Finite Group Databasebeta

← #46783769

Subgroups — #46783769

Order 33664.

382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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×#22554496C211yesmaximal, characteristic
2#30682512C211yesmaximal, characteristic, complemented
3C2×#22554398C211yesmaximal, characteristic, complemented
4#30681943C211yesmaximal, characteristic, complemented
5C2×#22554389C211yesmaximal, characteristic, complemented
6#30681698C211yesmaximal, characteristic, complemented
7C2×#124×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9#22554496—22no—
10#22554496—22no—
11C2×#16862364—21no—
12C2×#16862361—21no—
13C2×#16862360C2211yescharacteristic
14C2×#16862360C2211yescharacteristic
15#22554468—21no—
16#22554459—21no—
17#22554453—22no—
18#22554446—22no—
19#22554429C2211yescharacteristic
20#22554398—22no—
21#22554391—22no—
22#22554389—22no—
23C22×Q8×C263C2211yescharacteristic
24C22×D4×C263C2211yescharacteristic
25#124×C263—22no—
26#124×C263—22no—
27C2×C22⋊C4×C263—22no—
28C2×C42×C263C2211yescharacteristic
29#16862376—21no—
30#16862376—21no—
31#16862376—21no—
32#16862376—21no—
33C2×Dic526D411yescharacteristic
34C2×D1052D411yescharacteristic
35C2×C22⋊D263—21no—
36C2×C4×D263—21no—
37#16862364—24no—
38#16862361—24no—
39#16862360—21no—
40#16862360—21no—
41#16862360—21no—
42#16862360D412yes—
43C2×C263⋊C8—21no—
44C2×C263⋊C8—21no—
45C4⋊Dic263D412yes—
46Dic263⋊C4—24no—
47C22⋊Dic263—21no—
48(C2×D263)⋊C4—24no—
49C4×Dic263—21no—
50C24×C263—21no—
51C2×Q8×C263—21no—
52C2×Q8×C263—21no—
53C2×Q8×C263—21no—
54C2×Q8×C263—21no—
55C2×Q8×C263—21no—
56C2×Q8×C263—21no—
57C2×D4×C263—21no—
58C2×D4×C263—21no—
59C2×D4×C263—21no—
60C2×D4×C263—21no—
61C2×D4×C263—21no—
62C2×D4×C263D412yes—
63C22×C4×C263—21no—
64C22×C4×C263D412yes—
65C22×C4×C263C2311yescharacteristic
66C22⋊C4×C263—28no—
67C42×C263—21no—
68C42×C263D412yes—
69C22×D263—21no—
70Dic526—21no—
71Dic526—21no—
72D1052—21no—
73D1052—21no—
74C22⋊D263—41no—
75C22⋊D263—41no—
76C2×Dic263—22no—
77C2×Dic263—21no—
78C4×D263—41no—
79C4×D263—41no—
80C263⋊C8—22no—
81C263⋊C8—41no—
82C23×C263—22no—
83C23×C263—44no—
84C23×C263—41no—
85C23×C263—41no—
86C23×C263C2×D411yescharacteristic
87Q8×C263—41no—
88Q8×C263—41no—
89Q8×C263—41no—
90Q8×C263—41no—
91D4×C263—22no—
92D4×C263—22no—
93D4×C263—41no—
94D4×C263—41no—
95C2×C4×C263—22no—
96C2×C4×C263—22no—
97C2×C4×C263—22no—
98C2×C4×C263—22no—
99C2×C4×C263—42no—
100C2×C4×C263C2×D411yescharacteristic
101C2×C4×C263C2×D411yescharacteristic
102C2×C4×C263C2×D411yescharacteristic
103C2×C4×C263C2×D411yescharacteristic
104C2×C4×C263C2×D411yescharacteristic
105C2×C4×C263#4111yescharacteristic
106C22×C263—22no—
107C22×C263—44no—
108C22×C263—42no—
109C22×C263—82no—
110C22×C263—82no—
111C22×C263#12011yescharacteristic
112C22×C263#12011yescharacteristic
113C22×C263#12111yescharacteristic
114C2×D263—41no—
115C2×D263—42no—
116C4×C263—42no—
117C4×C263—42no—
118C4×C263#12011yescharacteristic
119C4×C263#12111yescharacteristic
120C4×C263#12111yescharacteristic
121C4×C263#12711yescharacteristic
122Dic263—41no—
123Dic263—42no—
124C2×C263—21no—
125C2×C263—21no—
126C2×C263—82no—
127C2×C263#39211yescharacteristic
128C2×C263#45412yes—
129D263—81no—
130C263#200311yescharacteristic, complemented, Sylow
131#2003—2631nomaximal, Sylow
132C2×AGL(1,ℤ/8)—2631no—
133#536—2631no—
134C2×#124D26311yescharacteristic, complemented
135C2×#104—2631no—
136#418—2631no—
137C2×#101—2631no—
138#339—2631no—
139C2×#41—2631no—
140C22×Q8C2×D26311yescharacteristic
141C22×D4C2×D26311yescharacteristic
142AGL(1,ℤ/8)—5262no—
143AGL(1,ℤ/8)—5262no—
144C2×SD16—5261no—
145C2×D8—5261no—
146C2×M16—2631no—
147C2×M16—2631no—
148C4⋊Q8—5261no—
149#124—22no—
150#124—22no—
151#124—5261no—
152#123—5262no—
153C22⋊Q8—5262no—
154#117—2631no—
155C2×C22⋊C4—22no—
156C2×C42C2×D26311yescharacteristic
157#104—5262no—
158#102—5262no—
159#101—5262no—
160C24—21no—
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—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—2631no—
178C2×D4—5261no—
179C2×D4C22⋊D26312yes—
180C22×C4—21no—
181C22×C4—5261no—
182C22×C4C22⋊D26312yes—
183C22×C4C22×D26311yescharacteristic
184SD16—5264no—
185D8—5264no—
186M16—2632no—
187M16—5261no—
188M16—5261no—
189M16—5261no—
190C2×C8—5261no—
191C2×C8—5261no—
192C4⋊C4—2632no—
193C4⋊C4—5264no—
194C22⋊C4—28no—
195C22⋊C4—5264no—
196C22⋊C4—5261no—
197C42—21no—
198C42—5261no—
199C42C22⋊D26312yes—
200C23—22no—
201C23—44no—
202C23—41no—
203C23—41no—
204C23—5261no—
205C23C2×C22⋊D26311yescharacteristic
206Q8—41no—
207Q8—41no—
208Q8—41no—
209Q8—41no—
210Q8—5261no—
211Q8—5261no—
212D4—22no—
213D4—22no—
214D4—41no—
215D4—41no—
216D4—5261no—
217D4—5261no—
218D4—10521no—
219D4—10521no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—42no—
225C2×C4—5262no—
226C2×C4—5261no—
227C2×C4—10521no—
228C2×C4—10521no—
229C2×C4D4×D26311yescharacteristic
230C2×C4D4×D26311yescharacteristic
231C2×C4D4×D26311yescharacteristic
232C2×C4C2×C22⋊D26311yescharacteristic
233C2×C4C2×C22⋊D26311yescharacteristic
234C2×C4#1686237511yescharacteristic
235C8—5262no—
236C8—10521no—
237C22—22no—
238C22—44no—
239C22—42no—
240C22—82no—
241C22—82no—
242C22—10521no—
243C22—10522no—
244C22#2255443811yescharacteristic
245C22#2255443911yescharacteristic
246C22#2255444211yescharacteristic
247C4—42no—
248C4—42no—
249C4—10521no—
250C4—10522no—
251C4#2255443811yescharacteristic
252C4#2255444111yescharacteristic
253C4#2255444211yescharacteristic
254C4#2255446611yescharacteristic
255C2—21no—
256C2—21no—
257C2—82no—
258C2—21041no—
259C2#3068184611yescharacteristic
260C2#3068211012yes—
subgroupG/H
centerC22#22554438
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC2×#124×C263C2
socleC22×C263#120
prime radicalC2×#22554496C2
hypercenterC2×#124D263
hypocenterC263#2003
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. #30682512C2semidirect
3. C2×#22554398C2semidirect
4. #30681943C2semidirect
5. C2×#22554389C2semidirect
6. #30681698C2semidirect
7. C2×#124×C263C2semidirect
130. C263#2003semidirect
134. C2×#124D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225544962
#306825122
C2×#225543982
#306819432
C2×#225543892
#306816982
C2×#124×C2632
#2003263