Finite Group Databasebeta

← #46781944

Subgroups — #46781944

Order 33664.

250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 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#30682608C211yesmaximal, characteristic
2#30682220C211yesmaximal, characteristic, complemented
3#30682140C211yesmaximal, characteristic, complemented
4#30681682C211yesmaximal, characteristic, complemented
5#30681670C211yesmaximal, characteristic, complemented
6#30681667C211yesmaximal, characteristic, complemented
7#486×C263C211yesmaximal, characteristic, complemented
8C2×#16862375—21no—
9C2×#16862363—21no—
10#22554466—21no—
11#22554442—22no—
12#22554441—21no—
13C4×Dic526C2211yescharacteristic
14C4×D1052C2211yescharacteristic
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
25#16862375—42no—
26#16862375—42no—
27C2×Dic526D411yescharacteristic
28C2×D1052D411yescharacteristic
29C2×C22⋊D263—22no—
30C2×C22⋊D263—22no—
31C22×Dic263—22no—
32C2×C4×D263—21no—
33#16862363—42no—
34C2×C263⋊C8—21no—
35C2×C263⋊C8—21no—
36C4⋊Dic263D411yescharacteristic
37C4⋊Dic263D411yescharacteristic
38Dic263⋊C4—21no—
39C22⋊Dic263—22no—
40(C2×D263)⋊C4—21no—
41C4×Dic263—21no—
42C2×Q8×C263—21no—
43C2×D4×C263—21no—
44C2×D4×C263—21no—
45C2×D4×C263D412yes—
46C2×C8×C263—21no—
47C4⋊C4×C263—21no—
48C4⋊C4×C263—21no—
49C42×C263C2311yescharacteristic
50C22×D263—21no—
51Dic526—21no—
52Dic526SD1612yescomplemented
53D1052—21no—
54D1052—21no—
55C22⋊D263—44no—
56C22⋊D263—82no—
57C2×Dic263—21no—
58C2×Dic263—21no—
59C2×Dic263—21no—
60C2×Dic263—44no—
61C4×D263—41no—
62C4×D263—41no—
63C263⋊C8—41no—
64C263⋊C8—41no—
65C23×C263—22no—
66Q8×C263—41no—
67Q8×C263—41no—
68D4×C263—42no—
69D4×C263—41no—
70D4×C263—41no—
71D4×C263—41no—
72D4×C263—41no—
73C2×C4×C263—41no—
74C2×C4×C263C2×D411yescharacteristic
75C2×C4×C263C2×D411yescharacteristic
76C2×C4×C263C2×D411yescharacteristic
77C8×C263—41no—
78C22×C263—42no—
79C22×C263—42no—
80C22×C263—42no—
81C22×C263#12011yescharacteristic
82C2×D263—41no—
83C2×D263—41no—
84C2×D263—41no—
85C4×C263—21no—
86C4×C263—81no—
87C4×C263C2×SD1611yescharacteristic
88C4×C263#13511yescharacteristic
89C4×C263AGL(1,ℤ/8)11yescharacteristic
90C4×C263AGL(1,ℤ/8)11yescharacteristic
91Dic263—22no—
92Dic263—41no—
93Dic263—41no—
94C2×C263—82no—
95C2×C263#44911yescharacteristic
96C2×C263#45011yescharacteristic
97C2×C263#45511yescharacteristic
98D263—81no—
99C263#164211yescharacteristic, complemented, Sylow
100#1642—2631nomaximal, Sylow
101#550—2631no—
102#486D26311yescharacteristic, complemented
103#475—2631no—
104#461—2631no—
105#331—2631no—
106Q8⋊C8—2631no—
107D4⋊C8—2631no—
108C2×#41—5261no—
109C2×SD16—5261no—
110C4⋊Q8C2×D26311yescharacteristic
111#127—5261no—
112#127C2×D26311yescharacteristic
113#121—5261no—
114#121—5262no—
115C4×Q8—2631no—
116C4×D4—2631no—
117C4×D4—5261no—
118#106—5261no—
119C4⋊C8—2631no—
120C4⋊C8—2631no—
121#103—5261no—
122#103—5261no—
123#102—22no—
124C4×C8C2×D26311yescharacteristic
125#41—10522no—
126#41—10522no—
127C2×Q8—21no—
128C2×Q8—2631no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—2631no—
132C2×D4—5262no—
133C2×D4—5262no—
134C2×D4C22⋊D26312yes—
135C22×C4—5262no—
136C22×C4—5261no—
137SD16—10522no—
138C2×C8—21no—
139C2×C8—5261no—
140C2×C8—5261no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—2631no—
144C4⋊C4—2631no—
145C4⋊C4—5261no—
146C22⋊C4—5262no—
147C22⋊C4—5261no—
148C42—5261no—
149C42C22×D26311yescharacteristic
150C23—22no—
151C23—5261no—
152Q8—41no—
153Q8—41no—
154Q8—2632no—
155Q8—5261no—
156D4—42no—
157D4—41no—
158D4—41no—
159D4—41no—
160D4—41no—
161D4—5261no—
162D4—5261no—
163D4—10524no—
164D4—21042no—
165C2×C4—41no—
166C2×C4—5261no—
167C2×C4—5261no—
168C2×C4—5261no—
169C2×C4—10524no—
170C2×C4—10521no—
171C2×C4—10521no—
172C2×C4D4×D26311yescharacteristic
173C2×C4D4×D26311yescharacteristic
174C2×C4C2×C22⋊D26311yescharacteristic
175C8—41no—
176C8—10521no—
177C8—10521no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—10521no—
182C22—10521no—
183C22—10521no—
184C22#2255443811yescharacteristic
185C4—21no—
186C4—81no—
187C4—5262no—
188C4—10521no—
189C4—10521no—
190C4SD16×D26311yescharacteristic
191C4#2255448911yescharacteristic
192C4#2255449411yescharacteristic
193C4#2255449711yescharacteristic
194C2—82no—
195C2—21041no—
196C2#3068208011yescharacteristic
197C2#3068208711yescharacteristic
198C2#3068211511yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#486×C263C2
socleC22×C263#120
prime radical#30682608C2
hypercenter#486D263
hypocenterC263#1642
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. #30682140C2semidirect
4. #30681682C2semidirect
5. #30681670C2semidirect
6. #30681667C2semidirect
7. #486×C263C2semidirect
52. Dic526SD16semidirect
99. C263#1642semidirect
102. #486D263semidirect

Maximal subgroups

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

subgroupindex
#306826082
#306822202
#306821402
#306816822
#306816702
#306816672
#486×C2632
#1642263