Finite Group Databasebeta

← #46783186

Subgroups — #46783186

Order 33664.

412 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 113 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×#16862360C211yesmaximal, characteristic, complemented
2C2×#22554391C212yesmaximal, complemented
3#30681798C211yesmaximal, characteristic, complemented
4#30681700C212yesmaximal, complemented
5C2×#121×C263C211yesmaximal, characteristic
6C2×#16862360—24no—
7C2×#16862360—22no—
8C22×C263⋊C8C2212yes—
9C2×C4⋊Dic263C2212yes—
10C2×C22⋊Dic263—21no—
11#22554391—24no—
12C263⋊#95—21no—
13C22×D4×C263—21no—
14C22×D4×C263C2211yescharacteristic
15C23×C4×C263C2211yescharacteristic
16#121×C263—22no—
17#121×C263C414yescomplemented
18C2×C4⋊C4×C263C2211yescharacteristic
19C2×C22⋊C4×C263—21no—
20C22×Dic263—22no—
21#16862360—28no—
22C2×C263⋊C8—22no—
23C2×C263⋊C8—22no—
24C2×C263⋊C8D414yescomplemented
25C4⋊Dic263—22no—
26C4⋊Dic263—22no—
27C22⋊Dic263—42no—
28C24×C263—21no—
29C24×C263D411yescharacteristic
30C2×D4×C263—24no—
31C2×D4×C263—22no—
32C2×D4×C263—21no—
33C2×D4×C263—22no—
34C2×D4×C263—44no—
35C2×D4×C263C2×C412yes—
36C22×C4×C263—22no—
37C22×C4×C263—22no—
38C22×C4×C263—21no—
39C22×C4×C263C2×C412yes—
40C22×C4×C263D411yescharacteristic
41C22×C4×C263D412yes—
42C22×C4×C263C2311yescharacteristic
43C4⋊C4×C263—21no—
44C4⋊C4×C263C2×C412yes—
45C22⋊C4×C263—24no—
46C2×Dic263—42no—
47C2×Dic263—42no—
48C2×Dic263—42no—
49C263⋊C8—24no—
50C23×C263—22no—
51C23×C263—22no—
52C23×C263—21no—
53C23×C263—21no—
54C23×C263—22no—
55C23×C263—42no—
56C23×C263—42no—
57C23×C263—41no—
58C23×C263—41no—
59C23×C263C22⋊C412yes—
60C23×C263C2×D411yescharacteristic
61D4×C263—24no—
62D4×C263—48no—
63D4×C263—41no—
64D4×C263—41no—
65C2×C4×C263—22no—
66C2×C4×C263—24no—
67C2×C4×C263—22no—
68C2×C4×C263—22no—
69C2×C4×C263—22no—
70C2×C4×C263—42no—
71C2×C4×C263C22⋊C412yes—
72C2×C4×C263C22×C411yescharacteristic
73C2×C4×C263C2×D412yes—
74C2×C4×C263C2×D411yescharacteristic
75C2×C4×C263#4112yes—
76C22×C263—22no—
77C22×C263—22no—
78C22×C263—22no—
79C22×C263—42no—
80C22×C263—42no—
81C22×C263—42no—
82C22×C263—42no—
83C22×C263—42no—
84C22×C263—82no—
85C22×C263—82no—
86C22×C263C2×C22⋊C411yescharacteristic
87C22×C263#12112yes—
88C22×C263AGL(1,ℤ/8)11yescharacteristic
89C22×C263AGL(1,ℤ/8)12yes—
90C22×C263#13711yescharacteristic
91C4×C263—22no—
92C4×C263—42no—
93C4×C263C4×D412yes—
94C4×C263#12011yescharacteristic
95C4×C263#12311yescharacteristic
96Dic263—82no—
97C2×C263—42no—
98C2×C263—82no—
99C2×C263#38611yescharacteristic
100C2×C263#41711yescharacteristic
101C2×C263#41811yescharacteristic
102C2×C263#46812yes—
103C2×C263#46912yes—
104C263#189511yescharacteristic, complemented, Sylow
105#1895—2631nomaximal, Sylow
106C22×M16—2631no—
107C2×#121D26311yescharacteristic
108C2×#102—2632no—
109#380—2631no—
110#340—2632no—
111C22×D4—21no—
112C22×D4C2×D26311yescharacteristic
113C23×C4C2×D26311yescharacteristic
114C2×M16—5264no—
115C2×M16—5262no—
116C22×C8—2632no—
117#121—22no—
118#121Dic26314yescomplemented
119C2×C4⋊C4—2632no—
120C2×C4⋊C4C2×D26311yescharacteristic
121C2×C22⋊C4—21no—
122C2×C22⋊C4—5261no—
123#102—5264no—
124#95—5261no—
125C24—21no—
126C24C22⋊D26311yescharacteristic
127C2×D4—24no—
128C2×D4—22no—
129C2×D4—21no—
130C2×D4—22no—
131C2×D4—44no—
132C2×D4C2×Dic26312yes—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—21no—
136C22×C4—5262no—
137C22×C4C2×Dic26312yes—
138C22×C4C22⋊D26311yescharacteristic
139C22×C4C22⋊D26312yes—
140C22×C4C22×D26311yescharacteristic
141M16—5268no—
142C2×C8—2634no—
143C2×C8—5262no—
144C2×C8—5262no—
145C4⋊C4—21no—
146C4⋊C4—5262no—
147C4⋊C4—5262no—
148C4⋊C4C2×Dic26312yes—
149C22⋊C4—24no—
150C22⋊C4—10522no—
151C23—22no—
152C23—21no—
153C23—22no—
154C23—21no—
155C23—22no—
156C23—42no—
157C23—41no—
158C23—42no—
159C23—41no—
160C23C22⋊Dic26312yes—
161C23C2×C22⋊D26311yescharacteristic
162D4—24no—
163D4—48no—
164D4—41no—
165D4—41no—
166C2×C4—22no—
167C2×C4—24no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—42no—
172C2×C4—10522no—
173C2×C4—10522no—
174C2×C4—10522no—
175C2×C4C22⋊Dic26312yes—
176C2×C4C22×Dic26311yescharacteristic
177C2×C4D4×D26312yes—
178C2×C4C2×C22⋊D26311yescharacteristic
179C2×C4#1686237512yes—
180C8—5264no—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—42no—
187C22—42no—
188C22—42no—
189C22—82no—
190C22—82no—
191C22C2×C22⋊Dic26311yescharacteristic
192C22#2255444212yes—
193C22#2255449511yescharacteristic
194C22#2255449612yes—
195C22#2255450011yescharacteristic
196C4—22no—
197C4—42no—
198C4—21042no—
199C4D4×Dic26312yes—
200C4#2255443811yescharacteristic
201C4#2255445111yescharacteristic
202C2—42no—
203C2—82no—
204C2#3068181811yescharacteristic
205C2#3068193911yescharacteristic
206C2#3068194311yescharacteristic
207C2#3068218212yes—
208C2#3068218912yes—
subgroupG/H
centerC23C2×C22⋊D263
commutatorC2×C4×C263C22×C4
FrattiniC22×C4C22×D263
Fitting, prime radicalC2×#121×C263C2
socleC23×C263C2×D4
cosocleC22×C4×C263C23
hypercenterC2×#121D263
hypocenterC263#1895
LCSG ▷ C2×C4×C263 ▷ C2×C263 ▷ C263
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C22×#16862360C2semidirect
2. C2×#22554391C2semidirect
3. #30681798C2semidirect
4. #30681700C2semidirect
17. #121×C263C4semidirect
24. C2×C263⋊C8D4semidirect
104. C263#1895semidirect
118. #121Dic263semidirect

Maximal subgroups

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

subgroupindex
C22×#168623602
C2×#225543912
#306817982
#306817002
C2×#121×C2632
#1895263