Finite Group Databasebeta

← #46784033

Subgroups — #46784033

Order 33664.

266 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 65 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#30682736C211yesmaximal, characteristic
2#30681962C211yesmaximal, characteristic, complemented
3C2×#22554398C211yesmaximal, characteristic, complemented
4#30681922C211yesmaximal, characteristic, complemented
5#30681920C211yesmaximal, characteristic, complemented
6C263⋊#338C211yesmaximal, characteristic, complemented
7C2×#104×C263C211yesmaximal, characteristic, complemented
8C2×#16862376C2211yescharacteristic
9#22554501—21no—
10#22554500—21no—
11#22554496—21no—
12#22554495—21no—
13#22554490—22no—
14C2×#16862360C2211yescharacteristic
15C2×#16862360C2211yescharacteristic
16C2×#16862360C2211yescharacteristic
17C4⋊(C263⋊C8)—22no—
18#22554398—21no—
19#22554398—21no—
20#22554389—21no—
21#22554388—21no—
22#22554387—21no—
23#22554386—21no—
24C2×#41×C263C2211yescharacteristic
25C2×M16×C263C2211yescharacteristic
26C2×C42×C263C2211yescharacteristic
27#104×C263—21no—
28#104×C263—21no—
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#16862366—22no—
38#16862364—22no—
39#16862363—22no—
40#16862361—22no—
41#16862360—21no—
42#16862360—21no—
43#16862360—21no—
44#16862360—21no—
45#16862360—21no—
46#16862360—21no—
47C2×C263⋊C8—21no—
48C2×C263⋊C8—21no—
49C2×C263⋊C8D412yes—
50#41×C263—21no—
51#41×C263—21no—
52#41×C263—21no—
53#41×C263—21no—
54C2×Q8×C263D411yescharacteristic
55C2×D4×C263—21no—
56C2×D4×C263D411yescharacteristic
57C22×C4×C263—21no—
58C22×C4×C263—21no—
59C22×C4×C263C2311yescharacteristic
60M16×C263—21no—
61M16×C263—21no—
62C2×C8×C263—21no—
63C42×C263—21no—
64C42×C263D411yescharacteristic
65C42×C263D411yescharacteristic
66C22×D263—21no—
67Dic526—21no—
68Dic526—21no—
69D1052—21no—
70D1052—21no—
71C22⋊D263—41no—
72C22⋊D263—41no—
73C2×Dic263—21no—
74C4×D263—41no—
75C4×D263—41no—
76C263⋊C8—22no—
77C263⋊C8—41no—
78C263⋊C8—41no—
79C23×C263—21no—
80C23×C263#4111yescharacteristic
81Q8×C263—21no—
82Q8×C263—21no—
83D4×C263—21no—
84D4×C263—21no—
85D4×C263—41no—
86D4×C263—41no—
87C2×C4×C263—21no—
88C2×C4×C263—21no—
89C2×C4×C263—21no—
90C2×C4×C263—42no—
91C2×C4×C263—41no—
92C2×C4×C263—41no—
93C2×C4×C263C2×D411yescharacteristic
94C2×C4×C263C2×D411yescharacteristic
95C2×C4×C263C2×D411yescharacteristic
96C2×C4×C263C2×D411yescharacteristic
97C2×C4×C263#4111yescharacteristic
98C2×C4×C263#4111yescharacteristic
99C8×C263—41no—
100C22×C263—41no—
101C22×C263—41no—
102C22×C263—81no—
103C22×C263#12111yescharacteristic
104C22×C263#12311yescharacteristic
105C22×C263#12311yescharacteristic
106C2×D263—41no—
107C2×D263—81no—
108C4×C263—22no—
109C4×C263—41no—
110C4×C263—41no—
111C4×C263#12011yescharacteristic
112C4×C263#12111yescharacteristic
113C4×C263#12111yescharacteristic
114C4×C263#12411yescharacteristic
115Dic263—41no—
116C2×C263—21no—
117C2×C263—21no—
118C2×C263—21no—
119C2×C263—81no—
120C2×C263#39411yescharacteristic
121D263—81no—
122C263#205011yescharacteristic, complemented, Sylow
123#2050—2631nomaximal, Sylow
124#575—2631no—
125#423—2631no—
126C2×#104—2631no—
127C2×#104D26311yescharacteristic, complemented
128#413—2631no—
129#413—2631no—
130#338—2631no—
131C2×#41—2631no—
132C2×#41C2×D26311yescharacteristic
133#137—5261no—
134#137—5261no—
135AGL(1,ℤ/8)—5261no—
136AGL(1,ℤ/8)—5261no—
137#135—5262no—
138C2×M16—2631no—
139C2×M16—2631no—
140C2×M16—2631no—
141C2×M16C2×D26311yescharacteristic
142C2×C42C2×D26311yescharacteristic
143C4⋊C8—5262no—
144#104—21no—
145#104—21no—
146#104—5261no—
147#104—5261no—
148#101—5261no—
149#101—5261no—
150#100—5261no—
151#100—5261no—
152#41—21no—
153#41—21no—
154#41—21no—
155#41—21no—
156#41—5261no—
157#41—5261no—
158#41—5261no—
159#41—5261no—
160C2×Q8—2631no—
161C2×Q8D105211yescharacteristic
162C2×D4—21no—
163C2×D4—2631no—
164C2×D4—5261no—
165C2×D4D105211yescharacteristic
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—5261no—
169C22×C4C22×D26311yescharacteristic
170Q16—5262no—
171SD16—5262no—
172SD16—5262no—
173D8—5262no—
174M16—21no—
175M16—21no—
176M16—5261no—
177M16—5261no—
178M16—5261no—
179M16—5261no—
180M16—5261no—
181M16—5261no—
182C2×C8—21no—
183C2×C8—2632no—
184C2×C8—5261no—
185C2×C8—5261no—
186C42—21no—
187C42C22⋊D26311yescharacteristic
188C42C22⋊D26311yescharacteristic
189C23—21no—
190C23—5261no—
191C23#1686237511yescharacteristic
192Q8—21no—
193Q8—21no—
194Q8—5261no—
195Q8—5261no—
196D4—21no—
197D4—21no—
198D4—41no—
199D4—41no—
200D4—5261no—
201D4—5261no—
202D4—10521no—
203D4—10521no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—5261no—
211C2×C4—10521no—
212C2×C4—10521no—
213C2×C4D4×D26311yescharacteristic
214C2×C4D4×D26311yescharacteristic
215C2×C4C2×C22⋊D26311yescharacteristic
216C2×C4C2×D105211yescharacteristic
217C2×C4#1686237511yescharacteristic
218C2×C4#1686237611yescharacteristic
219C8—41no—
220C8—5262no—
221C8—10521no—
222C8—10521no—
223C22—41no—
224C22—41no—
225C22—81no—
226C22—10521no—
227C22—21041no—
228C22#2255444211yescharacteristic
229C22#2255445211yescharacteristic
230C22#2255445411yescharacteristic
231C4—22no—
232C4—41no—
233C4—41no—
234C4—10521no—
235C4#2255444011yescharacteristic
236C4#2255444111yescharacteristic
237C4#2255444411yescharacteristic
238C4#2255445611yescharacteristic
239C2—21no—
240C2—21no—
241C2—21no—
242C2—81no—
243C2—21041no—
244C2#3068185411yescharacteristic
subgroupG/H
centerC4#22554456
commutator, cosocleC22×C4×C263C23
FrattiniC22×C4C22×D263
FittingC2×#104×C263C2
socleC2×C263#394
prime radical#30682736C2
hypercenterC2×#104D263
hypocenterC263#2050
LCSG ▷ C22×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #30681962C2semidirect
3. C2×#22554398C2semidirect
4. #30681922C2semidirect
5. #30681920C2semidirect
6. C263⋊#338C2semidirect
7. C2×#104×C263C2semidirect
122. C263#2050semidirect
127. C2×#104D263semidirect

Maximal subgroups

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

subgroupindex
#306827362
#306819622
C2×#225543982
#306819222
#306819202
C263⋊#3382
C2×#104×C2632
#2050263