutatorC2×C4×C263C22×C4
FrattiniC42C22×D263
Fitting, prime radical#532×C263C2
socleC22×C263C2×C22⋊C4
cosocleC42×C263C23
hypercenter#532D263
hypocenterC263#1553
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #30681995C2semidirect
2. #30681991C2semidirect
3. #30681684C2semidirect
4. #30681682C2semidirect
80. C263#1553semidirect

Maximal subgroups

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

subgroupindex
#306819952
#306819912
#306816842
#306816822
#532×C2632
#1553263