Finite Group Databasebeta

← #46781862

Subgroups — #46781862

Order 33664.

314 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×D1052C211yesmaximal, characteristic
2#30682312C211yesmaximal, characteristic, complemented
3#30682225C211yesmaximal, characteristic, complemented
4#30681681C211yesmaximal, characteristic, complemented
5D4⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
6#30681665C211yesmaximal, characteristic, complemented
7#476×C263C211yesmaximal, characteristic, complemented
8C22×D1052—21no—
9C2×D4×D263—21no—
10C2×#16862363—22no—
11#22554467C2211yescharacteristic
12#22554445—21no—
13#22554444—21no—
14#22554440—22no—
15C4×D1052C2211yescharacteristic
16#22554401—21no—
17C4⋊(C263⋊C8)C2211yescharacteristic, complemented
18#22554390—21no—
19C4×C263⋊C8C2211yescharacteristic, complemented
20C4⋊Q8×C263C2211yescharacteristic, complemented
21C4×D4×C263C2211yescharacteristic
22#106×C263—21no—
23C4⋊C8×C263C2211yescharacteristic, complemented
24#102×C263—21no—
25C23×D263—22no—
26C2×D1052—22no—
27C2×D1052—21no—
28C2×D1052—21no—
29C2×D1052—42no—
30C2×D1052—42no—
31C2×D1052D411yescharacteristic
32C2×D1052D412yes—
33C2×C22⋊D263—22no—
34D4×D263—42no—
35D4×D263—42no—
36C2×C4×D263—21no—
37#16862363—44no—
38C2×C263⋊C8—21no—
39C2×C263⋊C8—21no—
40C4⋊Dic263D411yescharacteristic
41(C2×D263)⋊C4—22no—
42(C2×D263)⋊C4—21no—
43C2×Q8×C263—21no—
44C2×D4×C263D411yescharacteristic
45C22×C4×C263—21no—
46C2×C8×C263—21no—
47C4⋊C4×C263—21no—
48C4⋊C4×C263—21no—
49C4⋊C4×C263D411yescharacteristic
50C22⋊C4×C263—21no—
51C42×C263C2311yescharacteristic
52C22×D263—21no—
53C22×D263—22no—
54C22×D263—44no—
55C22×D263—44no—
56C22×D263—82no—
57D1052—21no—
58D1052—42no—
59D1052—44no—
60D1052—41no—
61D1052—41no—
62D1052—41no—
63D1052—41no—
64D1052SD1612yescomplemented
65C22⋊D263—44no—
66C2×Dic263—21no—
67C4×D263—41no—
68C4×D263—41no—
69C263⋊C8—22no—
70C263⋊C8—41no—
71C23×C263—21no—
72Q8×C263—42no—
73D4×C263—21no—
74D4×C263SD1612yescomplemented
75C2×C4×C263—21no—
76C2×C4×C263—41no—
77C2×C4×C263—41no—
78C2×C4×C263—41no—
79C2×C4×C263C2×D411yescharacteristic
80C2×C4×C263C2×D411yescharacteristic
81C2×C4×C263C2×D411yescharacteristic
82C8×C263—41no—
83C22×C263—22no—
84C22×C263—41no—
85C22×C263—41no—
86C22×C263#12011yescharacteristic
87C2×D263—22no—
88C2×D263—41no—
89C2×D263—41no—
90C2×D263—42no—
91C2×D263—42no—
92C2×D263—42no—
93C2×D263—88no—
94C4×C263—21no—
95C4×C263—41no—
96C4×C263—81no—
97C4×C263C2×SD1611yescharacteristic
98C4×C263C2×SD1611yescharacteristic
99C4×C263AGL(1,ℤ/8)11yescharacteristic
100C4×C263AGL(1,ℤ/8)11yescharacteristic
101Dic263—41no—
102C2×C263—42no—
103C2×C263#45011yescharacteristic
104C2×C263#45011yescharacteristic
105C2×C263#45311yescharacteristic
106D263—42no—
107D263—82no—
108C263#162911yescharacteristic, complemented, Sylow
109#1629—2631nomaximal, Sylow
110D42—2631no—
111#492—2631no—
112#476—2631no—
113#476D26311yescharacteristic, complemented
114#331—2631no—
115D4⋊C8—2631no—
116D4⋊C8—2631no—
117C22×D4—5261no—
118C22×D4—5261no—
119C2×SD16—5262no—
120C4⋊Q8C2×D26311yescharacteristic, complemented
121#127—2631no—
122#121—5261no—
123#121—5261no—
124#120—5262no—
125C4×D4—2631no—
126C4×D4C2×D26311yescharacteristic
127#106—21no—
128#106—5261no—
129C4⋊C8—2631no—
130C4⋊C8C2×D26311yescharacteristic, complemented
131#102—21no—
132#102—5261no—
133C4×C8—2631no—
134C24—5262no—
135C2×Q8—21no—
136C2×D4—2631no—
137C2×D4—2632no—
138C2×D4—5262no—
139C2×D4—5262no—
140C2×D4—5261no—
141C2×D4—5261no—
142C2×D4—10522no—
143C2×D4—10522no—
144C2×D4—10522no—
145C2×D4—10522no—
146C2×D4C22⋊D26311yescharacteristic
147C22×C4—21no—
148C22×C4—5261no—
149SD16—10524no—
150C2×C8—21no—
151C2×C8—5261no—
152C2×C8—5261no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—2631no—
156C4⋊C4C22⋊D26311yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—5262no—
159C22⋊C4—5261no—
160C42C22×D26311yescharacteristic
161C23—21no—
162C23—5261no—
163C23—5262no—
164C23—10524no—
165C23—10524no—
166C23—21042no—
167Q8—42no—
168D4—21no—
169D4—2632no—
170D4—5261no—
171D4—10522no—
172D4—10524no—
173D4—10524no—
174D4—10521no—
175D4—10521no—
176D4—10521no—
177D4—10521no—
178D4#1686236312yescomplemented
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—5261no—
184C2×C4—10521no—
185C2×C4—10521no—
186C2×C4D4×D26311yescharacteristic
187C2×C4D4×D26311yescharacteristic
188C2×C4C2×C22⋊D26311yescharacteristic
189C8—41no—
190C8—5262no—
191C8—10521no—
192C22—22no—
193C22—41no—
194C22—41no—
195C22—5262no—
196C22—10521no—
197C22—10521no—
198C22—10522no—
199C22—10522no—
200C22—10522no—
201C22—21048no—
202C22#2255443811yescharacteristic
203C4—21no—
204C4—41no—
205C4—81no—
206C4—10521no—
207C4SD16×D26311yescharacteristic
208C4C2×#1686236311yescharacteristic
209C4#2255449511yescharacteristic
210C4#2255449711yescharacteristic
211C2—42no—
212C2—10522no—
213C2—21042no—
214C2#3068208711yescharacteristic
215C2#3068208811yescharacteristic
216C2#3068210411yescharacteristic
subgroupG/H
centerC22#22554438
commutator, cosocleC42×C263C23
FrattiniC42C22×D263
Fitting#476×C263C2
socleC22×C263#120
prime radicalD4×D1052C2
hypercenter#476D263
hypocenterC263#1629
LCSG ▷ C42×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #30682312C2semidirect
3. #30682225C2semidirect
4. #30681681C2semidirect
5. D4⋊(C263⋊C8)C2semidirect
6. #30681665C2semidirect
7. #476×C263C2semidirect
17. C4⋊(C263⋊C8)C22semidirect
19. C4×C263⋊C8C22semidirect
20. C4⋊Q8×C263C22semidirect
23. C4⋊C8×C263C22semidirect
64. D1052SD16semidirect
74. D4×C263SD16semidirect
108. C263#1629semidirect
113. #476D263semidirect
120. C4⋊Q8C2×D263semidirect
130. C4⋊C8C2×D263semidirect
178. D4#16862363semidirect

Maximal subgroups

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

subgroupindex
D4×D10522
#306823122
#306822252
#306816812
D4⋊(C263⋊C8)2
#306816652
#476×C2632
#1629263