Finite Group Databasebeta

← #46783187

Subgroups — #46783187

Order 33664.

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

normal subgroups only

This group has 442 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#30682445C211yesmaximal, characteristic
2C2×C42×D263C211yesmaximal, characteristic, complemented
3C2×#22554397C211yesmaximal, characteristic, complemented
4#30681901C211yesmaximal, characteristic, complemented
5#30681699C211yesmaximal, characteristic, complemented
6#30681698C211yesmaximal, characteristic, complemented
7C2×#104×C263C211yesmaximal, characteristic, complemented
8C22×C4×D263—21no—
9C22×C4×D263C2211yescharacteristic
10C2×#16862360C2211yescharacteristic
11#22554451—21no—
12#22554446C412yescomplemented
13#22554441C412yescomplemented
14#22554438—21no—
15C4×C22⋊D263—22no—
16#22554429C2211yescharacteristic
17C2×C4×Dic263—21no—
18C2×C4×Dic263C2211yescharacteristic
19C42×D263—22no—
20C42×D263—22no—
21#22554397—22no—
22(C2×D263)⋊C8—22no—
23C2×#41×C263C2211yescharacteristic
24C2×M16×C263C2211yescharacteristic
25C2×C42×C263C2211yescharacteristic
26#104×C263—22no—
27C23×D263D411yescharacteristic
28C2×C22⋊D263—22no—
29C22×Dic263—21no—
30C22×Dic263D411yescharacteristic
31C2×C4×D263—24no—
32C2×C4×D263—28no—
33C2×C4×D263—21no—
34C2×C4×D263—21no—
35C2×C4×D263—21no—
36C2×C4×D263—21no—
37C2×C4×D263C2×C412yes—
38C2×C4×D263D412yes—
39#16862360—21no—
40#16862360—21no—
41C2×C263⋊C8—21no—
42C4⋊Dic263C2×C412yescomplemented
43Dic263⋊C4—22no—
44C22⋊Dic263—22no—
45C22⋊Dic263—21no—
46(C2×D263)⋊C4—22no—
47C4×Dic263—24no—
48C4×Dic263—21no—
49C4×Dic263—21no—
50C4×Dic263D412yescomplemented
51#41×C263—21no—
52#41×C263—21no—
53#41×C263—21no—
54#41×C263—21no—
55C2×Q8×C263C2×C411yescharacteristic, complemented
56C2×D4×C263—21no—
57C2×D4×C263C2×C411yescharacteristic, complemented
58C22×C4×C263—21no—
59C22×C4×C263—21no—
60C22×C4×C263C2311yescharacteristic
61M16×C263—21no—
62M16×C263—21no—
63C2×C8×C263—21no—
64C42×C263—21no—
65C42×C263D412yescomplemented
66C22×D263—21no—
67C22×D263—21no—
68C22×D263—24no—
69C22×D263C22⋊C412yes—
70C22⋊D263—44no—
71C2×Dic263—24no—
72C2×Dic263—21no—
73C2×Dic263—22no—
74C2×Dic263—21no—
75C2×Dic263—22no—
76C2×Dic263C22⋊C412yes—
77C4×D263—216no—
78C4×D263—22no—
79C4×D263—22no—
80C4×D263—22no—
81C4×D263—22no—
82C263⋊C8—41no—
83C23×C263—21no—
84C23×C263C2×D411yescharacteristic
85Q8×C263—21no—
86Q8×C263—21no—
87D4×C263—21no—
88D4×C263—21no—
89D4×C263—41no—
90D4×C263—41no—
91C2×C4×C263—24no—
92C2×C4×C263—22no—
93C2×C4×C263—21no—
94C2×C4×C263—41no—
95C2×C4×C263—41no—
96C2×C4×C263C22×C411yescharacteristic
97C2×C4×C263C2×D411yescharacteristic
98C2×C4×C263C2×D411yescharacteristic
99C2×C4×C263C2×D411yescharacteristic
100C2×C4×C263#4111yescharacteristic
101C2×C4×C263#4111yescharacteristic
102C8×C263—41no—
103C22×C263—22no—
104C22×C263—41no—
105C22×C263—42no—
106C22×C263C2×C22⋊C411yescharacteristic
107C22×C263#12011yescharacteristic
108C22×C263#12311yescharacteristic
109C2×D263—24no—
110C2×D263—24no—
111C2×D263—22no—
112C2×D263—22no—
113C2×D263#10414yescomplemented
114C4×C263—24no—
115C4×C263—41no—
116C4×C263C4×D411yescharacteristic
117C4×C263C4×D411yescharacteristic
118C4×C263#12111yescharacteristic
119C4×C263#12111yescharacteristic
120Dic263—24no—
121Dic263—22no—
122Dic263—42no—
123C2×C263—21no—
124C2×C263—21no—
125C2×C263—81no—
126C2×C263#38611yescharacteristic
127C2×C263C2×#10412yes—
128D263—24no—
129C263#189611yescharacteristic, complemented, Sylow
130#1896—2631nomaximal, Sylow
131#525—2631no—
132C22×C42—2631no—
133C2×#104—2631no—
134C2×#104D26311yescharacteristic, complemented
135#407—2631no—
136#339—2631no—
137#339—2631no—
138C2×#41C2×D26311yescharacteristic
139C23×C4—2631no—
140C23×C4—5261no—
141C2×M16—2631no—
142C2×M16C2×D26311yescharacteristic
143#123—5261no—
144C22⋊Q8—2632no—
145#121—2632no—
146#120—5261no—
147C4×D4—5262no—
148#117—2631no—
149C2×C42—2631no—
150C2×C42—5262no—
151C2×C42—5261no—
152C2×C42—5262no—
153C2×C42C2×D26311yescharacteristic
154#104—22no—
155#104—5262no—
156C22⋊C8—5262no—
157C24—2631no—
158#41—21no—
159#41—21no—
160#41—21no—
161#41—21no—
162C2×Q8C4×D26311yescharacteristic, complemented
163C2×D4—21no—
164C2×D4—5262no—
165C2×D4C4×D26311yescharacteristic, complemented
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—2631no—
169C22×C4—2632no—
170C22×C4—2632no—
171C22×C4—5264no—
172C22×C4—5268no—
173C22×C4—5261no—
174C22×C4—5261no—
175C22×C4—5261no—
176C22×C4—5261no—
177C22×C4—5261no—
178C22×C4C22×D26311yescharacteristic
179M16—21no—
180M16—21no—
181M16—5261no—
182M16—5261no—
183C2×C8—21no—
184C2×C8—5261no—
185C4⋊C4—2632no—
186C4⋊C4—5262no—
187C22⋊C4—5262no—
188C22⋊C4—5262no—
189C22⋊C4—5261no—
190C42—21no—
191C42—2632no—
192C42—5264no—
193C42—5261no—
194C42—5261no—
195C42C22⋊D26312yescomplemented
196C23—21no—
197C23—2632no—
198C23—5264no—
199C23—5261no—
200C23—5261no—
201C23D4×D26311yescharacteristic
202Q8—21no—
203Q8—21no—
204D4—21no—
205D4—21no—
206D4—41no—
207D4—41no—
208D4—10524no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—2632no—
215C2×C4—52616no—
216C2×C4—5264no—
217C2×C4—5262no—
218C2×C4—5261no—
219C2×C4—5261no—
220C2×C4—5262no—
221C2×C4—5262no—
222C2×C4—5262no—
223C2×C4—5262no—
224C2×C4—5262no—
225C2×C4C2×C4×D26311yescharacteristic
226C2×C4D4×D26311yescharacteristic
227C2×C4D4×D26311yescharacteristic
228C2×C4C2×C22⋊D26311yescharacteristic
229C2×C4#1686237511yescharacteristic
230C2×C4#1686237611yescharacteristic
231C8—41no—
232C8—10521no—
233C22—22no—
234C22—42no—
235C22—41no—
236C22—2634no—
237C22—5264no—
238C22—5264no—
239C22—5262no—
240C22—5262no—
241C22C22⋊C4×D26311yescharacteristic
242C22#2255443811yescharacteristic
243C22#2255445211yescharacteristic
244C4—24no—
245C4—41no—
246C4—5264no—
247C4—5262no—
248C4—10522no—
249C4(C22⋊D263)⋊C411yescharacteristic
250C4C4×C22⋊D26311yescharacteristic
251C4#2255444111yescharacteristic
252C4#2255444311yescharacteristic
253C2—21no—
254C2—21no—
255C2—81no—
256C2—5264no—
257C2#3068181411yescharacteristic
258C2#104×D26312yes—
subgroupG/H
centerC2×C4D4×D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC2×#104×C263C2
socleC22×C263C2×C22⋊C4
prime radical#30682445C2
cosocleC22×C4×C263C23
hypercenterC2×#104D263
hypocenterC263#1896
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. C2×C42×D263C2semidirect
3. C2×#22554397C2semidirect
4. #30681901C2semidirect
5. #30681699C2semidirect
6. #30681698C2semidirect
7. C2×#104×C263C2semidirect
12. #22554446C4semidirect
13. #22554441C4semidirect
42. C4⋊Dic263C2×C4semidirect
50. C4×Dic263D4semidirect
55. C2×Q8×C263C2×C4semidirect
57. C2×D4×C263C2×C4semidirect
65. C42×C263D4semidirect
113. C2×D263#104semidirect
129. C263#1896semidirect
134. C2×#104D263semidirect
162. C2×Q8C4×D263semidirect
165. C2×D4C4×D263semidirect
195. C42C22⋊D263semidirect

Maximal subgroups

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

subgroupindex
#306824452
C2×C42×D2632
C2×#225543972
#306819012
#306816992
#306816982
C2×#104×C2632
#1896263