Finite Group Databasebeta

← #46783771

Subgroups — #46783771

Order 33664.

382 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#22554498C211yesmaximal, characteristic
2#30682512C211yesmaximal, characteristic, complemented
3C2×#22554459C211yesmaximal, characteristic, complemented
4C2×#22554396C211yesmaximal, characteristic, complemented
5#30681944C211yesmaximal, characteristic, complemented
6#30681699C211yesmaximal, characteristic, complemented
7C2×#101×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9C22×D1052C2211yescharacteristic
10#22554498—22no—
11#22554498—22no—
12C2×#16862365—21no—
13C2×D2104—21no—
14#22554468—21no—
15#22554459—22no—
16#22554459—21no—
17#22554459—22no—
18#22554453—22no—
19#22554446—22no—
20#22554429C2211yescharacteristic
21C2×(C2×D263)⋊C4—22no—
22C2×C4×Dic263C2211yescharacteristic
23#22554396—22no—
24#22554392—22no—
25C22×Q8×C263C2211yescharacteristic
26C2×M16×C263C2211yescharacteristic
27C2×M16×C263C2211yescharacteristic
28#101×C263—22no—
29C23×D263—21no—
30#16862376—21no—
31#16862376—21no—
32#16862376—21no—
33#16862376—21no—
34C2×Dic526D411yescharacteristic
35C2×D1052—21no—
36C2×D1052—21no—
37C2×D1052—21no—
38C2×D1052—21no—
39C2×D1052—21no—
40C2×D1052D411yescharacteristic
41C2×D1052D412yes—
42C2×C22⋊D263—21no—
43C22×Dic263—21no—
44C2×C4×D263—21no—
45#16862365—24no—
46D2104—24no—
47C4⋊Dic263D412yes—
48Dic263⋊C4—24no—
49C22⋊Dic263—21no—
50(C2×D263)⋊C4—28no—
51(C2×D263)⋊C4—24no—
52C4×Dic263—21no—
53C4×Dic263—21no—
54C4×Dic263D412yes—
55C2×Q8×C263—21no—
56C2×Q8×C263—21no—
57C2×Q8×C263—21no—
58C2×Q8×C263—21no—
59C2×Q8×C263—21no—
60C2×Q8×C263—21no—
61C22×C4×C263D412yes—
62C22×C4×C263C2311yescharacteristic
63M16×C263—21no—
64M16×C263—21no—
65M16×C263—21no—
66M16×C263D412yes—
67C2×C8×C263—21no—
68C2×C8×C263—21no—
69C22×D263—21no—
70C22×D263—22no—
71C22×D263—44no—
72C22×D263—41no—
73C22×D263—41no—
74Dic526—21no—
75Dic526—21no—
76D1052—21no—
77D1052—22no—
78D1052—22no—
79D1052—21no—
80D1052—41no—
81D1052—41no—
82C22⋊D263—41no—
83C22⋊D263—41no—
84C2×Dic263—22no—
85C2×Dic263—22no—
86C2×Dic263—21no—
87C2×Dic263—42no—
88C4×D263—41no—
89C4×D263—41no—
90C23×C263C2×D411yescharacteristic
91Q8×C263—41no—
92Q8×C263—41no—
93Q8×C263—41no—
94Q8×C263—41no—
95C2×C4×C263—22no—
96C2×C4×C263—22no—
97C2×C4×C263—22no—
98C2×C4×C263C2×D411yescharacteristic
99C2×C4×C263C2×D411yescharacteristic
100C2×C4×C263C2×D411yescharacteristic
101C2×C4×C263C2×D411yescharacteristic
102C2×C4×C263C2×D411yescharacteristic
103C2×C4×C263#4111yescharacteristic
104C8×C263—22no—
105C8×C263—41no—
106C22×C263—22no—
107C22×C263#12011yescharacteristic
108C22×C263#12011yescharacteristic
109C22×C263#12111yescharacteristic
110C2×D263—44no—
111C2×D263—41no—
112C2×D263—42no—
113C2×D263—42no—
114C2×D263—82no—
115C2×D263—82no—
116C4×C263—42no—
117C4×C263#12011yescharacteristic
118C4×C263#12111yescharacteristic
119C4×C263#12111yescharacteristic
120C4×C263#12711yescharacteristic
121Dic263—42no—
122Dic263—41no—
123Dic263—42no—
124C2×C263—21no—
125C2×C263—21no—
126C2×C263#39211yescharacteristic
127C2×C263#45412yes—
128D263—81no—
129D263—82no—
130C263#200311yescharacteristic, complemented, Sylow
131#2003—2631nomaximal, Sylow
132C2×AGL(1,ℤ/8)—2631no—
133#536—2631no—
134C2×#124—2631no—
135C2×#104—2631no—
136#418—2631no—
137C2×#101D26311yescharacteristic, complemented
138#339—2631no—
139C2×#41—2631no—
140C22×Q8C2×D26311yescharacteristic
141C22×D4—2631no—
142AGL(1,ℤ/8)—5262no—
143AGL(1,ℤ/8)—5262no—
144C2×SD16—5261no—
145C2×D8—5261no—
146C2×M16C2×D26311yescharacteristic
147C2×M16C2×D26311yescharacteristic
148C4⋊Q8—5261no—
149#124—5262no—
150#124—5262no—
151#124—5261no—
152#123—5262no—
153C22⋊Q8—5262no—
154#117—2631no—
155C2×C22⋊C4—5262no—
156C2×C42—2631no—
157#104—5262no—
158#102—5262no—
159#101—22no—
160C24—5261no—
161#41—5261no—
162#41—5261no—
163#41—5261no—
164#41—5261no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—21no—
171C2×Q8—2631no—
172C2×D4—2631no—
173C2×D4—2632no—
174C2×D4—5261no—
175C2×D4—5261no—
176C2×D4—5261no—
177C2×D4—5261no—
178C2×D4—5261no—
179C2×D4—5261no—
180C22×C4—5261no—
181C22×C4—5261no—
182C22×C4D105212yes—
183C22×C4C22×D26311yescharacteristic
184SD16—5264no—
185D8—5264no—
186M16—21no—
187M16—21no—
188M16—21no—
189M16C22⋊D26312yes—
190C2×C8—21no—
191C2×C8—21no—
192C4⋊C4—2632no—
193C4⋊C4—5264no—
194C22⋊C4—5268no—
195C22⋊C4—5264no—
196C22⋊C4—5261no—
197C42—2632no—
198C42—5261no—
199C42—5261no—
200C23—5262no—
201C23—5261no—
202C23—10524no—
203C23—10521no—
204C23—10521no—
205C23C2×D105211yescharacteristic
206Q8—41no—
207Q8—41no—
208Q8—41no—
209Q8—41no—
210Q8—5261no—
211Q8—5261no—
212D4—5261no—
213D4—5262no—
214D4—5262no—
215D4—5261no—
216D4—10521no—
217D4—10521no—
218D4—10521no—
219D4—10521no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—5262no—
224C2×C4—5262no—
225C2×C4—5261no—
226C2×C4—10522no—
227C2×C4—10521no—
228C2×C4—10521no—
229C2×C4D4×D26311yescharacteristic
230C2×C4D4×D26311yescharacteristic
231C2×C4D4×D26311yescharacteristic
232C2×C4D4×D26311yescharacteristic
233C2×C4C2×C22⋊D26311yescharacteristic
234C2×C4#1686237611yescharacteristic
235C8—22no—
236C8—41no—
237C22—22no—
238C22—10524no—
239C22—10522no—
240C22—10521no—
241C22—10522no—
242C22—21042no—
243C22—21042no—
244C22#2255444011yescharacteristic
245C22#2255444011yescharacteristic
246C22#2255444411yescharacteristic
247C4—42no—
248C4—10522no—
249C4—10522no—
250C4—10521no—
251C4#2255443811yescharacteristic
252C4#2255444311yescharacteristic
253C4#2255444311yescharacteristic
254C4#2255446611yescharacteristic
255C2—21no—
256C2—21no—
257C2—21042no—
258C2—21041no—
259C2#3068184711yescharacteristic
260C2#3068211312yes—
subgroupG/H
centerC22#22554440
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC2×#101×C263C2
socleC22×C263#120
prime radicalC2×#22554498C2
hypercenterC2×#101D263
hypocenterC263#2003
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #30682512C2semidirect
3. C2×#22554459C2semidirect
4. C2×#22554396C2semidirect
5. #30681944C2semidirect
6. #30681699C2semidirect
7. C2×#101×C263C2semidirect
130. C263#2003semidirect
137. C2×#101D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225544982
#306825122
C2×#225544592
C2×#225543962
#306819442
#306816992
C2×#101×C2632
#2003263