Finite Group Databasebeta

← #46781947

Subgroups — #46781947

Order 33664.

250 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 61 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#30682284C211yesmaximal, characteristic, complemented
2#30682223C211yesmaximal, characteristic, complemented
3#30682143C211yesmaximal, characteristic, complemented
4#30681682C211yesmaximal, characteristic, complemented
5Q8⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
6D4⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
7#550×C263C211yesmaximal, characteristic
8C2×#16862364—21no—
9#22554470C2211yescharacteristic
10#22554401—21no—
11C4⋊(C263⋊C8)C2211yescharacteristic
12C4⋊(C263⋊C8)C2211yescharacteristic
13#22554394—21no—
14#22554393—21no—
15#22554391—22no—
16C4×C263⋊C8C2211yescharacteristic
17C2×#41×C263—21no—
18#127×C263—21no—
19#127×C263C2211yescharacteristic
20#121×C263—22no—
21#121×C263—21no—
22C4×Q8×C263C2211yescharacteristic
23C4×D4×C263—21no—
24C4×D4×C263C2211yescharacteristic
25C2×Dic526—21no—
26#16862364—42no—
27C2×C263⋊C8—21no—
28C2×C263⋊C8—21no—
29C2×C263⋊C8—21no—
30C4⋊Dic263—21no—
31C4⋊Dic263—21no—
32#41×C263—42no—
33#41×C263—42no—
34C2×Q8×C263D411yescharacteristic
35C2×D4×C263—22no—
36C2×D4×C263—22no—
37C2×D4×C263—21no—
38C2×D4×C263—21no—
39C2×D4×C263D411yescharacteristic
40C2×D4×C263D412yes—
41C22×C4×C263—22no—
42C22×C4×C263—21no—
43C4⋊C4×C263—21no—
44C4⋊C4×C263D411yescharacteristic
45C4⋊C4×C263D411yescharacteristic
46C22⋊C4×C263—22no—
47C22⋊C4×C263—21no—
48C42×C263—21no—
49C42×C263C2311yescharacteristic
50Dic526—41no—
51Dic526—41no—
52C2×Dic263—41no—
53C263⋊C8—41no—
54C263⋊C8—41no—
55C263⋊C8—41no—
56C23×C263—21no—
57C23×C263—22no—
58Q8×C263—21no—
59Q8×C263SD1612yescomplemented
60D4×C263—21no—
61D4×C263—21no—
62D4×C263—42no—
63D4×C263—44no—
64D4×C263—41no—
65D4×C263—41no—
66D4×C263—41no—
67D4×C263—41no—
68D4×C263—82no—
69C2×C4×C263—21no—
70C2×C4×C263—21no—
71C2×C4×C263—21no—
72C2×C4×C263—44no—
73C2×C4×C263—41no—
74C2×C4×C263—41no—
75C2×C4×C263C2×D411yescharacteristic
76C2×C4×C263C2×D411yescharacteristic
77C2×C4×C263C2×D411yescharacteristic
78C22×C263—41no—
79C22×C263—42no—
80C22×C263—42no—
81C22×C263—41no—
82C22×C263—42no—
83C22×C263—41no—
84C22×C263#12011yescharacteristic
85C4×C263—22no—
86C4×C263—21no—
87C4×C263—41no—
88C4×C263—41no—
89C4×C263C2×SD1611yescharacteristic
90C4×C263#13511yescharacteristic
91C4×C263AGL(1,ℤ/8)11yescharacteristic
92C4×C263AGL(1,ℤ/8)11yescharacteristic
93Dic263—81no—
94C2×C263—81no—
95C2×C263—82no—
96C2×C263#44911yescharacteristic
97C2×C263#45011yescharacteristic
98C2×C263#45511yescharacteristic
99C263#164211yescharacteristic, complemented, Sylow
100#1642—2631nomaximal, Sylow
101#550D26311yescharacteristic
102#486—2631no—
103#475—2631no—
104#461—2631no—
105#331—2631no—
106Q8⋊C8—2631no—
107D4⋊C8—2631no—
108C2×#41—21no—
109C2×SD16—5261no—
110C4⋊Q8—2631no—
111#127—21no—
112#127C2×D26311yescharacteristic
113#121—22no—
114#121—21no—
115C4×Q8C2×D26311yescharacteristic
116C4×D4—21no—
117C4×D4C2×D26311yescharacteristic
118#106—5261no—
119C4⋊C8—2631no—
120C4⋊C8—2631no—
121#103—5261no—
122#103—5261no—
123#102—5262no—
124C4×C8—2631no—
125#41—42no—
126#41—42no—
127C2×Q8—5261no—
128C2×Q8C22⋊D26311yescharacteristic
129C2×D4—22no—
130C2×D4—22no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4C22⋊D26311yescharacteristic
134C2×D4C22⋊D26312yes—
135C22×C4—22no—
136C22×C4—21no—
137SD16—10522no—
138C2×C8—5261no—
139C2×C8—5261no—
140C2×C8—5261no—
141C4⋊C4—21no—
142C4⋊C4—5261no—
143C4⋊C4—5261no—
144C4⋊C4C22⋊D26311yescharacteristic
145C4⋊C4C22⋊D26311yescharacteristic
146C22⋊C4—22no—
147C22⋊C4—21no—
148C42—21no—
149C42C22×D26311yescharacteristic
150C23—22no—
151C23—21no—
152Q8—21no—
153Q8—10521no—
154Q8—10521no—
155Q8#1686236412yescomplemented
156D4—21no—
157D4—21no—
158D4—42no—
159D4—44no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—41no—
164D4—82no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—44no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—10521no—
172C2×C4C2×C22⋊D26311yescharacteristic
173C2×C4C2×C22⋊D26311yescharacteristic
174C2×C4C2×C22⋊D26311yescharacteristic
175C8—10521no—
176C8—10521no—
177C8—10521no—
178C22—42no—
179C22—41no—
180C22—41no—
181C22—42no—
182C22—42no—
183C22—41no—
184C22#2255443911yescharacteristic
185C4—21no—
186C4—22no—
187C4—41no—
188C4—41no—
189C4—21041no—
190C4C2×#1686236411yescharacteristic
191C4#2255449011yescharacteristic
192C4#2255449511yescharacteristic
193C4#2255449611yescharacteristic
194C2—82no—
195C2—81no—
196C2#3068208311yescharacteristic
197C2#3068208911yescharacteristic
198C2#3068211611yescharacteristic
subgroupG/H
centerC22#22554439
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting, prime radical#550×C263C2
socleC22×C263#120
hypercenter#550D263
hypocenterC263#1642
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #30682284C2semidirect
2. #30682223C2semidirect
3. #30682143C2semidirect
4. #30681682C2semidirect
5. Q8⋊(C263⋊C8)C2semidirect
6. D4⋊(C263⋊C8)C2semidirect
59. Q8×C263SD16semidirect
99. C263#1642semidirect
155. Q8#16862364semidirect

Maximal subgroups

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

subgroupindex
#306822842
#306822232
#306821432
#306816822
Q8⋊(C263⋊C8)2
D4⋊(C263⋊C8)2
#550×C2632
#1642263