Finite Group Databasebeta

← #46781162

Subgroups — #46781162

Order 33664.

262 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 67 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#30682485C211yesmaximal, characteristic
2#30681990C211yesmaximal, characteristic, complemented
3C4×#16862359C211yesmaximal, characteristic, complemented
4#30681667C211yesmaximal, characteristic, complemented
5D4⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
6#30681665C211yesmaximal, characteristic, complemented
7D4⋊C8×C263C211yesmaximal, characteristic, complemented
8C2×#16862376—21no—
9C2×#16862359—21no—
10#22554469C411yescharacteristic
11#22554466C411yescharacteristic
12#22554456—21no—
13#22554445C411yescharacteristic
14#22554443—21no—
15#22554441C411yescharacteristic
16C4×D1052C2211yescharacteristic
17C4×C22⋊D263—21no—
18C42×D263C2211yescharacteristic
19C4⋊(C263⋊C8)C2211yescharacteristic
20(C2×D263)⋊C8—21no—
21#22554380—21no—
22C4×C263⋊C8C2211yescharacteristic
23C8×Dic263—21no—
24C4×D4×C263C2211yescharacteristic
25C4⋊C8×C263C2211yescharacteristic
26C4×C8×C263C2211yescharacteristic
27#16862376—42no—
28#16862376—42no—
29C2×Dic526—21no—
30C2×D1052—21no—
31C2×D1052C2×C411yescharacteristic
32C2×C22⋊D263—21no—
33C2×C22⋊D263—21no—
34C2×C22⋊D263—21no—
35C2×C4×D263—21no—
36C2×C4×D263C2×C411yescharacteristic
37C2×C4×D263D411yescharacteristic
38C2×C4×D263D411yescharacteristic
39#16862359—24no—
40C2×C263⋊C8—21no—
41C2×C263⋊C8—21no—
42C4⋊Dic263C2×C411yescharacteristic
43Dic263⋊C4—21no—
44C22⋊Dic263—21no—
45(C2×D263)⋊C4—21no—
46(C2×D263)⋊C4—21no—
47C4×Dic263C2×C411yescharacteristic
48C4×Dic263D411yescharacteristic
49C4×Dic263D411yescharacteristic
50C2×D4×C263C2×C411yescharacteristic
51C22×C4×C263—21no—
52C2×C8×C263—21no—
53C2×C8×C263—21no—
54C4⋊C4×C263C2×C411yescharacteristic
55C22⋊C4×C263—21no—
56C42×C263C2311yescharacteristic
57C22×D263—21no—
58C22×D263C22⋊C411yescharacteristic
59Dic526—42no—
60D1052—21no—
61D1052—21no—
62D1052—42no—
63C22⋊D263—42no—
64C22⋊D263—42no—
65C22⋊D263—42no—
66C2×Dic263—21no—
67C2×Dic263C22⋊C411yescharacteristic
68C2×Dic263C22⋊C411yescharacteristic
69C2×Dic263C22⋊C411yescharacteristic
70C4×D263—21no—
71C4×D263—21no—
72C4×D263—21no—
73C4×D263—21no—
74C4×D263—22no—
75C4×D263—41no—
76C4×D263—41no—
77C263⋊C8—22no—
78C263⋊C8—41no—
79C23×C263—21no—
80D4×C263—21no—
81D4×C263—21no—
82C2×C4×C263—21no—
83C2×C4×C263—41no—
84C2×C4×C263—41no—
85C2×C4×C263C22×C411yescharacteristic
86C2×C4×C263C2×D411yescharacteristic
87C2×C4×C263C2×D411yescharacteristic
88C8×C263—22no—
89C8×C263—41no—
90C22×C263—41no—
91C22×C263—41no—
92C22×C263—41no—
93C22×C263C2×C22⋊C411yescharacteristic
94C2×D263—21no—
95C2×D263—21no—
96C2×D263—21no—
97C2×D263—41no—
98C2×D263—41no—
99C2×D263—41no—
100C4×C263—21no—
101C4×C263—41no—
102C4×C263#13111yescharacteristic
103C4×C263#13111yescharacteristic
104C4×C263AGL(1,ℤ/8)11yescharacteristic
105C4×C263AGL(1,ℤ/8)11yescharacteristic
106Dic263—21no—
107Dic263—21no—
108Dic263—41no—
109Dic263#10412yes—
110C2×C263—81no—
111C2×C263#40811yescharacteristic
112C2×C263#41811yescharacteristic
113C2×C263C2×#10411yescharacteristic
114D263—41no—
115D263—81no—
116C263#148411yescharacteristic, complemented, Sylow
117#1484—2631nomaximal, Sylow
118#532—2631no—
119#431—2631no—
120C4×M16—2631no—
121D4⋊C8—2631no—
122D4⋊C8—2631no—
123D4⋊C8—2631no—
124D4⋊C8D26311yescharacteristic, complemented
125C2×#41—5261no—
126C2×M16—5261no—
127C4⋊Q8—2631no—
128#127—2631no—
129#124—5261no—
130#121—2631no—
131#121—2631no—
132#121—5261no—
133C4×D4—2631no—
134C4×D4—5261no—
135C4×D4C2×D26311yescharacteristic
136C2×C42—2631no—
137C4⋊C8—2631no—
138C4⋊C8C2×D26311yescharacteristic
139C22⋊C8—5261no—
140#97—5261no—
141C4×C8—2631no—
142C4×C8—5261no—
143C4×C8C2×D26311yescharacteristic
144#41—10522no—
145#41—10522no—
146C2×Q8—5261no—
147C2×D4—2631no—
148C2×D4—5261no—
149C2×D4—5261no—
150C2×D4—5261no—
151C2×D4—5261no—
152C2×D4C4×D26311yescharacteristic
153C22×C4—21no—
154C22×C4—2631no—
155C22×C4—2631no—
156C22×C4—2631no—
157C22×C4—5261no—
158M16—5264no—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—5261no—
162C2×C8—5261no—
163C4⋊C4—2631no—
164C4⋊C4—5261no—
165C4⋊C4C4×D26311yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—5261no—
168C22⋊C4—5261no—
169C22⋊C4—5261no—
170C42—2631no—
171C42—2631no—
172C42—2631no—
173C42C22×D26311yescharacteristic
174C23—21no—
175C23—2631no—
176C23—5261no—
177Q8—10522no—
178D4—21no—
179D4—21no—
180D4—5261no—
181D4—5261no—
182D4—10522no—
183D4—10522no—
184D4—10522no—
185D4—10522no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—2631no—
190C2×C4—2631no—
191C2×C4—2631no—
192C2×C4—5262no—
193C2×C4—5261no—
194C2×C4—5261no—
195C2×C4—5261no—
196C2×C4—5261no—
197C2×C4—5261no—
198C2×C4—10521no—
199C2×C4—10521no—
200C2×C4C2×C4×D26311yescharacteristic
201C2×C4D4×D26311yescharacteristic
202C2×C4D4×D26311yescharacteristic
203C8—22no—
204C8—41no—
205C8—5262no—
206C8—10521no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—5261no—
211C22—5261no—
212C22—5261no—
213C22—10521no—
214C22—10521no—
215C22—10521no—
216C22C22⋊C4×D26311yescharacteristic
217C4—21no—
218C4—41no—
219C4—2632no—
220C4—5261no—
221C4—5261no—
222C4—10521no—
223C4#2255447611yescharacteristic
224C4#2255447811yescharacteristic
225C4#2255449411yescharacteristic
226C4#2255449711yescharacteristic
227C2—81no—
228C2—10521no—
229C2—21041no—
230C2#3068190311yescharacteristic
231C2#3068194111yescharacteristic
232C2#104×D26311yescharacteristic
subgroupG/H
centerC2×C4D4×D263
commutatorC2×C4×C263C22×C4
FrattiniC42C22×D263
FittingD4⋊C8×C263C2
socleC22×C263C2×C22⋊C4
prime radical#30682485C2
cosocleC42×C263C23
hypercenterD4⋊C8D263
hypocenterC263#1484
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #30681990C2semidirect
3. C4×#16862359C2semidirect
4. #30681667C2semidirect
5. D4⋊(C263⋊C8)C2semidirect
6. #30681665C2semidirect
7. D4⋊C8×C263C2semidirect
116. C263#1484semidirect
124. D4⋊C8D263semidirect

Maximal subgroups

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

subgroupindex
#306824852
#306819902
C4×#168623592
#306816672
D4⋊(C263⋊C8)2
#306816652
D4⋊C8×C2632
#1484263