Finite Group Databasebeta

← #46781214

Subgroups — #46781214

Order 33664.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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#30681994C211yesmaximal, characteristic, complemented
3#30681989C211yesmaximal, characteristic, complemented
4#30681667C211yesmaximal, characteristic, complemented
5D4⋊(C263⋊C8)C211yesmaximal, characteristic, complemented
6#30681665C211yesmaximal, characteristic, complemented
7D4⋊C8×C263C211yesmaximal, characteristic, complemented
8C2×#16862376—21no—
9#22554469C411yescharacteristic
10#22554466C411yescharacteristic
11#22554456—21no—
12#22554445C411yescharacteristic
13#22554443—21no—
14#22554441C411yescharacteristic
15C4×D1052C2211yescharacteristic
16C4×C22⋊D263—21no—
17C42×D263C2211yescharacteristic
18C4⋊(C263⋊C8)C2211yescharacteristic
19Dic263⋊C8—21no—
20(C2×D263)⋊C8—21no—
21(C2×D263)⋊C8—21no—
22#22554380—21no—
23C4×C263⋊C8C2211yescharacteristic
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
39C2×C263⋊C8—21no—
40C2×C263⋊C8—21no—
41C4⋊Dic263C2×C411yescharacteristic
42Dic263⋊C4—21no—
43C22⋊Dic263—21no—
44(C2×D263)⋊C4—21no—
45(C2×D263)⋊C4—21no—
46C4×Dic263C2×C411yescharacteristic
47C4×Dic263D411yescharacteristic
48C4×Dic263D411yescharacteristic
49C2×D4×C263C2×C411yescharacteristic
50C22×C4×C263—21no—
51C2×C8×C263—21no—
52C2×C8×C263—21no—
53C4⋊C4×C263C2×C411yescharacteristic
54C22⋊C4×C263—21no—
55C42×C263C2311yescharacteristic
56C22×D263—21no—
57C22×D263C22⋊C411yescharacteristic
58Dic526—42no—
59D1052—21no—
60D1052—21no—
61D1052—42no—
62C22⋊D263—42no—
63C22⋊D263—42no—
64C22⋊D263—42no—
65C2×Dic263—21no—
66C2×Dic263C22⋊C411yescharacteristic
67C2×Dic263C22⋊C411yescharacteristic
68C2×Dic263C22⋊C411yescharacteristic
69C4×D263—21no—
70C4×D263—21no—
71C4×D263—21no—
72C4×D263—21no—
73C4×D263—41no—
74C4×D263—41no—
75C4×D263—41no—
76C263⋊C8—41no—
77C263⋊C8—41no—
78C23×C263—21no—
79D4×C263—21no—
80D4×C263—21no—
81C2×C4×C263—21no—
82C2×C4×C263—41no—
83C2×C4×C263—41no—
84C2×C4×C263C22×C411yescharacteristic
85C2×C4×C263C2×D411yescharacteristic
86C2×C4×C263C2×D411yescharacteristic
87C8×C263—41no—
88C8×C263—41no—
89C22×C263—41no—
90C22×C263—41no—
91C22×C263—41no—
92C22×C263C2×C22⋊C411yescharacteristic
93C2×D263—21no—
94C2×D263—21no—
95C2×D263—21no—
96C2×D263—41no—
97C2×D263—41no—
98C2×D263—41no—
99C4×C263—21no—
100C4×C263—41no—
101C4×C263#13111yescharacteristic
102C4×C263#13111yescharacteristic
103C4×C263AGL(1,ℤ/8)11yescharacteristic
104C4×C263AGL(1,ℤ/8)11yescharacteristic
105Dic263—21no—
106Dic263—21no—
107Dic263—21no—
108Dic263—41no—
109C2×C263—81no—
110C2×C263#40811yescharacteristic
111C2×C263#41811yescharacteristic
112C2×C263#42111yescharacteristic
113D263—41no—
114D263—81no—
115C263#149611yescharacteristic, complemented, Sylow
116#1496—2631nomaximal, Sylow
117#532—2631no—
118#432—2631no—
119#431—2631no—
120D4⋊C8—2631no—
121D4⋊C8—2631no—
122D4⋊C8—2631no—
123D4⋊C8D26311yescharacteristic, complemented
124C2×#41—5261no—
125C4⋊Q8—2631no—
126#127—2631no—
127#124—5261no—
128#121—2631no—
129#121—2631no—
130#121—5261no—
131C4×D4—2631no—
132C4×D4—5261no—
133C4×D4C2×D26311yescharacteristic
134C2×C42—2631no—
135C4⋊C8—2631no—
136C4⋊C8—5261no—
137C4⋊C8C2×D26311yescharacteristic
138C22⋊C8—5261no—
139C22⋊C8—5261no—
140#97—5261no—
141C4×C8—2631no—
142C4×C8C2×D26311yescharacteristic
143#41—10522no—
144#41—10522no—
145C2×Q8—5261no—
146C2×D4—2631no—
147C2×D4—5261no—
148C2×D4—5261no—
149C2×D4—5261no—
150C2×D4—5261no—
151C2×D4C4×D26311yescharacteristic
152C22×C4—21no—
153C22×C4—2631no—
154C22×C4—2631no—
155C22×C4—2631no—
156C22×C4—5261no—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—5261no—
160C2×C8—5261no—
161C4⋊C4—2631no—
162C4⋊C4—5261no—
163C4⋊C4C4×D26311yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—5261no—
166C22⋊C4—5261no—
167C22⋊C4—5261no—
168C42—2631no—
169C42—2631no—
170C42—2631no—
171C42C22×D26311yescharacteristic
172C23—21no—
173C23—2631no—
174C23—5261no—
175Q8—10522no—
176D4—21no—
177D4—21no—
178D4—5261no—
179D4—5261no—
180D4—10522no—
181D4—10522no—
182D4—10522no—
183D4—10522no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—2631no—
188C2×C4—2631no—
189C2×C4—2631no—
190C2×C4—5261no—
191C2×C4—5261no—
192C2×C4—5261no—
193C2×C4—5261no—
194C2×C4—5261no—
195C2×C4—10521no—
196C2×C4—10521no—
197C2×C4—10521no—
198C2×C4C2×C4×D26311yescharacteristic
199C2×C4D4×D26311yescharacteristic
200C2×C4D4×D26311yescharacteristic
201C8—41no—
202C8—41no—
203C8—10521no—
204C8—10521no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—5261no—
209C22—5261no—
210C22—5261no—
211C22—10521no—
212C22—10521no—
213C22—10521no—
214C22C22⋊C4×D26311yescharacteristic
215C4—21no—
216C4—41no—
217C4—5261no—
218C4—5261no—
219C4—5261no—
220C4—10521no—
221C4#2255447611yescharacteristic
222C4#2255447811yescharacteristic
223C4#2255449411yescharacteristic
224C4#2255449711yescharacteristic
225C2—81no—
226C2—10521no—
227C2—21041no—
228C2#3068190311yescharacteristic
229C2#3068194111yescharacteristic
230C2#3068195311yescharacteristic
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#1496
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. #30681994C2semidirect
3. #30681989C2semidirect
4. #30681667C2semidirect
5. D4⋊(C263⋊C8)C2semidirect
6. #30681665C2semidirect
7. D4⋊C8×C263C2semidirect
115. C263#1496semidirect
123. D4⋊C8D263semidirect

Maximal subgroups

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

subgroupindex
#306824852
#306819942
#306819892
#306816672
D4⋊(C263⋊C8)2
#306816652
D4⋊C8×C2632
#1496263