Finite Group Databasebeta

← #46781768

Subgroups — #46781768

Order 33664.

288 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 51 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#30682496C211yesmaximal, characteristic
2#30682257C211yesmaximal, characteristic, complemented
3#30682254C211yesmaximal, characteristic, complemented
4#30681875C211yesmaximal, characteristic, complemented
5#30681671C211yesmaximal, characteristic, complemented
6#30681661C211yesmaximal, characteristic, complemented
7#327×C263C211yesmaximal, characteristic, complemented
8C2×D4×D263—21no—
9#22554455—21no—
10#22554452—21no—
11#22554444C2211yescharacteristic
12#22554442—21no—
13#22554440—21no—
14#22554438—21no—
15C2×C4⋊Dic263—21no—
16C2×C4⋊Dic263C2211yescharacteristic, complemented
17C2×(C2×D263)⋊C4—21no—
18C2×(C2×D263)⋊C4C2211yescharacteristic
19#22554402—21no—
20#22554401—21no—
21#22554392—21no—
22#22554391—21no—
23C22⋊(C263⋊C8)C2211yescharacteristic, complemented
24#121×C263C2211yescharacteristic
25C22⋊C8×C263C2211yescharacteristic, complemented
26#95×C263C2211yescharacteristic, complemented
27C23×D263—21no—
28C23×D263D411yescharacteristic
29C2×D1052—21no—
30C2×D1052D411yescharacteristic
31C2×C22⋊D263—21no—
32C2×C22⋊D263—21no—
33C2×C22⋊D263—21no—
34D4×D263—42no—
35D4×D263—42no—
36C22×Dic263—21no—
37C22×Dic263D411yescharacteristic
38C2×C4×D263—21no—
39C2×C263⋊C8—21no—
40C4⋊Dic263—21no—
41C4⋊Dic263—21no—
42C4⋊Dic263—42no—
43C4⋊Dic263D411yescharacteristic
44Dic263⋊C4—21no—
45C22⋊Dic263—21no—
46(C2×D263)⋊C4—21no—
47(C2×D263)⋊C4—21no—
48(C2×D263)⋊C4—21no—
49(C2×D263)⋊C4—21no—
50(C2×D263)⋊C4—42no—
51C2×D4×C263—21no—
52C2×D4×C263D411yescharacteristic
53C22×C4×C263—21no—
54C22×C4×C263C2311yescharacteristic
55C2×C8×C263—21no—
56C4⋊C4×C263D411yescharacteristic
57C22⋊C4×C263—21no—
58C22×D263—21no—
59C22×D263—21no—
60C22×D263—21no—
61C22×D263—42no—
62C22×D263—41no—
63C22×D263—41no—
64C22×D263—81no—
65C22×D263—81no—
66C22×D263SD1612yes—
67D1052—41no—
68D1052—42no—
69C22⋊D263—42no—
70C22⋊D263—41no—
71C22⋊D263—41no—
72C22⋊D263—81no—
73C2×Dic263—21no—
74C2×Dic263—21no—
75C2×Dic263—41no—
76C2×Dic263—41no—
77C2×Dic263—41no—
78C2×Dic263—41no—
79C4×D263—42no—
80C263⋊C8—41no—
81C23×C263—21no—
82C23×C263C2×D411yescharacteristic
83D4×C263—41no—
84D4×C263—41no—
85D4×C263—41no—
86C2×C4×C263—22no—
87C2×C4×C263—21no—
88C2×C4×C263—41no—
89C2×C4×C263—41no—
90C2×C4×C263—41no—
91C2×C4×C263C2×D411yescharacteristic
92C2×C4×C263C2×D411yescharacteristic
93C8×C263—41no—
94C22×C263—21no—
95C22×C263—21no—
96C22×C263—41no—
97C22×C263—41no—
98C22×C263—41no—
99C22×C263#12011yescharacteristic
100C22×C263C2×SD1611yescharacteristic
101C22×C263AGL(1,ℤ/8)11yescharacteristic
102C2×D263—22no—
103C2×D263—41no—
104C2×D263—41no—
105C2×D263—42no—
106C2×D263—41no—
107C2×D263—41no—
108C2×D263—41no—
109C2×D263—81no—
110C2×D263—84no—
111C4×C263—21no—
112C4×C263—21no—
113C4×C263—42no—
114C4×C263—41no—
115Dic263—41no—
116Dic263—41no—
117Dic263—81no—
118C2×C263—21no—
119C2×C263—21no—
120C2×C263—81no—
121C2×C263#45011yescharacteristic
122C2×C263#45311yescharacteristic
123C2×C263#45811yescharacteristic
124D263—42no—
125D263—81no—
126C263#161311yescharacteristic, complemented, Sylow
127#1613—2631nomaximal, Sylow
128#534—2631no—
129#481—2631no—
130#481—2631no—
131#399—2631no—
132#327—2631no—
133#327D26311yescharacteristic, complemented
134#323—2631no—
135C22×D4—5261no—
136#123—5261no—
137#123—5261no—
138#121—2631no—
139#121—5261no—
140#121C2×D26311yescharacteristic
141#120—5261no—
142#120—5261no—
143C2×C4⋊C4—2631no—
144C2×C4⋊C4—5261no—
145C2×C22⋊C4—2631no—
146C2×C22⋊C4—5261no—
147#106—5261no—
148#106—5261no—
149#102—5261no—
150#102—5261no—
151C22⋊C8—2631no—
152C22⋊C8C2×D26311yescharacteristic, complemented
153#95C2×D26311yescharacteristic, complemented
154C24—2631no—
155C24—5261no—
156C2×D4—21no—
157C2×D4—2631no—
158C2×D4—5261no—
159C2×D4—5261no—
160C2×D4—5261no—
161C2×D4—5261no—
162C2×D4—10522no—
163C2×D4—10522no—
164C2×D4D105211yescharacteristic
165C22×C4—21no—
166C22×C4—2631no—
167C22×C4—5261no—
168C22×C4—5261no—
169C22×C4C22×D26311yescharacteristic
170C2×C8—21no—
171C2×C8—5261no—
172C4⋊C4—2631no—
173C4⋊C4—5261no—
174C4⋊C4—5261no—
175C4⋊C4—5261no—
176C4⋊C4—10522no—
177C4⋊C4D105211yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—5261no—
180C22⋊C4—5261no—
181C22⋊C4—5261no—
182C22⋊C4—5261no—
183C22⋊C4—5261no—
184C22⋊C4—10522no—
185C23—21no—
186C23—2632no—
187C23—5261no—
188C23—5261no—
189C23—5261no—
190C23—10521no—
191C23—10521no—
192C23—10522no—
193C23—21041no—
194C23—21041no—
195C23D4×D26311yescharacteristic
196D4—41no—
197D4—41no—
198D4—41no—
199D4—10521no—
200D4—10522no—
201D4—10522no—
202D4—10521no—
203D4—10521no—
204D4—21041no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—5261no—
211C2×C4—5261no—
212C2×C4—10522no—
213C2×C4—10521no—
214C2×C4—10521no—
215C2×C4—10521no—
216C2×C4—10521no—
217C2×C4D4×D26311yescharacteristic
218C2×C4C2×D105211yescharacteristic
219C8—41no—
220C8—10521no—
221C22—21no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—5262no—
227C22—10522no—
228C22—10521no—
229C22—10521no—
230C22—10521no—
231C22—10521no—
232C22—10521no—
233C22—21041no—
234C22—21044no—
235C22#2255444011yescharacteristic
236C22SD16×D26311yescharacteristic
237C22#2255449411yescharacteristic
238C4—21no—
239C4—21no—
240C4—42no—
241C4—41no—
242C4—10521no—
243C4—10521no—
244C4—21041no—
245C2—21no—
246C2—21no—
247C2—81no—
248C2—10522no—
249C2—21041no—
250C2#3068209011yescharacteristic
251C2#3068210711yescharacteristic
252C2#3068212911yescharacteristic
subgroupG/H
centerC22#22554440
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
Fitting#327×C263C2
socleC22×C263#120
prime radical#30682496C2
hypercenter#327D263
hypocenterC263#1613
LCSG ▷ C22×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. #30682257C2semidirect
3. #30682254C2semidirect
4. #30681875C2semidirect
5. #30681671C2semidirect
6. #30681661C2semidirect
7. #327×C263C2semidirect
16. C2×C4⋊Dic263C22semidirect
23. C22⋊(C263⋊C8)C22semidirect
25. C22⋊C8×C263C22semidirect
26. #95×C263C22semidirect
126. C263#1613semidirect
133. #327D263semidirect
152. C22⋊C8C2×D263semidirect
153. #95C2×D263semidirect

Maximal subgroups

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

subgroupindex
#306824962
#306822572
#306822542
#306818752
#306816712
#306816612
#327×C2632
#1613263