Finite Group Databasebeta

← #46783828

Subgroups — #46783828

Order 33664.

406 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C22×#16862364C211yesmaximal, characteristic
2C2×#22554468C211yesmaximal, characteristic, complemented
3C2×#22554395C211yesmaximal, characteristic, complemented
4C2×#22554394C211yesmaximal, characteristic, complemented
5#30681841C211yesmaximal, characteristic
6#30681692C211yesmaximal, characteristic, complemented
7C22×SD16×C263C211yesmaximal, characteristic
8C22×Dic526C2211yescharacteristic
9C2×#16862364—22no—
10C2×#16862364—22no—
11C2×#16862364—22no—
12C22×C263⋊C8C2211yescharacteristic
13#22554468—22no—
14#22554468—22no—
15C2×C4⋊Dic263C2211yescharacteristic
16C2×Dic263⋊C4—22no—
17C2×C22⋊Dic263—22no—
18C2×C4×Dic263C2211yescharacteristic
19#22554395—22no—
20#22554394—22no—
21C22×Q8×C263C2211yescharacteristic
22C22×D4×C263C2211yescharacteristic
23C2×SD16×C263—22no—
24C2×SD16×C263—22no—
25C2×SD16×C263—22no—
26C22×C8×C263C2211yescharacteristic
27C2×Dic526—21no—
28C2×Dic526—21no—
29C2×Dic526—21no—
30C2×Dic526—21no—
31C2×Dic526—21no—
32C2×Dic526D412yes—
33C22×Dic263—21no—
34C22×Dic263—21no—
35C22×Dic263D412yes—
36#16862364—28no—
37C2×C263⋊C8—21no—
38C2×C263⋊C8—21no—
39C2×C263⋊C8D412yes—
40C4⋊Dic263—21no—
41C4⋊Dic263—21no—
42Dic263⋊C4—28no—
43C22⋊Dic263—44no—
44C4×Dic263—21no—
45C4×Dic263—21no—
46C24×C263—21no—
47C2×Q8×C263—21no—
48C2×Q8×C263—21no—
49C2×Q8×C263—21no—
50C2×Q8×C263—21no—
51C2×Q8×C263—21no—
52C2×Q8×C263D412yes—
53C2×D4×C263—21no—
54C2×D4×C263—21no—
55C2×D4×C263—21no—
56C2×D4×C263—21no—
57C2×D4×C263—21no—
58C2×D4×C263D412yes—
59C22×C4×C263—21no—
60C22×C4×C263C2311yescharacteristic
61SD16×C263—28no—
62C2×C8×C263—21no—
63C2×C8×C263—21no—
64C2×C8×C263D412yes—
65Dic526—22no—
66Dic526—22no—
67Dic526—41no—
68Dic526—41no—
69C2×Dic263—22no—
70C2×Dic263—22no—
71C2×Dic263—22no—
72C2×Dic263—41no—
73C2×Dic263—41no—
74C2×Dic263—41no—
75C2×Dic263—42no—
76C2×Dic263SD1614yescomplemented
77C263⋊C8—22no—
78C23×C263—22no—
79C23×C263—41no—
80C23×C263—41no—
81C23×C263—42no—
82C23×C263—42no—
83C23×C263C2×D411yescharacteristic
84Q8×C263—22no—
85Q8×C263—22no—
86Q8×C263—41no—
87Q8×C263—41no—
88D4×C263—22no—
89D4×C263—22no—
90D4×C263—41no—
91D4×C263—41no—
92C2×C4×C263—22no—
93C2×C4×C263—41no—
94C2×C4×C263—41no—
95C2×C4×C263C2×D411yescharacteristic
96C2×C4×C263C2×D411yescharacteristic
97C2×C4×C263C2×D411yescharacteristic
98C2×C4×C263C2×D411yescharacteristic
99C2×C4×C263C2×D411yescharacteristic
100C2×C4×C263#4111yescharacteristic
101C8×C263—22no—
102C22×C263—42no—
103C22×C263—44no—
104C22×C263—82no—
105C22×C263—81no—
106C22×C263—81no—
107C22×C263#12011yescharacteristic
108C22×C263#12111yescharacteristic
109C22×C263#12711yescharacteristic
110C22×C263C2×SD1612yes—
111C22×C263#13712yes—
112C4×C263—42no—
113C4×C263#12011yescharacteristic
114C4×C263#12011yescharacteristic
115C4×C263#12111yescharacteristic
116C4×C263#12111yescharacteristic
117Dic263—24no—
118Dic263—42no—
119Dic263—81no—
120C2×C263—82no—
121C2×C263#39211yescharacteristic
122C2×C263#44812yes—
123C2×C263#46112yes—
124C2×C263#49211yescharacteristic
125C2×C263#49711yescharacteristic
126C263#201311yescharacteristic, complemented, Sylow
127#2013—2631nomaximal, Sylow
128C22×SD16—2631no—
129C22×SD16D26311yescharacteristic
130C2×C4⋊Q8—2631no—
131C2×#103—2631no—
132C2×#103—2631no—
133#390—2631no—
134#336—2631no—
135C22×Q8—2631no—
136C22×Q8C2×D26311yescharacteristic
137C22×D4C2×D26311yescharacteristic
138C2×SD16—22no—
139C2×SD16—22no—
140C2×SD16—22no—
141C2×SD16—5262no—
142C2×SD16—5262no—
143C2×SD16—5262no—
144C22×C8—2631no—
145C22×C8C2×D26311yescharacteristic
146C4⋊Q8—5262no—
147C4⋊Q8—5262no—
148C2×C4⋊C4—2631no—
149C2×C4⋊C4—5262no—
150C2×C22⋊C4—5262no—
151C2×C42—2631no—
152#103—5262no—
153#103—5262no—
154C24—21no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—2632no—
161C2×Q8—5261no—
162C2×Q8—5261no—
163C2×Q8—5261no—
164C2×Q8—5261no—
165C2×Q8—5261no—
166C2×Q8C22⋊D26312yes—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4C22⋊D26312yes—
173C22×C4—21no—
174C22×C4—2632no—
175C22×C4—5261no—
176C22×C4—5261no—
177C22×C4C22×D26311yescharacteristic
178SD16—28no—
179SD16—5268no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—2632no—
183C2×C8—5261no—
184C2×C8—5261no—
185C2×C8C22⋊D26312yes—
186C4⋊C4—5268no—
187C4⋊C4—5261no—
188C4⋊C4—5261no—
189C22⋊C4—10524no—
190C42—5261no—
191C42—5261no—
192C23—22no—
193C23—41no—
194C23—41no—
195C23—42no—
196C23—42no—
197C23D4×D26311yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—41no—
201Q8—41no—
202Q8—5262no—
203Q8—5262no—
204Q8—10521no—
205Q8—10521no—
206D4—22no—
207D4—22no—
208D4—41no—
209D4—41no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—2634no—
214C2×C4—5262no—
215C2×C4—5262no—
216C2×C4—5262no—
217C2×C4—10521no—
218C2×C4—10521no—
219C2×C4—10521no—
220C2×C4—10522no—
221C2×C4D4×D26311yescharacteristic
222C2×C4D4×D26311yescharacteristic
223C2×C4C2×C22⋊D26311yescharacteristic
224C2×C4C2×C22⋊D26311yescharacteristic
225C2×C4C2×C22⋊D26311yescharacteristic
226C2×C4#1686237511yescharacteristic
227C8—22no—
228C8—5262no—
229C22—44no—
230C22—42no—
231C22—81no—
232C22—81no—
233C22—82no—
234C22#2255443811yescharacteristic
235C22#2255444211yescharacteristic
236C22#2255446611yescharacteristic
237C22SD16×D26312yes—
238C22#2255449912yes—
239C4—42no—
240C4—5264no—
241C4—10522no—
242C4—21041no—
243C4#2255443811yescharacteristic
244C4#2255443911yescharacteristic
245C4#2255444111yescharacteristic
246C4#2255444211yescharacteristic
247C2—82no—
248C2#3068184611yescharacteristic
249C2#3068207512yes—
250C2#3068214112yes—
251C2#3068230911yescharacteristic
252C2#3068232911yescharacteristic
subgroupG/H
centerC23D4×D263
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC22×SD16×C263C2
socleC23×C263C2×D4
prime radicalC22×D4×C263C22
hypercenterC22×SD16D263
hypocenterC263#2013
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#22554468C2semidirect
3. C2×#22554395C2semidirect
4. C2×#22554394C2semidirect
6. #30681692C2semidirect
76. C2×Dic263SD16semidirect
126. C263#2013semidirect

Maximal subgroups

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

subgroupindex
C22×#168623642
C2×#225544682
C2×#225543952
C2×#225543942
#306818412
#306816922
C22×SD16×C2632
#2013263