Finite Group Databasebeta

← #46781292

Subgroups — #46781292

Order 33664.

252 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 61 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#30682483C211yesmaximal, characteristic
2#30681992C211yesmaximal, characteristic, complemented
3#30681805C211yesmaximal, characteristic, complemented
4#30681673C211yesmaximal, characteristic, complemented
5#30681672C211yesmaximal, characteristic, complemented
6#30681671C211yesmaximal, characteristic, complemented
7#327×C263C211yesmaximal, characteristic, complemented
8C2×#16862375—21no—
9#22554469C411yescharacteristic, complemented
10#22554466C411yescharacteristic, complemented
11#22554456—21no—
12#22554444C2211yescharacteristic
13#22554442—21no—
14D4×Dic263C411yescharacteristic, complemented
15#22554432C411yescharacteristic, complemented
16(C22⋊D263)⋊C4—21no—
17C2×C4×Dic263C2211yescharacteristic
18Dic263⋊C8—21no—
19C22⋊(C263⋊C8)C2211yescharacteristic
20#22554380—21no—
21C263⋊#95—21no—
22C263⋊#95—21no—
23C263⋊#95C2211yescharacteristic
24#121×C263C2211yescharacteristic
25C22⋊C8×C263C2211yescharacteristic
26#95×C263C2211yescharacteristic
27#16862375—42no—
28#16862375—42no—
29C2×Dic526—21no—
30C2×D1052C2×C411yescharacteristic
31C2×C22⋊D263—21no—
32C2×C22⋊D263—21no—
33C2×C22⋊D263—21no—
34C22×Dic263—21no—
35C22×Dic263—21no—
36C22×Dic263D411yescharacteristic
37C22×Dic263D411yescharacteristic
38C2×C4×D263—21no—
39C2×C263⋊C8—21no—
40C4⋊Dic263C2×C411yescharacteristic
41Dic263⋊C4—21no—
42C22⋊Dic263—21no—
43(C2×D263)⋊C4—21no—
44(C2×D263)⋊C4—21no—
45C4×Dic263C2×C411yescharacteristic
46C4×Dic263C2×C411yescharacteristic
47C4×Dic263D411yescharacteristic
48C4×Dic263D411yescharacteristic
49C2×D4×C263—21no—
50C2×D4×C263C2×C411yescharacteristic
51C22×C4×C263—21no—
52C22×C4×C263C2311yescharacteristic
53C2×C8×C263—21no—
54C4⋊C4×C263C2×C411yescharacteristic
55C22⋊C4×C263—21no—
56C22×D263—21no—
57Dic526—42no—
58D1052—41no—
59C22⋊D263—42no—
60C22⋊D263—42no—
61C22⋊D263—41no—
62C22⋊D263—41no—
63C2×Dic263—21no—
64C2×Dic263—21no—
65C2×Dic263—21no—
66C2×Dic263—41no—
67C2×Dic263—42no—
68C2×Dic263—41no—
69C2×Dic263—41no—
70C2×Dic263—41no—
71C2×Dic263C22⋊C411yescharacteristic
72C2×Dic263C22⋊C411yescharacteristic
73C2×Dic263C22⋊C411yescharacteristic
74C2×Dic263C22⋊C411yescharacteristic
75C4×D263—42no—
76C263⋊C8—41no—
77C23×C263—21no—
78C23×C263C2×D411yescharacteristic
79D4×C263—41no—
80D4×C263—41no—
81D4×C263—41no—
82C2×C4×C263—21no—
83C2×C4×C263—41no—
84C2×C4×C263—41no—
85C2×C4×C263—41no—
86C2×C4×C263—41no—
87C2×C4×C263C22×C411yescharacteristic
88C2×C4×C263C2×D411yescharacteristic
89C8×C263—41no—
90C22×C263—21no—
91C22×C263—21no—
92C22×C263—41no—
93C22×C263—41no—
94C22×C263—41no—
95C22×C263C2×C22⋊C411yescharacteristic
96C22×C263AGL(1,ℤ/8)11yescharacteristic
97C22×C263AGL(1,ℤ/8)11yescharacteristic
98C2×D263—41no—
99C2×D263—41no—
100C2×D263—41no—
101C4×C263—21no—
102C4×C263—21no—
103C4×C263—41no—
104C4×C263—81no—
105Dic263—21no—
106Dic263—21no—
107Dic263—21no—
108Dic263—21no—
109Dic263—41no—
110Dic263—81no—
111C2×C263—21no—
112C2×C263—21no—
113C2×C263—81no—
114C2×C263#41011yescharacteristic
115C2×C263#41811yescharacteristic
116C2×C263#42111yescharacteristic
117D263—81no—
118C263#151411yescharacteristic, complemented, Sylow
119#1514—2631nomaximal, Sylow
120#532—2631no—
121#432—2631no—
122#383—2631no—
123#327—2631no—
124#327—2631no—
125#327—2631no—
126#327D26311yescharacteristic, complemented
127C2×#41—5261no—
128C4⋊Q8—2631no—
129#127—2631no—
130#124—5261no—
131#121—2631no—
132#121—5261no—
133#121C2×D26311yescharacteristic
134C4×D4—2631no—
135C4×D4—2631no—
136C4×D4—5261no—
137C2×C42—2631no—
138C4⋊C8—5261no—
139C22⋊C8—2631no—
140C22⋊C8C2×D26311yescharacteristic
141#97—5261no—
142#95—2631no—
143#95—5261no—
144#95—5261no—
145#95C2×D26311yescharacteristic
146#41—10522no—
147#41—10522no—
148C2×Q8—5261no—
149C2×D4—21no—
150C2×D4—2631no—
151C2×D4—5261no—
152C2×D4—5261no—
153C2×D4—5261no—
154C2×D4C4×D26311yescharacteristic
155C22×C4—21no—
156C22×C4—2631no—
157C22×C4—2631no—
158C22×C4—5261no—
159C22×C4—5261no—
160C22×C4—5261no—
161C22×C4C22×D26311yescharacteristic
162C2×C8—21no—
163C2×C8—5261no—
164C4⋊C4—2631no—
165C4⋊C4—5261no—
166C4⋊C4C4×D26311yescharacteristic
167C22⋊C4—21no—
168C22⋊C4—5261no—
169C22⋊C4—5261no—
170C22⋊C4—5261no—
171C42—2631no—
172C42—2631no—
173C42—2631no—
174C42—2631no—
175C23—21no—
176C23—5261no—
177C23D4×D26311yescharacteristic
178Q8—10522no—
179D4—41no—
180D4—41no—
181D4—41no—
182D4—10521no—
183D4—10522no—
184D4—10522no—
185D4—10521no—
186D4—10521no—
187C2×C4—21no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—2631no—
193C2×C4—2631no—
194C2×C4—2631no—
195C2×C4—2631no—
196C2×C4—5261no—
197C2×C4—5261no—
198C2×C4—5261no—
199C2×C4—10522no—
200C2×C4—10521no—
201C2×C4—10522no—
202C2×C4—10521no—
203C2×C4—10521no—
204C2×C4—10521no—
205C2×C4C2×C4×D26311yescharacteristic
206C2×C4D4×D26311yescharacteristic
207C8—41no—
208C8—10521no—
209C22—21no—
210C22—21no—
211C22—41no—
212C22—41no—
213C22—41no—
214C22—10521no—
215C22—10521no—
216C22—10521no—
217C22C22⋊C4×D26311yescharacteristic
218C22#2255449411yescharacteristic
219C22#2255449711yescharacteristic
220C4—21no—
221C4—21no—
222C4—41no—
223C4—81no—
224C4—5261no—
225C4—5261no—
226C4—5261no—
227C4—5261no—
228C4—10521no—
229C4—21041no—
230C2—21no—
231C2—21no—
232C2—81no—
233C2—21041no—
234C2#3068191011yescharacteristic
235C2#3068194111yescharacteristic
236C2#3068195311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#327×C263C2
socleC22×C263C2×C22⋊C4
prime radical#30682483C2
cosocleC22×C4×C263C23
hypercenter#327D263
hypocenterC263#1514
LCSG ▷ C2×C4×C263 ▷ C22×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #30681992C2semidirect
3. #30681805C2semidirect
4. #30681673C2semidirect
5. #30681672C2semidirect
6. #30681671C2semidirect
7. #327×C263C2semidirect
9. #22554469C4semidirect
10. #22554466C4semidirect
14. D4×Dic263C4semidirect
15. #22554432C4semidirect
118. C263#1514semidirect
126. #327D263semidirect

Maximal subgroups

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

subgroupindex
#306824832
#306819922
#306818052
#306816732
#306816722
#306816712
#327×C2632
#1514263