Finite Group Databasebeta

← #46783185

Subgroups — #46783185

Order 33664.

412 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 109 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×#22554444C211yesmaximal, characteristic
2C2×#22554392C212yesmaximal, complemented
3#30681798C211yesmaximal, characteristic, complemented
4#30681701C212yesmaximal, complemented
5C22×M16×C263C211yesmaximal, characteristic, complemented
6C22×D1052C2211yescharacteristic
7C22×C22⋊D263—21no—
8#22554444—22no—
9#22554444C414yescomplemented
10C2×C4⋊Dic263C2212yes—
11C2×C4⋊Dic263C2211yescharacteristic
12C2×C22⋊Dic263—21no—
13C2×(C2×D263)⋊C4—21no—
14#22554392—24no—
15C263⋊#95—21no—
16C23×C4×C263C2211yescharacteristic
17C2×M16×C263—22no—
18C2×M16×C263—24no—
19C22×C8×C263C2212yes—
20C23×D263—21no—
21C2×D1052—22no—
22C2×D1052—21no—
23C2×D1052—22no—
24C2×D1052C2×C412yes—
25C2×C22⋊D263—24no—
26C2×C22⋊D263—44no—
27C22×Dic263—21no—
28C22×Dic263—22no—
29C4⋊Dic263—21no—
30C4⋊Dic263—22no—
31C4⋊Dic263—22no—
32C4⋊Dic263C2×C412yes—
33C22⋊Dic263—42no—
34(C2×D263)⋊C4—24no—
35C24×C263D411yescharacteristic
36C22×C4×C263—22no—
37C22×C4×C263—22no—
38C22×C4×C263C2×C412yes—
39C22×C4×C263D412yes—
40C22×C4×C263D411yescharacteristic
41C22×C4×C263C2311yescharacteristic
42M16×C263—28no—
43C2×C8×C263—22no—
44C2×C8×C263—22no—
45C2×C8×C263D414yescomplemented
46C22×D263—22no—
47C22×D263—42no—
48C22×D263—42no—
49C22×D263—41no—
50C22×D263—41no—
51D1052—24no—
52D1052—41no—
53D1052—41no—
54C22⋊D263—48no—
55C2×Dic263—22no—
56C2×Dic263—42no—
57C2×Dic263—42no—
58C2×Dic263—42no—
59C2×Dic263—42no—
60C23×C263—22no—
61C23×C263—21no—
62C23×C263—22no—
63C23×C263—21no—
64C23×C263C22⋊C412yes—
65C23×C263C2×D411yescharacteristic
66C2×C4×C263—22no—
67C2×C4×C263—24no—
68C2×C4×C263—22no—
69C2×C4×C263—22no—
70C2×C4×C263C22⋊C412yes—
71C2×C4×C263C22×C411yescharacteristic
72C2×C4×C263C2×D412yes—
73C2×C4×C263C2×D411yescharacteristic
74C2×C4×C263#4112yes—
75C8×C263—24no—
76C22×C263—22no—
77C22×C263—22no—
78C22×C263—22no—
79C22×C263—42no—
80C22×C263—42no—
81C22×C263C2×C22⋊C411yescharacteristic
82C22×C263#12112yes—
83C22×C263AGL(1,ℤ/8)11yescharacteristic
84C22×C263AGL(1,ℤ/8)12yes—
85C22×C263#13711yescharacteristic
86C2×D263—42no—
87C2×D263—42no—
88C2×D263—42no—
89C2×D263—82no—
90C2×D263—82no—
91C4×C263—22no—
92C4×C263C4×D412yes—
93C4×C263#12011yescharacteristic
94C4×C263#12311yescharacteristic
95Dic263—42no—
96Dic263—82no—
97C2×C263—42no—
98C2×C263#38611yescharacteristic
99C2×C263#41711yescharacteristic
100C2×C263#41811yescharacteristic
101C2×C263#46812yes—
102C2×C263#46912yes—
103D263—82no—
104C263#189511yescharacteristic, complemented, Sylow
105#1895—2631nomaximal, Sylow
106C22×M16D26311yescharacteristic, complemented
107C2×#121—2631no—
108C2×#102—2632no—
109#380—2631no—
110#340—2632no—
111C22×D4—2631no—
112C22×D4—5261no—
113C23×C4C2×D26311yescharacteristic
114C2×M16—22no—
115C2×M16—24no—
116C22×C8C2×D26312yes—
117#121—2634no—
118#121—5262no—
119C2×C4⋊C4—2631no—
120C2×C4⋊C4—2632no—
121C2×C22⋊C4—5261no—
122C2×C22⋊C4—5261no—
123#102—5264no—
124#95—5261no—
125C24—5261no—
126C24D105211yescharacteristic
127C2×D4—2632no—
128C2×D4—5264no—
129C2×D4—5262no—
130C2×D4—5261no—
131C2×D4—5262no—
132C2×D4—10524no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—5261no—
136C22×C4—5262no—
137C22×C4C4×D26312yes—
138C22×C4C22⋊D26312yes—
139C22×C4D105211yescharacteristic
140C22×C4C22×D26311yescharacteristic
141M16—28no—
142C2×C8—22no—
143C2×C8—22no—
144C2×C8C22⋊D26314yescomplemented
145C4⋊C4—2632no—
146C4⋊C4—5261no—
147C4⋊C4—5262no—
148C4⋊C4—5262no—
149C22⋊C4—5264no—
150C22⋊C4—10522no—
151C23—22no—
152C23—21no—
153C23—22no—
154C23—21no—
155C23—5262no—
156C23—10522no—
157C23—10522no—
158C23—10521no—
159C23—10521no—
160C23(C2×D263)⋊C412yes—
161C23C2×D105211yescharacteristic
162D4—5264no—
163D4—10528no—
164D4—10521no—
165D4—10521no—
166C2×C4—22no—
167C2×C4—24no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—5262no—
171C2×C4—10522no—
172C2×C4—10522no—
173C2×C4—10522no—
174C2×C4—10522no—
175C2×C4(C2×D263)⋊C412yes—
176C2×C4C2×C4×D26311yescharacteristic
177C2×C4C2×C22⋊D26312yes—
178C2×C4C2×C22⋊D26311yescharacteristic
179C2×C4#1686237612yes—
180C8—24no—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—10522no—
187C22—10522no—
188C22—10522no—
189C22—21042no—
190C22—21042no—
191C22C2×(C2×D263)⋊C411yescharacteristic
192C22#2255444412yes—
193C22#2255449812yes—
194C22#2255449811yescharacteristic
195C22#2255450311yescharacteristic
196C4—22no—
197C4—10522no—
198C4—21042no—
199C4C4×C22⋊D26312yes—
200C4#2255443911yescharacteristic
201C4#2255445311yescharacteristic
202C2—42no—
203C2—21042no—
204C2#3068181711yescharacteristic
205C2#3068194011yescharacteristic
206C2#3068194411yescharacteristic
207C2#3068218412yes—
208C2#3068219112yes—
subgroupG/H
centerC23C2×D1052
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
FittingC22×M16×C263C2
socleC23×C263C2×D4
prime radicalC2×#22554444C2
cosocleC22×C4×C263C23
hypercenterC22×M16D263
hypocenterC263#1895
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
2. C2×#22554392C2semidirect
3. #30681798C2semidirect
4. #30681701C2semidirect
5. C22×M16×C263C2semidirect
9. #22554444C4semidirect
45. C2×C8×C263D4semidirect
104. C263#1895semidirect
106. C22×M16D263semidirect
144. C2×C8C22⋊D263semidirect

Maximal subgroups

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

subgroupindex
C2×#225544442
C2×#225543922
#306817982
#306817012
C22×M16×C2632
#1895263