Finite Group Databasebeta

← #46781872

Subgroups — #46781872

Order 33664.

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

normal subgroups only

This group has 256 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#30682312C211yesmaximal, characteristic, complemented
3#30682225C211yesmaximal, characteristic, complemented
4#30681681C211yesmaximal, characteristic, complemented
5Q8⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
6#30681665C211yesmaximal, characteristic, complemented
7#477×C263C211yesmaximal, characteristic, complemented
8C2×#16862377—21no—
9C2×#16862363—22no—
10#22554467—21no—
11#22554467C2211yescharacteristic
12#22554445—22no—
13#22554445—21no—
14C4×D1052—21no—
15C4×D1052C2211yescharacteristic
16#22554401—21no—
17C4⋊(C263⋊C8)C2211yescharacteristic
18#22554390—21no—
19C4×C263⋊C8C2211yescharacteristic
20C4⋊Q8×C263C2211yescharacteristic
21C4×Q8×C263C2211yescharacteristic
22#107×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—44no—
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—22no—
66C263⋊C8—41no—
67Q8×C263—21no—
68Q8×C263—42no—
69Q8×C263SD1612yescomplemented
70C2×C4×C263—21no—
71C2×C4×C263—21no—
72C2×C4×C263—41no—
73C2×C4×C263C2×D411yescharacteristic
74C2×C4×C263C2×D411yescharacteristic
75C2×C4×C263C2×D411yescharacteristic
76C8×C263—41no—
77C22×C263#12011yescharacteristic
78C2×D263—42no—
79C2×D263—41no—
80C2×D263—41no—
81C2×D263—42no—
82C2×D263—42no—
83C2×D263—41no—
84C4×C263—22no—
85C4×C263—21no—
86C4×C263—41no—
87C4×C263—81no—
88C4×C263C2×SD1611yescharacteristic
89C4×C263#13511yescharacteristic
90C4×C263AGL(1,ℤ/8)11yescharacteristic
91C4×C263#13711yescharacteristic
92Dic263—41no—
93C2×C263#45011yescharacteristic
94C2×C263#45211yescharacteristic
95C2×C263#45311yescharacteristic
96D263—81no—
97D263—82no—
98C263#163111yescharacteristic, complemented, Sylow
99#1631—2631nomaximal, Sylow
100#550—2631no—
101#492—2631no—
102#477D26311yescharacteristic, complemented
103#476—2631no—
104#331—2631no—
105Q8⋊C8—2631no—
106D4⋊C8—2631no—
107C2×#41—5261no—
108C2×SD16—5262no—
109C4⋊Q8C2×D26311yescharacteristic
110#127—2631no—
111#127—5261no—
112#121—5262no—
113#121—5261no—
114C4×Q8C2×D26311yescharacteristic
115C4×D4—2631no—
116C4×D4—5261no—
117#107—21no—
118#106—5261no—
119C4⋊C8—2631no—
120C4⋊C8C2×D26311yescharacteristic
121#103—21no—
122#102—5261no—
123C4×C8—2631no—
124#41—10522no—
125#41—10522no—
126C2×Q8—21no—
127C2×Q8C22⋊D26311yescharacteristic
128C2×D4—2631no—
129C2×D4—2632no—
130C2×D4—5262no—
131C2×D4—5262no—
132C2×D4—5261no—
133C2×D4—5261no—
134C22×C4—5262no—
135C22×C4—5261no—
136SD16—10524no—
137C2×C8—21no—
138C2×C8—5261no—
139C2×C8—5261no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—2631no—
144C4⋊C4C22⋊D26311yescharacteristic
145C22⋊C4—5262no—
146C22⋊C4—5261no—
147C42—21no—
148C42C22×D26311yescharacteristic
149C23—5261no—
150C23—5262no—
151Q8—21no—
152Q8—42no—
153Q8#1686236312yescomplemented
154D4—5261no—
155D4—5261no—
156D4—10522no—
157D4—10524no—
158D4—10521no—
159D4—10521no—
160D4—10521no—
161D4—10521no—
162D4—21042no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—5261no—
167C2×C4—10524no—
168C2×C4—10521no—
169C2×C4—10521no—
170C2×C4D4×D26311yescharacteristic
171C2×C4D4×D26311yescharacteristic
172C2×C4C2×C22⋊D26311yescharacteristic
173C8—41no—
174C8—5262no—
175C8—10521no—
176C22—10522no—
177C22—10521no—
178C22—10521no—
179C22—10522no—
180C22—10522no—
181C22—10521no—
182C22#2255443811yescharacteristic
183C4—22no—
184C4—21no—
185C4—41no—
186C4—81no—
187C4—10521no—
188C4C2×#1686236311yescharacteristic
189C4#2255449311yescharacteristic
190C4#2255449511yescharacteristic
191C4#2255450211yescharacteristic
192C2—21041no—
193C2—21042no—
194C2#3068208811yescharacteristic
195C2#3068209911yescharacteristic
196C2#3068210411yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#477×C263C2
socleC22×C263#120
prime radical#30682610C2
hypercenter#477D263
hypocenterC263#1631
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
2. #30682312C2semidirect
3. #30682225C2semidirect
4. #30681681C2semidirect
5. Q8⋊(C263⋊C8)C2semidirect
6. #30681665C2semidirect
7. #477×C263C2semidirect
69. Q8×C263SD16semidirect
98. C263#1631semidirect
102. #477D263semidirect
153. Q8#16862363semidirect

Maximal subgroups

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

subgroupindex
#306826102
#306823122
#306822252
#306816812
Q8⋊(C263⋊C8)2
#306816652
#477×C2632
#1631263