Finite Group Databasebeta

← #46781930

Subgroups — #46781930

Order 33664.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#30682674C211yesmaximal, characteristic
2#30682220C211yesmaximal, characteristic, complemented
3#30682145C211yesmaximal, characteristic, complemented
4#30681682C211yesmaximal, characteristic
5#30681670C211yesmaximal, characteristic, complemented
6#30681670C211yesmaximal, characteristic, complemented
7#486×C263C211yesmaximal, characteristic
8C2×#16862366—21no—
9#22554457—21no—
10#22554457—21no—
11#22554451—22no—
12C4×Dic526C2211yescharacteristic
13C4×Dic526C2211yescharacteristic
14D4×Dic263—21no—
15D4×Dic263—21no—
16#22554401—21no—
17C4⋊(C263⋊C8)C2211yescharacteristic
18C4⋊(C263⋊C8)C2211yescharacteristic
19#22554394—21no—
20#22554393—21no—
21C4⋊Q8×C263C2211yescharacteristic
22#127×C263C2211yescharacteristic
23#102×C263—22no—
24C4×C8×C263C2211yescharacteristic
25C2×Dic526D411yescharacteristic
26C2×Dic526D411yescharacteristic
27C22×Dic263—22no—
28#16862366—42no—
29C2×C263⋊C8—21no—
30C2×C263⋊C8—21no—
31C4⋊Dic263D411yescharacteristic
32C4⋊Dic263D411yescharacteristic
33Dic263⋊C4—21no—
34Dic263⋊C4—21no—
35C22⋊Dic263—22no—
36C22⋊Dic263—22no—
37C22⋊Dic263—22no—
38C4×Dic263—21no—
39C4×Dic263—21no—
40C2×Q8×C263—21no—
41C2×D4×C263—21no—
42C2×D4×C263—21no—
43C2×D4×C263D412yes—
44C2×C8×C263—21no—
45C4⋊C4×C263—21no—
46C4⋊C4×C263—21no—
47C42×C263C2311yescharacteristic
48Dic526—21no—
49Dic526—21no—
50Dic526—21no—
51Dic526—21no—
52C2×Dic263—21no—
53C2×Dic263—21no—
54C2×Dic263—21no—
55C2×Dic263—21no—
56C2×Dic263—82no—
57C263⋊C8—41no—
58C263⋊C8—41no—
59C23×C263—22no—
60Q8×C263—41no—
61Q8×C263—41no—
62D4×C263—42no—
63D4×C263—41no—
64D4×C263—41no—
65D4×C263—41no—
66D4×C263—41no—
67C2×C4×C263—41no—
68C2×C4×C263C2×D411yescharacteristic
69C2×C4×C263C2×D411yescharacteristic
70C2×C4×C263C2×D411yescharacteristic
71C8×C263—41no—
72C22×C263—42no—
73C22×C263—42no—
74C22×C263—42no—
75C22×C263#12011yescharacteristic
76C4×C263—21no—
77C4×C263—81no—
78C4×C263#13511yescharacteristic
79C4×C263#13511yescharacteristic
80C4×C263AGL(1,ℤ/8)11yescharacteristic
81C4×C263#13711yescharacteristic
82Dic263—41no—
83Dic263—41no—
84Dic263—41no—
85Dic263—41no—
86C2×C263—82no—
87C2×C263#44911yescharacteristic
88C2×C263#45211yescharacteristic
89C2×C263#45511yescharacteristic
90C263#164011yescharacteristic, complemented, Sylow
91#1640—2631nomaximal, Sylow
92#559—2631no—
93#486D26311yescharacteristic
94#475—2631no—
95#462—2631no—
96#331—2631no—
97Q8⋊C8—2631no—
98Q8⋊C8—2631no—
99C2×Q16—5261no—
100C4⋊Q8C2×D26311yescharacteristic
101#127C2×D26311yescharacteristic
102#124—5261no—
103#124—5261no—
104#123—5262no—
105C4×Q8—2631no—
106C4×Q8—2631no—
107C4×D4—5261no—
108C4×D4—5261no—
109#106—5261no—
110C4⋊C8—2631no—
111C4⋊C8—2631no—
112#103—5261no—
113#103—5261no—
114#102—22no—
115C4×C8C2×D26311yescharacteristic
116C2×Q8—21no—
117C2×Q8—2631no—
118C2×Q8—2631no—
119C2×D4—21no—
120C2×D4—21no—
121C2×D4C22⋊D26312yes—
122C22×C4—5262no—
123Q16—10522no—
124C2×C8—21no—
125C2×C8—5261no—
126C2×C8—5261no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—2631no—
130C4⋊C4—2631no—
131C4⋊C4—5261no—
132C4⋊C4—5261no—
133C22⋊C4—5262no—
134C22⋊C4—5262no—
135C22⋊C4—5262no—
136C42—5261no—
137C42—5261no—
138C42C22×D26311yescharacteristic
139C23—22no—
140Q8—41no—
141Q8—41no—
142Q8—5261no—
143Q8—5261no—
144Q8—5261no—
145Q8—5261no—
146D4—42no—
147D4—41no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—41no—
152C2×C4—5261no—
153C2×C4—5261no—
154C2×C4—5261no—
155C2×C4—5261no—
156C2×C4—21042no—
157C2×C4D4×D26311yescharacteristic
158C2×C4D4×D26311yescharacteristic
159C2×C4C2×C22⋊D26311yescharacteristic
160C8—41no—
161C8—10521no—
162C8—10521no—
163C22—42no—
164C22—42no—
165C22—42no—
166C22#2255443811yescharacteristic
167C4—21no—
168C4—81no—
169C4—10521no—
170C4—10521no—
171C4—10521no—
172C4—10521no—
173C4#2255448911yescharacteristic
174C4#2255449111yescharacteristic
175C4#2255449411yescharacteristic
176C4#2255449911yescharacteristic
177C2—82no—
178C2#3068208011yescharacteristic
179C2#3068209711yescharacteristic
180C2#3068211511yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#486×C263C2
socleC22×C263#120
prime radical#127×C263C22
hypercenter#486D263
hypocenterC263#1640
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #30682220C2semidirect
3. #30682145C2semidirect
5. #30681670C2semidirect
6. #30681670C2semidirect
90. C263#1640semidirect

Maximal subgroups

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

subgroupindex
#306826742
#306822202
#306821452
#306816822
#306816702
#486×C2632
#1640263