Finite Group Databasebeta

← #46781946

Subgroups — #46781946

Order 33664.

250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 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#30682610C211yesmaximal, characteristic
2#30682286C211yesmaximal, characteristic, complemented
3#30682140C211yesmaximal, characteristic, complemented
4#30681681C211yesmaximal, characteristic, complemented
5Q8⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
6#30681665C211yesmaximal, characteristic, complemented
7#475×C263C211yesmaximal, characteristic, complemented
8C2×#16862377—21no—
9C2×#16862363—21no—
10#22554467—21no—
11#22554467C2211yescharacteristic
12#22554445—22no—
13#22554445—21no—
14C4×D1052—21no—
15C4×D1052C2211yescharacteristic
16C4⋊(C263⋊C8)C2211yescharacteristic
17#22554394—21no—
18#22554390—22no—
19C4×C263⋊C8C2211yescharacteristic
20C4⋊Q8×C263C2211yescharacteristic
21C4×Q8×C263C2211yescharacteristic
22#106×C263—21no—
23C4⋊C8×C263C2211yescharacteristic
24#103×C263—21no—
25#16862377—42no—
26#16862377—42no—
27C2×D1052—22no—
28C2×D1052—22no—
29C2×D1052—21no—
30C2×D1052—21no—
31C2×D1052D411yescharacteristic
32C2×D1052D412yes—
33C2×C4×D263—22no—
34C2×C4×D263—21no—
35#16862363—42no—
36C2×C263⋊C8—21no—
37C2×C263⋊C8—21no—
38C4⋊Dic263D411yescharacteristic
39(C2×D263)⋊C4—22no—
40(C2×D263)⋊C4—21no—
41C2×Q8×C263—21no—
42C2×Q8×C263D411yescharacteristic
43C2×C8×C263—21no—
44C4⋊C4×C263—21no—
45C4⋊C4×C263—21no—
46C4⋊C4×C263—21no—
47C4⋊C4×C263D411yescharacteristic
48C42×C263—21no—
49C42×C263C2311yescharacteristic
50C22×D263—21no—
51C22×D263—22no—
52D1052—21no—
53D1052—21no—
54D1052—42no—
55D1052—44no—
56D1052—41no—
57D1052—41no—
58D1052—41no—
59D1052—41no—
60D1052—82no—
61C2×Dic263—21no—
62C4×D263—44no—
63C4×D263—41no—
64C4×D263—41no—
65C263⋊C8—41no—
66C263⋊C8—41no—
67Q8×C263—21no—
68Q8×C263—41no—
69Q8×C263—41no—
70Q8×C263SD1612yescomplemented
71C2×C4×C263—21no—
72C2×C4×C263—21no—
73C2×C4×C263—41no—
74C2×C4×C263C2×D411yescharacteristic
75C2×C4×C263C2×D411yescharacteristic
76C2×C4×C263C2×D411yescharacteristic
77C8×C263—41no—
78C22×C263#12011yescharacteristic
79C2×D263—41no—
80C2×D263—42no—
81C2×D263—42no—
82C2×D263—41no—
83C2×D263—42no—
84C2×D263—41no—
85C4×C263—22no—
86C4×C263—21no—
87C4×C263—41no—
88C4×C263—81no—
89C4×C263C2×SD1611yescharacteristic
90C4×C263#13511yescharacteristic
91C4×C263AGL(1,ℤ/8)11yescharacteristic
92C4×C263AGL(1,ℤ/8)11yescharacteristic
93Dic263—41no—
94C2×C263#44911yescharacteristic
95C2×C263#45011yescharacteristic
96C2×C263#45511yescharacteristic
97D263—81no—
98D263—82no—
99C263#164211yescharacteristic, complemented, Sylow
100#1642—2631nomaximal, Sylow
101#550—2631no—
102#486—2631no—
103#475D26311yescharacteristic, complemented
104#461—2631no—
105#331—2631no—
106Q8⋊C8—2631no—
107D4⋊C8—2631no—
108C2×#41—5261no—
109C2×SD16—5261no—
110C4⋊Q8C2×D26311yescharacteristic
111#127—2631no—
112#127—5261no—
113#121—5262no—
114#121—5261no—
115C4×Q8C2×D26311yescharacteristic
116C4×D4—2631no—
117C4×D4—5261no—
118#106—21no—
119C4⋊C8—2631no—
120C4⋊C8C2×D26311yescharacteristic
121#103—21no—
122#103—5261no—
123#102—5262no—
124C4×C8—2631no—
125#41—10522no—
126#41—10522no—
127C2×Q8—21no—
128C2×Q8C22⋊D26311yescharacteristic
129C2×D4—2631no—
130C2×D4—2632no—
131C2×D4—5262no—
132C2×D4—5262no—
133C2×D4—5261no—
134C2×D4—5261no—
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—21no—
144C4⋊C4—2631no—
145C4⋊C4C22⋊D26311yescharacteristic
146C22⋊C4—5262no—
147C22⋊C4—5261no—
148C42—21no—
149C42C22×D26311yescharacteristic
150C23—5262no—
151C23—5261no—
152Q8—21no—
153Q8—41no—
154Q8—41no—
155Q8#1686236312yescomplemented
156D4—5261no—
157D4—5261no—
158D4—10522no—
159D4—10524no—
160D4—10521no—
161D4—10521no—
162D4—10521no—
163D4—10521no—
164D4—21042no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—41no—
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—10522no—
179C22—10521no—
180C22—10521no—
181C22—10522no—
182C22—10522no—
183C22—10521no—
184C22#2255443811yescharacteristic
185C4—21no—
186C4—22no—
187C4—41no—
188C4—81no—
189C4—10521no—
190C4C2×#1686236311yescharacteristic
191C4#2255449111yescharacteristic
192C4#2255449511yescharacteristic
193C4#2255449711yescharacteristic
194C2—21042no—
195C2—21041no—
196C2#3068208211yescharacteristic
197C2#3068208811yescharacteristic
198C2#3068211411yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#475×C263C2
socleC22×C263#120
prime radical#30682610C2
hypercenter#475D263
hypocenterC263#1642
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #30682286C2semidirect
3. #30682140C2semidirect
4. #30681681C2semidirect
5. Q8⋊(C263⋊C8)C2semidirect
6. #30681665C2semidirect
7. #475×C263C2semidirect
70. Q8×C263SD16semidirect
99. C263#1642semidirect
103. #475D263semidirect
155. Q8#16862363semidirect

Maximal subgroups

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

subgroupindex
#306826102
#306822862
#306821402
#306816812
Q8⋊(C263⋊C8)2
#306816652
#475×C2632
#1642263