Finite Group Databasebeta

← #46783573

Subgroups — #46783573

Order 33664.

360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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#30682484C211yesmaximal, characteristic
2#30681961C211yesmaximal, characteristic, complemented
3C2×#22554398C211yesmaximal, characteristic, complemented
4C2×#22554397C211yesmaximal, characteristic, complemented
5C2×#22554396C211yesmaximal, characteristic, complemented
6C42×Dic263C211yesmaximal, characteristic, complemented
7C2×#104×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9C2×#16862360C2211yescharacteristic
10#22554468C411yescharacteristic, complemented
11#22554466C411yescharacteristic, complemented
12#22554459C411yescharacteristic, complemented
13#22554457C411yescharacteristic, complemented
14#22554442—22no—
15C4×C22⋊D263—22no—
16C2×C4×Dic263—22no—
17C2×C4×Dic263C2211yescharacteristic
18C2×C4×Dic263C2211yescharacteristic
19Dic263⋊C8—22no—
20#22554398—22no—
21#22554397—22no—
22#22554396—22no—
23C2×#41×C263C2211yescharacteristic
24C2×M16×C263C2211yescharacteristic
25C2×C42×C263C2211yescharacteristic
26#104×C263—22no—
27#16862376—21no—
28#16862376—21no—
29#16862376—21no—
30#16862376—21no—
31C2×Dic526C2×C411yescharacteristic
32C2×D1052C2×C411yescharacteristic
33C2×C22⋊D263—22no—
34C2×C22⋊D263—21no—
35C22×Dic263—21no—
36C22×Dic263D412yes—
37C2×C4×D263—21no—
38#16862360—21no—
39#16862360—21no—
40C2×C263⋊C8—21no—
41Dic263⋊C4—22no—
42C22⋊Dic263—22no—
43(C2×D263)⋊C4—22no—
44C4×Dic263—28no—
45C4×Dic263—21no—
46C4×Dic263C2×C411yescharacteristic
47C4×Dic263C2×C411yescharacteristic
48C4×Dic263D412yes—
49C4×Dic263D412yescomplemented
50#41×C263—21no—
51#41×C263—21no—
52#41×C263—21no—
53#41×C263—21no—
54C2×Q8×C263C2×C411yescharacteristic
55C2×D4×C263—21no—
56C2×D4×C263C2×C411yescharacteristic
57C22×C4×C263—21no—
58C22×C4×C263—21no—
59C22×C4×C263C2311yescharacteristic
60M16×C263—21no—
61M16×C263—21no—
62C2×C8×C263—21no—
63C42×C263—21no—
64C42×C263D412yescomplemented
65C22×D263—21no—
66Dic526—21no—
67Dic526—21no—
68D1052—21no—
69D1052—21no—
70C22⋊D263—41no—
71C22⋊D263—41no—
72C22⋊D263—44no—
73C2×Dic263—24no—
74C2×Dic263—22no—
75C2×Dic263—24no—
76C2×Dic263—21no—
77C2×Dic263C22⋊C412yes—
78C2×Dic263C22⋊C412yes—
79C4×D263—41no—
80C4×D263—41no—
81C263⋊C8—41no—
82C23×C263—21no—
83C23×C263C2×D411yescharacteristic
84Q8×C263—21no—
85Q8×C263—21no—
86D4×C263—21no—
87D4×C263—21no—
88D4×C263—41no—
89D4×C263—41no—
90C2×C4×C263—24no—
91C2×C4×C263—22no—
92C2×C4×C263—21no—
93C2×C4×C263—41no—
94C2×C4×C263—41no—
95C2×C4×C263C22×C411yescharacteristic
96C2×C4×C263C2×D411yescharacteristic
97C2×C4×C263C2×D411yescharacteristic
98C2×C4×C263C2×D411yescharacteristic
99C2×C4×C263#4111yescharacteristic
100C2×C4×C263#4111yescharacteristic
101C8×C263—41no—
102C22×C263—22no—
103C22×C263—41no—
104C22×C263—42no—
105C22×C263C2×C22⋊C411yescharacteristic
106C22×C263#12111yescharacteristic
107C22×C263#12111yescharacteristic
108C2×D263—41no—
109C2×D263—42no—
110C4×C263—24no—
111C4×C263—41no—
112C4×C263C4×D411yescharacteristic
113C4×C263C4×D411yescharacteristic
114C4×C263#12411yescharacteristic
115C4×C263#12711yescharacteristic
116Dic263—24no—
117Dic263—22no—
118Dic263—41no—
119Dic263#10414yescomplemented
120C2×C263—21no—
121C2×C263—21no—
122C2×C263—81no—
123C2×C263#39011yescharacteristic
124C2×C263C2×#10412yes—
125D263—81no—
126C263#196211yescharacteristic, complemented, Sylow
127#1962—2631nomaximal, Sylow
128#532—2631no—
129#423—2631no—
130C2×#104—2631no—
131C2×#104—2631no—
132C2×#104—2631no—
133C2×#104D26311yescharacteristic, complemented
134C43—2631no—
135C2×#41—2631no—
136C2×#41C2×D26311yescharacteristic
137C2×M16—2631no—
138C2×M16C2×D26311yescharacteristic
139C4⋊Q8—2631no—
140#127—2631no—
141#124—2631no—
142#124—2631no—
143#121—5262no—
144C4×D4—5262no—
145C2×C42—2631no—
146C2×C42—2631no—
147C2×C42—5262no—
148C2×C42C2×D26311yescharacteristic
149C4⋊C8—5262no—
150#104—22no—
151#104—5262no—
152#104—5262no—
153#104—5262no—
154#41—21no—
155#41—21no—
156#41—21no—
157#41—21no—
158#41—5261no—
159#41—5261no—
160#41—5261no—
161#41—5261no—
162C2×Q8—2631no—
163C2×Q8C4×D26311yescharacteristic
164C2×D4—21no—
165C2×D4—2631no—
166C2×D4—5262no—
167C2×D4—5261no—
168C2×D4C4×D26311yescharacteristic
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—2632no—
172C22×C4—5261no—
173C22×C4—5261no—
174C22×C4C22×D26311yescharacteristic
175M16—21no—
176M16—21no—
177M16—5261no—
178M16—5261no—
179C2×C8—21no—
180C2×C8—5261no—
181C4⋊C4—5262no—
182C22⋊C4—5262no—
183C22⋊C4—5262no—
184C42—21no—
185C42—2631no—
186C42—2631no—
187C42—2632no—
188C42—2632no—
189C42—5268no—
190C42—5261no—
191C42C22⋊D26312yescomplemented
192C23—21no—
193C23—5261no—
194C23D4×D26311yescharacteristic
195Q8—21no—
196Q8—21no—
197Q8—5261no—
198Q8—5261no—
199D4—21no—
200D4—21no—
201D4—41no—
202D4—41no—
203D4—5261no—
204D4—5261no—
205D4—10524no—
206D4—10521no—
207D4—10521no—
208C2×C4—24no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—2632no—
214C2×C4—2632no—
215C2×C4—5264no—
216C2×C4—5264no—
217C2×C4—5262no—
218C2×C4—5261no—
219C2×C4—10521no—
220C2×C4—10521no—
221C2×C4C2×C4×D26311yescharacteristic
222C2×C4D4×D26311yescharacteristic
223C2×C4D4×D26311yescharacteristic
224C2×C4C2×C22⋊D26311yescharacteristic
225C2×C4#1686237511yescharacteristic
226C2×C4#1686237611yescharacteristic
227C8—41no—
228C8—10521no—
229C22—22no—
230C22—42no—
231C22—41no—
232C22—10522no—
233C22—10521no—
234C22C22⋊C4×D26311yescharacteristic
235C22#2255444211yescharacteristic
236C22#2255444311yescharacteristic
237C4—24no—
238C4—41no—
239C4—2634no—
240C4—5264no—
241C4—5262no—
242C4—10521no—
243C4(C22⋊D263)⋊C411yescharacteristic
244C4C4×C22⋊D26311yescharacteristic
245C4#2255445611yescharacteristic
246C4#2255446611yescharacteristic
247C2—21no—
248C2—21no—
249C2—81no—
250C2—21041no—
251C2#3068183811yescharacteristic
252C2#104×D26312yes—
subgroupG/H
centerC2×C4D4×D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC2×#104×C263C2
socleC22×C263C2×C22⋊C4
prime radical#30682484C2
cosocleC22×C4×C263C23
hypercenterC2×#104D263
hypocenterC263#1962
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #30681961C2semidirect
3. C2×#22554398C2semidirect
4. C2×#22554397C2semidirect
5. C2×#22554396C2semidirect
6. C42×Dic263C2semidirect
7. C2×#104×C263C2semidirect
10. #22554468C4semidirect
11. #22554466C4semidirect
12. #22554459C4semidirect
13. #22554457C4semidirect
49. C4×Dic263D4semidirect
64. C42×C263D4semidirect
119. Dic263#104semidirect
126. C263#1962semidirect
133. C2×#104D263semidirect
191. C42C22⋊D263semidirect

Maximal subgroups

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

subgroupindex
#306824842
#306819612
C2×#225543982
C2×#225543972
C2×#225543962
C42×Dic2632
C2×#104×C2632
#1962263