Finite Group Databasebeta

← #46783189

Subgroups — #46783189

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#30682450C211yesmaximal, characteristic
2C2×C42×D263C211yesmaximal, characteristic, complemented
3C2×#22554398C211yesmaximal, characteristic, complemented
4C2×#22554396C211yesmaximal, characteristic, complemented
5#30681901C211yesmaximal, characteristic, complemented
6#30681697C211yesmaximal, characteristic, complemented
7#339×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9C22×C4×D263—21no—
10C22×C4×D263C2211yescharacteristic
11C2×#16862360C2211yescharacteristic
12#22554454—21no—
13#22554450C412yescomplemented
14#22554445C412yescomplemented
15#22554440—21no—
16C4×D1052—22no—
17C2×C4×Dic263—21no—
18C2×C4×Dic263C2211yescharacteristic
19C42×D263—22no—
20C42×D263—22no—
21#22554398—22no—
22#22554396—22no—
23(C2×D263)⋊C8—22no—
24C2×M16×C263C2211yescharacteristic
25#117×C263C2211yescharacteristic
26C2×C42×C263C2211yescharacteristic
27C23×D263D411yescharacteristic
28#16862376—21no—
29#16862376—21no—
30#16862376—21no—
31#16862376—21no—
32C2×Dic526C2×C411yescharacteristic, complemented
33C2×D1052—22no—
34C2×D1052C2×C411yescharacteristic, complemented
35C2×C22⋊D263—21no—
36C22×Dic263—21no—
37C22×Dic263D411yescharacteristic
38C2×C4×D263—24no—
39C2×C4×D263—28no—
40C2×C4×D263—21no—
41C2×C4×D263—21no—
42C2×C4×D263—21no—
43C2×C4×D263—21no—
44C2×C4×D263—21no—
45C2×C4×D263C2×C412yes—
46C2×C4×D263D412yes—
47#16862360—21no—
48#16862360—21no—
49C2×C263⋊C8—21no—
50C4⋊Dic263—22no—
51(C2×D263)⋊C4—22no—
52(C2×D263)⋊C4—22no—
53C4×Dic263—24no—
54C4×Dic263—21no—
55C4×Dic263D412yescomplemented
56C22×C4×C263—21no—
57C22×C4×C263C2311yescharacteristic
58M16×C263—21no—
59M16×C263—21no—
60C2×C8×C263—21no—
61C4⋊C4×C263C2×C412yescomplemented
62C22⋊C4×C263—21no—
63C42×C263—21no—
64C42×C263—21no—
65C42×C263D412yescomplemented
66C22×D263—21no—
67C22×D263—21no—
68C22×D263—24no—
69C22×D263—21no—
70C22×D263C22⋊C412yes—
71Dic526—21no—
72Dic526—21no—
73D1052—21no—
74D1052—21no—
75D1052—44no—
76C22⋊D263—41no—
77C22⋊D263—41no—
78C2×Dic263—24no—
79C2×Dic263—21no—
80C2×Dic263—22no—
81C2×Dic263—21no—
82C2×Dic263—21no—
83C2×Dic263C22⋊C412yes—
84C4×D263—216no—
85C4×D263—22no—
86C4×D263—22no—
87C4×D263—22no—
88C4×D263—22no—
89C4×D263—41no—
90C4×D263—41no—
91C263⋊C8—41no—
92C23×C263C2×D411yescharacteristic
93C2×C4×C263—24no—
94C2×C4×C263—22no—
95C2×C4×C263—22no—
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×C263C2×C22⋊C411yescharacteristic
105C22×C263#12011yescharacteristic
106C22×C263#12311yescharacteristic
107C2×D263—24no—
108C2×D263—24no—
109C2×D263—22no—
110C2×D263—22no—
111C2×D263—41no—
112C2×D263—42no—
113C2×D263#10414yescomplemented
114C4×C263—24no—
115C4×C263—42no—
116C4×C263C4×D411yescharacteristic
117C4×C263C4×D411yescharacteristic
118C4×C263#12111yescharacteristic
119C4×C263#12111yescharacteristic
120Dic263—24no—
121Dic263—22no—
122Dic263—41no—
123C2×C263—21no—
124C2×C263—21no—
125C2×C263#38611yescharacteristic
126C2×C263C2×#10412yes—
127D263—24no—
128D263—81no—
129C263#189611yescharacteristic, complemented, Sylow
130#1896—2631nomaximal, Sylow
131#525—2631no—
132C22×C42—2631no—
133C2×#104—2631no—
134C2×#104—2631no—
135#407—2631no—
136#339—2631no—
137#339D26311yescharacteristic, complemented
138C2×#41—2631no—
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#117C2×D26311yescharacteristic
149C2×C42—2631no—
150C2×C42—5262no—
151C2×C42—5261no—
152C2×C42—5262no—
153C2×C42C2×D26311yescharacteristic
154#104—5262no—
155#104—5262no—
156C22⋊C8—5262no—
157C24—2631no—
158#41—5261no—
159#41—5261no—
160#41—5261no—
161#41—5261no—
162C2×Q8—2631no—
163C2×D4—2631no—
164C2×D4—5262no—
165C2×D4—5261no—
166C22×C4—21no—
167C22×C4—2631no—
168C22×C4—2632no—
169C22×C4—2632no—
170C22×C4—5264no—
171C22×C4—5268no—
172C22×C4—5261no—
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—5262no—
186C4⋊C4C4×D26312yescomplemented
187C22⋊C4—21no—
188C22⋊C4—5262no—
189C22⋊C4—5262no—
190C42—21no—
191C42—21no—
192C42—2632no—
193C42—5264no—
194C42—5261no—
195C42D105212yescomplemented
196C23—2632no—
197C23—5264no—
198C23—5261no—
199C23—5261no—
200C23—5261no—
201C23D4×D26311yescharacteristic
202Q8—5261no—
203Q8—5261no—
204D4—5261no—
205D4—5261no—
206D4—10524no—
207D4—10521no—
208D4—10521no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—2632no—
213C2×C4—52616no—
214C2×C4—5264no—
215C2×C4—5262no—
216C2×C4—5261no—
217C2×C4—5261no—
218C2×C4—5262no—
219C2×C4—5262no—
220C2×C4—5262no—
221C2×C4—5262no—
222C2×C4—5261no—
223C2×C4—10521no—
224C2×C4—10521no—
225C2×C4C2×C4×D26311yescharacteristic
226C2×C4D4×D26311yescharacteristic
227C2×C4D4×D26311yescharacteristic
228C2×C4C2×D105211yescharacteristic
229C2×C4#1686237611yescharacteristic
230C2×C4#1686237711yescharacteristic
231C8—41no—
232C8—10521no—
233C22—22no—
234C22—2634no—
235C22—5264no—
236C22—5264no—
237C22—5262no—
238C22—5262no—
239C22—10522no—
240C22—10521no—
241C22C22⋊C4×D26311yescharacteristic
242C22#2255444011yescharacteristic
243C22#2255445511yescharacteristic
244C4—24no—
245C4—42no—
246C4—5264no—
247C4—5262no—
248C4—10521no—
249C4#2255443211yescharacteristic
250C4C4×D105211yescharacteristic
251C4#2255444311yescharacteristic
252C4#2255444511yescharacteristic
253C2—21no—
254C2—21no—
255C2—5264no—
256C2—21041no—
257C2#3068181611yescharacteristic
258C2#104×D26312yes—
subgroupG/H
centerC2×C4D4×D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting#339×C263C2
socleC22×C263C2×C22⋊C4
prime radical#30682450C2
cosocleC22×C4×C263C23
hypercenter#339D263
hypocenterC263#1896
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. C2×C42×D263C2semidirect
3. C2×#22554398C2semidirect
4. C2×#22554396C2semidirect
5. #30681901C2semidirect
6. #30681697C2semidirect
7. #339×C263C2semidirect
13. #22554450C4semidirect
14. #22554445C4semidirect
32. C2×Dic526C2×C4semidirect
34. C2×D1052C2×C4semidirect
55. C4×Dic263D4semidirect
61. C4⋊C4×C263C2×C4semidirect
65. C42×C263D4semidirect
113. C2×D263#104semidirect
129. C263#1896semidirect
137. #339D263semidirect
186. C4⋊C4C4×D263semidirect
195. C42D1052semidirect

Maximal subgroups

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

subgroupindex
#306824502
C2×C42×D2632
C2×#225543982
C2×#225543962
#306819012
#306816972
#339×C2632
#1896263